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A trijet is a jet aircraft powered by three jet engines . In general, passenger airline trijets are considered to be second-generation jet airliners , due to their innovative engine locations, in addition to the advancement of turbofan technology. Trijets are more efficient than quadjets , but not as efficient as twinjets , which replaced trijets as larger and more reliable turbofan engines became available.
The Dassault Falcon 7X /8X and the Dassault Falcon 900 are the only civilian trijets in production and the Chengdu J-36 is the only military trijet in production. [ citation needed ]
One consideration with trijets is positioning the central engine. This is usually accomplished by placing the engine along the centerline, but still poses difficulties. The most common configuration is having the central engine located in the rear fuselage and supplied with air by an S-shaped duct ; this is used on the Hawker Siddeley Trident , Boeing 727 , Tupolev Tu-154 , Lockheed L-1011 TriStar , and, more recently, the Dassault Falcon 7X . The S-duct has low drag, and since the third engine is mounted closer to the centerline, the aircraft will normally be easy to handle in the event of an engine failure. However, S-duct designs are more complex and costlier, particularly for an airliner. Furthermore, the central engine bay would require structural changes in the event of a major re-engining (remodeling of the engine). For example, the 727's central bay was only wide enough to fit a low-bypass turbofan and not the newer high-bypass turbofans which were quieter and more powerful. Boeing decided that a redesign was too expensive and ended its production instead of pursuing further development. The Lockheed Tristar's tail section was too short to fit an existing two-spool engine as it was designed only to accommodate the new three-spool Rolls-Royce RB211 engine, and delays in the RB211's development, in turn, pushed back the TriStar's entry into service which affected sales. [ 1 ]
The McDonnell Douglas DC-10 and related MD-11 use an alternative "straight-through" central engine layout, which allows for easier installation, modification, and access. It also has the additional benefit of being much easier to re-engine. However, this sacrifices aerodynamics compared to the S-duct. Also, as the engine is located much higher up than the wing-mounted engines, engine failure will produce a greater pitching moment, making it more difficult to control.
The placement of the remaining two engines varies. Most smaller aircraft, such as the Hawker Siddeley Trident and the Boeing 727 , as well as the intermediate-sized Tupolev Tu-154 , have two side-mount engine pylons in a T-tail configuration. The larger widebody Lockheed TriStar and DC-10/MD-11 mount an engine underneath each wing. Preliminary studies were done on the TriStar to reuse the fuselage and wing for a twinjet design though these never materialized due to Lockheed's lack of funds. Additionally in the late-1990s Boeing, which had taken over McDonnell Douglas, considered removing the tail engine from the MD-11 to make it a twinjet but instead cancelled MD-11 production altogether. [ 1 ]
Trijets are more efficient and cheaper than four-engine aircraft, as the engines are the most expensive part of the plane and having more engines consumes more fuel, particularly if quadjets and trijets share engines of similar power. For widebody aircraft this makes the trijet configuration more suited to a mid-size airliner compared to the quadjet layout for jumbo jets (i.e. the DC-10 versus the quadjet Boeing 747 ). However the difficulty and complexity of mounting the third engine through the tail will somewhat negate the cost/efficiency advantage. Nonetheless, this was worth the trade-off in the 1960s to the 1990s when widebody trijets and twinjets shared engines of similar output, such as when the DC-10, MD-11, Boeing's 767, and Airbus's A300, A310, and A330 were all powered by the General Electric CF6 , and the additional power from the third engine gave the DC-10/MD-11 advantages in longer range and/or heavier payload over the A300/A310/A330 twinjet. Since the 1990s, with further advancements in high-bypass turbofan technology, large twinjets have been equipped with purpose-designed engines such as the Boeing 777 's General Electric GE90 , allowing twinjets to perform the same tasks as most trijets and even many quadjets but more efficiently.
Due to their added thrust, trijets will have slightly improved takeoff performance compared to twinjets if an engine fails. Because takeoff performance for aircraft is usually calculated to include an extra margin to account for a possible engine failure, trijets are better able to take off from hot and high airports or those where terrain clearance near the runway is an issue.
Unlike twinjets, trijets are not required to land immediately at the nearest suitable airport if one engine fails. (This advantage is also shared with quadjets.) [ 2 ] This is advantageous if the aircraft is not near one of the operator's maintenance bases, as the pilots may then continue the flight and land at an airport where it is more suitable to perform repairs. Additionally, for trijets on the ground with one engine inoperative, approval can be granted to perform two-engine ferry flights. Prior to the introduction of ETOPS , only trijets and quadjets were able to perform long international flights over areas without any diversion airports. However, this advantage has largely disappeared in recent years as ETOPS-certified twin-engined aircraft are able to do so as well.
Another major advantage of the trijet design is that the wings can be located further aft on the fuselage, compared to twinjets and quadjets with all wing-mounted engines, allowing main cabin exit and entry doors to be more centrally located for quicker boarding and deplaning, ensuring shorter turnaround times. The rear-mounted engine and wings shift the aircraft's center of gravity rearwards, improving fuel efficiency , although this will also make the plane slightly less stable and more complex to handle during takeoff and landing. (The McDonnell Douglas DC-9 twinjet and its derivatives, whose engines are mounted on pylons near the rear empennage , have similar advantages/disadvantages of the trijet design, such as the wings located further aft and a more rearward center of gravity.) [ citation needed ]
The first trijet design to fly was the Tupolev Tu-73 bomber prototype, first flown in 1947. [ 3 ] The first commercial trijets were the Hawker Siddeley Trident (1962) and the Boeing 727 (1963). Both were compromises to meet airline requirements; in the case of the Trident, it was to meet BEA's changing needs, while the 727 had to be acceptable for three different airlines. Although collaboration between the manufacturers was considered, it did not come about. [ 4 ]
Early American twinjet designs were limited by the FAA 's 60-minute rule , whereby the flight path of twin-engine jetliners was restricted to within 60 minutes' flying time from a suitable airport, in case of engine failure. In 1964, this rule was lifted for trijet designs, as they had a greater safety margin.
For second-generation jet airliners, with the innovations of the high-bypass turbofan for greater efficiency and reduced noise, and the wide-body (twin-aisle) for greater passenger/cargo capacity, the trijet design was seen as the optimal configuration for the medium wide-body jet airliner, sitting in terms of size, range, and cost between quadjets (four-engine aircraft) and twinjets, and this led to a flurry of trijet designs. The four-engine Boeing 747 was popular for transoceanic flights due to its long-range and large size, but it was expensive and not all routes were able to fill its seating capacity, while the original models of the Airbus A300 twinjet were limited to short- to medium-range distances. During this period, different jet airliners shared engines of similar output, such as when the McDonnell Douglas DC-10 , Airbus A300 , and Boeing 767 were powered by the General Electric CF6 , the additional power from the third engine gave the DC-10 advantages in longer range and/or heavier payload over the A300 and 767 twinjets. Thus trijet designs such as the DC-10 and L-1011 TriStar represented the best compromise with medium- to long-range and medium size that US airlines sought for their domestic and transatlantic routes. As a result of these trijet wide-bodies, as well as the popularity of the Boeing 727, in their heyday of the 1980s trijets made up a majority of all such US jet airliners.
From 1985 to 2003 the number of such planes in service had sunk from 1488 to 602. The number of twinjets, on the other hand, had more than quadrupled in the same period. [ 5 ] Both Lockheed and McDonnell Douglas were financially weakened competing in the widebody market, which led to Lockheed ending production of the L-1011 in 1984 after producing only half the units needed to break even, while a number of fatal DC-10 crashes also slowed its sales. [ 1 ] In 1984 Boeing ended production of the 727, as its central engine bay would require an extremely expensive redesign to accommodate quieter high-bypass turbofans, and it was soon supplanted by Airbus with their A320 and Boeing with their 737 and 757 . Further advancements in high-bypass turbofan technology and subsequent relaxation in airline safety rules made the trijet and even the quadjet nearly obsolete for passenger services, as their range and payload could be covered more efficiently with large twinjets powered with purpose-designed engines such as the 777 's General Electric GE90 .
During the 1980s, McDonnell Douglas was the only Western manufacturer to continue development of the trijet design with an update to the DC-10 , the MD-11 , which initially held a range and payload advantage over its closest medium wide-body competitors which were twinjets, the in-production Boeing 767 and upcoming Airbus A330 . McDonnell Douglas had planned a new trijet called the MD-XX, which were lengthened versions of the MD-11 . The MD-XX Long Range aircraft would have been capable of traveling distances up to 8,320 nautical miles (15,410 km) and had a wingspan of 65 metres (213 ft). The project was canceled in 1996, one year before McDonnell Douglas was acquired by Boeing. Boeing ended production of the MD-11 after filling remaining customer orders since the MD-11 would have competed with the 767 and 777. A study to remove the MD-11's tail-mounted engine (which would have made it a twinjet) never came to fruition as it would have been very expensive, and the MD-11 had very little in common in terms of design or type rating with other Boeing airliners. [ 6 ] In contrast to McDonnell Douglas sticking with their existing trijet configuration, Airbus (which never produced a trijet aircraft) and Boeing worked on new widebody twinjet designs that would become the A330 and 777, respectively. The MD-11's long-range advantage was brief as it soon was threatened by the A330's four-engine derivative, the A340 , and the 777. The only other notable trijet development during the 1980s was in the Soviet Union , where the Tupolev Tu-154 was re-engined with the Soloviev D-30 engine as well as a new wing design and entered serial production from 1984 as the Tu-154M .
With the exceptions of the Dassault Falcon 7X , Falcon 8x , and Falcon 900 business jets, no manufacturer currently produces three-engine airliners.
Modern engines have extremely low failure rates and can generate much higher shaft power and thrust than early types. This makes twinjets more suitable than they were before for long-haul trans-oceanic operations, resulting in eased ETOPS restrictions; modern wide-body twin-engine jets usually have an ETOPS 180 or (in the case of the Boeing 777 and 787 ) ETOPS 330 rating, and even ETOPS 370 for the Airbus A350 . [ 7 ] As such, having more than two engines is no longer considered necessary, except for very large or heavy aircraft such as the Boeing 747 , Airbus A380 (over 400 seats in a mixed-class configuration), Antonov An-124 , and An-225 , or for flights through the Southern Hemisphere, primarily to and from Australia (which has not yet adopted the ETOPS 330 standard), where the most direct route for some flights is over Antarctica . [ 8 ]
Since 2000, both narrow-body and wide-body trijet production has ceased for almost all commercial aircraft, being replaced by twinjets . As of 2016, the Falcon 7X, 8X, and 900 business jets, all of which use S-ducts , are the only trijets in production. Trijets that are no longer in production, such as the 727 , Tu-154 , DC-10, and MD-11, have found second careers as cargo aircraft, as well as in limited charter, governmental, and military service. However, because of the average age of trijets and the COVID-19 pandemic , most non-private operators have chosen to retire quadjets and trijets and replace them with more efficient and cost-saving twinjets. Today, the only widely used trijet is the MD-11, mostly operated by UPS Airlines and FedEx Express in cargo service.
For smaller private and corporate operators, where maximum fuel efficiency is often less important than for scheduled-route operating airlines, trijets may still be of interest due to their immunity from ETOPS and the ability to take off from shorter runways and therefore have access to more airports. As a result, a sizeable number of trijets, such as the newly built Dassault Falcons , are in use by private operators and corporate flight departments.
Airbus filed a patent in 2008 for a new, twin-tail trijet design, whose tail engine appears to use a "straight" layout similar to the MD-11, but it is unknown if and when this will be developed or produced. [ 9 ] However, the proposed Boeing X-48 blended wing body design, Lockheed's N+2 design study, and Aerion AS2 supersonic business jet were also supposed to have three engines. [ 10 ] [ 11 ] The AS2 programme was cancelled in May 2021 when Aerion Corporation shut down. [ 12 ] [ 13 ]
Boom Technology 's planned Overture supersonic transport (SST) airliner was originally planned to use three engines, with the third engine installed in the tail with a Y-shaped duct and air intakes on both sides of the rear. However, a revised design with four engines located under a delta wing was unveiled at the Farnborough Airshow on July 19, 2022. [ 14 ]
On 26 December 2024, a trijet aircraft believed to be a Chengdu J-36 was spotted reportedly conducting test flights in Chengdu , Sichuan , China. Since the aircraft's serial number (36011) begins with '36,' following the People's Liberation Army Air Force convention, this model was presumably designated as J-36, but further information is limited. [ 15 ] | https://en.wikipedia.org/wiki/Trijet |
Trilateration is the use of distances (or "ranges") for determining the unknown position coordinates of a point of interest, often around Earth ( geopositioning ). [ 1 ] When more than three distances are involved, it may be called multilateration , for emphasis.
The distances or ranges might be ordinary Euclidean distances ( slant ranges ) or spherical distances (scaled central angles ), as in true-range multilateration ; or biased distances ( pseudo-ranges ), as in pseudo-range multilateration .
Trilateration or multilateration should not be confused with triangulation , which uses angles for positioning; and direction finding , which determines the line of sight direction to a target without determining the radial distance .
Multiple, sometimes overlapping and conflicting terms are employed for similar concepts – e.g., multilateration without modification has been used for aviation systems employing both true-ranges and pseudo-ranges. [ 2 ] [ 3 ] Moreover, different fields of endeavor may employ different terms. In geometry , trilateration is defined as the process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles , spheres or triangles . In surveying, trilateration is a specific technique. [ 4 ] [ 5 ] [ 6 ]
True-range multilateration (also termed range-range multilateration and spherical multilateration) is a method to determine the location of a movable vehicle or stationary point in space using multiple ranges ( distances ) between the vehicle/point and multiple spatially-separated known locations (often termed "stations"). [ 7 ] [ 8 ] Energy waves may be involved in determining range, but are not required.
True-range multilateration is both a mathematical topic and an applied technique used in several fields. A practical application involving a fixed location occurs in surveying . [ 9 ] [ 10 ] Applications involving vehicle location are termed navigation when on-board persons/equipment are informed of its location, and are termed surveillance when off-vehicle entities are informed of the vehicle's location.
Two slant ranges from two known locations can be used to locate a third point in a two-dimensional Cartesian space (plane), which is a frequently applied technique (e.g., in surveying). Similarly, two spherical ranges can be used to locate a point on a sphere, which is a fundamental concept of the ancient discipline of celestial navigation — termed the altitude intercept problem. Moreover, if more than the minimum number of ranges are available, it is good practice to utilize those as well. This article addresses the general issue of position determination using multiple ranges.
In two-dimensional geometry , it is known that if a point lies on two circles, then the circle centers and the two radii provide sufficient information to narrow the possible locations down to two – one of which is the desired solution and the other is an ambiguous solution. Additional information often narrow the possibilities down to a unique location. In three-dimensional geometry, when it is known that a point lies on the surfaces of three spheres, then the centers of the three spheres along with their radii also provide sufficient information to narrow the possible locations down to no more than two (unless the centers lie on a straight line).
Pseudo-range multilateration , often simply multilateration (MLAT) when in context, is a technique for determining the position of an unknown point, such as a vehicle, based on measurement of biased times of flight (TOFs) of energy waves traveling between the vehicle and multiple stations at known locations.
TOFs are biased by synchronization errors in the difference between times of arrival (TOA) and times of transmission (TOT): TOF=TOA-TOT . Pseudo-ranges (PRs) are TOFs multiplied by the wave propagation speed: PR=TOF ⋅ s . In general, the stations' clocks are assumed synchronized but the vehicle's clock is desynchronized.
In MLAT for surveillance , the waves are transmitted by the vehicle and received by the stations; the TOT is unique and unknown, while the TOAs are multiple and known. When MLAT is used for navigation (as in hyperbolic navigation ), the waves are transmitted by the stations and received by the vehicle; in this case, the TOTs are multiple but known, while the TOA is unique and unknown. In navigation applications, the vehicle is often termed the "user"; in surveillance applications, the vehicle may be termed the "target".
The vehicle's clock is considered an additional unknown, to be estimated along with the vehicle's position coordinates.
If d {\displaystyle d} is the number of physical dimensions being considered (e.g., 2 for a plane) and m {\displaystyle m} is the number of signals received (thus, TOFs measured), it is required that m ≥ d + 1 {\displaystyle m\geq d+1} .
Processing is usually required to extract the TOAs or their differences from the received signals, and an algorithm is usually required to solve this set of equations. An algorithm either: (a) determines numerical values for the TOT (for the receiver(s) clock) and d {\displaystyle d} vehicle coordinates; or (b) ignores the TOT and forms m − 1 {\displaystyle m-1} (at least d {\displaystyle d} ) time difference of arrivals (TDOAs), which are used to find the d {\displaystyle d} vehicle coordinates. Almost always, d = 2 {\displaystyle d=2} (e.g., a plane or the surface of a sphere) or d = 3 {\displaystyle d=3} (e.g., the real physical world). Systems that form TDOAs are also called hyperbolic systems, [ 11 ] for reasons discussed below.
A multilateration navigation system provides vehicle position information to an entity "on" the vehicle (e.g., aircraft pilot or GPS receiver operator). A multilateration surveillance system provides vehicle position to an entity "not on" the vehicle (e.g., air traffic controller or cell phone provider). By the reciprocity principle, any method that can be used for navigation can also be used for surveillance, and vice versa (the same information is involved). | https://en.wikipedia.org/wiki/Trilateration |
A trilemma is a difficult choice from three options, each of which is (or appears) unacceptable or unfavourable. There are two logically equivalent ways in which to express a trilemma: it can be expressed as a choice among three unfavourable options, one of which must be chosen, or as a choice among three favourable options, only two of which are possible at the same time.
The term derives from the much older term dilemma , a choice between two or more difficult or unfavourable alternatives. The earliest recorded use of the term was by the British preacher Philip Henry in 1672, and later, apparently independently, by the preacher Isaac Watts in 1725. [ 1 ]
One of the earliest uses of the trilemma formulation is that of the Greek philosopher Epicurus , rejecting the idea of an omnipotent and omnibenevolent God (as summarised by David Hume ): [ 2 ]
Although traditionally ascribed to Epicurus and called Epicurus' trilemma , it has been suggested that it may actually be the work of an early skeptic writer, possibly Carneades . [ 3 ]
In studies of philosophy, discussions, and debates related to this trilemma are often referred to as being about the problem of evil .
One well-known trilemma is sometimes used by Christian apologists considered a proof of the divinity of Jesus , [ 4 ] and is most commonly known in the version by C. S. Lewis . It proceeds from the premise that Jesus claimed to be God, and that therefore one of the following must be true: [ 5 ]
The trilemma, usually in Lewis' formulation, is often used in works of popular apologetics, although it is almost completely absent from discussions about the status of Jesus by professional theologians and biblical scholars. [ 6 ]
The "cruel trilemma" [ 7 ] was an English ecclesiastical and judicial weapon [ 8 ] developed in the first half of the 17th century, and used as a form of coercion and persecution. The format was a religious oath to tell the truth, imposed upon the accused prior to questioning. The accused, if guilty, would find themselves trapped between:
Outcry over this process led to the foundation of the right to not incriminate oneself being established in common law and was the direct precursor of the right to silence and non-self-incrimination in the Fifth Amendment to the United States Constitution .
In the theory of knowledge the Münchhausen trilemma is an argument against the possibility of proving any certain truth even in the fields of logic and mathematics. Its name is going back to a logical proof of the German philosopher Hans Albert .
This proof runs as follows: All of the only three possible attempts to get a certain justification must fail:
In John Stuart Mill 's On Liberty , as a part of his argument against the suppression of free speech, he describes the trilemma facing those attempting to justify such suppression (although he does not refer to it as a trilemma, Leo Parker-Rees (2009) [ citation needed ] identified it as such).
If free speech is suppressed, the opinion suppressed is either: [ 9 ]
The Buddhist philosopher Nagarjuna uses the trilemma in his Verses on the Middle Way , [ 10 ] giving the example that:
In 1952, the British magazine The Economist published a series of articles on an "Uneasy Triangle", which described "the three-cornered incompatibility between a stable price level, full employment, and ... free collective bargaining". The context was the difficulty maintaining external balance without sacrificing two sacrosanct political values: jobs for all and unrestricted labor rights. Inflation resulting from labor militancy in the context of full employment had put powerful downward pressure on the pound sterling. Runs on the pound then triggered a long series of economically and politically disruptive "stop-go" policies (deflation followed by reflation). [ 11 ] John Maynard Keynes had anticipated the severe problem associated with reconciling full employment with stable prices without sacrificing democracy and the associational rights of labor. [ 12 ] The same incompatibilities were also elaborated upon in Charles E. Lindblom 's 1949 book, Unions and Capitalism . [ 13 ]
In 1962 and 1963, a trilemma (or "impossible trinity") was introduced by the economists Robert Mundell and Marcus Fleming in articles discussing the problems with creating a stable international financial system. It refers to the trade-offs among the following three goals: a fixed exchange rate , national independence in monetary policy , and capital mobility. According to the Mundell–Fleming model of 1962 and 1963, a small, open economy cannot achieve all three of these policy goals at the same time: in pursuing any two of these goals, a nation must forgo the third. [ 14 ]
In 1989 Peter Swenson posited the existence of "wage policy trilemmas" encountered by trade unions trying to achieve three egalitarian goals simultaneously. One involved attempts to compress wages within a bargaining sector while compressing wages between sectors and maximizing access to employment in the sector. A variant of this "horizontal" trilemma was the "vertical" wage policy trilemma associated with trying simultaneously to compress wages, increase the wage share of value added at the expense of profits, and maximize employment. These trilemmas helped explain instability in unions' wage policies and their political strategies seemingly designed to resolve the incompatibilities. [ 15 ]
Steven Pinker proposed another social trilemma in his books How the Mind Works and The Blank Slate : that a society cannot be simultaneously "fair", "free", and "equal". If it is "fair", individuals who work harder will accumulate more wealth; if it is "free", parents will leave the bulk of their inheritance to their children; but then it will not be "equal", as people will begin life with different fortunes. [ citation needed ]
Economist Dani Rodrik argues in his book, The Globalization Paradox , that democracy, national sovereignty, and global economic integration are mutually incompatible. Democratic states pose obstacles to global integration (e. g. regulatory laws, taxes and tariffs) to protect their own economies. Therefore, if we need to achieve complete economic integration, it is necessary to also remove democratic nations states. A government of some nation state could possibly pursue the goal of global integration on the expense of its own population, but that would require an authoritarian regime. Otherwise, the government would be likely replaced in the next elections. [ 16 ]
In Moral Hazard in Teams , [ 17 ] economist Bengt Holmström demonstrated a trilemma that arises from incentive systems . For any team of risk-neutral agents , no incentive system of revenue distribution can satisfy all three of the following conditions: Pareto efficiency , balanced budget , and Nash stability . This entails three optimized outcomes:
In social choice theory , economist Kenneth Arrow proved that it is impossible to create a social welfare function that simultaneously satisfies three key criteria: Pareto efficiency , non-dictatorship and independence of irrelevant alternatives .
Following the Brexit referendum , the first May government decided that not only should the United Kingdom leave the European Union but also that it should leave the European Union Customs Union and the European Single Market. This meant that a customs and regulatory border would arise between the UK and the EU. Whilst the sea border between Great Britain and continental Europe was expected to present manageable challenges, the UK/EU border in Ireland was recognised as having rather more intractable issues. These were summarised in what became known as the " Brexit trilemma ", because of three competing objectives: no hard border on the island ; no customs border in the Irish Sea ; and no British participation in the European Single Market and the European Union Customs Union. It is not possible to have all three. [ 18 ]
Zionists have often desired that Israel be democratic , have a Jewish identity , and encompass (at least) the land of Mandatory Palestine . However, these desires (or " desiderata ") seemingly form an inconsistent triad , and thus a trilemma. Palestine has an Arab majority, so any democratic state encompassing all of Palestine would likely have a binational or Arab identity .
However, Israel could be:
This observation appears in " From Beirut to Jerusalem " (1989), by Thomas Friedman , who attributes it to the political scientist Aryeh Naor [ he ] (historically, the 'trilema' is inexact since early Zionist activists often (a) believed that Jews would migrate to Palestine in sufficiently large numbers; (b) proposed forms of bi-national governance; (c) preferred forms of communism over democracy).
The "Žižek trilemma" is a humorous formulation on the incompatibility of certain personal virtues under a constraining ideological framework. Often attributed to the philosopher Slavoj Žižek , it is actually quoted by him as the product of an anonymous source:
One cannot but recall here a witty formula of life under a hard Communist regime : Of the three features—personal honesty, sincere support of the regime and intelligence—it was possible to combine only two, never all three. If one were honest and supportive, one was not very bright; if one were bright and supportive, one was not honest; if one were honest and bright, one was not supportive. [ 19 ]
Arthur C. Clarke cited a management trilemma encountered when trying to achieve production quickly and cheaply while maintaining high quality. [ 20 ] In the software industry, this means that one can pick any two of: fastest time to market, highest software quality (fewest defects), and lowest cost (headcount). This is the basis of the popular project management aphorism "Quick, Cheap, Good: Pick two," conceptualized as the project management triangle or " quality, cost, delivery ".
The Stanford Encyclopedia of Philosophy is said [ 21 ] to have overcome the trilemma that an encyclopedia cannot be authoritative, comprehensive and up-to-date all at the same time for any significant duration.
The RAID technology may offer two of three desirable values: (relative) inexpensiveness, speed or reliability ( RAID 0 is fast and cheap, but unreliable; RAID 6 is extremely expensive and reliable, with correct performance and so on). A common phrase in data storage, which is the same in project management, is "fast, cheap, good: choose two".
The same saying has been pastiched in silent computing as "fast, cheap, quiet: choose two".
In researching magnetic recording, used in hard drive storage, a trilemma arises due to the competing requirements of readability, writeability and stability (known as the Magnetic Recording Trilemma). Reliable data storage means that for very small bit sizes the magnetic medium must be made of a material with a very high coercivity (ability to maintain its magnetic domains and withstand any undesired external magnetic influences). [ 22 ] But this coercivity must be overridden by the drive head when data is written, which means an extremely strong magnetic field in a very tiny space, [ 22 ] [ 23 ] but the size occupied by one bit of data eventually becomes so small that the strongest magnetic field able to be created in the space available, is not strong enough to allow data writing. [ 22 ] In effect, a point exists at which it becomes impractical or impossible to make a working disk drive because magnetic writing activity is no longer possible on such a small scale. [ 24 ] [ 22 ] Heat-assisted magnetic recording (HAMR) and Microwave Assisted Magnetic Recording (MAMR) are technologies that aim to modify coercivity during writing only, to work around the trilemma [ 25 ] ..
Anonymous communication protocols can offer two of the three desirable properties: strong anonymity, low bandwidth overhead, low latency overhead. [ 26 ]
Some anonymous communication protocols offer anonymity at the cost of high bandwidth overhead, that means the number of messages exchanged between the protocol parties is very high. Some offer anonymity with the expense of latency overhead (there is a high delay between when the message is sent by the sender and when it is received by the receiver). There are protocols which aims to keep the bandwidth overhead and latency overhead low, but they can only provide a weak form of anonymity. [ 27 ]
Kleinberg demonstrated through an axiomatic approach to clustering that no clustering method can satisfy all three of the following fundamental properties at the same time: [ 28 ]
The CAP theorem , covering guarantees provided by distributed systems , and Zooko's triangle concerning naming of participants in network protocols , are both examples of other trilemmas in technology. | https://en.wikipedia.org/wiki/Trilemma |
In geometry , the trilinear coordinates x : y : z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. Trilinear coordinates are an example of homogeneous coordinates . The ratio x : y is the ratio of the perpendicular distances from the point to the sides (extended if necessary) opposite vertices A and B respectively; the ratio y : z is the ratio of the perpendicular distances from the point to the sidelines opposite vertices B and C respectively; and likewise for z : x and vertices C and A .
In the diagram at right, the trilinear coordinates of the indicated interior point are the actual distances ( a' , b' , c' ), or equivalently in ratio form, ka' : kb' : kc' for any positive constant k . If a point is on a sideline of the reference triangle, its corresponding trilinear coordinate is 0. If an exterior point is on the opposite side of a sideline from the interior of the triangle, its trilinear coordinate associated with that sideline is negative. It is impossible for all three trilinear coordinates to be non-positive.
The ratio notation x : y : z {\displaystyle x:y:z} for trilinear coordinates is often used in preference to the ordered triple notation ( x , y , z ) , {\displaystyle (x,y,z),} with the latter reserved for triples of directed distances ( a ′ , b ′ , c ′ ) {\displaystyle (a',b',c')} relative to a specific triangle. The trilinear coordinates x : y : z , {\displaystyle x:y:z,} can be rescaled by any arbitrary value without affecting their ratio. The bracketed, comma-separated triple notation ( x , y , z ) {\displaystyle (x,y,z)} can cause confusion because conventionally this represents a different triple than e.g. ( 2 x , 2 y , 2 z ) , {\displaystyle (2x,2y,2z),} but these equivalent ratios x : y : z = {\displaystyle x:y:z={}\!} 2 x : 2 y : 2 z {\displaystyle 2x:2y:2z} represent the same point.
The trilinear coordinates of the incenter of a triangle △ ABC are 1 : 1 : 1 ; that is, the (directed) distances from the incenter to the sidelines BC, CA, AB are proportional to the actual distances denoted by ( r , r , r ) , where r is the inradius of △ ABC . Given side lengths a, b, c we have:
Note that, in general, the incenter is not the same as the centroid ; the centroid has barycentric coordinates 1 : 1 : 1 (these being proportional to actual signed areas of the triangles △ BGC , △ CGA , △ AGB , where G = centroid.)
The midpoint of, for example, side BC has trilinear coordinates in actual sideline distances ( 0 , Δ b , Δ c ) {\displaystyle (0,{\tfrac {\Delta }{b}},{\tfrac {\Delta }{c}})} for triangle area Δ , which in arbitrarily specified relative distances simplifies to 0 : ca : ab . The coordinates in actual sideline distances of the foot of the altitude from A to BC are ( 0 , 2 Δ a cos C , 2 Δ a cos B ) , {\displaystyle (0,{\tfrac {2\Delta }{a}}\cos C,{\tfrac {2\Delta }{a}}\cos B),} which in purely relative distances simplifies to 0 : cos C : cos B . [ 1 ] : p. 96
Trilinear coordinates enable many algebraic methods in triangle geometry. For example, three points
are collinear if and only if the determinant
equals zero. Thus if x : y : z is a variable point, the equation of a line through the points P and U is D = 0 . [ 1 ] : p. 23 From this, every straight line has a linear equation homogeneous in x, y, z . Every equation of the form l x + m y + n z = 0 {\displaystyle lx+my+nz=0} in real coefficients is a real straight line of finite points unless l : m : n is proportional to a : b : c , the side lengths, in which case we have the locus of points at infinity. [ 1 ] : p. 40
The dual of this proposition is that the lines
concur in a point ( α , β , γ ) if and only if D = 0 . [ 1 ] : p. 28
Also, if the actual directed distances are used when evaluating the determinant of D , then the area of triangle △ PUX is KD , where K = − a b c 8 Δ 2 {\displaystyle K={\tfrac {-abc}{8\Delta ^{2}}}} (and where Δ is the area of triangle △ ABC , as above) if triangle △ PUX has the same orientation (clockwise or counterclockwise) as △ ABC , and K = − a b c 8 Δ 2 {\displaystyle K={\tfrac {-abc}{8\Delta ^{2}}}} otherwise.
Two lines with trilinear equations l x + m y + n z = 0 {\displaystyle lx+my+nz=0} and l ′ x + m ′ y + n ′ z = 0 {\displaystyle l'x+m'y+n'z=0} are parallel if and only if [ 1 ] : p. 98, #xi
where a, b, c are the side lengths.
The tangents of the angles between two lines with trilinear equations l x + m y + n z = 0 {\displaystyle lx+my+nz=0} and l ′ x + m ′ y + n ′ z = 0 {\displaystyle l'x+m'y+n'z=0} are given by [ 1 ] : Art. 48
Thus they are perpendicular if [ 1 ] : Art. 49
The equation of the altitude from vertex A to side BC is [ 1 ] : p.98, #x
The equation of a line with variable distances p, q, r from the vertices A, B, C whose opposite sides are a, b, c is [ 1 ] : p. 97, #viii
The trilinears with the coordinate values a', b', c' being the actual perpendicular distances to the sides satisfy [ 1 ] : p. 11
for triangle sides a, b, c and area Δ . This can be seen in the figure at the top of this article, with interior point P partitioning triangle △ ABC into three triangles △ PBC , △ PCA , △ PAB with respective areas 1 2 a a ′ , 1 2 b b ′ , 1 2 c c ′ . {\displaystyle {\tfrac {1}{2}}aa',{\tfrac {1}{2}}bb',{\tfrac {1}{2}}cc'.}
The distance d between two points with actual-distance trilinears a i : b i : c i is given by [ 1 ] : p. 46
or in a more symmetric way
The distance d from a point a' : b' : c' , in trilinear coordinates of actual distances, to a straight line l x + m y + n z = 0 {\displaystyle lx+my+nz=0} is [ 1 ] : p. 48
The equation of a conic section in the variable trilinear point x : y : z is [ 1 ] : p.118
It has no linear terms and no constant term.
The equation of a circle of radius r having center at actual-distance coordinates ( a', b', c' ) is [ 1 ] : p.287
The equation in trilinear coordinates x, y, z of any circumconic of a triangle is [ 1 ] : p. 192
If the parameters l, m, n respectively equal the side lengths a, b, c (or the sines of the angles opposite them) then the equation gives the circumcircle . [ 1 ] : p. 199
Each distinct circumconic has a center unique to itself. The equation in trilinear coordinates of the circumconic with center x' : y' : z' is [ 1 ] : p. 203
Every conic section inscribed in a triangle has an equation in trilinear coordinates: [ 1 ] : p. 208
with exactly one or three of the unspecified signs being negative.
The equation of the incircle can be simplified to [ 1 ] : p. 210, p.214
while the equation for, for example, the excircle adjacent to the side segment opposite vertex A can be written as [ 1 ] : p. 215
Many cubic curves are easily represented using trilinear coordinates. For example, the pivotal self-isoconjugate cubic Z ( U, P ) , as the locus of a point X such that the P -isoconjugate of X is on the line UX is given by the determinant equation
Among named cubics Z ( U, P ) are the following:
For any choice of trilinear coordinates x : y : z to locate a point, the actual distances of the point from the sidelines are given by a' = kx , b' = ky , c' = kz where k can be determined by the formula k = 2 Δ a x + b y + c z {\displaystyle k={\tfrac {2\Delta }{ax+by+cz}}} in which a, b, c are the respective sidelengths BC, CA, AB , and ∆ is the area of △ ABC .
A point with trilinear coordinates x : y : z has barycentric coordinates ax : by : cz where a, b, c are the sidelengths of the triangle. Conversely, a point with barycentrics α : β : γ has trilinear coordinates α a : β b : γ c . {\displaystyle {\tfrac {\alpha }{a}}:{\tfrac {\beta }{b}}:{\tfrac {\gamma }{c}}.}
Given a reference triangle △ ABC , express the position of the vertex B in terms of an ordered pair of Cartesian coordinates and represent this algebraically as a vector B → , {\displaystyle {\vec {B}},} using vertex C as the origin. Similarly define the position vector of vertex A as A → . {\displaystyle {\vec {A}}.} Then any point P associated with the reference triangle △ ABC can be defined in a Cartesian system as a vector P → = k 1 A → + k 2 B → . {\displaystyle {\vec {P}}=k_{1}{\vec {A}}+k_{2}{\vec {B}}.} If this point P has trilinear coordinates x : y : z then the conversion formula from the coefficients k 1 and k 2 in the Cartesian representation to the trilinear coordinates is, for side lengths a, b, c opposite vertices A, B, C ,
and the conversion formula from the trilinear coordinates to the coefficients in the Cartesian representation is
More generally, if an arbitrary origin is chosen where the Cartesian coordinates of the vertices are known and represented by the vectors A → , B → , C → {\displaystyle {\vec {A}},{\vec {B}},{\vec {C}}} and if the point P has trilinear coordinates x : y : z , then the Cartesian coordinates of P → {\displaystyle {\vec {P}}} are the weighted average of the Cartesian coordinates of these vertices using the barycentric coordinates ax, by, cz as the weights. Hence the conversion formula from the trilinear coordinates x, y, z to the vector of Cartesian coordinates P → {\displaystyle {\vec {P}}} of the point is given by
where the side lengths are | https://en.wikipedia.org/wiki/Trilinear_coordinates |
In fibers , trilobal is a cross-section shape with three distinct sides. The shape is advantageous for optical reflective properties and is used in textile fibers . Silk fibers' rounded edges and triangular cross section contribute to their luster ; in some cases, synthetic fibers are manufactured to mimic this trilobal shape to give them a silk-like appearance. [ 1 ] Filaments with a round cross section have less brilliance than trilobal filaments. [ 2 ] [ 3 ]
The dictionary definition of Trilobal at Wiktionary is a combination of the words "Tri" for three and "lobal" for sides.
Trilobal shape helps in altering hand and increasing the luster. Many synthetic fibres, such as polyester and nylon , are manufactured in Trilobal cross sectional shape for the purpose of enhancing the brilliance and changing the handle. [ 1 ] [ 2 ] [ 3 ] [ 4 ] Luster adds aesthetic values in fabrics, contributes to their attractiveness. Occasionally, this adds value to their quality assessment. [ 3 ] [ 5 ] [ 6 ]
Synthetic fibers are particularly suitable for specific effects such as crimping and texturizing due to their adaptability during production. [ 7 ] Trilobal cross section helps alter texture and several physical attributes such as strength and static properties, in addition to providing brightness to the fibres. [ 8 ] [ 4 ] The trilobal cross sectional shape helps to reduce manufacturing defects in filaments. [ 9 ]
This article about textiles is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trilobal |
Trimastix is a genus of excavate protists , the sole occupant of the order Trimastigida. [ 1 ] Trimastix are bacterivorous, free living and anaerobic . It was first observed in 1881 by William Kent . [ 2 ] There are few known species, and the genus's role in the ecosystem is largely unknown. However, it is known that they generally live in marine environments within the tissues of decaying organisms to maintain an anoxic environment. [ 3 ] Much interest in this group is related to its close association with other members of Preaxostyla . These organisms do not have classical mitochondria , and as such, much of the research involving these microbes is aimed at investigating the evolution of mitochondria. [ 4 ]
A freshwater flagellate of similar morphology used to be included in this genus as Trimastix pyriformis , [ 5 ] but was moved to Paratrimastix in 2015. [ 6 ]
Trimastix were first described by William Kent in 1881 when he observed a Trimastix cell in a sample sourced from decaying fuci seaweed . He described the genus at the time as free-swimming naked animalcules that are oval, or pear shaped, with a membranous border and three flagella inserted on the anterior end. Kent observed one flagellum facing forwards and two facing backwards. [ 2 ] It was also noted in this account that Trimastix had a visually apparent nucleus and contractile vacuole but no visual oral aperture. [ 2 ] Kent determined that Trimastix was a distinct genus, despite similarities to Dallingeria , because of the lateral border he observed which was not present in Dallingeria . [ 2 ]
It was later determined that the lateral border Kent was referring to was in fact the oral aperture of Trimastix , which also contained a fourth flagella. [ 3 ] Today, the morphology of Trimastix is better understood, including details not initially observed by Kent, such as Trimastix lacking a conventional mitochondrion. [ 7 ] Current research indicates that despite there being no evidence that the organelle can produce ATP , there are certain mitochondrial functions that it appears to have maintained. [ 8 ]
Trimastix can only survive in anaerobic habitats, but unlike many anaerobes without typical mitochondria, Trimastix are not parasitic. Trimastix instead consume bacteria through their ventral groove. [ 3 ] In order to maintain an anoxic environment without parasitism or endosymbiosis, Trimastix are most often found inside the tissues of dead and decaying marine vegetation. [ 3 ]
Trimastix cells are oblong broad anteriorly and taper posteriorly. [ 3 ] Trimastix is 20 μm long and 8 μm wide. [ 3 ] A kinetid of four flagella is located on the anterior end of the cell with one flagella anteriorly oriented, two flagella posteriorly oriented, and the fourth flagella sitting within an oral groove on the ventral side. [ 7 ] Trimastix have one anterior pear-shaped nucleus that contains a large nucleolus . [ 3 ]
Trimastix species do not have typical aerobic mitochondria, but they do have remnants of an ancestral mitochondrion , in the form of a hydrogenosome - or mitosome -like organelle. [ 8 ] There is no evidence this organelle produces ATP . The organelle still appears to be targeted by proteins involved in amino acid metabolism, transport and maturation of proteins, and transport of metabolites [ 8 ] so it likely retains some mitochondrial function relating to those areas. | https://en.wikipedia.org/wiki/Trimastix |
Trimaximal mixing [ 1 ] (also known as threefold maximal mixing [ 2 ] ) refers to the highly symmetric , maximally CP-violating , 3 × 3 {\displaystyle 3\times 3} fermion mixing configuration, characterised by a unitary matrix ( U {\displaystyle U} ) having all its elements equal in modulus
( | U a i | = 1 / 3 {\displaystyle |U_{ai}|=1/{\sqrt {3}}} , a , i = 1 , 2 , 3 {\displaystyle a,i=1,2,3} ) as may be written, e.g.:
where ω = exp ( i 2 π / 3 ) {\displaystyle \omega =\exp(i2\pi /3)} and ω ¯ = exp ( − i 2 π / 3 ) {\displaystyle {\bar {\omega }}=\exp(-i2\pi /3)} are the complex cube roots of unity. In the standard PDG [ 3 ] convention, trimaximal mixing corresponds to: θ 12 = θ 23 = π / 4 {\displaystyle \theta _{12}=\theta _{23}=\pi /4} , θ 13 = sin − 1 ( 1 / 3 ) {\displaystyle \theta _{13}=\sin ^{-1}(1/{\sqrt {3}})} and δ = π / 2 {\displaystyle \delta =\pi /2} . The Jarlskog C P {\displaystyle CP} -violating parameter J {\displaystyle J} [ 4 ] takes its extremal value | J | = 1 / ( 6 3 ) {\displaystyle |J|=1/(6{\sqrt {3}})} .
Originally proposed as a candidate lepton mixing matrix , [ 5 ] [ 6 ] and actively studied [ 1 ] [ 2 ] [ 7 ] [ 8 ] as such (and even as a candidate quark mixing matrix [ 9 ] ), trimaximal mixing is now definitively ruled-out as a phenomenologically viable lepton mixing scheme by neutrino oscillation experiments, especially the Chooz reactor experiment, [ 10 ] in favour of the no longer tenable (related) tribimaximal mixing [ 11 ] scheme. | https://en.wikipedia.org/wiki/Trimaximal_mixing |
The Trimble ASCII Interface Protocol is a digital communication interface which uses printable ASCII characters over a serial link. [ 1 ] It is used to communicate with Global Positioning System receivers. [ 2 ]
This article related to telecommunications is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trimble_ASCII_Interface_Protocol |
Trimedoxime bromide ( INN ), also known as dipyroxime or TMB-4 , is an oxime used in the treatment of organophosphate poisoning [ 1 ] It is chemically related to asoxime , pralidoxime , and obidoxime . [ 2 ]
This article about medicinal chemistry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trimedoxime_bromide |
Trimethyl orthoformate ( TMOF ) is the organic compound with the formula HC(OCH 3 ) 3 . A colorless liquid, it is the simplest orthoester . It is a reagent used in organic synthesis for the formation of methyl ethers . [ 3 ] The product of reaction of an aldehyde with trimethyl orthoformate is an acetal . In general cases, these acetals can be deprotected back to the aldehyde by using hydrochloric acid .
Trimethyl orthoformate is prepared on an industrial scale by the methanolysis of hydrogen cyanide : [ 4 ]
Trimethyl orthoformate can also be prepared from the reaction between chloroform and sodium methoxide , an example of the Williamson ether synthesis .
Trimethyl orthoformate is a useful building block for creating methoxymethylene groups and heterocyclic ring systems. It introduces a formyl group to a nucleophilic substrate, e.g. RNH 2 to form R-NH-CHO, which can undergo further reactions. It is used in the production of some fungicides (for example: azoxystrobin and picoxystrobin), as well as for some members of the floxacin family of antibacterial drugs .
A number of pharmaceutical intermediates are also made from trimethyl orthoformate. [ 4 ]
Trimethyl orthoformate is also an effective reagent for converting compatible carboxylic acids to their corresponding methyl esters. [ 5 ] Alternatively, acid-catalyzed esterifications with methanol can be driven closer to completion by employing trimethyl orthoformate to convert water byproduct to methanol and methyl formate . | https://en.wikipedia.org/wiki/Trimethyl_orthoformate |
Trimethylamine N -oxide ( TMAO ) is an organic compound with the formula ( C H 3 ) 3 N O . It is in the class of amine oxides . Although the anhydrous compound is known, trimethylamine N -oxide is usually encountered as the dihydrate . Both the anhydrous and hydrated materials are white, water-soluble solids.
TMAO is found in the tissues of marine crustaceans and marine fish, where it prevents water pressure from distorting proteins and thus killing the animal. The concentration of TMAO increases with the depth at which the animal lives; TMAO is found in high concentrations in the deepest-living described fish species, Pseudoliparis swirei , which was found in the Mariana Trench , at a recorded depth of 8,076 m (26,496 ft). [ 1 ] [ 2 ]
In animals, TMAO is a product of the oxidation of trimethylamine , a common metabolite of trimethyl quaternary ammonium compounds, like choline , trimethylglycine , and L-carnitine . [ 3 ] High TMAO concentrations are associated with an increased risk of all-cause mortality and cardiovascular disease. [ 4 ] [ 5 ] [ 6 ]
Trimethylamine N -oxide is an osmolyte found in molluscs, crustaceans, and all marine fishes and bony fishes. It is a protein stabilizer that serves to counteract the protein-destabilizing effects of pressure. In general, the bodies of animals living at great depths are adapted to high pressure environments by having pressure-resistant biomolecules and small organic molecules present in their cells, known as piezolytes, of which TMAO is the most abundant. These piezolytes give the proteins the flexibility they need to function properly under great pressure. [ 1 ] [ 2 ] [ 7 ] [ 8 ] [ 9 ]
TMAO decomposes to trimethylamine (TMA), which is the main odorant that is characteristic of degrading seafood. [ citation needed ]
TMAO levels increase with consumption of animal protein such as eggs, red meat , shellfish and total fish consumption. [ 10 ] [ 11 ] Plant-based diets such as vegan, vegetarian and the Mediterranean diet lower TMAO levels. [ 11 ] [ 12 ]
TMAO can be synthesized from trimethylamine by treatment with hydrogen peroxide : [ 13 ]
The dihydrate is dehydrated by azeotropic distillation from dimethylformamide . [ 14 ]
Trimethylamine oxide is used in protein folding experiments to counteract the unfolding effects of urea . [ 15 ]
In the organometallic chemistry reaction of nucleophilic abstraction , (CH 3 ) 3 NO is employed as a decarbonylation agent according to the following stoichiometry :
where M is a metal. This reaction is used to decomplex organic ligands from metals, e.g. from ( diene )Fe(CO) 3 . [ 13 ]
It is used in certain oxidation reactions, e.g. the conversion of alkyl iodides to the corresponding aldehyde . [ 16 ]
The effects of TMAO on the backbone and charged residues of peptides are found to stabilize compact conformations, [ 17 ] whereas effects of TMAO on nonpolar residues lead to peptide swelling. This suggests competing mechanisms of TMAO on proteins, which accounts for hydrophobic swelling, backbone collapse, and stabilization of charge-charge interactions. These mechanisms are observed in Trp cage. [ 18 ]
Trimethylaminuria is a rare defect in the production of the enzyme flavin-containing monooxygenase 3 ( FMO3 ). [ 19 ] [ 20 ] Those suffering from trimethylaminuria are unable to convert choline-derived trimethylamine into trimethylamine oxide. Trimethylamine then accumulates and is released in the person's sweat, urine, and breath, giving off a strong fishy odor. [ citation needed ]
High circulating TMAO concentrations are associated with an increased risk of all-cause mortality . [ 4 ] [ 21 ]
High circulating TMAO concentrations are associated with an increased risk of cardiovascular events [ 4 ] [ 21 ] and strokes in particular. [ 22 ]
High circulating TMAO concentrations are associated with an increased risk of hypertension . [ 23 ] [ 24 ]
Exposure limit guidelines with a detailed description of toxicity are available such as "Recommendation from the Scientific Committee on Occupational Exposure Limits" by the European Union Commission. [ 25 ] | https://en.wikipedia.org/wiki/Trimethylamine_N-oxide |
Trimethylamine N -oxide reductase (TOR or TMAO reductase, EC 1.7.2.3) is a microbial enzyme that can reduce trimethylamine N -oxide (TMAO) into trimethylamine (TMA), as part of the electron transport chain . The enzyme has been purified from E. coli and the photosynthetic bacteria Roseobacter denitrificans . [ 1 ]
Trimethylamine oxide is found at high concentrations in the tissues of fish, and the bacterial reduction of this compound to foul-smelling trimethylamine is a major process in the spoilage of fish. [ 2 ]
TMAO reductase has an enzyme commission (EC) number of 1.7.2.3. EC numbers are a system of enzyme nomenclature, and each part of this nomenclature refers to a progressive classification of the enzyme with regards to its reaction. The first number defines the reaction type, the second number provides information on involved compounds, the third number specifies the type of reaction, and the fourth number completes the unique serial number for each enzyme. [ 3 ]
Trimethylamine N-oxide reductase has the EC number 1.7.2.3, and these components refer to the following enzyme classifications:
TMAO is an organic osmolyte that has the useful biological function of protecting proteins against denaturing stresses such as high concentration of urea. [ 5 ] Various bacteria grow anaerobically using TMAO as an alternative electron transport chain , allowing for growth on non-fermentable carbon sources such as glycerol . [ 6 ] Bacteria capable of reducing TMAO to TMA are found throughout three different ecological niches. TMAO-reducing, to date, has been observed in marine bacteria, photosynthetic bacteria living in shallow ponds, and in enterobacteria . [ 5 ]
TMAO reductases have been studied in several organisms, and a common conserved feature is the presence of a molybdenum cofactor in all the known terminal enzymes. [ 5 ]
Based on their substrate specificity, these enzymes can be divided into two groups:
The first group consists of species such as Escherichia coli , Shewanella putrefaciens , and Roseobacter denitrificans while the second group consists of species such as Proteus vulgaris , Rhodobacter capsulatus , and Rhodobacter sphaeroides . [ 5 ]
The TMAO respiratory system has been mostly widely studied at the molecular level in E. coli and Rhodobacter species.
In E. coli , TMAO reductase is encoded by the tor CAD operon. The torC gene encodes a pentahemic c-type cytochrome (TorC). TorC is likely to transfer electrons directly to the periplasmic TorA terminal enzyme encoded by the torA gene. [ 5 ] The anaerobic expression of the torCAD operon is strictly controlled by the presence of TMAO or related compounds. [ 7 ]
There are several different metabolic pathways that involve TMAO and TMA . The reduction of TMAO to TMA, catalyzed by TMAO reductase, as part of the electron transport chain follows the following reaction:
NADH + H + + trimethylamine N-oxide ⇌ {\displaystyle \rightleftharpoons } NAD + + trimethylamine + H 2 O
However, both the R. denitrificans and E. coli enzymes can accept electrons from cytochromes : [ 8 ]
Other reactions involving TMAO and TMA include: [ 9 ]
In E. coli , it has been shown that an inducible, periplasmic TMAO reductase is responsible for almost all TMAO reduction (with the rest being DMSO reduction). While no structural analysis of this E. coli enzyme has been reported, TMAO reductase from Shewanella massilia has been isolated and characterized at a resolution of 2.5 Å. [ 10 ]
TMAO reductases have been studied in several organisms, and a common feature is the presence of a molybdenum cofactor in all the known terminal enzymes. The common form of the molybdopterin molecule is a tricyclic ring system comprising a pterin group fused to a pyran ring. The role of this pyran ring could be a way of controlling the oxidation state of the molybdenum cofactor and/or facilitating proton diffusion. Furthermore, the arrangement of aromatic residues in the funnel-like entrance leading to the active center is closely related to that of DMSO reductase structures. A hydrophobic pocket, formed by two tryptophan and two tyrosine residues, is also present in the TMAO reductase and contains highly conserved residues. [ 10 ]
When comparing TMAO reductase of S. massilia to DMSO reductase from R. Sphaeroides and R. capsulatus, the overall structure is strikingly similar. However, one major difference in TMAO reductase is a missing tyrosine (Tyr114), in DMSO reductase of R. capsulatus . It is replaced by a threonine (Thr116) in the TMAO reductase, and the backbone stretch around this residue, from residue 100 to 116, is not identical to that in the DMSO reductases. A direct consequence of the missing residue is a wider accessible space, adjacent to the molybdenum active center, which potentially exists to accommodates the somewhat bulkier trimethylamine-oxide molecules more easily than the dimethylsulfoxide molecules . [ 10 ] This different demonstrates how an enzyme's form is almost always directly tied to its function.
However, recent discrepancies have risen regarding the structure of the TMAO reductase active site. The proposed active site contains several anomalous bond lengths; one Mo-O bond length is too short for a Mo-O single-bond coordination, and the four Mo-S bond lengths are all considerably longer than expected. Moreover, the proposed molybdenum coordination of the active site is extremely crowded, with the distances between several supposedly nonbonding atoms being significantly shorter than the sum of their van der Waals radii and some bond angles being unreasonably small. Now, it is being hypothesized that this overcrowding is due to the cocrystallization of multiple forms of the enzyme. [ 11 ] | https://en.wikipedia.org/wiki/Trimethylamine_N-oxide_reductase |
This page provides supplementary chemical data on Trimethylarsine .
The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet ( MSDS ) for this chemical from a reliable source such as SIRI , and follow its directions. | https://en.wikipedia.org/wiki/Trimethylarsine_(data_page) |
Trimethylenemethane (often abbreviated TMM ) is a chemical compound with formula C 4 H 6 . It is a neutral free molecule with two unsatisfied valence bonds , and is therefore a highly reactive free radical . Formally, it can be viewed as an isobutylene molecule C 4 H 8 with two hydrogen atoms removed from the terminal methyl groups .
The electronic structure of trimethylenemethane was discussed in 1948. [ 1 ] [ 2 ] It is a neutral four-carbon molecule containing four pi molecular orbitals. When trapped in a solid matrix at about 90 K (−183 °C), the six hydrogen atoms of the molecule are equivalent. Thus, it can be described either as zwitterion , or as the simplest conjugated hydrocarbon that cannot be given a Kekulé structure . It can be described as the superposition of three states:
It has a triplet ground state ( 3 A 2 ′/ 3 B 2 ), and is therefore a diradical in the stricter sense of the term. [ 3 ] Calculations predict a planar molecule with three-fold rotational symmetry, with approximate bond lengths 1.40 Å (C–C) and 1.08 Å (C–H). The H–C–H angle in each methylene is about 121°. [ 1 ]
Of the three singlet excited states , the first one, 1 1 A 1 (1.17 eV above ground), is a closed shell diradical with flat geometry and fully degenerate threefold ( D 3h ) symmetry. The second one, 1 1 B 2 (also at 1.17 eV), is an open-shell radical with a D 3h -symmetric equilibrium between three equal geometries; each has a longer C–C bond (1.48 Å) and two shorter ones (1.38 Å), and is flat and bilaterally symmetric except that the longer methylene is twisted 79° out of the plane ( C 2 symmetry). The third singlet state, 2 1 A 1 / 1 A 1 ′ (3.88 eV), is also a D 3h -symmetric equilibrium of three geometries; each is planar with one shorter C–C bond and two longer ones ( C 2ν symmetry). [ 1 ]
The next higher energy states are degenerate triplets, 1 3 A 1 and 2 3 B 2 (4.61 eV), with one excited electron; and a quintet state, 5 B 2 (7.17 eV), with the p orbitals occupied by single electrons and D 3h symmetry. [ 1 ]
Trimethylenemethane was first obtained from photolysis of the diazo compound 4-methylene-Δ 1 -pyrazoline with expulsion of nitrogen, in a frozen dilute glassy solution at −196 °C (77 K). [ 3 ]
It was also obtained from photolysis of 3-methylenecyclobutanone , both in cold solution and in the form of a single crystal, with expulsion of carbon monoxide. In both cases, trimethylenemethane was detected by electron spin resonance spectroscopy . [ 3 ]
Trimethylenemethane has been obtained also by treating potassium with 2-iodomethyl-3-iodopropene and isobutylene diiodide ( IH 2 C ) 2 C= CH 2 in the gas phase. However the product quickly dimerizes to yield 1,4-dimethylenecyclohexane, and also 2-methylpropene by abstracting two hydrogen atoms from other molecules (hydrocarbon or potassium hydride ). [ 4 ]
A number of organometallic complexes have been prepared, starting with Fe( C 4 H 6 )(CO) 3 , which was obtained by the ring-opening of methylenecyclopropane with diiron nonacarbonyl ( Fe 2 (CO) 9 ). [ 3 ] The same complex was prepared by the salt metathesis reaction of disodium tetracarbonylferrate ( Na 2 Fe (CO) 4 ) with 1,1-bis(chloromethyl)ethylene (H 2 C=C(CH 2 Cl) 2 ). [ 5 ] Related reactions give M(TMM)(CO) 4 (M = Cr, Mo). The reaction leading to (TMM)Mo(CO) 4 also gives Mo( C 8 H 12 )(CO) 3 containing a dimerized TMM ligand. [ 5 ]
TMM complexes have been examined for their potential in organic synthesis , specifically in the trimethylenemethane cycloaddition reaction with only modest success. One example is a palladium-catalyzed [3+2] cycloaddition of trimethylenemethane. [ 6 ] | https://en.wikipedia.org/wiki/Trimethylenemethane |
Trimethylgallium , often abbreviated to TMG or TMGa , is the organogallium compound with the formula Ga(CH 3 ) 3 . It is a colorless, pyrophoric liquid. [ 1 ] Unlike trimethylaluminium , TMG adopts a monomeric structure. [ 2 ] When examined in detail, the monomeric units are clearly linked by multiple weak Ga---C interactions, reminiscent of the situation for trimethylindium . [ 3 ]
Two forms of TMG are typically investigated: Lewis base adducts or TMG itself. All are prepared by reactions of gallium trichloride with various methylating agents. When the methylation is conducted with methylmagnesium iodide in diethyl ether , the product is the poorly volatile diethyl ether adduct. As noted by TMG discoverers Kraus and Toonder in 1933, the ether ligand is not readily lost, although it may be displaced with liquid ammonia. [ 4 ] When the alkylation is conducted with methyl lithium in the presence of a tertiary phosphine the air-stable phosphine adduct is obtained:
Heating the solid phosphine adduct under vacuum liberates the base-free TMG: [ 1 ]
Other non-volatile bases have been described. [ 5 ] Other methylating agents for the synthesis of TMG include dimethylzinc and trimethylaluminium .
TMG is the preferred metalorganic source of gallium for metalorganic vapour phase epitaxy (MOVPE) of gallium-containing compound semiconductors , such as GaAs , GaN , GaP , GaSb , InGaAs , InGaN , AlGaInP , InGaP , AlInGaNP and Ga 2 O 3 . [ 6 ] These material are used in the production of LED lighting and semiconductors as a metalorganic chemical vapor deposition precursor. | https://en.wikipedia.org/wiki/Trimethylgallium |
Trimethylindium , often abbreviated to TMI or TMIn , is the organoindium compound with the formula In(CH 3 ) 3 . It is a colorless, pyrophoric solid. [ 2 ] Unlike trimethylaluminium , but akin to trimethylgallium , TMI is monomeric. [ 3 ]
TMI is prepared by the reaction of indium trichloride with methyl lithium . [ 2 ] [ 4 ]
Compared to trimethylaluminium and trimethylgallium , InMe 3 is a weaker Lewis acid . It forms adducts with secondary amines and phosphines . [ 5 ] A complex with the heterocyclic triazine ligand (Pr i NCH 2 ) 3 forms a complex with 6-coordinate In, where the C-In-C angles are 114°-117° with three long bonds to the tridentate ligand with N-In-N angles of 48.6° and long In-N bonds of 278 pm. [ 6 ]
In the gaseous state InMe 3 is monomeric, with a trigonal planar structure, and in benzene solution it is tetrameric. [ 5 ] In the solid state there are two polymorphs, a tetragonal phase which is obtained, for example, by sublimation and a lower density rhombohedral phase discovered in 2005, [ 7 ] when InMe 3 re-crystallised from hexane solution.
In the tetragonal form InMe 3 is tetrameric as in benzene solution and there is bridging between tetramers to give an infinite network. Each indium atom is five coordinate, in a distorted trigonal planar configuration, the three shortest bonds (ca. 216 pm) are those in the equatorial plane, with longer axial bonds, 308 pm for the In-C bonds joining the InMe 3 units to form the tetramers and 356 pm for the In-C linking the tetramers into an infinite network. [ 8 ] The solid state structures of GaMe 3 and TlMe 3 are similar. [ 8 ] The association in the solid state accounts for the high melting point of 89°–89.8 °C compared to triethylindium which melts at −32 °C. [ 5 ]
The rhombohedral form of InMe 3 consists of cyclic hexamers with 12 membered (InC) 6 rings in an extended chair conformation . The hexamers are interlinked into an infinite network. Indium atoms are five coordinate the equatorial In-C distances average 216.7pm almost identical to the average for the tetragonal form, and the axial bonds are 302.8pm joining the InMe 3 units into hexamers and 313.4 pm linking the hexamers to form the infinite network. [ 7 ]
Indium is a component of several compound semiconductors , including as InP, InAs, InN , InSb , GaInAs , InGaN , AlGaInP , AlInP, and AlInGaNP. These materials are prepared by metalorganic vapour phase epitaxy ( MOVPE ) and TMI is the preferred source for the indium component. High purity in TMI (99.9999% pure or greater) is essential for many of these applications. For some materials, electron mobilities are observed as high as 287,000 cm²/Vs at 77 K and 5400 cm²/Vs at 300 K, and background carrier concentration as low as 6×10 13 cm −3 . [ 9 ] [ 10 ]
The vapor pressure equation log P (Torr) = 10.98–3204/T (K) describes TMI within a wide range of MOVPE growth conditions. [ 11 ]
TMI is pyrophoric . [ 12 ] | https://en.wikipedia.org/wiki/Trimethylindium |
Trimethylolethane trinitrate ( TMETN ), also known as metriol trinitrate ( METN , MTN , METRTN ) or nitropentaglycerin , is a nitrate ester . It is a high explosive similar to nitroglycerin . It is a transparent oily liquid, colorless to light brown. It is odorless. It is used in some solid propellants and smokeless powders as a plasticizer . Its chemical formula is CH 3 −C(CH 2 −O−NO 2 ) 3 .
TMETN was first prepared and patented in Italy under name Metriolo . Germans began producing it before World War II, when it was demonstrated to be an erosion and flash-reducing agent in smokeless powders. It is a liquid explosive with properties similar to nitroglycerin, but more stable to heat. It is prepared by nitration of trimethylolethane (metriol). It does not induce headaches.
TMETN can be initiated by friction, impact, and electrostatic discharge. It can be used as a high-viscosity plasticizer-binder together with nitrocellulose , but its poor colloidal properties has made such use rare. Long-term milling can however assist here; success can also be achieved by adding an inert plasticizer and a volatile solvent/colloidal agent. [ 1 ]
TMETN is miscible with ether and acetone. It is insoluble in 95% sulfuric acid. [ 2 ] It can be used as a plasticizer together with, or as an alternative to, triethyleneglycol dinitrate (TEGDN). It can also be used as a monopropellant ; [ 3 ] in fact triethylene glycol dinitrate , diethylene glycol dinitrate , and trimethyloleate trinitrate are being considered as replacements for nitroglycerin in propellants. [ 4 ] | https://en.wikipedia.org/wiki/Trimethylolethane_trinitrate |
Trimethylolpropane ethoxylate ( TPEG ) is a trifunctional polyether compound derived from trimethylolpropane . [ 1 ]
TPEG is produced by ethoxylation of trimethylolpropane . [ 1 ]
TPEG is used in the production of polyurethane foams, elastomers , and sealants. [ 1 ] | https://en.wikipedia.org/wiki/Trimethylolpropane_ethoxylate |
Trimethylsilyl azide is the organosilicon compound with the formula (CH 3 ) 3 SiN 3 . A colorless liquid, it is a reagent in organic chemistry , serving as the equivalent of hydrazoic acid . [ 3 ]
Trimethylsilyl azide is commercially available. It may be prepared by the reaction of trimethylsilyl chloride and sodium azide : [ 4 ]
The compound hydrolyzes to hydrazoic acid : [ 5 ]
The compound adds to ketones and aldehydes to give the siloxy azides and subsequently tetrazoles: [ 3 ]
It ring-opens epoxides to give azido alcohols.
It has been used in the Oseltamivir total synthesis .
Trimethylsilyl azide is incompatible with moisture, strong oxidizing agents, and strong acids. Azides are often explosive, as illustrated by their use in air bags . | https://en.wikipedia.org/wiki/Trimethylsilyl_azide |
Trimethylsilyl chloride , also known as chlorotrimethylsilane is an organosilicon compound ( silyl halide ), with the formula (CH 3 ) 3 SiCl , often abbreviated Me 3 SiCl or TMSCl . It is a colourless volatile liquid that is stable in the absence of water. It is widely used in organic chemistry.
TMSCl is prepared on a large scale by the direct process , the reaction of methyl chloride with a silicon-copper alloy. The principal target of this process is dimethyldichlorosilane , but substantial amounts of the trimethyl and monomethyl products are also obtained. [ 1 ] The relevant reactions are (Me = methyl , CH 3 ): x MeCl + Si ⟶ { Me 3 SiCl , Me 2 SiCl 2 , MeSiCl 3 , etc. {\displaystyle x\ {\ce {MeCl + Si}}\longrightarrow {\begin{cases}{\ce {Me3SiCl}},\\[2pt]{\ce {Me2SiCl2}},\\[2pt]{\ce {MeSiCl3}},\\[2pt]{\text{etc.}}\end{cases}}}
Typically about 2–4% of the product stream is the monochloride, which forms an azeotrope with MeSiCl 3 .
TMSCl is reactive toward nucleophiles, resulting in the replacement of the chloride. In a characteristic reaction of TMSCl, the nucleophile is water, resulting in hydrolysis to give the hexamethyldisiloxane : 2 Me 3 SiCl + H 2 O ⟶ Me 3 Si − O − SiMe 3 + 2 HCl {\displaystyle {\ce {2 Me3SiCl + H2O -> Me3Si-O-SiMe3 + 2 HCl}}} The related reaction of trimethylsilyl chloride with alcohols can be exploited to produce anhydrous solutions of hydrochloric acid in alcohols, which find use in the mild synthesis of esters from carboxylic acids and nitriles as well as, acetals from ketones . Similarly, trimethylsilyl chloride is also used to silanize laboratory glassware , making the surfaces more lipophilic . [ 2 ]
By the process of silylation , polar functional groups such as alcohols and amines readily undergo reaction with trimethylsilyl chloride, giving trimethylsilyl ethers and trimethylsilyl amines . These new groups "protect" the original functional group by removing the labile protons and decreasing the basicity of the heteroatom. The lability of the Me 3 Si−O and Me 3 Si−N groups allow them to be easily removed afterwards ("deprotected"). Trimethylsilylation can also be used to increase the volatility of a compound, enabling gas chromatography of normally nonvolatile substances such as glucose .
Trimethylsilyl chloride also reacts with carbanions to give trimethylsilyl derivatives. [ 3 ] Lithium acetylides react to give trimethylsilyl alkynes such as bis(trimethylsilyl)acetylene . Such derivatives are useful protected forms of alkynes.
In the presence of triethylamine and lithium diisopropylamide , enolisable aldehydes , ketones and esters are converted to trimethylsilyl enol ethers . [ 4 ] Despite their hydrolytic instability, these compounds have found wide application in organic chemistry; oxidation of the double bond by epoxidation or dihydroxylation can be used to return the original carbonyl group with an alcohol group at the alpha carbon. The trimethylsilyl enol ethers can also be used as masked enolate equivalents in the Mukaiyama aldol addition .
Dehydration of metal chlorides with trimethylsilyl chloride in THF gives the solvate as illustrated by the case of chromium trichloride : [ 5 ] CrCl 3 ⋅ 6 H 2 O + 12 Me 3 SiCl ⟶ CrCl 3 ( THF ) 3 + 6 ( Me 3 Si ) 2 O + 12 HCl {\displaystyle {\ce {CrCl3 * 6 H2O + 12 Me3SiCl -> CrCl3(THF)3 + 6 (Me3Si)2O + 12 HCl}}}
Trimethylsilyl chloride is used to prepare other trimethylsilyl halides and pseudohalides , including trimethylsilyl fluoride, trimethylsilyl bromide, trimethylsilyl iodide , trimethylsilyl cyanide , trimethylsilyl azide , [ 6 ] and trimethylsilyl trifluoromethanesulfonate (TMSOTf). These compounds are produced by a salt metathesis reaction between trimethylsilyl chloride and a salt of the (pseudo)halide (MX): MX + Me 3 Si − Cl ⟶ MCl + Me 3 Si − X {\displaystyle {\ce {MX + Me3Si-Cl -> MCl + Me3Si-X}}} TMSCl, lithium, and nitrogen molecule react to give tris(trimethylsilyl)amine , under catalysis by nichrome wire or chromium trichloride : 3 Me 3 SiCl + 3 Li + 1 2 N 2 ⟶ ( Me 3 Si ) 3 N + 3 LiCl {\displaystyle {\ce {3 Me3SiCl + 3 Li}}+{\tfrac {1}{2}}\,{\ce {N2 -> (Me3Si)3N + 3 LiCl}}} Using this approach, atmospheric nitrogen can be introduced into organic substrate. For example, tris(trimethylsilyl)amine reacts with α,δ,ω-tri ketones to give tricyclic pyrroles . [ 7 ]
Reduction of trimethylsilyl chloride give hexamethyldisilane : 2 Me 3 SiCl + 2 Na ⟶ 2 NaCl + Me 3 Si − SiMe 3 {\displaystyle {\ce {2 Me3SiCl + 2 Na -> 2 NaCl + Me3Si-SiMe3}}} | https://en.wikipedia.org/wiki/Trimethylsilyl_chloride |
Trimethylsilyl cyanide is the chemical compound with the formula ( C H 3 ) 3 Si C N . This volatile liquid consists of a cyanide group, that is CN, attached to a trimethylsilyl group. The molecule is used in organic synthesis as the equivalent of hydrogen cyanide . It is prepared by the reaction of lithium cyanide and trimethylsilyl chloride: [ 1 ] [ 2 ]
The molecule exhibits the structure of a nitrile-like compound, having the structural formula (CH 3 ) 3 Si−C≡N . The compound exists in a rapid equilibrium with a small amount of the isomeric isocyanide (CH 3 ) 3 Si−N + ≡C − . [ 3 ] By contrast, the nearly isostructural tert -butyl nitrile does not readily isomerize to tert -butyl isocyanide . The isocyanide isomer can be stabilized by complexation to metals. [ 4 ]
Trimethylsilyl cyanide hydrolyzes to give hydrogen cyanide and trimethylsilanol :
In its principal application, it adds across carbon-oxygen double bonds, for example in an aldehyde , to form a new carbon-carbon bond: [ 2 ]
The product is an O -silylated cyanohydrin .
One use of this reagent is to convert pyridine - N - oxides into 2-cyanopyridine. This transformation is best done in dichloromethane solution using dimethyl carbamoyl chloride as the activating electrophile . It is possible to use benzoyl chloride but the yields and regioselectivity of the addition of the cyano group are lower.
Acetone cyanohydrin can be used to reversibly generate the cyanide anion. [ 5 ]
(4)
Trimethylsilyl cyanide behaves equivalently to hydrogen cyanide , a potent poison. [ 2 ] The compound can be disposed of by using a mixture of alkali hydroxide and bleach. [ 6 ] | https://en.wikipedia.org/wiki/Trimethylsilyl_cyanide |
Trimethylsilyl iodide ( iodotrimethylsilane or TMSI ) is an organosilicon compound with the chemical formula (CH 3 ) 3 SiI. It is a colorless, volatile liquid at room temperature.
Trimethylsilyl iodide may be prepared by the oxidative cleavage of hexamethyldisilane by iodine [ 2 ] or by the cleavage of hexamethyldisiloxane with aluminium triiodide . [ 2 ] [ 3 ]
Trimethylsilyl iodide is used to introduce the trimethylsilyl group onto alcohols (ROH):
This type of reaction may be useful for gas chromatography analysis; the resultant silyl ether is more volatile than the underivatized original materials. [ 4 ] However, for the preparation of bulk trimethylsilylated material, trimethylsilyl chloride may be preferred due to its lower cost.
TMSI reacts with alkyl ethers (ROR′), forming silyl ethers (ROSiMe 3 ) and iodoalkanes (RI) that can be hydrolyzed to alcohols (ROH). [ 5 ]
Trimethylsilyl iodide is also used for the removing of the Boc protecting group , [ 2 ] [ 6 ] [ 7 ] especially where other deprotection methods are too harsh for the substrate. [ 8 ] | https://en.wikipedia.org/wiki/Trimethylsilyl_iodide |
Trimethylsilylpropanoic acid ( TMSP or TSP ) is a chemical compound containing a trimethylsilyl group. It is used as internal reference in nuclear magnetic resonance for aqueous solvents (e.g. D 2 O). For that use it is often deuterated (3-(trimethylsilyl)-2,2,3,3-tetradeuteropropionic acid or TMSP- d 4 ). [ 1 ] Other internal references that are frequently used in NMR experiments are DSS and tetramethylsilane .
This article about an organic compound is a stub . You can help Wikipedia by expanding it .
This nuclear magnetic resonance –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trimethylsilylpropanoic_acid |
Trimethylsulfoxonium iodide is an organosulfur compound with the chemical formula [( C H 3 ) 3 S = O ] + I − . It is a sulfoxonium salt derived from dimethylsulfoxide . It is iodide salt of a common sulfoxonium cation . This compound, a colorless solid, is commercially available. It may be prepared by the alkylation of dimethyl sulfoxide with iodomethane : [ 1 ]
The trimethylsulfoxonium ion features a tetrahedral molecular geometry at sulfur center. The ion has idealized C 3v symmetry . It is isoelectronic with trimethylphosphine oxide .
Trimethylsulfoxonium iodide is used to generate dimethyloxosulfonium methylide by reaction with sodium hydride . [ 2 ] The latter compound is used to prepare epoxides from ketones and aldehydes.
This article about a salt (chemistry) is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trimethylsulfoxonium_iodide |
In light-frame construction , a trimmer is a timber or metal beam (joist) used to create an opening around a stairwell, skylight, chimney, and the like. Trimmers are installed parallel to the primary floor or ceiling joists and support headers , which run perpendicular to the primary joists. [ 1 ] [ 2 ]
It can also refer to a jack stud that supports a header above a window or door opening.
Traditionally, a stud which was less than full length was sometimes referred to as a cripple . [ 3 ] [ 4 ] [ 5 ]
This article about a civil engineering topic is a stub . You can help Wikipedia by expanding it .
This architecture -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trimmer_(construction) |
In biology , trimorphism is the existence in certain plants and animals of three distinct forms, especially in connection with the reproductive organs .
In trimorphic plants there are three forms, differing in the lengths of their pistils and stamens , in size and color of their pollen grains, and in some other respects; and, as in each of the three forms there are two sets of stamens, the three forms possess altogether six sets of stamens and three kinds of pistils. These organs are so proportioned in length to each other that half the stamens in two of the forms stand on a level with the stigma of the third form. To obtain full fertility with these plants, it is necessary that the stigma of the one should be fertilized by pollen taken from the stamens of corresponding height in another form. Hence six unions are legitimate, that is, fully fertile, and 12 are illegitimate, or more or less unfertile. Wallace has shown that the females of certain butterflies from the Malay Archipelago appear in three conspicuously distinct forms without intermediate links.
In crystallography , trimorphism refers to the occurrence of certain forms in minerals which have the same chemical composition , but are referable to three systems of crystallization .
This plant physiology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trimorphism |
Trimyristin is a saturated fat and the triglyceride of myristic acid with the chemical formula C 45 H 86 O 6 . Trimyristin is a white to yellowish-gray solid that is insoluble in water, but soluble in ethanol , acetone , benzene , chloroform , dichloromethane , ether , and TBME .
Trimyristin is found naturally in many vegetable fats and oils .
The isolation of trimyristin from powdered nutmeg is a common introductory-level college organic chemistry experiment. [ 8 ] [ 9 ] It is an uncommonly simple natural product extraction because nutmeg oil generally consists of over eighty percent trimyristin. Trimyristin makes up between 20-25% of the overall mass of dried, ground nutmeg. Separation is generally carried out by steam distillation and purification uses extraction from ether followed by distillation or rotary evaporation to remove the volatile solvent . The extraction of trimyristin can also be done with diethyl ether at room temperature, due to its high solubility in the ether. The experiment is frequently included in curricula, both for its relative ease and to provide instruction in these techniques. Trimyristin can then be used to prepare myristic acid [ 10 ] or one of its salts [ 11 ] as an example of saponification .
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trimyristin |
The Trinder glucose activity test is a diagnostic test used in medicine to determine the presence of glucose or glucose oxidase . The test employs the Trinder reagent , and is a colour change test resulting from the Trinder reaction .
The Trinder reagent, named after P. Trinder of the Biochemistry Department of the Royal Infirmary in Sunderland (see the article listed in further reading ), comprises an aminoantipyrine (such as 4-aminoantipyrine ) and phenol (p-hydroxybenzene). [ 1 ] [ 2 ]
The Trinder reaction is the reaction between hydrogen peroxide and the phenol and aminoantipyrine to form a quinone ( quinoneimine ), catalyzed by the presence of a peroxidase (such as horseradish peroxidase ). [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] The hydrogen peroxide is itself produced by an initial reaction where the glucose is oxidised in the presence of the glucose oxidase catalyst into H 2 O 2 and gluconic acid . [ 2 ] [ 3 ]
The quinone is red-violet in colour, [ 3 ] [ 5 ] with the intensity of the colour being in proportion to the glucose concentration. [ 3 ] The colour is measured at 505 nm, [ 2 ] 510 nm, [ 4 ] or 540 nm. [ 3 ]
Diagnostic kits containing the Trinder reagent are available, including one from Sigma-Aldrich . [ 2 ]
The Stanbio Single Reagent Glucose Method is based upon the Trinder technique. [ 3 ] [ 6 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it .
This medical diagnostic article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trinder_glucose_activity_test |
The Trinder spot test is a diagnostic test used in medicine to determine exposure to salicylates , particularly to salicylic acid . The test employs the Trinder reagent (a.k.a. Trinder solution ) which is mixed with a patient's urine . The colour change, resulting from the Trinder reaction , is immediate, enabling rapid bedside assessment. [ 1 ] [ 2 ]
The Trinder solution/reagent is a pre-mixed solution of 10% ferric chloride . [ 1 ] It can be prepared by combining 40 g of mercuric chloride and 40 g of ferric nitrate in 850 ml of type II deionized water , and then adding 10 ml of concentrated hydrochloric acid to the solution and diluting to a volume of 1 litre with more type II deionized water. [ 2 ] [ 3 ]
The test for the Trinder reaction is to mix 1 ml of urine with 1 ml of the Trinder reagent in a test tube . The test is positive if a colour change results. [ 3 ] The specific colour changes are:
The test has a sensitivity of 94% and a specificity of 74% for identifying patients whose salicylate concentrations are greater than 30 mg per decilitre (2.17 mmol/L). [ 1 ] False positive concentrations (2.8 to 14.3 mg per decilitre) have been reported to occur in neonates with hyperbilirubinemia , premature neonates, and children who are seriously ill (e.g. children who have extensive burns). [ 3 ]
The reaction between iron(III) and pharmaceuticals was first adapted for clinical use by P. Trinder (after whom the test, reaction, and reagent are now named), of the Biochemistry Department of the Royal Infirmary in Sunderland , in 1954 (see the article listed in further reading ). Salicylic acid , salicylamide , and methyl salicylate all react with iron(III) via the phenol group which is next to their –COOH, –CONH 2 , or –COOCH 3 functional groups. The Trinder reaction has been used for the determination of the presence of oxytetracycline in 1991, of ciprofloxacin in 1992, and of norfloxacin in 1993, in each case using a solution of iron(III) in sulphuric acid. It has also been used for the determination of the presence of bromazepam in 1992, using an iron(II) solution in a hydrochloric acid rather than an iron(III) solution. [ 4 ] | https://en.wikipedia.org/wiki/Trinder_reagent |
Trinitroanisole is a chemical compound that exists as pale yellow crystals with a melting point of 68 °C. It is highly toxic. It is an explosive with a detonation velocity of 7200 meters per second . [ 1 ] The compound's primary hazard is a blast of an instantaneous explosion, not flying projectiles or fragments. [ 2 ]
Trinitroanisole was first prepared in 1849 by the French chemist Auguste Cahours by reacting p-anisic acid (French: acide anisique ) with a mixture of sulfuric acid and fuming nitric acid . [ 3 ] [ 4 ]
Trinitroanisole can be prepared by the reaction of 2,4-dinitrochlorobenzene with methanol in the presence of sodium hydroxide followed by the nitration of the resulting product. Alternatively, it can be prepared directly by the reaction of picryl chloride with methanol in the presence of sodium hydroxide. [ 1 ]
Historically, trinitroanisole was used as a military explosive (e.g., Japanese Type 91 or German Trinol ), having the advantage of being made from readily obtainable raw materials such as phenol . However, due to its toxicity and tendency to form picric acid and dangerous picrate salts, its use has largely been abandoned. | https://en.wikipedia.org/wiki/Trinitroanisole |
Trinitroethylorthocarbonate , also known as TNEOC , is an organic compound with the chemical formula C(OCH 2 C(NO 2 ) 3 ) 4 . It is an oxidizer with excellent chemical stability. [ citation needed ] Its explosion point is 238 °C, and it begins to be decomposed at 200 °C. Its explosion heat is 5.797 J/g and specific volume is 694 L/kg. [ 1 ] Its structure is closely related to that of trinitroethylorthoformate (TNEOF). Both are highly explosive and very shock-sensitive, and may be dissolved in nitroalkanes to reduce their shock-sensitivity. [ 1 ]
TNEOC can be prepared by the reaction of trinitroethanol with carbon tetrachloride , catalyzed by FeCl 3 : [ 2 ] | https://en.wikipedia.org/wiki/Trinitroethylorthocarbonate |
Trinitroethylorthoformate also known as TNEOF is an explosive with excellent chemical stability. It does not have hygroscopicity, does not dissolve in water, and does not react with acids. It decomposes in aqueous sodium hydroxide solution to release formaldehyde odor. The explosion point of TNEOF is 229 °C, though it begins to decompose at 190 °C. Its explosion heat is 6.3076 J/g and specific volume is 682 L/kg. [ 1 ] Its structure is closely related to that of trinitroethylorthocarbonate (TNEOC). Both are highly explosive and very shock-sensitive, and may be dissolved in nitroalkanes to reduce their shock-sensitivity. [ 1 ]
Trinitroethanol is reacted with chloroform under a catalyst of FeCl 3 .
This organic chemistry article is a stub . You can help Wikipedia by expanding it .
This explosives -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trinitroethylorthoformate |
Trinitrotriazine , or 2,4,6-trinitro-1,3,5-triazine , is a theoretical explosive compound. Synthesis of this compound has been elusive despite its simple structure, [ 1 ] [ 2 ] as conventional nitration of triazine becomes increasingly more difficult as more nitro groups are added. A successful route would more likely proceed by trimerisation of nitryl cyanide . [ 3 ] The precursor nitryl cyanide was first synthesized by Rahm et al. in 2014. [ 4 ]
Trinitrotriazine has a neutral oxygen balance , potentially making it a very powerful explosive, though calculations predict it would be fairly unstable and inferior to the related compound 3,6-dinitro-1,2,4,5-tetrazine. [ 5 ]
This article about theoretical chemistry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trinitrotriazine |
In elementary algebra , a trinomial is a polynomial consisting of three terms or monomials . [ 1 ]
A trinomial equation is a polynomial equation involving three terms. An example is the equation x = q + x m {\displaystyle x=q+x^{m}} studied by Johann Heinrich Lambert in the 18th century. [ 2 ]
This polynomial -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trinomial |
In biology, trinomial nomenclature is the system of names for taxa below the rank of species . These names have three parts. The usage is different in zoology and botany .
In zoological nomenclature , a trinomen ( pl. trinomina ), trinominal name, or ternary name is the name of a subspecies .
A trinomen is a name with three parts: generic name , specific name and subspecific name . The first two parts alone form the binomen or species name. All three names are typeset in italics, and only the first letter of the generic name is capitalised. No indicator of rank is included: in zoology , subspecies is the only rank below that of species. [ 1 ] For example: " Buteo jamaicensis borealis is one of the subspecies of the red-tailed hawk ( Buteo jamaicensis )."
Examples include Gorilla gorilla gorilla ( Savage and Wyman , 1847) for the western lowland gorilla [ 2 ] and Gorilla gorilla diehli ( Matschie , 1903) for the Cross River gorilla [ 3 ] (which are subspecies of Gorilla gorilla , the western gorilla ); Bison bison bison ( Linnaeus , 1758) for the plains bison [ 4 ] and Bison bison athabascae (Rhoads, 1898) for the wood bison [ 5 ] (which are subspecies of Bison bison , the American bison ).
In a taxonomic publication, a name is incomplete without an author citation and publication details. This indicates who published the name, in what publication, and the date of the publication. For example: " Phalacrocorax carbo novaehollandiae (Stephens, 1826)" denotes a subspecies of the great cormorant ( Phalacrocorax carbo ) introduced by James Francis Stephens in 1826 [ 6 ] under the subspecies name novaehollandiae ("of New Holland ").
If the generic and specific name have already been mentioned in the same paragraph, they are often abbreviated to initial letters. For example, one might write: "The great cormorant Phalacrocorax carbo has a distinct subspecies in Australasia , the black shag P. c. novaehollandiae ".
While binomial nomenclature came into being and immediately gained widespread acceptance in the mid-18th century, it was not until the early 20th century that the current unified standard of trinominal nomenclature was agreed upon. This became the standard mainly because of tireless promotion by Elliott Coues – even though trinomina in the modern usage were pioneered in 1828 by Carl Friedrich Bruch and around 1850 were widely used especially by Hermann Schlegel and John Cassin . As late as the 1930s, the use of trinomina was not fully established in all fields of zoology. Thus, when referring especially European works of the preceding era, the nomenclature used is usually not in accord with contemporary standards.
For algae, fungi, plants, and their fossils, there is an indeterminate number of infraspecific ranks allowed below the level of species. The secondary ranks below the species rank are variety and forma , and more ranks can be made by using the prefix "sub" to make subspecies, subvariety, subforma. Very rarely even more forms are created, such as supersubspecies. Not all of these ranks need to be specified, for example, some authors prefer to divide plant species into subspecies, while others prefer to use varieties. [ 7 ]
These ranks are components of a biological classification , for example Corylopsis sinensis var. calvescens f. veitchiana is an ornamental garden plant. [ 8 ] However, a name is not the same as a classification, and the name of this plant is a trinomial with only three parts, [ 9 ] the two parts of the species name Corylopsis sinensis , plus the forma epithet veitchiana , to give Corylopsis sinensis f. veitchiana . | https://en.wikipedia.org/wiki/Trinomial_nomenclature |
The trinomial triangle is a variation of Pascal's triangle . The difference between the two is that an entry in the trinomial triangle is the sum of the three (rather than the two in Pascal's triangle) entries above it:
1 1 1 1 1 2 3 2 1 1 3 6 7 6 3 1 1 4 10 16 19 16 10 4 1 {\displaystyle {\begin{matrix}&&&&1\\&&&1&1&1\\&&1&2&3&2&1\\&1&3&6&7&6&3&1\\1&4&10&16&19&16&10&4&1\end{matrix}}}
The k {\displaystyle k} -th entry of the n {\displaystyle n} -th row is denoted by
Rows are counted starting from 0. The entries of the n {\displaystyle n} -th row are indexed starting with − n {\displaystyle -n} from the left, and the middle entry has index 0. The symmetry of the entries of a row about the middle entry is expressed by the relationship
The n {\displaystyle n} -th row corresponds to the coefficients in the polynomial expansion of the expansion of the trinomial ( 1 + x + x 2 ) {\displaystyle (1+x+x^{2})} raised to the n {\displaystyle n} -th power: [ 1 ]
or, symmetrically,
hence the alternative name trinomial coefficients because of their relationship to the multinomial coefficients :
Furthermore, the diagonals have interesting properties, such as their relationship to the triangular numbers .
The sum of the elements of n {\displaystyle n} -th row is 3 n {\displaystyle 3^{n}} .
The trinomial coefficients can be generated using the following recurrence formula : [ 1 ]
where ( n k ) 2 = 0 {\displaystyle {n \choose k}_{2}=0} for k < − n {\displaystyle \ k<-n} and k > n {\displaystyle \ k>n} .
The middle entries of the trinomial triangle
were studied by Euler and are known as central trinomial coefficients .
The only known prime central trinomial coefficients are 3, 7 and 19 at n = 2, 3 and 4.
The n {\displaystyle n} -th central trinomial coefficient is given by
Their generating function is [ 2 ]
Euler noted the following exemplum memorabile inductionis fallacis ("notable example of fallacious induction"):
where F n {\displaystyle F_{n}} is the n -th Fibonacci number . For larger n {\displaystyle n} , however, this relationship is incorrect. George Andrews explained this fallacy using the general identity [ 3 ]
The triangle corresponds to the number of possible paths that can be taken by the king in a game of chess . The entry in a cell represents the number of different paths (using a minimum number of moves) the king can take to reach the cell.
The coefficient of x k {\displaystyle x^{k}} in the expansion of ( 1 + x + x 2 ) n {\displaystyle \left(1+x+x^{2}\right)^{n}} gives the number of different ways to draw k {\displaystyle k} cards from two identical sets of n {\displaystyle n} playing cards each. [ 4 ] For example, from two sets of the three cards A, B, C, the different drawings are:
For example,
In particular, this provides the formula ( 24 12 − 24 ) 2 = ( 24 − 12 ) 2 = ( 24 12 ) 2 {\displaystyle {24 \choose 12-24}_{2}={24 \choose -12}_{2}={24 \choose 12}_{2}} for the number of different hands in the card game Doppelkopf .
Alternatively, it is also possible to arrive at this expression by considering the number of ways of choosing p {\displaystyle p} pairs of identical cards from the two sets, which is the binomial coefficient ( n p ) {\displaystyle {n \choose p}} . The remaining k − 2 p {\displaystyle k-2p} cards can then be chosen in ( n − p k − 2 p ) {\displaystyle {n-p \choose k-2p}} ways, [ 4 ] which can be written in terms of the binomial coefficients as
The example above corresponds to the three ways of selecting two cards without pairs of identical cards (AB, AC, BC) and the three ways of selecting a pair of identical cards (AA, BB, CC). | https://en.wikipedia.org/wiki/Trinomial_triangle |
A trinucleotide repeat expansion , also known as a triplet repeat expansion , is the DNA mutation responsible for causing any type of disorder categorized as a trinucleotide repeat disorder . These are labelled in dynamical genetics as dynamic mutations . [ 1 ] Triplet expansion is caused by slippage during DNA replication, also known as "copy choice" DNA replication. [ 2 ] Due to the repetitive nature of the DNA sequence in these regions, 'loop out' structures may form during DNA replication while maintaining complementary base pairing between the parent strand and daughter strand being synthesized. If the loop out structure is formed from the sequence on the daughter strand this will result in an increase in the number of repeats. However, if the loop out structure is formed on the parent strand, a decrease in the number of repeats occurs. It appears that expansion of these repeats is more common than reduction. Generally, the larger the expansion the more likely they are to cause disease or increase the severity of disease. Other proposed mechanisms for expansion and reduction involve the interaction of RNA and DNA molecules. [ 3 ]
In addition to occurring during DNA replication , trinucleotide repeat expansion can also occur during DNA repair . [ 4 ] When a DNA trinucleotide repeat sequence is damaged , it may be repaired by processes such as homologous recombination , non-homologous end joining , mismatch repair or base excision repair . Each of these processes involves a DNA synthesis step in which strand slippage might occur leading to trinucleotide repeat expansion. [ 4 ]
The number of trinucleotide repeats appears to predict the progression, severity, and age of onset of Huntington's disease and similar trinucleotide repeat disorders. [ 5 ] Other human diseases in which triplet repeat expansion occurs are fragile X syndrome , several spinocerebellar ataxias , myotonic dystrophy and Friedreich's ataxia . [ 4 ]
The first documentation of anticipation in genetic disorders was in the 1800s. However, from the eyes of geneticists, this relationship was disregarded and attributed to ascertainment bias ; because of this, it took almost 200 years for a link between onset of disease and trinucleotide repeats (TNR) to be acknowledged. [ 6 ]
The following findings of served as support for TNR's link to onset of disease; the detection of various repeats within these diseases demonstrated this relationship.
Because of these discoveries, ideas involving anticipation in disease began to develop, and curiosity formed about how the causes could be related to TNRs. [ 6 ] After the breakthroughs, the four mechanisms for TNRs were determined, and more types of repeats were identified as well. [ 9 ] Repeat composition and location are used to determine the mechanism of a given expansion. [ 9 ] Onwards from 1995, it was also possible to observe the formation of hairpins in triplet repeats, which consisted of repeating CG pairs and a mismatch. [ 11 ]
During the decade after evidence that linked TNR to onset of disease was found, focus was placed on studying repeat length and dynamics on diseases, as well as investigating the mechanism behind parent-child disease inheritance. [ 6 ] Research has shown that there is a clear inverse relationship between the length of the repeats in parents and the age of disease onset in children; therefore, the lengths of TNRs are used to predict age of disease onset as well as outcome in clinical diagnosis . [ 12 ] [ 13 ] In addition to this finding, another aspect of the diseases, the high variability of onset, was revealed. [ 6 ] Although the onset of HD could be predicted by examining TNR length inheritance, the onset could vary up to fourfold depending on the patient, leading to the possibility of existence of age-modifying factors for disease onset; there were notable efforts in this search. [ 14 ] [ 15 ] Currently, CAG repeat length is considered the biggest onset age modifier for TNR diseases. [ 16 ] [ 17 ]
Detection of TNRs was made difficult by limited technology and methods early on, and years passed before the development of sufficient ways to measure the repeats. [ 6 ] When PCR was first attempted in the detection of TNRs, multiple band artifacts were prevalent in the results, and this made recognition of TNRs troublesome; at the time, debate centered around whether disease was brought on by smaller amounts of short expansions or a small amount of long expansions. [ 6 ] [ 18 ] Since then, accurate methods have been established over the years. Together, the following clinically necessary protocols have 99% accuracy in measuring TNRs. [ 6 ]
These repetitive sequences lead to instability amongst the DNA strands after reaching a certain threshold number of repeats, which can result in DNA slippage during replication. [ 23 ] The most common and well-known triplet repeats are CAG, GCG, CTG, CGG, and GAA. During DNA replication, the strand being synthesized can misalign with its template strand due to the dynamic nature and flexibility of these triplet repeats. [ 24 ] This slippage allows for the strand to find a stable intermediate amongst itself through base pairing, forming a secondary structure other than a duplex. [ 24 ]
In terms of location, these triplet repeats can be found in both coding and non-coding regions. CAG and GCN repeats, which lead to polyglutamine and polyalanine tracts respectively, are normally found in the coding regions. [ 25 ] At the 5' untranslated region, CGG and CAG repeats are found and responsible for fragile X syndrome and spinocerebellar ataxia 12. [ 25 ] At the 3' untranslated region, CTG repeats are found, while GAA repeats are located in the intron region. Other disease-causing repeats, but not triplet repeats, have been located in the promoter region. [ 25 ] Once the number of repeats exceeds normal levels, Triplet Repeat Expansions (TRE) become more likely and the number of triplet repeats can typically increase to around 100 in coding regions and up to thousands in non-coding regions. [ 25 ] This difference is due to overexpression of glutamine and alanine, which is selected against due to cell toxicity. [ 26 ]
Depending on the sequence of the repeat, at least three intermediates with different secondary structures are known to form. [ 27 ] A CGG repeat will form a G-quadruplex due to Hoogsteen base pairing, while a GAA repeat forms a triplex due to negative supercoiling. [ 25 ] [ 27 ] CAG, CTG, and CGG repeats form a hairpin. After the hairpin forms, the primer realigns with the 3' end of the newly synthesized strand and continues the synthesis, leading to triplet repeat expansion. [ 23 ] The structure of the hairpin is based on a stem and a loop that contains both Watson-Crick base pairs and mismatched pairs. [ 25 ] In CTG and CAG repeats, the number of nucleotides present in the loop depends on if the number of triplet repeats is odd or even. [ 28 ] An even number of repeats forms a tetraloop structure, while an odd number leads to the formation of a triloop. [ 28 ] [ 29 ]
In trinucleotide repeat expansion there is a certain threshold or maximum amount of repeats that can occur before a sequence becomes unstable. Once this threshold is reached the repeats will start to rapidly expand causing longer and longer expansions in future generations. [ 30 ] Once it hits this minimum allele size which is normally around 30-40 repeats, diseases and instability can be contracted, but if the number of repeats found within a sequence are below the threshold it will remain relatively stable. [ 30 ] There is still not enough research found to understand the molecular nature that causes thresholds but researchers are continuing to study that the possibility could lie with the formation of the secondary structure when these repeats occur. It was found that diseases associated with trinucleotide repeat expansions contained secondary structures with hairpins, triplexes, and slipped-strand duplexes. [ 30 ] These observations have led to the hypothesis that the threshold is determined by the number of repeats that must occur to stabilize the formation of these unwanted secondary structures, due to the fact that when these structures form there is an increased number of mutations [ 31 ] that will form in the sequence resulting in more trinucleotide expansion.
Research suggests that there is a direct, important correlation between the sex of the parent that transmits the mutation and the degree and phenotype of disorder in the child., [ 32 ] [ 33 ] The degree of repeat expansion and whether or not an expansion will occur has been directly linked to the sex of the transmitting parent in both non-coding and coding trinucleotide repeat disorders. [ 32 ] For example, research regarding the correlation between Huntington's Disease CAG trinucleotide repeat and parental transmission has found that there is a strong correlation between the two with differences in maternal and paternal transmission. [ 32 ] Maternal transmission has been observed to only consist of an increase in repeat units of 1 while the paternal transmission is typically anywhere from 3 to 9 extra repeats. [ 32 ] Paternal transmission is almost always responsible for large repeat transmission resulting in the early onset of Huntington's Disease while maternal transmission results in affected individuals experiencing symptom onset mirroring that of their mother., [ 32 ] [ 34 ] While this transmission of a trinucleotide repeat expansion is regarded to be a result of "meiotic instability", the degree to which meiosis plays a role in this process and the mechanism is not clear and numerous other processes are predicted to simultaneously play a role in this process. [ 32 ]
One proposed but highly unlikely mechanism that plays a role in trinucleotide expansion transmission occurs during meiotic or mitotic recombination. [ 32 ] It is suggested that during these processes it is possible for a homologous repeat misalignment, commonly known for causing alpha-globin locus deletions, causes the meiotic instability of a trinucleotide repeat expansion. [ 32 ] This process is unlikely to contribute to the transmission and presence of trinucleotide repeat expansions due to differences in expansion mechanisms. [ 32 ] Trinucleotide repeat expansions typically favor expansions of the CAG region but, in order for the unequal homologous exchange to be a plausible suggestion, these repeats would have to go through expansion and contraction events at the same time. [ 32 ] In addition, numerous diseases that result from transmitted trinucleotide repeat expansions, such as Fragile X syndrome, involve unstable trinucleotide repeats on the X chromosome that cannot be explained by meiotic recombination. [ 32 ] Research has shown that although unequal homologous recombination is unlikely to be the sole cause of transmitted trinucleotide repeat expansions, this homologous recombination likely plays a minor role in the length of some trinucleotide repeat expansions. [ 32 ]
DNA replication errors are predicted to be the main perpetrator of trinucleotide repeat expansion transmission in many predicted models due to the difficulty of Trinucleotide Repeat Expansion (TRE). [ 32 ] TREs have been shown to occur during DNA replication in both in vitro and in vivo studies, allowing for these long tracts of triplet repeats to assemble rapidly in different mechanisms that can result in either small scale or large scale expansions. [ 25 ]
These expansions can occur through either strand slippage or flap ligation. [ 25 ] Okazaki fragments are a key element of the proposed error in DNA replication. [ 32 ] It is suggested that the small size of Okazaki fragments, typically between 150 and 200 nucleotides long, makes them more likely to fall off or "slip" off the lagging strand, which creates room for trinucleotide repeats to attach to the lagging strand copy. [ 32 ] In addition to this possibility of trinucleotide repeat expansion changes occurring due to slippage of Okazaki fragments, the ability of CG-rich trinucleotide repeat expansion sequences to form a special hairpin, toroid, and triplex DNA structures contributes to this model, suggesting error occurs during DNA replication. [ 32 ] Hairpin structures can form as a result of the freedom of the lagging strand during DNA replication and are typically observed to form in extremely long trinucleotide repeat sequences. [ 32 ] Research has found that this hairpin formation depends on the orientation of the trinucleotide repeats within each CAG/CTG trinucleotide strand. [ 32 ] Strands that have duplex formation by CTG repeats in the leading strand are observed to result in extra repeats, while those without CTG repeats in the leading strand result in repeat deletions. [ 32 ] These intermediates can pause activity of the replication fork based on their interaction with DNA polymerases through strand slippage. [ 25 ] Contractions occur when the replication fork skips over the intermediate on the Okazaki fragment. Expansions occur when the fork reverses and restarts, which forms a chicken-foot structure. [ 25 ] This structure results in the unstable intermediate forming on the nascent leading strand, leading to further TRE. [ 25 ] Furthermore, this intermediate can avoid mismatch repair due to its affinity for the MSH-2-MSH3 complex, which stabilizes the hairpin instead of repairing it. [ 25 ] [ 27 ] In non-dividing cells, a process called flap-ligation can be responsible for TRE. [ 25 ] [ 27 ] 8-oxo-guanine DNA glycosylase removes a guanine and forms a nick in the sequence. [ 25 ] The coding strand then forms a flap due to displacement, which prevents removal by an endonuclease. When the repair process finishes for either mechanism, the length of the expansion is equivalent to the number of triplet repeats involved in the formation of the hairpin intermediate. [ 25 ]
Two mechanisms have been proposed for large scale repeats: template switching and break-induced replication. [ 27 ]
Template switching, a mechanism for large scale GAA repeats that can double the number of triplet repeats, has been proposed. [ 27 ] GAA repeats expand when their repeat length is greater than the Okazaki fragment's length. [ 27 ] These repeats are involved in the stalling of the replication fork as these repeats form a triplex when the 5' flap of TTC repeats fold back. [ 27 ] Okazaki fragment synthesis continues when the template is switched to the nascent leading strand. [ 27 ] The Okazaki fragment eventually ligates back to the 5' flap, which results in TRE. [ 27 ]
A different mechanism, based on break-induced replication, has been proposed for large scale CAG repeats and can also occur in non-dividing cells. [ 27 ] At first, this mechanism follows the same process as the small scale strand slippage mechanism until replication fork reversal. [ 27 ] An endonuclease then cleaves the chicken-foot structure, which results in a one-ended double strand break. [ 27 ] The CAG repeat of this broken daughter strand forms a hairpin and invades the CAG strand on the sister chromatid, which results in expansion of this repeat in a migrating D-loop DNA synthesis. [ 27 ] This synthesis continues until it reaches the replication fork and is cleaved, which results in an expanded sister chromatid. [ 27 ]
Fragile X syndrome is the second most common form of intellectual disability affecting 1 in 2,000-4,000 women and 1 in 4,000-8,000 men, women being twice as likely to inherit this disability due to their XX chromosomes. [ 35 ] This disability arises from a mutation at the end of the X chromosome in the FMR1 gene (fragile X mental retardation gene) which produces a protein essential for brain development called FMRP. [ 35 ] Individuals with fragile X syndrome experience a variety of symptoms at varying degrees that depend on gender and mutation degree such as attention deficit disorders, irritability, stimuli sensitivity, various anxiety disorders, depression, and/or aggressive behavior. [ 35 ] Some treatments for these symptoms seen in individuals with Fragile X syndrome include SSRI 's, antipsychotic medications, stimulants, folic acid , and mood stabilizers. [ 35 ]
Fragile X syndrome is caused by expansion of CGG repeats in the FMR1 gene. In males without fragile X syndrome, the CGG repeat number ranges from 53 to 200 while those affected have greater than 200 repeats of this trinucleotide sequence located at the end of the X chromosome on band Xq28.3.1 . [ 36 ] Carriers that have repeats falling within the 53 to 200 repeat range are said to have "premutation alleles", as the alleles within this range approach 200, the likelihood of expansion to a full mutation increases, and the mRNA levels are elevated five-fold. [ 36 ] Research has shown that individuals with premutation alleles in the range of 59-69 repeats have about a 30% risk of developing full mutation and compared to those in the high range of ≥ 90 repeats. [ 37 ] Fragile X syndrome carriers (those that fall within the premutation range) typically have unmethylated alleles, normal phenotype, and normal levels of FMR1 mRNA and FMRP protein. [ 36 ] Fragile X syndrome men possess alleles in the full mutation range (>200 repeats) with FMRP protein levels much lower than normal and experience hypermethylation of the promoter region of the FMR1 gene. [ 36 ] Some men with alleles in the full mutation range experience partial or no methylation which results in only slightly abnormal phenotypes due to only slight down-regulation of FMR1 gene transcription. [ 36 ] Unmethylated and partially methylated alleles in the mutation range experience increased and normal levels of FMR1 mRNA when compared to normal controls. [ 36 ] In contrast, when unmethylated alleles reach a repeat number of approximately 300, the transcription levels are relatively unaffected and operate at normal levels; the transcription levels of repeats greater than 300 is currently unknown. [ 36 ]
The CGG trinucleotide repeat expansion is present within the FMR1 mRNA and its interactions are responsible for promoter silencing. [ 36 ] The CGG trinucleotide expansion resides within the 5' untranslated region of the mRNA, which undergoes hybridization to form a complementary CGG repeat portion. [ 36 ] The binding of this genomic repeat to the mRNA results in silencing of the promoter. [ 36 ] Beyond this point, the mechanism of promoter silencing is unknown and still being further investigated. [ 36 ]
Huntington's disease (HD) is a dominantly, paternally transmitted neurological disorder that affects 1 in 15,000-20,000 people in many Western populations. [ 38 ] HD involves the basal ganglia and the cerebral cortex and manifests as symptoms such as cognitive, motor, and/or psychiatric impairment. [ 38 ]
This autosomal dominant disorder results from the expansions of a trinucleotide repeat which involves CAG in exon 1 of the IT15 gene. [ 39 ] The majority of all juvenile HD cases stem from the transmission of a high CAG trinucleotide repeat number that is a result of paternal gametogenesis . [ 40 ] While an individual without HD has a number of CAG repeats that fall within a range between 9 and 37, an individual with HD has CAG is typically found to have repeats in a range between 37 and 102. [ 39 ] Research has shown an inverse relationship between the number of trinucleotide repeats and age of onset, however, no relationship between trinucleotide repeat numbers and rate of HD progression and/or effected individual's body weight has been observed. [ 39 ] Severity of functional decline has been found to be similar across a wide range of individuals with varying numbers of CAG repeats and differing ages of onset, therefore, it is suggested that the rate of disease progression is also linked to factors other than the CAG repeat such as environmental and/or genetic factors. [ 39 ]
Myotonic dystrophy is a rare muscular disorder in which numerous bodily systems are affected. There are four forms of Myotonic Dystrophy: mild phenotype and late-onset, onset in adolescence/young adulthood, early childhood featuring only learning disabilities, and a congenital form. [ 41 ] Individuals with Myotonic Dystrophy experience severe, debilitating physical symptoms such as muscle weakness, heartbeat issues, and difficulty breathing that can be improved through treatment to maximize patients' mobility and everyday activity to alleviate some stress of their caretakers. [ 42 ] The muscles of individuals with Myotonic Dystrophy feature an increase of type 1 fibers as well as an increased deterioration of these type 1 fibers. [ 42 ] In addition to these physical ailments, individuals with Myotonic Dystrophy have been found to experience varying internalized disorders such as anxiety and mood disorders as well as cognitive delays, attention deficit disorders , autism spectrum disorders , lower IQ's, and visual-spatial difficulties. [ 42 ] Research has shown that there is a direct correlation between expansion repeat number, IQ, and an individual's degree of visual-spatial impairment. [ 42 ]
Myotonic dystrophy results from a (CTG)n trinucleotide repeat expansion that resides in a 3' untranslated region of a serine/threonine kinase coding transcript. [ 43 ] This (CTG)n trinucleotide repeat is located within leukocytes ; the length of the repeat and the age of the individual have been found to be directly related to disease progression and type 1 muscle fiber predominance. [ 43 ] Age and (CTG)n length only have small correlation coefficients to disease progression, research suggests that various other factors play a role in disease progression such as changes in signal transduction pathway , somatic expression, and cell heterogeneity in (CTG)n repeats. [ 43 ]
Friedreich's ataxia is a progressive neurological disorder. Individuals experience gait and speech disturbances due to degeneration of the spinal cord and peripheral nerves. Other symptoms may include cardiac complications and diabetes. Typical age at symptom onset is 5–15, with symptoms progressively getting worse over time. [ 44 ]
Friedreich's ataxia is an autosomal recessive disorder cause by a GAA expansion in the intron of the FXN gene. This gene codes for the protein frataxin , a mitochondrial protein involved in iron homeostasis. The mutation impairs transcription of the protein, so affected cells produce only 5-10% of the frataxin of healthy cells. [ 45 ] This leads to iron accumulation in the mitochondria, and makes cells vulnerable to oxidative damage.
Research shows that GAA repeat length is correlated with disease severity. [ 46 ]
The precise timing of TNR occurrence varies by disease. Although the exact timing for FXS is not certain, research has suggested that the earliest CGG expansions for this disorder are seen in primary oocytes . [ 47 ] [ 48 ] It has been proposed that the repeat expansion happens in the maternal oocyte during meiotic cell cycle arrest in prophase I , however the mechanism remains nebulous. [ 49 ] [ 50 ] Maternally inherited premutation alleles may expand into full mutation alleles (greater than 200 repeats), resulting in decreased production of the FMR-1 gene product FMRP and causing fragile X mental retardation syndrome. [ 51 ] For females, the large repeat expansions are based upon repair, while for males, the shortening of long repeat expansions is due to replication; therefore, their sperm lack these repeats, and paternal inheritance of long repeat expansions does not occur. [ 52 ] [ 53 ] [ 54 ] Between weeks 13 and 17 of human fetal development , the large CGG repeats are shortened. [ 54 ]
Many similarities can be drawn between DM1 and FXS involving aspects of mutation. Full maternal inheritance is present within DM1, repeat expansion length is linked to maternal age and the earliest instance of expansions is seen in the two-cell stage of preimplantation embryos. [ 55 ] [ 56 ] There is a positive correlation between male inheritance and allele length. [ 57 ] A study of mice found the exact timing of CTG repeat expansion to be during development of spermatogonia . [ 58 ] In DM1 and FXS, it is hypothesized that expansion of TNRs occurs by means of multiple missteps by DNA polymerase in replication. [ 59 ] [ 60 ] An inability of DNA polymerase to properly move across the TNR may cause transactivation of translesion polymerases (TLPs), which will attempt to complete the replication process and overcome the block. It is understood that as the DNA polymerase fails in this way, the resulting single-stranded loops left behind in the template strand undergo deletion, affecting TNR length. This process leaves the potential for TNR expansions to occur. [ 15 ]
In Huntington's disease (HD), the exact timing has not been determined; however there are a number of proposed points during germ cell development at which expansion is thought to occur. [ 61 ] [ 62 ]
Spinocerebellar ataxia type 1 (SCA1) CAG repeats are most often passed down through paternal inheritance and similarities can be seen with HD. [ 15 ] The tract size for offspring of mothers with these repeats does not display any degree of change. [ 64 ] Because TNR instability is not present in young female mice, and female SCA1 patient age and instability are directly related, expansions must occur in inactive oocytes. [ 65 ] A trend has seemed to emerge of larger expansions occurring in cells inactive in division and smaller expansions occurring in actively dividing or nondividing cells. [ 15 ]
Trinucleotide repeat expansion, is a DNA mutation that is responsible for causing any type of disorder classified as a trinucleotide repeat disorder. These disorders are progressive and affect the sequences of the human genome, frequently within the nervous system. So far the available therapeutics only have modest results at best [ 66 ] with emphasis on the research and studying of genomic manipulation. The most advanced available therapies aim to target mutated gene expression by using antisense oligonucleotides (ASO) or RNA interference (RNAi) to target the messenger RNA (mRNA). [ 66 ] While solutions for the interventions of this disease is a priority, RNAi and ASO have only reached clinical trial stages.
RNA interference is a mechanism that can be used to silence the expression of genes, RNAi is a naturally occurring process that is leveraged using synthetic small interfering RNAs (siRNAs) that are used to change the action and duration of the natural RNAi process. [ 67 ] Another synthetic RNA is the short hairpin RNAs (shRNA) [ 67 ] these can also be used to monitor the action and predictability of the RNAi process.
RNAi begins with RNase Dicer cleaving a 21-25 nucleotide long stand of double stranded RNA substrates into small fragments. This process results in the creation of the siRNA duplexes that will be used by the complex RNA induced silencing complex (RISC). [ 67 ] The RISC contains the antisense that will bind to complementary mRNA strands, once they are bound they are cleaved by the protein found within the RISC complex called Argonaute 2 (Ago2) between the bases 10 and 11 relative to the 5' end. Before the cleavage of the mRNA strand the double stranded antisense of the siRNA is also cleaved by the Ago2 complex, this leaves a single stranded guide within the RISC compound that will be used to find the desired mRNA strand resulting in this process to have specificity. [ 68 ] Some problems that may occur is if the guide single strand siRNA within the RISC complex may become unstable when cleaved and begin to unwind, resulting in binding to an unfavorable mRNA strand. The perfect complementary guides for the targeted RNAs are easily recognized and will be cleaved within the RISC complex; if there is only partial complementary pairing between the guide strand and the targeted mRNA may cause the incorrect translation or destabilization at the target sites. [ 68 ]
Antisense oligonucleotides (ASOs) are small strand single stranded oligodeoxynucleotides approximately 15-20 nucleic acids in length that can alter the expression of a protein. [ 69 ] The goal of using these antisense oligonucleotides are the decrease in protein expression of a specific target usually by the inhibition of the RNase H endonuclease, as well as inhibition of the 5' cap formation or alteration of the splicing process. [ 70 ] In the native state ASOs are rapidly digested, this requires the use of phosphorylation order for the ASO to go through the cell membranes.
Despite the obvious benefits that antisense therapeutics can bring to the world with their ability to silence neural disease, there are many issues with the development of this therapy. One problem is the ASOs are highly susceptible to degradation by the nucleases [ 71 ] within the body. This results in a high amount of chemical modification when altering the chemistry to allow for the nucleases to surpass the degradation of these synthetic nucleic acids. Native ASOs have a very short half-life even before being filtered throughout the body especially in the kidney and with the a high negative charge makes the crossing through the vascular system or membranes very difficult when trying to reach the targeted DNA or mRNA strands. With all these barriers, the chemical modifications may lead to devastating effects when being introduced into the body making each problem develop more and more side effects.
The synthetic oligonucleotides are negatively charged molecules that are chemically modified in order for the molecule to regulate the gene expression within the cell. Some issues that come about this process is the toxicity and variability that can come about with chemical modification. [ 70 ] The goal of the ASO is to modulate the gene expression through proteins which can be done in 2 complex ways; a)the RNase H-dependent oligonucleotides, which induce the degradation of mRNA, and (b) the steric-blocker oligonucleotides, which physically prevent or inhibit the progression of splicing or the translational machinery. The majority of investigated ASOs utilize the first mechanism with the Rnase H enzyme that hydrolyzes an RNA strand, when this enzyme is assisted using the oligonucleotides the reduction of RNA expression is efficiently reduced by 80-95% and can still inhibit expression on any region of the mRNA. | https://en.wikipedia.org/wiki/Trinucleotide_repeat_expansion |
Trioecy / t r aɪ ˈ iː s i / , also spelled triecy , is a sexual system characterized by the coexistence of males , females , and hermaphrodites . It has been found in both plants and animals . [ 1 ] [ 2 ] Like androdioecy and gynodioecy , trioecy is a mixed mating systems . [ 3 ]
Trioecy is also called tridioecy / ˌ t r aɪ d aɪ ˈ iː s i / and subdioecy / ˌ s ʌ b d aɪ ˈ iː s i / . [ 4 ]
The term trioecy comes from the Neo-Latin word Trioecia , a former order of trioecious plants. [ 5 ]
Trioecy may be an unstable transient state [ 6 ] associated with evolutionary transitioning from gynodioecy to dioecy . [ 7 ] [ 6 ] In brachiopod species, trioecy usually breaks into androdioecy or gynodioecy. [ 8 ] Other studies show that trioecious populations originated from gonochoristic ancestors which were invaded by a mutant selfing hermaphrodite, creating a trioecious population. [ 1 ] It has been suggested that chromosomal duplication plays an important part in the evolution of trioecy. [ 9 ]
But one study found that trioecy can be stable under nucleocytoplasmic sex determination . [ 10 ] Another theoretical analysis indicates that trioecy could be evolutionary stable in plant species if a large amount of pollinators vary geographically. [ 11 ]
Trioecy is a relatively common sexual system in plants, [ 12 ] estimated to occur in about 3.6% of flowering plant species, [ 10 ] although most reports of trioecy could be misinterpretations of gynodioecy . [ 13 ] It is rare as well as poorly understood in animals. [ 12 ]
The following species have been observed to exhibit a trioecious breeding system. | https://en.wikipedia.org/wiki/Trioecy |
In chemistry , a triol is an organic compound containing three hydroxyl groups ( −OH functional groups ), [ 1 ] such as glycerol .
This article about an alcohol is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Triol |
Trion is a basic unit of the neural network model of cortical organization called trion model . [ 1 ] This unit represents a highly structured and interconnected aggregate of about a hundred of neurons with the overall diameter of about 0.7 mm. Each trion has three levels of firing activity, and thus a cluster of trions can produce a complex firing pattern which changes rapidly (millisecond scale) according to probabilistic ( Monte Carlo ) rules. [ 2 ] [ 3 ]
This neuroscience article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trion_(neural_networks) |
The triose phosphate translocator is an integral membrane protein found in the inner membrane of chloroplasts . It exports triose phosphate ( Dihydroxyacetone phosphate ) in exchange for inorganic phosphate and is therefore classified as an antiporter . The imported phosphate is then used for ATP regeneration via the light-dependent-reaction; the ATP may then for example be used for further reactions in the Calvin-cycle. The translocator protein is responsible for exporting all the carbohydrate produced in photosynthesis by plants and therefore most of the carbon in food that one eats has been transported by the triose phosphate translocator. [ 1 ] Its three-dimensional structure was reported in 2017, revealing how it recognizes two different substrates to catalyze the strict 1:1 exchange. [ 2 ]
This photosynthesis article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Triose_phosphate_translocator |
Trioxane refers to any of three isomeric organic compounds composed of a six-membered ring with three carbon atoms and three oxygen atoms, having the molecular formula C 3 H 6 O 3 .
The three isomers are:
This article about a hypothetical chemical compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trioxane |
Trioxidane (systematically named dihydrogen trioxide , [ 2 ] [ 3 ] ), also called hydrogen trioxide [ 4 ] [ 5 ] is an inorganic compound with the chemical formula H[O] 3 H (can be written as [H( μ -O 3 )H] or [H 2 O 3 ] ). It is one of the unstable hydrogen polyoxides . [ 4 ] In aqueous solutions, trioxidane decomposes to form water and singlet oxygen :
The reverse reaction, the addition of singlet oxygen to water, typically does not occur in part due to the scarcity of singlet oxygen. In biological systems, however, ozone is known to be generated from singlet oxygen, and the presumed mechanism is an antibody-catalyzed production of trioxidane from singlet oxygen. [ 2 ]
Trioxidane can be obtained in small, but detectable, amounts in reactions of ozone and hydrogen peroxide , or by the electrolysis of water . Larger quantities have been prepared by the reaction of ozone with organic reducing agents at low temperatures in a variety of organic solvents, such as the anthraquinone process . It is also formed during the decomposition of organic hydrotrioxides (ROOOH). [ 3 ] Alternatively, trioxidane can be prepared by reduction of ozone with 1,2-diphenylhydrazine at low temperature. Using a resin-bound version of the latter, relatively pure trioxidane can be isolated as a solution in organic solvent. Preparation of high purity solutions is possible using the methyltrioxorhenium(VII) catalyst. [ 5 ] In acetone- d 6 at −20 °C, the characteristic 1 H NMR signal of trioxidane could be observed at a chemical shift of 13.1 ppm. [ 3 ] Solutions of hydrogen trioxide in diethyl ether can be safely stored at −20 °C for as long as a week. [ 5 ]
The reaction of ozone with hydrogen peroxide is known as the "peroxone process". This mixture has been used for some time for treating groundwater contaminated with organic compounds. The reaction produces H 2 O 3 and H 2 O 5 . [ 6 ]
In 1970-75, Giguère et al. observed infrared and Raman spectra of dilute aqueous solutions of trioxidane. [ 4 ] In 2005, trioxidane was observed experimentally by microwave spectroscopy in a supersonic jet. The molecule exists in a skewed structure, with an oxygen–oxygen–oxygen–hydrogen dihedral angle of 81.8°. The oxygen–oxygen bond lengths of 142.8 picometer are slightly shorter than the 146.4 pm oxygen–oxygen bonds in hydrogen peroxide . [ 7 ] Various dimeric and trimeric forms also seem to exist.
There is a trend of increasing gas-phase acidity and corresponding p K a as the number of oxygen atoms in the chain increases in HO n H structures ( n =1,2,3). [ 8 ]
Trioxidane readily decomposes into water and singlet oxygen, with a half-life of about 16 minutes in organic solvents at room temperature, but only milliseconds in water. It reacts with organic sulfides to form sulfoxides , but little else is known of its reactivity.
Recent research found that trioxidane is the active ingredient responsible for the antimicrobial properties of the well known ozone / hydrogen peroxide mix. Because these two compounds are present in biological systems as well it is argued that an antibody in the human body can generate trioxidane as a powerful oxidant against invading bacteria. [ 2 ] [ 9 ] The source of the compound in biological systems is the reaction between singlet oxygen and water (which proceeds in either direction, of course, according to concentrations), with the singlet oxygen being produced by immune cells. [ 3 ] [ 10 ]
Computational chemistry predicts that more oxygen chain molecules or hydrogen polyoxides exist and that even indefinitely long oxygen chains can exist in a low-temperature gas. With this spectroscopic evidence a search for these type of molecules can start in interstellar space . [ 7 ] A 2022 publication suggested the possibility of the presence of detectable concentrations of polyoxides in the atmosphere. [ 11 ] | https://en.wikipedia.org/wiki/Trioxidane |
A trip computer is a computer fitted to some cars ; most modern trip computers record, calculate, and display the distance travelled, the average speed, the average fuel consumption, and real-time fuel consumption.
The first, mechanical trip computers, such as the Halda Speedpilot, produced by a Swedish taximeter manufacturer, were made in the 1950s as car accessories to enable the driver to maintain a given time schedule, particularly useful in rallying. One was installed as standard equipment in the 1958 Saab GT750 . The 1952 Fiat 1900 came standard with a complex mechanical device, called mediometro in Italian, that showed the average speed. [ 1 ] [ 2 ] In 1978, the Cadillac division of General Motors introduced the "Cadillac Trip Computer", available on the Cadillac Seville ; Chrysler also launched an electric trip computer on its low-end Omni/Horizon . [ 3 ] They can range from basic to complex. The most basic trip computers incorporate average fuel mileage and perhaps an outside temperature display. Mid-range versions often include information on fuel, speed, distance, cardinal heading (compass), and elapsed time. The most advanced trip computers are reserved for high-end cars and often display average calculations for two drivers, a stop watch, tire-pressure information, over-speed warnings, and many other features.
Sometimes the trip computer's display is in the gauge cluster, the dashboard or navigation-system screen, or an overhead console. Some displays include information about scheduled maintenance. The current Acura TL does this in stages, first alerting the driver with a "Due Soon" message; once the programmed mileage is reached, the message is "Due Now"; when more time or distance has elapsed, the message changes to "Past Due". Mercedes-Benz vehicles constantly monitor the quality of the oil and alert the driver when the oil has degraded to a certain extent. GM and FCA vehicles provide oil change alerts based on the number and length of trips, engine temperature, and other factors. Some vehicles also use the trip computer to allow owners to change certain aspects of vehicle behavior, e.g. how the power locks work, but in most cars "setting preferences" is now done through a center screen also used for the backup camera and radio.
Some trip computers can display the diagnostic codes that mechanics use. This is especially useful when the mechanic wants to see the codes while driving the car. In 2004, Linear Logic developed the ScanGauge , which at the time was the only easily installed (via OBDII ) accessory that worked as a trip computer, 4 simultaneous digital gauges, and a diagnostic trouble-code reader. This device has available 12 different measurements which can be used as the 4 digital gauges. The units of measure can be independently selected between miles/km, gallons/liters, Celsius/Fahrenheit, and PSI/kPa.
In 2008, the OBDuino project announced [ 4 ] a low-cost DIY trip computer design using the OBDII interface and the Arduino hobbyist microcontroller platform, released under the GPL open source license. | https://en.wikipedia.org/wiki/Trip_computer |
Triparental mating is a form of bacterial conjugation where a conjugative plasmid present in one bacterial strain assists the transfer of a mobilizable plasmid present in a second bacterial strain into a third bacterial strain. [ 1 ] Plasmids are introduced into bacteria for such purposes as transformation , cloning , or transposon mutagenesis. Triparental matings can help overcome some of the barriers to efficient plasmid mobilization. For instance, if the conjugative plasmid and the mobilizable plasmid are members of the same incompatibility group they do not need to stably coexist in the second bacterial strain for the mobilizable plasmid to be transferred.
Triparental mating was identified in yeasts in 1960 and then in Escherichia coli in 1962. [ 2 ]
Five to seven days are required to determine if the
plasmid was successfully introduced into the new bacterial
strain and confirm that there is no carryover of the helper or
donor strain.
In contrast, electroporation does not require a helper or
donor strain. This helps
avoid possible contamination with other strains. The introduction
of the plasmid can be verified in the recipient
strain in two days, making electroporation a faster and
more efficient method of transformation. Electroporation however does not work with all bacteria and is mostly limited to well-characterized model organisms. | https://en.wikipedia.org/wiki/Triparental_mating |
The tripartite motif family ( TRIM ) is a protein family. [ 1 ]
Many TRIM proteins are induced by interferons , which are important component of resistance to pathogens and several TRIM proteins are known to be required for the restriction of infection by lentiviruses . TRIM proteins are involved in pathogen-recognition and by regulation of transcriptional pathways in host defence. [ 2 ]
The tripartite motif is always present at the N-terminus of the TRIM proteins. The TRIM motif includes the following three domains: [ 1 ]
The C-terminus of TRIM proteins contain either:
The TRIM family is split into two groups that differ in domain structure and genomic organization: [ 3 ]
Members of the family include:
This protein -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Tripartite_motif_family |
Tripartite symbiosis is a type of symbiosis involving three species. This can include any combination of plants , animals , fungi , bacteria , or archaea , often in interkingdom symbiosis .
Ants of Attini cultivate fungi. Microfungi , specialized to be parasites of the fungus gardens, coevolved with them. [ 1 ]
Allomerus decemarticulatus ants use Trimmatostroma sp. to create structures within Hirtella physophora . [ 2 ] [ 3 ] The fungi are connected endophytically and actively transfer nitrogen. [ 4 ]
The mycobiont in a lichen can form a relationship with both cyanobacteria and green algae as photobionts concurrently. [ 5 ] [ 6 ] [ 7 ]
Rhizobia are nitrogen-fixating bacteria that form symbiotic relationships with legumes . Sometimes, this is aided by the presence of a fungal species. [ 8 ] This is most effective in undistributed soil. [ 9 ] The presence of mycorrhizae can improve the rhizobial- liquorice nutrient transfer in droughts. [ 10 ] Soybeans in particular can improve their ability to withstand soil salinity with the presence of both rhizobium and mycorrhizae. [ 11 ]
This ecology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Tripartite_symbiosis |
Tripartite synapse refers to the functional integration and physical proximity of:
It also refers as well as the combined contributions of these three synaptic components to the production of activity at the chemical synapse . [ 1 ] Tripartite synapses occur at a number of locations in the central nervous system with astrocytes , a type of glial cell, [ 1 ] and may also exist with Muller glia of retinal ganglion cells [ 2 ] and Schwann cells at the neuromuscular junction . [ 3 ] The term was first introduced in the late 1990s to account for a growing body of evidence that glia are not merely passive neuronal support cells but, instead, play an active role in the integration of synaptic information through bidirectional communication with the neuronal components of the synapse as mediated by neurotransmitters and gliotransmitters . [ 4 ]
Evidence for the role of astrocytes in the integration and processing of synaptic integration presents itself in a number of ways:
In a 2013 published research study titled Glutamate-Dependent Neuroglial Calcium Signaling Differ Between Young and Adult Brain, it was found that the tripartite synapse is not found in the adult brain. Earlier published research had discussed how astrocytes had metabotropic glutamate receptor 5 (mGluR5)–dependent increases in cytosolic calcium ions (Ca2+). However, astrocytic expression of mGluR5 was lost by the third postnatal week in mice and was not present in human cortical astrocytes. The results of the study indicate that neuroglial signaling the adult brain may be fundamentally different than the young brain. [ 10 ]
Maiken Nedergaard , M.D., D.M.Sc., lead author of the study and co-director of the University of Rochester Medical Center (URMC) Center for Translational Neuromedicine stated:
If this concept was correct, it should have given rise to a clinical trial by now. It has not, which tells us that with so many labs work on this for 20 years that there must be something wrong.
She also stated that:
Our findings demonstrate that the tripartite synaptic model is incorrect. This concept does not represent the process for transmitting signals between neurons in the brain beyond the developmental stage.
In collaboration with the University of Rochester’s Institute of Optics, Nedergaard and her team had developed a new 2-photon microscope that had allowed researchers to observe glia activity in the living brain, which allowed observable data for the study. [ 11 ]
Study shows that current model for brain signaling is flawed (youtube.com) | https://en.wikipedia.org/wiki/Tripartite_synapse |
The triphenylmethyl radical (often shortened to trityl radical after 1927 suggestion by Helferich et al. [ 1 ] ) is an organic compound with the formula (C 6 H 5 ) 3 C. It is a persistent radical . It was the first radical ever to be described in organic chemistry . Because of its accessibility, the trityl radical has been heavily exploited. [ 2 ]
The triphenylmethyl radical can be prepared by homolysis of triphenylmethyl chloride 1 by a metal like silver or zinc in benzene or diethyl ether . The radical 2 forms a chemical equilibrium with the quinoid -type dimer 3 ( Gomberg's dimer ). In benzene the concentration of the radical is 2%. [ 3 ]
Solutions containing the radical are yellow ; when the temperature of the solution is raised, the yellow color becomes more intense as the equilibrium is shifted in favor of the radical rather than the colorless dimer, in accordance with Le Chatelier's principle .
The triphenylmethyl radical exhibits green photoluminescence . Further reaction of the quinoid dimer with another triphenylmethyl radical produces a quinoid radical that exhibits red photoluminescence. [ 4 ]
When exposed to air, the radical rapidly oxidizes to the peroxide , and the color of the solution changes from yellow to colorless. Likewise, the radical reacts with iodine to triphenylmethyl iodide.
While the triphenyl radical itself forms a quinoid dimer, alkyl substitution at the para ring positions inhibits dimer formation entirely. [ 5 ] Other derivatives of the triphenyl radical with certain substituted phenyl groups do form dimers with a hexaphenylethane -like structure. For example, the tris(3,5-di- tert -butylphenyl) radical dimerizes to give hexakis(3,5-di- t -butylphenyl)ethane, with a bond length of 1.67 Å for the central carbon–carbon bond. Theoretical calculations on a very high level of theory indicate that van der Waals attraction between the tert -butyl groups create a potential minimum that is absent in the unsubstituted molecule. [ 6 ] [ 7 ] Other derivatives have been reported as the quinoid dimer [ 8 ]
The class of tri aryl -methyl radicals have applications in the synthesis of organic magnets . [ 9 ]
The radical was discovered by Moses Gomberg in 1900 at the University of Michigan . [ 10 ] [ 11 ] [ 12 ] He tried to prepare hexaphenylethane from triphenylmethyl chloride and zinc in benzene in a Wurtz reaction and found that the product, based on its behaviour towards iodine and oxygen, was far more reactive than anticipated. The discovered structure was used in the development of ESR spectroscopy and confirmed by it. [ 13 ] [ 14 ] [ 15 ] The triphenylmethyl radical, and the larger class of triarylmethyl radicals, are called Gomberg radicals . [ 4 ] [ 9 ]
The correct quinoid structure for the dimer was suggested as early as 1904 but this structure was soon after abandoned by the scientific community in favor of hexaphenylethane ( 4 ). [ 16 ] It subsequently took until 1968 for its rediscovery when researchers at the Vrije Universiteit Amsterdam published proton NMR data. [ 17 ] | https://en.wikipedia.org/wiki/Triphenylmethyl_radical |
Triphenylphosphine dichloride is an organophosphorus compound with the chemical formula (C 6 H 5 ) 3 PCl 2 , often abbreviated as Ph 3 PCl 2 , where Ph is phenyl . It is a chlorinating agent widely used in organic chemistry. Applications include the conversion of alcohols and ethers to alkyl chlorides , the cleavage of epoxides to vicinal dichlorides and the chlorination of carboxylic acids to acyl chlorides . [ 2 ]
In polar solvents such as acetonitrile , Ph 3 PCl 2 adopts an ionic phosphonium salt structure, [Ph 3 PCl] + Cl − (chlorotriphenylphosphonium chloride), [ 4 ] whereas in non-polar solvents like diethyl ether it exists as a non-solvated trigonal bipyramidal molecule. [ 5 ] Two [Ph 3 PCl] + species can also adopt an unusual dinuclear ionic structure—both interacting with a Cl − via long Cl–Cl contacts. [ 4 ]
Triphenylphosphine dichloride is usually prepared fresh by the addition of chlorine to triphenylphosphine .
Both reagents are typically used in solution to ensure the correct stoichiometry . [ 2 ]
Ph 3 PCl 2 can also be obtained by the reaction of iodobenzene dichloride ( PhICl 2 ) and triphenylphosphine. [ 6 ]
Alternatively, Ph 3 PCl 2 can be obtained by chlorination of triphenylphosphine oxide with, for example, phosphorus trichloride , as in Grignard's original 1931 synthesis. [ 1 ] | https://en.wikipedia.org/wiki/Triphenylphosphine_dichloride |
Triphenyltin compounds are organotin compounds with the general formula (C 6 H 5 ) 3 SnX. They contain the triphenyltin group, (C 6 H 5 ) 3 Sn, or Ph 3 Sn, which consists of an atom of tin bonded to three phenyl groups . Examples of triphenyltins include:
Triphenyltin compounds have been used extensively as algicides and molluscicides in antifouling products since the 1960s, together with tributyltin compounds , [ 1 ] and both these classes of compounds are of local (but not global) environmental concern because they are persistent organic pollutants . [ 2 ] They are also used in organic synthesis to generate radicals or cleave carbon-oxygen bonds . [ 3 ] | https://en.wikipedia.org/wiki/Triphenyltin_compounds |
Triphenyltin hydride is the organotin compound with the formula (C 6 H 5 ) 3 SnH. It is a colorless distillable oil that is soluble in organic solvents. It is often used as a source of "H · " to generate radicals or cleave carbon-oxygen bonds.
Ph 3 SnH, as it is more commonly abbreviated, is prepared by treatment of triphenyltin chloride with lithium aluminium hydride . [ 1 ] Although Ph 3 SnH is treated as a source of "H · ", in fact it does not release free hydrogen atoms , which are extremely reactive species. Instead, Ph 3 SnH transfers H to substrates usually via a radical chain mechanism. This reactivity exploits the relatively good stability of "Ph 3 Sn · " [ 1 ] | https://en.wikipedia.org/wiki/Triphenyltin_hydride |
Triphosgene ( bis(trichloromethyl) carbonate ( BTC )) is a chemical compound with the formula OC(OCCl 3 ) 2 . It is used as a solid substitute for phosgene , which is a gas and diphosgene , which is a liquid. [ 5 ] [ 6 ] Triphosgene is stable up to 200 °C. [ 7 ] Triphosgene is used in a variety of halogenation reactions. [ 8 ]
This compound is commercially available. It is prepared by exhaustive free radical chlorination of dimethyl carbonate : [ 6 ]
Triphosgene can be easily recrystallized from hot hexanes.
Triphosgene is used as a reagent in organic synthesis as a source of CO 2+ . It behaves like phosgene, to which it cracks thermally:
Alcohols are converted to carbonates. Primary and secondary amines are converted to ureas and isocyanates . [ 6 ] [ 7 ] [ 9 ] [ 10 ]
Triphosgene has been used to synthesize chlorides. [ 8 ] Some Alkyl chlorides are prepared by treating alcohols with a mixture of triphosgene and pyridine . Alkyl dichlorides and trichlorides can similarly be synthesized using triphosgene. Vinyl chlorides are synthesized from ketones using triphosgene and DMF to form a Vilsmeier reagent , followed by a ring opening by chloride ions. Aryl chlorides can also be produced using a Vilsmeier reagent from triphosgene and DMF.
The vapor pressure of Triphosgene is sufficiently high for it to reach concentrations that are considered toxicologically unsafe. [ 11 ] While several properties of triphosgene are not yet readily available, it is known that it is very toxic if inhaled. A toxic gas is emitted if it comes in contact with water. [ 12 ] There is a lack of information and variability regarding the proper handling of triphosgene. It is assumed to have the same risks as phosgene. [ 13 ] [ 14 ] | https://en.wikipedia.org/wiki/Triphosgene |
The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei ( alpha particles ) are transformed into carbon . [ 1 ] [ 2 ]
Helium accumulates in the cores of stars as a result of the proton–proton chain reaction and the carbon–nitrogen–oxygen cycle .
Nuclear fusion reaction of two helium-4 nuclei produces beryllium-8 , which is highly unstable, and decays back into smaller nuclei with a half-life of 8.19 × 10 −17 s , unless within that time a third alpha particle fuses with the beryllium-8 nucleus [ 3 ] to produce an excited resonance state of carbon-12 , [ 4 ] called the Hoyle state , which nearly always decays back into three alpha particles, but once in about 2421.3 times releases energy and changes into the stable base form of carbon-12. [ 5 ] When a star runs out of hydrogen to fuse in its core, it begins to contract and heat up. If the central temperature rises to 10 8 K, [ 6 ] six times hotter than the Sun's core, alpha particles can fuse fast enough to get past the beryllium-8 barrier and produce significant amounts of stable carbon-12.
The net energy release of the process is 7.275 MeV.
As a side effect of the process, some carbon nuclei fuse with additional helium to produce a stable isotope of oxygen and energy:
Nuclear fusion reactions of helium with hydrogen produces lithium-5 , which also is highly unstable, and decays back into smaller nuclei with a half-life of 3.7 × 10 −22 s .
Fusing with additional helium nuclei can create heavier elements in a chain of stellar nucleosynthesis known as the alpha process , but these reactions are only significant at higher temperatures and pressures than in cores undergoing the triple-alpha process. This creates a situation in which stellar nucleosynthesis produces large amounts of carbon and oxygen, but only a small fraction of those elements are converted into neon and heavier elements. Oxygen and carbon are the main "ash" of helium-4 burning.
Material that accretes from a companion star onto the surface of a neutron star may begin this helium-burning process in a local region. The burning wave is estimated to travel at 50 to 500 km/s, traversing the surface in around one second. Within this second, the neutron star rapidly rotates, moving the brighter burning region in and out of view. This intensity modulation allows the rotational frequency to be measured, sometimes up to 300 Hz.
Some neutron stars have been measured with such an intensity modulation at 600 Hz. A suggested origin is neutron stars which rotate at 300 Hz, but have two burning regions. The second burning region is theorized to form almost immediately after the first, exactly on the opposite side of the neutron star, due to the convergence of gravitational wave from the initial thermonuclear ignition. [ 7 ]
The triple-alpha process is ineffective at the pressures and temperatures early in the Big Bang . One consequence of this is that no significant amount of carbon was produced in the Big Bang.
Ordinarily, the probability of the triple-alpha process is extremely small. However, the beryllium-8 ground state has almost exactly the energy of two alpha particles. In the second step, 8 Be + 4 He has almost exactly the energy of an excited state of 12 C . This resonance greatly increases the probability that an incoming alpha particle will combine with beryllium-8 to form carbon. The existence of this resonance was predicted by Fred Hoyle before its actual observation, based on the physical necessity for it to exist, in order for carbon to be formed in stars. The prediction and then discovery of this energy resonance and process gave very significant support to Hoyle's hypothesis of stellar nucleosynthesis , which posited that all chemical elements had originally been formed from hydrogen, the true primordial substance. The anthropic principle has been cited to explain the fact that nuclear resonances are sensitively arranged to create large amounts of carbon and oxygen in the universe. [ 8 ] [ 9 ]
The triple-alpha steps are strongly dependent on the temperature and density of the stellar material. The power released by the reaction is approximately proportional to the temperature to the 40th power, and the density squared. [ 10 ] In contrast, the proton–proton chain reaction produces energy at a rate proportional to the fourth power of temperature, the CNO cycle at about the 17th power of the temperature, and both are linearly proportional to the density. This strong temperature dependence has consequences for the late stage of stellar evolution, the red-giant stage.
For lower mass stars on the red-giant branch , the helium accumulating in the core is prevented from further collapse only by electron degeneracy pressure. The entire degenerate core is at the same temperature and pressure, so when its density becomes high enough, fusion via the triple-alpha process rate starts throughout the core. The core is unable to expand in response to the increased energy production until the pressure is high enough to lift the degeneracy. As a consequence, the temperature increases, causing an increased reaction rate in a positive feedback cycle that becomes a runaway reaction. This process, known as the helium flash , lasts a matter of seconds but burns 60–80% of the helium in the core. During the core flash, the star's energy production can reach approximately 10 11 solar luminosities which is comparable to the luminosity of a whole galaxy , [ 11 ] although no effects will be immediately observed at the surface, as the whole energy is used up to lift the core from the degenerate to normal, gaseous state. Since the core is no longer degenerate, hydrostatic equilibrium is once more established and the star begins to "burn" helium at its core and hydrogen in a spherical layer above the core. The star enters a steady helium-burning phase which lasts about 10% of the time it spent on the main sequence (the Sun is expected to burn helium at its core for about a billion years after the helium flash). [ 12 ]
In higher mass stars, which evolve along the asymptotic giant branch , carbon and oxygen accumulate in the core as helium is burned, while hydrogen burning shifts to further-out layers, resulting in an intermediate helium shell. However, the boundaries of these shells do not shift outward at the same rate due to differing critical temperatures and temperature sensitivities for hydrogen and helium burning. When the temperature at the inner boundary of the helium shell is no longer high enough to sustain helium burning, the core contracts and heats up, while the hydrogen shell (and thus the star's radius) expand outward. Core contraction and shell expansion continue until the core becomes hot enough to reignite the surrounding helium. This process continues cyclically – with a period on the order of 1000 years – and stars undergoing this process have periodically variable luminosity. These stars also lose material from their outer layers in a stellar wind driven by radiation pressure , which ultimately becomes a superwind as the star enters the planetary nebula phase. [ 13 ]
The triple-alpha process is highly dependent on carbon-12 and beryllium-8 having resonances with slightly more energy than helium-4 . Based on known resonances, by 1952 it seemed impossible for ordinary stars to produce carbon as well as any heavier element. [ 14 ] Nuclear physicist William Alfred Fowler had noted the beryllium-8 resonance, and Edwin Salpeter had calculated the reaction rate for 8 Be, 12 C, and 16 O nucleosynthesis taking this resonance into account. [ 15 ] [ 16 ] However, Salpeter calculated that red giants burned helium at temperatures of 2·10 8 K or higher, whereas other recent work hypothesized temperatures as low as 1.1·10 8 K for the core of a red giant.
Salpeter's paper mentioned in passing the effects that unknown resonances in carbon-12 would have on his calculations, but the author never followed up on them. It was instead astrophysicist Fred Hoyle who, in 1953, used the abundance of carbon-12 in the universe as evidence for the existence of a carbon-12 resonance. The only way Hoyle could find that would produce an abundance of both carbon and oxygen was through a triple-alpha process with a carbon-12 resonance near 7.68 MeV, which would also eliminate the discrepancy in Salpeter's calculations. [ 14 ]
Hoyle went to Fowler's lab at Caltech and said that there had to be a resonance of 7.68 MeV in the carbon-12 nucleus. (There had been reports of an excited state at about 7.5 MeV. [ 14 ] ) Fred Hoyle's audacity in doing this is remarkable, and initially, the nuclear physicists in the lab were skeptical. Finally, a junior physicist, Ward Whaling, fresh from Rice University , who was looking for a project decided to look for the resonance. Fowler permitted Whaling to use an old Van de Graaff generator that was not being used. Hoyle was back in Cambridge when Fowler's lab discovered a carbon-12 resonance near 7.65 MeV a few months later, validating his prediction. The nuclear physicists put Hoyle as first author on a paper delivered by Whaling at the summer meeting of the American Physical Society . A long and fruitful collaboration between Hoyle and Fowler soon followed, with Fowler even coming to Cambridge. [ 17 ]
The final reaction product lies in a 0+ state (spin 0 and positive parity). Since the Hoyle state was predicted to be either a 0+ or a 2+ state, electron–positron pairs or gamma rays were expected to be seen. However, when experiments were carried out, the gamma emission reaction channel was not observed, and this meant the state must be a 0+ state. This state completely suppresses single gamma emission, since single gamma emission must carry away at least 1 unit of angular momentum . Pair production from an excited 0+ state is possible because their combined spins (0) can couple to a reaction that has a change in angular momentum of 0. [ 18 ]
Carbon is a necessary component of all known life. 12 C, a stable isotope of carbon, is abundantly produced in stars due to three factors:
Some scholars argue the 7.656 MeV Hoyle resonance, in particular, is unlikely to be the product of mere chance. Fred Hoyle argued in 1982 that the Hoyle resonance was evidence of a "superintellect"; [ 14 ] Leonard Susskind in The Cosmic Landscape rejects Hoyle's intelligent design argument. [ 22 ] Instead, some scientists believe that different universes, portions of a vast " multiverse ", have different fundamental constants: [ 23 ] according to this controversial fine-tuning hypothesis, life can only evolve in the minority of universes where the fundamental constants happen to be fine-tuned to support the existence of life. Other scientists reject the hypothesis of the multiverse on account of the lack of independent evidence. [ 24 ] | https://en.wikipedia.org/wiki/Triple-alpha_process |
The triple bar or tribar , ≡ , is a symbol with multiple, context-dependent meanings indicating equivalence of two different things. Its main uses are in mathematics and logic. It has the appearance of an equals sign ⟨=⟩ with a third line.
The triple bar character in Unicode is code point U+2261 ≡ IDENTICAL TO ( ≡, ≡ ). [ 1 ] The closely related code point U+2262 ≢ NOT IDENTICAL TO ( ≢, ≢ ) is the same symbol with a slash through it, indicating the negation of its mathematical meaning. [ 1 ]
In LaTeX mathematical formulas, the code \equiv produces the triple bar symbol and \not\equiv produces the negated triple bar symbol ≢ {\displaystyle \not \equiv } as output. [ 2 ]
In logic , it is used with two different but related meanings. It can refer to the if and only if connective, also called material equivalence. [ 3 ] This is a binary operation whose value is true when its two arguments have the same value as each other. [ 4 ] Alternatively, in some texts ⇔ is used with this meaning, while ≡ is used for the higher-level metalogical notion of logical equivalence , according to which two formulas are logically equivalent when all models give them the same value. [ 5 ] Gottlob Frege used a triple bar for a more philosophical notion of identity, in which two statements (not necessarily in mathematics or formal logic) are identical if they can be freely substituted for each other without change of meaning. [ 6 ]
In mathematics, the triple bar is sometimes used as a symbol of identity or an equivalence relation (although not the only one; other common choices include ~ and ≈). [ 7 ] [ 8 ] Particularly, in geometry , it may be used either to show that two figures are congruent or that they are identical. [ 9 ] In number theory, it has been used beginning with Carl Friedrich Gauss (who first used it with this meaning in 1801) to mean modular congruence : a ≡ b ( mod N ) {\displaystyle a\equiv b{\pmod {N}}} if N divides a − b . [ 10 ] [ 11 ]
In category theory , triple bars may be used to connect objects in a commutative diagram , indicating that they are actually the same object rather than being connected by an arrow of the category. [ 12 ]
This symbol is also sometimes used in place of an equal sign for equations that define the symbol on the left-hand side of the equation, to contrast them with equations in which the terms on both sides of the equation were already defined. [ 13 ] An alternative notation for this usage is to typeset the letters "def" above an ordinary equality sign, a = d e f b {\displaystyle a\mathrel {\stackrel {\scriptscriptstyle \mathrm {def} }{=}} b} . [ 14 ] Similarly, another alternative notation for this usage is to precede the equals sign with a colon, a := b {\displaystyle a:=b} . The colon notation has the advantage that it reflects the inherent asymmetry in the definition of one object from already defined objects.
In botanical nomenclature , the triple bar denotes homotypic synonyms (those based on the same type specimen ), to distinguish them from heterotypic synonyms (those based on different type specimens), which are marked with an equals sign . [ 15 ]
In chemistry , the triple bar can be used to represent a triple bond between atoms. For example, HC≡CH is a common shorthand for acetylene [ 16 ] (systematic name: ethyne).
In the APL programming language, the ≡ and ≢ symbols are used to compare to two arrays for equality and inequality respectively. This is in contrast to the symbols = and ≠ which compares the individual elements in an order array with the elements of another array.
In mobile , web , and general application design, a similar symbol is sometimes used as an interface element, where it is called a hamburger icon . The element typically indicates that a navigation menu can be accessed when the element is activated; the bars of the symbol may be seen as stylized menu items, and some variations of this symbols add more bars, or bullet points to each bar, to enhance this visual similarity. [ 17 ] Usage of this symbol dates back to the early computer interfaces developed at Xerox PARC in the 1980s. [ 18 ] It is also similar to the icon frequently used to indicate justified text alignment . It is an oft-used component of Google's Material Design guidelines and many Android apps and web apps that follow these guidelines make use of the hamburger menu. | https://en.wikipedia.org/wiki/Triple_bar |
A triple bond in chemistry is a chemical bond between two atoms involving six bonding electrons instead of the usual two in a covalent single bond . Triple bonds are stronger than the equivalent single bonds or double bonds , with a bond order of three. The most common triple bond is in a nitrogen N 2 molecule; the second most common is that between two carbon atoms, which can be found in alkynes . Other functional groups containing a triple bond are cyanides and isocyanides . Some diatomic molecules, such as diphosphorus [ 1 ] and carbon monoxide , are also triple bonded. In skeletal formulae the triple bond is drawn as three parallel lines (≡) between the two connected atoms. [ 2 ] [ 3 ] [ 4 ]
Triple bonding can be explained in terms of orbital hybridization . In the case of acetylene, each carbon atom has two sp-orbitals and two p-orbitals . The two sp-orbitals are linear, with 180° bond angles , and occupy the x-axis in the cartesian coordinate system . The p-orbitals are perpendicular to the sp-orbitals on the y-axis and the z-axis. When the atoms approach each other, the sp orbitals overlap to form an sp-sp sigma bond . At the same time the p z -orbitals approach and together they form a p z -p z pi-bond . Likewise, the other pair of p y -orbitals form a p y -p y pi-bond. The result is formation of one sigma bond and two pi bonds.
In the bent bond model , the triple bond can also formed by the overlapping of three sp 3 lobes without the need to invoke a pi-bond. [ 5 ]
Many elements beyond oxygen can form triple bonds. These bonds are common in some transition metals. Hexa(tert-butoxy)ditungsten(III) and Hexa(tert-butoxy)dimolybdenum(III) are well known examples, in which the metal-metal bond distance is about 233 pm. [ 6 ] Hexa(tert-butoxy)ditungsten(III) has attracted particular attention for its reactions with alkynes, leading to metal-carbon triple bonded compounds of the formula RC≡W(OBut) 3 [ 7 ]
Additionally, phosphorus can exist as the highly reactive diatomic molecule diphosphorus , which has roughly half the bond-dissociation energy of dinitrogen. [ 1 ] | https://en.wikipedia.org/wiki/Triple_bond |
Triple deck theory is a theory that describes a three-layered boundary-layer structure when sufficiently large disturbances are present in the boundary layer. This theory is able to successfully explain the phenomenon of boundary layer separation , but it has found applications in many other flow setups as well, [ 1 ] including the scaling of the lower-branch instability ( T-S ) of the Blasius flow , [ 2 ] [ 3 ] etc. James Lighthill , Lev Landau and others were the first to realize that to explain boundary layer separation, different scales other than the classical boundary-layer scales need to be introduced. These scales were first introduced independently by James Lighthill and E. A. Müller in 1953. [ 4 ] [ 5 ] The triple-layer structure itself was independently discovered by Keith Stewartson (1969) [ 6 ] and V. Y. Neiland (1969) [ 7 ] and by A. F. Messiter (1970). [ 8 ] Stewartson and Messiter considered the separated flow near the trailing edge of a flat plate, whereas Neiland studied the case of a shock impinging on a boundary layer.
Suppose x {\displaystyle x} and y {\displaystyle y} are the streamwise and transverse coordinate with respect to the wall and R e {\displaystyle Re} be the Reynolds number , the boundary layer thickness is then δ = R e − 1 / 2 {\displaystyle \delta =Re^{-1/2}} . The boundary layer coordinate is η = y R e 1 / 2 {\displaystyle \eta =yRe^{1/2}} . Then the thickness of each deck is
Lower deck : y ∼ R e − 5 / 8 Middle deck : y ∼ R e − 4 / 8 Upper deck : y ∼ R e − 3 / 8 . {\displaystyle {\begin{aligned}{\text{Lower deck}}:&\quad y\sim Re^{-5/8}\\{\text{Middle deck}}:&\quad y\sim Re^{-4/8}\\{\text{Upper deck}}:&\quad y\sim Re^{-3/8}.\end{aligned}}}
The lower deck is characterized by viscous, rotational disturbances, whereas the middle deck (same thickness as the boundary-layer thickness) is characterized by inviscid, rotational disturbances. The upper deck, which extends into the potential flow region, is characterized by inviscid, irrotational disturbances.
The interaction zone identified by Lighthill in the streamwise direction is
Interaction zone : x ∼ R e − 3 / 8 . {\displaystyle {\text{Interaction zone}}:\quad x\sim Re^{-3/8}.}
The most important aspect of the triple-deck formulation is that pressure is not prescribed, and so it has to be solved as part of the boundary-layer problem. This coupling between velocity and pressure reintroduces ellipticity to the problem, which is in contrast to the parabolic nature of the classical boundary layer of Prandtl . [ 9 ]
Let the length scales be normalized with the plate length L {\displaystyle L} and the velocity scale by the free-stream velocity U {\displaystyle U} ; then the only parameter in the problem is the Reynolds number R e = U L / ν {\displaystyle Re=UL/\nu } . Let the origin ( x , y ) = ( 0 , 0 ) {\displaystyle (x,y)=(0,0)} of the coordinate system be located at the trailing edge of the plate. Further let ( u , v ) {\displaystyle (u,v)} be the non-dimensional velocity components, p {\displaystyle p} be the non-dimensional pressure field and ψ {\displaystyle \psi } be the non-dimensional stream function such that u = ∂ ψ / ∂ y {\displaystyle u=\partial \psi /\partial y} and v = − ∂ ψ / ∂ x {\displaystyle v=-\partial \psi /\partial x} . For shortness of notation, let us introduce the small parameter ε = 1 / R e 1 / 8 {\displaystyle \varepsilon =1/Re^{1/8}} . The coordinate for horizontal interaction and for the three decks can then be defined by [ 10 ]
As χ → − ∞ {\displaystyle \chi \to -\infty } (or x → 0 − {\displaystyle x\to 0^{-}} ), the solution should approach the asymptotic behaviour of the Blasius solution , which is given by
where f B ( η ) {\displaystyle f_{B}(\eta )} is the Blasisus function which satisfies f B ‴ + f B f B ″ = 0 {\displaystyle f_{B}'''+f_{B}f_{B}''=0} subjected to f B ( 0 ) = f B ′ ( 0 ) = f B ′ ( ∞ ) − 1 = 0 {\displaystyle f_{B}(0)=f_{B}'(0)=f_{B}'(\infty )-1=0} . As χ → + ∞ {\displaystyle \chi \to +\infty } (or x → 0 + {\displaystyle x\to 0^{+}} ), the solution should approach the asymptotic behaviour of the Goldstein's near wake, which is given by
where μ = 1.1321 {\displaystyle \mu =1.1321} and λ = 0.8789 {\displaystyle \lambda =0.8789} . The Goldstein's inner wake solution is not needed here.
The solution in the middle deck is found to be
where A ( χ ) {\displaystyle A(\chi )} is referred to as the displacement function and P ( χ ) {\displaystyle P(\chi )} is referred to as the pressure function , to be determined from the upper and lower deck problems. Note that the correction to the Blasius stream function is of the order ε {\displaystyle \varepsilon } , although the pressure perturbation is only order ε 2 . {\displaystyle \varepsilon ^{2}.}
In the upper deck, the solution is found to given by
where β = 1.2168 {\displaystyle \beta =1.2168} . Furthermore, the upper deck problem also provides the relation between the displacement and the pressure function as
in which p . v . {\displaystyle \mathrm {p.v.} } stands for Cauchy principal value . One may notice that the pressure function and the derivative of the displacement function (aka transverse velocity) forms a Hilbert transform pair.
In the lower deck, the solution is given by
where Ψ ( χ , ξ ) {\displaystyle \Psi (\chi ,\xi )} will satisfy a boundary-layer type equations driven by the pressure gradient d P / d χ {\displaystyle dP/d\chi } and the slip-velocity of order ε 2 {\displaystyle \varepsilon ^{2}} generated by the middle deck. It is convenient to introduce u ^ = ∂ Ψ / ∂ ξ {\displaystyle {\hat {u}}=\partial \Psi /\partial \xi } and v ^ = − ∂ Ψ / ∂ χ {\displaystyle {\hat {v}}=-\partial \Psi /\partial \chi } , where u ^ {\displaystyle {\hat {u}}} and v ^ {\displaystyle {\hat {v}}} must satisfy
These equations are subjected to the conditions
where α = 1.6552 {\displaystyle \alpha =1.6552} . The displacement function A ( χ ) {\displaystyle A(\chi )} and therefore P ( χ ) {\displaystyle P(\chi )} must be obtained as part of the solution. The above set of equations may resemble normal boundary-layer equations, however it has an elliptic character since the pressure gradient term now is non-local, i.e., the pressure gradient at a location χ {\displaystyle \chi } depends on other locations as well. Because of this, these equations are sometimes referred to as the interactive boundary-layer equations. The numerical solution of these equations were obtained by Jobe and Burggraf in 1974. [ 11 ] | https://en.wikipedia.org/wiki/Triple_deck_theory |
Download coordinates as:
A triple divide or triple watershed is a point on Earth's surface where three drainage basins meet. A triple divide results from the intersection of two drainage divides . Triple divides range from prominent mountain peaks to minor side peaks, down to simple slope changes on a ridge which are otherwise unremarkable. The elevation of a triple divide can be thousands of meters to barely above sea level. Triple divides are a common hydrographic feature of any terrain that has rivers, streams and/or lakes.
Topographic triple divides do not necessarily respect the underground path of water . Thus, depending on the infiltration and the different geological layers, the hydrologic triple divide is often offset from the topographic triple divide.
A hydrological apex is a triple divide whose waters flow into three different oceans . Triple Divide Peak in the U.S. state of Montana or, depending on definition, Snow Dome in Canada are the only such places on Earth. [ notes 1 ]
An unnamed hill on the border between the Central African Republic and South Sudan : the exact point is at 09°08′24″N 23°28′07″E / 9.14000°N 23.46861°E / 9.14000; 23.46861 ( Congo-Nile-Lake Chad Triple Divide ) . Water from this point flows to the Atlantic Ocean via the Congo River , to the Mediterranean Sea via the Nile , or to endorheic Lake Chad . At this point meet the second, third and eighth largest drainage basins in the world, making it one of the most important triple divides on earth. [ 1 ]
Antarctica is completely circled by the Southern Ocean , and has no triple divides.
Older definitions of the oceans did not include the Southern Ocean, and instead had the Atlantic, Pacific and Indian Oceans touch the shores of Antarctica. Based on this outdated definition, Dome Argus is the highest point in the East Antarctic ice sheet and could be considered a triple divide if it is assumed that the ice forms a watershed. ( 80°22′S 77°21′E / 80.367°S 77.350°E / -80.367; 77.350 ( Dome Argus ) ) [ 2 ]
Asia is dominated by endorheic basins . In Northeastern Mongolia , the endoheric basin meets the watersheds of the Selenga and the Amur , rivers that flow to the Arctic and the Pacific Ocean, respectively. In Tibet , the basin meets the watersheds of the Nu and the Yangtze , rivers that flow to the Indian and the Pacific Ocean, respectively.
Australia has two continental drainage divide tripoints, both close to each other along Queensland's Great Dividing Range . Both are named after two 1845 exploration party leaders who sought to solve the question of Australia's rivers, Thomas Mitchell and Edmund Kennedy .
North America has 3 triple divides in the United States which are intersections of continental divides, and a fourth one in British Columbia. Waters at these triple divides flow into three different oceans, seas or gulfs. Triple Divide Peak in Montana is considered the triple divide "hydrological apex" of North America, though Snow Dome on the Alberta - British Columbia border also has a claim depending on how the Arctic and Atlantic oceans are defined. North America is the only continent that has a triple point dividing basins draining into three different oceans. [ 6 ] Where the Continental Divide splits and joins to form the boundary of the Great Divide Basin, it forms two triple points.
Other points are often considered to be triple divides because they separate basins of continental rivers.
The highest elevation (4,040 m or 13,240 ft) significant triple divide in the lower 48 states of the United States, in Kings Canyon National Park in Fresno/Inyo counties, California, is a sub-peak of Mount Wallace of the central Sierra Nevada:
Numerous other triple divide points result from intersection of river basin divides, including:
There are triple points in South America where the divide splits. | https://en.wikipedia.org/wiki/Triple_divide |
In computing , triple modular redundancy , sometimes called triple-mode redundancy , [ 1 ] ( TMR ) is a fault-tolerant form of N-modular redundancy, in which three systems perform a process and that result is processed by a majority-voting system to produce a single output. If any one of the three systems fails, the other two systems can correct and mask the fault.
The TMR concept can be applied to many forms of redundancy , such as software redundancy in the form of N-version programming , and is commonly found in fault-tolerant computer systems .
Space satellite systems often use TMR, [ 2 ] [ 3 ] although satellite RAM usually uses Hamming error correction . [ 4 ]
Some ECC memory uses triple modular redundancy hardware (rather than the more common Hamming code ), because triple modular redundancy hardware is faster than Hamming error correction hardware. [ 5 ] Called repetition code , some communication systems use N-modular redundancy as a simple form of forward error correction . For example, 5-modular redundancy communication systems (such as FlexRay ) use the majority of 5 samples – if any 2 of the 5 results are erroneous, the other 3 results can correct and mask the fault.
Modular redundancy is a basic concept, dating to antiquity, while the first use of TMR in a computer was the Czechoslovak computer SAPO , in the 1950s.
The general case of TMR is called N-modular redundancy , in which any positive number of replications of the same action is used. The number is typically taken to be at least three, so that error correction by majority vote can take place; it is also usually taken to be odd, so that no ties may happen. [ 6 ]
The 3-input majority gate output is 1 if two or more of the inputs of the majority gate are 1; output is 0 if two or more of the majority gate's inputs are 0. Thus, the majority gate is the carry output of a full adder , i.e., the majority gate is a voting machine . [ 7 ]
The 3-input majority gate can be represented by the following boolean equation and truth table :
In TMR, three identical logic circuits (logic gates) are used to compute the same set of specified Boolean function. If there are no circuit failures, the outputs of the three circuits are identical. But due to circuit failures, the outputs of the three circuits may be different.
Assuming the Boolean function computed by the three identical logic gates has value 1, then: (a) if no circuit has failed, all three circuits produce an output of value 1, and the majority gate output has value 1. (b) if one circuit fails and produces an output of 0, while the other two are working correctly and produce an output of 1, the majority gate output is 1, i.e., it still has the correct value. And similarly for the case when the Boolean function computed by the three identical circuits has value 0. Thus, the majority gate output is guaranteed to be correct as long as no more than one of the three identical logic circuits has failed. [ 7 ]
For a TMR system with a single voter of reliability (probability of working) R v and three components of reliability R m , the probability of it being correct can be shown to be R TMR = R v (3 R m 2 – 2 R m 3 ) . [ 6 ]
TMR systems should use data scrubbing – rewrite flip-flops periodically – in order to avoid accumulation of errors. [ 8 ]
The majority gate itself could fail. This can be protected against by applying triple redundancy to the voters themselves. [ 9 ]
In a few TMR systems, such as the Saturn Launch Vehicle Digital Computer and functional triple modular redundancy (FTMR) systems, the voters are also triplicated. Three voters are used – one for each copy of the next stage of TMR logic. In such systems there is no single point of failure . [ 10 ] [ 11 ]
Even though only using a single voter brings a single point of failure – a failed voter will bring down the entire system – most TMR systems do not use triplicated voters. This is because the majority gates are much less complex than the systems that they guard against, so they are much more reliable . [ 7 ] By using the reliability calculations, it is possible to find the minimum reliability of the voter for TMR to be a win. [ 6 ]
To use triple modular redundancy, a ship must have at least three chronometers ; two chronometers provided dual modular redundancy , allowing a backup if one should cease to work, but not allowing any error correction if the two displayed a different time, since in case of contradiction between the two chronometers, it would be impossible to know which one was wrong (the error detection obtained would be the same of having only one chronometer and checking it periodically). Three chronometers provided triple modular redundancy, allowing error correction if one of the three was wrong, so the pilot would take the average of the two with closer reading (vote for average precision).
There is an old adage to this effect, stating: "Never go to sea with two chronometers; take one or three." [ 12 ]
Mainly this means that if two chronometers contradict, how do you know which one is correct? At one time this observation or rule was an expensive one as the cost of three sufficiently accurate chronometers was more than the cost of many types of smaller merchant vessels. [ 13 ] Some vessels carried more than three chronometers – for example, HMS Beagle carried 22 chronometers . [ 14 ] However, such a large number was usually only carried on ships undertaking survey work as was the case with the Beagle .
In the modern era, ships at sea use GNSS navigation receivers (with GPS , GLONASS & WAAS etc. support) – mostly running with WAAS or EGNOS support so as to provide accurate time (and location). | https://en.wikipedia.org/wiki/Triple_modular_redundancy |
In thermodynamics , the triple point of a substance is the temperature and pressure at which the three phases ( gas , liquid , and solid ) of that substance coexist in thermodynamic equilibrium . [ 1 ] It is that temperature and pressure at which the sublimation , fusion , and vaporisation curves meet. For example, the triple point of mercury occurs at a temperature of −38.8 °C (−37.8 °F) and a pressure of 0.165 m Pa .
In addition to the triple point for solid, liquid, and gas phases, a triple point may involve more than one solid phase, for substances with multiple polymorphs . Helium-4 is unusual in that it has no sublimation/deposition curve and therefore no triple points where its solid phase meets its gas phase. Instead, it has a vapor-liquid- superfluid point, a solid-liquid-superfluid point, a solid-solid-liquid point, and a solid-solid-superfluid point. None of these should be confused with the lambda point , which is not any kind of triple point.
The first mention of the term "triple point" was on August 3, 1871 by James Thomson , brother of Lord Kelvin . [ 2 ] The triple points of several substances are used to define points in the ITS-90 international temperature scale, ranging from the triple point of hydrogen (13.8033 K) to the triple point of water (273.16 K, 0.01 °C, or 32.018 °F).
Before 2019, the triple point of water was used to define the kelvin , the base unit of thermodynamic temperature in the International System of Units (SI). [ 3 ] The kelvin was defined so that the triple point of water is exactly 273.16 K, but that changed with the 2019 revision of the SI , where the kelvin was redefined so that the Boltzmann constant is exactly 1.380 649 × 10 −23 J⋅K −1 , and the triple point of water became an experimentally measured constant.
Following the 2019 revision of the SI, the value of the triple point of water is no longer used as a defining point. However, its empirical value remains important: the unique combination of pressure and temperature at which liquid water , solid ice , and water vapour coexist in a stable equilibrium is approximately 273.16 ± 0.0001 K [ 4 ] and a vapour pressure of 611.657 pascals (6.11657 mbar; 0.00603659 atm). [ 5 ] [ 6 ]
Liquid water can only exist at pressures equal to or greater than the triple point. Below this, in the vacuum of outer space , solid ice sublimates , transitioning directly into water vapor when heated at a constant pressure. Conversely, above the triple point, solid ice first melts into liquid water upon heating at a constant pressure, then evaporates or boils to form vapor at a higher temperature.
For most substances, the gas–liquid–solid triple point is the minimum temperature where the liquid can exist. For water, this is not the case. The melting point of ordinary ice decreases with pressure, as shown by the phase diagram 's dashed green line. Just below the triple point, compression at a constant temperature transforms water vapor first to solid and then to liquid.
Historically, during the Mariner 9 mission to Mars , the triple point pressure of water was used to define "sea level". Now, laser altimetry and gravitational measurements are preferred to define Martian elevation. [ 7 ]
At high pressures, water has a complex phase diagram with 15 known phases of ice and several triple points, including 10 whose coordinates are shown in the diagram. For example, the triple point at 251 K (−22 °C) and 210 MPa (2070 atm) corresponds to the conditions for the coexistence of ice Ih (ordinary ice), ice III and liquid water, all at equilibrium. There are also triple points for the coexistence of three solid phases, for example ice II , ice V and ice VI at 218 K (−55 °C) and 620 MPa (6120 atm).
For those high-pressure forms of ice which can exist in equilibrium with liquid, the diagram shows that melting points increase with pressure. At temperatures above 273 K (0 °C), increasing the pressure on water vapor results first in liquid water and then a high-pressure form of ice. In the range 251–273 K , ice I is formed first, followed by liquid water and then ice III or ice V, followed by other still denser high-pressure forms.
Triple-point cells are used in the calibration of thermometers . For exacting work, triple-point cells are typically filled with a highly pure chemical substance such as hydrogen, argon, mercury, or water (depending on the desired temperature). The purity of these substances can be such that only one part in a million is a contaminant, called "six nines" because it is 99.9999% pure. A specific isotopic composition (for water, VSMOW ) is used because variations in isotopic composition cause small changes in the triple point. Triple-point cells are so effective at achieving highly precise, reproducible temperatures, that an international calibration standard for thermometers called ITS–90 relies upon triple-point cells of hydrogen , neon , oxygen , argon , mercury , and water for delineating six of its defined temperature points.
This table lists the gas–liquid–solid triple points of several substances. Unless otherwise noted, the data come from the U.S. National Bureau of Standards (now NIST , National Institute of Standards and Technology). [ 9 ]
Notes: | https://en.wikipedia.org/wiki/Triple_point |
In geometry and algebra , the triple product is a product of three 3- dimensional vectors, usually Euclidean vectors . The name "triple product" is used for two different products, the scalar -valued scalar triple product and, less often, the vector -valued vector triple product .
The scalar triple product (also called the mixed product , box product , or triple scalar product ) is defined as the dot product of one of the vectors with the cross product of the other two.
Geometrically, the scalar triple product
is the (signed) volume of the parallelepiped defined by the three vectors given.
Strictly speaking, a scalar does not change at all under a coordinate transformation. (For example, the factor of 2 used for doubling a vector does not change if the vector is in spherical vs. rectangular coordinates.) However, if each vector is transformed by a matrix then the triple product ends up being multiplied by the determinant of the transformation matrix. That is, the triple product of covariant vectors is more properly described as a scalar density .
T a ⋅ ( T b × T c ) = det ( T a T b T c ) = det ( T ( a b c ) ) = det ( T ) det ( a b c ) = det ( T ) ( a ⋅ ( b × c ) ) {\displaystyle {\begin{aligned}T\mathbf {a} \cdot (T\mathbf {b} \times T\mathbf {c} )&=\det \left({\begin{matrix}T\mathbf {a} &T\mathbf {b} &T\mathbf {c} \end{matrix}}\right)\\&=\det \left(T\left({\begin{matrix}\mathbf {a} &\mathbf {b} &\mathbf {c} \end{matrix}}\right)\right)\\&=\det(T)\det \left({\begin{matrix}\mathbf {a} &\mathbf {b} &\mathbf {c} \end{matrix}}\right)\\&=\det(T)(\mathbf {a} \cdot (\mathbf {b} \times \mathbf {c} ))\end{aligned}}}
Some authors use "pseudoscalar" to describe an object that looks like a scalar but does not transform like one. Because the triple product transforms as a scalar density not as a scalar, it could be called a "pseudoscalar" by this broader definition. However, the triple product is not a "pseudoscalar density".
When a transformation is an orientation-preserving rotation, its determinant is +1 and the triple product is unchanged. When a transformation is an orientation-reversing rotation then its determinant is −1 and the triple product is negated. An arbitrary transformation could have a determinant that is neither +1 nor −1 .
In exterior algebra and geometric algebra the exterior product of two vectors is a bivector , while the exterior product of three vectors is a trivector . A bivector is an oriented plane element and a trivector is an oriented volume element, in the same way that a vector is an oriented line element.
Given vectors a , b and c , the product
is a trivector with magnitude equal to the scalar triple product, i.e.
and is the Hodge dual of the scalar triple product. As the exterior product is associative brackets are not needed as it does not matter which of a ∧ b or b ∧ c is calculated first, though the order of the vectors in the product does matter. Geometrically the trivector a ∧ b ∧ c corresponds to the parallelepiped spanned by a , b , and c , with bivectors a ∧ b , b ∧ c and a ∧ c matching the parallelogram faces of the parallelepiped.
The triple product is identical to the volume form of the Euclidean 3-space applied to the vectors via interior product . It also can be expressed as a contraction of vectors with a rank-3 tensor equivalent to the form (or a pseudotensor equivalent to the volume pseudoform); see below .
The vector triple product is defined as the cross product of one vector with the cross product of the other two. The following relationship holds:
This is known as triple product expansion , or Lagrange's formula , [ 2 ] [ 3 ] although the latter name is also used for several other formulas . Its right hand side can be remembered by using the mnemonic "ACB − ABC", provided one keeps in mind which vectors are dotted together. A proof is provided below . Some textbooks write the identity as a × ( b × c ) = b ( a ⋅ c ) − c ( a ⋅ b ) {\displaystyle \mathbf {a} \times (\mathbf {b} \times \mathbf {c} )=\mathbf {b} (\mathbf {a} \cdot \mathbf {c} )-\mathbf {c} (\mathbf {a} \cdot \mathbf {b} )} such that a more familiar mnemonic "BAC − CAB" is obtained, as in “back of the cab”.
Since the cross product is anticommutative, this formula may also be written (up to permutation of the letters) as:
From Lagrange's formula it follows that the vector triple product satisfies:
which is the Jacobi identity for the cross product. Another useful formula follows:
These formulas are very useful in simplifying vector calculations in physics . A related identity regarding gradients and useful in vector calculus is Lagrange's formula of vector cross-product identity: [ 4 ]
This can be also regarded as a special case of the more general Laplace–de Rham operator Δ = d δ + δ d {\displaystyle \Delta =d\delta +\delta d} .
The x {\displaystyle x} component of u × ( v × w ) {\displaystyle \mathbf {u} \times (\mathbf {v} \times \mathbf {w} )} is given by:
Similarly, the y {\displaystyle y} and z {\displaystyle z} components of u × ( v × w ) {\displaystyle \mathbf {u} \times (\mathbf {v} \times \mathbf {w} )} are given by:
By combining these three components we obtain:
If geometric algebra is used the cross product b × c of vectors is expressed as their exterior product b ∧ c , a bivector . The second cross product cannot be expressed as an exterior product, otherwise the scalar triple product would result. Instead a left contraction [ 6 ] can be used, so the formula becomes [ 7 ]
The proof follows from the properties of the contraction. [ 6 ] The result is the same vector as calculated using a × ( b × c ).
In geometric algebra, three bivectors can also have a triple product. This product mimic the standard triple vector product. The antisymmetric product of three bivectors is.
This proof is made by taking dual of the geometric algebra version of the triple vector product until all vectors become bivectors.
This was three duals. This must also be done to the left side.
By negating both side we obtain:
In tensor notation , the triple product is expressed using the Levi-Civita symbol : [ 8 ] a ⋅ [ b × c ] = ε i j k a i b j c k {\displaystyle \mathbf {a} \cdot [\mathbf {b} \times \mathbf {c} ]=\varepsilon _{ijk}a^{i}b^{j}c^{k}} and ( a × [ b × c ] ) i = ε i j k a j ε k ℓ m b ℓ c m = ε i j k ε k ℓ m a j b ℓ c m , {\displaystyle (\mathbf {a} \times [\mathbf {b} \times \mathbf {c} ])_{i}=\varepsilon _{ijk}a^{j}\varepsilon ^{k\ell m}b_{\ell }c_{m}=\varepsilon _{ijk}\varepsilon ^{k\ell m}a^{j}b_{\ell }c_{m},} referring to the i {\displaystyle i} -th component of the resulting vector. This can be simplified by performing a contraction on the Levi-Civita symbols , ε i j k ε k ℓ m = δ i j ℓ m = δ i ℓ δ j m − δ i m δ j ℓ , {\displaystyle \varepsilon _{ijk}\varepsilon ^{k\ell m}=\delta _{ij}^{\ell m}=\delta _{i}^{\ell }\delta _{j}^{m}-\delta _{i}^{m}\delta _{j}^{\ell }\,,} where δ j i {\displaystyle \delta _{j}^{i}} is the Kronecker delta function ( δ j i = 0 {\displaystyle \delta _{j}^{i}=0} when i ≠ j {\displaystyle i\neq j} and δ j i = 1 {\displaystyle \delta _{j}^{i}=1} when i = j {\displaystyle i=j} ) and δ i j ℓ m {\displaystyle \delta _{ij}^{\ell m}} is the generalized Kronecker delta function . We can reason out this identity by recognizing that the index k {\displaystyle k} will be summed out leaving only i {\displaystyle i} and j {\displaystyle j} . In the first term, we fix i = l {\displaystyle i=l} and thus j = m {\displaystyle j=m} . Likewise, in the second term, we fix i = m {\displaystyle i=m} and thus l = j {\displaystyle l=j} .
Returning to the triple cross product, ( a × [ b × c ] ) i = ( δ i ℓ δ j m − δ i m δ j ℓ ) a j b ℓ c m = a j b i c j − a j b j c i = b i ( a ⋅ c ) − c i ( a ⋅ b ) . {\displaystyle (\mathbf {a} \times [\mathbf {b} \times \mathbf {c} ])_{i}=(\delta _{i}^{\ell }\delta _{j}^{m}-\delta _{i}^{m}\delta _{j}^{\ell })a^{j}b_{\ell }c_{m}=a^{j}b_{i}c_{j}-a^{j}b_{j}c_{i}=b_{i}(\mathbf {a} \cdot \mathbf {c} )-c_{i}(\mathbf {a} \cdot \mathbf {b} )\,.}
Consider the flux integral of the vector field F {\displaystyle \mathbf {F} } across the parametrically-defined surface S = r ( u , v ) {\displaystyle S=\mathbf {r} (u,v)} : ∬ S F ⋅ n ^ d S {\textstyle \iint _{S}\mathbf {F} \cdot {\hat {\mathbf {n} }}\,dS} . The unit normal vector n ^ {\displaystyle {\hat {\mathbf {n} }}} to the surface is given by r u × r v | r u × r v | {\textstyle {\frac {\mathbf {r} _{u}\times \mathbf {r} _{v}}{|\mathbf {r} _{u}\times \mathbf {r} _{v}|}}} , so the integrand F ⋅ ( r u × r v ) | r u × r v | {\textstyle \mathbf {F} \cdot {\frac {(\mathbf {r} _{u}\times \mathbf {r} _{v})}{|\mathbf {r} _{u}\times \mathbf {r} _{v}|}}} is a scalar triple product. | https://en.wikipedia.org/wiki/Triple_product |
The triple product rule , known variously as the cyclic chain rule , cyclic relation , cyclical rule or Euler's chain rule , is a formula which relates partial derivatives of three interdependent variables. The rule finds application in thermodynamics , where frequently three variables can be related by a function of the form f ( x , y , z ) = 0, so each variable is given as an implicit function of the other two variables. For example, an equation of state for a fluid relates temperature , pressure , and volume in this manner. The triple product rule for such interrelated variables x , y , and z comes from using a reciprocity relation on the result of the implicit function theorem , and is given by
where each factor is a partial derivative of the variable in the numerator, considered to be a function of the other two.
The advantage of the triple product rule is that by rearranging terms, one can derive a number of substitution identities which allow one to replace partial derivatives which are difficult to analytically evaluate, experimentally measure, or integrate with quotients of partial derivatives which are easier to work with. For example,
Various other forms of the rule are present in the literature; these can be derived by permuting the variables { x , y , z }.
An informal derivation follows. Suppose that f ( x , y , z ) = 0. Write z as a function of x and y . Thus the total differential dz is
Suppose that we move along a curve with dz = 0, where the curve is parameterized by x . Thus y can be written in terms of x , so on this curve
Therefore, the equation for dz = 0 becomes
Since this must be true for all dx , rearranging terms gives
Dividing by the derivatives on the right hand side gives the triple product rule
Note that this proof makes many implicit assumptions regarding the existence of partial derivatives, the existence of the exact differential dz , the ability to construct a curve in some neighborhood with dz = 0, and the nonzero value of partial derivatives and their reciprocals. A formal proof based on mathematical analysis would eliminate these potential ambiguities.
Suppose a function f ( x , y , z ) = 0 , where x , y , and z are functions of each other. Write the total differentials of the variables d x = ( ∂ x ∂ y ) d y + ( ∂ x ∂ z ) d z {\displaystyle dx=\left({\frac {\partial x}{\partial y}}\right)dy+\left({\frac {\partial x}{\partial z}}\right)dz} d y = ( ∂ y ∂ x ) d x + ( ∂ y ∂ z ) d z {\displaystyle dy=\left({\frac {\partial y}{\partial x}}\right)dx+\left({\frac {\partial y}{\partial z}}\right)dz} Substitute dy into dx d x = ( ∂ x ∂ y ) [ ( ∂ y ∂ x ) d x + ( ∂ y ∂ z ) d z ] + ( ∂ x ∂ z ) d z {\displaystyle dx=\left({\frac {\partial x}{\partial y}}\right)\left[\left({\frac {\partial y}{\partial x}}\right)dx+\left({\frac {\partial y}{\partial z}}\right)dz\right]+\left({\frac {\partial x}{\partial z}}\right)dz} By using the chain rule one can show the coefficient of dx on the right hand side is equal to one, thus the coefficient of dz must be zero ( ∂ x ∂ y ) ( ∂ y ∂ z ) + ( ∂ x ∂ z ) = 0 {\displaystyle \left({\frac {\partial x}{\partial y}}\right)\left({\frac {\partial y}{\partial z}}\right)+\left({\frac {\partial x}{\partial z}}\right)=0} Subtracting the second term and multiplying by its inverse gives the triple product rule ( ∂ x ∂ y ) ( ∂ y ∂ z ) ( ∂ z ∂ x ) = − 1. {\displaystyle \left({\frac {\partial x}{\partial y}}\right)\left({\frac {\partial y}{\partial z}}\right)\left({\frac {\partial z}{\partial x}}\right)=-1.}
This section is based on chapter 5 of Pippard. [ 1 ]
Suppose we are given four real variables ( x , y , z , w ) {\displaystyle (x,y,z,w)} , restricted to move on a 2-dimensional C 2 {\displaystyle C^{2}} surface in R 4 {\displaystyle \mathbb {R} ^{4}} . Then, if we know two of them, we can determine the other two uniquely (generically).
In particular, we may take any two variables as the independent variables, and let the other two be the dependent variables, then we can take all these partial derivatives.
Proposition: ( ∂ x ∂ y ) z ( ∂ y ∂ z ) x ( ∂ z ∂ x ) y = − 1 {\displaystyle \left({\frac {\partial x}{\partial y}}\right)_{z}\left({\frac {\partial y}{\partial z}}\right)_{x}\left({\frac {\partial z}{\partial x}}\right)_{y}=-1}
Proof. We can ignore w {\displaystyle w} . Then locally the surface is just a x + b y + c z + d = 0 {\displaystyle ax+by+cz+d=0} . Then ( ∂ x ∂ y ) z = − b a {\displaystyle \left({\frac {\partial x}{\partial y}}\right)_{z}=-{\frac {b}{a}}} , etc. Now multiply them.
The ideal gas law relates the state variables of pressure (P), volume (V), and temperature (T) via
which can be written as
so each state variable can be written as an implicit function of the other state variables:
From the above expressions, we have
A geometric realization of the triple product rule can be found in its close ties to the velocity of a traveling wave
shown on the right at time t (solid blue line) and at a short time later t +Δ t (dashed). The wave maintains its shape as it propagates, so that a point at position x at time t will correspond to a point at position x +Δ x at time t +Δ t ,
This equation can only be satisfied for all x and t if k Δ x − ω Δ t = 0 , resulting in the formula for the phase velocity
To elucidate the connection with the triple product rule, consider the point p 1 at time t and its corresponding point (with the same height) p̄ 1 at t +Δ t . Define p 2 as the point at time t whose x-coordinate matches that of p̄ 1 , and define p̄ 2 to be the corresponding point of p 2 as shown in the figure on the right. The distance Δ x between p 1 and p̄ 1 is the same as the distance between p 2 and p̄ 2 (green lines), and dividing this distance by Δ t yields the speed of the wave.
To compute Δ x , consider the two partial derivatives computed at p 2 ,
Dividing these two partial derivatives and using the definition of the slope (rise divided by run) gives us the desired formula for
where the negative sign accounts for the fact that p 1 lies behind p 2 relative to the wave's motion. Thus, the wave's velocity is given by
For infinitesimal Δ t , Δ x Δ t = ( ∂ x ∂ t ) {\displaystyle {\frac {\Delta x}{\Delta t}}=\left({\frac {\partial x}{\partial t}}\right)} and we recover the triple product rule | https://en.wikipedia.org/wiki/Triple_product_rule |
Triplet-triplet annihilation ( TTA ) is an energy transfer mechanism where two molecules in their triplet excited states interact to form a ground state molecule and an excited molecule in its singlet state . [ 1 ] This mechanism is example of Dexter energy transfer mechanism. [ 2 ] In triplet-triplet annihilation, one molecule transfers its excited state energy to the second molecule, resulting in the first molecule returning to its ground state and the second molecule being promoted to a higher excited singlet state. [ 1 ]
Triplet-triplet annihilation was first discovered in the 1960s to explain the observation of delayed fluorescence in anthracene derivatives. [ 3 ] [ 4 ] [ 5 ] [ 6 ]
Triplet-triplet annihilation combines the energy of two triplet-excited molecules onto one molecule to produce a higher excited state. Since the higher excited state is an emissive singlet state, TTA can be used to achieve photon upconversion which is a process that converts the energy of two photons into one photon of higher energy. [ 7 ] [ 8 ] To achieve photon upconversion through triplet-triplet annihilation two types of molecules are often combined: a sensitizer and an emitter (annihilator). [ 9 ] The sensitizer absorbs the low energy photon and populates its first excited triplet state (T 1 ) through intersystem crossing . The sensitizer then transfers the excitation energy to the emitter, resulting in a triplet excited emitter and a ground state sensitizer. Two triplet-excited emitters can then undergo triplet-triplet annihilation to produce a singlet excited state (S 1 ) of the emitter, which can emit an upconverted photon.
For efficient TTA upconversion, the sensitizer should absorb strongly in the desired excitation range and have high conversion efficiency from the singlet excited state to the triplet excited state. [ 9 ] The emitter should have a singlet energy level just below twice the energy of the first triplet excited state. Both the emitter and sensitizer should have long triplet-state lifetimes so that the TTA mechanism has enough time to occur. [ 9 ]
Triplet-triplet annihilation upconversion (TTA-UC) materials have the advantages of needing low excitation power and having changeable emission and excitation light wavelengths. [ 10 ] Due to these advantages, many applications of TTA-UC materials have been explored.
Solar cells are electrical devices that convert sunlight to electricity. However, due to the properties of the materials composing solar cells, many solar cells do not harvest low energy (with wavelength above 800 nm) photons efficiently. Thus, the ability for TTA-UC materials to combine the energy of two low energy photons into one high energy photon is desirable to capture more of the energy from sunlight. [ 9 ]
Light-emitting materials that can convert non-emissive triplet states into emissive singlet states are crucial in organic light-emitting diodes (OLEDs) as, statistically, 75% of the excited states formed in an OLED are triplet states. [ 11 ] TTA materials are well suited to use in OLEDs due to their low operational voltage, small drop-off in efficiency when increasing brightness, and low cost. However, most TTA materials emit photons that are blue to deep blue, which limits their applications in OLEDs until the colour variety diversifies. [ 9 ]
In photolysis cancer therapy, light is used to selectively break bonds which releases and activates a target drug molecule. The drug molecule can be released near or in tumour sites to combat the disease. TTA-UC materials that can be excited by near-infrared light are desirable for this application since near-infrared light penetrates tissue well. [ 10 ] | https://en.wikipedia.org/wiki/Triplet-triplet_annihilation |
In quantum mechanics , a triplet state , or spin triplet , is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three allowed values of the spin's projection along a given axis m S = −1, 0, or +1, giving the name "triplet".
Spin , in the context of quantum mechanics, is not a mechanical rotation but a more abstract concept that characterizes a particle's intrinsic angular momentum. It is particularly important for systems at atomic length scales, such as individual atoms , protons , or electrons .
A triplet state occurs in cases where the spins of two unpaired electrons , each having spin s = 1 ⁄ 2 , align to give S = 1, in contrast to the more common case of two electrons aligning oppositely to give S = 0, a spin singlet . Most molecules encountered in daily life exist in a singlet state because all of their electrons are paired, but molecular oxygen is an exception. [ 1 ] At room temperature , O 2 exists in a triplet state, which can only undergo a chemical reaction by making the forbidden transition into a singlet state. This makes it kinetically nonreactive despite being thermodynamically one of the strongest oxidants. Photochemical or thermal activation can bring it into the singlet state , which makes it kinetically as well as thermodynamically a very strong oxidant.
In a system with two spin-1/2 particles – for example the proton and electron in the ground state of hydrogen – measured on a given axis, each particle can be either spin up or spin down so the system has four basis states in all
using the single particle spins to label the basis states, where the first arrow and second arrow in each combination indicate the spin direction of the first particle and second particle respectively.
More rigorously
where s 1 {\displaystyle s_{1}} and s 2 {\displaystyle s_{2}} are the spins of the two particles, and m 1 {\displaystyle m_{1}} and m 2 {\displaystyle m_{2}} are their projections onto the z axis. Since for spin-1/2 particles, the | 1 2 , m ⟩ {\textstyle \left|{\frac {1}{2}},m\right\rangle } basis states span a 2-dimensional space, the | 1 2 , m 1 ⟩ | 1 2 , m 2 ⟩ {\textstyle \left|{\frac {1}{2}},m_{1}\right\rangle \left|{\frac {1}{2}},m_{2}\right\rangle } basis states span a 4-dimensional space.
Now the total spin and its projection onto the previously defined axis can be computed using the rules for adding angular momentum in quantum mechanics using the Clebsch–Gordan coefficients . In general
substituting in the four basis states
returns the possible values for total spin given along with their representation in the | 1 2 , m 1 ⟩ | 1 2 , m 2 ⟩ {\textstyle \left|{\frac {1}{2}},m_{1}\right\rangle \left|{\frac {1}{2}},m_{2}\right\rangle } basis. There are three states with total spin angular momentum 1: [ 2 ] [ 3 ]
which are symmetric and a fourth state with total spin angular momentum 0:
which is antisymmetric. The result is that a combination of two spin-1/2 particles can carry a total spin of 1 or 0, depending on whether they occupy a triplet or singlet state.
In terms of representation theory , what has happened is that the two conjugate 2-dimensional spin representations of the spin group SU(2) = Spin(3) (as it sits inside the 3-dimensional Clifford algebra ) have tensored to produce a 4-dimensional representation. The 4-dimensional representation descends to the usual orthogonal group SO(3) and so its objects are tensors, corresponding to the integrality of their spin. The 4-dimensional representation decomposes into the sum of a one-dimensional trivial representation (singlet, a scalar , spin zero) and a three-dimensional representation (triplet, spin 1) that is nothing more than the standard representation of SO(3) on R 3 {\displaystyle R^{3}} . Thus the "three" in triplet can be identified with the three rotation axes of physical space. [ citation needed ] | https://en.wikipedia.org/wiki/Triplet_state |
Triploid block is a phenomenon describing the formation of nonviable progeny after hybridization of flowering plants that differ in ploidy . The barrier is established in the endosperm , a nutritive tissue supporting embryo growth. [ 1 ] [ 2 ] This phenomenon usually happens when autopolyploidy occurs in diploid plants. Triploid blocks lead to reproductive isolation . The triploid block effects have been explained as possibly due to genomic imprinting in the endosperm. [ 1 ] Triploid block can be partially overcome by chemical treatment with 5-Azacytidine. [ 3 ]
This botany article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Triploid_block |
The tripod or jacket [ 1 ] is a type of foundation for offshore wind turbines . The tripod is generally more expensive than other types of foundation. However, for large turbines and higher water depth, the cost disadvantage might be compensated when durability is also taken into account.
The exploration of offshore wind energy started with the introduction of monopile foundations for wind turbines in a range from 1 up to 3MW in water depth of about 10 to 20m during the 1990s. [ 2 ] Germany has been facing water depths up to 40m, when it joined this new field of renewable energy . At the same time the 5MW turbine class appeared. One representative of this new turbine generation was the Multibrid M5000 with a rotor diameter of 116m, later 135m under the labels Areva and Adwen .
The first prototype of this machine was erected in Bremerhaven in 2004 onshore. Already in this stage Bremerhaven had supported the development on behalf of BIS Bremerhavener Gesellschaft für Investitionsförderung und Stadtentwicklung mbH.
Since the new century, there has been a search for a feasible foundation for the upcoming large turbines and greater water depths, in light of the available geotechnical assessment methods, fabrication processes, pile driving equipment and logistic and installation equipment.
One result was the Tripod foundation. The first design was drawn by OWT – Offshore Wind Technology in Leer (Germany) in 2005. The Tripod was integrally designed with the tower from this early beginning. The three-legged structure reaches from the sea bed up to typically 20m above the sea water level, keeping the bolted flange on top safely apart from the crest of the waves. This section allows to be outfitted onshore with all functionalities needed in terms of boat landing, cable guiding and last but not least corrosion protection systems. The central column is designed as an open system allowing an unrestricted water exchange in each tide cycle . This circumstance is beneficial when the corrosion protection system has to be designed for the inner surfaces.
The Tripod is fixed with midsized pin piles at the sea bed. The piles might be pre piled or post piled. A suction bucket foundation was designed as well. The first tower section, called S3, is foreseen to be mounted offshore on top of the Tripod with a bolted flange connection. This section contains the outer service platform and the entry door. This section is independently accessible for electrical equipment and cold commissioning procedures. Additionally it provides simply height, what can be saved on Tripod side. The height of a Tripod amounts already about 60m for 40m water depth.
In 2006 a Tripod onshore demonstrator was designed by OWT for Multibrid GmbH, manufactured and erected in Bremerhaven, Germany, by WeserWind GmbH Offshore Construction Georgsmarienhütte. This was the beginning of a long lasting collaboration between the turbine developer and manufacturer Multibrid, the foundation designer OWT and the fabricator WeserWind. Meanwhile, the design covers the demands of an offshore turbine foundation to sufficient extent, the fabrication was even challenging regarding size and shape of the structure. That time WeserWind was supported in terms of fabrication and assembly by its sister company IAG Industrieanlagenbau Georgsmarienhütte GmbH, a member of the Georgsmarienhütte group as well. The first operation of the turbine was accompanied by the research project IMO-Wind. [ 3 ] The first steps in condition monitoring have been undertaken including the determination of stress curves, the so-called "Hot spot" Survey, in order to enable the comparison with calculation models.
In 2008 Tripods were built as a substructure for six Multibrid M5000 offshore wind turbines in the Alpha Ventus project. Alpha Ventus was planned as a first test field for the exploration of offshore wind energy in German waters. The project organisation has been Deutsche Offshore-Testfeld und Infrastruktur GmbH & Co. KG, DOTI. It was founded in 2006 by EWE AG (47,5%), E.ON Climate & Renewables Central Europe GmbH and Vattenfall Europe Windkraft GmbH (each 26,25%) assisted by Stiftung Offshore Windenergie. The German Federal Ministry of Environment BMU supported a number of research projects, which were summarized in the RAVE initiative (Research at Alpha Ventus). A broad basis of experience and knowledge was gained for the construction, commissioning and operation for future offshore wind farms . The Tripods were fabricated by Aker Kvaerner in Verdal, Norway. A horizontal assembly of the Tripods was realized in accordance to the local fabrication experience of the yard, coming from large oil and gas jacket fabrication, with subsequent upending and of course upright sailing from Norway to the offshore terminal in Eemshaven. The transportation of the Tripods to the location was done by Taklift 4 from Boskalis one by one.
The year 2010 marked the next milestone in rolling out the M5000 turbine with the Tripod foundation. The two projects Borkum West II and Global Tech I decided to erect their farms using this technology platform. 40 Tripods were ordered by each project in first instance nearly at the same time. Anticipating this demand WeserWind has developed a serial production approach for Tripods in the years before, together with Dr. Möller GmbH / IMS Nord, [ 4 ] Bremerhaven. The key parameters of this approach are the upright assembly concept, the setup of an assembly line with up to nine work stations, the transportation of the growing structures on behalf of heavy load rail carriers along the assembly line and the integrated load out operation to a tailor-made pontoon. Based on this concept Georgsmarienhütte released the investment program building this assembly shop with two parallel lines at Lunedeich, Bremerhaven. The building was operational in the beginning of 2011 and in June the first Borkum-West II-Tripod was completed.
In December 2011 the pontoon was baptised and the offshore terminal ABC-Peninsula was commissioned by BLG Logistics Solutions GmbH & Co. KG after essential upgrading. Finally 100 Tripods have been built at this site in the years from 2011 to 2013. The cycle time for the whole plant was reached with down to five calendar days per structure. The load out cycle was achieved to four hours. Also SIAG Emden and the consortium Iemants N.V. with Eiffage Construction Métallique S.A.S. in Vlissingen produced in total 20 Tripods in that time in upright position. The offshore transportation technology has been developed significantly since Alpha Ventus. The Offshore Construction Jack Up “Innovation” by HGO InfraSea Solutions GmbH & Co. KG was commissioned in 2012 and did her first job for Global Tech 1 carrying three Tripods and pile sets per sail. The crane ships “Stanislaw Yudin” and “Oleg Strassnow” by SHL Seaway Heavy Lifting were in operation for Borkum West II.
The peculiarity of the Tripod is the combination of the above-water structure like a Monopile solution with small exposed surface, robust performance in risk scenarios and easy transition to the tower part with the supporting effect and performance of a lattice structure. Hot spots are avoided in the aggressive environment of splash zone by design allowing a free corrosion fatigue assessment.
In the wind energy, the coordination of the dynamics of the structure, characterized by the frequencies it mainly swings, is of special importance due to the excitation by the turbine rotor. The Tripod behaviour is between the Monopile, which tends to be softer and the Jacket, which in turn is more rigid.
The application area in terms of water depth was initially predicted to at least 25 meters water depth up to 50m. [ 5 ] The impressively growing Monopile technology within the last years moved their field of application far to 40m nowadays. Therefore, the Tripod disappeared from the scene. Beside the higher fabrication effort for Tripods, transport and installation efforts might become even more comparable the more the structures grow. Finally the dedicated suitability of the Tripod to corrosion protection systems will remain a significant difference to the Monopile. The performance of the structures over the life time and due diligence assessments of the assets in later life cycle stages might give reason for reconciliation of the arguments.
Comparable to other lattice structures like Jackets, the Tripod is fixed with piles in the sea bed. The number of three legs results in sufficient stability in the unpiled or ungrouted situation what comes back with a reliable weather window for installation. The design parameters for the piles can be independently chosen from the Tripod itself and reflect the geotechnical needs explicitly. There is no need to apply scour protection.
The connection to the pile is usually achieved using a grouted connection. This is a technique where special concrete is poured in the joint gap between pile and pile sleeve. Due to the resulting composite effect the loads are transferred from the sleeve to the pile, and thus into the ground. A submerged grouting process requires high competence in design, planning and execution of the processes. The stable moderate temperature under water supports the temperature sensitive grout curing process.
The supporting action is based on the deflection of the bending moment of the tower to the piles, which are then essentially only pulled or pushed. This requires a combination of upper and lower legs which build up the leverage. Alternatively, a suction bucket can be used instead of the pile. In comparison, the monopile distributes its loads by laterally stabilizing into the ground.
Tubular nodes are the characteristic design element in lattice structures, where tubes intersect each other. It is preferred that incoming tubes, the stubs, remain in certain ratio of the diameters (0.8) to the continuous tube, the chord, to achieve efficient load bearing effects. This effect determines to the final dimensional ratios.
The plate thicknesses within offshore foundations are well adapted to the local load situations. A balanced material utilisation can be achieved by design because the dimension of an offshore foundation is large compared to the dimension of hot rolled plates . Tripods and Monopiles are shell structures . Their wall thickness is relatively small compared to the diameter. Therefore, they have to be proven in terms of shell buckling . The tower, central tube and legs are assembled of cylindrical or conical sections, cans, with an individual length of 2 to 4m. The wall thicknesses are in the range of 40 to 60mm in the central column, a few cans in high-stress areas up to 90mm. The wall thicknesses of the conical legs range from 20 to 30mm.
The lifetime is a central requirement to the design. In the classic oil and gas industry offshore wave loads have already been taken into account. The operation of wind turbine generators causes additionally high dynamic operating loads. This was impressively observed with the Growian project, what was a two bladed 3MW onshore turbine, what failed in 1983 for this reason.
FEM methods are mainly used for the assessments. Only these more extensive tools allow to reflect the stress curves in detail and to provide accuracy as it is required for the design. The calculation times have been considerably reduced by scripted modelling and increasing computing speeds, which increased the iterations speeds and thus improved the optimization results. [ 6 ]
The Tripod foundation for offshore wind turbines represents a remarkable contribution to the beginning of the industrial utilisation of offshore wind energy in German waters. It was born within a creative nut shell of German offshore wind pioneers and it expanded its potential gaining further partners to a large multidisciplinary team realising the vision. The fact, that 126 turbines founded on top of Tripods are nowadays operational, is the result of a long lasting reliable collaboration of a number of stakeholders.
A desk top study has been performed in 2014 assessing the feasibility of the foundation concept to the next turbine generation with 8MW and rotor diameter beyond 160m. It was essential to demonstrate the limited weight increase carrying the even higher loads and thus approving all the existing fabrication and installation processes from the projects done before.
Today the grown knowledge in offshore engineering from the Tripod decade is a kind of immaterial asset to be put into new projects using Monopile, Jacket or why not Tripod concepts, exploring the recent state of the art for lowering the cost of energy. | https://en.wikipedia.org/wiki/Tripod_(foundation) |
Tripod Beta is an incident and accident analysis methodology made available by the Stichting Tripod Foundation [ 1 ] via the Energy Institute . The methodology is designed to help an accident investigator analyse the causes of an incident or accident in conjunction with conducting the investigation. This helps direct the investigation as the investigator will be able to see where more information is needed about what happened, or how or why the incident occurred.
Tripod Beta was developed by Shell International Exploration and Production B.V. as the result of Shell-funded academic research in the 1980s and 1990s. Such research contributed towards the development of the Swiss cheese model of accident causation, and in the late 1990s and early 2000s, towards the development of the Hearts and Minds safety culture toolkit.
The research was based on the following hypotheses
The early research focused on a predictive tool to identify underlying causes of incidents before they occurred rather than an incident investigation methodology This would later become the basis for Tripod Delta .
The incident investigation methodology whilst always part of the research came later around 1990. initial Tripod Investigation followed a tabular approach as graphical program was not yet available
Following the 1988 Piper Alpha disaster and Lord Cullen report in 1990, Shell International created a team to look at Safety management systems and Safety Cases. That team worked until 2004 they developed a number of approaches, the EP forum (later the Oil and Gas Producers Association) guidance on Safety cases was founded on work by that team. The team worked closely with Leiden and Manchester Universities to the understanding of accident causation that had been developed in the 1984–2000 research program.
In 1992 Microsoft released windows version 3.1. That gave the team the ability for the first time to create graphical representations of the theories developed. Two software-based tools were developed: Bow Tie [ 2 ] and Tripod Beta, respectively. [ 3 ] [ 4 ]
In 1998, following publicity of Tripod Beta, Shell International Exploration and Production B.V. transferred copyright of the Tripod Beta methodology to the Stichting Tripod Foundation, a charitable body under Dutch law. The Foundation's purpose is to promote best practice in industry through the sensible usage of Tripod technologies to aid in the understanding and prevention of accidents and incidents. In 2012 the Foundation partnered with the Energy Institute in the UK in order to help achieve this. The Energy Institute currently publishes the official guide on using the Tripod Beta methodology. [ 5 ] The Stichting Tripod Foundation also accredits approved training courses, and assesses the competence of users of the Tripod methodology. Users who are assessed as competent in Tripod Beta are accredited as 'Tripod Practitioners'.
Tripod Beta is a methodology that can be conducted via pen and paper or using specialized software. [ 6 ] [ 7 ]
The methodology combines a number of theories of accident causation into generating a single model (a 'Tripod tree') of an accident or incident, most notably the Swiss cheese model (barrier-based risk management) and human factors-oriented theories such as GEMS (Generic Error-modelling system). [ 8 ] [ page needed ] as well as the worldwide accepted as a 'mainstream model 'GOP' (Gap, Outcome and Power) by Martin Fishbein and Icek Ajzen, expanding on the 'Theory of Reasoned Action' (TRA) (WIKI)...
A Tripod tree is divided into three sections.
An Event in terms of Tripod Beta is the unexpected, unwanted or adverse outcome of a willfully carried out and intended process. The sequence such Events in an incident are shown in the tree as a series of 'trios', a simple logic (AND) gate that tells how the combination of two events led to an outcome. The outcome can then become an event that can combine with another event to cause a subsequent outcome, and so on.
As the sequence of trios goes forward in time, the tree ends when the last incident occurs, but if relevant can also take into account what happened after the incident (such as emergency response).
Potential events may also be investigated; Such Events that did not 'materialize' either because a 'barrier' prevented it from happening, or by sheer 'randomness' which is less likely.
As the sequence goes backwards in time, the tree usually begins with the last 'normal' Event, i.e. an event that was a normal part of ( business) operations.
This represents a logical place at which to start investigating an incident, as everything that happened after this was unusual and therefore worth investigating 'what went wrong?'.
A trio has three elements: the Event (the outcome, a change in state to an object, causing an effect such as an injury), the object (the person or thing that was changed (damaged), and the agent of change (the energy, 'driving' force or hazard that caused change or damage to the object). A logic test is used to ensure the correct identification of these elements: 'Agent of change' acts upon 'object' and results in 'event'. For example, 'Fire' acts upon 'Person' and results in 'Person burnt by fire'.
The Tripod practitioner first models the incident by constructing a series of Trios that explain 'what happened'.
Trees usually have between two and five trios via interconnecting nodes, where either an Event turns into an 'Agent of Change'in a subsequent trio, or an Object at the same time turns into an Event if affected by another Agent of Change.
In Tripod theory, accidents are managed through the usage of 'Barriers'. Barriers are ( intended) functions of a (safety) management system, such as automated trips, relief valves, etc. that prevent an Agent of Change or hazard from causing an unexpected change or incident. Barriers are often people's actions (interventions) conducting critical tasks (such as responding to alarms) often described by rules and procedures but not necessarily.
Incidents are therefore 'allowed' to happen by the ineffectiveness at this particular point in time of one or more of these barriers.
Once the Tripod practitioner has created a series of Trios the next step is to identify the barriers that should have been in place to prevent the incident occurring. This is done for each individual Trio. Only barriers that could have actually mitigated or prevented the next event are considered. Predominantly, 'Failed Barriers' are considered. These are the barriers that should have prevented the incident but failed for various reasons. For example, a barrier to prevent injury in a car is a seat belt; however, this barrier may fail because the driver did not wear a seat belt, or the seat belt mechanism itself was faulty.
'Missing Barriers' (barriers that should have been in place according to 'best practice' but had not been established by the organisation), 'Inadequate Barriers' (barriers that functioned as intended but could not achieve the required function to prevent the incident; for example, a seat belt will only prevent serious injury under certain circumstances) and 'Effective Barriers' (barriers that succeeded in preventing the subsequent event) are also considered. If the analysis is modelling a 'Potential Event', unless the event was only prevented through sheer luck, there will be one or more Effective Barrier within the incident trajectory. For example, a seat belt functions to prevent the death of the driver.
Once the investigator has identified the sequence of events, and the Failed-, Missing-, and Inadequate- Barriers, the next step is to understand the causes of these being ineffective when needed.
In Tripod theory, barriers fail because of human action or inaction. This may be human action directly related to the barrier functionality (such as the driver not wearing the seat belt), but may also be indirect, such as a failure during the design or installation of the barrier, or the failure of management to consider implementing the barrier. This human action or inaction is called the 'Immediate Cause'. This is the substandard act or human error . Often, when (non-Tripod) investigations determine that the cause of an accident was due to human error, in Tripod-terms this would relate to the immediate cause only.
The reasons for substandard acts and human error cannot always be definitively known, however it is known that human errors have situation or psychological precursors. These 'Preconditions' are aspects of the working environment that are likely to have contributed towards the substandard action or inaction. For example, typical Preconditions may be: fatigue due to improper work-life balance; perception that a guard is not required, loss of situation awareness, improper motivation, poor supervision; rushing in order to complete a job quickly; noisy or dark environment; confusing procedures, incorrect understanding of work objective, etc.
Through interviews and investigation the investigator is able to identify a number of Preconditions that likely contributed towards the substandard action.
In Tripod theory, Preconditions represent aspects of the working environment that organisations should try to manage, usually via good leadership, safety culture, and a well-documented and implemented (safety) management system. For example: fatigue of the workforce can be managed by adequate shift rotas, and policies on shift length and overtime; rushing in order to complete a job quickly can be managed by leaders not sending conflicting messages that prioritize productivity over safety, etc. These weaknesses or failures of leadership, culture or management systems are the underlying causes of accidents and incidents. They help create, or fail to correct, the Preconditions.
The investigator looks for evidence of management system-level failures that created or failed to control the Preconditions. For example, this may be ambiguously worded, or lack of, written policy, unclear management-level responsibilities, apparent lack of visibility of leadership, ineffective risk management processes, etc. Tripod Beta encourages the investigator to consider these aspects of the incident.
Importantly, Tripod Beta placed great emphasis on identifying the Underlying Causes of accidents and incidents because, whilst many aspects of an accident (such as the sequence of events, Barriers and Preconditions) may be quite specific to a particular accident or incident, Underlying Causes will be non-specific to an accident and likely will be the cause of, or potential cause of, many different accidents and incidents, even those that seem completely unrelated.
The outcome of a Tripod Beta analysis are usually a number of recommendations for improvements within the organisation in order to prevent the same or other incidents occurring. Recommendations may or may not be formed by the person investigating.
Recommendations focus only on two aspects of the Tripod analysis: the Barriers and the Underlying Causes.
It is important to strengthen or reinstate the barriers so that the particular operation that was investigated can continue. Recommendations for improving Barriers are to prevent the same (or similar) incident happening and may involve fixing equipment or putting in place extra checks and additional independent barriers where barriers overly rely on human performance.
As Underlying Causes can be causal in many different types of incident, tackling the Underlying Causes may have the greater benefit in the long-term at preventing multiple incidents. Recommendations to tackle Underlying Causes are often aimed at management system level and are sometimes much harder to implement.
Recommendations are not made for other aspects of the incident (such as the Immediate Causes) as such recommendations will be unlikely to be effective at preventing further incidents. For example, recommendations for improving Immediate Causes (the substandard actions) often focus on retraining or punishing the person involved, which will be unlikely to prevent other people making the same error in future. | https://en.wikipedia.org/wiki/Tripod_Beta |
Tripotassium phosphate, also called tribasic potassium phosphate [ 3 ] is a water-soluble salt with the chemical formula K 3 PO 4 . (H 2 O) x (x = 0, 3, 7, 9). [ 4 ] Tripotassium phosphate is basic: a 1% aqueous solution has a pH of 11.8. [ 4 ]
Tripotassium phosphate is produced by the neutralization of phosphoric acid with potassium hydroxide : [ 4 ]
Tripotassium phosphate has few industrial applications, however it is commonly used as a base in laboratory-scale organic chemistry. Being insoluble in organic solvents, it is an easily removed proton acceptor in organic synthesis . The anhydrous salt is especially basic. [ 5 ] Some of the reactions are listed below:
Tripotassium phosphate can be used in foods as a buffering agent , emulsifying agent , and for nutrient fortification. It can serve as a sodium-free substitute for trisodium phosphate . The ingredient is most common in dry cereals but is also found in meat, sauces, and cheeses. [ 10 ] | https://en.wikipedia.org/wiki/Tripotassium_phosphate |
Tripping pipe (or "Making a round trip" or simply "Making a trip") is the physical act of pulling the drill string out of the wellbore and then running it back in. This is done by physically breaking out or disconnecting (when pulling out of the hole) every other 2 or 3 joints of drill pipe at a time (called a stand ) and racking them vertically in the derrick . When feasible the driller will start each successive trip on a different "break" so that after several trips fresh pipe dope will have been applied (when running back in the hole) to every segment of the drill string.
The most typical reason for tripping pipe is to replace a worn-out drill bit . Though there are many problems that occur to warrant the tripping of pipe. Downhole tools such as MWD (measurement while drilling), LWD (logging while drilling) or mud motors break down quite often. Another common reason for tripping is to replace damaged drill pipe. It is important to get the pipe out of the wellbore quickly and safely before it can snap.
Drill bits wear and tear like most any other piece of equipment. Once a bit becomes too worn to drill at an adequate rate or make a full-gauge hole, or if the bearings are thought to be near failure, a trip is undertaken to replace the bit. A trip is not considered a bit trip when the purpose of replacing the bit is to change sizes. This is only done when the crew "sets surface, intermediate or longstring" as appropriate.
A fishing trip is when a crew is forced to trip pipe to retrieve loose items in the wellbore . This can result from something being dropped in the hole, i.e. a tool, that would cause damage to the bit if the crew attempted to drill with it on bottom.
Another major cause is known as a "twist off". Twisting off is when the drill string parts by failing catastrophically under the torsional stress. This may happen if the drill string below is pinched in the wellbore, or as the result of a structural weakening of the pipe caused by a washout or a crack in a threaded connection member.
When pipe snaps or a part of the bit breaks off, the crew has to recover all of the separated items from the wellbore. Recovering snapped pipe usually involves placing a specialized tool (an "overshot") with grips set inside of it over the broken pipe in an attempt to capture it. The grip works in a manner similar to Chinese fingercuffs . Sometimes the jagged top of the fish must be milled back to a round outside shape before the overshot can slip over it. The overshot contains a packoff device to make a pressure seal so circulation can be reestablished through the bit to facilitate recovery of the fish. For a broken bit, a magnet is commonly used to remove all of the broken parts.
A cracked pipe can lead to a broken string. Extra care is taken when tripping for one so that too much pull does not cause the cracked pipe to snap. Cracked pipes (i.e., washouts) are usually noticed by a sudden drop in pressure. The crew will usually pump "fastline" (small lengths of manila rope taken from unraveled catline) down the drill string to make a temporary plug and time the pressure to see when it rises back to normal. This enables the crew to know how far down to expect the cracked pipe to be within a few stands; also strands of these rope segments may be seen at the point of washout. Most trips for a cracked pipe are not complete trips like a fishing trip or a bit trip. These can be as simple as only going a few stands down, to pulling the drill collars.
Logging of the open hole may take place at various depths while drilling, and almost always at the end of the drilling operation. The drill string will be removed from the wellbore to allow a logging crew to conduct a survey of the well. After the logging is completed at total depth, the crew will run the drill string back into the well and then proceed to lay it down when coming out of the hole prior to installing the final set of casing (the "production casing").
These trips are routinely expected by the crew. Setting surface occurs after the wellbore is drilled to the predetermined surface depth (e.g., after drilling below fresh water strata). The crew will remove the entire drill string to allow surface casing to be emplaced. The procedure is similar for setting intermediate, only that it typically involves a much longer drill string to be removed. Setting longstring is usually a one time operation combining both surface and intermediate casing. This saves the time of only having to undertake one pipe trip as opposed to two pipe trips. | https://en.wikipedia.org/wiki/Tripping_(pipe) |
A triptych ( / ˈ t r ɪ p t ɪ k / TRIP -tik ) is a work of art (usually a panel painting ) that is divided into three sections, or three carved panels that are hinged together and can be folded shut or displayed open. It is therefore a type of polyptych , the term for all multi-panel works. The middle panel is typically the largest and it is flanked by two smaller related works, although there are triptychs of equal-sized panels. The form can also be used for pendant jewelry.
Beyond its association with art, the term is sometimes used more generally to connote anything with three parts, particularly if integrated into a single unit. [ 1 ]
The word triptych was formed in English by compounding the prefix tri- with the word diptych . [ 2 ] Diptych is borrowed from the Latin diptycha , which itself is derived from the Late Greek δίπτυχα ( díptycha ) ' pair of writing tablets ' . δίπτυχα is the neuter plural of δίπτυχος ( díptychos ) ' double-folded ' . [ 3 ]
The triptych form appears in early Christian art, and was a popular standard format for altar paintings from the Middle Ages onwards. Its geographical range was from the eastern Byzantine churches to the Celtic churches in the west. During the Byzantine period, triptychs were often used for private devotional use, along with other relics such as icons. [ 4 ] Renaissance painters such as Hans Memling and Hieronymus Bosch used the form. Sculptors also used it. Triptych forms also allow ease of transport.
From the Gothic period onward, both in Europe and elsewhere, altarpieces in churches and cathedrals were often in triptych form. One such cathedral with an altarpiece triptych is Llandaff Cathedral . The Cathedral of Our Lady in Antwerp , Belgium, contains two examples by Rubens , and Notre Dame de Paris is another example of the use of triptych in architecture. The form is echoed by the structure of many ecclesiastical stained glass windows .
The triptych form's transportability was exploited during World War Two when a private citizens' committee in the United States commissioned painters and sculptors to create portable three-panel hinged altarpieces for use by Christian and Jewish U.S. troops for religious services. [ 5 ] By the end of the war, 70 artists had created 460 triptychs. Among the most prolific were Violet Oakley , Nina Barr Wheeler , and Hildreth Meiere . [ 6 ]
The triptych format has been used in non-Christian faiths, including, Judaism, Islam, and Buddhism. For example: the triptych Hilje-j-Sherif displayed at the National Museum of Oriental Art , Rome, Italy, and a page of the Qur'an at the Museum of Turkish and Islamic Arts in Istanbul, Turkey, exemplify Ottoman religious art adapting the motif. [ 7 ] Likewise, Tibetan Buddhists have used it in traditional altars. [ 8 ]
Although strongly identified as a religious altarpiece form, triptychs outside that context have been created, some of the best-known examples being works by Max Beckmann and Francis Bacon . When Bacon's 1969 triptych, Three Studies of Lucian Freud , was sold in 2013 for $142.4 million, [ 9 ] it was the highest price ever paid for an artwork at auction at that time. [ 10 ] That record was broken in May 2015 by $179.4 million for Pablo Picasso 's 1955 painting Les Femmes d’Alger . [ 11 ]
A photographic triptych is a common style used in modern commercial artwork. The photographs are usually arranged with a plain border between them. The work may consist of separate images that are variants on a theme, or may be one larger image split into three. [ 12 ] [ 13 ] [ 14 ] | https://en.wikipedia.org/wiki/Triptych |
A tripwire is a passive triggering mechanism. Typically, a wire or cord is attached to a device for detecting or reacting to physical movement.
Such tripwires may be attached to one or more mines — especially fragmentation or bounding mines — in order to increase the area where triggering may occur. Trip wires are frequently used in booby traps — where either a tug on the wire, or the release of tension on it, will trigger the explosives.
Soldiers sometimes detect the presence of tripwires by spraying the area with Silly String . It will settle to the ground in areas where there are no wires; where wires are present, the "strings" will rest on the taut wires without triggering the explosive, due to the product's light weight. Its use in detecting tripwires was first discovered in 1993 by Sergeant First Class David B. Chandler, Chief Instructor of the United States Army 's Sapper Leader Course . That year it was introduced to students attending the course, and it was later used in combat for this purpose by U.S. troops in the Iraq War . [ 1 ] [ 2 ] [ 3 ]
Another detection method is the use of green line lasers to illuminate and thus expose trip and command wires. The bright laser beam reflects off the tripwire and can be seen by the user.
A tripwire may be installed in the vicinity of industrial equipment, such as a conveyor belt to enable workers to stop the equipment quickly. [ 4 ] These may also be called emergency stop pull-cords. [ 5 ] | https://en.wikipedia.org/wiki/Tripwire |
The triquetrum (derived from the Latin tri- ["three"] and quetrum ["cornered"]) was the medieval name for an ancient astronomical instrument first described by Ptolemy ( c. 90 – c. 168 ) in the Almagest (V. 12). Also known as Parallactic Rulers , it was used for determining altitudes of heavenly bodies. Ptolemy calls it a " parallactic instrument " and seems to have used it to determine the zenith distance and parallax of the Moon . [ 1 ] [ 2 ] [ self-published source? ]
The triquetrum performed the same function as the quadrant and was devised to overcome the difficulty of graduating arcs and circles. It consisted of a vertical post with a graduated scale and two pivoted arms hinged at the top and bottom, the upper arm carrying sights. The two arms were joined so that their ends could slide. As a person sighted along the upper arm, the lower one changed its angle. By reading the position of the lower rod, in combination with the vertical length, the zenith distance (or, alternatively, the altitude ) of a celestial object could be calculated. [ 1 ] [ 3 ]
The triquetrum was one of the most popular astronomical instruments until the invention of the telescope, it could measure angles with a better precision than the astrolabe . [ 2 ] Copernicus describes its use in the fourth book of the De revolutionibus orbium coelestium (1543) under the heading " Instrumenti parallactici constructio ." [ 2 ] The instrument was also used by Tycho Brahe [ 4 ] in the same century. | https://en.wikipedia.org/wiki/Triquetrum_(astronomy) |
Tris(2-phenylpyridine)iridium , abbreviated [Ir(ppy) 3 ] is the organoiridium complex with the formula Ir(C 6 H 4 -C 5 H 4 N) 3 . The complex, a yellow-green solid, is a derivative of Ir 3+ bound to three monoanionic 2-pyridinylphenyl ligands . It is electroluminescent , emitting green light. The complex is observed with the facial stereochemistry, which is chiral.
The complex is prepared by cyclometalation reactions of 2-phenylpyridine and iridium trichloride , as represented by this idealized equation: [ 1 ] [ 2 ]
The complex and many analogues have been investigated for application in photoredox catalysis . Its excited state has a reduction potential of −2.14 V, nearly 1 V more negative than the reduction potential of excited [Ru(bipy) 3 ] 2+ . [ 3 ] | https://en.wikipedia.org/wiki/Tris(2-phenylpyridine)iridium |
Tris(4-bromophenyl)ammoniumyl hexachloroantimonate is the organic compound with the formula [(4-BrC 6 H 4 ) 3 N]SbCl 6 . [ 1 ] Commonly known as magic blue , it is the hexachloroantimonate salt of an amine radical cation . It is a blue solid that reacts with many solvents but is soluble in acetonitrile . The compound is a popular oxidizing agent in organic and organometallic chemistry , with a reduction potential of 0.67 V versus ferrocene /ferrocenium ( acetonitrile solution) or 0.70 V versus ferrocene /ferrocenium ( dichloromethane solution). [ 2 ]
The structure of the cation consists of a three-bladed propeller structure with a planar amine. It is nearly identical to the parent triphenylamine . The weakly coordinating anion is SbCl − 6 , which is octahedral. [ 3 ] | https://en.wikipedia.org/wiki/Tris(4-bromophenyl)ammoniumyl_hexachloroantimonate |
Tris((1-benzyl-4-triazolyl)methyl)amine (TBTA) is a tertiary amine containing the 1,2,3-triazole moiety. When used as a ligand, complexed to copper(I), it allows for quantitative, regioselective formal Huisgen 1,3-dipolar cycloadditions between alkynes and azides , in a variety of aqueous and organic solvents.
It is believed that the ligand promotes catalysis through the stabilization of the copper(I)-oxidation state, while still allowing for the catalytic cycle of the CuAAC reaction to proceed.
Single crystal X-ray diffraction of the Cu(I) complex of tris((1-benzyl-4-triazolyl)methyl)amine revealed an unusual dinuclear dication with one triazole unit bridging two metal centers, and is an effective catalyst for the 'click' cycloaddition reaction. The structure of the complex of TBTA with Cu(II) in the crystalline state is trigonal bipyramidal and can be reduced to the active 'click' catalyst form by sodium ascorbate, copper metal, or other reducing agents.
In the literature, it has been gaining widespread use as a biochemical tool for the tagging of proteins and enzymes. The compound is now commercially available through Sigma-Aldrich and Invitrogen. It may be prepared by the click reaction between tripropargylamine and benzyl azide : [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Tris(benzyltriazolylmethyl)amine |
Tris(bipyridine)ruthenium(II) chloride is the chloride salt coordination complex with the formula [Ru(bpy) 3 ]Cl 2 . This polypyridine complex is a red crystalline salt obtained as the hexahydrate , although all of the properties of interest are in the cation [Ru(bpy) 3 ] 2+ , which has received much attention because of its distinctive optical properties. The chlorides can be replaced with other anions , such as PF 6 − .
This salt is prepared by treating an aqueous solution of ruthenium trichloride with 2,2'-bipyridine . In this conversion, Ru(III) is reduced to Ru(II), and hypophosphorous acid is typically added as a reducing agent. [ 1 ] [Ru(bpy) 3 ] 2+ is octahedral, containing a central low spin d 6 Ru(II) ion and three bidentate bpy ligands. The Ru-N distances are 2.053(2), shorter than the Ru-N distances for [Ru(bpy) 3 ] 3+ . [ 2 ] The complex is chiral, with D 3 symmetry . It has been resolved into its enantiomers . In its lowest lying triplet excited state the molecule is thought to attain lower C 2 symmetry, as the excited electron is localized primarily on a single bipyridyl ligand. [ 3 ] [ 4 ]
[Ru(bpy) 3 ] 2+ absorbs ultraviolet and visible light. Aqueous solutions of [Ru(bpy) 3 ]Cl 2 are orange due to a strong MLCT absorption at 452 ± 3 nm ( extinction coefficient of 14,600 M −1 cm −1 ). Further absorption bands are found at 285 nm corresponding to ligand centered π * ← π transitions and a weak transition around 350 nm (d-d transition). [ 5 ] Light absorption results in formation of an excited state have a relatively long lifetime of 890 ns in acetonitrile [ 6 ] and 650 ns in water. [ 6 ] The excited state relaxes to the ground state by emission of a photon or non-radiative relaxation. The quantum yield is 2.8% in air-saturated water at 298 K and the emission maximum wavelength is 620 nm. [ 7 ] The long lifetime of the excited state is attributed to the fact that it is triplet , whereas the ground state is a singlet state and in part due to the fact that the structure of the molecule allows for charge separation. Singlet-triplet transitions are forbidden and therefore often slow .
Like all molecular excited states, the triplet excited state of [Ru(bpy) 3 ] 2+ has both stronger oxidizing and reducing properties than its ground state. This situation arises because the excited state can be described as an Ru 3+ complex containing a bpy •− radical anion as a ligand. Thus, the photochemical properties of [Ru(bpy) 3 ] 2+ are reminiscent of the photosynthetic assembly , which also involves separation of an electron and a hole . [ 8 ]
[Ru(bpy) 3 ] 2+ has been examined as a photosensitizer for both the oxidation and reduction of water. Upon absorbing a photon, [Ru(bpy) 3 ] 2+ converts to the aforementioned triplet state, denoted [Ru(bpy) 3 ] 2+ *. This species transfers an electron, located on one bpy ligand, to a sacrificial oxidant such as peroxodisulfate (S 2 O 8 2− ). The resulting [Ru(bpy) 3 ] 3+ is a powerful oxidant and oxidizes water into O 2 and protons via a catalyst . [ 9 ] Alternatively, the reducing power of [Ru(bpy) 3 ] 2+ * can be harnessed to reduce methylviologen , a recyclable carrier of electrons, which in turn reduces protons at a platinum catalyst. For this process to be catalytic, a sacrificial reductant, such as EDTA 4− or triethanolamine is provided to return the Ru(III) back to Ru(II).
Derivatives of [Ru(bpy) 3 ] 2+ are numerous. [ 10 ] [ 11 ] Such complexes are widely discussed for applications in biodiagnostics, photovoltaics and organic light-emitting diode , but no derivative has been commercialized. Application of [Ru(bpy) 3 ] 2+ and its derivatives to fabrication of optical chemical sensors is arguably one of the most successful areas so far. [ 12 ]
Photoredox catalysis exploits [Ru(bpy) 3 ] 2+ as a sensitizer as a strategy for organic synthesis. Many analogues of [Ru(bpy) 3 ] 2+ are employed as well. These transformations exploit the redox properties of [Ru(bpy) 3 ] 2+ * and its reductively quenched derivative [Ru(bpy) 3 ] + . [ 13 ] [ 14 ] [ 15 ] [ 16 ]
Metal bipyridine as well as related phenanthroline complexes are generally bioactive, as they can act as intercalating agents . | https://en.wikipedia.org/wiki/Tris(bipyridine)ruthenium(II)_chloride |
Tris(cyclooctatetraene)triiron or Fe 3 (COT) 3 , also referred to as the Lavallo- Grubbs compound (after its discoverers [ 1 ] ) is an organoiron compound with the formula Fe 3 (C 8 H 8 ) 3 . It is a pyrophoric, black crystalline solid, which is insoluble in common organic solvents.The compound represents a rare example of a hydrocarbon analogue of the well-known Triiron dodecacarbonyl (Fe 3 (CO) 12 ), originally prepared by Dewar and Jones in the early 20th century. [ 2 ]
Lavello and Grubbs discovered the compound unexpectedly when trying to prepare noncarbonyl, low coordinate, Fe(0) complexes of N-heterocyclic carbenes (NHCs). They found that reactions of Fe(COT) 2 and the NHC, 1,3-bis(2,4,6-trimethylphenyl)-4,5-dihydroimidazol-2-ylidene (SIMes), produced tetrametallic, Fe(I)-Fe(0) mixed valent NHC-COT complexes. In an attempt to characterize intermediates of the unusual transformation, they employed the more sterically hindered NHC, 1,3-bis(2,6-diisopropylphenyl)-4,5-dihydroimidazol-2-ylidene (SIPr) (with Dipp substituents). [ 1 ]
In benzene , the Dipp substituted NHC reacts with Fe(COT) 2 to produce large black rhomboidal crystals of tris(cyclooctatetraene)triiron over 24 h at room temperature. Notably, the reaction was found to occur with catalytic amounts of NHC (10 mol%) yielding 67% of Fe 3 (COT) 3 after 24 h ( turn over number =9.5). The synthesis is optimized when the reaction is conducted at 45 °C, yielding 95% conversion to the tris(cyclooctatetraene)triiron cluster. They also highlighted that heating Fe(COT) 2 in benzene without any NHC to 100 °C for 24 h forms trace amounts of Fe 3 (COT) 3 , but also large amounts of iron metal . Unsurprisingly, elemental analysis of the cluster affirms a 1:1 Fe:COT ratio. [ 1 ]
The formation of Fe 3 (COT) 3 from Fe(COT) 2 has been calculated to be slightly exothermic(15 kcal/mol). [ 3 ]
Other NHCs lead to other unique mixed NHC-COT low valent iron complexes. Lavallo and Grubbs rationalize the transformation by emphasizing the capacity of NHCs to catalytically induce the formation of metal-metal bonds , [ 4 ] where the steric hindrance of the NHC is essential, in particular, for the lability of the NHC (in coordination and dissociation) in the cycle. The bulky NHC is proposed to prevent reduction of COT by a bimetallic [(L)Fe 2 (COT) 2 ] intermediate, where steric constraints block the bonding hapticity required to ligate a reduced form of COT. Another possibility put forward is that reduction of COT occurs only following coordination by a second carbene in the case of SIMes during the catalytic cycle. The sterically hindered NHC prevents such a transformation from occurring. [ 5 ]
The discoverers were reluctant to assert an oxidation state of the iron centers in the compound, instead deferring the details of the electronic structure to computational studies. [ 1 ]
The crystal structure reveals that the three iron centers arrange in an equilateral triangle (nearly ideal; Fe1 = 59.67°, Fe2 = 60.15°, and Fe3 = 60.18°) The corresponding bond lengths are similar to one another, (Fe1–Fe2 = 2.829 Å, Fe1–Fe3 = 2.815 Å, and Fe2–Fe3 = 2.830 Å), and reflective of Fe-Fe single bonds. [ 10 ] As a trinuclear cluster, it would be thought to have a stable 48-electron closed-shell configuration (24 electrons from the three iron atoms and 24 electrons from the three COT rings). [ 11 ] [ 12 ] [ 13 ]
In the original depiction, each COT ligand acts as an η 3 and η 5 donor, and thus, some degree of π-allylic and pentadienyl bonding modes can be inferred – though the degree of metal-to-ligand electron transfer is uncertain. [ 14 ] [ 15 ] Computational models suggest the binding mode to lie between η 3 and η 5 , as small shifts in geometry make each mode effectively equivalent (see section on fluxional behavior). Furthermore, DFT calculations with the BLYP functional using a TZP basis set for iron and DZP for carbon and hydrogen estimate a Hirshfeld charge of 0.08 on the iron centers (and Voronoi deformation density of 0.00). Interestingly, all of the bond orders of the C-C ring lie between 1.26 and 1.33, sharply contrasting the discrete single and double bonds of free cyclooctatetraene , or COT complexes with non-bound olefins. [ 13 ] [ 16 ]
Doubly reduced COT (dianion) [ 17 ] is known to adopt a planar (aromatic) conformation to metal centers, which is not observed in Fe 3 (COT) 3 . However, arguments also exist that such conformations are more related to binding efficiency than aromaticity. [ 18 ]
In computational studies (BP86), when Fe 3 (C 8 H 8 ) 3 is optimized as a singlet (gas phase), the iron centers are arranged in an ideal equilateral triangle, as experimentally observed in the crystal structure. In such an electronic configuration, each iron atom achieves an 18-electron configuration through pseudo η 5 and η 3 coordination to alternating COT ligands. However, if the compound is optimized as a triplet structure, the iron centers instead are a scalene triangle , featuring significant Jahn-Teller distortions . [ 3 ]
Additional NBO analysis of the singlet structure reveals Wiberg Bond Indices of 0.22 for the Fe-Fe bonds, closely reminiscent of that of D 3h Fe 3 (CO) 12 (0.18). [ 3 ] [ 19 ]
The V conformation of COT has an angle at 135° and is thought to be highly stabilized via bonding with the iron atoms (in free COT, this conformation is disfavored by approximately 36 kcal/mol). [ 13 ]
Fascinatingly, in benzene solution, 1 H NMR reveals a single broadened resonance with a chemical shift at -3.15 ppm. This suggests that the cyclooctatetraene ligands are highly fluxional and some degree of paramagnetism . [ 1 ]
COT is known to be a highly fluxional ligand in other compounds too, such compounds being deemed “ring-whizzers” (like the related ( cyclooctatetraene)iron tricarbony l). [ 20 ] [ 21 ]
The conformational fluxionality is supported by computational studies which show very low barriers to COT rotation (on the scale of 1.4 kcal/mol) and rocking (0.1 kcal/mol). The transformation from the C 3h singlet conformation to the triplet C 2v conformation have been calculated to be nearly isoenergetic, driving the possibility of the singlet state existing in equilibrium with the triplet state- an explanation for the observation of paramagnetic NMR resonances at ambient temperatures. [ 13 ]
The compound is highly reactive and pyrophoric, self-igniting in air. [ 1 ] The lack of reactivity studies may be in part sourced from its very low solubility in organic solvents. However, it may be able to find use as a specialized source of reactive low-valent iron.
Computational studies have estimated COT dissociation from Fe 3 (COT) 3 to be 57 kcal/mol uphill, which would not be readily accessible at room temperature in solution. [ 13 ]
With analogy to Fe 3 (CO) 12 , [ 22 ] the compound could potentially be susceptible to Fe-Fe bond homolysis via photoexcitation.
At the time of discovery, it was the only homoleptic trimetallic non-carbonyl cluster featuring hydrocarbon ligands. An isolobal analogy [ 23 ] can be made with the related Fe 3 (CO) 10 (μ-CO) 2 [ 24 ] cluster first prepared by Jones and Dewar. [ 2 ] [ 19 ] [ 1 ]
Alternatively, the compound could be compared to ferrocene. In this interpretation, each iron fragment bears an η 3 allyl and η 5 pentadienyl ligand as depicted. Under Green and Parkin's covalent bond classification method, this would yield LX and L 2 X respectively. Then additionally, the iron centers donate a pair of electrons into an adjacent empty iron orbital as an adduct (donor-acceptor pairs L and Z type), to overall yield ML 3 X 4 (18 electrons). [ 25 ] In fact, the bond orders in ferrocene and Fe3(COT)3 are reported to be very similar. [ 13 ]
In fact, Fe 3 (CO) 12 and the group 5 analogues, Ru 3 (CO) 12 and Os 3 (CO) 12 are also known to feature highly fluxional CO ligands in solution (and even in the solid state). [ 26 ] [ 27 ] [ 28 ]
Hypoelectronic derivatives (M=Ti, Cr, V, Mn) of Fe 3 (C 8 H 8 ) 3 would be predicted to have metal multiple bonds. Some somewhat related compounds, notably, Ti 2 (C 8 H 8 ) 3 [ 29 ] [ 30 ] [ 31 ] and Cr 2 (C 8 H 8 ) 3 [ 29 ] [ 32 ] have been experimentally isolated. | https://en.wikipedia.org/wiki/Tris(cyclooctatetraene)triiron |
Tris(dimethylamino)aluminium dimer , formally bis(μ-dimethylamino)tetrakis(dimethylamino)dialuminium, is an amide complex of aluminium . This compound may be used as a precursor to other aluminium complexes.
Commercially available, this compound may be prepared from lithium dimethylamide and aluminium trichloride . [ 2 ]
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Tris(dimethylamino)aluminium_dimer |
Tris( tert -butoxy)silanethiol is a silicon compound containing three tert -butoxy groups and a rare Si–S–H functional group . This colourless compound serves as a hydrogen donor in radical chain reactions . It was first prepared by alcoholysis of silicon disulfide and purified by distillation: [ 1 ]
Since 1962 it was thoroughly studied including its acid-base properties [ 2 ] [ 3 ] and coordination chemistry with metal ions. It coordinates to metal ions via the sulfur and oxygen donor atoms. [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] | https://en.wikipedia.org/wiki/Tris(tert-butoxy)silanethiol |
Carbonyl hydrido tris(triphenylphosphine)rhodium(I) [Carbonyl(hydrido)tris(triphenylphosphane)rhodium(I)] is an organorhodium compound with the formula [RhH(CO)(PPh 3 ) 3 ] (Ph = C 6 H 5 ). It is a yellow, benzene-soluble solid, which is used industrially for hydroformylation . [ 1 ]
[RhH(CO)(PPh 3 ) 3 ] was first prepared by the reduction of [RhCl(CO)(PPh 3 ) 2 ] , e.g. with sodium tetrahydroborate , or triethylamine and hydrogen, in ethanol in the presence of excess triphenylphosphine :
It can also be prepared from an aldehyde, rhodium trichloride and triphenylphosphine in basic alcoholic media. [ 2 ]
The complex adopts a trigonal bipyramidal geometry with trans CO and hydrido ligands, resulting in pseudo -C 3v symmetry . The Rh-P, Rh-C, and Rh-H distances are 2.32, 1.83, and 1.60 Å, respectively. [ 3 ] [ 4 ] This complex is one of a small number of stable pentacoordinate rhodium hydrides.
This precatalyst was uncovered in attempts to use tris(triphenylphosphine)rhodium chloride as a hydroformylation catalyst. It was found that the complex would quickly carbonylate and that the catalytic activity of the resulting material was enhanced by a variety of additives but inhibited by halides. This inhibition did not occur in the presence of base, suggesting that the hydrido-complex represented the catalytic form of the complex. [ 5 ]
[RhH(CO)(PPh 3 ) 3 ] is a catalyst for the selective hydroformylation of 1-olefins to produce aldehydes at low pressures and mild temperatures. The selectivity for n-aldehydes increases in the presence of excess PPh 3 and at low CO partial pressures. [ 1 ] The first step in the hydroformylation process is the dissociative substitution of an alkene for a PPh 3 . The migratory insertion of this 18-electron complex can result in either a primary or secondary rhodium alkyl. This step sets the regiochemistry of the product, however it is rapidly reversible. The 16-electron alkyl complex undergoes migratory insertion of a CO to form the coordinately unsaturated acyl. This species once again gives an 18-electron acyl complex. [ 6 ] The last step involves β-H elimination via hydrogenolysis which results in the cleavage of the aldehyde product and regeneration of the rhodium catalyst. | https://en.wikipedia.org/wiki/Tris(triphenylphosphine)rhodium_carbonyl_hydride |
Tris-buffered saline ( TBS ) is a buffer used in some biochemical techniques to maintain the pH within a relatively narrow range. Tris (with HCl) has a slightly alkaline buffering capacity in the 7–9.2 range. The conjugate acid of Tris has a pK a of 8.07 at 25 °C. The pK a declines approximately 0.03 units per degree Celsius rise in temperature. This can lead to relatively dramatic pH shifts when there are shifts in solution temperature. Sodium chloride concentration may vary from 100 to 200 mM, tris concentration from 5 to 100 mM and pH from 7.2 to 8.0. A common formulation of TBS is 150 mM NaCl, 50 mM Tris-HCl, pH 7.6. TBS can also be prepared by using commercially made TBS buffer tablets or pouches. [ 1 ]
TBS is isotonic and non-toxic. It can be used to dilute substances used in laboratory experiments. Additives can be used to add to a compound's functionality.
TBS is often used in immuno-blotting for both membrane washing and antibody dilution. [ 2 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Tris-buffered_saline |
In geometry , given a triangle ABC , there exist unique points A´ , B´ , and C´ on the sides BC , CA , AB respectively, such that: [ 1 ]
This is point X 369 in Clark Kimberling's Encyclopedia of Triangle Centers . [ 2 ] Uniqueness and a formula for the trilinear coordinates of X 369 were shown by Peter Yff late in the twentieth century. The formula involves the unique real root of a cubic equation . [ 2 ]
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trisected_perimeter_point |
Trish Kerin is an Australian safety expert, engineer, and was director of the Institution of Chemical Engineers (IChemE), [ 1 ] science communicator, and one of the Science Technology Australia, Superstars of STEM 2023-2024 cohort. [ 2 ]
Kerin graduated with honours in mechanical engineering at RMIT in 1994. [ 3 ] Following graduation, Kerin worked for several years in project management, operational and safety roles for the gas, chemical and oil industries. [ 4 ]
Kerin has been a board member of the Australian National Offshore Petroleum Safety and Environmental Management Authority. She is a Chartered Engineer, registered Professional Process Safety Engineer, as well as a Fellow of IChemE, Engineers Australia and a senior member of the American Institute of Chemical Engineers. Kerin also holds a diploma in OHS, as well as a Master of Leadership and is a Graduate of the Australian Institute of Company Directors.
Kerin is the director of the IChemE Safety Centre, and leads a team that helps organisations share and learn about process safety. Kerin uses her engineering experience and leadership to help organisations improve process safety outcomes. [ 4 ]
Kerin's work involves safety and risk minimisation in the workplace. She commented, in The Chemical Engineer publication,
“People have a right to stay safe, no matter where they are. As chemical engineers address our global challenges and pivot our technologies to deliver a low-carbon future, all those engaged in process safety will be a crucial component in minimising the risk of operating in new fields.” [ 5 ]
Kerin is the author of two books, " The Platypus Philosophy ", on how to identify and manage weak signals, in safety processing. [ 6 ] The second book is " Lets talk about your leadership ", learning through the art of storytelling. [ 7 ]
Select peer-reviewed publications include:
Kerin, T. (2016) The evolution of process safety standards and legislation following landmark events—what have we learnt? Process Safety Progress 35 (2), 165–170–17. [ 8 ]
Kerin, T. (2018) Accounting for hindsight bias: improving learning through interactive case studies. Loss Prevention Bulletin. 264: 17. [ 9 ]
Kerin, T. (2020) Taming the wild river rapids: How process safety can apply outside the process industries. Process safety progress 39 (1), e12088. [ 10 ]
Kerin was interviewed for Occham's Razor, on the ABC, about chemical safety and improving safety processes, with Tegan Taylor. They discussed how "everyone has a right to be safe at work", and Kerin shared a creative way to encourage spotting warning signs early, saving mistakes ahead of time. [ 11 ]
Kerin also hosts a podcast with Endeavour Business Media's Chemical Processing Magazine called "Process Safety with Trish and Traci", as well as regular column called "Stay Safe". [ 12 ] | https://en.wikipedia.org/wiki/Trish_Kerin |
A triskelion or triskeles is an ancient motif consisting either of a triple spiral exhibiting rotational symmetry or of other patterns in triplicate that emanate from a common center. The spiral design can be based on interlocking Archimedean spirals , or represent three bent human limbs. It occurs in artifacts of the European Neolithic and Bronze Ages with continuation into the Iron Age , especially in the context of the La Tène culture [ 1 ] and of related Celtic traditions. The actual triskeles symbol of three human legs is found especially in Greek antiquity , beginning in archaic pottery and continued in coinage of Classical Greece .
In the Hellenistic period , the symbol became associated with the island of Sicily , appearing on coins minted under Dionysius I of Syracuse beginning in c. 382 BCE . [ 2 ] It later appears in heraldry , and, other than in the flag of Sicily , came into use in the arms and flags of the Isle of Man (known in the Manx language as ny tree cassyn ' the three legs ' ). [ 3 ]
Greek τρισκελής ( triskelḗs ) means ' three-legged ' [ 4 ] from τρι- ( tri- ), ' three times ' [ 5 ] and σκέλος ( skelos ), ' leg ' . [ 6 ] While the Greek adjective τρισκελής ' three-legged ' ( e.g. of a table) is ancient, use of the term for the symbol is modern, introduced in 1835 by Honoré Théodoric d'Albert de Luynes as French triskèle , [ 7 ] and adopted in the spelling triskeles following Otto Olshausen (1886). [ 8 ] The form triskelion (as it were Greek τρισκέλιον [ 9 ] ) is a diminutive which entered English usage in numismatics in the late-19th century. [ 10 ] [ 11 ] The form consisting of three human legs (as opposed to the triple spiral) has also been called a " triquetra of legs", also triskelos or triskel . [ 12 ]
The triple spiral symbol, or three-spiral volute , appears in many early cultures: the first appeared in Malta (4400–3600 BCE); the second in the astronomical calendar of the megalithic tomb of Newgrange in Ireland built around 3200 BCE; [ 13 ] as well as on Mycenaean vessels. The Neolithic -era symbol of three conjoined spirals may have had triple significance similar to the imagery that lies behind the triskelion. [ 14 ] It is carved into the rock of a stone lozenge near the main entrance of the prehistoric Newgrange monument in what is now County Meath , Ireland. [ 13 ] It also appears on a 1st-century BCE dolmen tomb in Rathkenny in County Meath. [ 15 ]
There is also an example of a triskele on a stone fragment discovered in Gloucestershire , England, that, as of 2023, is held by the British Museum and thought to date from between the Neolithic period and the Bronze Age. [ 16 ]
The triskelion was a motif in the art of the Iron Age Celtic La Tène culture . [ 1 ]
The triskeles proper, composed of three human legs, is younger than the triple spiral found in decorations on Greek pottery , especially as a design shown on Hoplite shields and later Greek and Anatolian coinage . An early example is found on the Shield of Achilles in an Attic hydria of the late-6th century BCE. [ 17 ] It is found on coinage in Lycia and on staters of Pamphylia (at Aspendos in 370–333 BCE) and Pisidia . The meaning of the Greek triskeles is not recorded directly. The Duke of Luynes , in his 1835 study, noted the co-occurrence of the symbol with the eagle, the cockerel, the head of Medusa , Perseus , three crescent moons, three ears of corn, and three grains of corn. [ citation needed ] From this, he reconstructed a feminine divine triad that he identified with the triple goddess Hecate . [ 7 ] [ 18 ]
The triskeles was adopted as emblem by the rulers of Syracuse . It is possible that this usage is related with the Greek name of the island of Sicily , Τρινακρία ( Trinacria ) ' having three headlands ' . [ 19 ] The Sicilian triskeles is shown with the head of Medusa at the center. [ 20 ] The ancient symbol has been re-introduced in modern flags of Sicily since 1848. The oldest find of a triskeles in Sicily is a vase dated to the late-7th century BCE of which researchers speculated a Minoan-Mycenaean origin (and for which no proof has been given). [ 21 ]
Late examples of the triple spiral symbols are found in Iron Age Europe , carved in rock in Castro Culture settlements in Galicia , Asturias , and Northern Portugal . The symbol took on new meaning to Irish Celtic Christians before the 5th century CE as a symbol of the Trinity . [ citation needed ]
The triple spiral design is found as a decorative element in Gothic architecture . The three legs (triskeles) symbol is rarely found as a charge in late medieval heraldry , notably as the arms of the King of Mann ( Armorial Wijnbergen , c. 1280 ), and as canting arms in the city seal of the Bavarian city of Füssen (dated 1317).
The town of Dukla in Poland has used three hunting bugles arranged in triskelion shape as its symbol since the 16th century. [ 22 ] [ 23 ]
The triskeles was included in the design of the Army Gold Medal awarded to British Army majors and above who had taken a key part in the Battle of Maida (1806). [ 24 ] An early flag of Sicily , proposed in 1848, included the Sicilian triskeles or "Trinacria symbol". Later versions of Sicilian flags have retained the emblem, including the one officially adopted in 2000. The flag of the Isle of Man (1932) shows a heraldic design of a triskeles of three armoured legs.
The flag and coat of arms of the Bavarian town of Füssen , Germany, contain a triskele, [ 25 ] [ 26 ] as does the flag of the Russian autonomous region of Ust-Orda Buryat Okrug . [ 27 ]
In the Republic of Ireland the triskelion is displayed in hospitals and care centres to indicate that a patient is dying or has died. [ 28 ] [ 29 ] It is based on the historical use of the triskele in Celtic Ireland and it is used as an alternative to religious imagery. In this context, the three spirals represent the cycle of birth, life and death. [ 29 ]
The spiral is used by some polytheistic reconstructionist or neopagan groups. As a "Celtic symbol", it is used primarily by groups with a Celtic cultural orientation and, less frequently, can also be found in use by various eclectic or syncretic traditions such as Neopaganism . The spiral triskele is one of the primary symbols of Celtic Reconstructionist Paganism , used to represent a variety of triplicities in cosmology and theology; it is also a favoured symbol due to its association with Manannán mac Lir , a sea god within Irish mythology . [ 30 ]
Other uses of triskelion-like emblems include the logo for the Trisquel Linux distribution and the seal of the United States Department of Transportation . [ 31 ]
In the 1960s television programme Star Trek , members of the crew are forced to fight to the death on a triskelion playing surface in the episode The Gamesters of Triskelion .
A specific version of the triskele comprising three sevens has been adopted by neo-Nazis . In South Africa the Afrikaner Weerstandsbeweging (AWB), an Afrikaner nationalist , neo-Nazi organisation and political party (founded 1973), uses it as its symbol in place of a swastika . [ 32 ] The Blood & Honour neo-Nazi group also uses it. [ 33 ] The 27th SS Volunteer Division Langemarck 's shoulder strap cipher was a triskele (though not involving sevens). [ 34 ] Use of the triskele can be a prosecutable offence under German law, depending on the context in which it is used. [ 34 ]
Stylised versions of the Triskelion are commonly used as a symbol for BDSM .
The boric acid and triethylborane molecules are triskelion-shaped as seen in the images. The molecular point group of triskelion-shaped molecules is C 3h . [ 35 ] [ 36 ] The endocytic protein, clathrin , is triskelion-shaped, as well as the Ediacaran organism Tribrachidium . [ 37 ] | https://en.wikipedia.org/wiki/Triskelion |
A Trisonic Wind Tunnel ( TWT ) is a wind tunnel so named because it is capable of testing in three speed regimes – subsonic , transonic , and supersonic . The earliest known trisonic wind tunnel was dated to 1950 and was located in El Segundo, California before it closed in 2007. [ 1 ] [ 2 ] Other trisonic wind tunnels currently in operation are those located at NASA 's Marshall Space Flight Center , [ 3 ] [ 4 ] National Researach Council Canada's 1.5 m Trisonic Wind Tunnel Research Facility and the French-German Research Institute of Saint-Louis, [ 5 ] ISRO 's Vikram Sarabhai Space Centre (VSSC) in Thiruvananthapuram , and 1.2m Trisonic Wind Tunnel Facility at National Aerospace Laboratories . [ 6 ] [ 7 ]
The El Segundo Trisonic Wind Tunnel or North American Trisonic Wind Tunnel (NATWT) was a wind tunnel that was located in El Segundo, California . [ 8 ] It was built by North American Aviation in the 1950s. The tunnel had a maximum testing speed of Mach 3.5.
The NATWT was a blow-down type tunnel. In contrast to a continuous wind tunnel, a blow-down wind tunnel only provides air for short period. A continuous wind tunnel is driven by large fans and typically is only capable of subsonic speeds. Because a blow-down tunnel can build up pressure over a long period time, it can release air at faster speeds.
The NATWT used two Westinghouse motors, totaling 10,000 hp and consuming 8 megawatts of electricity, that drove two compressors . NATWT had its own substation to supply its high electrical demand. During the hot summer season, NATWT ran on a night schedule to balance its load with public air conditioning.
The compressors pressurized eight large spheres totaling 214,000 cubic feet (6,100 m 3 ). These spheres were connected to a single manifold that connected to a valve mechanism. When the valve was opened, the compressed air passed through the settling chamber, nozzle , and the test section, where instrumented aerodynamic models were mounted. A diffusing area that expanded in size slowed the air before it was exhausted vertically into the atmosphere. The diffuser area included a colander -like sieve made of 1-inch-thick (25 mm) steel to catch debris in the event of a catastrophic model failure .
The speed of the air was determined by the pressure of the spheres and the cross sectional area of the wind tunnel nozzle and diffuser. A smaller cross section in the nozzle caused the air to move faster. The NATWT could change the shape of the nozzle by operating a series of hydraulic pistons that would bend one-inch thick steel plates into the desired contour.
A distinguishing feature of the NATWT was the size of its test section [7 by 7 feet (2.1 m × 2.1 m)]. Unlike most blow-down wind tunnels, the NATWT test section had a so-called "walk in" test section that could accommodate very large aerodynamic models. Large models have several advantages:
Because of the "walk in" nature of NATWT, the tunnel was designed with the possibility that someone could accidentally be locked in the tunnel. Two large emergency safety switches were provided. One was located at the test section, the other at the diffuser area. When either of these safety switches were activated, the valve could not be opened.
Another feature of NATWT was the ability to visualize airflow over a model surface. By using optics built into the test section, an engineer could view air disturbance patterns as they were occurring during a test.
When Rockwell International purchased North American Aviation, it also gained ownership of the NATWT. The NATWT was then gifted to the University of California, Los Angeles (UCLA) in 1998, with the intention of NATWT becoming a university research facility. It became known as the Micro Craft Trisonic Wind Tunnel. In 2007, UCLA decided to close the trisonic wind tunnel, citing environmental issues. [ 9 ]
The last test to be conducted at TWT was completed on August 28, 2007. It was designated as test TWT 807. TWT was demolished in 2009. [ 1 ] | https://en.wikipedia.org/wiki/Trisonic_Wind_Tunnel |
Trisoxazolines (Often abbreviated TRISOX or TOX ) are a class of tridentate , chiral ligands composed of three oxazoline rings. Despite being neutral they are able to form stable complexes with high oxidation state metals, such as rare earths , [ 1 ] due to the chelate effect . The ligands have been investigated for molecular recognition and their complexes are used in asymmetric catalysts and polymerisation .
Trisoxazolines can either be synthesised directly, from suitable tripodal starting materials, or built up in a modular manner. [ 2 ] These approaches can be used to give ligands of differing symmetries, with the direct synthesis route giving homochiral ligands with C 3 rotational symmetry and the modular approach typically being used to give asymmetric compounds (C 1 symmetry), which are either heterochiral or possess a mix of both chiral and achiral groups. These differences in symmetry can significantly effect the coordination chemistry of the ligands [ 3 ] and the catalytic activity of their complexes, with C 3 symmetric ligands often being better for asymmetric catalysis . [ 4 ] [ 5 ]
Suitable tripodal compounds, such as trimesic acid [ 6 ] and nitrilotriacetic acid , [ 7 ] can be converted directly to trisoxazolines. The simplicity of this approach is beneficial, however it only allows a limited variety of structures to be produced, due to the limited range of available starting materials.
Modular synthesis allows for a more diverse range of structures, however the multi-step reactions can result in lower overall yields. In general synthesis involves the generation of separate mono‑oxazoline (typically halogenated) and bis-oxazoline units, which are then coupled using a strong base such as t BuLi [ 8 ] or KN(SiMe 3 ) 2 .
In addition to the inclusion of heterochirality, modular synthesis also allows for the synthesis of 'lopsided' structures which have application as scorpionate ligands . [ 9 ]
Trisoxazolines have been used for the copper catalysed Friedel–Crafts alkylation of indoles , largely with alkylidene malonates, with good yields and ee's reported. A number of interesting solvent effects have also been observed, including a relationship between enantioselectivity and the steric bulk of the solvent when using of alcohols [ 10 ] and a reversal of enantioselectivity when changing the reaction solvent from coordinating solvents to weakly coordinating solvents. [ 11 ]
Rare-earth complexes incorporating TRISOX ligands have been found to be highly effective catalysts for the polymerisation of α-alkenes and are notable for producing polyolefins with very high tacticities . [ 12 ] [ 13 ] Computational modelling of the polymerisation mechanism indicates that kinetic factors likely account for the high tacticity. [ 14 ]
Trisoxazolines baring a benzene backbone have been investigated for molecular recognition and have shown promising selectivity for the recognition of ammonium [ 15 ] alkylammonium and sugar species, [ 16 ] including examples of chiral recognition. | https://en.wikipedia.org/wiki/Trisoxazolines |
Tristar and Red Sector Incorporated ( TRSI ) is a demogroup which formed in 1990. It came about from the longest-running cooperation in scene history. [ 1 ] RSI existed from 1985, before being joined by the "T" later on. Evolving from the Commodore 64 to the Amiga and later to PC and various game console platforms - like the PlayStation , Xbox , Nintendo - and set-ups like Arduino, Android or Blu-ray, TRSI released a number of digital productions, dedicated to experimenting in phreaking or network alteration. [ 2 ] Its members were spread around the world and still contribute to computer scene art and code after more than 27 years of history.
Red Sector Incorporated (RSI) was founded with a focus on the Commodore 64 as a group for cracks , fixes, trainers , packs, intros and demos . The founders were three suppliers from Canada : Bill Best, Greg and Kangol Kid. After the initial formation in the spring of 1985, The Skeleton and Baudsurfer set up RSI's first domain, "The Pirates Ship" BBS the following summer, which eventually became the "Dawn of Eternity" BBS.
At the end of the year, Irata [ 3 ] and Mister Zeropage were asked to join the group and set up a European section in Germany , with Irata being the group's main trader, followed by additional importers in the United States . Slogans at the time included "No risk, no fun - Red Sector Number One" and "Red Sector - The Leading Force". [ 4 ] The Light Circle was a basis for several future European members of RSI, a coalition of Radwar Enterprises, Cracking Force Berlin and Flash Cracking Formation.
Red Sector Incorporated first released on the Amiga 1000 in 1986. During the summer, RSI decided to concentrate on the Amiga and formed an Amiga division.
In the beginning of 1987, Red Sector's Commodore 64 section became dormant, to bundle forces on the Amiga. At this time, RSI's first Amiga demo was coded by HQC and released to the Scene. It was followed by the second, "Twilight with Music" by Karsten Obarski . At the end of the year, a short-term cooperation was formed with Ghenna of Defjam, marking the first group cooperation on the Amiga. | https://en.wikipedia.org/wiki/Tristar_and_Red_Sector_Incorporated |
Trithorax-group proteins ( TrxG ) are a heterogeneous collection of proteins whose main action is to maintain gene expression . They can be categorized into three general classes based on molecular function:
plus other TrxG proteins not categorized in the first three classes. [ 1 ]
The founding member of TrxG proteins, trithorax (trx), was discovered ~1978 by Philip Ingham as part of his doctoral thesis while a graduate student in the laboratory of J.R.S. Whittle at the University of Sussex . [ 2 ] Histone-lysine N -methyltransferase 2A is the human homolog of trx. [ 2 ]
The table contains names of Drosophila TrxG members. Homologs in other species may have different names.
Trithorax-group proteins typically function in large complexes formed with other proteins. The complexes formed by TrxG proteins are divided into two groups:
histone-modifying complexes and ATP -dependent chromatin-remodeling complexes. The main function of TrxG proteins, along with polycomb group (PcG) proteins, is regulating gene expression. Whereas PcG proteins are typically associated with gene silencing , TrxG proteins are most commonly linked to gene activation . The trithorax complex activates gene transcription by inducing trimethylation of lysine 4 of histone H3 ( H3K4me3 ) at specific sites in chromatin recognized by the complex. [ 1 ] Ash1 domain is involved in H3K36 methylation. Trithorax complex also interacts with CBP (CREB binding protein) which is an acetyltransferase to acetylate H3K27 . [ 3 ] This gene activation is reinforced by acetylation of histone H4 . The actions of TrxG proteins are often described as 'antagonistic' of PcG proteins function. [ 4 ] Aside from gene regulation, evidence suggests TrxG proteins are also involved in other processes including apoptosis , cancer, and stress responses. [ 5 ] [ 6 ] [ 7 ]
During development, TrxG proteins maintain activation of required genes, particularly the Hox genes , after maternal factors are depleted. [ 8 ] This is accomplished by preserving the epigenetic marks, specifically H3K4me3, established by maternally-supplied factors. [ 9 ] TrxG proteins are also implicated in X-chromosome inactivation , which occurs during early embryogenesis . [ 10 ] As of 2011 [update] it is unclear whether TrxG activity is required in every cell during the entire development of an organism or only during certain stages in certain cell types. [ 11 ] | https://en.wikipedia.org/wiki/Trithorax-group_proteins |
Tritium (from Ancient Greek τρίτος (trítos) ' third ' ) or hydrogen-3 (symbol T or 3 H ) is a rare and radioactive isotope of hydrogen with a half-life of ~12.33 years. The tritium nucleus (t, sometimes called a triton ) contains one proton and two neutrons , whereas the nucleus of the common isotope hydrogen-1 ( protium ) contains one proton and no neutrons, and that of non-radioactive hydrogen-2 ( deuterium ) contains one proton and one neutron. Tritium is the heaviest particle-bound isotope of hydrogen. It is one of the few nuclides with a distinct name. The use of the name hydrogen-3, though more systematic, is much less common.
Naturally occurring tritium is extremely rare on Earth. The atmosphere has only trace amounts, formed by the interaction of its gases with cosmic rays . It can be produced artificially by irradiation of lithium or lithium-bearing ceramic pebbles in a nuclear reactor and is a low-abundance byproduct in normal operations of nuclear reactors.
Tritium is used as the energy source in radioluminescent lights for watches, night sights for firearms, numerous instruments and tools, and novelty items such as self-illuminating key chains. It is used in a medical and scientific setting as a radioactive tracer . Tritium is also used as a nuclear fusion fuel, along with more abundant deuterium , in tokamak reactors and in hydrogen bombs . Tritium has also been used commercially in betavoltaic devices such as NanoTritium batteries .
Tritium was first detected in 1934 by Ernest Rutherford , Mark Oliphant and Paul Harteck after bombarding deuterium with deuterons (deuterium nuclei). Deuterium is another isotope of hydrogen, which occurs naturally with an abundance of 0.015%. [ 2 ] [ 3 ] Their experiment could not isolate tritium, which was first accomplished in 1939 by Luis Alvarez and Robert Cornog , who also realized tritium's radioactivity. [ 4 ] [ 5 ] Willard Libby recognized in 1954 that tritium could be used for radiometric dating of water and wine . [ 6 ]
The half life of tritium is listed by the National Institute of Standards and Technology as 4,500 ± 8 days ( 12.33 ± 0.02 years ) [ 7 ] – an annualized rate of approximately 5.5% per year. Tritium decays into helium-3 by beta-minus decay as shown in this nuclear equation:
releasing 18.6 keV of energy in the process. The electron 's kinetic energy varies, with an average of 5.7 keV, while the remaining energy is carried off by the nearly undetectable electron antineutrino . Beta particles from tritium can penetrate only about 6.0 millimetres (0.24 in) of air, and they are incapable of passing through the dead outermost layer of human skin. [ 8 ] Because of their low energy compared to other beta particles, the amount of bremsstrahlung generated is also lower. The unusually low energy released in the tritium beta decay makes the decay (along with that of rhenium-187 ) useful for absolute neutrino mass measurements in the laboratory.
The low energy of tritium's radiation makes it difficult to detect tritium-labeled compounds except by using liquid scintillation counting .
Tritium is most often produced in nuclear reactors by neutron activation of lithium-6 . The release and diffusion of tritium and helium produced by the fission of lithium can take place within ceramics known as breeder ceramics . Production of tritium from lithium-6 in such breeder ceramics is possible with neutrons of any energy, though the cross section is higher when the incident neutrons have lower energy, reaching more than 900 barns for thermal neutrons . This is an exothermic reaction, yielding 4.8 MeV . [ 9 ] In comparison, fusion of deuterium with tritium releases about 17.6 MeV. For applications in proposed fusion energy reactors, such as ITER , pebbles consisting of lithium bearing ceramics including Li 2 TiO 3 and Li 4 SiO 4 , are being developed for tritium breeding within a helium-cooled pebble bed, also known as a breeder blanket. [ 10 ]
High-energy neutrons can also produce tritium from lithium-7 in an endothermic reaction, consuming 2.466 MeV. This was discovered when the 1954 Castle Bravo nuclear test produced an unexpectedly high yield. [ 11 ] Prior to this test, it was incorrectly assumed that 7 3 Li would absorb a neutron to become 8 3 Li , which would beta-decay to 8 4 Be , which in turn would decay to two 4 2 He nuclei on a total timeframe much longer than the duration of the explosion.
High-energy neutrons irradiating boron-10 , also occasionally produce tritium: [ 12 ]
A more common result of boron-10 neutron capture is 7 Li and a single alpha particle . [ 13 ]
Especially in pressurized water reactors which only partially thermalize neutrons, the interaction between relatively fast neutrons and the boric acid added as a chemical shim produces small but non-negligible quantities of tritium.
Tritium is also produced in heavy water-moderated reactors whenever a deuterium nucleus captures a neutron. This reaction has a small absorption cross section , making heavy water a good neutron moderator , and relatively little tritium is produced. Even so, cleaning tritium from the moderator may be desirable after several years to reduce the risk of its escaping to the environment. Ontario Power Generation 's "Tritium Removal Facility" is capable of processing up to 2,500 tonnes (2,500 long tons; 2,800 short tons) of heavy water a year, and it separates out about 2.5 kg (5.5 lb) of tritium, making it available for other uses. [ 14 ] CANDU reactors typically produce 130 grams (4.6 oz) of tritium per year, which is recovered at the Darlington Tritium Recovery Facility (DTRF) attached to the 3,512 MW electric Darlington Nuclear Generating Station in Ontario. The total production at DTRF between 1989 and 2011 was 42.5 kilograms (94 lb) – with an activity of 409 megacuries (15,100 PBq): an average of about 2 kilograms (4.4 lb) per year. [ 15 ]
Deuterium's absorption cross section for thermal neutrons is about 0.52 millibarn , whereas that of oxygen-16 ( 16 O) is about 0.19 millibarn and that of oxygen-17 ( 17 O) is about 240 millibarns. While 16 O is by far the most common isotope of oxygen in both natural oxygen and heavy water; depending on the method of isotope separation , heavy water may be slightly richer in 17 O and 18 O . Due to both neutron capture and (n, α ) reactions (the latter of which produce 14 C , an undesirable long-lived beta emitter, from 17 O) they are net "neutron consumers" and are thus undesirable in a moderator of a natural uranium reactor which needs to keep neutron absorption outside the fuel as low as feasible. Some facilities that remove tritium also remove (or at least reduce the content of) 17 O and 18 O, which can – at least in principle – be used for isotope labeling .
India, which also has a large fleet of pressurized heavy water reactors (initially CANDU technology but since indigenized and further developed IPHWR technology), also removes at least some of the tritium produced in the moderator/coolant of its reactors but due to the dual use nature of tritium and the Indian nuclear bomb program, less information about this is publicly available than for Canada.
Tritium is an uncommon product of the nuclear fission of uranium-235 , plutonium-239 , and uranium-233 , with a production of about one atom per 10 4 fissions. [ 16 ] [ 17 ] The main pathways of tritium production include ternary fission . The release or recovery of tritium needs to be considered in the operation of nuclear reactors , especially in the reprocessing of nuclear fuel and storage of spent nuclear fuel . The production of tritium is not a goal, but a side-effect. It is discharged to the atmosphere in small quantities by some nuclear power plants. [ 18 ] Voloxidation is an optional additional step in nuclear reprocessing that removes volatile fission products (such as all isotopes of hydrogen) before an aqueous process begins. This would in principle enable economic recovery of the produced tritium but even if the tritium is only disposed and not used, it has the potential to reduce tritium contamination in the water used, reducing radioactivity released when the water is discharged since tritiated water cannot be removed from "ordinary" water except by isotope separation.
Given the specific activity of tritium at 9,650 curies per gram (357 TBq/g), one TBq is equivalent to roughly 2.8 milligrams (0.043 gr).
In June 2016 the Tritiated Water Task Force released a report [ 21 ] on the status of tritium in tritiated water at Fukushima Daiichi nuclear plant , as part of considering options for final disposal of the stored contaminated cooling water. This identified that the March 2016 holding of tritium on-site was 760 TBq (equivalent to 2.1 g of tritium or 14 mL of pure tritiated water) in a total of 860,000 m 3 of stored water. This report also identified the reducing concentration of tritium in the water extracted from the buildings etc. for storage, seeing a factor of ten decrease over the five years considered (2011–2016), 3.3 MBq/L to 0.3 MBq/L (after correction for the 5% annual decay of tritium).
According to a report by an expert panel considering the best approach to dealing with this issue, " Tritium could be separated theoretically , but there is no practical separation technology on an industrial scale. Accordingly, a controlled environmental release is said to be the best way to treat low-tritium-concentration water." [ 22 ] After a public information campaign sponsored by the Japanese government, the gradual release into the sea of the tritiated water began on 24 August 2023 and is the first of four releases through March 2024. [ 23 ] The entire process will take "decades" to complete. [ 24 ] China reacted with protest. [ 25 ] [ 26 ] The IAEA has endorsed the plan. The water released is diluted to reduce the tritium concentration to less than 1500 Bq/L, far below the limit recommended in drinking water by the WHO. [ 27 ]
Tritium's decay product helium-3 has a very large cross section (5330 barns) for reacting with thermal neutrons , expelling a proton; hence, it is rapidly converted back to tritium in nuclear reactors . [ 28 ]
Tritium occurs naturally due to cosmic rays interacting with atmospheric gases. In the most important reaction for natural production, a fast neutron (which must have energy greater than 4.0 MeV [ 29 ] ) interacts with atmospheric nitrogen :
Worldwide, the production of tritium from natural sources is 148 peta becquerels per year. The global equilibrium inventory of tritium created by natural sources remains approximately constant at 2,590 petabecquerels. This is due to a fixed production rate, and losses proportional to the inventory. [ 30 ]
Tritium for American nuclear weapons was produced in special heavy water reactors at the Savannah River Site until their closures in 1988. With the Strategic Arms Reduction Treaty (START) after the end of the Cold War , the existing supplies were sufficient for the new, smaller number of nuclear weapons for some time.
225 kg (496 lb) of tritium was produced in the United States from 1955 to 1996. [ a ] Since it continually decays into helium-3, the total amount remaining was about 75 kg (165 lb) at the time of the report, [ 31 ] [ 11 ] and about 16 kg (35 lb) as of 2023. [ 32 ]
Tritium production was resumed with irradiation of rods containing lithium (replacing the usual control rods containing boron , cadmium , or hafnium ), at the reactors of the commercial Watts Bar Nuclear Plant from 2003 to 2005 followed by extraction of tritium from the rods at the Tritium Extraction Facility at the Savannah River Site beginning in November 2006. [ 33 ] [ 34 ] Tritium leakage from the rods during reactor operations limits the number that can be used in any reactor without exceeding the maximum allowed tritium levels in the coolant. [ 35 ]
Tritium has an atomic mass of 3.016 049 28 Da . Diatomic tritium ( T 2 or 3 H 2 ) is a gas at standard temperature and pressure . Combined with oxygen , it forms tritiated water ( 3 H 2 O ).
Compared to hydrogen in its natural composition on Earth, tritium has a higher melting point (20.62 K vs. 13.99 K), a higher boiling point (25.04 K vs. 20.27 K), a higher critical temperature (40.59 K vs. 32.94 K) and a higher critical pressure (1.8317 MPa vs. 1.2858 MPa). [ 36 ]
Tritium's specific activity is 9,650 curies per gram (3.57 × 10 14 Bq /g). [ 37 ]
Tritium figures prominently in studies of nuclear fusion due to its favorable reaction cross section and the large amount of energy (17.6 MeV) produced through its reaction with deuterium:
All atomic nuclei contain protons as their only charged particles. They therefore repel one another because like charges repel ( Coulomb's law ). However, if the atoms have a high enough temperature and pressure (for example, in the core of the Sun), then their random motions can overcome such repulsion, and they can come close enough for the strong nuclear force to take effect, fusing them into heavier atoms.
A tritium nucleus (triton), containing one proton and two neutrons, has the same charge as any hydrogen nucleus, and it experiences the same electrostatic repulsion when close to another nucleus. However, the neutrons in the triton increase the attractive strong nuclear force when close enough to another nucleus. As a result, tritium can fuse more easily with other light atoms, than ordinary hydrogen can.
The same is true, albeit to a lesser extent, of deuterium. This is why brown dwarfs ("failed" stars ) cannot fuse normal hydrogen, but they do fuse a small minority of deuterium nuclei.
Like the other isotopes of hydrogen , tritium is difficult to confine. Rubber, plastic, and some kinds of steel are all somewhat permeable. This has raised concerns that if tritium were used in large quantities, in particular for fusion reactors , it might contribute to radioactive contamination , though its short half-life should prevent significant long-term accumulation in the atmosphere.
The high levels of atmospheric nuclear weapons testing that took place prior to the enactment of the Partial Nuclear Test Ban Treaty proved to be unexpectedly useful to oceanographers. The high levels of tritium oxide introduced into upper layers of the oceans have been used in the years since then to measure the rate of mixing of the upper layers of the oceans with their lower levels.
Since tritium is a low energy beta (β) emitter , it is not dangerous externally (its β particles cannot penetrate the skin), [ 30 ] but it can be a radiation hazard if inhaled, ingested via food or water, or absorbed through the skin. [ 38 ] [ 39 ] [ 40 ] [ 41 ] [ 42 ]
Organisms can take up 3 1 H HO, as they would H 2 O. [ 43 ] Plants convert 3 1 H HO into organically bound tritium (OBT), and are consumed by animals. 3 1 H HO is retained in humans for around 12 days, with a small portion of it remaining in the body. [ 44 ] Tritium can be passed along the food chain as one organism feeds on another, though the metabolism of OBT is less understood than that of 3 1 H HO. [ 44 ] Tritium can incorporate to RNA and DNA molecules within organisms which can lead to somatic and genetic impacts. These can emerge in later generations. [ 45 ]
3 1 H HO has a short biological half-life in the human body of 7 to 14 days, which both reduces the total effects of single-incident ingestion and precludes long-term bioaccumulation of 3 1 H HO from the environment. [ 40 ] [ 46 ] The biological half-life of tritiated water in the human body, which is a measure of body water turn-over, varies with the season. Studies on the biological half-life of occupational radiation workers for free water tritium in a coastal region of Karnataka , India, show that the biological half-life in winter is twice that of the summer. [ 46 ] If tritium exposure is suspected or known, drinking uncontaminated water will help replace the tritium from the body. Increasing sweating, urination or breathing can help the body expel water and thereby the tritium contained in it. However, care should be taken that neither dehydration nor a depletion of the body's electrolytes results, as the health consequences of those things (particularly in the short term) can be more severe than those of tritium exposure.
Tritium has leaked from 48 of 65 nuclear sites in the US. In one case, leaking water contained 7.5 microcuries (280 kBq) of tritium per liter, which is 375 times the current EPA limit for drinking water, and 28 times the World Health Organization 's recommended limit. [ 47 ] This is equivalent to 0.777 nanograms per litre (5.45 × 10 −8 gr/imp gal) or roughly 0.8 parts per trillion .
The US Nuclear Regulatory Commission states that in normal operation in 2003, 56 pressurized water reactors released 40,600 curies (1,500,000 GBq) of tritium (maximum: 2,080 Ci (77,000 GBq); minimum: 0.1 Ci (3.7 GBq); average: 725 Ci (26,800 GBq)) and 24 boiling water reactors released 665 Ci (24.6 TBq) (maximum: 174 Ci (6,400 GBq); minimum: 0 Ci; average: 27.7 Ci (1,020 GBq)), in liquid effluents. [ 48 ] 40,600 Ci (1,500,000 GBq) of tritium weigh about 4.207 grams (0.1484 oz).
The legal limits for tritium in drinking water vary widely from country to country. Some figures are given below:
The American limit results in a dose of 4.0 millirems (or 40 micro sieverts in SI units ) per year per EPA regulation 40CFR141, and is based on outdated dose calculation standards of National Bureau of Standards Handbook 69 circa 1963. Four millirem per year is about 1.3% of the natural background radiation (~3 mSv). For comparison, the banana equivalent dose (BED) is set at 0.1 μSv, so the statutory limit in the US is set at 400 BED. Updated dose calculation standards based on International Commission on Radiological Protection Report 30 and used in the NRC Regulation 10CFR20 results in a dose of 0.9 millirem (9 μSv) per year at 740 Bq/L (20 nCi/L). [ 40 ]
Tritiation of drug candidates allows detailed analysis of their absorption and metabolism . [ 53 ] Tritium has also been used for biological radiometric assays, in a process akin to radiocarbon dating . For example, [ 3 H] retinyl acetate was traced through the bodies of rats. [ 54 ]
The beta particles from small amounts of tritium cause chemicals called phosphors to glow. This radioluminescence is used in self-powered lighting devices called betalights , which are used for night illumination of firearm sights, watches, exit signs , map lights, navigational compasses (such as current-use M-1950 U.S. military compasses ), knives and a variety of other devices. [ d ] As of 2000 [update] , commercial demand for tritium is 400 grams (0.88 lb) per year [ 11 ] and the cost is $30,000 per gram ($850,000/oz) [ 55 ] or more. [ 56 ]
Tritium is an important component in nuclear weapons; it is used to enhance the efficiency and yield of fission bombs and the fission stages of hydrogen bombs in a process known as " boosting " as well as in external neutron initiators for such weapons.
These are devices incorporated in nuclear weapons which produce a pulse of neutrons when the bomb is detonated to initiate the fission reaction in the fissionable core (pit) of the bomb, after it is compressed to a critical mass by explosives. Actuated by an ultrafast switch like a krytron , a small particle accelerator drives ions of tritium and deuterium to energies above the 15 keV or so needed for deuterium-tritium fusion and directs them into a metal target where the tritium and deuterium are adsorbed as hydrides . High-energy fusion neutrons from the resulting fusion radiate in all directions. Some of these strike plutonium or uranium nuclei in the primary's pit, initiating a nuclear chain reaction . The quantity of neutrons produced is large in absolute numbers, allowing the pit to quickly achieve neutron levels that would otherwise need many more generations of chain reaction, though still small compared to the total number of nuclei in the pit.
Before detonation, a few grams of tritium–deuterium gas are injected into the hollow " pit " of fissile material. The early stages of the fission chain reaction supply enough heat and compression to start deuterium–tritium fusion; then both fission and fusion proceed in parallel, the fission assisting the fusion by continuing heating and compression, and the fusion assisting the fission with highly energetic (14.1- MeV ) neutrons. As the fission fuel depletes and also explodes outward, it falls below the density needed to stay critical by itself, but the fusion neutrons make the fission process progress faster and continue longer than it would without boosting. Increased yield comes overwhelmingly from the increased fission. The energy from the fusion itself is much smaller because the amount of fusion fuel is much smaller. Effects of boosting include:
The tritium in a warhead is continually undergoing radioactive decay, becoming unavailable for fusion. Also, its decay product , helium-3, absorbs neutrons. This can offset or reverse the intended effect of the tritium, which was to generate many free neutrons, if too much helium-3 has accumulated. Therefore, boosted bombs need fresh tritium periodically. The estimated quantity needed is 4 grams (0.14 oz) per warhead. [ 11 ] To maintain constant levels of tritium, about 0.20 grams (0.0071 oz) per warhead per year must be supplied to the bomb.
One mole of deuterium-tritium gas contains about 3.0 grams (0.11 oz) of tritium and 2.0 grams (0.071 oz) of deuterium. In comparison, the 20 moles of plutonium in a nuclear bomb consists of about 4.5 kilograms (9.9 lb) of plutonium-239 .
Since tritium undergoes radioactive decay, and is also difficult to confine physically, the much larger secondary charge of heavy hydrogen isotopes needed in a true hydrogen bomb uses solid lithium deuteride as its source of deuterium and tritium, producing the tritium in situ during secondary ignition.
During the detonation of the primary fission bomb stage in a thermonuclear weapon ( Teller–Ulam staging ), the sparkplug , a cylinder of 235 U/ 239 Pu at the center of the fusion stage(s), begins to fission in a chain reaction, from excess neutrons channeled from the primary. The neutrons released from the fission of the sparkplug split lithium-6 into tritium and helium-4, while lithium-7 is split into helium-4, tritium, and one neutron. As these reactions occur, the fusion stage is compressed by photons from the primary and fission of the 238 U or 238 U/ 235 U jacket surrounding the fusion stage. Therefore, the fusion stage breeds its own tritium as the device detonates. In the extreme heat and pressure of the explosion, some of the tritium is then forced into fusion with deuterium, and that reaction releases even more neutrons.
Since this fusion process requires an extremely high temperature for ignition, and it produces fewer and less energetic neutrons (only fission, deuterium-tritium fusion, and 7 3 Li splitting are net neutron producers), lithium deuteride is not used in boosted bombs, but rather for multi-stage hydrogen bombs.
Tritium is an important fuel for controlled nuclear fusion in both magnetic confinement and inertial confinement fusion reactor designs. The National Ignition Facility (NIF) uses deuterium–tritium fuel, and the experimental fusion reactor ITER will also do so. The deuterium–tritium reaction is favorable since it has the largest fusion cross section (about 5.0 barns ) and it reaches this maximum cross section at the lowest energy (about 65 keV center-of-mass) of any potential fusion fuel. As tritium is very rare on earth, concepts for fusion reactors often include the breeding of tritium. During the operation of envisioned breeder fusion reactors, Breeding blankets , often containing lithium as part of ceramic pebbles, are subjected to neutron fluxes to generate tritium to complete the fuel cycle. [ 57 ]
The Tritium Systems Test Assembly (TSTA) was a facility at the Los Alamos National Laboratory dedicated to the development and demonstration of technologies required for fusion-relevant deuterium–tritium processing.
Tritium can be used in a betavoltaic device to create an atomic battery to generate electricity .
Tritium is used in various electron tubes, such as the Zellweger ZE22/3 glow tube . These devices contain a small amount of tritium to ionize the fill gas, typically a noble gas like neon or argon . This ionization ensures reliable and consistent operation by providing a steady current when a high voltage is applied, enhancing the device's performance and stability. The tritium is sealed within a glass envelope with two electrodes, one of which is coated with the radioactive material to create an ion path between the electrodes. [ 58 ]
Aside from chlorofluorocarbons , tritium can act as a transient tracer and can "outline" the biological, chemical, and physical paths throughout the world's oceans because of its evolving distribution. [ 59 ] Tritium has thus been used as a tool to examine ocean circulation and ventilation and, for such purposes, is usually measured in tritium units, where 1 TU is defined as 1 tritium atom per 10 18 hydrogen atoms, [ 59 ] equal to about 0.118 Bq/liter. [ 60 ] [ 61 ] [ 62 ] As noted earlier, nuclear tests, mainly in the Northern Hemisphere at high latitudes, throughout the late 1950s and early 1960s introduced lots of tritium into the atmosphere, especially the stratosphere . Before these nuclear tests, there were only about 3-4 kg of tritium on the Earth's surface; but these amounts rose by 2-3 orders of magnitude during the post-test period. [ 59 ] Some sources reported natural background levels were exceeded by about 1,000 TU in 1963 and 1964 and the isotope is used in the northern hemisphere to estimate the age of groundwater and construct hydrogeologic simulation models. [ 63 ] Estimated atmospheric levels at the height of weapons testing to approach 1,000 TU and pre-fallout levels of rainwater to be between 5 and 10 TU. [ 64 ] In 1963 Valentia Island Ireland recorded 2,000 TU in precipitation. [ 65 ]
While in the stratosphere (post-test period), the tritium interacted with and oxidized to water molecules and was present in much of the rapidly produced rainfall, making tritium a prognostic tool for studying the evolution and structure of the water cycle as well as the ventilation and formation of water masses in the North Atlantic. [ 59 ]
Bomb-tritium data were used from the Transient Tracers in the Ocean (TTO) program in order to quantify the replenishment and overturning rates for deep water located in the North Atlantic. [ 66 ]
Bomb-tritium also enters the deep ocean around the Antarctic. [ 67 ] Most of the bomb tritiated water (H 3 HO) throughout the atmosphere can enter the ocean through the following processes:
These processes make H 3 HO a great tracer for time scales of up to a few decades. [ 66 ]
Using the data from these processes for 1981, the 1-TU isosurface lies between 500 and 1,000 meters deep in the subtropical regions and then extends to 1,500–2,000 meters south of the Gulf Stream due to recirculation and ventilation in the upper portion of the Atlantic Ocean. [ 59 ] To the north, the isosurface deepens and reaches the floor of the abyssal plain which is directly related to the ventilation of the ocean floor over 10–20 year time-scales. [ 59 ]
Also evident in the Atlantic Ocean is the tritium profile near Bermuda between the late 1960s and late 1980s. There is a downward propagation of the tritium maximum from the surface (1960s) to 400 meters (1980s), which corresponds to a deepening rate of about 18 meters per year. [ 59 ] There are also tritium increases at 1,500 m depth in the late 1970s and 2,500 m in the middle of the 1980s, both of which correspond to cooling events in the deep water and associated deep water ventilation. [ 59 ]
From a study in 1991, the tritium profile was used as a tool for studying the mixing and spreading of newly formed North Atlantic Deep Water (NADW), corresponding to tritium increases to 4 TU. [ 66 ] This NADW tends to spill over sills that divide the Norwegian Sea from the North Atlantic Ocean and then flows to the west and equatorward in deep boundary currents. This process was explained via the large-scale tritium distribution in the deep North Atlantic between 1981 and 1983. [ 66 ] The sub-polar gyre tends to be freshened (ventilated) by the NADW and is directly related to the high tritium values (>1.5 TU). Also evident was the decrease in tritium in the deep western boundary current by a factor of 10 from the Labrador Sea to the Tropics , which is indicative of loss to ocean interior due to turbulent mixing and recirculation. [ 66 ]
In a 1998 study, tritium concentrations in surface seawater and atmospheric water vapor (10 meters above the surface) were sampled at the following locations: the Sulu Sea , Fremantle Bay , the Bay of Bengal , Penang Bay , and the Strait of Malacca . [ 68 ] Results indicated that the tritium concentration in surface seawater was highest at the Fremantle Bay (about 0.40 Bq/liter), which could be accredited to the mixing of runoff of freshwater from nearby lands due to large amounts found in coastal waters. [ 68 ] Typically, lower concentrations were found between 35 and 45 ° south, and near the equator . Results also indicated that (in general) tritium has decreased over the years (up to 1997) due to the physical decay of bomb tritium in the Indian Ocean . As for water vapor, the tritium concentration was about one order of magnitude greater than surface seawater concentrations (ranging from 0.46 to 1.15 Bq/L). [ 68 ] Therefore, the water vapor tritium is not affected by the surface seawater concentration; thus, the high tritium concentrations in the vapor were concluded to be a direct consequence of the downward movement of natural tritium from the stratosphere to the troposphere (therefore, the ocean air showed a dependence on latitudinal change). [ 68 ]
In the North Pacific Ocean , the tritium (introduced as bomb tritium in the Northern Hemisphere) spread in three dimensions. There were subsurface maxima in the middle and low latitude regions, which is indicative of lateral mixing (advection) and diffusion processes along lines of constant potential density ( isopycnals ) in the upper ocean. [ 69 ] Some of these maxima even correlate well with salinity extrema. [ 69 ] In order to obtain the structure for ocean circulation, the tritium concentrations were mapped on 3 surfaces of constant potential density (23.90, 26.02, and 26.81). [ 69 ] Results indicated that the tritium was well-mixed (at 6 to 7 TU) on the 26.81 isopycnal in the subarctic cyclonic gyre and there appeared to be a slow exchange of tritium (relative to shallower isopycnals) between this gyre and the anticyclonic gyre to the south; also, the tritium on the 23.90 and 26.02 surfaces appeared to be exchanged at a slower rate between the central gyre of the North Pacific and the equatorial regions. [ 69 ]
The depth penetration of bomb tritium can be separated into three distinct layers:
Trace amounts of radioactive materials from atomic weapons testing settled throughout the Mississippi River System . Tritium concentrations have been used to understand the residence times of continental hydrologic systems such as lakes, streams, and rivers. [ 70 ] In a 2004 study, several rivers were taken into account during the examination of tritium concentrations (starting in the 1960s) throughout the Mississippi River Basin: Ohio River (largest input to the Mississippi River flow), Missouri River , and Arkansas River . [ 70 ] The highest tritium concentrations were found in 1963 across locations throughout these rivers. The peak correlates with implementation of the US & Soviet atmospheric test ban treaty in 1962. The overall highest concentrations occurred in the Missouri River (1963) and were greater than 1,200 TU while the lowest concentrations were found in the Arkansas River (never greater than 850 TU and less than 10 TU in the mid-1980s). [ 70 ]
As for the mass flux of tritium through the main stem of the Mississippi River into the Gulf of Mexico , data indicated that approximately 780 grams of tritium has flowed out of the River and into the Gulf between 1961 and 1997, [ 70 ] an average of 21.7 grams/yr and 7.7 PBq/yr. Current fluxes through the Mississippi River are 1 to 2 grams, per year as opposed to the pre-bomb period fluxes of roughly 0.4 grams per year. [ 70 ] | https://en.wikipedia.org/wiki/Tritium |
Tritium radioluminescence is the use of gaseous tritium , a radioactive isotope of hydrogen , to create visible light. Tritium emits electrons through beta decay and, when they interact with a phosphor material, light is emitted through the process of phosphorescence . The overall process of using a radioactive material to excite a phosphor and ultimately generate light is called radioluminescence . As tritium illumination requires no electrical energy, it has found wide use in applications such as emergency exit signs , illumination of wristwatches, and portable yet very reliable sources of low intensity light which won't degrade human night vision. Gun sights for night use and small lights (which need to be more reliable than battery powered lights, yet not interfere with night vision or be bright enough to easily give away one's location) used mostly by military personnel fall under the latter application.
Tritium was found to be an ideal energy source for self-luminous compounds in 1953 and the idea was patented by Edward Shapiro on 29 October 1953, in the US (2749251 – Source of Luminosity). [ 1 ]
Tritium lighting is made using glass tubes with a phosphor layer in them and tritium gas inside the tube. Such a tube is known as a "gaseous tritium light source" (GTLS), or beta light (since the tritium undergoes beta decay ), or tritium lamp.
The tritium in a gaseous tritium light source undergoes beta (β) decay, releasing electrons that cause the phosphor layer to phosphoresce . [ 2 ]
During manufacture, a length of borosilicate glass tube that has had the internal surface coated with a phosphor -containing material is filled with tritium. The tube is then sealed at the desired length using a carbon dioxide laser . Borosilicate is preferred for its strength and resistance to breakage. In the tube, the tritium gives off a steady stream of electrons due to β decay. These particles excite the phosphor, causing it to emit a low, steady glow.
Tritium is not the only material that can be used for self-powered lighting. Radium was used to make self-luminous paint from the early 20th century to about 1970. Promethium briefly replaced radium as a radiation source. Tritium is the only radiation source used in radioluminescent light sources today due to its low radiological toxicity and commercial availability. [ 3 ]
Various preparations of the phosphor compound can be used to produce different colors of light. For example, doping zinc sulfide phosphor with different metals can change the emission wavelength. [ 4 ] Some of the colors that have been manufactured in addition to the common phosphors are green, red, blue, yellow, purple, orange, and white.
The GTLSs used in watches give off a small amount of light: Not enough to be seen in daylight, but visible in the dark from a distance of several meters. The average such GTLS has a useful life of 10–20 years. The rate of β emissions decreases by half in each half-life (12.33 years). Also, phosphor degradation will cause the brightness of a tritium tube to drop by more than half in that period. The more tritium is initially placed in the tube, the brighter it is to begin with, and the longer its useful life. Tritium exit signs usually come in three brightness levels guaranteed for 10, 15, or 20-year useful life expectancies. [ 5 ] The difference between the signs is how much tritium the manufacturer installs.
The light produced by GTLSs varies in color and size. Green usually appears as the brightest color with a brightness as high as 2 cd/m 2 [ 6 ] and red appears the least bright. For comparison, most consumer desktop liquid crystal displays have luminances of 200 to 300 cd/m 2 . [ 7 ] Sizes range from tiny tubes small enough to fit on the hand of a watch to ones the size of a pencil. Large tubes (5 mm diameter and up to 100 mm long) are usually only found in green, and can surprisingly be not as bright as the standard 22.5 mm × 3 mm sized tritium, this is due to the lower concentration and high cost of tritium; this smaller size is usually the brightest and is used mainly in keychains available commercially. [ citation needed ]
These light sources are most often seen as "permanent" illumination for the hands of wristwatches intended for diving, nighttime, or combat use. They are also used in glowing novelty keychains and in self-illuminated exit signs . They are favored by the military for applications where a power source may not be available, such as for instrument dials in aircraft, compasses , and sights for weapons. In the case of solid tritium light sources, the tritium replaces some of the hydrogen atoms in the paint, which also contains a phosphor such as zinc sulfide.
Tritium lights or beta lights were formerly [ when? ] used in fishing lures. Some flashlights have slots for tritium vials so that the flashlight can be easily located in the dark.
Tritium is used to illuminate the iron sights of some small arms. The reticle on the SA80 's optical SUSAT sight as well as the LPS 4x6° TIP2 telescopic sight of a PSL rifle , contains a small amount of tritium for the same effect as an example of tritium use on a rifle sight. The electrons emitted by the radioactive decay of the tritium cause phosphor to glow, thus providing a long-lasting (several years) and non-battery-powered firearms sight that is visible in dim lighting conditions. The tritium glow is not noticeable in bright conditions such as during daylight, however; consequently some manufacturers have started to integrate fiber optic sights with tritium vials to provide bright, high-contrast firearms sights in both bright and dim conditions.
Though these devices contain a radioactive substance, it is currently believed that self-powered lighting does not pose a significant health concern. A 2007 report by the UK government's Health Protection Agency Advisory Group on Ionizing Radiation declared the health risks of tritium exposure to be double that previously set by the International Commission on Radiological Protection , [ 8 ] but encapsulated tritium lighting devices, typically taking the form of a luminous glass tube embedded in a thick block of clear plastic, prevent the user from being exposed to the tritium at all unless the device is broken apart.
Tritium presents no external beta radiation threat when encapsulated in non-hydrogen-permeable containers due to its low penetration depth, which is too short to penetrate intact human skin. However, GTLS devices do emit low levels of X-rays due to bremsstrahlung . [ 9 ] According to a report by the OECD , [ 10 ] any external radiation from a gaseous tritium light device is solely due to bremsstrahlung, usually in the range of 8–14 keV. The bremsstrahlung dose rate cannot be calculated from the properties of tritium alone, as the dose rate and effective energy is dependent on the form of containment. A bare, cylindrical vial GTLS constructed of 0.1 mm thick glass that is 10 mm long and 0.5 mm in diameter will yield a surface dose rate of 100 millirads per hour per curie. If the same vial were instead constructed of 1 mm thick glass and enclosed in a plastic covering that is 2–3 mm thick, the GTLS will yield a surface dose rate of 1 millirad per hour per curie. The dose rate measured from 10 mm away will be two orders of magnitude lower than the measured surface dose rate. Given that the half-value thickness of 10 keV photon radiation in water is about 1.4 mm, the attenuation provided by tissue overlaying blood-forming organs is considerable.
The primary danger from tritium arises if it is inhaled, ingested, injected, or absorbed into the body. This results in the absorption of the emitted radiation in a small region of the body, again due to the low penetration depth. The biological half-life of tritium – the time it takes for half of an ingested dose to be expelled from the body – is low, at only 12 days. Tritium excretion can be accelerated further by increasing water intake to 3–4 liters/day. [ 11 ] Direct, short-term exposure to small amounts of tritium is mostly harmless. If a tritium tube breaks, one should leave the area and allow the gas to diffuse into the air. Tritium exists naturally in the environment, but in very small quantities.
Products containing tritium are controlled by law because tritium is used in boosted fission weapons and thermonuclear weapons (though in quantities several thousand times larger than that in a keychain). In the US, devices such as self-luminous exit signs, gauges, wristwatches, etc. that contain small amounts of tritium are under the jurisdiction of the Nuclear Regulatory Commission , and are subject to possession, distribution, and import and export regulations found in 10 CFR Parts, 30, 32, and 110. They are also subject to regulations for possession, use, and disposal in certain states. Luminous products containing more tritium than needed for a wristwatch are not widely available at retail outlets in the United States. [ citation needed ]
They are readily sold and used in the UK and US. They are regulated in England and Wales by environmental health departments of local councils. [ citation needed ] In Australia products containing tritium are licence exempt if they contain less than 1 × 10 6 becquerels per gram (2.7 × 10 −5 Ci /g) tritium and have a total activity of less than 1 × 10 9 becquerels (0.027 Ci), except for in safety devices where the limit is 74 × 10 9 becquerels (2.0 Ci) total activity. [ 12 ] | https://en.wikipedia.org/wiki/Tritium_radioluminescence |
Tritrophic interactions in plant defense against herbivory describe the ecological impacts of three trophic levels on each other: the plant, the herbivore , and its natural enemies. They may also be called multitrophic interactions when further trophic levels , such as soil microbes, endophytes , or hyperparasitoids (higher-order predators) are considered. [ 1 ] [ 2 ] Tritrophic interactions join pollination and seed dispersal as vital biological functions which plants perform via cooperation with animals . [ 3 ]
Natural enemies— predators , pathogens , and parasitoids that attack plant-feeding insects—can benefit plants by hindering the feeding behavior of the harmful insect. It is thought that many plant traits have evolved in response to this mutualism to make themselves more attractive to natural enemies. This recruitment of natural enemies functions to protect against excessive herbivory and is considered an indirect plant defense mechanism. [ 3 ] Traits attractive to natural enemies can be physical, as in the cases of domatia and nectaries ; [ 1 ] or chemical, as in the case of induced plant volatile chemicals that help natural enemies pinpoint a food source. [ 4 ]
Humans can take advantage of tritrophic interactions in the biological control of insect pests.
Plants produce secondary metabolites known as allelochemicals . Rather than participating in basic metabolic processes , they mediate interactions between a plant and its environment, often attracting, repelling, or poisoning insects. [ 5 ] [ 6 ] They also help produce secondary cell wall components such as those that require amino acid modification. [ 7 ]
In a tritrophic system, volatiles , which are released into the air, are superior to surface chemicals in drawing foraging natural enemies from afar. Plants also produce root volatiles which will drive tritrophic interactions between below-ground herbivores and their natural enemies. [ 8 ] Some plant volatiles can be smelled by humans and give plants like basil, eucalyptus, and pine their distinctive odors. [ 1 ] The mixture and ratios of individual volatiles emitted by a plant under given circumstances (also referred to as synomones in the context of natural enemy attraction) is referred to as a volatile profile. These are highly specific to certain plant species and are detectable meters from the source. Predators and parasitoids exploit the specificity of volatile profiles to navigate the complex infochemical signals presented by plants in their efforts to locate a particular prey species. [ 1 ]
The production of volatiles is likely to be beneficial given two conditions: that they are effective in attracting natural enemies and that the natural enemies are effective in removing or impeding herbivores. However, volatile chemicals may not have evolved initially for this purpose; they act in within-plant signaling, [ 9 ] attraction of pollinators, [ 10 ] or repulsion of herbivores that dislike such odors. [ 1 ]
When an herbivore starts eating a plant, the plant may respond by increasing its production of volatiles or changing its volatile profile . This plasticity is controlled by either the jasmonic acid pathway or the salicylic acid pathway , depending largely on the herbivore; these substances are often called herbivore-induced plant volatiles (HIPVs). [ 1 ] [ 4 ] The plant hormone jasmonic acid increases in concentration when plants are damaged and is responsible for inducing the transcription of enzymes that synthesize secondary metabolites. [ 7 ] This hormone also aids in the production of defensive proteins such as α-amylase inhibitors , as well as lectins . Since α-amylase breaks down starch, α-amylase inhibitors prevent insects from deriving nutrition from starch. [ 7 ] Lectins likewise interfere with insect nutrient absorption as they bind to carbohydrates. [ 7 ]
Though volatiles of any kind have an attractive effect on natural enemies, this effect is stronger for damaged plants than for undamaged plants, [ 1 ] perhaps because induced volatiles signal definitive and recent herbivore activity. The inducibility gives rise to the idea that plants are sending out a "distress call" to the third trophic level in times of herbivore attack.
Natural enemies can distinguish between mechanical tissue damage, which might occur during events other than herbivory, and damage that is the direct result of insect feeding behavior. The presence of herbivore saliva or regurgitant mediates this differentiation, and the resulting chemical pathway leads to a stronger natural enemy response than mechanical damage could. [ 11 ] [ 12 ] [ 13 ] [ 14 ] The reliability of HIPVs in broadcasting the location of prey means that, for many foraging enemies, induced plant volatiles are more attractive than even the odors emitted by the prey insect itself. [ 15 ]
Plants are able to determine what types of herbivore species are present, and will react differently given the herbivore's traits. If certain defense mechanisms are not effective, plants may turn to attracting natural enemies of herbivore populations. For example, wild tobacco plants use nicotine , a neurotoxin , to defend against herbivores. However, when faced with nicotine-tolerant herbivores, they will attract natural enemies. [ 16 ]
When herbivores trigger an inducible chemical defense pathway, the resulting HIPVs may be emitted either from the site of feeding damage (local induction) or from undamaged tissues belonging to a damaged plant (systemic induction). For example, when an herbivore feeds on a single corn seedling leaf, the plant will emit volatiles from all its leaves, whether or not they too have been damaged. Locally induced defenses aid parasitoids in targeting their foraging behaviors to the exact location of the herbivore on the plant. Systemic defenses are less spatially specific and may serve to confuse the enemy once the source plant is located. A plant might employ both local and systemic responses simultaneously. [ 1 ]
Natural enemies must survive long enough and respond quickly enough to plant volatiles in order to benefit the plant through predatory behavior. Certain plant structures, called domatia , can selectively reinforce mutualisms with natural enemies and increase the fitness benefit they receive from that mutualism by ensuring the survival and proximity of natural enemies. Domatia provide a kind of housing or refuge for predators from both abiotic stressors , such as desiccation, and biotic stressors, such as predation from higher-order predators. Therefore, they not only ensure better survival, but eliminate the time required for natural enemies to locate and travel to the damaged plant. Natural enemies that make use of domatia are often said to serve as "bodyguards" for the plant on or in which they live. Domatia may be as well-developed as acacia tree thorns or as simple and incidental as a depression or crevice in a leaf stem, but they are distinguishable from galls and other similar structures in that they are not induced by the insect but formed constitutively by the plant. [ 1 ]
As long as natural enemies have some potential to be omnivorous , plants can provide food resources to encourage their retention and increase the impact they have on herbivore populations. This potential, however, can hinge on a number of the insect's traits. For example, hemipteran predators can use their sucking mouthparts to make use of leaves, stems, and fruits, but spiders with chelicerae cannot. [ 17 ] Still, insects widely considered to be purely carnivorous have been observed to diverge from expected feeding behavior. [ 18 ] Some plants simply tolerate a low level of herbivory by natural enemies for the service they provide in ridding the plant of more serious herbivores. Others, however, have structures thought to serve no purpose other than attracting and provisioning natural enemies. These structures derive from a long history of coevolution between the first and third trophic levels. A good example is the extrafloral nectaries that many myrmecophytes and other angiosperms sport on leaves, bracts, stems, and fruits. Nutritionally, extrafloral nectaries are similar to floral nectaries, but they do not lead the visiting insect to come into contact with pollen. Their existence is therefore not the product of a pollinator–plant mutualism, but rather a tritrophic, defensive interaction. [ 17 ]
The field of chemical ecology has elucidated additional types of plant multitrophic interactions that entail the transfer of defensive compounds across multiple trophic levels. [ 19 ] For example, certain plant species in the Castilleja and Plantago genera have been found to produce defensive compounds called iridoid glycosides that are sequestered in the tissues of the Taylor's checkerspot butterfly larvae that have developed a tolerance for these compounds and are able to consume the foliage of these plants. [ 20 ] [ 21 ] These sequestered iridoid glycosides then confer chemical protection against bird predators to the butterfly larvae. [ 20 ] [ 21 ] Another example of this sort of multitrophic interaction in plants is the transfer of defensive alkaloids produced by endophytes living within a grass host to a hemiparasitic plant that is also using the grass as a host. [ 22 ]
Exploitation of tritrophic interactions can benefit agricultural systems. Biocontrol of crop pests can be exerted by the third trophic level, given an adequate population of natural enemies. [ 24 ] [ 25 ] However, the widespread use of pesticides or Bt crops can undermine natural enemies’ success. [ 26 ] [ 27 ] [ 28 ] In some cases, populations of predators and parasitoids are decimated, necessitating even greater use of insecticide because the ecological service they provided in controlling herbivores has been lost.
Even when pesticides are not widely used, monocultures often have difficulty support natural enemies in great enough numbers for them to diminish pest populations. [ citation needed ] A lack of diversity in the first trophic level is linked to low abundance in the third because alternative resources that are necessary for stable, large natural enemy populations are missing from the system. Natural enemy diets can be subsidized by increasing landscape diversity through companion planting , border crops, cover crops , intercropping , or tolerance of some weed growth. [ 23 ] When nectar or other sugar -rich resources are provided, the natural enemy population thrives. [ 29 ]
Beyond domatia and nutritional rewards, other plant characteristics influence the colonization of plants by natural enemies. These can include the physical size, shape, density, maturity, colour, and texture of a given plant species. Specific plant features such as the hairiness or glossiness of vegetation can have mixed effects on different natural enemies. For example, trichomes decrease hunting efficiency of many natural enemies, as trichomes tend to slow or prevent movement due to the physical obstacles they present or the adhesive secretions they produce. However, sometimes the prey species may be more impeded than the predator. For example, when the whitefly prey of the parasitoid Encarsia formosa is slowed by plant hairs, the parasitoid can detect and parasitize a higher number of juvenile whiteflies. [ 24 ]
Many predatory coccinelid beetles have a preference for the type of leaf surface they frequent. Presented with the opportunity to land on glossy or hairy Brassica oleracea foliage, the beetles prefer the glossy foliage as they are better able to cling to these leaves. Studies are evaluating the effect of various plant genotypes on natural enemies. [ 24 ]
Two ways the release of volatile organic compounds (VOCs) may benefit plants are the deterrence of herbivores and the attraction of natural enemies. [ 30 ] Synthetic products could replicate the distinct VOC profiles released by different plants; these products could be applied to plants suffering from pests that are targeted by the attracted natural enemy. [ 30 ] This could cause natural enemies to enter crops that are occupied by pest populations that would otherwise likely remain undetected by the natural enemies. [ 31 ]
The four elements that must be considered before manipulating VOCs are as follows: The VOCs must effectively aid the natural enemy in finding the prey; the pest must have natural enemies present; the fitness cost of potentially attracting more herbivores must be exceeded by attracting natural enemies; and the natural enemies must not be negatively affected by direct plant defenses that may be present. [ 32 ]
The level of domestication of cotton plants correlates to indirect defense investment in the form of extrafloral nectaries. Wild varieties produce higher volumes of nectar and attract a wider variety of natural enemies. [ 33 ] Thus, the process of breeding new cotton varieties has overlooked natural resistance traits in the pursuit of high-yielding varieties that can be protected by pesticides. Plants bearing extrafloral nectaries have lower pest levels along with greater levels of natural enemies. [ 34 ] These findings illustrate the potential benefits that could be gained through incorporating the desirable genetics of wild varieties into cultivated varieties.
Certain tropical plants host colonies of ants in their hollow domatia and provide the ants with nutrition delivered from nectaries or food bodies. These ant colonies have become dependent on the host plants for their survival and therefore actively protect the plant; this protection can take the form of killing or warding off pests, weeds, and certain fungal pathogens. Chinese citrus farmers have capitalized on this mutualistic relationship for many years by incorporating artificial ant nests into their crops to suppress pests. [ 35 ]
Parasitoids have successfully been incorporated into biological pest control programs for many years. Plants can influence the effect of parasitoids on herbivores by releasing chemical cues that attract parasitoids and by providing food sources or domatia. [ 1 ] Certain parasitoids may be dependent on this plant relationship. Therefore, in agricultural areas where parasitoid presence is desired, ensuring the crops being grown meet all of these requirements is likely to promote higher parasitoid populations and better pest control. [ 31 ]
In a sugar beet crop, when only beets were grown, few aphids were parasitized. However, when collard crops were grown next to the sugar beets, parasitism of aphids increased. Collard crops release more VOCs than sugar beets. As a result, the companion collard plants attract more aphid parasitoids, which kill aphids in both the collard and the nearby sugar beets. [ 36 ]
In a related study, ethylene and other compounds released by rice plants in response to brown planthopper feeding attracted a facultative parasitoid that parasitizes brown planthopper eggs. [ 30 ]
In another study, the presence of plant extrafloral nectaries in cotton crops caused parasitoids to spend more time in the cotton and led to the parasitization of more moth larva than in cotton crops with no nectaries. Since the publication of this study, most farmers have switched to cotton varieties with nectaries. [ 37 ] A separate study found that a naturalized cotton variety emitted seven times more VOCs than cultivated cotton varieties when experiencing feeding damage. [ 38 ] It is unknown whether this generalizes to other crops; there are cases of other crops that do not show the same trend. [ 31 ]
These findings reveal the specific variables a farmer can manipulate to influence parasitoid populations and illustrate the potential impact parasitoid habitat management can have on pest control. [ 31 ] In the case of cotton and other similar high-VOC crop scenarios, there is interest in genetically engineering the chemical pathways of cultivated varieties to selectively produce the high VOC's that were observed in the naturalized varieties in order to attract greater natural enemy populations. This presents challenges but could produce promising pest control opportunities. [ 39 ]
Entomopathogens are another group of organisms that are influenced by plants. The extent of the influence largely depends on the evolutionary history shared between the two and the pathogens' method of infection and survival duration outside of a host. Different insect host plants contain compounds that cause modulate insect mortality when certain entomopathogens are simultaneously injected. Increases in mortality of up to 50-fold have been recorded. However, certain plants influence entomopathogens in negative ways, reducing their efficacy. [ 40 ]
It is primarily the leaf surface of the plant that influences the entomopathogen; plants can release various exudates , phytochemicals , and alleolochemicals through their leaves, some of which have the ability to inactivate certain entomopathogens. [ 40 ] In contrast, in other plant species, leaf characteristics can increase the efficacy of entomopathogens. For example, the mortality of pea aphids was higher in the group of aphids that were found on plants with fewer wax exudates than in those on plants with more wax exudates. This reduced waxiness increases the transmission of Pandora neoaphidus conidia from the plant to the aphids. [ 41 ]
Feeding-induced volatiles emitted by different plants increase the amount of spores released by certain entomopathogenic fungi , increasing the likelihood of infection of some herbivores but not others. Plants can also influence pathogen efficacy indirectly, and this typically occurs either by increasing the susceptibility of the herbivore hosts or by changing their behavior. This influence can often take the form of altered growth rates, herbivore physiology, or feeding habits. Thus, there are various ways that host plant species can influence entomopathogenic interactions. [ 40 ]
In one study, brassicas were found to defend themselves by acting as a vector for entomopathogens. Virus-infected aphids feeding on the plants introduce a virus into the phloem. The virus is passively transported in the phloem and carried throughout the plant. This causes aphids feeding apart from the infected aphids to become infected as well. This finding offers the possibility of injecting crops with compatible entomopathogenic viruses to defend against susceptible insect pests. [ 42 ]
Less studied than above-ground interactions, but proving to be increasingly important, are the below-ground interactions that influence plant defense . [ 43 ] There is a complex network of signal transduction pathways involved in plant responses to stimuli, and soil microbes can influence these responses. Certain soil microbes aid plant growth, producing increased tolerance to various environmental stressors, and can protect their host plants from many different pathogens by inducing systemic resistance. [ 44 ] Organisms in above- and below-ground environments can interact indirectly through plants. Many studies have shown both the positive and negative effects that one organism in one environment can have on other organisms in the same or opposite environment, with the plant acting as the intermediary. [ 43 ]
The colonization of plant roots with mycorhizae typically results in a mutualistic relationship between the plant and the fungus, inducing a number of changes in the plant. Such colonization has a mixed impact on herbivores; insects with different feeding methods are affected differently, some positively and others negatively. [ 45 ] The mycorhizal species involved also matters. One common species, Rhizophagus irregularis , has been observed to have a negative effect on the feeding success of chewing herbivores, whereas other species studied have positive effects. [ 45 ]
The roots of some maize plants produce a defense chemical when roots are damaged by leaf beetle larvae; this chemical attracts the entomopathogenic nematode species Heterorhabditis megidis . Only certain maize varieties produce this chemical; plants that release the chemical see up to five times as much parasitization of leaf beetle larvae as those that do not. Incorporating these varieties or their genes into commercial maize production could increase the efficacy of nematode treatments. [ 46 ]
Further studies suggest that the plant-emitted chemicals act as the primary source of attractant to the nematodes. Herbivores are believed to have evolved to evade detection on the part of the nematodes, whereas the plants have evolved to release highly attractive chemical signals. A high degree of specificity is involved; species that make up these tritrophic interactions have evolved with one another over a long period of time and as a result have close interrelationships. [ 47 ]
Microorganisms can also influence tritrophic interactions. The bacterium Klebsiella aerogenes produces the volatile 2,3-butanediol, which modulates interactions between plants, pathogens, and insects. [ 48 ] When maize plants are grown in a soil culture containing the bacterium or the plants are inoculated with the bacterium, the maize is more resistant to the fungus Setosphaeria turcica . [ 48 ] The bacterium does not deter insect herbivory; it actually increases weight gain and leaf consumption in the caterpillar Spodoptera littoralis . [ 48 ] However, the parasitic wasp Cotesia marginiventris is attracted more readily to maize plants grown in soil cultures containing either the volatile-producing bacterium or pure 2,3-butanediol. [ 48 ]
Sustainable crop production is becoming increasingly important, if humans are to support a growing population and avoid a collapse of production systems. [ 49 ] While the understanding and incorporation of tritrophic interactions in pest control offers a promising control option, the sustainable biological control of pests requires a dynamic approach that involves diversity in all of the species present, richness in natural enemies, and limited adverse activity (i.e., minimal pesticide use). This approach is especially important in conservation biological control efforts. [ 50 ]
There are typically more than three trophic levels at play in a given production setting, so the tritrophic interaction model may represent an oversimplification. [ 31 ] Furthermore, ecological complexity and interactions between species of the same trophic level can come into play. Research thus far has had a relatively narrow focus, which may be suitable for controlled environments such as greenhouses but which has not yet addressed multi-generational plant interactions with dynamic communities of organisms. [ 51 ] | https://en.wikipedia.org/wiki/Tritrophic_interactions_in_plant_defense |
Trituration (Latin, grinding ) is the name of several different methods used to process materials. In one sense, it is a form of comminution (reducing the particle size of a substance). In another sense, it is the production of a homogeneous powdered material by mixing and grinding component materials thoroughly. [ 1 ] For example, a dental amalgam is formed by combining particles of a metal, usually gold or silver, with mercury . | https://en.wikipedia.org/wiki/Trituration |
The triune brain was a once popular, now proven false, [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] model of the evolution of the vertebrate forebrain and behavior, proposed by the American physician and neuroscientist Paul D. MacLean in the 1960s. The triune brain consists of the reptilian complex ( basal ganglia ), the paleomammalian complex ( limbic system ), and the neomammalian complex ( neocortex ), viewed each as independently conscious, and as structures sequentially added to the forebrain in the course of evolution. According to the model, the basal ganglia are in charge of primal instincts, the limbic system is in charge of emotions, and the neocortex is responsible for objective or rational thoughts.
Since the 1970s, the concept of the triune brain has been subject to criticism in evolutionary and developmental neuroscience [ 2 ] and is regarded as a myth. [ 6 ] Although it overlaps in some respects with contemporary understanding of the brain, [ 7 ] the triune brain hypothesis is no longer espoused by comparative neuroscientists in the post-2000 era [ 8 ] due to harsh criticism against it. [ 9 ]
MacLean originally formulated his model in the 1960s and propounded it at length in his 1990 book The Triune Brain in Evolution . The triune brain hypothesis became familiar to a broad popular audience through Carl Sagan 's Pulitzer Prize winning 1977 book The Dragons of Eden .
"Reptilian complex" (also known as the "R-complex", "reptilian brain" or "lizard brain") was the name MacLean gave to the basal ganglia , structures derived from the floor of the forebrain during development. The term derives from the idea that comparative neuroanatomists once believed that the forebrains of reptiles and birds were dominated by these structures. MacLean proposed that the reptilian complex was responsible for species-typical instinctual behaviours involved in aggression, dominance, territoriality, and ritual displays. [ 10 ]
This consists of the septum , amygdalae , hypothalamus , hippocampal complex , and cingulate cortex . MacLean first introduced the term " limbic system " to refer to this set of interconnected brain structures in a paper in 1952. MacLean's recognition of the limbic system as a major functional system in the brain was widely accepted among neuroscientists, and is generally regarded as his most important contribution to the field. MacLean maintained that the structures of the limbic system arose early in mammalian evolution (hence "paleomammalian", with paleo- meaning old ) and were responsible for the motivation and emotion involved in feeding, reproductive behaviour, and parental behaviour. [ citation needed ]
This consists of the cerebral neocortex , a structure found uniquely in higher mammals, and especially humans. MacLean regarded its addition as the most recent step in the evolution of the mammalian brain, conferring the ability for language, abstraction, planning, and perception. [ citation needed ]
The triune brain model argues that these structures are relatively independent from one another, but that they are still connected to each other in some form or another. [ 1 ]
The model views different cognitive behaviors as caused by three different entities instead of one. The reptilian complex is said to control all of the instinctual and impulsive actions, while the neomammalian complex is responsible for keeping the primitive instincts constrained. An example is controlling the impulse of eating. It seems that if one is hungry, then that means the reptilian complex is commanding the body to eat. However, an individual has the rational choice not to eat when hungry, and this rational thought is said to be controlled by the neomammalian complex. The model thus suggest that these two (and three depending on the situation) structures are in a perpetual battle to control the body.
These interactions between the neocortex and the reptilian brain often seem competitive as the conscious thought generated by the neocortex can suppress the primitive thoughts generated by the reptilian complex. Thus, the model suggests that the interactions between structures are not constructive, but that they are conflicting due to the anatomical separation of the brain. [ 11 ]
This separation of structures proposed an underlying difference between consciousness and unconscious behaviour and argued that the reason why humans are such intelligent and conscious species is due to the not-so-common neocortex that they possess, unlike most other animals. [ 11 ] This detachment contributes to the idea that the three complexes interact with each other separately rather than a single construct interacting with itself.
MacLean originally formulated the triune brain hypothesis in the 1960s, drawing on comparative neuroanatomical work done by Ludwig Edinger , Elizabeth C. Crosby and Charles Judson Herrick early in the twentieth century. [ 12 ] [ 13 ] The 1980s saw a rebirth of interest in comparative neuroanatomy, motivated in part by the availability of a variety of new neuroanatomical techniques for charting the circuitry of animal brains. Subsequent findings according to human brain evolution expert Terrence Deacon, have refined the traditional neuroanatomical ideas upon which MacLean based his hypothesis. Deacon mentioned that 'the evolutionary addition of different parts of the brain is simply not realistic. However, all the parts of the brain were already existing, they were just further developed upon as the homosapien species evolved and gained life experiences.' [ 14 ]
For example, the basal ganglia (structures derived from the floor of the forebrain and making up MacLean's reptilian complex) were shown to take up a much smaller portion of the forebrains of reptiles and birds (together called sauropsids ) than previously supposed, and to exist in amphibians and fish as well as mammals and sauropsids. Because the basal ganglia are found in the forebrains of all modern vertebrates, they most likely date to the common evolutionary ancestor of the vertebrates, more than 500 million years ago, rather than to the origin of reptiles. [ citation needed ]
Recent behavioral studies do not support the traditional view of sauropsid behavior as stereotyped and ritualistic (as in MacLean's reptilian complex). Birds have been shown to possess highly sophisticated cognitive abilities, such as the toolmaking of the New Caledonian crow and the language-like categorization abilities of the grey parrot . [ 15 ] Structures of the limbic system, which MacLean proposed arose in early mammals, have now been shown to exist across a range of modern vertebrates. The "paleomammalian" trait of parental care of offspring is widespread in birds and occurs in some fishes as well. Thus, like the basal ganglia, the evolution of these systems presumably dates to a common vertebrate ancestor. [ 13 ] [ 16 ]
Finally, recent studies based on paleontological data or comparative anatomical evidence strongly suggest that the neocortex was already present in the earliest emerging mammals. [ 13 ] In addition, although non-mammals do not have a neocortex in the true sense (that is, a structure comprising part of the forebrain roof, or pallium, consisting of six characteristic layers of neurons), they possess pallial regions, and some parts of the pallium are considered homologous to the mammalian neocortex. While these areas lack the characteristic six neocortical layers, birds and reptiles generally possess three layers in the dorsal pallium (the homolog of the mammalian neocortex). [ 13 ] [ 16 ] The telencephalon of birds and mammals makes neuroanatomical connections with other telecencephalic structures [ 13 ] like those made by neocortex. It mediates similar functions such as perception, learning and memory, decision making, motor control, conceptual thinking.
The triune model of the mammalian brain is seen as an oversimplified organizing theme in the field of comparative neuroscience. [ 18 ] It continues to hold public interest because of its simplicity. [ 2 ]
Howard Bloom , in his 1995 book The Lucifer Principle , references the concept of the triune brain in his explanations of certain aspects of human behavior. Arthur Koestler made MacLean's concept of the triune brain the centerpiece of much of his later work, notably The Ghost in the Machine . English novelist Julian Barnes quotes MacLean on the triune brain in the foreword to his 1982 novel Before She Met Me . Peter A. Levine uses the triune brain concept in his book Waking the Tiger to explain his somatic experiencing approach to healing trauma. [ citation needed ] In the series of novels written by Lee Child featuring knight-errant figure Jack Reacher , Reacher often experiences messages from what he calls his "lizard brain" that alert him to potential danger. In Disco Elysium , the player character interfaces directly with his limbic system and "ancient reptilian brain" at various points throughout the game, alongside the players skill set acting as a representation of his posterior neocortex. [ 19 ]
Glynda-Lee Hoffmann, in her book The Secret Dowry of Eve, Women's Role in the Development of Consciousness , references the triune theory explored by MacLean and goes one step further. Her theory about human behavior, and the problems we create with that behavior, distinguishes the prefrontal cortex as uniquely different from the rest of the neocortex. The prefrontal cortex, with its agenda of integration, is the part of the brain that can get the other parts to work together for the good of the individual. Hoffmann claims that in many humans the reptilian cortex (agenda: territory and reproduction; in humans that translates to power and sex) is out of control, and the amygdala stokes the fear that leads to more bad behavior. [ 20 ] | https://en.wikipedia.org/wiki/Triune_brain |
The triune continuum paradigm ( triune : "both three and one at the same time") is a paradigm for general system modeling published in 2002. [ 1 ] The paradigm allows for building of rigorous conceptual frameworks employed for systems modeling in various application contexts (highly tailored as well as interdisciplinary).
As stated in the Cambridge Dictionary of Philosophy : [ 2 ] "Paradigm, as used by Thomas Kuhn ( The Structure of Scientific Revolutions , 1962), refers to a set of scientific and metaphysical beliefs that make up a theoretical framework within which scientific theories can be tested, evaluated and if necessary revised."
The triune continuum paradigm holds true to this definition by defining a set of scientific principles within which conceptual frameworks used for system modeling in different contexts can be built, tested, evaluated, and revised. [ 3 ]
For an existent modeling framework, the paradigm allows the framework to be tested against its principles, showing framework deficiencies, if any, explaining how to fix the deficiencies in a possible revision of the framework. When building a new system modeling framework, the paradigm provides guidelines on how to do so, assuring the resulting quality of the framework.
According to Herrera et al., [ 4 ] the triune continuum paradigm is a complete theoretical base that can be used for building or for improving modern modeling frameworks that are employed for system modeling in different contexts, in particular in software development and in the engineering of enterprise information systems .
The triune continuum paradigm is based on three theories: on Tarski's theory of truth , on Russell's theory of types , and on the theory of the triune continuum. [ 5 ] The theories, when applied to general system modeling, produce three principles: [ 3 ]
The triune continuum paradigm can be applied in practice either to improve an existing system modeling framework or to design a new system modeling framework for a given purpose. | https://en.wikipedia.org/wiki/Triune_continuum_paradigm |
Triuret is an organic compound with the formula (H 2 NC(O)NH) 2 CO. It is a product from the pyrolysis of urea . Triuret is a colorless, crystalline, hygroscopic solid, slightly soluble in cold water or ether, and more soluble in hot water. It is a planar molecule. The central carbonyl is hydrogen-bonded to both terminal amino groups. [ 2 ]
The compound is typically prepared by heating thin layers of urea, the thin layers facilitating escape of ammonia :
It can also prepared by treatment of urea with phosgene : [ 3 ]
A similar synthesis employs urea and dimethyl carbonate with potassium methoxide as a catalyst: [ 4 ]
The original synthesis entailed oxidation of uric acid with hydrogen peroxide. [ 5 ]
Triuret is a complicating by-product in the industrial synthesis of melamine from urea. | https://en.wikipedia.org/wiki/Triuret |
A trivalent group 14 radical (also known as a trivalent tetrel radical ) is a molecule that contains a group 14 element (E = C, Si, Ge, Sn, Pb) with three bonds and a free radical , having the general formula of R 3 E•. Such compounds can be categorized into three different types, depending on the structure (or equivalently the orbital in which the unpaired electron resides) and the energetic barrier to inversion. A molecule that remains rigidly in a pyramidal structure has an electron in a sp 3 orbital is denoted as Type A . A structure that is pyramidal, but flexible, is denoted as Type B . And a planar structure with an electron that typically would reside in a pure p orbital is denoted as Type C . The structure of such molecules has been determined by probing the nature of the orbital that the unpaired electron resides in using spectroscopy, as well as directly with X-ray methods. [ 3 ] Trivalent tetrel radicals tend to be synthesized from their tetravalent counterparts (i.e. R 3 EY where Y is a species that will dissociate).
While the trivalent triphenylmethyl radical , which was the first organic radical described, has been known for over 100 years, [ 4 ] [ 5 ] [ 6 ] characterization of transient, persistent, or stable radicals of heavier tetrel compounds have been only accessible in recent years (from the 1960s to the present). The most recent large advance has been the characterization of the first stable trivalent lead radical, as described in 2007. [ 3 ] [ 7 ]
Such developments have only been made in recent years because these compounds tend to be highly reactive (with respect to reactions such as dimerization and radical chain reactions). There have been two main approaches for stabilization. Firstly electronic stabilization , the tetrel is connected to an electron-rich atom such as oxygen, nitrogen, or fluorine. Secondly steric stabilization , the tetrel is surrounded by bulky ligands (such as -Y(SiMe 3 ) 2 (Y = N, CH), -Si(SiMe 3 ) 2 Et (-Ebt), or -Si(SiMe 3 ) 3 (-Hyp)). It has become convention to describe a radical that can persist long enough for spectroscopic or chemical analysis as persistent and a radical that can persist indefinitely as stable . [ 7 ] Trivalent tetrels can also synthesized in a cyclic structure (e.g. Ar 3 Ge 3 •). This class of molecules tends to be slightly more stable than the acyclic analogues as there is a stabilization through the delocalization of the unpaired electrons within the π-system. [ 8 ]
Trivalent radicals can be prepared from the tetrel hydride (for arbitrary radical species Z). [ 9 ]
They can also be formed by oxidation of the salt (typically with GeCl 2 •dioxane in Et 2 O). [ 10 ]
They can be formed via photolysis. [ 10 ]
Or they can be formed via thermal disproportionation ( thermolysis ) of the related dimeric species. [ 11 ]
These can also be formed via gamma-irradiation of an ER 4 complex. [ 8 ] [ 12 ]
As well as by a reduction pathway. [ 8 ]
Information about the structure of these trivalent tetrels has been determined by mainly EPR spectroscopy and X-ray crystallography, however the geometry of transient small molecules has been determined via resonance-enhanced multiphoton ionization , transient UV absorption spectroscopy, and microwave spectroscopy by determining vibrational and rotational resonance frequencies. [ 8 ]
Electron paramagnetic resonance has been paramount for the study of trivalent tetrels as the hyperfine coupling to the tetrel reveals the orbital in which the unpaired electron resides, and the orbital composition directly correlates to the structure of the molecule. The isotropic component of the hyperfine coupling to the central tetrel scales proportionally with the spin density in the valence s orbital on that atom (see the Figure on the right). By comparing this isotropic hyperfine coupling constant to the theoretical hyperfine splitting of an electron in a pure valence s orbital, [ 19 ] one can calculate the percent of the unpaired spin density in the valence s orbital. Similarly, the ratio of the anisotropic hyperfine coupling constant to the anisotropic hyperfine coupling of a single electron in a pure atomic p orbital reveals the percent of spin occupation in a valence p orbital. However, measurement of the anisotropic component of the hyperfine tensor are more difficult and not as frequent in literature.
The percent of spin occupation in the valence s orbital can be used to directly probe the structure of these molecules. If the spin occupation 100% in a p orbital, then the molecule will have a Type C planar structure. However, if there is 25% s orbital and 75% p orbital occupation, then the molecule will have a pyramidal Type A structure. Any intermediate value is possible and would correspond to a Type B structure. Values of greater than 25% s orbital contribution can also be found upon coordination of a tetrel to electronegative ligands (-OR, -F, -NR 2 , -Cl). [ 13 ]
There is also a correlation between the g-shift (∆g = g meas - g e ) and the geometry for series of compounds with ligands of similar electronegativities. More electronegative ligands correspond to more tetrahedral geometries. Lower g values correlate more with pyramidal structures, while higher g values correlate with planar structures. [ 11 ] [ 20 ] It has also been demonstrated using tris(trialkylsilyl)silyl radicals that the more bulky the ligands are, the more a planar structure will be favored, and the lower the hyperfine coupling constant will be. [ 21 ]
It has been shown that there are two main factors that dictate whether a complex will be a Type A, B, or C structure. The lighter the tetrel, the more it will have a tendency to remain planar. This has been ascribed due to the pseudo Jahn–Teller effect , as the E-R anti-bonding orbitals (of R 3 E•) can more significantly mix with the non-bonding SOMO (singly occupied molecular orbital) due to a more electropositive and diffuse central atom. The barrier for inversion has been calculated at the NL-SCF/TZ2P level to be increasing for EH 3 • C, Si, Ge, Sn at 0.0, 3.7, 3.8, 7.0 kcal/mol (the barrier for inversion of methyl radical is zero as it is most stable in a planar Type C structure). [ 22 ] | https://en.wikipedia.org/wiki/Trivalent_group_14_radicals |
In evolutionary biology and evolutionary psychology , the Trivers–Willard hypothesis , [ 1 ] formally proposed by Robert Trivers and Dan Willard in 1973, suggests that female mammals adjust the sex ratio of offspring in response to maternal condition , so as to maximize their reproductive success ( fitness ). For example, it may predict greater parental investment in males by parents in "good conditions" and greater investment in females by parents in "poor conditions" (relative to parents in good conditions). The reasoning for this prediction is as follows: Assume that parents have information on the sex of their offspring and can influence their survival differentially. While selection pressures exist to maintain a 1:1 sex ratio , [ 2 ] evolution will favor local deviations from this if one sex has a likely greater reproductive payoff than is usual.
Trivers and Willard also identified a circumstance in which reproducing individuals might experience deviations from expected offspring reproductive value—namely, varying maternal condition. In polygynous species, males may mate with multiple females, and low-condition males will achieve fewer or no matings. Parents in relatively good condition would then be under selection for mutations causing production and investment in sons (rather than daughters), because of the increased chance of mating experienced by these good-condition sons. Mating with multiple females conveys a large reproductive benefit, whereas daughters could translate their condition into only smaller benefits. An opposite prediction holds for poor-condition parents—selection will favor production and investment in daughters, so long as daughters are likely to be mated, while sons in poor condition are likely to be out-competed by other males and end up with zero mates (i.e. those sons will be a reproductive dead end).
The hypothesis was used to explain why, for example, red deer mothers would produce more sons when they are in good condition, and more daughters when in poor condition. In polyandrous species where some females mate with multiple males (and others get no matings) and males mate with one/few females (i.e. "sex-role reversed" species), these predictions from the Trivers–Willard hypothesis are reversed: parents in good condition will invest in daughters in order to have a daughter that can out-compete other females to attract multiple males, whereas parents in poor condition will avoid investing in daughters who are likely to get out-competed, and will instead invest in sons in order to gain at least some grandchildren.
"Condition" can be assessed in multiple ways, including body size, parasite loads , or dominance , which has also been shown in macaques ( Macaca sylvanus ) to affect the sex of offspring, with dominant females giving birth to more sons and non-dominant females giving birth to more daughters. [ 3 ] Consequently, high-ranking females give birth to a higher proportion of males than those who are low-ranking.
In their original paper, Trivers and Willard were unaware of a biochemical mechanism which could result in biased sex ratios. One possible explanation is that a high level of circulating glucose in the mother's bloodstream favors the survival of male blastocysts . [ 4 ] This conclusion is based on the observed male-skewed survival rates (to expanded blastocyst stages) when bovine blastocysts were exposed to heightened levels of glucose. As blood glucose levels are highly correlated with access to high-quality food, [ 5 ] they may serve as a proxy for maternal condition.
The Trivers–Willard hypothesis has been applied to resource differences among individuals in a society as well as to resource differences among societies . Investigations in humans pose a number of practical and methodological difficulties, [ 6 ] but while a 2007 review of previous research found that empirical evidence for the hypothesis was mixed, the author noted that it received greater support from better-designed studies. One such example cited was a 1997 analysis of Hungarian Romani – a low-status group with a preference for females, who "had a female-biased sex ratio at birth, were more likely to abort a child after having had one or more daughters, nursed their daughters longer, and sent their daughters to school for longer". [ 7 ] | https://en.wikipedia.org/wiki/Trivers–Willard_hypothesis |
In chemistry , a trivial name is a non- systematic name for a chemical substance . That is, the name is not recognized according to the rules of any formal system of chemical nomenclature such as IUPAC inorganic or IUPAC organic nomenclature. A trivial name is not a formal name and is usually a common name .
Generally, trivial names are not useful in describing the essential properties of the thing being named. Properties such as the molecular structure of a chemical compound are not indicated. And, in some cases, trivial names can be ambiguous or will carry different meanings in different industries or in different geographic regions (for example, a trivial name such as white metal can mean various things). Trivial names are simpler. As a result, a limited number of trivial chemical names are retained names , an accepted part of the nomenclature.
Trivial names often arise in the common language; they may come from historic usages in, for example, alchemy . Many trivial names pre-date the institution of formal naming conventions. Names can be based on a property of the chemical, including appearance (color, taste or smell), consistency, and crystal structure; a place where it was found or where the discoverer comes from; the name of a scientist; a mythological figure; an astronomical body; the shape of the molecule; and even fictional figures. All elements that have been isolated have trivial names.
In scientific documents, international treaties, patents and legal definitions, names for chemicals are needed that
identify them unambiguously. This need is satisfied by systematic names . One such system, established by the International Union of Pure and Applied Chemistry (IUPAC), was established in 1950. Other systems have been developed by the American Chemical Society , the International Organization for Standardization , and the World Health Organization . However, chemists still use many names that are not systematic because they are traditional or because they are more convenient than the systematic names. These are called trivial names . The word "trivial", often used in a pejorative sense, was intended to mean "commonplace". [ 1 ]
In addition to trivial names, chemists have constructed semi-trivial names by appending a standard symbol to a trivial stem. [ 2 ] Some trivial and semi-trivial names are so widely used that they have been officially adopted by IUPAC; these are known as retained names .
The common names used for pesticides did not become commonplace through repeated informal usage, The names are granted by ISO committee (TC81), who approve the common name according to ISO1750. [ 3 ]
Traditional names of elements are trivial, some originating in alchemy . IUPAC has accepted these names, but has also defined systematic names of elements that have not yet been prepared. It has adopted a procedure by which the scientists who are credited with preparing an element can propose a new name. Once the IUPAC has accepted such a (trivial) name, it replaces the systematic name. [ 1 ]
Nine elements were known by the Middle Ages : gold , silver , tin , mercury , copper , lead , iron , sulfur , and carbon . [ 4 ] Mercury was named after the planet, but its symbol was derived from the Latin hydrargyrum , which itself comes from the Greek υδράργυρος , meaning liquid silver; mercury is also known as quicksilver in English. [ 1 ] The symbols for the other eight are derived from their Latin names. [ 4 ]
Systematic nomenclature began after Louis-Bernard Guyton de Morveau stated the need for "a constant method of denomination, which helps the intelligence and relieves the memory". [ 5 ] The resulting system was popularized by Antoine Lavoisier 's publication of Méthode de nomenclature chimique (Method of Chemical Nomenclature) in 1787. Lavoisier proposed that elements be named after their properties. For the next 125 years, most chemists followed this suggestion, using Greek and Latin roots to compose the names; for example, hydrogen ("water-producing"), oxygen ("acid-producing"), nitrogen ("soda-producing"), bromine ("stink"), and argon were based on Greek roots, while the names of iodine and chlorine were derived from the Greek words for their characteristic colors. Indium , rubidium , and thallium were similarly named for the colors of particular lines in their emission spectra . Iridium , which forms compounds of many different colors, takes its name from iris , the Latin for "rainbow". [ 4 ] The noble gases have all been named for their origin or properties. Helium comes from the Greek helios , meaning "Sun" because it was first detected as a line in the spectrum of the Sun (it is not known why the suffix -ium , which is used for metals, was chosen). [ 6 ] The other noble gases are neon ("new"), argon ("slow, lazy"), krypton ("hidden"), xenon ("stranger"), and radon ("from radium"). [ 7 ]
Many more elements have been given names that have little or nothing to do with their properties. Elements have been named for celestial bodies ( helium , selenium , tellurium , for the Sun, Moon, and Earth; cerium and palladium for Ceres and Pallas , two asteroids ). They have been named for mythological figures, including Titans in general ( titanium ) and Prometheus in particular ( promethium ); Roman and Greek gods ( uranium , neptunium , and plutonium ) and their descendants ( tantalum for Tantalus , a son of Zeus, and niobium for Niobe , a daughter of Tantalus); and Norse deities ( vanadium for the goddess Vanadis and thorium for the god Thor ). [ 7 ]
Some elements were named for aspects of the history of their discovery. In particular, technetium and promethium were so named because the first samples detected were artificially synthesised ; neither of the two has any isotope sufficiently stable to occur in nature on Earth in significant quantities. The connection to the Titan Prometheus was that he had been fabled to have stolen fire from the gods for mankind.
Discoverers of some elements named them after their home country or city. Marie Curie named polonium after Poland ; ruthenium , gallium , germanium , and lutetium were based on the Latin names for Russia, France, Germany, and Paris. Other elements are named after the place where they were discovered. Four elements — terbium , erbium , ytterbium , and yttrium — were named after the Swedish village Ytterby , where ores containing them were extracted. [ 4 ] Other elements named after places are magnesium (after Magnesia ), strontium , scandium , europium , thulium (after an old Roman name for an unidentified northern region), holmium , copper (derived from Cyprus , where it was mined in the Roman era), hafnium , rhenium , americium , berkelium , californium , and darmstadtium . [ 7 ]
For the elements up to 92 (uranium), naming elements after people was discouraged. The two exceptions are indirect, the elements being named after minerals that were themselves named after people. These were gadolinium (found in gadolinite , named after the Finnish chemist Johan Gadolin ) and samarium (the mineral samarskite was named after a Russian mining engineer, Vasili Samarsky-Bykhovets ). Among the transuranium elements , this restriction was relaxed; there followed curium (after the Curies), einsteinium ( Albert Einstein ), fermium ( Enrico Fermi ), mendelevium ( Dmitri Mendeleev ), nobelium ( Alfred Nobel ) and lawrencium ( Ernest Lawrence ). [ 7 ] [ 8 ] : 320
IUPAC has established international standards for naming elements. The first scientist or laboratory to isolate an element has the right to propose a name; after a review process, a final decision is made by the IUPAC Council. In keeping with tradition, names can be based on a mythological concept or character, astronomical object, mineral, place, property of the element or scientist. [ 5 ] For those elements that have not yet been discovered, IUPAC has established a systematic name system. The names combine syllables that represent the digits of the atomic number , followed by "-ium". For example, "unununium" is element 111 ("un" being the syllable for 1). [ 9 ] However, once the element has been found, the systematic name is replaced by a trivial one, in this case roentgenium . [ 1 ]
The IUPAC names for elements are intended for use in the official languages. At the time of the first edition of the IUPAC Red Book (which contains the rules for inorganic compounds), those languages were English and French; now English is the sole official language. [ 10 ] However, other languages still have their own names for elements. The chemical symbol for tungsten , W, is based on the German name Wolfram , which is found in wolframite and comes from the German for "wolf's foam", how the mineral was known to Saxon miners. The name tungsten means "heavy stone", a description of scheelite , another mineral in which tungsten is found. [ 11 ] Russian names for hydrogen, oxygen and carbon are vodorod , kislorod and uglerod (generating water, acid and coal respectively). The German names for hydrogen, oxygen, and nitrogen are Wasserstoff (water substance), Sauerstoff (acid substance), and Stickstoff (smothering substance).
The corresponding Chinese names are qīngqì (light gas), yǎngqì (nourishing gas), and dànqì (diluting gas). A method for translating chemical names into Chinese was developed by John Fryer and Xu Shou in 1871. Where traditional names were well established, they kept them; otherwise, a single character was created. [ N 1 ]
Early terminology for compound chemicals followed similar rules to the naming of elements. The names could be based on the appearance of the substance, including all five senses. In addition, chemicals were named after the consistency, crystalline form, a person or place, its putative medical properties or method of preparation. [ 13 ] : 68
Salt ( sodium chloride ) is soluble and is used to enhance the taste of food. Substances with similar properties came to be known as salts, in particular Epsom salt ( magnesium sulfate , found in a bitter saline spring in the English town of Epsom ). Ammonium (with the little-used systematic name azanium [ 14 ] ) was first extracted from sal ammoniac , meaning "salt of Amun". Ancient Romans noticed crystals of it in Egyptian temples devoted to the god Amun ; the crystals had condensed from the smoke of burning camel dung. [ 15 ] Lead acetate was called sugar of lead . [ 13 ] : 70, 77–78 However, other names like sugar of lead ( lead(II) acetate ), butter of antimony ( antimony trichloride ), oil of vitriol ( sulfuric acid ), and cream of tartar ( potassium bitartrate ) borrowed their language from the kitchen. [ 13 ] : 65–66 Many more names were based on color; for example, hematite , orpiment , and verdigris come from words meaning "blood-like stone", "gold pigment", and "green of Greece". [ 13 ] : 70
Some names are based on their use. Lime is a general name for materials combining calcium with carbonates, oxides or hydroxides; the name comes from a root "sticking or adhering"; its earliest use was as mortar for construction. [ 16 ]
Water has several systematic names, including oxidane (the IUPAC name), hydrogen oxide , and dihydrogen monoxide (DHMO). The latter was the basis of the dihydrogen monoxide hoax , a document that was circulated warning readers of the dangers of the chemical (for example, it is fatal if inhaled ). [ 17 ] [ 18 ]
In organic chemistry, some trivial names derive from a notable property of the thing being named. For instance, lecithin , the common name for phosphatidylcholine , was originally isolated from egg yolk . The word is coined from the Greek λέκιθος (lékithos) for yolk . [ 19 ] [ 20 ]
Many trivial names continue to be used because their sanctioned equivalents are considered too cumbersome for everyday use. For example, " tartaric acid ", a compound found in wine , has a systematic name of 2,3-dihydroxybutanedioic acid. The pigment β-Carotene has an IUPAC name of 1,3,3-trimethyl-2-[(1 E ,3 E ,5 E ,7 E ,9 E ,11 E ,13 E ,15 E ,17 E )-3,7,12,16-tetramethyl-18-(2,6,6-trimethylcyclohexen-1-yl)octadeca-1,3,5,7,9,11,13,15,17-nonaenyl]cyclohexene. [ 21 ] However, the trivial name can be potentially confusing. Based on its name, one might come to the conclusion that the molecule theobromine contains one or more bromine atoms. In reality it is an alkaloid similar in structure to caffeine.
Several organic molecules have semitrivial names where the suffixes -ane (for an alkane ) or -ene (for an alkene ) are added to a name based on the shape of the molecule. [ 8 ] : xi Some are pictured below. Other examples include barrelene (shaped like a barrel), [ 8 ] : 58 fenestrane (having a window-pane motif), [ 8 ] : 55 ladderane (a ladder shape), olympiadane (having a shape with the same topology as the Olympic rings) and quadratic acid (also known as squaric acid ).
The bohemic acid complex is a mixture of chemicals obtained through fermentation of a species of actinobacteria . In 1977 the components were isolated and have been found useful as antitumor agents and anthracycline antibiotics . The authors named the complex (and one of its components, bohemamine) after the opera La bohème by Puccini , and the remaining components were named after characters in the opera: alcindoromycin (Alcindoro), collinemycin (Colline), marcellomycin (Marcello), mimimycin (Mimi), musettamycin (Musetta), rudolphomycin (Rodolfo) and schaunardimycin (Schaunard). [ 8 ] : 64 [ 22 ] However, the relationships between the characters do not correctly reflect the chemical relationships. [ 23 ]
A research lab at Lepetit Pharmaceuticals, led by Piero Sensi, was fond of coining nicknames for chemicals that they discovered, later converting them to a form more acceptable for publication. The antibiotic rifampicin was named after a French movie, Rififi , about a jewel heist. They nicknamed another antibiotic " Mata Hari " before changing the name to matamycin . [ 23 ] | https://en.wikipedia.org/wiki/Trivial_name |
In the mathematical field of representation theory , a trivial representation is a representation ( V , φ ) of a group G on which all elements of G act as the identity mapping of V . A trivial representation of an associative or Lie algebra is a ( Lie ) algebra representation for which all elements of the algebra act as the zero linear map ( endomorphism ) which sends every element of V to the zero vector .
For any group or Lie algebra, an irreducible trivial representation always exists over any field , and is one-dimensional, hence unique up to isomorphism. The same is true for associative algebras unless one restricts attention to unital algebras and unital representations.
Although the trivial representation is constructed in such a way as to make its properties seem tautologous, it is a fundamental object of the theory. A subrepresentation is equivalent to a trivial representation, for example, if it consists of invariant vectors; so that searching for such subrepresentations is the whole topic of invariant theory .
The trivial character is the character that takes the value of one for all group elements.
This algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Trivial_representation |
In topology , a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such spaces are commonly called indiscrete , anti-discrete , concrete or codiscrete . Intuitively, this has the consequence that all points of the space are "lumped together" and cannot be distinguished by topological means. Every indiscrete space can be viewed as a pseudometric space in which the distance between any two points is zero.
The trivial topology is the topology with the least possible number of open sets , namely the empty set and the entire space, since the definition of a topology requires these two sets to be open. Despite its simplicity, a space X with more than one element and the trivial topology lacks a key desirable property: it is not a T 0 space .
Other properties of an indiscrete space X —many of which are quite unusual—include:
In some sense the opposite of the trivial topology is the discrete topology , in which every subset is open.
The trivial topology belongs to a uniform space in which the whole cartesian product X × X is the only entourage .
Let Top be the category of topological spaces with continuous maps and Set be the category of sets with functions. If G : Top → Set is the functor that assigns to each topological space its underlying set (the so-called forgetful functor ), and H : Set → Top is the functor that puts the trivial topology on a given set, then H (the so-called cofree functor ) is right adjoint to G . (The so-called free functor F : Set → Top that puts the discrete topology on a given set is left adjoint to G .) [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Trivial_topology |
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