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The jumping-Jupiter scenario specifies an evolution of giant- planet migration described by the Nice model , in which an ice giant (an additional Neptune-mass planet ) is scattered inward by Saturn and then ejected by Jupiter , causing their semi-major axes to jump, and thereby quickly separating their orbits . [ 1 ] The jumping-Jupiter scenario was proposed by Ramon Brasser, Alessandro Morbidelli , Rodney Gomes, Kleomenis Tsiganis, and Harold Levison after their studies revealed that the smooth divergent migration of Jupiter and Saturn resulted in an inner Solar System significantly different from the current Solar System. [ 1 ] During this migration secular resonances swept through the inner Solar System exciting the orbits of the terrestrial planets and the asteroids, leaving the planets' orbits too eccentric , [ 1 ] and the asteroid belt with too many high- inclination objects. [ 2 ] The jumps in the semi-major axes of Jupiter and Saturn described in the jumping-Jupiter scenario can allow these resonances to quickly cross the inner Solar System without altering orbits excessively, [ 1 ] although the terrestrial planets remain sensitive to its passage. [ 3 ] [ 4 ]
The jumping-Jupiter scenario also results in a number of other differences with the original Nice model. The fraction of lunar impactors from the core of the asteroid belt during the Late Heavy Bombardment is significantly reduced, [ 5 ] most of the Jupiter trojans are captured during Jupiter's encounters with the ice giant, [ 6 ] as are Jupiter's irregular satellites . [ 7 ] In the jumping-Jupiter scenario, the likelihood of preserving four giant planets on orbits resembling their current ones appears to increase if the early Solar System originally contained an additional ice giant , which was later ejected by Jupiter into interstellar space . [ 8 ] However, this remains an atypical result, [ 9 ] as is the preservation of the current orbits of the terrestrial planets. [ 4 ]
In the original Nice model a resonance crossing results in a dynamical instability that rapidly alters the orbits of the giant planets. The original Nice model begins with the giant planets in a compact configuration with nearly circular orbits. Initially, interactions with planetesimals originating in an outer disk drive a slow divergent migration of the giant planets. This planetesimal-driven migration continues until Jupiter and Saturn cross their mutual 2:1 resonance . The resonance crossing excites the eccentricities of Jupiter and Saturn. The increased eccentricities create perturbations on Uranus and Neptune , increasing their eccentricities until the system becomes chaotic and orbits begin to intersect. Gravitational encounters between the planets then scatter Uranus and Neptune outward into the planetesimal disk. The disk is disrupted, scattering many of the planetesimals onto planet-crossing orbits. A rapid phase of divergent migration of the giant planets is initiated and continues until the disk is depleted. Dynamical friction during this phase dampens the eccentricities of Uranus and Neptune stabilizing the system. In numerical simulations of the original Nice model the final orbits of the giant planets are similar to the current Solar System . [ 10 ]
Later versions of the Nice model begin with the giant planets in a series of resonances. This change reflects some hydrodynamic models of the early Solar System . In these models, interactions between the giant planets and the gas disk result in the giant planets migrating toward the central star, in some cases becoming hot Jupiters . [ 11 ] However, in a multiple-planet system, this inward migration may be halted or reversed if a more rapidly migrating smaller planet is captured in an outer orbital resonance . [ 12 ] The Grand Tack hypothesis, which posits that Jupiter's migration is reversed at 1.5 AU following the capture of Saturn in a resonance, is an example of this type of orbital evolution. [ 13 ] The resonance in which Saturn is captured, a 3:2 or a 2:1 resonance, [ 14 ] [ 15 ] and the extent of the outward migration (if any) depends on the physical properties of the gas disk and the amount of gas accreted by the planets. [ 15 ] [ 16 ] [ 17 ] The capture of Uranus and Neptune into further resonances during or following this outward migration results in a quadruply resonant system, [ 18 ] with several stable combinations having been identified. [ 19 ] Following the dissipation of the gas disk, the quadruple resonance is eventually broken due to interactions with planetesimals from the outer disk. [ 20 ] Evolution from this point resembles the original Nice model with an instability beginning either shortly after the quadruple resonance is broken [ 20 ] or after a delay during which planetesimal-driven migration drives the planets across a different resonance. [ 19 ] However, there is no slow approach to the 2:1 resonance as Jupiter and Saturn either begin in this resonance [ 15 ] [ 17 ] or cross it rapidly during the instability. [ 18 ]
The stirring of the outer disk by massive planetesimals can trigger a late instability in a multi-resonant planetary system. As the eccentricities of the planetesimals are excited by gravitational encounters with Pluto-mass objects, an inward migration of the giant planets occurs. The migration, which occurs even if there are no encounters between planetesimals and planets, is driven by a coupling between the average eccentricity of the planetesimal disk and the semi-major axes of the outer planets. Because the planets are locked in resonance , the migration also results in an increase in the eccentricity of the inner ice giant . The increased eccentricity changes the precession frequency of the inner ice giant, leading to the crossing of secular resonances . The quadruple resonance of the outer planets can be broken during one of these secular-resonance crossings. Gravitational encounters begin shortly afterward due to the close proximity of the planets in the previously resonant configuration. The timing of the instability caused by this mechanism, typically occurring several hundred million years after the dispersal of the gas disk, is fairly independent of the distance between the outer planet and the planetesimal disk. In combination with the updated initial conditions, this alternative mechanism for triggering a late instability has been called the Nice 2 model . [ 20 ]
Encounters between Jupiter and an ice giant during the giant planet migration are required to reproduce the current Solar System. In a series of three articles Ramon Brasser, Alessandro Morbidelli , Rodney Gomes, Kleomenis Tsiganis, and Harold Levison analyzed the orbital evolution of the Solar System during giant planet migration. The first article demonstrated that encounters between an ice giant and at least one gas giant were required to reproduce the oscillations of the eccentricities of the gas giants. [ 21 ] The other two demonstrated that if Jupiter and Saturn underwent a smooth planetesimal-driven separation of their orbits the terrestrial planets would have orbits that are too eccentric and too many of the asteroids would have orbits with large inclinations. They proposed that the ice giant encountered both Jupiter and Saturn, causing the rapid separation of their orbits, thereby avoiding the secular resonance sweeping responsible for the excitation of orbits in the inner Solar System. [ 1 ] [ 2 ]
Exciting the oscillations of the eccentricities of the giant planets requires encounters between planets. Jupiter and Saturn have modest eccentricities that oscillate out of phase, with Jupiter reaching maximum eccentricity when Saturn reaches its minimum and vice versa. A smooth migration of the giant planets without resonance crossings results in very small eccentricities. Resonance crossings excite their mean eccentricities , with the 2:1 resonance crossing reproducing Jupiter's current eccentricity, but these do not generate the oscillations in their eccentricities. Recreating both requires either a combination of resonance crossings and an encounter between Saturn and an ice giant, or multiple encounters of an ice giant with one or both gas giants . [ 21 ]
During the smooth migration of the giant planets the ν5 secular resonance sweeps through the inner Solar System , exciting the eccentricities of the terrestrial planets. When planets are in a secular resonance the precessions of their orbits are synchronized, keeping their relative orientations and the average torques exerted between them fixed. The torques transfer angular momentum between the planets causing changes in their eccentricities and, if the orbits are inclined relative to one another, their inclinations. If the planets remain in or near secular resonances these changes can accumulate resulting in significant changes in eccentricity and inclination. [ 22 ] During a ν5 secular resonance crossing this can result in the excitation of the terrestrial planet's eccentricity, with the magnitude of the increase depending on the eccentricity of Jupiter and the time spent in the secular resonance. [ 23 ] For the original Nice model the slow approach to Jupiter's and Saturn's 2:1 resonance results in an extended interaction of the ν5 secular resonance with Mars, driving its eccentricity to levels that can destabilize the inner Solar System, potentially leading to collisions between planets or the ejection of Mars. [ 1 ] [ 23 ] In later versions of the Nice model Jupiter's and Saturn's divergent migration across (or from) the 2:1 resonance is more rapid and the nearby ν5 resonance crossings of Earth and Mars are brief, thus avoiding the excessive excitation of their eccentricities in some cases. Venus and Mercury, however, reach significantly higher eccentricities than are observed when the ν5 resonance later crosses their orbits. [ 1 ]
A smooth planetesimal-driven migration of the giant planets also results in an asteroid belt orbital distribution unlike that of the current asteroid belt. As it sweeps across the asteroid belt the ν16 secular resonance excites asteroid inclinations. It is followed by the ν6 secular resonance which excites the eccentricities of low- inclination asteroids. [ 2 ] If the secular resonance sweeping occurs during a planetesimal driven migration, which has a timescale of 5 million years or longer, the remaining asteroid belt is left with a significant fraction of asteroids with inclinations greater than 20°, which are relatively rare in the current asteroid belt. [ 22 ] The interaction of the ν6 secular resonance with the 3:1 mean-motion resonance also leaves a prominent clump in the semi-major-axis distribution that is not observed. [ 2 ] The secular resonance sweeping would also leave too many high inclination asteroids if the giant planet migration occurred early, with all of the asteroids initially in low eccentricity and inclination orbits, [ 24 ] and also if the orbits of the asteroids were excited by Jupiter's passage during the Grand Tack. [ 25 ]
Encounters between an ice giant and both Jupiter and Saturn accelerate the separation of their orbits, limiting the effects of secular resonance sweeping on the orbits of the terrestrial planets and the asteroids. To prevent the excitation of orbits of the terrestrial planets and asteroids the secular resonances must sweep rapidly through the inner Solar System. The small eccentricity of Venus indicates that this occurred on a timescale of less than 150,000 years, much shorter than in a planetesimal driven migration. [ 22 ] The secular resonance sweeping can be largely avoided, however, if the separation of Jupiter and Saturn was driven by gravitational encounters with an ice giant. These encounters must drive the Jupiter–Saturn period ratio quickly from below 2.1 to beyond 2.3, the range where the secular resonance crossings occur. This evolution of the giant planets orbits has been named the jumping-Jupiter scenario after a similar process proposed to explain the eccentric orbits of some exoplanets. [ 1 ] [ 2 ]
The jumping-Jupiter scenario replaces the smooth separation of Jupiter and Saturn with a series of jumps, thereby avoiding the sweeping of secular resonances through the inner Solar System as their period ratio crosses from 2.1 to 2.3. [ 1 ] In the jumping-Jupiter scenario an ice giant is scattered inward by Saturn onto a Jupiter-crossing orbit and then scattered outward by Jupiter. [ 2 ] Saturn's semi-major axis is increased in the first gravitational encounter and Jupiter's reduced by the second with the net result being an increase in their period ratio. [ 2 ] In numerical simulations the process can be much more complex: while the trend is for Jupiter's and Saturn's orbits to separate, depending on the geometry of the encounters, individual jumps of Jupiter's and Saturn's semi-major axes can be either up and down. [ 6 ] In addition to numerous encounters with Jupiter and Saturn, the ice giant can encounter other ice giant(s) and in some cases cross significant parts of the asteroid belt. [ 26 ] The gravitational encounters occur over a period of 10,000–100,000 years, [ 2 ] and end when dynamical friction with the planetesimal disk dampens the ice giant's eccentricity, raising its perihelion beyond Saturn's orbit; or when the ice giant is ejected from the Solar System. [ 9 ] A jumping-Jupiter scenario occurs in a subset of numerical simulations of the Nice model, including some done for the original Nice model paper. [ 1 ] The chances of Saturn scattering an ice giant onto a Jupiter-crossing orbit increases when the initial Saturn–ice giant distance is less than 3 AU , and with the 35- Earth-mass planetesimal belt used in the original Nice model, typically results in the ejection of the ice giant. [ 27 ]
The frequent loss of the giant planet encountering Jupiter in simulations has led some to propose that the early Solar System began with five giant planets. In numerical simulations of the jumping-Jupiter scenario the ice giant is often ejected following its gravitational encounters with Jupiter and Saturn, leaving planetary systems that begin with four giant planets with only three. [ 8 ] [ 28 ] Although beginning with a higher-mass planetesimal disk was found to stabilize four-planet systems, the massive disk either resulted in excess migration of Jupiter and Saturn after the encounters between an ice giant and Jupiter or prevented these encounters by damping eccentricities. [ 8 ] This problem led David Nesvorný to investigate planetary systems beginning with five giant planets. After conducting thousands of simulations he reported that simulations beginning with five giant planets were 10 times as likely to reproduce the current orbits of the outer planets. [ 29 ] A follow-up study by Nesvorny and Alessandro Morbidelli sought initial resonant configurations that would reproduce the semi-major axis of the four outer planets, Jupiter's eccentricity, and a jump from <2.1 to >2.3 in Jupiter's and Saturn's period ratio. While less than 1% of the best four-planet models met these criteria roughly 5% of the best five-planet models were judged successful, with Jupiter's eccentricity being the most difficult to reproduce. [ 9 ] A separate study by Konstantin Batygin and Michael E. Brown found similar probabilities (4% vs 3%) of reproducing the current outer Solar System beginning with four or five giant planets using the best initial conditions. [ 30 ] [ 28 ] Their simulations differed in that the planetesimal disk was placed close to the outer planet resulting in a period of migration before planetary encounters began. Criteria included reproducing the oscillations of Jupiter's and Saturn's eccentricities, a period when Neptune's eccentricity exceeded 0.2 during which hot classical Kuiper belt objects were captured, and the retention of a primordial cold classical Kuiper belt , [ 30 ] but not the jump in Jupiter's and Saturn's period ratio. [ 9 ] Their results also indicate that if Neptune's eccentricity exceeded 0.2, preserving a cold classical belt may require the ice giant to be ejected in as little as 10,000 years. [ 28 ]
Neptune's migration into the planetesimal disk before planetary encounters begin allows Jupiter to retain a significant eccentricity and limits its migration after the ejection of the fifth ice giant. Jupiter's eccentricity is excited by resonance crossings and gravitational encounters with the ice giant and is damped due to secular friction with the planetesimal disk. Secular friction occurs when the orbit of a planet suddenly changes and results in the excitation of the planetesimals' orbits and the reduction of the planet's eccentricity and inclination as the system relaxes. If gravitational encounters begin shortly after the planets leave their multi-resonant configuration, this leaves Jupiter with a small eccentricity. However, if Neptune first migrates outward disrupting the planetesimal disk, its mass is reduced and the eccentricities and inclinations of the planetesimals are excited. When planetary encounters are later triggered by a resonance crossing this lessens the impact of secular friction allowing Jupiter's eccentricity to be maintained. The smaller mass of the disk also reduces the divergent migration of Jupiter and Saturn following the ejection of the fifth planet. This can allow Jupiter's and Saturn's period ratio to jump beyond 2.3 during the planetary encounters without exceeding the current value once the planetesimal disk is removed. Although this evolution of the outer planet's orbits can reproduce the current Solar System, it is not the typical result in simulations that begin with a significant distance between the outer planet and the planetesimal disk as in the Nice 2 model. [ 9 ] An extended migration of Neptune into the planetesimal disk before planetary encounters begin can occur if the disk's inner edge was within 2 AU of Neptune's orbit. This migration begins soon after the protoplanetary disk dissipates, resulting in an early instability, and is most likely if the giant planets began in a 3:2, 3:2, 2:1, 3:2 resonance chain. [ 31 ]
A late instability can occur if Neptune first underwent a slow dust-driven migration towards a more distant planetesimal disk. For a five planet system to remain stable for 400 million years the inner edge of the planetesimal disk must be several AU beyond Neptune's initial orbit. Collisions between planetesimals in this disk creates debris that is ground down to dust in a collisional cascade. The dust drifts inward due to Poynting–Robertson drag, eventually reaching the orbits of the giant planets. Gravitational interactions with the dust causes the giant planets to escape from their resonance chain roughly 10 million years after the dissipation of the gas disk. The gravitational interactions then result in a slow dust-driven migration of the planets until Neptune approaches the inner edge of the disk. A more rapid planetesimal-driven migration of Neptune into the disk then ensues until the orbits of the planets are destabilized following a resonance crossing. The dust driven migration requires 7–22 Earth-masses of dust, depending on the initial distance between Neptune's orbit and the inner edge of the dust disk. The rate of the dust-driven migration slows with time as the amount of dust the planets encounters declines. As a result, the timing of the instability is sensitive to the factors that control the rate of dust generation such as the size distribution and the strength of the planetesimals. [ 31 ]
The jumping-Jupiter scenario results in a number of differences with the original Nice model.
The rapid separation of Jupiter's and Saturn's orbits causes the secular resonances to quickly cross the inner Solar System. The number of asteroids removed from the core of the asteroid belt is reduced, leaving an inner extension of the asteroid belt as the dominant source of rocky impactors. The likelihood of preserving the low eccentricities of the terrestrial planets increases to above 20% in a selected jumping-Jupiter model. Since the modification of orbits in the asteroid belt is limited, its depletion and the excitement of its orbits must have occurred earlier. However, asteroid orbits are modified enough to shift the orbital distribution produced by a grand tack toward that of the current asteroid belt, to disperse collisional families, and to remove fossil Kirkwood gaps. The ice giant crossing the asteroid belt allows some icy planetesimals to be implanted into the inner asteroid belt.
In the outer Solar System icy planetesimals are captured as Jupiter trojans when Jupiter's semi-major axis jumps during encounters with the ice giant. Jupiter also captures irregular satellites via three body interactions during these encounters. The orbits of Jupiter's regular satellites are perturbed, but in roughly half of simulations remain in orbits similar to those observed. Encounters between an ice giant and Saturn perturb the orbit of Iapetus and may be responsible for its inclination. The dynamical excitement of the outer disk by Pluto-massed objects and its lower mass reduces the bombardment of Saturn's moons. Saturn's tilt is acquired when it is captured in a spin-orbit resonance with Neptune. A slow and extended migration of Neptune into the planetesimal disk before planetary encounters begin leaves the Kuiper belt with a broad inclination distribution. When Neptune's semi-major axis jumps outward after it encounters the ice giant objects captured in its 2:1 resonance during its previous migration escape, leaving a clump of low inclination objects with similar semi-major axes. The outward jump also releases objects from the 3:2 resonance, reducing the number of low inclination plutinos remaining at the end of Neptune's migration.
Most of the rocky impactors of the Late Heavy Bombardment originate from an inner extension of the asteroid belt yielding a smaller but longer lasting bombardment. The innermost region of the asteroid belt is currently sparsely populated due to the presence of the ν6 secular resonance . In the early Solar System, however, this resonance was located elsewhere and the asteroid belt extended farther inward, ending at Mars-crossing orbits. [ 5 ] During the giant planet migration the ν6 secular resonance first rapidly traversed the asteroid belt removing roughly half of its mass, much less than in the original Nice model. [ 2 ] When the planets reached their current positions the ν6 secular resonance destabilized the orbits of the innermost asteroids. Some of these quickly entered planet crossing orbit initiating the Late Heavy Bombardment. Others entered quasi-stable higher inclination orbits, later producing an extended tail of impacts, with a small remnant surviving as the Hungarias . [ 5 ] The increase in the orbital eccentricities and inclinations of the destabilized objects also raised impact velocities, resulting in a change in the size distribution of lunar craters, [ 32 ] and in the production of impact melt in the asteroid belt. [ 33 ] The innermost (or E-belt ) asteroids are estimated to have produced nine basin-forming impacts on the Moon between 4.1 and 3.7 billion years ago with three more originating from the core of the asteroid belt. [ 5 ] The pre-Nectarian basins, part of the LHB in the original Nice model , [ 34 ] are thought to be due to the impacts of leftover planetesimals from the inner Solar System. [ 5 ]
The magnitude of the cometary bombardment is also reduced. The giant planets outward migration disrupts the outer planetesimal disk causing icy planetesimals to enter planet crossing orbits. Some of them are then perturbed by Jupiter onto orbits similar to those of Jupiter-family comets. These spend a significant fraction of their orbits crossing the inner Solar System raising their likelihood of impacting the terrestrial planets and the moon. [ 35 ] In the original Nice model this results in a cometary bombardment with a magnitude similar to the asteroid bombardment. [ 34 ] However, while low levels of iridium detected from rocks dating from this era have been cited as evidence of a cometary bombardment, [ 36 ] other evidence such as the mix of highly siderophile elements in lunar rocks, [ 37 ] and oxygen isotope ratios in the fragments of impactors are not consistent with a cometary bombardment. [ 38 ] The size distribution of lunar craters is also largely consistent with that of the asteroids, leading to the conclusion the bombardment was dominated by asteroids. [ 39 ] The bombardment by comets may have been reduced by a number of factors. The stirring of the orbits by Pluto-massed objects excites of the inclinations of the orbits of the icy planetimals, reducing the fraction of objects entering Jupiter-family orbits from 1/3 to 1/10. The mass of the outer disk in the five-planet model is roughly half that of the original Nice model. The magnitude of the bombardment may have been reduced further due to the icy planetesimals undergoing significant mass loss, or their having broken up as they entered the inner Solar System. The combination of these factors reduces the estimated largest impact basin to the size of Mare Crisium, roughly half the size of the Imbrium basin. [ 35 ] Evidence of this bombardment may have been destroyed by later impacts by asteroids. [ 40 ]
A number of issues have been raised regarding the connection between the Nice model and the Late Heavy Bombardment. Crater counts using topographic data from the Lunar Reconnaissance Orbiter find an excess of small craters relative to large impact-basins when compared to the size distribution of the asteroid belt. [ 41 ] However, if the E-belt was the product of collisions among a small number of large asteroids, it may have had a size distribution that differed from that of the asteroid belt with a larger fraction of small bodies. [ 42 ] A recent work has found that the bombardment originating from the inner band of asteroids would yield only two lunar basins and would be insufficient to explain ancient impact spherule beds. It suggests instead that debris from a massive impact was the source, noting that this would better match the size distribution of impact craters. [ 43 ] A second work concurs, finding that the asteroid belt was probably not the source of the Late Heavy Bombardment. Noting the lack of direct evidence of cometary impactors, it proposes that leftover planetesimals were the source of most impacts and that Nice model instability may have occurred early. [ 44 ] If a different crater scaling law is used, however, the Nice model is more likely to produce the impacts attributed to the Late Heavy bombardment and more recent impact craters. [ 45 ] [ 46 ]
A giant-planet migration in which the ratio of the periods of Jupiter and Saturn quickly cross from below 2.1 to greater than 2.3 can leave the terrestrial planets with orbits similar to their current orbits. The eccentricities and inclinations of a group of planets can be represented by the angular momentum deficit (AMD), a measure of the differences of their orbits from circular coplanar orbits. A study by Brasser, Walsh, and Nesvorny found that when a selected jumping-Jupiter model was used, the current angular momentum deficit has a reasonable chance (~20%) of being reproduced in numerical simulations if the AMD was initially between 10% and 70% of the current value. The orbit of Mars is largely unchanged in these simulations indicating that its initial orbit must have been more eccentric and inclined than those of the other planets. [ 3 ] The jumping-Jupiter model used in this study was not typical, however, being selected from among only 5% with Jupiter and Saturn's period ratio jumped to beyond 2.3 while reproducing other aspects of the outer Solar System. [ 9 ]
The overall success rate of jumping-Jupiter models with a late instability reproducing both the inner and outer Solar System is small. When Kaib and Chambers conducted a large number of simulations starting with five giant planets in a resonance chain and Jupiter and Saturn in a 3:2 resonance, 85% resulted in the loss of a terrestrial planet, less than 5% reproduce the current AMD, and only 1% reproduce both the AMD and the giant planet orbits. [ 4 ] In addition to the secular-resonance crossings, the jumps in Jupiter's eccentricity when it encounters an ice giant can also excite the orbits of the terrestrial planets. [ 23 ] This led them to propose that the Nice model migration occurred before the formation of the terrestrial planets and that the LHB had another cause. [ 4 ] However, the advantage of an early migration is significantly reduced by the requirement that the Jupiter–Saturn period ratio jump to beyond 2.3 to reproduce the current asteroid belt. [ 24 ] [ 25 ]
An early instability could be responsible for the low mass of Mars. If the instability occurs early the eccentricities of the embryos and planetesimals in the Mars region are excited causing many of them being ejected. This deprives Mars of material ending its growth early leaving Mars smaller relative to Earth and Venus. [ 47 ]
The jumping-Jupiter model can reproduce the eccentricity and inclination of Mercury's orbit. Mercury's eccentricity is excited when it crosses a secular resonance with Jupiter. When relativistic effects are included, Mercury's precession rate is faster, which reduces the impact of this resonance crossing, and results in a smaller eccentricity similar to its current value. Mercury's inclination may be the result of it or Venus crossing a secular resonance with Uranus. [ 48 ]
The rapid traverse of resonances through the asteroid belt can leave its population and the overall distribution of its orbital elements largely preserved. [ 2 ] In this case the asteroid belt's depletion, the mixing of its taxonomical classes , and the excitation of its orbits, yielding a distribution of inclinations peaked near 10° and eccentricities peaked near 0.1, must have occurred earlier. [ 26 ] These may be the product of Jupiter's Grand Tack , provided that an excess of higher eccentricity asteroids is removed due to interactions with the terrestrial planets. [ 49 ] [ 26 ] Gravitational stirring by planetary embryos embedded in the asteroid belt could also produce its depletion, mixing, and excitation. [ 50 ] However, most if not all of the embryos must have been lost before the instability. [ 2 ] A mixing of asteroids types could be the product of asteroids being scattered into the belt during the formation of the planets. [ 51 ] [ 52 ] An initially small mass asteroid belt could have its inclinations and eccentricities excited by secular resonances that hopped across the asteroid belt if Jupiter's and Saturn's orbits became chaotic while in resonance. [ 53 ]
The orbits of the asteroids could be excited during the instability if the ice giant spent hundreds of thousands of years on a Jupiter crossing orbit. Numerous gravitational encounters between the ice giant and Jupiter during this period would cause frequent variations in Jupiter's semi-major axis, eccentricity and inclination. The forcing exerted by Jupiter on the orbits of the asteroids and the semi-major axes where it was strongest, would also vary, causing a chaotic excitation of the asteroids orbits that could reach or exceed their present level. The highest eccentricity asteroids would be later be removed by encounters with the terrestrial planets. The eccentricities of the terrestrial planets are excited beyond the current values during this process, however, requiring that the instability occur before their formation in this case. [ 54 ] Gravitational stirring by embryos during the instability could increase the number of asteroids entered unstable orbits, resulting in the loss of 99-99.9% of its mass. [ 47 ]
The sweeping of resonances and the penetration of the ice giant into the asteroid belt results in the dispersal of asteroid collisional families formed during or before the Late Heavy Bombardment . A collisional family's inclinations and eccentricities are dispersed due to the sweeping secular resonances, including those inside mean motion resonances, with the eccentricities being most affected. Perturbations by close encounters with the ice giant result in the spreading of a family's semi-major axes. Most collisional families would thus become unidentifiable by techniques such as the hierarchical clustering method, [ 55 ] and V-type asteroids originating from impacts on Vesta could be scattered to the middle and outer asteroid belt. [ 56 ] However, if the ice giant spent a short time crossing the asteroid belt, some collisional families may remain recognizable by identifying the V-shaped patterns in plots of semi-major axes vs absolute magnitude produced by the Yarkovsky effect. [ 57 ] [ 58 ] The survival of the Hilda collisional family, a subset of the Hilda group thought to have formed during the LHB because of the current low collision rate, [ 59 ] may be due to its creation after Hilda's jump-capture in the 3:2 resonance as the ice giant was ejected. [ 26 ] The stirring of semi-major axes by the ice giant may also remove fossil Kirkwood gaps formed before the instability. [ 53 ]
Planetesimals from the outer disc are embedded in all parts of the asteroid belt, remaining as P- and D-type asteroids . While Jupiter's resonances sweep across the asteroid belt, outer disk planetesimals are captured by its inner resonances, evolve to lower eccentricities via secular resonances within these resonances, and are released onto stable orbits as Jupiter's resonances move on. [ 60 ] Other planetesimals are implanted in the asteroid belt during encounters with the ice giant, either directly leaving them with aphelia higher than that of the ice giant's perihelia , or by removing them from a resonance. Jumps in Jupiter's semi-major axis during its encounters with the ice giant shift the locations of its resonances, releasing some objects and capturing others. Many of those remaining after its final jump, along with others captured by the sweeping resonances as Jupiter migrates to its current location, survive as parts of the resonant populations such as the Hildas, Thule , and those in the 2:1 resonance. [ 61 ] Objects originating in the asteroid belt can also be captured in the 2:1 resonance, [ 62 ] along with a few among the Hilda population. [ 26 ] The excursions the ice giant makes into the asteroid belt allows the icy planetesimals to be implanted farther into the asteroid belt, with a few reaching the inner asteroid belt with semi-major axis less than 2.5 AU. Some objects later drift into unstable resonances due to diffusion or the Yarkovsky effect and enter Earth-crossing orbits , with the Tagish Lake meteorite representing a possible fragment of an object that originated in the outer planetesimal disk. Numerical simulations of this process can roughly reproduce the distribution of P- and D-type asteroids and the size of the largest bodies, with differences such as an excess of objects smaller than 10 km being attributed to losses from collisions or the Yarkovsky effect, and the specific evolution of the planets in the model. [ 61 ]
Most of the Jupiter trojans are jump-captured shortly after gravitational encounters between Jupiter and an ice giant. During these encounters Jupiter's semi-major axis can jump by as much as 0.2 AU , displacing the L4 and L5 points radially, and releasing many existing Jupiter trojans. New Jupiter trojans are captured from the population of planetesimals with semi-major axes similar to Jupiter's new semi-major axis. [ 6 ] The captured trojans have a wide range of inclinations and eccentricities, the result of their being scattered by the giant planets as they migrated from their original location in the outer disk. Some additional trojans are captured, and others lost, during weak-resonance crossings as the co-orbital regions become temporarily chaotic . [ 6 ] [ 63 ] Following its final encounters with Jupiter the ice giant may pass through one of Jupiter's trojan swarms, scattering many, and reducing its population. [ 6 ] In simulations, the orbital distribution of Jupiter trojans captured and the asymmetry between the L4 and L5 populations is similar to that of the current Solar System and is largely independent of Jupiter's encounter history. Estimates of the planetesimal disk mass required for the capture of the current population of Jupiter trojans range from 15 to 20 Earth masses, consistent with the mass required to reproduce other aspects of the outer Solar System. [ 6 ] [ 22 ]
Planetesimals are also captured as Neptune trojans during the instability when Neptune's semimajor axis jumps. [ 64 ] The broad inclination distribution of the Neptune trojans indicates that the inclinations of their orbits must have been excited before they were captured. [ 65 ] The number of Neptune trojans may have been reduced due to Uranus and Neptune being closer to a 2:1 resonance in the past. [ 66 ]
Jupiter captures a population of irregular satellites and the relative size of Saturn's population is increased.
During gravitational encounters between planets, the hyperbolic orbits of unbound planetesimals around one giant planet are perturbed by the presence of the other. If the geometry and velocities are right, these three-body interactions leave the planetesimal in a bound orbit when planets separate. Although this process is reversible, loosely bound satellites including possible primordial satellites can also escape during these encounters, tightly bound satellites remain and the number of irregular satellites increases over a series of encounters. Following the encounters, the satellites with inclinations between 60° and 130° are lost due to the Kozai resonance and the more distant prograde satellites are lost to the evection resonance. [ 67 ] Collisions among the satellites result in the formation of families, in a significant loss of mass, and in a shift of their size distribution. [ 68 ] The populations and orbits of Jupiter's irregular satellites captured in simulations are largely consistent with observations. [ 7 ] Himalia , which has a spectra similar to asteroids in the middle of the asteroid belt, [ 69 ] is somewhat larger than the largest captured in simulations. If it was a primordial object its odds of surviving the series of gravitational encounters range from 0.01 - 0.3, with the odds falling as the number increases. [ 7 ] Saturn has more frequent encounters with the ice giant in the jumping-Jupiter scenario, and Uranus and Neptune have fewer encounters if that was a fifth giant planet. This increases the size of Saturn's population relative to Uranus and Neptune when compared to the original Nice model, producing a closer match with observations. [ 7 ] [ 70 ]
The orbits of Jupiter's regular satellites can remain dynamically cold despite encounters between the giant planets. Gravitational encounters between planets perturb the orbits of their satellites, exciting inclinations and eccentricities, and altering semi-major axes. If these encounters would lead to results inconsistent with the observations, for example, collisions between or the ejections of satellites or the disruption of the Laplace resonance of Jupiter's moons Io , Europa and Ganymede , this could provide evidence against jumping-Jupiter models. In simulations, collisions between or the ejection of satellites was found to be unlikely, requiring an ice giant to approach within 0.02 AU of Jupiter. More distant encounters that disrupted the Laplace resonance were more common, though tidal interactions often lead to their recapture. [ 71 ] A sensitive test of jumping-Jupiter models is the inclination of Callisto 's orbit, which isn't damped by tidal interactions. Callisto's inclination remained small in six out of ten 5-planet models tested in one study (including some where Jupiter acquired irregular satellites consistent with observations), [ 72 ] and another found the likelihood of Jupiter ejecting a fifth giant planet while leaving Callisto's orbit dynamically cold at 42%. [ 73 ] Callisto is also unlikely to have been part of the Laplace resonance, because encounters that raise it to its current orbit leave it with an excessive inclination. [ 71 ]
The encounters between planets also perturb the orbits of the moons of the other outer planets. Saturn's moon Iapetus could have been excited to its current inclination, if the ice giant's closest approach was out of the plane of Saturn's equator. If Saturn acquired its tilt before the encounters, Iapetus's inclination could also be excited due to multiple changes of its semi-major axis, because the inclination of Saturn's Laplace plane would vary with the distance from Saturn. In simulations, Iapetus was excited to its current inclination in five of ten of the jumping-Jupiter models tested, though three left it with excessive eccentricity. The preservation of Oberon's small inclination favors the 5-planet models, with only a few encounters between Uranus and an ice giant, over 4-planet models in which Uranus encounters Jupiter and Saturn. The low inclination of Uranus's moon Oberon, 0.1°, was preserved in nine out of ten of five planet models, while its preservation was found to be unlikely in four planet models. [ 72 ] [ 74 ] The encounters between planets may have also be responsible for the absence of regular satellites of Uranus beyond the orbit of Oberon. [ 74 ]
The loss of ices from the inner satellites due to impacts is reduced. Numerous impacts of planetesimals onto the satellites of the outer planets occur during the Late Heavy Bombardment. In the bombardment predicted by the original Nice model, these impacts generate enough heat to vaporize the ices of Mimas, Enceladus and Miranda. [ 75 ] The smaller mass planetesimal belt in the five planet models reduces this bombardment. Furthermore, the gravitational stirring by Pluto-massed objects in the Nice 2 model excites the inclinations and eccentricities of planetesimals. This increases their velocities relative to the giant planets, decreasing the effectiveness of gravitational focusing, thereby reducing the fraction of planetesimals impacting the inner satellites. Combined these reduce the bombardment by an order of magnitude. [ 76 ] Estimates of the impacts on Iapetus are also less than 20% of that of the original Nice model. [ 77 ]
Some of the impacts are catastrophic, resulting in the disruption of the inner satellites. In the bombardment of the original Nice model this may result in the disruption of several of the satellites of Saturn and Uranus. An order of magnitude reduction in the bombardment avoids the destruction of Dione and Ariel; but Miranda, Mimas, Enceladus, and perhaps Tethys would still be disrupted. These may be second generation satellites formed from the re-accretion of disrupted satellites. In this case Mimas would not be expected to be differentiated and the low density of Tethys may be due to it forming primarily from the mantle of a disrupted progenitor. [ 78 ] Alternatively they may have accreted later from a massive Saturnian ring, [ 79 ] or even as recently as 100 Myr ago after the last generation of moons were destroyed in an orbital instability. [ 80 ]
Jupiter's and Saturn's tilts can be produced by spin-orbit resonances. A spin-orbit resonance occurs when the precession frequency of a planet's spin-axis matches the precession frequency of another planet's ascending node. These frequencies vary during the planetary migration with the semi-major axes of the planets and the mass of the planetesimal disk. Jupiter's small tilt may be due to a quick crossing of a spin-orbit resonance with Neptune while Neptune's inclination was small, for example, during Neptune's initial migration before planetary encounters began. Alternatively, if that crossing occurred when Jupiter's semi-major axis jumped, it may be due to its current proximity to spin-orbit resonance with Uranus. Saturn's large tilt can be acquired if it is captured in a spin-orbit resonance with Neptune as Neptune slowly approached its current orbit at the end of the migration. [ 81 ] The final tilts of Jupiter and Saturn are very sensitive to the final positions of the planets: Jupiter's tilt would be much larger if Uranus migrated beyond its current orbit, Saturn's would be much smaller if Neptune's migration ended earlier or if the resonance crossing was more rapid. Even in simulations where the final position of the giant planets are similar to the current Solar System, Jupiter's and Saturn's tilt are reproduced less than 10% of the time. [ 82 ]
A slow migration of Neptune covering several AU results in a Kuiper belt with a broad inclination distribution. As Neptune migrates outward it scatters many objects from the planetesimal disk onto orbits with larger semi-major axes. Some of these planetesimals are then captured in mean-motion resonances with Neptune. While in a mean-motion resonance, their orbits can evolve via processes such as the Kozai mechanism , reducing their eccentricities and increasing their inclinations; or via apsidal and nodal resonances, which alter eccentricities and inclinations respectively. Objects that reach low-eccentricity high-perihelion orbits can escape from the mean-motion resonance and are left behind in stable orbits as Neptune's migration continues. [ 83 ] [ 84 ] The inclination distribution of the hot classical Kuiper belt objects is reproduced in numerical simulations where Neptune migrated smoothly from 24 AU to 28 AU with an exponential timescale of 10 million years before jumping outward when it encounters with a fifth giant planet and with a 30 million years exponential timescale thereafter. [ 85 ] The slow pace and extended distance of this migration provides sufficient time for inclinations to be excited before the resonances reach the region of Kuiper belt where the hot classical objects are captured and later deposited. [ 86 ] If Neptune reaches an eccentricity greater than 0.12 following its encounter with the fifth giant planet hot classical Kuiper belt objects can also be captured due to secular forcing. Secular forcing causes the eccentricities of objects to oscillate, allowing some to reach smaller eccentricity orbits that become stable once Neptune reaches a low eccentricity. [ 87 ] The inclinations of Kuiper belt objects can also be excited by secular resonances outside resonances, however, preventing the inclination distribution from being used to definitely determine the speed of Neptune's migration. [ 88 ]
The objects that remain in the mean-motion resonances at the end of Neptune's migration form the resonant populations such as the plutinos . Few low inclination objects resembling the cold classical objects remain among the plutinos at the end of the Neptune's migration. The outward jump in Neptune's semi-major axes releases the low-inclination low-eccentricity objects that were captured as Neptune's 3:2 resonance initially swept outward. Afterwards, the capture of low inclination plutinos was largely prevented due to the excitation of inclinations and eccentricities as secular resonances slowly sweep ahead of it. [ 85 ] [ 89 ] The slow migration of Neptune also allows objects to reach large inclinations before capture in resonances and to evolve to lower eccentricities without escaping from resonance. [ 86 ] The number of planetesimals with initial semi-major axes beyond 30 AU must have been small to avoid an excess of objects in Neptune's 5:4 and 4:3 resonances. [ 90 ]
Encounters between Neptune and Pluto-massed objects reduce the fraction of Kuiper belt objects in resonances. Velocity changes during the gravitational encounters with planetesimals that drive Neptune's migration cause small jumps in its semi-major axis, yielding a migration that is grainy instead of smooth. The shifting locations of the resonances produced by this rough migration increases the libration amplitudes of resonant objects, causing many to become unstable and escape from resonances. The observed ratio of hot classical objects to plutinos is best reproduced in simulations that include 1000–4000 Pluto-massed objects (i.e. large dwarf planets ) or about 1000 bodies twice as massive as Pluto, making up 10–40% of the 20-Earth-mass planetesimal disk, with roughly 0.1% of this initial disk remaining in various parts of the Kuiper belt. The grainy migration also reduces the number of plutinos relative to objects in the 2:1 and 5:2 resonances with Neptune, and results in a population of plutinos with a narrower distribution of libration amplitudes. [ 85 ] A large number of Pluto-massed objects would requires the Kuiper belt's size distribution to have multiple deviations from a constant slope. [ 91 ]
The kernel of the cold classical Kuiper belt objects is left behind when Neptune encounters the fifth giant planet. The kernel is a concentration of Kuiper belt objects with small eccentricities and inclinations, and with semi-major axes of 44–44.5 AU identified by the Canada–France Ecliptic Plane Survey. [ 92 ] As Neptune migrates outward low-inclination low-eccentricity objects are captured by its 2:1 mean-motion resonance. These objects are carried outward in this resonance until Neptune reaches 28 AU. At this time Neptune encounters the fifth ice giant, which has been scattered outward by Jupiter. The gravitational encounter causes Neptune's semi-major axis to jump outward. The objects that were in the 2:1 resonance, however, remain in their previous orbits and are left behind as Neptune's migration continues. Those objects that have been pushed-out a short distance have small eccentricities and are added to the local population of cold classical KBOs. [ 89 ] Others that have been carried longer distances have their eccentricities excited during this process. While most of these are released on higher eccentricity orbits a few have their eccentricities reduced due to a secular resonance within the 2:1 resonance and released as part of the kernel or earlier due to Neptune's grainy migration. [ 93 ] Among these are objects from regions no longer occupied by dynamically cold objects that formed in situ, such as between 38 and 40 AU. Pushing out in resonance allows these loosely bound, neutrally colored or 'blue' binaries to be implanted without encountering Neptune. [ 94 ] The kernel has also been reproduced in a simulation in which a more violent instability occurred without a preceding migration of Neptune and the disk was truncated at ~44.5 AU. [ 95 ]
The low eccentricities and inclinations of the cold classical belt objects places some constraints on the evolution of Neptune's orbit. They would be preserved if the eccentricity and inclination of Neptune following its encounter with another ice giant remained small (e < 0.12 and i < 6°) or was damped quickly. [ 96 ] [ 97 ] This constraint may be relaxed somewhat if Neptune's precession is rapid due to strong interactions with Uranus or a high surface density disk. [ 87 ] A combination of these may allow the cold classical belt to be reproduced even in simulations with more violent instabilities. [ 97 ] If Neptune's rapid precession rate drops temporarily, a 'wedge' of missing low eccentricity objects can form beyond 44 AU. [ 98 ] The appearance of this wedge can also be reproduced if the size of objects initially beyond 45 AU declined with distance. [ 89 ] A more extended period of Neptune's slow precession could allow low eccentricity objects to remain in the cold classical belt if its duration coincided with that of the oscillations of the objects' eccentricities. [ 99 ] A slow sweeping of resonances, with an exponential timescale of 100 million years, while Neptune has a modest eccentricity can remove the higher-eccentricity low-inclination objects, truncating the eccentricity distribution of the cold classical belt objects and leaving a step near the current position of Neptune's 7:4 resonance. [ 100 ]
In the scattered disk , a slow and grainy migration of Neptune leaves detached objects with perihelia greater than 40 AU clustered near its resonances. Planetesimals scattered outward by Neptune are captured in resonances, evolve onto lower-eccentricity higher-inclination orbits, and are released onto stable higher perihelion orbits. Beyond 50 AU this process requires a slower migration of Neptune for the perihelia to be raised above 40 AU. As a result, in the scattered disk fossilized high-perihelion objects are left behind only during the latter parts of Neptune's migration, yielding short trails (or fingers) on a plot of eccentricity vs. semi-major axis, near but just inside the current locations of Neptune's resonances. The extent of these trails is dependent on the timescale of Neptune's migration and extends farther inward if the timescale is longer. The release of these objects from resonance is aided by a grainy migration of Neptune which may be necessary for an object like 2004 XR 190 to have escaped from Neptune's 8:3 resonance. [ 101 ] [ 102 ] If the encounter with the fifth planet leaves Neptune with a large eccentricity the semi-major axes of the high perihelion objects would be distributed more symmetrically about Neptune's resonances, [ 103 ] unlike the objects observed by OSSOS. [ 104 ]
The dynamics of the scattered disk left by Neptune's migration varies with distance. During Neptune's outward migration many objects are scattered onto orbits with semi-major axes greater than 50 AU. Similar to in the Kuiper belt, some of these objects are captured by and remain in a resonance with Neptune, while others escape from resonance onto stable orbits after their perihelia are raised. Other objects with perihelia near Neptune's also remain at the end of Neptune's migration. The orbits of these scattering objects vary with time as they continue to interact with Neptune, with some of them entering planet crossing orbits, briefly becoming centaurs or comets before they are ejected from the Solar System. Roughly 80% of the objects between 50 and 200 AU have stable, resonant or detached, orbits with semi-major axes that vary less than 1.5 AU per billion years. The remaining 20% are actively scattering objects with semi-major axes that vary significantly due to interactions with Neptune. Beyond 200 AU most objects in the scattered disc are actively scattering. The total mass deposited in the scattered disk is about twice that of the classical Kuiper belt, with roughly 80% of the objects surviving to the present having semi-major axes less than 200 AU. [ 105 ] Lower inclination detached objects become scarcer with increasing semi-major axis, [ 102 ] [ 90 ] possible due to stable mean motion resonances, or the Kozai resonance within these resonances, requiring a minimum inclination that increases with semi-major axis. [ 106 ] [ 107 ]
If the hypothetical Planet Nine exists and was present during the giant planet migration, a cloud of objects with similar semi-major axes would be formed. Objects scattered outward to semi-major axes greater than 200 AU would have their perihelia raised by the dynamical effects of Planet Nine decoupling them from the influence of Neptune. The semi-major axes of the objects dynamically controlled by Planet Nine would be centered on its semi-major axis, ranging from 200 AU to ~2000 AU, with most objects having semi-major axes greater than that of Planet Nine. Their inclinations would be roughly isotropic, ranging up to 180 degrees. The perihelia of these object would cycle over periods of over 100 Myr, returning many to the influence of the Neptune. The estimated mass remaining at the current time is 0.3 – 0.4 Earth masses. [ 105 ]
Some of the objects scattered onto very distant orbits during the giant planet migration are captured in the Oort cloud. The outer Oort cloud, semi-major axes greater than 20,000 AU, forms quickly as the galactic tide raises the perihelion of object beyond the orbits of the giant planets. The inner Oort cloud forms more slowly, from the outside in, due to the weaker effect of the galactic tide on objects with smaller semi-major axes. Most objects captured in the outer Oort cloud are scattered outward by Saturn, without encountering Jupiter, with some being scattered outward by Uranus and Neptune. Those captured in the inner Oort cloud are primarily scattered outward by Neptune. Roughly 6.5% of the planetesimals beyond Neptune's initial orbit, approximately 1.3 Earth masses, are captured in the Oort cloud with roughly 60% in the inner cloud. [ 105 ]
Objects may also have been captured earlier and from other sources. As the Sun left its birth cluster objects could have been captured in the Oort cloud from other stars. [ 108 ] If the gas disk extended beyond the orbits of the giant planets when they cleared their neighborhoods comet-sized object are slowed by gas drag preventing them from reaching the Oort cloud. [ 109 ] However, if Uranus and Neptune formed late, some of the objects cleared from their neighborhood after the gas disk dissipates may be captured in the Oort cloud. [ 105 ] If the Sun remained in its birth cluster at this time, or during the planetary migration if that occurred early, the Oort cloud formed would be more compact. [ 110 ]
Solar System → Local Interstellar Cloud → Local Bubble → Gould Belt → Orion Arm → Milky Way → Milky Way subgroup → Local Group → Local Sheet → Virgo Supercluster → Laniakea Supercluster → Local Hole → Observable universe → Universe Each arrow ( → ) may be read as "within" or "part of". | https://en.wikipedia.org/wiki/Jumping-Jupiter_scenario |
Jumping libraries or junction-fragment libraries are collections of genomic DNA fragments generated by chromosome jumping . These libraries allow the analysis of large areas of the genome and overcome distance limitations in common cloning techniques.
A jumping library clone is composed of two stretches of DNA that are usually located many kilobases away from each other. The stretch of DNA located between these two "ends" is deleted by a series of biochemical manipulations carried out at the start of this cloning technique.
Chromosome jumping (or chromosome hopping) was first described in 1984 by Collins and Weissman. [ 1 ] At the time, cloning techniques allowed for generation of clones of limited size (up to 240kb), and cytogenetic techniques allowed for mapping such clones to a small region of a particular chromosome to a resolution of around 5-10Mb. Therefore, a major gap remained in resolution between available technologies, and no methods were available for mapping larger areas of the genome. [ 1 ]
This technique is an extension of "chromosome walking" that allows larger "steps" along the chromosome.
If steps of length N kb are desired, very high molecular weight DNA is necessary. Once isolated, it is partially digested with a frequent-cutting restriction enzyme (such as MboI or BamHI ). Next, obtained fragments are selected for size which should be around N kb in length. DNA must then be ligated at low concentration to favour ligation into circles rather than formation of multimers. A DNA marker (such as the amber suppressor tRNA gene supF) can be included at this time point within the covalently linked circle to allow for selection of junction fragments. Circles are subsequently fully digested with a second restriction enzyme (such as EcoRI ) to generate a large number of fragments. Such fragments are ligated into vectors (such as a λ vector) which should be selected for using the DNA marker introduced earlier. The remaining fragments thus represent the library of junction fragments, or "jumping library". [ 1 ] The next step is to screen this library with a probe that represents a "starting point" of the desired "chromosome hop", i.e. determining the location of the genome that is being interrogated. Clones obtained from this final selection step will consist of DNA that is homologous to our probe, separated by our DNA marker from another DNA sequence that was originally located N kb away (thus being called "jumping"). [ 1 ] By generating several libraries of different N values, eventually the entire genome can be mapped, allowing movement from one location to another, while controlling direction, by any value of N desired. [ 1 ]
The original technique of chromosome jumping was developed in the laboratories of Collins and Weissman at Yale University in New Haven, U.S. [ 1 ] and the laboratories of Poustka and Lehrach at the European Molecular Biology Laboratory in Heidelberg, Germany. [ 2 ]
Collins and Weissman's method [ 1 ] described above encountered some early limitations. The main concern was with avoiding non-circularized fragments. Two solutions were suggested: either screening junction fragments with a given probe or adding a second size-selection step after the ligation to separate single circular clones (monomers) from clones ligated to each other (multimers). The authors also suggested that other markers such as the λ cos site or antibiotic resistance genes should be considered (instead of the amber suppressor tRNA gene) to facilitate selection of junction clones.
Poustka and Lehrach [ 2 ] suggested that full digestion with rare-cutting restrictions enzymes (such as NotI) should be used for the first step of the library construction instead of partial digestion with a frequently cutting restriction enzyme. This would significantly reduce the number of clones from millions to thousands. However, this could create problems with circularizing the DNA fragments since these fragments would be very long, and would also lose the flexibility in choice of end points that one gets in partial digests. One suggestion for overcoming these problems would be to combine the two methods, i.e. to construct a jumping library from DNA fragments digested partially with a commonly cutting restriction enzyme and completely with a rare cutting restriction enzyme and circularizing them into plasmids cleaved with both enzymes. Several of these "combination" libraries were completed in 1986. [ 2 ] [ 3 ]
In 1991, Zabarovsky et al. [ 4 ] proposed a new approach for construction of jumping libraries. This approach included the use of two separate λ vectors for library construction, and a partial filling-in reaction that removes the need for a selectable marker. This filling-in reaction worked by destroying the specific cohesive ends (resulting from restriction digests) of the DNA fragments that were nonligated and noncircularized, thus preventing them from cloning into the vectors, in a more energy-efficient and accurate manner. Furthermore, this improved technique required less DNA to start with, and also produced a library that could be transferred into a plasmid form, making it easier to store and replicate. Using this new approach, they successfully constructed a human NotI jumping library from a lymphoblastoid cell line and a human chromosome 3-specific NotI jumping library from a human chromosome 3 and mouse hybrid cell line. [ 4 ]
Second-generation or "Next-Gen" (NGS) techniques have evolved radically: the sequencing capacity has increased more than ten thousandfold and the cost has dropped by over one million-fold since 2007(National Human Genome Research Institute). NGS has revolutionized the genetic field in many ways.
A library is often prepared by random fragmentation of DNA and ligation of common adaptor sequences. [ 5 ] [ 6 ] However, the generated short reads challenge the identification of structural variants, such as indels, translocations, and duplication. Large regions of simple repeats can further complicate the alignment. [ 7 ] Alternatively, a jumping library can be used with NGS for the mapping of structural variation and scaffolding of de novo assemblies. [ 8 ]
Jumping libraries can be categorized according to the length of the incorporated DNA fragments.
In a short-jump library, 3 kb genomic DNA fragments are ligated with biotinylate ends and circularized. The circular segments are then sheared into small fragments and the biotinylated fragments are selected by affinity assay for paired-end sequencing.
There are two issues related to short-jump libraries. First, a read can pass through the biotinylated circularization junction and reduce the effective read length. Second, reads from non-jumped fragments (i.e. fragments without the circularization junction) are sequenced and reduce genomic coverage. It has been reported that non-jumped fragments range from 4% to 13%, depending on the size of selection. The first problem might be solved by shearing circles into a larger size and select for those larger fragments. The second problem can be addressed by using a custom barcoded jumping library. [ 9 ] [ 10 ]
This jumping library uses adaptors containing markers for fragment selection in combination with barcodes for multiplexing. The protocol was developed by Talkowski et al. [ 9 ] and based on mate-pair library preparation for SOLiD sequencing. The selected DNA fragment size is 3.5 – 4.5 kb. Two adaptors were involved: one containing an EcoP15I recognition site and an AC overhang; the other containing a GT overhang, a biotinylated thymine, and an oligo barcode. The circularized DNA was digested and the fragments with biotynylated adaptors were selected for (see Figure 3). The EcoP15I recognition site and barcode help to distinguish junction fragments from nonjump fragments. These targeted fragments should contain 25 to 27bp of genomic DNA, the EcoP15I recognition site, the overhang, and the barcode. [ 9 ]
This library construction process is similar to that of the short-jump library except that the condition is optimized for longer fragments (5 kb). [ 10 ]
This library construction process is also similar to that of short-jump library except that transfection using the E. coli vector is required for amplification of large (40 kb) DNA fragments. In addition, the fosmids can be modified to facilitate the conversion into jumping library compatible with certain next generation sequencers. [ 8 ] [ 10 ]
The segments resulting from circularization during constructing jumping library are cleaved, and DNA fragments with markers will be enriched and subjected to paired-end sequencing.
These DNA fragments are sequenced from both ends and generate pairs of reads. The genomic distance between the reads in each pair is approximately known and used for the assembly process.
For example, a DNA clone generated by random fragmentation is about 200 bp, and a read from each end is around 180 bp, overlapping each other.
This should be distinguished from mate-pair sequencing, which is basically a combination of next generation sequencing with jumping libraries.
Different assembly tools have been developed to handle jumping library data. One example is DELLY. DELLY was developed to discover genomic structural variants and "integrates short insert paired-ends, long-range mate-pairs and split-read alignments" to detect rearrangements at sequence level. [ 11 ]
An example of joint development of new experimental design and algorithm development is demonstrated by the ALLPATHS-LG assembler. [ 12 ]
When used for detection of genetic and genomic changes, jumping clones require validation by Sanger sequencing .
In the early days, chromosome walking from genetically linked DNA markers was used to identify and clone disease genes. However, the large molecular distance between known markers and the gene of interest was complicating the cloning process. In 1987, a human chromosome jumping library was constructed to clone the cystic fibrosis gene. Cystic fibrosis is an autosomal recessive disease affecting 1 in 2000 Caucasians. This was the first disease in which the usefulness of the jumping libraries was demonstrated. Met oncogene was a marker tightly linked to the cystic fibrosis gene on human chromosome 7, and the library was screened for a jumping clone starting at this marker. The cystic fibrosis gene was determined to localize 240kb downstream of the met gene. Chromosome jumping helped reduce the mapping "steps" and bypass the highly repetitive regions in the mammalian genome. [ 13 ] Chromosome jumping also allowed the production of probes required for faster diagnosis of this and other diseases. [ 1 ]
Balanced chromosomal rearrangements can have a significant contribution to diseases, as demonstrated by the studies of leukemia. [ 14 ] However, many of them are undetected by chromosomal microarray. Karyotyping and FISH can identify balanced translocations and inversions but are labor-intensive and provide low resolution (small genomic changes are missed).
A jumping library NGS combined approach can be applied to identify such genomic changes. For example, Slade et al. applied this method to fine map a de novo balanced translocation in a child with Wilms' tumor . [ 15 ] For this study, 50 million reads were generated, but only 11.6% of these could be mapped uniquely to the reference genome, which represents approximately a sixfold coverage.
Talkowski et al. [ 9 ] compared different approaches to detect balanced chromosome alterations, and showed that modified jumping library in combination with next generation DNA sequencing is an accurate method for mapping chromosomal breakpoints. Two varieties of jumping libraries (short-jump libraries and custom barcoded jumping libraries) were tested and compared to standard sequencing libraries.
For standard NGS, 200-500bp fragments are generated. About 0.03%–0.54% of fragments represent chimeric pairs, which are pairs of end-reads that are mapped to two different chromosomes. Therefore, very few fragments cover the breakpoint area.
When using short-jump libraries with fragments of 3.2–3.8kb, the percentage of chimeric pairs increased to 1.3%. With Custom Barcoded Jumping Libraries, the percentage of chimeric pairs further increased to 1.49%. [ 9 ]
Conventional cyto genetic testing cannot offer the gene-level resolution required to predict the outcome of a pregnancy and whole genome deep sequencing is not practical for routine prenatal diagnosis. Whole-genome jumping library could complement conventional prenatal testing. This novel method was successfully applied to identify a case of CHARGE syndrome . [ 6 ]
In metagenomics , regions of the genomes that are shared between strains are typically longer than the reads. This complicates the assembly process and makes reconstructing individual genomes for a species a daunting task. [ 10 ] Chimeric pairs that are mapped far apart in the genome can facilitate the de novo assembly process. By using a longer-jump library, Ribeiro et al. demonstrated that the assemblies of bacterial genomes were of high quality while reducing both cost and time. [ 16 ]
The cost of sequencing has dropped dramatically while the cost of construction of jumping libraries has not. Therefore, as new sequencing technologies and bioinformatic tools are developed, jumping libraries may become redundant. | https://en.wikipedia.org/wiki/Jumping_library |
Rolling hairpin replication ( RHR ) is a unidirectional, strand displacement form of DNA replication used by parvoviruses, a group of viruses that constitute the family Parvoviridae . Parvoviruses have linear, single-stranded DNA (ssDNA) genomes in which the coding portion of the genome is flanked by telomeres at each end that form hairpin loops . During RHR, these hairpin loops repeatedly unfold and refold to change the direction of DNA replication so that replication progresses in a continuous manner back and forth across the genome. RHR is initiated and terminated by an endonuclease encoded by parvoviruses that is variously called NS1 or Rep, and RHR is similar to rolling circle replication , which is used by ssDNA viruses that have circular genomes.
Before RHR begins, a host cell DNA polymerase converts the genome to a duplex form in which the coding portion is double-stranded and connected to the terminal hairpins. From there, messenger RNA (mRNA) that encodes the viral initiator protein is transcribed and translated to synthesize the protein. The initiator protein commences RHR by binding to and nicking the genome in a region adjacent to a hairpin called the origin and establishing a replication fork with its helicase activity. Nicking leads to the hairpin unfolding into a linear, extended form. The telomere is then replicated and both strands of the telomere refold back in on themselves to their original turn-around forms. This repositions the replication fork to switch templates to the other strand and move in the opposite direction. Upon reaching the other end, the same process of unfolding, replication, and refolding occurs.
Parvoviruses vary in whether both hairpins are the same or different. Homotelomeric parvoviruses such as adeno-associated viruses (AAV), i.e. those that have identical or similar telomeres, have both ends replicated by terminal resolution, the previously described process. Heterotelomeric parvoviruses such as minute virus of mice (MVM), i.e. those that have different telomeres, have one end replicated by terminal resolution and the other by an asymmetric process called junction resolution. During asymmetric junction resolution, the duplex extended form of the telomere reorganizes into a cruciform-shaped junction , and the correct orientation of the telomere is replicated off the lower arm of the cruciform. As a result of RHR, a replicative molecule that contains numerous copies of the genomes is synthesized. The initiator protein periodically excises progeny ssDNA genomes from this replicative concatemer.
Parvoviruses are a family of DNA viruses that have single-stranded DNA (ssDNA) genomes enclosed in rugged, icosahedral protein capsids 18–26 nanometers (nm) in diameter. [ 1 ] Unlike most other ssDNA viruses, which have circular genomes that form a loop, parvoviruses have linear genomes with short terminal sequences at each end of the genome. These termini are capable of being formed into structures called hairpins or hairpin loops and consist of short, imperfect palindromes. [ 2 ] [ 3 ] Varying from virus to virus, the coding region of the genome is 4–6 kilobases (kb) in length, and the termini are 116–550 nucleotides (nt) in length each. The hairpin sequences provide most of the cis -acting information needed for DNA replication and packaging. [ 1 ] [ 4 ]
Parvovirus genomes may be either positive-sense or negative-sense . Some species, such as adeno-associated viruses (AAV) like AAV2, package a roughly equal number of positive-sense and negative-sense strands into virions, others, such as minute virus of mice (MVM), show preference toward packaging negative-sense strands, and others have varying proportions. [ 4 ] Because of this disparity, the 5′-end (usually pronounced "five prime end") of the strand that encodes the non-structural proteins is called the "left end", and the 3′-end (usually pronounced "three prime end") is called the "right end". [ 3 ] In reference to the negative-sense strand, the 3′-end is the left side and the 5′-end is the right side. [ 4 ] [ 5 ]
Parvoviruses replicate their genomes through a process called rolling hairpin replication (RHR), which is a unidirectional, strand displacement form of DNA replication. Before replication, the coding portion of the ssDNA genome is converted to a double-strand DNA (dsDNA) form, which is then cleaved by a viral protein to initiate replication. Sequential unfolding and refolding of the hairpin termini acts to reverse the direction of synthesis, which allows replication to go back and forth along the genome to synthesize a continuous duplex replicative form (RF) DNA intermediate. Progeny ssDNA genomes are then excised from the RF intermediate. [ 4 ] [ 6 ] While the general aspects of RHR are conserved across genera and species, the exact details likely vary. [ 7 ]
Parvovirus genomes have distinct starting points of replication that contain palindromic DNA sequences. These sequences are able to alternate between inter- and intrastrand basepairing throughout replication, and they serve as self-priming telomeres at each end of the genome. [ 2 ] They also contain two key sites necessary for replication used by the initiator protein: a binding site and a cleavage site. [ 8 ] Telomere sequences have significant complexity and diversity, suggesting that they perform additional functions for many species. [ 1 ] [ 9 ] In MVM, for example, the left-end hairpin contains binding sites for transcription factors that modulate gene expression from an adjacent promoter . For AAV, the hairpins can bind to MRE11/Rad50/NBS1 (MRN) complexes and Ku70/80 heterodimers, which are involved in sensing and repairing DNA. [ 5 ] In general, however, they have the same basic structure: imperfect palindromes in which a fully or primarily basepaired region terminates into an axial symmetry. These palindromes can fold into a variety of structures such as a Y-shaped structure and a cruciform-shaped structure. During replication, the termini act as hinges in which the imperfectly basepaired or partial cruciform regions surrounding the axis provide a favorable environment for unfolding and refolding of the hairpin. [ 2 ] [ 3 ] [ 4 ]
Some parvoviruses, such as AAV2, are homotelomeric, meaning the two palindromic telomeres are similar or identical and form part of larger (inverted) terminal repeat ((I)TR) sequences. Replication at each terminal ending is therefore similar. Other parvoviruses, such as MVM, are heterotelomeric, meaning they have two physically different telomeres. As a result, heterotelomeric parvoviruses tend to have a more complex replication process since the two telomeres have different replication processes. [ 2 ] [ 3 ] [ 4 ] In general, homotelomeric parvoviruses replicate both ends via a process called terminal resolution, whereas heterotelomeric parvoviruses replicate one end by terminal resolution and the other end by an asymmetric process called junction resolution. [ 4 ] [ 5 ] [ 6 ] [ 10 ] Whether a genus is hetero- or homotelomeric, along with other genomic characteristics, is shown in the following table. [ 4 ]
The entire process of rolling hairpin replication, which has distinct, sequential stages, can be summarized as follows: [ 4 ] [ 5 ] [ 7 ]
Upon cell entry, a tether about 24 nucleotides in length that attaches the viral protein NS1, essential in replication, to the virion is cleaved off the virion to be reattached later. [ 3 ] After cell entry, virions accumulate in the cell nucleus while the genome is still contained within the capsid. These capsids may be reconfigured to an open or transitioned state during entry. The exact mechanism by which the genome leaves the capsid is unclear. [ 9 ] For AAV, it has been suggested that nuclear factors disassemble the capsid, whereas for MVM, it appears as if the genome is ejected in a 3′-to-5′ direction from an opening in the capsid called a portal. [ 5 ]
Parvoviruses lack genes capable of inducing resting cells to enter their DNA synthesis phase (S-phase). Additionally, naked ssDNA is likely to be unstable, perceived as foreign by the host cell, or improperly replicated by host DNA repair . For these reasons, the genome must either be converted rapidly to its less obstructive, more stable duplex form or retained within the capsid until it is uncoated during S-phase. Typically, the latter occurs and virion remains silent in the nucleus until the host cell enters S-phase by itself. During this waiting period, virions may make use of certain strategies to evade host defense mechanisms to protect their hairpins and DNA to reach S-phase, [ 9 ] though it is unclear how this occurs. [ 4 ] Since the genome is packaged as ssDNA, creation of a complementary strand is necessary before gene expression . [ 5 ] [ 9 ]
DNA polymerases are only able to synthesize DNA in a 5′ to 3′ direction, and they require a basepair primer to begin synthesis. Parvoviruses address these limitations by using their termini as primers for complementary strand synthesis. [ 9 ] A 3′ hydroxyl end of the left-hand (3′) terminus pairs with an internal base to prime initial DNA synthesis, resulting in the conversion of the ssDNA genome to its first duplex form. [ 1 ] [ 7 ] This is a monomeric double-stranded DNA molecule in which the two strands are covalently cross-linked to each other at the left-end by a single copy of the viral telomere. Synthesis of the duplex form precedes NS1 expression so that when the replication fork during initial complementary strand synthesis reaches the right (5′) end, it does not displace and copy the right-end hairpin. This allows the 3′-end of the new DNA strand to be covalently ligated to the 5′-end of the right hairpin by a host ligase, thereby creating the duplex molecule. During this step, the tether sequence that was present before viral entry into the cell is resynthesized. [ 6 ]
Once an infected cell enters S-phase, parvovirus genomes are converted to their duplex form by host replication machinery, and mRNA that encodes non-structural (NS) proteins is transcribed starting from a viral promoter (P4 for MVM). [ 4 ] [ 5 ] [ 9 ] One of these NS proteins is usually called NS1 but also Rep1 or Rep68/78 for the genus Dependoparvovirus , which AAV belongs to. [ 4 ] NS1 is a site-specific DNA binding protein that acts as the replication initiator protein [ 9 ] via nickase activity. [ 15 ] It also mediates excision of both ends of the genome from duplex RF intermediates via a transesterification reaction that introduces a nick into specific duplex origin sequences. [ 4 ] Key components of NS1 include an HUH endonuclease domain toward the N-terminus of the protein and a superfamily 3 (SF3) helicase toward the C-terminus , [ 16 ] as well as ATPase activity. [ 1 ] It binds to ssDNA, RNA, and site-specifically on duplex DNA at reiterations of the tetranucleotide sequence 5′-ACCA-3′ 1–3 . [ 1 ] [ 9 ] These sequences are present in the viral replication origin sites and repeated at multiple sites throughout the genome in more or less degenerative forms. [ 15 ]
NS1 nicks the covalently-closed right-end telomere via a transesterification reaction that liberates a basepaired 3′ nucleotide as a free hydroxyl (-OH). [ 4 ] This reaction is assisted by a host DNA-binding protein from the high mobility group 1/2 (HMG1/2) family and is made in the replication origin, OriR , which was created by sequences in and immediately adjacent to the right hairpin. The left-end telomere of MVM, a heterotelomeric parvovirus, contains sequences that can give rise to replication origins in higher-order duplex intermediates, but these sequences are inactive in the hairpin terminus of the monomeric molecule, so NS1 always initiates replication at the right end. [ 6 ]
The 3′-OH that is freed by nicking acts as a primer for the DNA polymerase to start complementary strand synthesis [ 8 ] while NS1 remains covalently attached to the 5′-end via a tyrosine residue. [ 1 ] Consequently, a copy of NS1 remains attached to the 5′-end of all RF and progeny DNA throughout replication, packaging, and virion release. [ 4 ] [ 6 ] NS1 is only able to bind to this specific site by assembling into homodimers or higher order multimers, which happens naturally with the addition of adenosine triphosphate (ATP) that is likely mediated by NS1's helicase domain. In vivo studies have shown that NS1 can form into a variety of oligomeric states, but it most likely assembles into hexamers to fulfill the functions of both the endonuclease domain and helicase domain. [ 15 ]
Starting from the location at the nick, it is thought that NS1 organizes a replication fork and acts as the replicative 3′-to-5′ helicase. Near its C-terminus, NS1 contains an acidic transcriptional activation domain. This domain acts to upregulate transcription starting from a viral promoter (P38 for MVM) when NS1 is bound to a series of 5′-ACCA-3′ motifs, called the tar sequence, positioned upstream (toward the 5′-end) of the promoter unit, and via interaction with NS1 and various transcription factors. [ 15 ] NS1 also recruits the cellular replication protein A (RPA) complex, which is essential for establishing the new replication fork and for binding and stabilizing displaced single strands. [ 6 ]
While NS1 is the only non-structural protein essential for all parvoviruses, some have other individual proteins that are essential for replication. For MVM, NS2 appears to reprogram the host cell for efficient DNA amplification, single-strand progeny synthesis, capsid assembly, and virion export, though it seems to lack direct involvement in these processes. NS2 initially accumulates up to three times more quickly than NS1 in the early S-phase but is turned-over rapidly by a proteasome-mediated pathway. As the infectious cycle progresses, NS2 becomes less common as P38-driven transcription becomes more prominent. [ 15 ] Another example is the nuclear phosphoprotein NP1 of bocaviruses, which, if not synthesized, results in non-viable progeny genomes. [ 5 ]
As viral NS proteins accumulate, they commandeer host cell replication apparati, terminating host cell DNA synthesis and causing viral DNA amplification to begin. Interference with host DNA replication may be due to direct effects on host replication proteins that are not essential for viral replication, by extensive nicking of host DNA, or by the restructuring of the nucleus during viral infection. Early in infection, parvoviruses establish replication foci in the nucleus that are termed autonomous parvovirus-associated replication (APAR) bodies. NS1 co-localizes with replicating viral DNA in these structures with other cellular proteins necessary for viral DNA synthesis, [ 15 ] while other complexes not required for replication are sequestered from APAR bodies. The exact manner by which proteins are included or excluded from APAR bodies is unclear and appears to vary from species to species and between cell types. [ 5 ] As infection progresses, APAR microdomains begin to coalesce with other, formerly distinct, nuclear bodies to form progressively larger nuclear inclusions where viral replication and virion assembly occur. After S-phase begins, the host cell is forced to synthesize viral DNA and cannot leave S-phase. [ 17 ]
The right-end hairpin of MVM contains 248 nucleotides [ 10 ] organized into a cruciform shape. [ 1 ] This region is almost perfectly basepaired, with just three unpaired bases at the axis and a mismatched region positioned 20 nucleotides from the axis. A three nucleotide insertion, AGA or TCT, on one strand separates opposing pairs of NS1 binding sites, creating a 36 basepair-length palindrome that can assume an alternate cruciform configuration. This configuration is expected to destabilize the duplex, which facilitates its ability to function as a hinge. The mismatch of the unpaired bases, rather than the three-nucleotide sequence itself, may help to promote instability of duplex DNA. [ 10 ]
Fully-duplex linear forms of the right-end hairpin sequence also function as NS1-dependent origins. For many parvoviral telomeres, however, only an initiator binding site next to the nick site is required for the origin function so that the minimal sequences required for nicking are less than 40 basepairs in length. For MVM, the minimal right-end origin is around 125 basepairs in length and includes most of the hairpin sequence because at least three recognition elements are involved: the nick site 5′-CTWWTCA-3′ (element 1), positioned seven nucleotides upstream from a duplex NS1-binding site (element 2) that is oriented to have the attached NS1 complex extending over the nick site, and a second NS1-binding site (element 3), which is adjacent to the hairpin axis. [ 10 ]
The second binding site is over 100 basepairs away from the nick site but is required for NS1-mediated cleavage. [ 10 ] In vivo , there is slight variation in the position of the nick, plus or minus one nucleotide, with one position preferred. During nicking, this site is likely exposed as a single strand and is potentially stabilized as a minimal stem-loop by the tetranucleotide inverted repeats to the sides of the site. Optimal forms of the NS1-binding site contain at least three tandem copies of the 5′-ACCA-3′ sequence. Modest alterations to these motifs only have a small effect on affinity, which suggests that each tetranucleotide motif is recognized by different molecules in the NS1 complex. The NS1-binding site that positions NS1 over the nick site in the right-end origin is a high affinity site. [ 18 ]
With ATP, NS1 binds asymmetrically over the aforementioned sequence, protecting a region 41 basepairs in length from digestion. This footprint extends just five nucleotides beyond the 3′-end of the ACCA repeat but 22 nucleotides beyond the 5′-end so that the footprint ends 15 nucleotides beyond the nick site, placing NS1 in position to nick the origin. Nicking only occurs if the second, distant NS1-binding site is also present in the origin and the entire complex is activated by addition of HMG1. [ 18 ]
In the absence of NS1, HMG1 binds the hairpin sequence independently, causing it to bend, without protecting any region from digestion. HMG1 can also directly bind to NS1 and mediates interactions between NS1 molecules bound to their recognition elements in the origin, so it is essential for formation of the cleavage complex. The ability of the axis region to reconfigure into a cruciform does not appear to be important in this process. Cleavage is dependent on the correct spacing of the elements of the origin, so additions and deletions can be lethal, whereas substitutions can be tolerated. Addition of HMG1 appears to only slightly adjust the sequences protected by NS1, but the conformation of the intervening DNA changes, folding into a double helical loop that extends about 30 basepairs through a guanine -rich element in the hairpin stem. Between this element and the nick site there are five thymidine residues included in the loop, and the site has a region to its side containing many alternating adenine and thymine residues, which likely increases flexibility. The creation of the loop likely allows the terminus to assume a specific 3-dimensional structure required to activate the nickase since origins that fail to reconfigure into a double-helical loop once HMG1 is added are not nicked. [ 18 ]
Following nicking, a replication fork is established at the newly exposed 3′ nucleotide that proceeds to unfold and copy the right-end hairpin through a series of melting and reannealing reactions. [ 9 ] [ 18 ] This process begins once NS1 nicks the inboard end of the original hairpin. The terminal sequence is then copied in the opposite direction, which produces an inverted copy of the original sequence. [ 9 ] The end result is a duplex extended-form terminus that contains two copies of the terminal sequence. [ 18 ] While NS1 is required for this, it is unclear if unfolding is mediated by its helicase activity in front of the fork or by destabilization of the duplex following DNA binding at one of its 5′-(ACCA) n -3′ recognition sites. [ 6 ] This process is usually called terminal resolution but also hairpin transfer or hairpin resolution. [ 6 ] [ 9 ] Terminal resolution occurs with each round of replication, so progeny genomes contain an equal number of each terminal orientation. The two orientations are termed "flip" and "flop", [ 5 ] [ 6 ] and may be represented as R and r, or B and b, for the flip and flop of the right-end telomere and L and l, or A and a, for the flip and flop of the left-end telomere. [ 7 ] [ 19 ] Since parvoviral terminal palindromes are imperfect, it is easy to identify which orientation is which. [ 1 ]
The extended-form duplex telomeres generated during terminal resolution are melted, mediated by NS1 with ATP hydrolysis , causing individual strands to fold back on themselves to create hairpin "rabbit ear" structures that have the flip and flop of the termini. This requires the NS1 helicase activity as well as its site-specific binding activity, the latter of which enables NS1 to bind to symmetrical copies of NS1-binding sites that surround the axis of the extended-form terminus. [ 10 ] [ 20 ]
Rabbit ear formation allows the 3′ nucleotide of the newly synthesized DNA strand to pair with an internal base, which repositions the replication fork in a strand-switching maneuver that primes synthesis of additional linear sequences. [ 10 ] Switching from DNA synthesis to rabbit-ear formation at the end of terminal resolution may require different types of NS1 complexes. Alternatively, the NS1 complex may remain intact during this switch, being ready to start stand displacement synthesis following refolding into rabbit ears. [ 20 ] After the replication fork is repositioned, replication continues toward the left end, using the newly synthesized DNA strand as a template. [ 7 ]
At the left end of the genome, NS1 is probably required to unfold the hairpin. NS1 appears to be directly involved in melting-out and reconfiguring the resulting extended-form left-end duplexes into rabbit ear structures, though this reaction seems to be less efficient than at the right-end terminus. Dimeric and tetrameric concatemers of the genome are generated successively for MVM. In these concatemers, alternating unit-length genomes are fused through a palindromic junction in left-end to left-end and right-end to right-end orientations. [ 1 ] [ 10 ] In total, RHR results in coding sequences of the genome being copied twice as often as the termini. [ 1 ] [ 7 ] [ 10 ] Both linear and hairpin configurations of the right-end telomere support initiation of RHR, so resolution of duplex right-end to right-end junctions can occur symmetrically on the basepaired duplex sequence or after this complex is melted and reconfigured into two hairpins. It is unclear which of these two reactions is more common since both appear to produce identical results. [ 20 ]
For AAV, each telomere is 125 bases in length and capable folding into a T-shaped hairpin. AAV contains a Rep gene that encodes for four Rep proteins, two of which, Rep68 and Rep78, act as replication initiator proteins and fulfill the same functions, such the nickase and helicase activities, as NS1. They recognize and bind to a (GAGC) 3 sequence in the stem region of the terminus and nick a site 20 bases away termed trs . The same process of terminal resolution as MVM is done for AAV, but at both ends. The other two Rep proteins, Rep52 and Rep40, are not involved in DNA replication but are implicated in synthesis of progeny. AAV replication is dependent on a helper virus that is either an adenovirus or a herpesvirus that coinfects the cell. In the absence of coinfection, the AAV genome is integrated into the host cell's DNA until coinfection occurs. [ 1 ]
A general rule is that parvoviruses with identical termini, i.e. homotelomeric parvoviruses such as AAV and B19, replicate both ends by terminal resolution, generating equal numbers of flips and flops of each telomere. [ 1 ] [ 4 ] [ 6 ] Parvoviruses that have different termini, i.e. heterotelomeric parvoviruses like MVM, replicate one end by terminal resolution and the other end by asymmetric junction resolution, which conserves a single-sequence orientation and requires different structural arrangements and cofactors to activate NS1's nickase. [ 4 ] [ 10 ] AAV DNA intermediates containing covalently linked sense and antisense strands yield genomic concatemers under denaturing conditions, indicating that AAV replication also synthesizes duplex concatemers that require some form of junction resolution. [ 10 ]
In negative-sense MVM genomes, the left-end hairpin is 121 nucleotides in length and exists in a single flip sequence orientation. This telomere is Y-shaped and contains small internal palindromes that fold into the "ears" of the Y, a duplex stem region 43 nucleotides in length that is interrupted by an asymmetric thymidine residue, and a mismatched "bubble" sequence in which the 5′-GAA-3′ sequence on the inboard arm is opposite of 5′-GA-3′ in the outboard strand. [ 1 ] [ 20 ] Sequences in this hairpin are involved in both replication and regulation of transcription. The elements involved in these two functions separate the two arms of the hairpin. [ 20 ]
The left-end telomere of MVM, and likely of all heterotelomeric parvoviruses, cannot function as a replication origin in its hairpin configuration. Instead, a single origin on the lower strand is created when the hairpin is unfolded, extended, and copied to form a duplex basepaired sequence that spans adjacent genomes in the dimer RF. Within this structure, the sequence from the outboard arm that surrounds a GA/TC [ 1 ] dinucleotide serves as an origin, OriL TC . The equivalent GAA/TTC sequence on the inboard arm that contains the bubble trinucleotide, called OriL GAA , does not serve as an origin. The inboard arm and hairpin configuration of the terminus instead appear to function as upstream control elements for the viral transcriptional promoter P4. Additionally, the ability to segregate one arm from nicking appears essential for replication. [ 20 ]
The minimal linear left-end origin is about 50 basepairs long and extends from two 5′-ACGT-3′ motifs, spaced five nucleotides apart at one end, to a position seven basepairs beyond the nick site. The bubble's GA sequence itself is relatively unimportant, but the space that it occupies is necessary for the origin to function. [ 1 ] [ 20 ] Within the origin, there are three recognition sequences: an NS1-binding site that orients the NS1 complex over the nick site 5′-CTWWTCA-3′, which is located 17 nucleotides downstream (toward the 3′-end), and the two ACGT motifs. These motifs bind a heterodimeric cellular factor called either parvovirus initiation factor (PIF) or glucocorticoid modulating element-binding protein (GMEB). [ 21 ]
PIF is a site-specific DNA-binding heterodimeric complex that contains two subunits, p96 and p79, and functions as a transcription modulator in the host cell. It binds DNA via a KDWK fold and recognizes two ACGT half-sites. The spacing between these sites can vary significantly for PIF, from one to nine nucleotides, with an optimal spacing of six. PIF stabilizes the binding of NS1 on the active form of the left-end origin, OriL TC , but not on the inactive form, OriL GAA , because the two complexes are able to establish contact over the bubble binucleotide. The left-end hairpin of all other species in the Protoparvovirus genus, [ note 6 ] of which MVM belongs, have bubble asymmetries and PIF-binding sites, though with slight variation in spacing. This suggests that they all share a similar origin segregation mechanism. [ 21 ]
Due to the location of the active origin OriL TC in the dimer junction, synthesis of new copies of the left-end hairpin in the correct, i.e.flip, orientation is not straightforward since a replication fork moving from this site through the linear bridge structure should synthesize new DNA in the flop orientation. Instead, the left-hand MVM dimer junction is resolved asymmetrically in a process that creates a cruciform intermediate. This maneuver accomplishes two things: it allows synthesis of the new DNA in the correct sequence orientation, and it creates a structure that can be resolved by NS1. This "heterocruciform" model of synthesis suggests that resolution is driven by the NS1 helicase activity and depends on the inherent instability of the duplex palindrome, a property that allows it to switch between its linear and cruciform configurations. [ 21 ]
NS1 initially introduces a single-strand nick in OriL TC in the B ("right") arm of the junction and becomes covalently attached to the DNA on the 5′ side of the nick, exposing a basepaired 3′ nucleotide. Two outcomes can then occur, depending on the speed with which a replication fork is assembled. If assembly is rapid, then while the junction is in its linear configuration, "read-through" synthesis copies the upper strand, which regenerates the duplex junction and displaces a positive-sense strand that feeds back into the replicative pool. This promotes MVM DNA amplification but does not lead to synthesis of new terminal sequences in the correct orientation or to junction resolution. [ 22 ]
To create a resolvable structure, the initial nicking must be followed by melting and rearrangement of the dimer junction into a cruciform. This is driven by the 3′-to-5′ helicase activity of the 5′-linked NS1 complex. Once this cruciform extends to include sequences beyond the nick site, the exposed primer at the nick site in OriL TC undergoes template switching by annealing with its complement in the lower arm of the cruciform. If a fork assembles after this point, then the subsequent synthesis unfolds and copies the lower cruciform arm. This creates a heterocruciform intermediate that contains the newly synthesized telomere in the flip sequence orientation that is attached to the lower strand of the B arm. [ 22 ] This modified junction is called MJ2. [ 23 ]
The lower arm of MJ2 is an extended-form duplex palindrome that is essentially identical to those generated during terminal resolution. Once MJ2 is synthesized, the lower arm becomes susceptible to rabbit-ear formation. This repositions the 3′ nucleotide of the newly synthesized copy of the lower arm so that it pairs with inboard sequences on the junction's B arm to prime strand displacement synthesis. If a replication fork is created at this 3′ nucleotide, then the lower strand of the B arm is copied, creating an intermediate junction called MJ1 and progressively displacing the upper strand. This leads to the release of the newly synthesized B turn-around (B-ta) sequence. The residual cruciform, called δJ, is partially single-stranded at the upper part of the B arm and contains the intact upper strand of the junction paired to the lower strand of the A ("left") arm, with an intact copy of the left-end hairpin, ending in a 5′ NS1 complex. Since δJ carries the NS1 helicase, it is presumed to periodically alter configuration. [ 22 ] [ 23 ]
The next step is less certain but can be inferred based on what is known about the process thus far. The NS1 helicase is expected to create a dynamic structure in which the nick site in δJ in the normally inactive A side is temporarily but repeatedly exposed in a single-stranded form during duplex-to-hairpin rearrangements, which allows NS1 to engage the nick site in the origin OriL GAA without the help of a cofactor. The nick would leave NS1 covalently attached to the positive-sense "B" strand of δJ and lead to the release of this strand. Nicking also leaves open a basepaired 3′ nucleotide on the "A" strand of δJ to prime DNA synthesis. If a replication fork is established here, then the A strand is unfolded and copied to create its duplex extended form. [ 23 ]
When MVM genomes replicate in vivo , the aforementioned nick may not occur because both ends of the dimer replicative form contain an efficient number of right-end hairpin origins. Therefore, replication forks may progress back toward the dimer junction from the genome's right end, copying the top strand of the B arm before the final resolution nick. This bypasses dimer bridge resolution and recycles the top strand into a replicating duplex dimer pool. In a closely related virus, LuIII, the single-strand nick releases a positive-sense strand with its left-end hairpin in the flop orientation. Unlike MVM, LuIII packages strands of both sense with equal frequency. In the negative-sense strands, the left-end hairpins are all in the flip orientation, while in the positive-sense strands, there are an equal number of flip and flop orientations. Compared to MVM, LuIII contains a two-base insertion immediately 3′ of the nick site in the right origin, which impairs its efficiency. Because of this, the reduced efficiency of replication fork assembly in the genome's right end may favor single-strand nicking by giving it more time to occur. [ 23 ]
Individual progeny genomes are excised from genomic replicative concatemers starting by introducing breaks in replication origins, usually by the replication initiator protein. This results in the establishment of new replication forks that replicate the telomeres in a combination of terminal resolution and junction resolution and displaces individual ssDNA genomes from the replicative molecule. [ 7 ] [ 20 ] At the end of this process, the telomeres are folded back inwards to form hairpins on excised genomes. The extended-form termini created during excision resemble the extended-form molecules prior to terminal resolution, so they can be melted out and refolded into rabbit ears for additional rounds of replication. [ 1 ] Within an infected cell, numerous replicative concatemers are therefore able to arise. [ 7 ]
Displacement of progeny ssDNA genomes either occurs: predominantly or exclusively during active DNA replication, or when cells are assembling viral particles. Displacement of single strands may therefore be associated with packaging viral DNA into capsids. Earlier research suggested that the preassembled viral particle may sequester the genome in a 5′-to-3′ direction as it is displaced from the fork, but more recent research suggests that packaging is performed in a 3′-to-5′ direction driven by the NS1 helicase using newly synthesized single strands. [ 24 ]
It is not clear if these single strands are released into the nucleoplasm so that packaging complexes are physically separate from replication complexes or if the replication intermediates serve as both replication and packaging substrates. In the latter case, newly displaced progeny genomes would be kept in the replication complex via interactions between their 5′-linked NS1 molecules and NS1 or capsid proteins that are physically associated with replicating DNA. [ 24 ] Genomes are inserted into the capsid via an entrance called a portal situated at one of the icosahedral 5-fold axes of the capsid, [ 4 ] which is possibly opposite of the opening from which genomes are expelled early in the replication cycle. [ 5 ]
Strand selection for encapsidation likely does not involve specific packaging signals but may be predictable by the Kinetic Hairpin Transfer (KHT) mathematical model, which explains the distribution of the strands and terminal conformations of packaged genomes in terms of the efficiency with which each terminus type can undergo reactions that allow it to be copied and reformed. In other words, the KHT model postulates that the relative efficiency with which two genomic termini are resolved and replicated determines the distribution of amplified replication intermediates created during infection and ultimately the efficiency with which ssDNAs of characteristic polarity and terminal orientations are excised, which will then be packaged with equal efficiency. [ 4 ] [ 24 ]
Preferential excision of particular genomes is only apparent during packaging. Therefore, among parvoviruses that package strands of one sense, replication appears to be biphasic. At early times, both sense strands are excised. This is followed by a switch in the replication mode that allows for exclusive synthesis of a single sense for packaging. A modified form of the KHT model, called the preferential strand displacement model, proposes that the aforementioned switch in replication is caused by the onset of packaging because the substrate for packaging is probably a newly displaced DNA molecule. [ 24 ] For heterotelomeric parvoviruses, imbalance of origin firing leads to preferential displacement of negative sense strands from the right-end origin. The relative frequency of sense strands in packaged virions can therefore be used to infer the type of resolution mechanism used during excision. [ 5 ]
Shortly after the start of S-phase, translation of viral mRNA leads to the accumulation of capsid proteins in the nucleus. These proteins form into oligomers that are assembled into intact empty capsids. After encapsidation, complete virions may be exported from the nucleus to the exterior of the cell before disintegration of the nucleus. Disruption of the host cell environment may also occur later on in infection. This results in cell lysis via necrosis or apoptosis , which releases virions to the outside of the cell. [ 4 ] [ 17 ]
Many small replicons that have circular genomes such as circular ssDNA viruses and circular plasmids replicate via rolling circle replication (RCR), which is a unidirectional, strand displacement form of DNA replication similar to RHR. In RCR, successive rounds of replication, which proceeds in a loop around the genome, are initiated and terminated by site-specific single-strand nicks made by a replicon-encoded endonuclease, variously called the nickase, relaxase, mobilization protein (mob), transesterase, or replication protein (Rep). The replication initiator protein of parvoviruses is genetically related to these other endonucleases. [ 17 ]
RCR initiator proteins contain three motifs considered to be important for replication. Two of these are retained within parvovirus initiator proteins: an HUHUUU cluster, which is presumed to bind to a Mg 2+ ion required for nicking, and a YxxxK motif that contains the active-site tyrosine residue that attacks the phosphodiester bond of target DNA. In contrast to RCR initiator proteins, which can join together DNA strands, RHR initiator proteins have only vestigial traces of being able to perform ligation. [ 17 ]
RCR begins when the initiator protein nicks a DNA strand at a specific sequence in the replication origin region. This is done through a transesterification reaction that forms a 5′-phosphate bond that connects the DNA to the active-site tyrosine and frees the 3′-end hydroxyl (3′-OH) adjacent to the nick site. The 3′-end is then used as a primer for the host DNA polymerase to begin replication while the initiator protein remains attached to the 5′-end of the "original" strand. After one loop of replication around the circular genome, the initiator protein returns to the nick site, i.e. the original initiator complex, while still attached to the parent strand and attacks the regenerated duplex nick site, or a nearby second site in some cases, by means of a topoisomerase -like nicking-joining reaction. [ 17 ]
During the aforementioned reaction, the initiator protein cleaves a new nick site and is transferred across the analogous phosphodiester bond. It thereby becomes attached to the new 5′-end while ligating the 5′-end of the first strand to which it was originally attached to the 3′-end of the same strand. This second mechanism varies depending on the replicon. Some replicons such as the virus ΦX174 contain a second active tyrosine residue in the initiator protein. Others use the analogous active-site tyrosine in a second initiator protein that is present as part of a multimeric nickase complex. [ 17 ]
This second nicking reaction may occur after one loop or successive loops may occur in which a concatemer containing multiple copies of the genome is created. The result of this nick is that displaced genomes become detached from the replicative molecule. These copies of the genome are ligated and may either be encapsidated into progeny capsids, provided they are monomeric, or converted to a covalently-closed double-stranded form by a host DNA polymerase for further replication. While RHR generally involves replication of both sense strands in a continuous process, RCR has complementary strand synthesis and genomic strand synthesis occur separately. [ 7 ]
The strategies used in RHR to engage the nick site are also present in RCR. Most RCR origins are in the form of duplex DNA that has to be melted before nicking. RCR initiators accomplish this by binding to specific DNA-binding sequences in the origin next to the initiation site. [ 17 ] The latter site is then melted in a process that consumes ATP and which is assisted by the ability of the separated strands to reconfigure into stem-loop structures. In these structures, the nick site is presented on an exposed loop. Like RHR initiator proteins, many RCR initiator proteins contain helicase activity, which allows them to melt the DNA prior to nicking and serve as the 3′-to-5′ helicase in the replication fork. [ 19 ] | https://en.wikipedia.org/wiki/Junction_resolution |
In geometry , Jung's theorem is an inequality between the diameter of a set of points in any Euclidean space and the radius of the minimum enclosing ball of that set. It is named after Heinrich Jung , who first studied this inequality in 1901. Algorithms also exist to solve the smallest-circle problem explicitly.
Consider a compact set
and let
be the diameter of K , that is, the largest Euclidean distance between any two of its points. Jung's theorem states that there exists a closed ball with radius
that contains K . The boundary case of equality is attained by the regular n - simplex .
The most common case of Jung's theorem is in the plane , that is, when n = 2. In this case the theorem states that there exists a circle enclosing all points whose radius satisfies
and this bound is as tight as possible since when K is an equilateral triangle (or its three vertices) one has r = d 3 . {\displaystyle r={\frac {d}{\sqrt {3}}}.}
For any bounded set S {\displaystyle S} in any metric space , d / 2 ≤ r ≤ d {\displaystyle d/2\leq r\leq d} . The first inequality is implied by the triangle inequality for the center of the ball and the two diametral points, and the second inequality follows since a ball of radius d {\displaystyle d} centered at any point of S {\displaystyle S} will contain all of S {\displaystyle S} . Both these inequalities are tight:
Versions of Jung's theorem for various non-Euclidean geometries are also known (see e.g. Dekster 1995, 1997). | https://en.wikipedia.org/wiki/Jung's_theorem |
Robin Scagell Prof Lucie Green Patron:
The Society for Popular Astronomy ( SPA ) is a national astronomical society based in the United Kingdom for beginners to amateur astronomy . [ 1 ]
It was founded in 1953 as the Junior Astronomical Society [ 2 ] by experienced amateur astronomers including Patrick Moore , Ernest Noon and Eric Turner to encourage beginners to the science and to promote astronomy among the general public.
The term "Junior" was used to denote its role compared to the long-established society the British Astronomical Association . The name was changed in 1994 to make clear that the society was for beginners of all ages, and for those who wanted a less technical approach. In 2007 a new Young Stargazer category of membership was introduced to cater specifically for members aged under 16.
The society's first patron was Dr J G Porter whose BBC radio broadcasts about astronomy preceded television's long-running series The Sky At Night . Since his death, the role has been held by certain Astronomers Royal . The society's president, who serves a two-year term, is usually a senior professional astronomer .
The SPA aims to show that astronomy can be fun and to promote an interest in observing the sky among its members. The SPA has a number of observing sections whose work members can participate in. These cover observations of aurorae , comets , deep sky , the Moon , meteors , occultations , the planets , the Sun and variable stars .
The society publishes a magazine, Popular Astronomy , which from 2011 is being published every two months. Previously it was a quarterly publication, but it now includes material that was carried in now-defunct separate regular printed News Circulars. A members-only email newsletter provides immediate news of major discoveries as well as information and reminders about society meetings and events.
The SPA offers advisory services on choosing a telescope , electronic imaging , photography and the GCSE astronomy examination.
"Popular Astronomy", Popular Astronomy , Society for Popular Astronomy, ISSN 0261-0892 | https://en.wikipedia.org/wiki/Junior_Astronomical_Society |
Junitoite is a mineral with formula CaZn 2 Si 2 O 7 ·H 2 O. It was discovered at the Christmas mine in Christmas, Arizona , and described in 1976. The mineral is named for mineral chemist Jun Ito (1926–1978).
Junitoite is transparent to translucent and is colorless, milk-white, or colored due to alteration. Crystals grow up to 5 millimetres (0.20 in) and have high quality faces. [ 2 ]
Junitoite occurs in fractures through pods of sphalerite . It formed by retrograde metamorphism and oxidation of tactite , also resulting in kinoite. [ 2 ] [ 4 ] [ 5 ] The mineral is known from New Jersey and the type locality in Arizona. [ 3 ] Junitoite occurs in association with apophyllite , calcite , kinoite , smectite , and xonotlite . [ 2 ]
In 1968, Jun Ito published the results of synthesis of various lead calcium zinc silicates. The formula of one phase, designated X 3 , was identified as probably CaZnSi 2 O 6 ·H 2 O. [ 6 ] When he described junitoite, Sidney Williams identified the mineral's formula as CaZn 2 Si 2 O 7 ·H 2 O, based on communications with Ito. [ 4 ] [ 7 ]
The mineral's crystal structure was first determined in 1985 and refined in 2012. [ 5 ] [ 8 ] The mineral crystallizes in the orthorhombic crystal system . [ 2 ] The structure is formed by chains of corner-sharing ZnO 4 tetrahedra linked together by Si 2 O 7 tetrahedral pairs. Calcium ions occupy vacancies and coordinate to five oxygen atoms and one water molecule. [ 9 ]
The first known specimen of junitoite was collected from the Christmas mine at Christmas, Arizona , and entered the collection of Joe Ana Ruiz. Geologist Robert A. Jenkins noticed the mineral in kinoite specimens, submitting Ruiz's sample to Sidney A. Williams for study. Further samples came from the collections of Ruiz and Raymond Diaz. [ 4 ]
Williams identified the specimens as a new mineral and described it in the journal American Mineralogist in 1976. He named it junitoite in honor of Jun Ito, the mineral chemist who noted the compound of which the mineral is composed. [ 7 ] The International Mineralogical Association approved the mineral as IMA 1975-042. [ 10 ] The type material is housed in the University of Arizona , Harvard University , the National Museum of Natural History , the University of Paris , the National School of Mines , and The Natural History Museum . [ 2 ] | https://en.wikipedia.org/wiki/Junitoite |
A Junker test is a mechanical test to determine the point at which a bolted joint loses its preload when subjected to shear loading caused by transverse vibration .
Design engineers apply the Junker test to determine the point at which fastener securing elements – such as lock nuts , wedges and lock washers – fail when subjected to vibration . The data collected by the test enables design engineers to specify fasteners that will perform under a wide range of conditions without loosening.
Research into the causes of vibration-induced self-loosening of threaded fasteners spans six decades and the causes of self-loosening are now well understood. [ 1 ] It was pioneering experimental research into the behaviour of bolted joints under transverse loads, conducted by German engineer Gerhard Junker in the late 1960s [ 2 ] which underpins modern theories on self-loosening behaviour.
Junker’s test methodology and apparatus described in his 1969 paper has since become known as the Junker test and has been adopted into international fastener standards such as DIN 65151, [ 3 ] the Junker test is the established method used for analysing the self-loosening behaviour of secured and unsecured threaded fasteners under transverse loading conditions by vibration testing. | https://en.wikipedia.org/wiki/Junker_test |
JunoCam (or JCM ) is the visible-light camera/telescope onboard NASA's Juno spacecraft that entered orbit around Jupiter in 2016. The camera is operated by the JunoCam Digital Electronics Assembly (JDEA). Both the camera and JDEA were built by Malin Space Science Systems . JunoCam takes a swath of imaging as the spacecraft rotates; the camera is fixed to the spacecraft, so as it rotates, it gets one sweep of observation. [ 1 ] It has a field of view of 58 degrees with four filters (3 for visible light). [ 2 ]
Originally, due to telecommunications constraints, Juno was expected to only be able to return about 40 megabytes of camera data during each 11-day orbital period (the orbital period was later modified). The downlink average data rate of around 325 bits per second will limit the number of images that are captured and transmitted during each orbit to somewhere between 10 and 100 depending on the compression level used. [ 3 ] This is comparable to the previous Galileo mission that orbited Jupiter, which captured thousands of images [ 4 ] despite its slow data rate of 1000 bits per second (at maximum compression levels) due to antenna problems that prevented operation with its planned 135,000 bit-per-second communications link.
The primary observation target is Jupiter itself, although limited images of some of Jupiter's moons have been taken and more are intended. [ 5 ] JunoCam successfully returned detailed images of Ganymede after Juno's flyby on June 7, 2021, [ 6 ] with further opportunities including planned flybys of Europa on September 29, 2022, and two of Io scheduled for December 30, 2023 and February 3, 2024. These flybys will also reduce Juno's orbital period to 33 days. [ 7 ]
The JunoCam project is led by Candice Hansen-Koharcheck . [ 8 ] JunoCam is not one of the probe's core scientific instruments; it was put on board primarily for public science and outreach, to increase public engagement, with all images available on NASA's website. [ 9 ] It is capable of being used for science, and does have some coordinated activities in regards to this, as well as to engage amateur and as well as professional infrared astronomers. [ 5 ]
The JunoCam physical and electronic interfaces are largely based on the MARDI instrument for the Mars Science Laboratory . However, the housing and some aspects of the camera's inner mechanism have been modified to provide stable operation in Jupiter's intense radiation environment and magnetic fields.
Part of its mission will be to provide close up views of Jupiter's polar region and lower-latitude cloud belts, and at Juno ' s intended orbit the camera is able to take images at up to 15 kilometres (9.3 mi) per pixel resolution. However, within one hour of closest approach to Jupiter it can take up to 3 kilometres (1.9 mi) pixel, thus exceeding the resolution of Cassini up to that time on Saturn. [ 1 ]
In addition to visible light filters, it also has a near infrared filter to help detect clouds; a methane filter in addition the visible color filters. The camera is a "push-broom" type imager , generating an image as the spacecraft turns moving the sensor in sweeping motion over the observation area. [ 10 ]
One of the constraints for JunoCam hardware was mass, which limited the size of the optics. [ 11 ]
The camera and the mission were not designed to study the moons of Jupiter . [ 12 ] JunoCam has a field of view that is too wide to resolve any detail in the Jovian moons except during close flybys. Jupiter itself may only appear to be 75 pixels across from JunoCam when Juno reaches the furthest point of its orbit around the planet. [ 3 ] At its closest approaches, JunoCam could achieve 15 km/pixel resolution from 4300 km, while Hubble has taken images of up to 119 km/pixel from 600 million km. [ 13 ]
The camera uses a Kodak image sensor, the KODAK KAI-2020, capable of color imaging at 1600 x 1200 pixels: less than 2 megapixels. [ 14 ] It has a field of view of 58 degrees with four filters (red, green, blue, and a methane band) to provide color imaging. [ 10 ] The low resolution, rigid mounting, and lossy compression applied before transmission makes it effectively the Juno " dashcam ".
Juno ' s orbit is highly elongated and takes it close to the poles (within 4,300 kilometres (2,700 mi)), but then far beyond Callisto 's orbit, the most distant Galilean moon . [ 12 ] This orbital design helps the spacecraft (and its complement of scientific instruments) avoid Jupiter's radiation belts, which have a record of damaging spacecraft electronics and solar panels. The Juno Radiation Vault with its titanium walls also aids in protecting and shielding Juno's electronics. [ 15 ] Despite the intense magnetosphere of Jupiter , JunoCam was expected to be operational for at least the first eight orbits (September 2017), [ 16 ] but as of December 2023 (57 orbits) remains active and has also been re-purposed from an outreach-only camera to a scientific instrument to study the dynamics of Jupiter's clouds, polar storms, and moons. [ 17 ] [ 18 ] The camera sensor experienced noticeable damage from radiation during the 56th orbit in late 2023, increasing noise in the resulting images. However, there is still enough detail to produce sharp imagery through more intensive processing.
In 2005 the Italian Space Agency (ASI) proposed an additional visible light instrument "ItaCam", but instead they built a near-infrared camera/spectrometer, the Jovian Infrared Auroral Mapper (JIRAM) and a Ka-band transponder. ASI previously contributed a near-infrared instrument to the Cassini–Huygens Saturn probe. The Ka-band instrument, KaTS , is a component of the Gravity Science experiment . [ 12 ]
Other cameras manufactured by Malin Space Science Systems:
Other Juno instruments: | https://en.wikipedia.org/wiki/JunoCam |
Junwang Tang, MAE, FRSC and FIMMM, is the Founding Director of Industrial Catalysis Center, and Carbon Neutrality Chair Professor of Materials Chemistry and Catalysis at the Department of Chemical Engineering, Tsinghua University and Visiting Professor at University College London (UCL) . He also served as the Director of the University Material Hub at UCL (2016–2019).
Tang was educated at Northeastern University (China) , where he received his BSc degree in chemistry in 1995. Then he attended the Institute of Metal Research in China and was awarded a MSc degree in inorganic materials in 1998. In 2001, Tang was awarded a PhD in physical chemistry with research on heterogeneous catalytic conversion of NO to N 2 , supervised by Tao Zhang at Dalian Institute of Chemical Physics (DICP) , China [ 2 ]
In 2002, Tang was awarded a Japan Society for the Promotion of Science ( JSPS ) search Fellowship and NIMS Researcher, enable to expand his research in photocatalysis in the National Institute for Materials Science (NIMS) , Japan. [ 3 ] In 2005, he was appointed as a senior research associate in the Department of Chemistry at Imperial College London , UK. [ 4 ]
In 2009, Tang was appointed as a lecturer in energy (permanent position) in Department of Chemical Engineering at University College London , then promoted to a senior lecturer in 2011, a readership in 2014 and finally a full professor of materials chemistry and engineering in 2017. During this period, he was also appointed as the director of University Materials Hub. [ 5 ] In 2022, Tang moved from UCL to Tsinghua University.
Tang is a member of the Academy of Europe / Academia Europaea , [ 6 ] a Royal Society Leverhulme Trust Senior Research Fellow, [ 7 ] a Fellow of European Academy of Sciences , [ 8 ] a Fellow of Royal Society of Chemistry . He also sits on the editorial board of four international journals, e.g. editor of Applied Catalysis B : Environmental , editor-in-chief of Journal of Advanced Chemical Engineering , associate editor of Asia-Pacific Journal of Chemical Engineering and associate editor of Chin Journal of Catalysis , as well as a member of the committees of the RSC Chemical Nanoscience & Nanotechnology. He also sits on the panel of a few counties’ National Science Foundations.
Tang's research interests encompass photocatalytic/thermocatalytic small molecule activation (e.g. CH 4 , [ 9 ] [ 10 ] N 2 , [ 11 ] H 2 O, [ 12 ] C 6 H 6 and CO 2 [ 13 ] [ 14 ] ) and microwave catalysis (e.g. plastic recycling ), [ 15 ] together with the investigation of the underlying charge dynamics and kinetics by state-of-the-art spectroscopies. [ 16 ] [ 17 ] According to Google Scholar , these research activities result into >250 journal papers in reputable journals. [ 18 ]
This article incorporates text available under the CC BY 4.0 license. | https://en.wikipedia.org/wiki/Junwang_Tang |
Juozas Matulis (19 March 1899 – 25 June 1993) was a Lithuanian chemist, physicist and long-time president of the Lithuanian Academy of Sciences .
In 1912, Matulis graduated from Juodpėnai Elementary School. He then studied at the Liepoja Gymnasium from 1920 he served in the electrical engineering battalion of the Lithuanian army. in 1923 Assistant Head of the Organization Department of the Post, Telegraph and Telephone Board. [ 1 ]
In 1924, he graduated from the Adult Gymnasium of the Lithuanian Teachers' Trade Union in Kaunas and entered the Technical Faculty of the University of Lithuania . In 1925, he was transferred to the Physics and Chemistry Department of the Faculty of Mathematics and Natural Sciences. From 1925, Mautlis participated in the activities of the Lithuanian Social Democratic Party and was a member of its student organization Žiežirba. [ 1 ]
In 1928, he was accepted to the University of Lithuania as a junior laboratory assistant and in 1929 he graduated from the university. From 1930 he was chief assistant of the Chemistry Department of Kaunas University . In 1931–1933, he completed an internship at the University of Leipzig and in 1934 he received a doctorate in chemistry. [ 2 ]
From 1936, he was associate professor and from 1940 the Dean of the Faculty of Mathematical Sciences and Natural Sciences of Vilnius University . Matulis career reached new heights after the Soviet occupation of Lithuania in 1940 . In 1941, he was elected as an academician of the Academy of Sciences of the Lithuanian SSR and secretary of the Department of Natural Sciences. After the war, Matulis became the chairman of the restoration committee of the Lithuanian Academy of Sciences and in 1946, he was elected chairman of the Academy of Sciences, a position he held until 1984. [ 2 ] He was also a Corresponding Member of the Academy of Sciences of the Soviet Union . [ 3 ] Matulis was the founder of the national electrochemical school in Lithuania.
As politician he was a deputy of the Supreme Soviet of the Lithuanian SSR from 1947, and from 1959 to 1963 he was its deputy chairman. Matulis became a member of the Communist Party of Lithuania in 1950 and was a member of its Central Committee from 1956 to 1986. [ 4 ] | https://en.wikipedia.org/wiki/Juozas_Matulis |
The Jupiter barrier is the name for a region of the Solar System characterized by the gravitational influence of Jupiter on passing interstellar and in-system objects. Specifically, it is the region where these objects (which include asteroids and comets ) are attracted to Jupiter and are either captured in its orbit or destroyed through impacting the planet.
Jupiter has been nicknamed the Solar System's "cosmic vacuum cleaner" by astronomers who speculate that its gravity reduces the amount of objects reaching the inner Solar System , protecting the smaller planets from impact events . Because such collisions can nearly , if not completely, destroy all life on a planet, the protection of the Jupiter barrier may have supported the evolution of biological complexity on Earth.
This astronomy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Jupiter_barrier |
The Jupiter mass , also called Jovian mass , is the unit of mass equal to the total mass of the planet Jupiter . This value may refer to the mass of the planet alone, or the mass of the entire Jovian system to include the moons of Jupiter . Jupiter is by far the most massive planet in the Solar System . It is approximately 2.5 times as massive as all of the other planets in the Solar System combined. [ 2 ]
Jupiter mass is a common unit of mass in astronomy that is used to indicate the masses of other similarly-sized objects, including the outer planets , extrasolar planets , and brown dwarfs , as this unit provides a convenient scale for comparison.
The current best known value for the mass of Jupiter can be expressed as 1 898 130 yottagrams : [ 1 ]
M J = ( 1.89813 ± 0.00019 ) × 10 27 kg , {\displaystyle M_{\mathrm {J} }=(1.89813\pm 0.00019)\times 10^{27}{\text{ kg}},}
which is about 1 ⁄ 1000 as massive as the Sun (is about 0.1% M ☉ ): [ 3 ]
M J = 1 1047.348644 ± 0.000017 M ⊙ ≈ ( 9.547919 ± 0.000002 ) × 10 − 4 M ⊙ . {\displaystyle M_{\mathrm {J} }={\frac {1}{1047.348644\pm 0.000017}}M_{\odot }\approx (9.547919\pm 0.000002)\times 10^{-4}M_{\odot }.}
Jupiter is 318 times as massive as Earth:
M J = 3.1782838 × 10 2 M ⊕ . {\displaystyle M_{\mathrm {J} }=3.1782838\times 10^{2}M_{\oplus }.}
Jupiter's mass is 2.5 times that of all the other planets in the Solar System combined—this is so massive that its barycenter with the Sun lies beyond the Sun's surface at 1.068 solar radii from the Sun's center. [ 4 ]
Because the mass of Jupiter is so large compared to the other objects in the Solar System , the effects of its gravity must be included when calculating satellite trajectories and the precise orbits of other bodies in the Solar System, including the Moon and even Pluto.
Theoretical models indicate that if Jupiter had much more mass than it does at present, its atmosphere would collapse, and the planet would shrink. [ 5 ] For small changes in mass, the radius would not change appreciably, but above about 500 M E (1.6 Jupiter masses) [ 5 ] the interior would become so much more compressed under the increased pressure that its volume would decrease despite the increasing amount of matter. As a result, Jupiter is thought to have about as large a diameter as a planet of its composition and evolutionary history can achieve. [ 6 ] The process of further shrinkage with increasing mass would continue until appreciable stellar ignition was achieved, as in high-mass brown dwarfs having around 50 Jupiter masses. [ 7 ] Jupiter would need to be about 80 times as massive to fuse hydrogen and become a star . [ 8 ]
The mass of Jupiter is derived from the measured value called the Jovian mass parameter , which is denoted with GM J . The mass of Jupiter is calculated by dividing GM J by the constant G . For celestial bodies such as Jupiter, Earth and the Sun, the value of the GM product is known to many orders of magnitude more precisely than either factor independently. The limited precision available for G limits the uncertainty of the derived mass. For this reason, astronomers often prefer to refer to the gravitational parameter, rather than the explicit mass. The GM products are used when computing the ratio of Jupiter mass relative to other objects.
In 2015, the International Astronomical Union defined the nominal Jovian mass parameter to remain constant regardless of subsequent improvements in measurement precision of M J . This constant is defined as exactly
( G M ) J N = 1.266 8653 × 10 17 m 3 / s 2 {\displaystyle ({\mathcal {GM}})_{\mathrm {J} }^{\mathrm {N} }=1.266\,8653\times 10^{17}{\text{ m}}^{3}/{\text{s}}^{2}}
If the explicit mass of Jupiter is needed in SI units, it can be calculated by dividing GM by G , where G is the gravitational constant . [ 9 ]
The majority of Jupiter's mass is hydrogen and helium. These two elements make up more than 87% of the total mass of Jupiter. [ 10 ] The total mass of heavy elements other than hydrogen and helium in the planet is between 11 and 45 M E . [ 11 ] The bulk of the hydrogen on Jupiter is solid hydrogen. [ 12 ] Evidence suggests that Jupiter contains a central dense core. If so, the mass of the core is predicted to be no larger than about 12 M E . The exact mass of the core is uncertain due to the relatively poor knowledge of the behavior of solid hydrogen at very high pressures. [ 10 ] | https://en.wikipedia.org/wiki/Jupiter_mass |
The Jupiter project was to be a new high-end model of Digital Equipment Corporation (DEC) 's PDP-10 mainframe computers. This project was cancelled in 1983, as the PDP-10 was increasingly eclipsed by the VAX supermini machines (descendants of the PDP-11 ). DEC recognized then that the PDP-10 and VAX product lines were competing with each other and decided to concentrate its software development effort on the more profitable VAX. The PDP-10 was finally dropped from DEC's line in 1983, following the failure of the Jupiter Project at DEC to build a viable new model. [ 1 ]
This computer hardware article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Jupiter_project |
The Jupiter radius or Jovian radius ( R J or R Jup ) has a value of 71,492 km (44,423 mi), or 11.2 Earth radii ( R 🜨 ) [ 2 ] (one Earth radius equals 0.08921 R J ). The Jupiter radius is a unit of length used in astronomy to describe the radii of gas giants and some exoplanets . It is also used in describing brown dwarfs .
The general shape of the planet Jupiter has been directly measured from radio occultations of passing spacecraft, starting with the Pioneer and Voyager missions. This gives an overall margin of error of about 5 km. Estimates of the radii at one bar pressure are then determined through extrapolation. The planet Jupiter has the approximate shape of an oblate spheroid , which is mainly set by the rate of rotation. This gives a difference of about 10% between the polar and equatorial radii. The polar radius has been determined with an accuracy of ±10 km, as of 1987. Density fluctuations within the planet can create variations in the equatorial radius of up to 30 km. The winds in the outer atmosphere can vary the radius by up to 4 km. [ 3 ]
In 2015, the International Astronomical Union defined the nominal equatorial Jovian radius to remain constant regardless of subsequent improvements in measurement precision of R J . This constant is defined as exactly:
Similarly, the nominal polar Jovian radius is defined to be exactly:
These values correspond to the radius of Jupiter at 1 bar of pressure. The common usage is to refer to the equatorial radius, unless the polar radius is specifically needed.
For comparison, one Solar radius is equivalent to: | https://en.wikipedia.org/wiki/Jupiter_radius |
Planetary symbols are used in astrology and traditionally in astronomy to represent a classical planet (which includes the Sun and the Moon) or one of the modern planets. The classical symbols were also used in alchemy for the seven metals known to the ancients , which were associated with the planets , and in calendars for the seven days of the week associated with the seven planets. The original symbols date to Greco-Roman astronomy ; their modern forms developed in the 16th century, and additional symbols would be created later for newly discovered planets.
The seven classical planets, their symbols, days and most commonly associated planetary metals are:
The International Astronomical Union (IAU) discourages the use of these symbols in modern journal articles, and their style manual proposes one- and two-letter abbreviations for the names of the planets for cases where planetary symbols might be used, such as in the headings of tables. [ 1 ] The modern planets with their traditional symbols and IAU abbreviations are:
The symbols of Venus and Mars are also used to represent female and male in biology following a convention introduced by Carl Linnaeus in the 1750s.
The origins of the planetary symbols can be found in the attributes given to classical deities. The Roman planisphere of Bianchini (2nd century, currently in the Louvre , inv. Ma 540) [ 2 ] shows the seven planets represented by portraits of the seven corresponding gods, each a bust with a halo and an iconic object or dress, as follows: Mercury has a caduceus and a winged cap; Venus has a necklace and a shining mirror; Mars has a war-helmet and a spear; Jupiter has a laurel crown and a staff; Saturn has a conical headdress and a scythe; the Sun has rays emanating from his head; and the Moon has a crescent atop her head.
The written symbols for Mercury, Venus, Jupiter, and Saturn have been traced to forms found in late Greek papyri. [ 3 ] [ b ]
Early forms are also found in medieval Byzantine codices which preserve horoscopes. [ 4 ]
A diagram in the astronomical compendium by Johannes Kamateros (12th century) closely resembles the 11th-century forms shown above, with the Sun represented by a circle with a single ray, Jupiter by the letter zeta (the initial of Zeus , Jupiter's counterpart in Greek mythology), Mars by a round shield in front of a diagonal spear, and the remaining classical planets by symbols resembling the modern ones, though without the crosses seen in modern versions of Mercury, Venus, Jupiter and Saturn. [ citation needed ] These crosses first appear in the late 15th or early 16th century. According to Maunder, the addition of crosses appears to be "an attempt to give a savour of Christianity to the symbols of the old pagan gods." [ 5 ] The modern forms of the classical planetary symbols are found in a woodcut of the seven planets in a Latin translation of Abu Ma'shar al-Balkhi 's De Magnis Coniunctionibus printed at Venice in 1506, represented as the corresponding gods riding chariots. [ 6 ]
Earth is not one of the classical planets, as "planets" by definition were "wandering stars" as seen from Earth's surface.
Earth's status as planet is a consequence of heliocentrism in the 16th century.
Nonetheless, there is a pre-heliocentric symbol for the world, now used as a planetary symbol for the Earth. This is a circle crossed by two lines, horizontal and vertical, representing the world divided by four rivers into the four quarters of the world (often translated as the four "corners" of the world): . A variant, now obsolete, had only the horizontal line: . [ 7 ]
A medieval European symbol for the world – the globus cruciger , (the globe surmounted by a Christian cross ) – is also used as a planetary symbol; it resembles an inverted symbol for Venus.
The planetary symbols for Earth are encoded in Unicode at U+1F728 🜨 ALCHEMICAL SYMBOL FOR VERDIGRIS and U+2641 ♁ EARTH .
The crescent shape has been used to represent the Moon since antiquity. In classical antiquity, it is worn by lunar deities ( Selene/Luna , Artemis/Diana , Men , etc.) either on the head or behind the shoulders, with its horns pointing upward.
The representation of the moon as a simple crescent with the horns pointing to the side (as a heraldic crescent increscent or crescent decrescent ) is attested from late Classical times.
The same symbol can be used in a different context not for the Moon itself but for a lunar phase , as part of a sequence of four symbols
for "new moon" (U+1F311 🌑︎), "waxing" (U+263D ☽︎), "full moon" (U+1F315 🌕︎) and "waning" (U+263E ☾︎).
The symbol ☿ for Mercury is a caduceus (a staff intertwined with two serpents), a symbol associated with Mercury / Hermes throughout antiquity. Some time after the 11th century, a cross was added to the bottom of the staff to make it seem more Christian. [ 3 ]
The ☿ symbol has also been used to indicate intersex , transgender , or non-binary gender . [ 8 ] A related usage is for the 'worker' or 'neuter' sex among social insects that is neither male nor (due to its lack of reproductive capacity) fully female, such as worker bees . [ 9 ] It was also once the designated symbol for hermaphroditic or 'perfect' flowers , [ 10 ] but botanists now use ⚥ for these. [ 11 ]
Its Unicode codepoint is U+263F ☿ MERCURY .
The Venus symbol , ♀, consists of a circle with a small cross below it.
It has been interpreted as a depiction of the hand-mirror of the goddess, which may also explain Venus's association with the planetary metal copper, as mirrors in antiquity were made of polished copper, [ 12 ] [ d ] though this is not certain. [ 3 ] In the Greek Oxyrhynchus Papyri 235 , the symbols for Venus and Mercury did not have the cross on the bottom stem, [ 3 ] and Venus appears without the cross (⚲) in Johannes Kamateros (12th century). [ citation needed ]
In botany and biology , the symbol for Venus is used to represent the female sex , alongside the symbol for Mars representing the male sex, [ 13 ] following a convention introduced by Linnaeus in the 1750s. [ 10 ] [ e ] Arising from the biological convention, the symbol also came to be used in sociological contexts to represent women or femininity . This gendered association of Venus and Mars has been used to pair them heteronormatively , describing women and men stereotypically as being so different that they can be understood as coming from different planets, an understanding popularized in 1992 by the book titled Men Are from Mars, Women Are from Venus . [ 14 ] [ 15 ]
Unicode encodes the symbol as U+2640 ♀ FEMALE SIGN , in the Miscellaneous Symbols block. [ f ]
The modern astronomical symbol for the Sun, the circumpunct ( U+2609 ☉ SUN ), was first used in the Renaissance . It possibly represents Apollo's golden shield with a boss ; it is unknown if it traces descent from the nearly identical Egyptian hieroglyph for the Sun.
Bianchini's planisphere , produced in the 2nd century, shows a circlet with rays radiating from it. [ 5 ] [ 2 ] In late Classical times, the Sun is attested as a circle with a single ray. A diagram in Johannes Kamateros' 12th century Compendium of Astrology shows the same symbol. [ 18 ] This older symbol is encoded by Unicode as U+1F71A 🜚 ALCHEMICAL SYMBOL FOR GOLD in the Alchemical Symbols block. Both symbols have been used alchemically for gold, as have more elaborate symbols showing a disk with multiple rays or even a face.
The Mars symbol , ♂, is a depiction of a circle with an arrow emerging from it, pointing at an angle to the upper right in Europe and to the upper left in India. [ 19 ] [ 20 ] It is also the old and obsolete symbol for iron in alchemy. In zoology and botany, it is used to represent the male sex (alongside the astrological symbol for Venus representing the female sex), [ 13 ] following a convention introduced by Linnaeus in the 1750s. [ 10 ]
The symbol dates from at latest the 11th century, at which time it was an arrow across or through a circle, thought to represent the shield and spear of the god Mars; in the medieval form, for example in the 12th-century Compendium of Astrology by Johannes Kamateros, the spear is drawn across the shield. [ 18 ] The Greek Oxyrhynchus Papyri show a different symbol, [ 3 ] perhaps simply a spear. [ 2 ]
Its Unicode codepoint is U+2642 ♂ MALE SIGN ( ♂ ).
The symbol for Jupiter , ♃, was originally a Greek zeta, Ζ , with a stroke indicating that it is an abbreviation (for Zeus , the Greek equivalent of Roman Jupiter).
Its Unicode codepoint is U+2643 ♃ JUPITER .
Salmasius and earlier attestations show that the symbol for Saturn, ♄, derives from the initial letters ( Kappa , rho ) of its ancient Greek name Κρόνος ( Kronos ), with a stroke to indicate an abbreviation . [ 10 ] By the time of Kamateros (12th century), the symbol had been reduced to a shape similar to a lower-case letter eta η, with the abbreviation stroke surviving (if at all) in the curl on the bottom-right end.
Its Unicode codepoint is U+2644 ♄ SATURN .
The symbols for Uranus were created shortly after its discovery in 1781. One symbol, ⛢, invented by J. G. Köhler and refined by Bode , was intended to represent the newly discovered metal platinum ; since platinum, commonly called white gold, was found by chemists mixed with iron, the symbol for platinum combines the alchemical symbols for iron , ♂, and gold , ☉. [ 21 ] [ 22 ] Gold and iron are the planetary metals for the Sun and Mars, and so share their symbols. Several orientations were suggested, but an upright arrow is now universal.
Another symbol, , was suggested by Lalande in 1784. In a letter to Herschel , Lalande described it as "a globe surmounted by the first letter of your name". [ 23 ] The platinum symbol tends to be used by astronomers, and the monogram by astrologers. [ 24 ]
For use in computer systems, the symbols are encoded U+26E2 ⛢ ASTRONOMICAL SYMBOL FOR URANUS and U+2645 ♅ URANUS .
Several symbols were proposed for Neptune to accompany the suggested names for the planet. Claiming the right to name his discovery, Urbain Le Verrier originally proposed to name the planet for the Roman god Neptune [ 25 ] and the symbol of a trident , [ 26 ] while falsely stating that this had been officially approved by the French Bureau des Longitudes . [ 25 ] In October, he sought to name the planet Leverrier , after himself, and he had loyal support in this from the observatory director, François Arago , [ 27 ] who in turn proposed a new symbol for the planet, . [ 28 ] However, this suggestion met with resistance outside France, [ 27 ] and French almanacs quickly reintroduced the name Herschel for Uranus , after that planet's discoverer Sir William Herschel , and Leverrier for the new planet, [ 29 ] though it was used by anglophone institutions. [ 30 ] Professor James Pillans of the University of Edinburgh defended the name Janus for the new planet, and proposed a key for its symbol. [ 26 ] Meanwhile, Struve presented the name Neptune on December 29, 1846, to the Saint Petersburg Academy of Sciences . [ 31 ] In August 1847, the Bureau des Longitudes announced its decision to follow prevailing astronomical practice and adopt the choice of Neptune , with Arago refraining from participating in this decision. [ 32 ] The planetary symbol was Neptune's trident , with the handle stylized either as a crossed , following Mercury, Venus, Jupiter, Saturn, and the asteroids, or as an orb , following the symbols for Uranus, Earth, and Mars. [ 7 ] The crossed variant is the more common today.
For use in computer systems, the symbols are encoded as U+2646 ♆ NEPTUNE and U+2BC9 ⯉ NEPTUNE FORM TWO .
Pluto was almost universally considered a planet from its discovery in 1930 until its re-classification as a dwarf planet (planetoid) by the IAU in 2006. Planetary geologists [ 33 ] and astrologers continue to treat it as a planet. The original planetary symbol for Pluto was , a monogram of the letters P and L. Astrologers generally use a bident with an orb. NASA has used the bident symbol since Pluto's reclassification. These symbols are encoded as U+2647 ♇ PLUTO and U+2BD3 ⯓ PLUTO FORM TWO .
In the 19th century, planetary symbols for the major asteroids were also in use, including 1 Ceres (a reaper's sickle , encoded U+26B3 ⚳ CERES ), 2 Pallas (a lance, U+26B4 ⚴ PALLAS ) and 3 Juno (a sceptre, encoded U+26B5 ⚵ JUNO ).
Encke (1850) used symbols for 5 Astraea , 6 Hebe , 7 Iris , 8 Flora and 9 Metis in the Berliner Astronomisches Jahrbuch . [ 34 ]
In the late 20th century, astrologers abbreviated the symbol for 4 Vesta (the sacred fire of Vesta , encoded U+26B6 ⚶ VESTA ), [ 35 ] and introduced new symbols for 5 Astraea ( , a stylised % sign, shift-5 on QWERTY keyboards for asteroid 5), 10 Hygiea encoded U+2BDA ⯚ HYGIEA ) [ 36 ] and for 2060 Chiron , discovered in 1977 (a key, U+26B7 ⚷ CHIRON ). [ 35 ] Chiron's symbol was adapted as additional centaurs were discovered; symbols for 5145 Pholus and 7066 Nessus have been encoded in Unicode. [ 36 ] The abbreviated Vesta symbol is now universal, and the astrological symbol for Pluto has been used astronomically for Pluto as a dwarf planet. [ 37 ]
In the early 21st century, symbols for the trans-Neptunian dwarf planets have been given Unicode codepoints , particularly Eris (the hand of Eris , ⯰, but also ⯱), Sedna , Haumea , Makemake , Gonggong , Quaoar and Orcus which are in Unicode. All (except Eris, for which the hand of Eris is a traditional Discordian symbol) were devised by Denis Moskowitz, a software engineer in Massachusetts. [ 37 ] [ 38 ]
Other symbols have also been invented by Moskowitz, for some smaller TNOs as well as many planetary moons. (Charon in particular coincidentally matches a symbol already existing in Unicode as an astrological Pluto.) However, these have not been broadly adopted. [ 37 ] [ 39 ]
From 1845 to 1855, many symbols were created for newly discovered asteroids. But by 1851, the spate of discoveries had led to a general abandonment of these symbols in favour of numbering all asteroids instead. [ 41 ] | https://en.wikipedia.org/wiki/Jupiter_symbol |
Jure Zupan is a Slovenian physicist and founder of chemomectrics research in Slovenia, known for his work in applications and development of artificial neural networks in chemistry.
Zupan was born in Ljubljana , Slovenia in 1943. He studied Physics at the University of Ljubljana and graduated in 1966. He obtained his PhD in Chemistry in 1972. He did his first research on the magnetic properties of solids at the Josef Stefan Institute , Ljubljana (1963–1973). In 1974 he has joined National Institute of Chemistry in Ljubljana to work on Computerized Databases, Chemometrics, and Artificial Intelligence. He did his post doctoral research at ETH Zürich (1975) and at NIH, Bethesda (1978).
Since 1985 he is a Full professor at the University of Ljubljana. He was Visiting Professor at the Arizona State University in Tempe, USA (1982), at the Vrije Universiteit Brussel , Belgium (1988), for 3 consecutive years (each year for three months) at the Technical University Munich , Germany (1990–1992), and at the University Rovira i Virgili , Tarragona, Spain (1995). After 1988 his research focused to the field of Artificial Neural Networks. He is now mostly interested in the multi-dimensional data representation and context extraction from large assembles of multi-dimensional data. He is member of the European Academy of Science (Salzburg) and member of the Engineering Academy of Slovenia.
Zupan is author and editor of 10 books and monographs and has co-authored more than 200 articles. With Johann Gasteiger he co-authored Neural Networks in Chemistry and Drug Design . [ 1 ] The book received more than 500 citations and was nominated the book of the month in 1993. [ citation needed ] | https://en.wikipedia.org/wiki/Jure_Zupan |
Jurin's law , or capillary rise , is the simplest analysis of capillary action —the induced motion of liquids in small channels [ 1 ] —and states that the maximum height of a liquid in a capillary tube is inversely proportional to the tube's diameter . Capillary action is one of the most common fluid mechanical effects explored in the field of microfluidics . Jurin's law is named after James Jurin , who discovered it between 1718 and 1719. [ 2 ] His quantitative law suggests that the maximum height of liquid in a capillary tube is inversely proportional to the tube's diameter. The difference in height between the surroundings of the tube and the inside, as well as the shape of the meniscus , are caused by capillary action . The mathematical expression of this law can be derived directly from hydrostatic principles and the Young–Laplace equation . Jurin's law allows the measurement of the surface tension of a liquid and can be used to derive the capillary length . [ 3 ]
The law is expressed as [ citation needed ]
where
It is only valid if the tube is cylindrical and has a radius ( r 0 ) smaller than the capillary length ( λ c 2 = γ / ( ρ g ) {\displaystyle \lambda _{\rm {c}}^{2}=\gamma /(\rho g)} ). In terms of the capillary length, the law can be written as
For a water-filled glass tube in air at standard conditions for temperature and pressure , γ = 0.0728 N/m at 20 °C, ρ = 1000 kg/m 3 , and g = 9.81 m/s 2 . Because water spreads on clean glass, the effective equilibrium contact angle is approximately zero. [ 4 ] For these values, the height of the water column is
Thus for a 2 m (6.6 ft) radius glass tube in lab conditions given above, the water would rise an unnoticeable 0.007 mm (0.00028 in). However, for a 2 cm (0.79 in) radius tube, the water would rise 0.7 mm (0.028 in), and for a 0.2 mm (0.0079 in) radius tube, the water would rise 70 mm (2.8 in).
Capillary action is used by many plants to bring up water from the soil. For tall trees (larger than ~10 m (32 ft)), other processes like osmotic pressure and negative pressures are also important. [ 5 ]
During the 15th century, Leonardo da Vinci was one of the first to propose that mountain streams could result from the rise of water through small capillary cracks. [ 3 ] [ 6 ]
It is later, in the 17th century, that the theories about the origin of capillary action begin to appear. Jacques Rohault erroneously supposed that the rise of the liquid in a capillary could be due to the suppression of air inside and the creation of a vacuum. The astronomer Geminiano Montanari was one of the first to compare the capillary action to the circulation of sap in plants. Additionally, the experiments of Giovanni Alfonso Borelli determined in 1670 that the height of the rise was inversely proportional to the radius of the tube.
Francis Hauksbee , in 1713, refuted the theory of Rohault through a series of experiments on capillary action, a phenomenon that was observable in air as well as in vacuum. Hauksbee also demonstrated that the liquid rise appeared on different geometries (not only circular cross sections), and on different liquids and tube materials, and showed that there was no dependence on the thickness of the tube walls. Isaac Newton reported the experiments of Hauskbee in his work Opticks but without attribution. [ 3 ] [ 6 ]
It was the English physiologist James Jurin , who finally in 1718 [ 2 ] confirmed the experiments of Borelli and the law was named in his honour. [ 3 ] [ 6 ]
The height h {\displaystyle h} of the liquid column in the tube is constrained by the hydrostatic pressure and by the surface tension . The following derivation is for a liquid that rises in the tube; for the opposite case when the liquid is below the reference level, the derivation is analogous but pressure differences may change sign. [ 1 ]
Above the interface between the liquid and the surface, the pressure is equal to the atmospheric pressure p a t m {\displaystyle p_{\rm {atm}}} . At the meniscus interface, due to the surface tension, there is a pressure difference of Δ p = p a t m − p i n t {\displaystyle \Delta p=p_{\rm {atm}}-p_{\rm {int}}} , where p i n t {\displaystyle p_{\rm {int}}} is the pressure on the convex side; and Δ p {\displaystyle \Delta p} is known as Laplace pressure . If the tube has a circular section of radius r 0 {\displaystyle r_{0}} , and the meniscus has a spherical shape, the radius of curvature is r = r 0 / cos θ {\displaystyle r=r_{0}/\cos \theta } , where θ {\displaystyle \theta } is the contact angle . The Laplace pressure is then calculated according to the Young-Laplace equation : Δ p = 2 γ r , {\displaystyle \Delta p={\frac {2\gamma }{r}},} where γ {\displaystyle \gamma } is the surface tension.
Outside and far from the tube, the liquid reaches a ground level in contact with the atmosphere. Liquids in communicating vessels have the same pressures at the same heights, so a point w {\displaystyle {\rm {w}}} , inside the tube, at the same liquid level as outside, would have the same pressure p w = p a t m {\displaystyle p_{\rm {w}}=p_{\rm {atm}}} . Yet the pressure at this point follows a vertical pressure variation as
where g {\displaystyle g} is the gravitational acceleration and ρ {\displaystyle \rho } the density of the liquid. This equation means that the pressure at point w {\displaystyle {\rm {w}}} is the pressure at the interface plus the pressure due to the weight of the liquid column of height h {\displaystyle h} . In this way, we can calculate the pressure at the convex interface p i n t = p w − ρ g h = p a t m − ρ g h . {\displaystyle p_{\rm {int}}=p_{\rm {w}}-\rho gh=p_{\rm {atm}}-\rho gh.}
The hydrostatic analysis shows that Δ p = ρ g h {\displaystyle \Delta p=\rho gh} , combining this with the Laplace pressure calculation we have: ρ g h = 2 γ cos θ r 0 , {\displaystyle \rho gh={\frac {2\gamma \cos \theta }{r_{0}}},} solving for h {\displaystyle h} returns Jurin's law. | https://en.wikipedia.org/wiki/Jurin's_law |
A jury theorem is a mathematical theorem proving that, under certain assumptions, a decision attained using majority voting in a large group is more likely to be correct than a decision attained by a single expert. It serves as a formal argument for the idea of wisdom of the crowd , for decision of questions of fact by jury trial , and for democracy in general. [ 1 ]
The first and most famous jury theorem is Condorcet's jury theorem . It assumes that all voters have independent probabilities to vote for the correct alternative, these probabilities are larger than 1/2, and are the same for all voters. Under these assumptions, the probability that the majority decision is correct is strictly larger when the group is larger; and when the group size tends to infinity, the probability that the majority decision is correct tends to 1.
There are many other jury theorems, relaxing some or all of these assumptions.
The premise of all jury theorems is that there is an objective truth , which is unknown to the voters. Most theorems focus on binary issues (issues with two possible states), for example, whether a certain defendant is guilty or innocent, whether a certain stock is going to rise or fall, etc. There are n {\displaystyle n} voters (or jurors), and their goal is to reveal the truth. Each voter has an opinion about which of the two options is correct. The opinion of each voter is either correct (i.e., equals the true state), or wrong (i.e., differs than the true state). This is in contrast to other settings of voting , in which the opinion of each voter represents his/her subjective preferences and is thus always "correct" for this specific voter. The opinion of a voter can be considered a random variable : for each voter, there is a positive probability that his opinion equals the true state.
The group decision is determined by the majority rule . For example, if a majority of voters says "guilty" then the decision is "guilty", while if a majority says "innocent" then the decision is "innocent". To avoid ties, it is often assumed that the number of voters n {\displaystyle n} is odd. Alternatively, if n {\displaystyle n} is even, then ties are broken by tossing a fair coin .
Jury theorems are interested in the probability of correctness - the probability that the majority decision coincides with the objective truth. Typical jury theorems make two kinds of claims on this probability: [ 1 ]
Claim 1 is often called the non-asymptotic part and claim 2 is often called the asymptotic part of the jury theorem.
Obviously, these claims are not always true, but they are true under certain assumptions on the voters. Different jury theorems make different assumptions.
Condorcet's jury theorem makes the following three assumptions:
The jury theorem of Condorcet says that these three assumptions imply Growing Reliability and Crowd Infallibility.
The opinions of different voters are often correlated, so Unconditional Independence may not hold. In this case, the Growing Reliability claim might fail.
Let p {\displaystyle p} be the probability of a juror voting for the correct alternative and c {\displaystyle c} be the (second-order) correlation coefficient between any two correct votes. If all higher-order correlation coefficients in the Bahadur representation [ 2 ] of the joint probability distribution of votes equal to zero, and ( p , c ) ∈ B n {\displaystyle (p,c)\in {\mathcal {B}}_{n}} is an admissible pair , then the probability of the jury collectively reaching the correct decision under simple majority is given by:
where I p {\displaystyle I_{p}} is the regularized incomplete beta function .
Example: Take a jury of three jurors ( n = 3 ) {\displaystyle (n=3)} , with individual competence p = 0.55 {\displaystyle p=0.55} and second-order correlation c = 0.4 {\displaystyle c=0.4} . Then P ( 3 , 0.55 , 0.4 ) = 0.54505 {\displaystyle P(3,0.55,0.4)=0.54505} . The competence of the jury is lower than the competence of a single juror, which equals to 0.55 {\displaystyle 0.55} . Moreover, enlarging the jury by two jurors ( n = 5 ) {\displaystyle (n=5)} decreases the jury competence even further, P ( 5 , 0.55 , 0.4 ) = 0.5196194 {\displaystyle P(5,0.55,0.4)=0.5196194} . Note that p = 0.55 {\displaystyle p=0.55} and c = 0.4 {\displaystyle c=0.4} is an admissible pair of parameters. For n = 5 {\displaystyle n=5} and p = 0.55 {\displaystyle p=0.55} , the maximum admissible second-order correlation coefficient equals ≈ 0.43 {\displaystyle \approx 0.43} .
The above example shows that when the individual competence is low but the correlation is high:
The above result is due to Kaniovski and Zaigraev. They also discuss optimal jury design for homogenous juries with correlated votes. [ 3 ]
There are several jury theorems that weaken the Independence assumption in various ways.
In binary decision problems, there is often one option that is easier to detect that the other one. For example, it may be easier to detect that a defendant is guilty (as there is clear evidence for guilt) than to detect that he is innocent. In this case, the probability that the opinion of a single voter is correct is represented by two different numbers: probability given that option #1 is correct, and probability given that option #2 is correct. This also implies that opinions of different voters are correlated . This motivates the following relaxations of the above assumptions:
Growing Reliability and Crowd Infallibility continue to hold under these weaker assumptions. [ 1 ]
One criticism of Conditional Competence is that it depends on the way the decision question is formulated. For example, instead of asking whether the defendant is guilty or innocent, one can ask whether the defendant is guilty of exactly 10 charges (option A), or guilty of another number of charges (0..9 or more than 11). This changes the conditions, and hence, the conditional probability. Moreover, if the state is very specific, then the probability of voting correctly might be below 1/2, so Conditional Competence might not hold. [ 4 ]
Another cause of correlation between voters is the existence of an opinion leader . Suppose each voter makes an independent decision, but then each voter, with some fixed probability, changes his opinion to match that of the opinion leader. Jury theorems by Boland [ 5 ] and Boland, Proschan and Tong [ 6 ] shows that, if (and only if) the probability of following the opinion leader is less than 1-1/2 p (where p is the competence level of all voters), then Crowd Infallibility holds.
In addition to the dependence on the true option, there are many other reasons for which voters' opinions may be correlated. For example:
It is possible to weaken the Conditional Independence assumption, and conditionalize on all common causes of the votes (rather than just the state). In other words, the votes are now independent conditioned on the specific decision problem . However, in a specific problem, the Conditional Competence assumption may not be valid. For example, in a specific problem with false evidence, it is likely that most voters will have a wrong opinion. Thus, the two assumptions - conditional independence and conditional competence - are not justifiable simultaneously (under the same conditionalization). [ 7 ]
A possible solution is to weaken Conditional Competence as follows. For each voter and each problem x , there is a probability p ( x ) that the voter's opinion is correct in this specific problem. Since x is a random variable, p ( x ) is a random variable too. Conditional Competence requires that p ( x ) > 1/2 with probability 1. The weakened assumption is:
A jury theorem by Dietrich and Spiekerman [ 8 ] says that Conditional Independence, Tendency to Competence, and Conditional Uniformity, together imply Growing Reliability. Note that Crowd Infallibility is not implied. In fact, the probability of correctness tends to a value which is below 1, if and only of Conditional Competence does not hold.
A jury theorem by Pivato [ 9 ] shows that, if the average covariance between voters becomes small as the population becomes large, then Crowd Infallibility holds (for some voting rule). There are other jury theorems that take into account the degree to which votes may be correlated. [ 10 ] [ 11 ]
Other ways to cope with voter correlation include causal networks , dependence structures, and interchangeability. [ 1 ] : 2.2
Different voters often have different competence levels, so the Uniformity assumption does not hold. In this case, both Growing Reliability and Crowd Infallibility may not hold. This may happen if new voters have much lower competence than existing voters, so that adding new voters decreases the group's probability of correctness. In some cases, the probability of correctness might converge to 1/2 (- a random decision) rather than to 1. [ 12 ]
Uniformity can be dismissed if the Competence assumption is strengthened. There are several ways to strengthen it:
instead of assuming that the voter identity is fixed, one can assume that there is a large pool of potential voters with different competence levels, and the actual voters are selected at random from this pool (as in sortition ).
A jury theorem by Ben Yashar and Paroush [ 15 ] shows that, under certain conditions, the correctness probability of a jury, or of a subset of it chosen at random, is larger than the correctness probability of a single juror selected at random. A more general jury theorem by Berend and Sapir [ 16 ] proves that Growing Reliability holds in this setting: the correctness probability of a random committee increases with the committee size. The theorem holds, under certain conditions, even with correlated votes. [ 17 ]
A jury theorem by Owen, Grofman and Feld [ 18 ] analyzes a setting where the competence level is random. They show what distribution of individual competence maximizes or minimizes the probability of correctness.
When the competence levels of the voters are known, the simple majority rule may not be the best decision rule. There are various works on identifying the optimal decision rule - the rule maximizing the group correctness probability. Nitzan and Paroush [ 19 ] show that, under Unconditional Independence, the optimal decision rule is a weighted majority rule, where the weight of each voter with correctness probability p i is log( p i /(1- p i )), and an alternative is selected if the sum of weights of its supporters is above some threshold. Grofman and Shapley [ 20 ] analyze the effect of interdependencies between voters on the optimal decision rule. Ben-Yashar and Nitzan [ 21 ] prove a more general result.
Dietrich [ 22 ] generalizes this result to a setting that does not require prior probabilities of the 'correctness' of the two alternative. The only required assumption is Epistemic Monotonicity, which says that, if under certain profile alternative x is selected, and the profile changes such that x becomes more probable, then x is still selected. Dietrich shows that Epistemic Monotonicity implies that the optimal decision rule is weighted majority with a threshold. In the same paper, he generalizes the optimal decision rule to a setting that does not require the input to be a vote for one of the alternatives. It can be, for example, a subjective degree of belief. Moreover, competence parameters do not need to be known. For example, if the inputs are subjective beliefs x 1 ,..., x n , then the optimal decision rule sums log( x i /(1- x i )) and checks whether the sum is above some threshold. Epistemic Monotonicity is not sufficient for computing the threshold itself; the threshold can be computed by assuming expected-utility maximization and prior probabilities.
A general problem with the weighted majority rules is that they require to know the competence levels of the different voters, which is usually hard to compute in an objective way. Baharad, Goldberger, Koppel and Nitzan [ 23 ] present an algorithm that solves this problem using statistical machine learning . It requires as input only a list of past votes; it does not need to know whether these votes were correct or not. If the list is sufficiently large, then its probability of correctness converges to 1 even if the individual voters' competence levels are close to 1/2.
Often, decision problems involve three or more options. This critical limitation was in fact recognized by Condorcet (see Condorcet's paradox ), and in general it is very difficult to reconcile individual decisions between three or more outcomes (see Arrow's theorem ).
This limitation may also be overcome by means of a sequence of votes on pairs of alternatives, as is commonly realized via the legislative amendment process. (However, as per Arrow's theorem, this creates a "path dependence" on the exact sequence of pairs of alternatives; e.g., which amendment is proposed first can make a difference in what amendment is ultimately passed, or if the law—with or without amendments—is passed at all.)
With three or more options, Conditional Competence can be generalized as follows:
A jury theorem by List and Goodin shows that Multioption Conditional Competence and Conditional Independence together imply Crowd Infallibility. [ 24 ] Dietrich and Spiekermann conjecture that they imply Growing Reliability too. [ 1 ] Another related jury theorem is by Everaere, Konieczny and Marquis. [ 25 ]
When there are more than two options, there are various voting rules that can be used instead of simple majority. The statistic and utilitarian properties of such rules are analyzed e.g. by Pivato. [ 26 ] [ 27 ]
Condorcet's theorem considers a direct majority system , in which all votes are counted directly towards the final outcome. Many countries use an indirect majority system , in which the voters are divided into groups. The voters in each group decide on an outcome by an internal majority vote; then, the groups decide on the final outcome by a majority vote among them. For example, [ 5 ] suppose there are 15 voters. In a direct majority system, a decision is accepted whenever at least 8 votes support it. Suppose now that the voters are grouped into 3 groups of size 5 each. A decision is accepted whenever at least 2 groups support it, and in each group, a decision is accepted whenever at least 3 voters support it. Therefore, a decision may be accepted even if only 6 voters support it.
Boland, Proschan and Tong [ 6 ] prove that, when the voters are independent and p>1/2, a direct majority system - as in Condorcet's theorem - always has a higher chance of accepting the correct decision than any indirect majority system.
Berg and Paroush [ 28 ] consider multi-tier voting hierarchies, which may have several levels with different decision-making rules in each level. They study the optimal voting structure, and compares the competence against the benefit of time-saving and other expenses.
Goodin and Spiekermann [ 29 ] compute the amount by which a small group of experts should be better than the average voters, in order for them to accept better decisions.
It is well-known that, when there are three or more alternatives, and voters have different preferences, they may engage in strategic voting , for example, vote for the second-best option in order to prevent the worst option from being elected. Surprisingly, strategic voting might occur even with two alternatives and when all voters have the same preference, which is to reveal the truth. For example, suppose the question is whether a defendant is guilty or innocent, and suppose a certain juror thinks the true answer is "guilty". However, he also knows that his vote is effective only if the other votes are tied. But, if other votes are tied, it means that the probability that the defendant is guilty is close to 1/2. Taking this into account, our juror might decide that this probability is not sufficient for deciding "guilty", and thus will vote "innocent". But if all other voters do the same, the wrong answer is derived. In game-theoretic terms, truthful voting might not be a Nash equilibrium . [ 30 ] This problem has been termed the swing voter's curse , [ 31 ] as it is analogous to the winner's curse in auction theory.
A jury theorem by Peleg and Zamir [ 32 ] shows sufficient and necessary conditions for the existence of a Bayesian-Nash equilibrium that satisfies Condorcet's jury theorem. Bozbay, Dietrich and Peters [ 33 ] show voting rules that lead to efficient aggregation of the voters' private information even with strategic voting.
In practice, this problem may not be very severe, since most voters care not only about the final outcome, but also about voting correctly by their conscience. Moreover, most voters are not sophisticated enough to vote strategically. [ 1 ] : 4.7
The notion of "correctness" may not be meaningful when making policy decisions, which are based on values or preferences, rather than just on facts.
Some defenders of the theorem hold that it is applicable when voting is aimed at determining which policy best promotes the public good, rather than at merely expressing individual preferences. On this reading, what the theorem says is that although each member of the electorate may only have a vague perception of which of two policies is better, majority voting has an amplifying effect. The "group competence level", as represented by the probability that the majority chooses the better alternative, increases towards 1 as the size of the electorate grows assuming that each voter is more often right than wrong.
Several papers show that, under reasonable conditions, large groups are better trackers of the majority preference. [ 34 ] : 323 [ 35 ] [ 36 ]
The applicability of jury theorems, in particular, Condorcet's Jury Theorem (CJT) to democratic processes is debated, as it can prove majority rule to be a perfect mechanism or a disaster depending on individual competence. Recent studies show that, in a non-homogeneous case, the theorem's thesis does not hold almost surely (unless weighted majority rule is used with stochastic weights that are correlated with epistemic rationality but such that every voter has a minimal weight of one). [ 37 ] | https://en.wikipedia.org/wiki/Jury_theorem |
Just in sequence ( JIS ) is an inventory strategy that matches just in time (JIT) and complete fit in sequence with variation of assembly line production. Components and parts arrive at a production line right in time as scheduled before they get assembled. Feedback from the manufacturing line is used to coordinate transport to and from the process area . When implemented successfully, JIS improves a company's return on assets (ROA) , without loss in flexibility, quality or overall efficiency. JIS is mainly implemented with car manufacture.
JIS is sometimes called In-Line Vehicle Sequencing ( ILVS ).
Just in sequence (JIS) is just one specialised strategy to achieve just in time (JIT). The process concept of JIT sees buffers at the production line as waste in capital bound. The aim is to eliminate buffers as much as possible at the expense of stability when disturbances arise. Just In Sequence is one of the most extreme applications of the concept, where components arrive Just In Time and sequenced for consumption.
The sequencing allows companies to eliminate supply buffers as soon as the quantity in component part buffers necessary is reduced to a minimum. If not sequencing according to scheduled variety of production, all required components must be stocked in buffers. For flexible production lines, such as a modern automotive assembly line, the variety is an option to produce directly on customer orders. As soon as the next order arrives at the work center, the scheduler distributes the supply orders inline with the production sequence of the final production line.
However, with JIS the buffer quantities are displaced upward in material flow to the components suppliers. It is a misinterpretation of JIS to assume that all buffers will be eliminated. Hence just the cost for buffer inventory becomes re-allocated to the producers of the supplies. Sequencing eliminates buffers in the final assembly line by consolidating all similar components into distributed and sequenced buffers, which partly reside on the paths of transport to final assembly. This strategy thus reduces the line-side inventory buffer. However, the effect is worse when the sequence does not get correctly scheduled upwards or when the transport line gets congested.
Just In Sequence processes are typically implemented only after the company has achieved a high degree of competency on Just In Time processes. The first step for the organization is to implement JIT processes to synchronize all manufacturing and material departments inside the plant and to collaborate with suppliers, customers, and sub-contractors to reduce inventory buffers to within a few hours. This process typically uncovers deep manufacturing and logistic issues that are not easy to overcome (see JIT Implementation for more details). The manufacturing company can only benefit from sequencing items once these problems have been resolved successfully and components are delivered Just In Time.
Sequencing can be implemented in a Just In Time supply operation at many levels, bringing ever-higher inventory reduction and financial benefits:
Just In Sequence implementations introduce a number of new process requirements on top of Just In Time practices. A production sequence or final assembly sequence must be shared upwards to suppliers and sub-contractors. Feedback to customers must be organized according to the scheduled output to earn all positive financial effects. For these and other reasons, the actual production sequence must be "broadcast" out to all relevant parties once it is firm. This "broadcast" can be done over the phone, paper, email, or other automated IT system. UN/EDIFACT supports an EDI message standard called DELJIT as one standardized way to communicate this information.
Once the sequence is broadcast, each party must immediately take action to deliver sequenced parts in time. In many cases the turn-around time from broadcast to final assembly is less than 2 hours, with some components required in 30 minutes or less. With this time frame, there is little room for errors. In addition, quality inspection and poka-yoke must be implemented in the sequencing step to guarantee that the sequenced components match the assembly sequence perfectly. In many cases, suppliers must manage periodic sequence reversals, for example, when loading racks into a truck, since the first rack into the truck is the last one to come out. Employees and systems must also properly manage exceptional scenarios, such as re-processing damaged items after initial sequencing, skipping slots for scrapped items, etc. Just In Sequence implementations can only be successful if all of these processes are implemented correctly and all people involved understand what is at stake.
In many manufacturing operations, the actual production sequence cannot be planned ahead of time with enough certainty to enable sequencing. The main reason is that some manufacturing processes require re-work frequently so that a scheduled sequence becomes irrelevant. For example, painting operations in an automotive plant can have re-work levels of up to 20% (USA, Southern Europe).
Stephan M. Wagner and Victor Silveira-Camargos, 2009, Decision model for the application of just-in-sequence , in: Decision Sciences Institute Proceedings of the 40th annual conference, New Orleans, USA. | https://en.wikipedia.org/wiki/Just_in_sequence |
In coding theory , Justesen codes form a class of error-correcting codes that have a constant rate, constant relative distance, and a constant alphabet size.
Before the Justesen error correction code was discovered, no error correction code was known that had all of these three parameters as a constant.
Subsequently, other ECC codes with this property have been discovered, for example expander codes .
These codes have important applications in computer science such as in the construction of small-bias sample spaces .
Justesen codes are derived as the code concatenation of a Reed–Solomon code and the Wozencraft ensemble .
The Reed–Solomon codes used achieve constant rate and constant relative distance at the expense of an alphabet size that is linear in the message length.
The Wozencraft ensemble is a family of codes that achieve constant rate and constant alphabet size, but the relative distance is only constant for most of the codes in the family.
The concatenation of the two codes first encodes the message using the Reed–Solomon code, and then encodes each symbol of the codeword further using a code from the Wozencraft ensemble – using a different code of the ensemble at each position of the codeword.
This is different from usual code concatenation where the inner codes are the same for each position. The Justesen code can be constructed very efficiently using only logarithmic space .
The Justesen code is the concatenation of an ( N , K , D ) q k {\displaystyle (N,K,D)_{q^{k}}} outer code C o u t {\displaystyle C_{out}} and different ( n , k , d ) q {\displaystyle (n,k,d)_{q}} inner codes C i n i {\displaystyle C_{in}^{i}} , for 1 ≤ i ≤ N {\displaystyle 1\leq i\leq N} .
More precisely, the concatenation of these codes, denoted by C o u t ∘ ( C i n 1 , . . . , C i n N ) {\displaystyle C_{out}\circ (C_{in}^{1},...,C_{in}^{N})} , is defined as follows. Given a message m ∈ [ q k ] K {\displaystyle m\in [q^{k}]^{K}} , we compute the codeword produced by an outer code C o u t {\displaystyle C_{out}} : C o u t ( m ) = ( c 1 , c 2 , . . , c N ) {\displaystyle C_{out}(m)=(c_{1},c_{2},..,c_{N})} .
Then we apply each code of N linear inner codes to each coordinate of that codeword to produce the final codeword; that is, C o u t ∘ ( C i n 1 , . . , C i n N ) ( m ) = ( C i n 1 ( c 1 ) , C i n 2 ( c 2 ) , . . , C i n N ( c N ) ) {\displaystyle C_{out}\circ (C_{in}^{1},..,C_{in}^{N})(m)=(C_{in}^{1}(c_{1}),C_{in}^{2}(c_{2}),..,C_{in}^{N}(c_{N}))} .
Look back to the definition of the outer code and linear inner codes, this definition of the Justesen code makes sense because the codeword of the outer code is a vector with N {\displaystyle N} elements, and we have N {\displaystyle N} linear inner codes to apply for those N {\displaystyle N} elements.
Here for the Justesen code, the outer code C o u t {\displaystyle C_{out}} is chosen to be Reed Solomon code over a field F q k {\displaystyle \mathbb {F} _{q^{k}}} evaluated over F q k − { 0 } {\displaystyle \mathbb {F} _{q^{k}}-\{0\}} of rate R {\displaystyle R} , 0 {\displaystyle 0} < R {\displaystyle R} < 1 {\displaystyle 1} .
The outer code C o u t {\displaystyle C_{out}} have the relative distance δ o u t = 1 − R {\displaystyle \delta _{out}=1-R} and block length of N = q k − 1 {\displaystyle N=q^{k}-1} . The set of inner codes is the Wozencraft ensemble { C i n α } α ∈ F q k ∗ {\displaystyle \{C_{in}^{\alpha }\}_{\alpha \in \mathbb {F} _{q^{k}}^{*}}} .
As the linear codes in the Wonzencraft ensemble have the rate 1 2 {\displaystyle {\frac {1}{2}}} , Justesen code is the concatenated code C ∗ = C o u t ∘ ( C i n 1 , C i n 2 , . . , C i n N ) {\displaystyle C^{*}=C_{out}\circ (C_{in}^{1},C_{in}^{2},..,C_{in}^{N})} with the rate R 2 {\displaystyle {\frac {R}{2}}} . We have the following theorem that estimates the distance of the concatenated code C ∗ {\displaystyle C^{*}} .
Let ε > 0. {\displaystyle \varepsilon >0.} Then C ∗ {\displaystyle C^{*}} has relative distance of at least ( 1 − R − ε ) H q − 1 ( 1 2 − ε ) . {\displaystyle (1-R-\varepsilon )H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right).}
In order to prove a lower bound for the distance of a code C ∗ {\displaystyle C^{*}} we prove that the Hamming distance of an arbitrary but distinct pair of codewords has a lower bound. So let Δ ( c 1 , c 2 ) {\displaystyle \Delta (c^{1},c^{2})} be the Hamming distance of two codewords c 1 {\displaystyle c^{1}} and c 2 {\displaystyle c^{2}} . For any given
we want a lower bound for Δ ( C ∗ ( m 1 ) , C ∗ ( m 2 ) ) . {\displaystyle \Delta (C^{*}(m_{1}),C^{*}(m_{2})).}
Notice that if C o u t ( m ) = ( c 1 , ⋯ , c N ) {\displaystyle C_{out}(m)=(c_{1},\cdots ,c_{N})} , then C ∗ ( m ) = ( C i n 1 ( c 1 ) , ⋯ , C i n N ( c N ) ) {\displaystyle C^{*}(m)=(C_{in}^{1}(c_{1}),\cdots ,C_{in}^{N}(c_{N}))} . So for the lower bound Δ ( C ∗ ( m 1 ) , C ∗ ( m 2 ) ) {\displaystyle \Delta (C^{*}(m_{1}),C^{*}(m_{2}))} , we need to take into account the distance of C i n 1 , ⋯ , C i n N . {\displaystyle C_{in}^{1},\cdots ,C_{in}^{N}.}
Suppose
Recall that { C i n 1 , ⋯ , C i n N } {\displaystyle \left\{C_{in}^{1},\cdots ,C_{in}^{N}\right\}} is a Wozencraft ensemble . Due to "Wonzencraft ensemble theorem", there are at least ( 1 − ε ) N {\displaystyle (1-\varepsilon )N} linear codes C i n i {\displaystyle C_{in}^{i}} that have distance H q − 1 ( 1 2 − ε ) ⋅ 2 k . {\displaystyle H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right)\cdot 2k.} So if for some 1 ⩽ i ⩽ N , c i 1 ≠ c i 2 {\displaystyle 1\leqslant i\leqslant N,c_{i}^{1}\neq c_{i}^{2}} and the code C i n i {\displaystyle C_{in}^{i}} has distance ⩾ H q − 1 ( 1 2 − ε ) ⋅ 2 k , {\displaystyle \geqslant H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right)\cdot 2k,} then
Further, if we have T {\displaystyle T} numbers 1 ⩽ i ⩽ N {\displaystyle 1\leqslant i\leqslant N} such that c i 1 ≠ c i 2 {\displaystyle c_{i}^{1}\neq c_{i}^{2}} and the code C i n i {\displaystyle C_{in}^{i}} has distance ⩾ H q − 1 ( 1 2 − ε ) ⋅ 2 k , {\displaystyle \geqslant H_{q}^{-1}({\tfrac {1}{2}}-\varepsilon )\cdot 2k,} then
So now the final task is to find a lower bound for T {\displaystyle T} . Define:
Then T {\displaystyle T} is the number of linear codes C i n i , i ∈ S {\displaystyle C_{in}^{i},i\in S} having the distance H q − 1 ( 1 2 − ε ) ⋅ 2 k . {\displaystyle H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right)\cdot 2k.}
Now we want to estimate | S | . {\displaystyle |S|.} Obviously | S | = Δ ( C o u t ( m 1 ) , C o u t ( m 2 ) ) ⩾ ( 1 − R ) N {\displaystyle |S|=\Delta (C_{out}(m_{1}),C_{out}(m_{2}))\geqslant (1-R)N} .
Due to the Wozencraft Ensemble Theorem , there are at most ε N {\displaystyle \varepsilon N} linear codes having distance less than H q − 1 ( 1 2 − ε ) ⋅ 2 k , {\displaystyle H_{q}^{-1}({\tfrac {1}{2}}-\varepsilon )\cdot 2k,} so
Finally, we have
This is true for any arbitrary m 1 ≠ m 2 {\displaystyle m_{1}\neq m_{2}} . So C ∗ {\displaystyle C^{*}} has the relative distance at least ( 1 − R − ε ) H q − 1 ( 1 2 − ε ) , {\displaystyle (1-R-\varepsilon )H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right),} which completes the proof.
We want to consider the "strongly explicit code". So the question is what the "strongly explicit code" is. Loosely speaking, for linear code, the "explicit" property is related to the complexity of constructing its generator matrix G.
That in effect means that we can compute the matrix in logarithmic space without using the brute force algorithm to verify that a code has a given satisfied distance.
For the other codes that are not linear, we can consider the complexity of the encoding algorithm.
So by far, we can see that the Wonzencraft ensemble and Reed-Solomon codes are strongly explicit. Therefore, we have the following result:
Corollary: The concatenated code C ∗ {\displaystyle C^{*}} is an asymptotically good code(that is, rate R {\displaystyle R} > 0 and relative distance δ {\displaystyle \delta } > 0 for small q) and has a strongly explicit construction.
The following slightly different code is referred to as the Justesen code in MacWilliams/MacWilliams. It is the particular case of the above-considered
Justesen code for a very particular Wonzencraft ensemble:
Let R be a Reed-Solomon code of length N = 2 m − 1, rank K and minimum weight N − K + 1.
The symbols of R are elements of F = GF(2 m ) and the codewords are obtained by taking every polynomial ƒ over F of degree less than K and listing the values of ƒ on the non-zero elements of F in some predetermined order.
Let α be a primitive element of F . For a codeword a = ( a 1 , ..., a N ) from R , let b be the vector of length 2 N over F given by
and let c be the vector of length 2 N m obtained from b by expressing each element of F as a binary vector of length m . The Justesen code is the linear code containing all such c .
The parameters of this code are length 2 m N , dimension m K and minimum distance at least
where ℓ {\displaystyle \ell } is the greatest integer satisfying ∑ i = 1 ℓ ( 2 m i ) ≤ N − K + 1 {\displaystyle \sum _{i=1}^{\ell }{\binom {2m}{i}}\leq N-K+1} . (See MacWilliams/MacWilliams for a proof.) | https://en.wikipedia.org/wiki/Justesen_code |
The Justice Department ( JD ) was founded in the United Kingdom by animal liberation activists who declared they were willing to use a diversity of tactics up to and including violence against their opponents. Calling for " abusers to have but a taste of the fear and anguish their victims suffer on a daily basis" , activists distanced themselves from the Animal Liberation Front 's guidelines of nonviolent resistance . [ 1 ] [ 2 ]
The first recorded action took place during Christmas 1993, when pipe bombs in poster tubes were sent to Shamrock Farm , a supplier of primates for animal experimentation . The group had formed the same leaderless-resistance model as the ALF, which consists of small, autonomous, covert cells acting independently. [ 3 ] Members of the Justice Department are thought to include both supporters of the far-right and the far-left who engage in a common interest, which is animal rights. [ 4 ]
The name has also been used in the United States with activists claiming hundreds of attacks in the UK against animal testing companies, their suppliers, animal researchers , hunters (including the Royal Family ), and even the British National Party HQ. [ 3 ] [ 4 ] [ 5 ] By sending explosive devices and razor blades in the post, and leaving incendiary devices on shelves, The Independent labeled the political violence "the most sustained and sophisticated bombing campaign in mainland Britain since the IRA was at its height." [ 6 ] with the FBI declaring them to be "the most dangerous animal activists in operation" .
The Animal Liberation Front achieved what other methods have not while adhering to nonviolence . A separate idea was established that decided animal abusers had been warned long enough. ... The time has come for abusers to have but a taste of the fear and anguish their victims suffer on a daily basis. [ 1 ] [ 5 ]
The group formed the same leaderless-resistance model as the ALF, consisting of small, autonomous, covert cells acting independently. A cell may consist of just one person. The name is used as a tag to claim responsibility for supporters of the Justice Department concept, rather than to denote an actually existing organization. The animal liberation movement in the 1990s believed there to be less than 30 individuals as part of the Department, operating in separate cells of five or fewer people; living normal lives, normal jobs and an uncommon stereotype of a squatter. [ citation needed ]
In The Independent newspaper it was claimed that the Justice Department is regarded as the "terrorist wing" of the Animal Liberation Front (ALF). Some ALF activists reject the association, telling the newspaper: "You cannot be in favour of animal rights and at the same time attack people because at the end of the day people are animals, too." [ citation needed ]
By 1995, security forces grew concerned over not just the scale of the campaign, but also the sophistication of activists. The technology used in the bomb making was compared to that of the IRA, with hoax bombs designed to frighten the public rather than harm, although sometimes capable of maiming or killing. At the time Deputy Assistant Commissioner John Howley, overall head of both the Special Branch and the anti-terrorist branch, claimed it was not terrorism because there was no clear motive to overthrow the government. [ 6 ]
The existence of activists calling themselves the Justice Department or Animal Rights Militia (ARM), another name used by violent activists, reflects a struggle within the radical animal rights movement in general, between those who believe violence is justified, and those who insist the movement should reject it in favour of nonviolent resistance . [ 7 ] Furthermore, criticism from the mainstream animal rights movement includes comparing animal rights and the struggles to abolish slavery and emancipate women , which the League Against Cruel Sports thinks is "stupid and naive" . [ 6 ]
While the ALF is a non-violent group, Robin Webb has noted that some people may simultaneously be involved in actions staged by the Justice Department, the ALF and the ARM, since: [ 8 ]
If someone wishes to act as the Animal Rights Militia or the Justice Department, simply put, the third policy of the ALF , to take all reasonable precautions not to endanger life, no longer applies.
Steven Best has coined the term "extensional self-defense" to describe actions carried out in defense of animals by human beings acting as "proxy agents." [ 9 ] He argues that, in carrying out acts of extensional self-defense, activists have the moral right to engage in acts of sabotage or even violence. [ 9 ] Extensional self-defense is justified, he writes, because animals are "so vulnerable and oppressed they cannot fight back to attack or kill their oppressors." [ 10 ] Best argues that the principle of extensional self-defense mirrors the penal code statues known as the " necessity defense ," which can be invoked when a defendant believes that the illegal act was necessary to avoid imminent and great harm. [ 10 ] [ 11 ] Best says that "extensional self defense" has been put into practice in some African countries, where hired armed soldiers occasionally use lethal force against poachers who would kill rhinos, elephants and other endangered animals. [ 12 ] In testimony to the Senate in 2005, Jerry Vlasak stated that he regarded violence against Huntingdon Life Sciences as an example of extensional self-defense. [ 13 ] [ 14 ]
The first recorded Justice Department action took place during Christmas 1993, when two-foot-long poster tubes with explosive devices were sent to Shamrock Farm , a supplier of primates for animal research; the action carried claims of HIV-infected needles. Eleven more devices were intercepted by Special Branch at sorting offices with one that was not recovered. It targeted the manager of GlaxoSmithKline in Hereford , who was also a member of the RSPCA 's animal experimentation advisory board and Institute of Animal Technicians council. He opened the package which exploded in his face. Days later the group targeted Boots in Cornwall , publicly stating that they had replaced products on their shelves with devices. Boots issued an alert to their eleven hundred stores after one customer bought one of the products and contacted the police who deactivated the device. [ 3 ]
There were at least 31 bomb attacks against hunts and their followers during 1994 and scores of others... Most of the devices are believed to have come from the Justice Department. [ 6 ]
Activists working as the Justice Department have sent out letter bombs and envelopes rigged with poisoned razor blades. [ 4 ] In 1994, a rat trap equipped with razor blades was sent to Prince Charles after he took his sons on their first foxhunt . Tom King, a former Defence Secretary , was sent an incendiary device, which failed to explode, after he defended foxhunting during a debate in parliament. Michael Howard , at the time Home Secretary, also received one.
Shortly after, the group set fire to two boats belonging to the owner of Garetmar kennels (formally known as Cottagepatch) in Hampshire and sent two videos disguised incendiary devices to the Boots store in Cambridge , which was intercepted, and another to the British National Party (BNP) HQ in South London ; injuring Alfred Waite. [ 3 ] : 503 Another round of devices by the now quite violent group were claimed to be increasingly sophisticated and random yet again injured staff, this time of ferry company Stena Sealink, which were attacked in Gloucestershire , Oxford , Edinburgh and Kent , in connection with the live exports trade. This resulted in ferry companies involved in live exports pulling out because of fear for their staff and their safety. [ 3 ] : 503–504 Bloodsports enthusiast and hunt master Nick Fawcett was also one of the main targets of the Justice Department receiving several JD packages, with police blowing two up outside his home. [ 6 ]
The Justice Department in April were then accused of sending four letter bombs from London to senior politicians William Waldegrave (the then Minister of Agriculture, Fisheries and Food ) and again to Tom King (a former Defence Secretary ), a fur warehouse in Glasgow and an animal testing company in Edinburgh. Mr Waldegrave was targeted at his family farm in Chewton Mendip , Somerset , but the device was spotted by a postman and dismantled by a bomb disposal team. This was due to his apparent lack of action on banning the live exports trade and veal crates , with booby-trapped razor blades sent to his home in January, threatening letters and protests from animal rights activists. The campaign was condemned by Compassion in World Farming , while Mr Waldegrave dismissing the actions as "stupidity". The other bombs were intercepted at Westminster , a postroom and at the fur company in a controlled explosion. [ 15 ]
Dear animal killing scum! Hope we sliced your finger wide open and that you now die from the rat poison we smeared on the razor blade. [ 5 ]
In January, the group claimed responsibility for sending envelopes with blades soaked in rat poison to 80 researchers, hunting guides, and others in the United States, and in British Columbia and Alberta , Canada. [ 5 ] David Barbarash , a Vancouver -based activist who became North American spokesman for the Animal Liberation Front, was charged in connection with the attacks, but the case against him was dropped. [ 3 ] Threats pursued in March, after the Department claimed sending out another 87 booby-trapped envelopes. [ 16 ] the letter said: "It is unfortunate such drastic actions must be taken but in war, people die," "And we haven't even started yet." . [ 17 ]
In August after a few years of inactivity, a US-based group sent razor blades and a picture of a bomb from New York City to Knox County Mink Farm, Ohio . Previously targeted by the ALF in 1996 when they released 8,000 from the premises, they warned the farm that they had a year to "get out of the bloody fur trade" and release all their mink, signed by the Justice Department Anti-Fur Task Force . [ 18 ]
By October the group had prepared 83 envelopes containing razor blades and a strongly worded warning, sent from Las Vegas , urging primate researchers in Oregon to end their work by Autumn 2000. They were warned; "If you do not heed our warning, your violence will be turned back on you." by the activists. No injuries were reported from the attacks, but the FBI swiftly classified them as the most dangerous animal activists in operation. The packages were received by researchers from UCSF , Stanford University , University of Washington , Tulane University and elsewhere. A special agent labelled the activity animal enterprise terrorism . [ 19 ]
A new round of threats was investigated by the FBI in November after The Justice Department of UCLA claimed they sent HIV-infected razors to UCLA neuroscientist , animal researcher and Speaking of Research member David Jentsch. He received razor blades and a threatening note law enforcement claim. The North American Animal Liberation Press Office posted an anonymous communiqué from the group, who claimed they carried out the action because Jentsch uses primates for government-funded testing of drug addiction. [ 20 ]
Since 2006, activists have claimed numerous acts of sabotage , vandalism, criminal damage and firebombing against UCLA faculty or property, on and off campus, including the Animal Liberation Brigade setting fire to his car in March 2009. According to the university, Jentsch studies methamphetamine addiction, tobacco dependence in teenagers, and the cognitive disabilities affecting schizophrenia patients, with much of his work funded by the National Institutes of Health . [ 21 ]
Relating to the video disguised devices that were sent to Stena Sealink, a Coventry man, Guerjeet Aujla, was arrested by the Anti Terrorist Squad and was classified as a Category A prisoner and Justice Department bomber after clues were found in his bedroom linking him to the devices. In the case, the judge believed that he was not responsible for the other attacks, only those to the ferry company, and that his guilty plea showed genuine remorse. He was sentenced to six years imprisonment, the lowest possible sentence the judge was able to pass concerning the attacks that caused harm to individuals. [ 3 ] : 504–505 | https://en.wikipedia.org/wiki/Justice_Department_(animal_rights) |
A consortium of researchers in Bangladesh successfully completed draft genome sequencing for the jute plant .
The consortium consisted of Dhaka University , Bangladesh Jute Research Institute , and software company DataSoft Systems Bangladesh Ltd. [ 1 ] It worked in collaboration with Centre for Chemical Biology, University of Science Malaysia , and University of Hawaii at Manoa .
On June 16, 2010, Bangladeshi Prime Minister Sheikh Hasina disclosed in the parliament that Bangladeshi researchers had successfully completed the draft genome sequencing, which was anticipated to contribute to improvements in jute fiber production. [ 2 ]
It all began in February 2008, when Maqsudul Alam approached Professor Ahmad Shamsul Islam , Coordinator of GNOBB (Global Network of Bangladeshi Biotechnologists), regarding the possibility of sequencing the jute genome. The Bangladeshi scientific community, which was already exploring the idea of sequencing the jute genome, responded positively to this offer, initiating the process.
The endeavor started with many long conference calls between Dr. Alam and plant molecular biologists , Professors Haseena Khan and Zeba Islam Seraj of the Department of Biochemistry and Molecular Biology, University of Dhaka . They established connections with the University of Hawaii and the University of Science Malaysia for technical support, and prepared a project proposal to secure funding from various institutions.
Initially, there were many assurances, but the reality proved different. In the early stages, the Genome Research Center USA and the University of Science Malaysia provided some technical support to collect research data on jute from around the world. As the volume of data grew, a supercomputer became necessary for analysis. There was still a pressing need for funding to support field research.
The "Swapnajatra" team became frustrated due to the lack of proper support, and it became difficult to keep the team members engaged. In 2009, The Daily Prothom Alo published an article about the research that changed everything. Agriculture Minister Matia Chowdhury introduced Dr. Maqsudul Alam to Prime Minister Sheikh Hasina and assured him of further support. [ 3 ] Thus, the team "Swapnajatra" regained their confidence and continued their work.
Genomic DNA (gDNA) from Tossa Jute ( Corchorus olitorius O-4) was used for high-throughput Next Generation Sequencing (NGS) platforms, including 454 GS FLX, Illumina/Solexa, and SOLiD. More than 50X coverage (over 100 billions of A, C, G, and Ts) of Jute genome-sequencing data were used for the draft assembly. Several open-source and commercial genome assembly and annotation pipelines were used to assemble and analyze the raw data. To validate the draft genome, transcriptome analysis was also carried out. For data analysis, different computational resources, ranging from a high-performance Cluster Server to Dell servers to Silicon Graphics SGI Altix-350 and 450, were used. [ 4 ] | https://en.wikipedia.org/wiki/Jute_genome |
A juvenile is an individual organism (especially an animal ) that has not yet reached its adult form, sexual maturity or size. Juveniles can look very different from the adult form, particularly in colour, and may not fill the same niche as the adult form. [ 1 ] In many organisms the juvenile has a different name from the adult (see List of animal names ).
Some organisms reach sexual maturity in a short metamorphosis , such as ecdysis in many insects and some other arthropods . For others, the transition from juvenile to fully mature is a more prolonged process— puberty in humans and other species (like higher primates and whales ), for example. In such cases, juveniles during this transformation are sometimes called subadults .
Many invertebrates cease development upon reaching adulthood. The stages of such invertebrates are larvae or nymphs .
In vertebrates and some invertebrates (e.g. spiders ), larval forms (e.g. tadpoles ) are usually considered a development stage of their own, and "juvenile" refers to a post-larval stage that is not fully grown and not sexually mature. In amniotes , the embryo represents the larval stage. Here, a "juvenile" is an individual in the time between hatching/birth/germination and reaching maturity.
This developmental biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Juvenile_(organism) |
Jyā , koṭi-jyā and utkrama-jyā are three trigonometric functions introduced by Indian mathematicians and astronomers. The earliest known Indian treatise containing references to these functions is Surya Siddhanta . [ 1 ] These are functions of arcs of circles and not functions of angles. Jyā and koti-jyā are closely related to the modern trigonometric functions of sine and cosine . In fact, the origins of the modern terms of "sine" and "cosine" have been traced back to the Sanskrit words jyā and koti-jyā. [ 1 ]
Let 'arc AB' denote an arc whose two extremities are A and B of a circle with center 'O'. If a perpendicular BM is dropped from B to OA, then:
If the radius of the circle is R and the length of arc AB is s , the angle subtended by arc AB at O measured in radians is θ = s / R . The three Indian functions are related to modern trigonometric functions as follows:
An arc of a circle is like a bow and so is called a dhanu or chāpa which in Sanskrit means "a bow".
The straight line joining the two extremities of an arc of a circle is like the string of a bow and this line is a chord of the circle. This chord is called a jyā which in Sanskrit means "a bow-string", presumably translating Hipparchus 's χορδή with the same meaning [ citation needed ] .
The word jīvá is also used as a synonym for jyā in geometrical literature. [ 2 ] At some point, Indian astronomers and mathematicians realised that computations would be more convenient if one used the halves of the chords instead of the full chords and associated the half-chords with the halves of the arcs. [ 1 ] [ 3 ] The half-chords were called ardha-jyā s or jyā-ardha s. These terms were again shortened to jyā by omitting the qualifier ardha which meant "half of".
The Sanskrit word koṭi has the meaning of "point, cusp", and specifically "the curved end of a bow ".
In trigonometry, it came to denote "the complement of an arc to 90°". Thus koṭi-jyā is "the jyā of the complementary arc". In Indian treatises, especially in commentaries, koṭi-jyā is often abbreviated as kojyā . The term koṭi also denotes "the side of a right angled triangle". Thus koṭi-jyā could also mean the other cathetus of a right triangle, the first cathetus being the jyā . [ clarification needed ] [ 1 ]
Utkrama means "inverted", thus utkrama-jyā means "inverted chord".
The tabular values of utkrama-jyā are derived from the tabular values of jyā by subtracting the elements from the radius in the reversed order. [ clarification needed ] This is really [ clarification needed ] the arrow between the bow and the bow-string and hence it has also been called bāṇa , iṣu or śara all meaning "arrow". [ 1 ]
An arc of a circle which subtends an angle of 90° at the center is called a vritta-pāda (a quadrat of a circle). Each zodiacal sign defines an arc of 30° and three consecutive zodiacal signs defines a vritta-pāda . The jyā of a vritta-pāda is the radius of the circle. The Indian astronomers coined the term tri-jyā to denote the radius of the base circle, the term tri-jyā being indicative of "the jyā of three signs". The radius is also called vyāsārdha , viṣkambhārdha , vistarārdha , etc., all meaning "semi-diameter". [ 1 ]
According to one convention, the functions jyā and koti-jyā are respectively denoted by "Rsin" and "Rcos" treated as single words. [ 1 ] Others denote jyā and koti-jyā respectively by "Sin" and "Cos" (the first letters being capital letters in contradistinction to the first letters being small letters in ordinary sine and cosine functions). [ 3 ]
The origins of the modern term sine have been traced to the Sanskrit word jyā , [ 4 ] [ 5 ] or more specifically to its synonym jīvá .
This term was adopted in medieval Islamic mathematics , transliterated in Arabic as jība ( جيب ). Since Arabic is written without short vowels – and as a borrowing the long vowel is here denoted with yāʾ – this was interpreted as the homograph jaib , jayb ( جيب ), which means "bosom". The text's 12th-century Latin translator used the Latin equivalent for "bosom", sinus . [ 6 ] When jyā became sinus , it has been suggested that by analogy kojyā became co-sinus . However, in early medieval texts, the cosine is called the complementi sinus "sine of the complement", suggesting the similarity to kojyā is coincidental. [ 7 ] | https://en.wikipedia.org/wiki/Jyā,_koti-jyā_and_utkrama-jyā |
Ján Mináč (born 15 June 1953) is a Slovak-Canadian mathematician who is a professor of mathematics at The University of Western Ontario . His research interests include Galois groups , Galois cohomology , quadratic forms , and nonlinear dynamics .
Mináč received his bachelor's degree and his master's level RNDr. degree from Comenius University , Czechoslovakia in 1976 and 1977 respectively. He then earned his Ph.D. in 1986 from Queen’s University in Canada under the supervision of Paulo Ribenboim . The title of his thesis is "Galois Groups, Order Spaces, and Valuations". [ 1 ]
His brother Matej Mináč is a film director.
Mináč was a member of Mathematical Sciences Research Institute at Berkeley from 1986 to 1987 and then an NSF Postdoctoral Fellow at the University of California at Berkeley from 1987 to 1989. Afterward, he joined the University of Western Ontario as an assistant professor in 1989. He became an associate professor in 1991 and a full professor in 2003. [ 2 ]
Mináč and Nguyễn Duy Tân formulated the Mináč-Tân conjectures on the vanishing of Massey products over fields and the kernel unipotent conjecture. [ 3 ] [ 4 ] [ 5 ] He has also worked on Galois theory and quadratic forms, [ 6 ] Galois Demushkin groups, [ 7 ] [ 8 ] mild pro-2-groups , [ 9 ] Galois modules , [ 10 ] small quotients of Absolute Galois groups , [ 11 ] [ 12 ] [ 13 ] ghosts in group cohomology , [ 14 ] Koszulity properties of Galois cohomology, [ 15 ] [ 16 ] and Zassenhaus filtrations. [ 17 ] [ 18 ] [ 19 ]
Mináč has also worked on non-linear dynamics in networks and its applications to computational neuroscience. [ 20 ]
Mináč received the Distinguished Research Professor Award at Western University during the years 2004-2005 and 2020-2021. [ 21 ] [ 22 ] In 2019, he became a Fellow of the Canadian Mathematical Society . [ 23 ] During the year 2022-2023, he was a fellow at the Western Academy for Advanced Research. [ 24 ] In 2013 he received an Excellence in Teaching Award from the Canadian Mathematical Society. [ 25 ] Mináč also received multiple teaching awards at the University of Western Ontario. | https://en.wikipedia.org/wiki/Ján_Mináč |
János Körner is a Hungarian mathematician who works on information theory and combinatorics . [ 1 ]
Körner studied Mathematics at the Eötvös Loránd University in Budapest with a degree in 1970 [ 2 ] and was then at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences until 1992. From 1981 to 1983 he was at the Bell Laboratories and in 1987–88 at Télécom Paris (ENST) in Paris. [ 2 ] He has been a professor at the Sapienza University of Rome since 1993. [ 1 ]
Over his career, he frequently collaborated with fellow information theorists such as Rudolf Ahlswede , Katalin Marton , and Imre Csiszár . Together with Rudolf Ahlswede and Peter Gács he proved the blowing-up lemma. [ 3 ] Besides information theory, he also works on extremal graph theory .
In 2014 he received the Claude E. Shannon Award . [ 2 ] He served as Associated editor of the IEEE Transactions on Information Theory on multiple occasions. He is a member of the Hungarian Academy of Sciences. [ 1 ] | https://en.wikipedia.org/wiki/János_Körner |
Józef Maria Hoene-Wroński ( / ˈ h oʊ n ə ˈ v r ɒ n s k i / ; Polish: [ˈjuzɛf ˈxɛnɛ ˈvrɔj̃skʲi] ; French : Josef Hoëné-Wronski [ʒozɛf ɔɛne vʁɔ̃ski] ; 23 August 1776 – 9 August 1853) was a Polish messianist philosopher , mathematician , physicist , inventor , lawyer , occultist [ 1 ] and economist .
In mathematics, he is known for introducing a novel series expansion for a function in response to Joseph Louis Lagrange 's use of infinite series. The coefficients in Wroński's new series form the Wronskian , a determinant Thomas Muir named in 1882. As an inventor, he is credited with designing some of the first caterpillar vehicles . [ 2 ]
He was born as Hoëné in 1776 but changed his name in 1815 to Józef Wroński. [ 3 ] Later in life he changed his name to Józef Maria Hoene-Wroński, [ 3 ] without using his family's original French spelling Hoëné. At no point in his life, neither in Polish or French, was he known as Hoëné-Wroński; nor was the common French transliteration, Josef Hoëné-Wronski, ever his official name in his native Poland (though it might have served as his chosen French nom de plume on some work). [ citation needed ]
His father, Antoni Höhne ( pl , de ), was the municipal architect of Poznań . Antoni originally came from the small Bohemian village of Leukersdorf (present-day Čermná which is now a part of Libouchec ). In later life, he settled in western Poland marrying Elżbieta Pernicka in Wolsztyn in 1773. In the same place and a few years later on, in 1776, their son Józef Maria was born. Józef was educated in Poznań and Warsaw . In 1794 he served in Poland's Kościuszko Uprising as a second lieutenant of artillery, was taken prisoner, and remained until 1797 in the Russian Army. After resigning in the rank of lieutenant colonel in 1798, he studied in the Holy Roman Empire until 1800, when he enlisted in the Polish Legion at Marseille . There he began his scientific and scholarly work and conceived the idea of a great philosophical system. Ten years later he moved to Paris where he would spend most of his life working unremittingly to the last in the most difficult material circumstances.
He wrote exclusively in French , in the desire that his ideas, of whose immortality he was convinced, be accessible to all; he worked, he said, "through France for Poland." He published over a hundred works, and left many more in manuscript; at 75 years of age and nearing death, he exclaimed: "God Almighty, there's still so much more I wanted to say!"
In science, Hoene-Wroński set himself an extraordinary task: the complete reform of philosophy as well as that of mathematics, astronomy and technology. He elaborated not only a system of philosophy, but also applications to politics, history, economics, law, psychology, music and pedagogy . It was his aspiration to reform human knowledge in an "absolute, that is, ultimate" manner.
In 1803, Wroński joined the Marseille Observatory, and began developing an enormously complex theory of the structure and origin of the universe . During this period, he took up a correspondence with nearly all of the major scientists and mathematicians of his day, and was well respected at the observatory. In 1803 Wroński "experienced a mystical illumination, which he regarded as the discovery of the Absolute." [ 4 ]
In 1810, he published the results of his scientific research in a massive tome, which he advocated as a new foundation for all of science and mathematics. His theories were strongly Pythagorean , holding numbers and their properties to be the fundamental underpinning of essentially everything in the universe. His claims were met with little acceptance, and his research and theories were generally dismissed as grandiose rubbish. His earlier correspondence with major figures meant that his writings garnered more attention than a typical crackpot theory , even earning a review from the great mathematician Joseph Louis Lagrange (which turned out to be categorically unfavorable). [ 5 ] In the ensuing controversy, he was forced to leave the observatory.
He immediately turned his focus towards applying philosophy to mathematics (his critics believed that this meant dispensing with mathematical rigor in favor of generalities). In 1812, he published a paper purporting to show that every equation has an algebraic solution, directly contradicting results which had been recently published by Paolo Ruffini ; Ruffini turned out to be correct.
He later turned his attention to disparate and largely unsuccessful pursuits such as a fantastical design for caterpillar -like vehicles which he intended to replace railroad transportation, but did not manage to persuade anyone to give the design serious attention. In 1819, he travelled to England in an attempt to obtain financial backing from the Board of Longitude to build a device to determine longitude at sea. After initial difficulties, he was given an opportunity to address the Board, but his pretentious address, On the Longitude , contained much philosophizing and generalities, but no concrete plans for a working device, and thus failed to gain any support from the Board. [ 6 ] He remained for several years in England and, in 1821, published an introductory text on mathematics in London , which moderately improved his financial situation.
In 1822, he returned to France, and again took up a combination of mathematics and far-fetched ideas, despite being in poverty and scorned by intellectual society. Along with his continuing Pythagorean obsession, he spent much time working on several notoriously futile endeavors, including attempts to build a perpetual motion machine , to square the circle and to build a machine to predict the future (which he dubbed the prognometre ).
In 1852, shortly before his death, he did find a willing audience for his ideas: the occultist Eliphas Levi who met Wroński and was greatly impressed and "attracted by his religious and scientific utopianism." Wroński was "a powerful catalyst" for Levi's occultism. [ 4 ]
Wroński died in 1853 in Neuilly-sur-Seine , France, on the outskirts of Paris.
During his lifetime, nearly all his work was dismissed as nonsense. However, some of it came to be regarded in a more favourable light in later years. Although most of his inflated claims were groundless, his mathematical work contains flashes of deep insight and many important intermediary results, the most significant of which was his work on series . He had strongly criticized Lagrange for his use of infinite series, introducing instead a novel series expansion for a function. His criticisms of Lagrange were for the most part unfounded but the coefficients in Wroński's new series proved important after his death, forming a determinant now known as the Wronskian (the name which Thomas Muir had given them in 1882).
The level of Wroński's scientific and scholarly accomplishments and the amplitude of his objectives placed Wroński in the first rank of European metaphysicians in the early 19th century. But the abstract formalism and obscurity of his thought, the difficulty of his language, his boundless self-assurance and his uncompromising judgments of others alienated him from most of the scientific community. He was perhaps the most original of the Polish metaphysicians, but others were more representative of the Polish outlook.
Books
Letters | https://en.wikipedia.org/wiki/Józef_Maria_Hoene-Wroński |
Baron Jöns Jacob Berzelius ( Swedish: [jœns ˈjɑ̌ːkɔb bæˈʂěːlɪɵs] ; [ 1 ] 20 August 1779 – 7 August 1848) was a Swedish chemist. Berzelius is considered, along with Robert Boyle , John Dalton , and Antoine Lavoisier , to be one of the founders of modern chemistry . [ 2 ] Berzelius became a member of the Royal Swedish Academy of Sciences in 1808 and served from 1818 as its principal functionary. He is known in Sweden as the "Father of Swedish Chemistry". During his lifetime he did not customarily use his first given name, and was universally known simply as Jacob Berzelius. [ 3 ]
Although Berzelius began his career as a physician , his enduring contributions were in the fields of electrochemistry , chemical bonding and stoichiometry . In particular, he is noted for his determination of atomic weights and his experiments that led to a more complete understanding of the principles of stoichiometry, which is the branch of chemistry pertaining to the quantitative relationships between elements in chemical compounds and chemical reactions and that these occur in definite proportions. This understanding came to be known as the "Law of Constant Proportions" . [ 4 ]
Berzelius was a strict empiricist , expecting that any new theory must be consistent with the sum of contemporary chemical knowledge. He developed improved methods of chemical analysis, which were required to develop the basic data in support of his work on stoichiometry. He investigated isomerism , allotropy , and catalysis , phenomena that owe their names to him. [ 5 ] Berzelius was among the first to articulate the differences between inorganic compounds and organic compounds . [ 6 ] [ 7 ] Among the many minerals and elements he studied, he is credited with discovering cerium and selenium , and with being the first to isolate silicon and thorium . Following on his interest in mineralogy , Berzelius synthesized and chemically characterized new compounds of these and other elements.
Berzelius demonstrated the use of an electrochemical cell to decompose certain chemical compounds into pairs of electrically opposite constituents. From this research, he articulated a theory that came to be known as electrochemical dualism , contending that chemical compounds are oxide salts, bonded together by electrostatic interactions . This theory, while useful in some contexts, came to be seen as insufficient. [ 4 ] Berzelius's work with atomic weights and his theory of electrochemical dualism led to his development of a modern system of chemical formula notation that showed the composition of any compound both qualitatively and quantitatively. His system abbreviated the Latin names of the elements with one or two letters and applied superscripts to designate the number of atoms of each element present in the compound. Later, chemists changed to use of subscripts rather than superscripts. [ 4 ]
Berzelius was born in the parish of Väversunda in Östergötland in Sweden. His father Samuel Berzelius was a school teacher in the nearby city of Linköping , and his mother Elizabeth Dorothea Sjösteen was a homemaker. [ 8 ] His parents were both from families of church pastors. Berzelius lost both his parents at an early age. His father died in 1779, after which his mother married a pastor named Anders Eckmarck, who gave Berzelius a basic education including knowledge of the natural world . Following the death of his mother in 1787, relatives in Linköping took care of him. There he attended the school today known as Katedralskolan . [ 9 ] As a teenager, he took a position as a tutor at a farm near his home, during which time he became interested in collecting flowers and insects and their classification . [ 10 ]
Berzelius later enrolled as a medical student at Uppsala University , from 1796 to 1801. Anders Gustaf Ekeberg , the discoverer of tantalum , taught him chemistry during this time. He worked as an apprentice in a pharmacy, during which time he also learned practical matters in the laboratory such as glassblowing. [ 10 ] On his own during his studies, he successfully repeated the experimentation conducted by Swedish chemist Carl William Scheele which led to Scheele's discovery of oxygen . [ 9 ] He also worked with a physician in the Medevi mineral springs. During this time, he conducted an analysis of the water from this source. Additionally as part of his studies, in 1800, Berzelius learned about Alessandro Volta 's electric pile , the first device that could provide a constant electric current (i.e., the first battery). He constructed a similar battery for himself, consisting of alternating disks of copper and zinc, and this was his initial work in the field of electrochemistry. [ 4 ] [ 10 ]
As thesis research in his medical studies, he examined the influence of galvanic current on several diseases. This line of experimentation produced no clear-cut evidence for such influence. [ 10 ] Berzelius graduated as a medical doctor in 1802. He worked as a physician near Stockholm until the chemist and mine-owner Wilhelm Hisinger recognized his abilities as an analytical chemist and provided him with a laboratory. [ 7 ]
In 1807, Berzelius was appointed professor in chemistry and pharmacy at the Karolinska Institute . [ 4 ] Between 1808 and 1836, Berzelius worked together with Anna Sundström , who acted as his assistant and was the first female chemist in Sweden. [ 11 ]
In 1808, he was elected a member of the Royal Swedish Academy of Sciences . At this time, the Academy had been stagnating for several years, since the era of romanticism in Sweden had led to less interest in the sciences. In 1818, Berzelius was elected the Academy's secretary and held the post until 1848. During Berzelius' tenure , he is credited with revitalising the Academy and bringing it into a second golden era (the first being the astronomer Pehr Wilhelm Wargentin 's period as secretary from 1749 to 1783). [ 12 ] He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1822. [ 13 ] In 1827, he became correspondent of the Royal Institute of the Netherlands, and in 1830 associate member. [ 14 ] In 1837, he was elected a member of the Swedish Academy , on chair number 5.
Berzelius was active in the temperance movement . Along with Bengt Franc-Sparre [ sv ] , August von Hartmansdorff [ sv ] , Anders Retzius , Samuel Owen , George Scott , and others, he was one of the founders of the Svenska nykterhetssällskapet (the Swedish Temperance Society) in 1837 and its first chairman. [ 15 ] Berzelius wrote the foreword to one of Carl af Ekenstam's [ sv ] works on the topic, of which 50,000 copies were printed. [ 16 ]
Through much of his life, Berzelius suffered various medical ailments. These included recurrent migraine headaches and then later on he suffered from gout . He also had episodes of depression . [ 10 ]
In 1818, Berzelius had a nervous breakdown , said to be due to the stress of his work. [ 9 ] The medical advice he received was to travel and take vacation. However, during this time, Berzelius traveled to France to work in the chemical laboratories of Claude Louis Berthollet . [ 10 ]
In 1835, at the age of 56, he married Elizabeth Poppius, the 24-year-old daughter of a Swedish cabinet minister. [ 10 ]
He died on 7 August 1848 at his home in Stockholm, where he had lived since 1806. [ 17 ] He is buried in the Solna Cemetery. [ 9 ]
Soon after arriving in Stockholm, Berzelius wrote a chemistry textbook for his medical students, Lärbok i Kemien , which was his first significant scientific publication. He had conducted experimentation, in preparation for writing this textbook, on the compositions of inorganic compounds, which was his earliest work on definite proportions. [ 4 ] In 1813–4, he submitted a lengthy essay (published in five separate articles) on the proportions of elements in compounds. The essay commenced with a general description, [ 18 ] [ 19 ] introduced his new symbolism, and examined all the known elements. [ 20 ] [ 21 ] The essay ended with a table of the "specific weights" (relative atomic masses) of the elements, where oxygen was set to 100, and a selection of compounds written in his new formalism. [ 22 ] [ 23 ] [ 24 ] This work provided evidence in favour of the atomic theory proposed by John Dalton : that inorganic chemical compounds are composed of atoms of different elements combined in whole number amounts . In discovering that atomic weights are not integer multiples of the atomic weight of hydrogen, Berzelius also disproved Prout's hypothesis that elements are built up from atoms of hydrogen. [ 25 ] : 682–683 Berzelius's last revised version of his atomic weight tables was first published in a German translation of his Textbook of Chemistry in 1826. [ 26 ]
In order to aid his experiments, he developed a system of chemical notation in which the elements composing any particular chemical compound were given simple written labels—such as O for oxygen, or Fe for iron —with their proportions in the chemical compound denoted by numbers. Berzelius thus invented the system of chemical notation still used today, the main difference being that instead of the subscript numbers used today (e.g., H 2 O or Fe 2 O 3 ), Berzelius used superscripts (H 2 O or Fe 2 O 3 ). [ 27 ]
Berzelius is credited with discovering the chemical elements cerium and selenium and with being the first to isolate silicon , thorium , titanium and zirconium . Berzelius discovered cerium in 1803 [ 28 ] and selenium in 1817. [ 29 ] Berzelius also discovered how to isolate silicon in 1824, [ 30 ] and thorium in 1824. [ 31 ] [ 32 ] Students working in Berzelius's laboratory also discovered lithium , lanthanum , and vanadium . [ 33 ]
Berzelius discovered amorphous silicon by repeating an experiment performed by Gay-Lussac and Thénard in which they reacted silicon tetrafluoride with potassium metal which produced very impure silicon. In a variation of this experiment Berzelius heated potassium fluorosilicate with potassium. It produced potassium silicide which he then stirred with water to produce relatively pure silicon powder. Berzelius recognized this powder as the new element of silicon, which he called silicium, [ 34 ] a name proposed earlier by Davy . [ 35 ]
Berzelius was the first to isolate zirconium in 1824, but pure zirconium was not produced until 1925, by Anton Eduard van Arkel and Jan Hendrik de Boer . [ 36 ]
Berzelius is credited with originating the chemical terms " catalysis ", [ 37 ] " polymer ," " isomer ," " protein " and " allotrope ," although his original definitions in some cases differ significantly from modern usage. [ 38 ] As an example, he coined the term "polymer" in 1833 to describe organic compounds which shared identical empirical formulas but which differed in overall molecular weight, the larger of the compounds being described as "polymers" of the smallest. [ 39 ] At this time the concept of chemical structure had not yet been developed so that he considered only the numbers of atoms of each element. In this way, he viewed for example glucose (C 6 H 12 O 6 ) as a polymer of formaldehyde (CH 2 O), even though we now know that glucose is not a polymer of the monomer formaldehyde. [ 40 ]
Berzelius was the first person to make the distinction between organic compounds (those containing carbon), and inorganic compounds. In particular, he advised Gerardus Johannes Mulder in his elemental analyses of organic compounds such as coffee , tea , and various proteins . The term protein itself was coined by Berzelius, in 1838, after Mulder observed that all proteins seemed to have the same empirical formula and came to the erroneous conclusion that they might be composed of a single type of very large molecule . The term is derived from the Greek, meaning "of the first rank", and Berzelius proposed the name because proteins were so fundamental to living organisms. [ 41 ]
In 1808, Berzelius discovered that lactic acid occurs in muscle tissue, not just in milk.
The term biliverdin was coined by Berzelius in 1840, although he preferred "bilifulvin" (yellow/red) over "bilirubin" (red). [ 42 ]
Berzelius stated in 1810 that living things work by some mysterious "vital force", [ 43 ] a hypothesis called vitalism . Vitalism had first been proposed by prior researchers, although Berzelius contended that compounds could be distinguished by whether they required any organisms in their synthesis ( organic compounds ) or whether they did not ( inorganic compounds ). However, in 1828, Friedrich Wöhler accidentally obtained urea , an organic compound, by heating ammonium cyanate . This showed that an organic compound such as urea could be prepared synthetically and not exclusively by living organisms. Berzelius corresponded with Wöhler on the urea synthesis findings. However, the notion of vitalism continued to persist, until further work on abiotic synthesis of organic compounds provided substantial evidence against vitalism. [ 44 ] [ 45 ]
Berzelius was a prolific correspondent with leading scientists of his time, such as Gerardus Johannes Mulder , Claude Louis Berthollet , Humphry Davy , Friedrich Wöhler , Eilhard Mitscherlich and Christian Friedrich Schönbein .
In 1812, Berzelius traveled to London, England, including Greenwich to meet with prominent British scientists of the time. These included Humphry Davy, chemist William Wollaston , physician-scientist Thomas Young , astronomer William Herschel , chemist Smithson Tennant , and inventor James Watt , among others. Berzelius also visited Davy's laboratory. After his visit to Davy's laboratory, Berzelius remarked, "A tidy laboratory is a sign of a lazy chemist." [ 38 ]
Humphry Davy in 1810 proposed that chlorine is an element. Berzelius rejected this claim because of his belief that all acids were based on oxygen. Since chlorine forms a strong acid (muriatic acid, modern HCl), chlorine must contain oxygen and thus cannot be an element. However, in 1812, Bernard Courtois proved that iodine is an element. Then in 1816 Joseph-Louis Gay-Lussac demonstrated that prussic acid (hydrogen cyanide) contains only hydrogen, carbon, and nitrogen, and no oxygen. These findings persuaded Berzelius that not all acids contain oxygen, and that Davy and Gay-Lussac were correct: chlorine and iodine are indeed elements.
In 1818 Berzelius was ennobled by King Carl XIV Johan . In 1835, he received the title of friherre . [ 46 ]
In 1820 he was elected a member of the American Philosophical Society . [ 47 ]
The Royal Society of London gave Berzelius the Copley Medal in 1836 with the citation "For his systematic application of the doctrine of definite proportions to the analysis of mineral bodies, as contained in his Nouveau Systeme de Mineralogie, and in other of his works." [ citation needed ]
In 1840, Berzelius was named Knight of the Order of Leopold . [ 48 ] In 1842, he received the honor Pour le Mérite for Sciences and Arts. [ 49 ]
The mineral berzelianite , a copper selenide , was discovered in 1850 and named after him by James Dwight Dana . [ 50 ] [ 51 ]
In 1852, Stockholm, Sweden, built a public park and statue , both to honor Berzelius. Berzeliusskolan , a school situated next to his alma mater , Katedralskolan, is named for him. In 1890, a fairly prominent street in Gothenburg was named Berzeliigatan (Berzelii street) in his honour.
In 1898, the Swedish Academy of Sciences opened the Berzelius Museum in honor of Berzelius. The holdings of the museum included many items from his laboratory. The museum was opened on the occasion of fiftieth anniversary of Berzelius's death. Invitees at the ceremony marking the occasion included scientific dignitaries from eleven European nations and the United States, many of whom gave formal addresses in honor of Berzelius. [ 52 ] The Berzelius Museum was later moved to the observatory that is part of the Swedish Academy of Sciences. [ 7 ]
In 1939 his portrait appeared on a series of postage stamps commemorating the bicentenary of the founding of the Swedish Academy of Sciences. [ 53 ] In addition to Sweden, Grenada likewise honored him. [ 10 ]
The Berzelius secret society at Yale University is named in his honor.
Berzeliustinden , a 1,211-metre (3,973 ft) mountain on Spitsbergen, is named in Berzelius' honor. | https://en.wikipedia.org/wiki/Jöns_Jacob_Berzelius |
In the mathematical theory of Kleinian groups , Jørgensen's inequality is an inequality involving the traces of elements of a Kleinian group , proved by Troels Jørgensen ( 1976 ). [ 1 ]
The inequality states that if A and B generate a non-elementary discrete subgroup of the SL 2 ( C ), then
The inequality gives a quantitative estimate of the discreteness of the group: many of the standard corollaries bound
elements of the group away from the identity. For instance, if A is parabolic ,
then
where ‖ ⋅ ‖ {\displaystyle \|\cdot \|} denotes the usual norm on SL 2 ( C ). [ 2 ]
Another consequence in the parabolic case is the existence of cusp neighborhoods in hyperbolic 3-manifolds : if G is a
Kleinian group and j is a parabolic element of G with fixed point w , then there is a horoball based at w which projects to a cusp neighborhood in the quotient space H 3 / G {\displaystyle \mathbb {H} ^{3}/G} . Jørgensen's inequality
is used to prove that every element of G which does not have a fixed point at w moves the horoball entirely
off itself and so does not affect the local geometry of the quotient at w ; intuitively, the geometry is entirely determined
by the parabolic element. [ 3 ] | https://en.wikipedia.org/wiki/Jørgensen's_inequality |
In physics and mathematics , the κ-Poincaré algebra , named after Henri Poincaré , is a deformation of the Poincaré algebra into a Hopf algebra . In the bicrossproduct basis, introduced by Majid-Ruegg [ 1 ] its commutation rules reads:
Where P μ {\displaystyle P_{\mu }} are the translation generators, R j {\displaystyle R_{j}} the rotations and N j {\displaystyle N_{j}} the boosts.
The coproducts are:
The antipodes and the counits :
The κ-Poincaré algebra is the dual Hopf algebra to the κ-Poincaré group , and can be interpreted as its “infinitesimal” version.
This algebra -related article is a stub . You can help Wikipedia by expanding it .
This mathematical physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K-Poincaré_algebra |
In physics and mathematics , the κ-Poincaré group , named after Henri Poincaré , is a quantum group , obtained by deformation of the Poincaré group into a Hopf algebra .
It is generated by the elements a μ {\displaystyle a^{\mu }} and Λ μ ν {\displaystyle {\Lambda ^{\mu }}_{\nu }} with the usual constraint:
where η μ ν {\displaystyle \eta ^{\mu \nu }} is the Minkowskian metric :
The commutation rules reads:
In the (1 + 1)-dimensional case the commutation rules between a μ {\displaystyle a^{\mu }} and Λ μ ν {\displaystyle {\Lambda ^{\mu }}_{\nu }} are particularly simple. The Lorentz generator in this case is:
and the commutation rules reads:
The coproducts are classical, and encode the group composition law:
Also the antipodes and the counits are classical, and represent the group inversion law and the map to the identity:
The κ-Poincaré group is the dual Hopf algebra to the K-Poincaré algebra , and can be interpreted as its “finite” version.
This algebra -related article is a stub . You can help Wikipedia by expanding it .
This mathematical physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K-Poincaré_group |
The K/U Ratio is the ratio of a slightly volatile element , potassium (K), to a highly refractory element, uranium (U). It is a useful way to measure the presence of volatile elements on planetary surfaces. The K/U ratio helps explain the evolution of the planetary system and the origin of Earth's Moon.
In planetary science , volatiles are the group of chemical elements and chemical compounds with low boiling points that are associated with a planet 's or a moon 's crust or atmosphere .
Very low boiling temperature examples include nitrogen , water , carbon dioxide , ammonia , hydrogen , methane and sulfur dioxide .
In contrast with volatiles, elements and compounds with high boiling points are known as refractory substances . [ 1 ]
On the basis of available data, which is sparse for Mars and very uncertain for Venus, the three inner planets then become progressively more depleted in K passing from Mars to Earth to Venus. [ 2 ]
Some elements like potassium, uranium, and thorium are naturally radioactive and give off gamma rays as they decay. Electromagnetic radiation from these isotopes can be detected by a Gamma-Ray Spectrometer (GRS) dropped toward the planetary surface or observed from orbit. An orbiting instrument can map the surface distribution of many elements for an entire planet.
Uncrewed spacecraft programs such as Venera and the Vega program have flown to Venus and sent back data allowing estimates of the K/U ratio of the surface rocks. [ 3 ]
The Lunar Prospector mission used a GRS to map the Earth's Moon.
To determine the elemental makeup of the Martian surface, the Mars Odyssey used a GRS and two neutron detectors.
These GRS readings can be compared to direct elemental measurements of chondrites meteorites, Earth, and Moon samples brought back from Apollo program missions, as well as to meteorites that are believed to have come from Mars. [ 4 ]
K and U move together during geochemical processes and have long-lived radioisotopes that emit gamma rays . [ 5 ] It is calculated as a ratio of one to the other on an equal mass basis which is often μ g r a m [ e l e m e n t ] / g r a m {\displaystyle \mu gram[element]/gram} .
This creates a compelling explanation for the evolution of the Solar System .
This result is consistent with an increasing temperature toward the Sun during its early protoplanetary nebula phase. [ 5 ]
The temperature at the early stage of Solar System formation was in excess of 1,000 K at the distance of Earth from the Sun, and as low as 200–100K at the distances of Jupiter and Saturn.
At the high temperatures for Earth, no volatiles would be in the solid state , and the dust would be made up of silicate and metal. [ 6 ]
The continental crust and lower mantle have average K/U values of about 12,000. mid-ocean ridge basalt (MORB) or upper mantle have more volatiles and have a K/U ratio of about 19,000. [ 2 ]
Volatile depletion explains why Earth's sodium (volatile) content is about 10% of its calcium (refractory) content, despite the similar abundance in chondrites. [ 5 ] [ 6 ]
The Moon stands out as being very depleted in volatiles. [ 7 ]
The Moon not only lacks water and atmospheric gases, but also lacks moderately volatile elements such as K, Na, and Cl. The Earth's K/U ratio is 12,000, while the Moon has a K/U ratio of only 2,000. [ 5 ] This difference suggests that the material that formed the Moon was subjected to temperatures considerably higher than the Earth.
The prevailing theory is that the Moon formed out of the debris left over from a collision between Earth and an astronomical body the size of Mars, approximately 4.5 billion years ago, about 20 to 100 million years after the Solar System coalesced. [ 8 ] This is called the Giant-impact hypothesis .
It is hypothesized that most of the outer silicates of the colliding body would be vaporized, whereas a metallic core would not. Hence, most of the collisional material sent into orbit would consist of silicates, leaving the coalescing Moon deficient in iron. The more volatile materials that were emitted during the collision probably would escape the Solar System, whereas silicates would tend to coalesce. [ 9 ]
The ratios of the Moon's volatile elements are not explained by the giant-impact hypothesis. If the giant-impact hypothesis is correct, they must be due to some other cause. [ 10 ]
Farther from the Sun, the temperature was low enough that volatile elements would precipitate as ices. [ 6 ] The two are separated by a snow line controlled by the temperature distribution around the Sun.
Formed farthest from the Sun, the carbonaceous chondrites have the highest K/U ratios. Ordinary chondrites which form closer in are only about 10% depleted in K relative to U.
The fine-grained matrix which fills spaces between the chondrules , however, appears to have formed at rather different temperatures in the various classes of chondrites. For this reason the volatile abundances of different classes of chondrites can vary. One particularly important class is the carbonaceous chondrites because of their high carbon content. In these meteorites, chondrules coexist with minerals that are only stable below 100 °C, so they contain materials that formed in both high- and low-temperature environments and were only later collected together. Further evidence for the primordial attributes of carbonaceous chondrites comes from the fact that they have compositions very similar to the nonvolatile element composition of the Sun. [ 5 ]
Mercury was surveyed by the MESSENGER mission with its Gamma-Ray Spectrometer. [ 11 ] [ 12 ] The K/U ratios for Mercury could range between 8,000 and 17,000 which would imply a volatile rich planet. However, metal/silicate partitioning data for K and U still needs additional experiments at the conditions of Mercury's core formation to understand this unusual high ratio. [ 13 ] | https://en.wikipedia.org/wiki/K-U_ratio |
Κ-casein , or kappa casein , is a mammalian milk protein involved in several important physiological processes. Chymosin (found in rennet ) splits K-casein into an insoluble peptide (para kappa-casein) and water-soluble glycomacropeptide (GMP). GMP is responsible for an increased efficiency of digestion, prevention of neonate hypersensitivity to ingested proteins, and inhibition of gastric pathogens. [ 1 ] The human gene for κ-casein is CSN3 .
Caseins are a family of phosphoproteins ( αS1 , αS2 , β , κ) that account for nearly 80% of bovine milk proteins [ 3 ] and that form soluble aggregates are known as "casein micelles" in which κ-casein molecules stabilize the structure. There are several models that account for the spatial conformation of casein in the micelles. [ 4 ] One of them proposes that the micellar nucleus is formed by several submicelles, the periphery consisting of microvillosities of κ-casein [ 5 ] [ 6 ] Another model suggests that the nucleus is formed by casein-interlinked fibrils. [ 7 ] Finally, the most recent model [ 8 ] proposes a double link among the caseins for gelling to take place. All 3 models consider micelles as colloidal particles formed by casein aggregates wrapped up in soluble κ-casein molecules.
Milk-clotting proteases act on the soluble portion, κ-casein, thus originating an unstable micellar state that
results in clot formation. [ 9 ]
Chymosin (EC 3.4.23.4) is an aspartic protease that specifically hydrolyzes the peptide bond in Phe105-Met106 of κ- casein and is considered to be the most efficient protease for the cheesemaking industry. [ 10 ] However, there are milk-clotting proteases able to cleave other peptide bonds in the κ-casein chain, such as the endothiapepsin produced by Endothia parasitica . [ 11 ] There are also several milk-clotting proteases that, being able to cleave the Phe105-Met106 bond in the κ-casein molecule, also cleave other peptide bonds in other caseins, such as those produced by Cynara cardunculus [ 6 ] [ 12 ] [ 13 ] or even bovine chymosin. [ 14 ] This allows the manufacture of different cheeses with a variety of rheological and organoleptic properties.
The milk-clotting process consists of three main phases: [ 15 ]
Each step follows a different kinetic pattern, the limiting step in milk-clotting being the degradation rate of κ-casein. The kinetic pattern of the second step of the milk-clotting process is influenced by the cooperative nature of micellar flocculation, [ 16 ] [ 13 ] whereas the rheological properties of the gel formed depend on the type of action of the proteases, the type of milk, and the patterns of casein proteolysis. [ 13 ] The overall process is influenced by several different factors, such as pH or temperature. [ 12 ] [ 9 ]
The conventional way of quantifying a given milk-clotting enzyme [ 17 ] employs milk as the substrate and determines the time elapsed before the appearance of milk clots. However, milk clotting may take place without the participation of enzymes because of variations in physicochemical factors, such as low pH or high temperature. [ 6 ] [ 3 ] [ 9 ] Consequently, this may lead to confusing and irreproducible results, particularly when the enzymes have low activity. At the same time, the classical method is not specific enough, in terms of setting the precise onset of milk gelation, such that the determination of the enzymatic units involved becomes difficult and unclear. Furthermore, although it has been reported that κ-casein hydrolysis follows typical Michaelis–Menten kinetics, [ 15 ] it is difficult to determine with the classic milk-clotting assay.
To overcome this, several alternative methods have been proposed, such as the determination of halo diameter in agar-gelified milk, [ 17 ] colorimetric measurement, [ 18 ] or determination of the rate of degradation of casein previously labeled with either a radioactive tracer [ 19 ] or a fluorochrome compound. [ 20 ] All these methods use casein as the substrate to quantify proteolytic or milk-clotting activities.
Κ-casein labeled with the fluorochrome fluorescein isothiocyanate ( FITC ) to yield the fluorescein thiocarbamoyl ( FTC ) derivative. This substrate is used to determinate the milk clotting activity of proteases. [ 21 ]
FTC-κ-casein method affords accurate and precise determinations of κ-caseinolytic degradation, the first step in the milk-clotting process. This method is the result of a modification to the one described by S.S. Twining (1984). The main modification was substituting the substrate previously used ( casein ) by κ-casein labeled with the fluorochrome fluorescein isothiocyanate (FITC) to yield the fluorescein thiocarbamoyl (FTC) derivative. This variation allows quantification of the κ-casein molecules degraded in a more precise and specific way, detecting only those enzymes able to degrade such molecules. The method described by Twining (1984), however, was designed to detect the proteolytic activity of a considerably larger variety of enzymes.
FTC-κ-casein allows the detection of different types of proteases at levels when no milk clotting is yet apparent, demonstrating its higher sensitivity over currently used assay procedures.
Therefore, the method may find application as an indicator during the purification or characterization of new
milk-clotting enzymes. | https://en.wikipedia.org/wiki/K-casein |
In geometry , a hyperrectangle (also called a box , hyperbox , k {\displaystyle k} -cell or orthotope [ 2 ] ), is the generalization of a rectangle (a plane figure ) and the rectangular cuboid (a solid figure ) to higher dimensions . A necessary and sufficient condition is that it is congruent to the Cartesian product of finite intervals . [ 3 ] This means that a k {\displaystyle k} -dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every k {\displaystyle k} -cell is compact . [ 4 ] [ 5 ]
If all of the edges are equal length, it is a hypercube . A hyperrectangle is a special case of a parallelotope .
For every integer i {\displaystyle i} from 1 {\displaystyle 1} to k {\displaystyle k} , let a i {\displaystyle a_{i}} and b i {\displaystyle b_{i}} be real numbers such that a i < b i {\displaystyle a_{i}<b_{i}} . The set of all points x = ( x 1 , … , x k ) {\displaystyle x=(x_{1},\dots ,x_{k})} in R k {\displaystyle \mathbb {R} ^{k}} whose coordinates satisfy the inequalities a i ≤ x i ≤ b i {\displaystyle a_{i}\leq x_{i}\leq b_{i}} is a k {\displaystyle k} -cell . [ 6 ]
A k {\displaystyle k} -cell of dimension k ≤ 3 {\displaystyle k\leq 3} is especially simple. For example, a 1-cell is simply the interval [ a , b ] {\displaystyle [a,b]} with a < b {\displaystyle a<b} . A 2-cell is the rectangle formed by the Cartesian product of two closed intervals, and a 3-cell is a rectangular solid.
The sides and edges of a k {\displaystyle k} -cell need not be equal in (Euclidean) length; although the unit cube (which has boundaries of equal Euclidean length) is a 3-cell, the set of all 3-cells with equal-length edges is a strict subset of the set of all 3-cells.
A four-dimensional orthotope is likely a hypercuboid. [ 7 ]
The special case of an n -dimensional orthotope where all edges have equal length is the n - cube or hypercube. [ 2 ]
By analogy, the term "hyperrectangle" can refer to Cartesian products of orthogonal intervals of other kinds, such as ranges of keys in database theory or ranges of integers , rather than real numbers . [ 8 ]
The dual polytope of an n -orthotope has been variously called a rectangular n - orthoplex , rhombic n - fusil , or n - lozenge . It is constructed by 2 n points located in the center of the orthotope rectangular faces.
An n -fusil's Schläfli symbol can be represented by a sum of n orthogonal line segments: { } + { } + ... + { } or n { }.
A 1-fusil is a line segment . A 2-fusil is a rhombus . Its plane cross selections in all pairs of axes are rhombi . | https://en.wikipedia.org/wiki/K-cell_(mathematics) |
In X-ray absorption spectroscopy , the K-edge is a sudden increase in x-ray absorption occurring when the energy of the X-rays is just above the binding energy of the innermost electron shell of the atoms interacting with the photons. The term is based on X-ray notation , where the innermost electron shell is known as the K-shell. Physically, this sudden increase in attenuation is caused by the photoelectric absorption of the photons. For this interaction to occur, the photons must have more energy than the binding energy of the K-shell electrons (K-edge). A photon having an energy just above the binding energy of the electron is therefore more likely to be absorbed than a photon having an energy just below this binding energy or significantly above it. [ 1 ]
The energies near the K-edge are also objects of study, and provide other information.
The two radiocontrast agents iodine and barium have ideal K-shell binding energies for absorption of X-rays: 33.2 keV and 37.4 keV respectively, which is close to the mean energy of most diagnostic X-ray beams. Similar sudden increases in attenuation may also be found for other inner shells than the K shell; the general term for the phenomenon is absorption edge . [ 2 ]
Dual-energy computed tomography techniques take advantage of the increased attenuation of iodinated radiocontrast at lower tube energies to heighten the degree of contrast between iodinated radiocontrast and other high attenuation biological material present in the body such as blood and hemorrhage. [ 3 ]
Metal K-edge spectroscopy is a spectroscopic technique used to study the electronic structures of transition metal atoms and complexes . This method measures X-ray absorption caused by the excitation of a 1s electron to valence bound states localized on the metal, which creates a characteristic absorption peak called the K-edge. The K-edge can be divided into the pre-edge region (comprising the pre-edge and rising edge transitions) and the near-edge region (comprising the intense edge transition and ~150 eV above it).
The K-edge of an open shell transition metal ion displays a weak pre-edge 1s-to-valence-metal-d transition at a lower energy than the intense edge jump. This dipole-forbidden transition gains intensity through a quadrupole mechanism and/or through 4p mixing into the final state. The pre-edge contains information about ligand fields and oxidation state . Higher oxidation of the metal leads to greater stabilization of the 1s orbital with respect to the metal d orbitals, resulting in higher energy of the pre-edge. Bonding interactions with ligands also cause changes in the metal's effective nuclear charge (Z eff ), leading to changes in the energy of the pre-edge.
The intensity under the pre-edge transition depends on the geometry around the absorbing metal and can be correlated to the structural symmetry in the molecule. [ 4 ] Molecules with centrosymmetry have low pre-edge intensity, whereas the intensity increases as the molecule moves away from centrosymmetry. This change is due to the higher mixing of the 4p with the 3d orbitals as the molecule loses centrosymmetry.
A rising-edge follows the pre-edge, and may consist of several overlapping transitions that are hard to resolve. The energy position of the rising-edge contains information about the oxidation state of the metal.
In the case of copper complexes, the rising-edge consists of intense transitions, which provide information about bonding. For Cu I species, this transition is a distinct shoulder and arises from intense electric-dipole-allowed 1s→4p transitions. The normalized intensity and energy of the rising-edge transitions in these Cu I complexes can be used to distinguish between two-, three- and four-coordinate Cu I sites. [ 5 ] In the case of higher-oxidation-state copper atoms, the 1s→4p transition lies higher in energy, mixed in with the near-edge region. However, an intense transition in the rising-edge region is observed for Cu III and some Cu II complexes from a formally forbidden two electron 1s→4p+shakedown transition. This “shakedown” process arises from a 1s→4p transition that leads to relaxation of the excited state, followed by a ligand-to-metal charge transfer to the excited state.
This rising-edge transition can be fitted to a valence bond configuration (VBCI) model to obtain the composition of the ground state wavefunction and information on ground state covalency . The VBCI model describes the ground and excited state as a linear combination of the metal-based d-state and the ligand-based charge transfer state. The higher the contribution of the charge transfer state to the ground state, the higher is the ground state covalency indicating stronger metal-ligand bonding.
The near-edge region is difficult to quantitatively analyze because it describes transitions to continuum levels that are still under the influence of the core potential. This region is analogous to the EXAFS region and contains structural information. Extraction of metrical parameters from the edge region can be obtained by using the multiple-scattering code implemented in the MXAN software. [ 6 ]
Ligand K-edge spectroscopy is a spectroscopic technique used to study the electronic structures of metal-ligand complexes . [ 7 ] This method measures X-ray absorption caused by the excitation of ligand 1s electrons to unfilled p orbitals ( principal quantum number n ≤ 4 {\displaystyle n\leq 4} ) and continuum states, which creates a characteristic absorption feature called the K-edge.
Transitions at energies lower than the edge can occur, provided they lead to orbitals with some ligand p character; these features are called pre-edges. Pre-edge intensities ( D 0 ) are related to the amount of ligand (L) character in the unfilled orbital:
where ψ ∗ {\displaystyle \psi ^{*}} is the wavefunction of the unfilled orbital, r is the transition dipole operator, and α 2 {\displaystyle \alpha ^{2}} is the "covalency" or ligand character in the orbital. Since ψ ∗ = 1 − α 2 | M d ⟩ − α | L n p ⟩ {\displaystyle \psi ^{*}={\sqrt {1-\alpha ^{2}}}\vert M_{d}\rangle -\alpha \vert L_{np}\rangle } , the above expression relating intensity and quantum transition operators can be simplified to use experimental values:
where n is the number of absorbing ligand atoms, h is the number of holes, and I s is the transition dipole integral which can be determined experimentally. Therefore, by measuring the intensity of pre-edges, it is possible to experimentally determine the amount of ligand character in a molecular orbital. | https://en.wikipedia.org/wiki/K-edge |
The K-factor is the bending capacity of sheet metal , and by extension the forumulae used to calculate this. [ 1 ] [ 2 ] [ 3 ] Mathematically it is an engineering aspect of geometry . [ 4 ] Such is its intricacy
in precision sheet metal bending [ 5 ] (with press brakes in particular) that its proper application in engineering has been termed an art. [ 4 ] [ 5 ]
This metallurgy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K-factor_(metallurgy) |
In linear algebra , a k -frame is an ordered set of k linearly independent [ citation needed ] vectors in a vector space ; thus, k ≤ n , where n is the dimension of the space, and an n -frame is precisely an ordered basis .
If the vectors are orthogonal , or orthonormal , the frame is called an orthogonal frame , or orthonormal frame , respectively.
This mathematics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K-frame |
In computer science , a family of hash functions is said to be k -independent , k -wise independent or k -universal [ 1 ] if selecting a function at random from the family guarantees that the hash codes of any designated k keys are independent random variables (see precise mathematical definitions below). Such families allow good average case performance in randomized algorithms or data structures, even if the input data is chosen by an adversary. The trade-offs between the degree of independence and the efficiency of evaluating the hash function are well studied, and many k -independent families have been proposed.
The goal of hashing is usually to map keys from some large domain (universe) U {\displaystyle U} into a smaller range, such as m {\displaystyle m} bins (labelled [ m ] = { 0 , … , m − 1 } {\displaystyle [m]=\{0,\dots ,m-1\}} ). In the analysis of randomized algorithms and data structures, it is often desirable for the hash codes of various keys to "behave randomly". For instance, if the hash code of each key were an independent random choice in [ m ] {\displaystyle [m]} , the number of keys per bin could be analyzed using the Chernoff bound . A deterministic hash function cannot offer any such guarantee in an adversarial setting, as the adversary may choose the keys to be the precisely the preimage of a bin. Furthermore, a deterministic hash function does not allow for rehashing : sometimes the input data turns out to be bad for the hash function (e.g. there are too many collisions), so one would like to change the hash function.
The solution to these problems is to pick a function randomly from a large family of hash functions. The randomness in choosing the hash function can be used to guarantee some desired random behavior of the hash codes of any keys of interest. The first definition along these lines was universal hashing , which guarantees a low collision probability for any two designated keys. The concept of k {\displaystyle k} -independent hashing, introduced by Wegman and Carter in 1981, [ 2 ] strengthens the guarantees of random behavior to families of k {\displaystyle k} designated keys, and adds a guarantee on the uniform distribution of hash codes.
The strictest definition, introduced by Wegman and Carter [ 2 ] under the name "strongly universal k {\displaystyle _{k}} hash family", is the following. A family of hash functions H = { h : U → [ m ] } {\displaystyle H=\{h:U\to [m]\}} is k {\displaystyle k} -independent if for any k {\displaystyle k} distinct keys ( x 1 , … , x k ) ∈ U k {\displaystyle (x_{1},\dots ,x_{k})\in U^{k}} and any k {\displaystyle k} hash codes (not necessarily distinct) ( y 1 , … , y k ) ∈ [ m ] k {\displaystyle (y_{1},\dots ,y_{k})\in [m]^{k}} , we have:
This definition is equivalent to the following two conditions:
Often it is inconvenient to achieve the perfect joint probability of m − k {\displaystyle m^{-k}} due to rounding issues. Following, [ 3 ] one may define a ( μ , k ) {\displaystyle (\mu ,k)} -independent family to satisfy:
Observe that, even if μ {\displaystyle \mu } is close to 1, h ( x i ) {\displaystyle h(x_{i})} are no longer independent random variables, which is often a problem in the analysis of randomized algorithms. Therefore, a more common alternative to dealing with rounding issues is to prove that the hash family is close in statistical distance to a k {\displaystyle k} -independent family, which allows black-box use of the independence properties.
The original technique for constructing k -independent hash functions, given by Carter and Wegman, was to select a large prime number p , choose k random numbers modulo p , and use these numbers as the coefficients of a polynomial of degree k − 1 whose values modulo p are used as the value of the hash function. All polynomials of the given degree modulo p are equally likely, and any polynomial is uniquely determined by any k -tuple of argument-value pairs with distinct arguments, from which it follows that any k -tuple of distinct arguments is equally likely to be mapped to any k -tuple of hash values. [ 2 ]
In general the polynomial can be evaluated in any finite field .
Besides the fields modulo prime, a popular choice is the field of size 2 n {\displaystyle 2^{n}} , which supports fast finite field arithmetic on modern computers.
This was the approach taken by Daniel Lemire and Owen Kaser for CLHash. [ 4 ]
Tabulation hashing is a technique for mapping keys to hash values by partitioning each key into bytes , using each byte as the index into a table of random numbers (with a different table for each byte position), and combining the results of these table lookups by a bitwise exclusive or operation. Thus, it requires more randomness in its initialization than the polynomial method, but avoids possibly-slow multiplication operations. It is 3-independent but not 4-independent. [ 5 ] Variations of tabulation hashing can achieve higher degrees of independence by performing table lookups based on overlapping combinations of bits from the input key, or by applying simple tabulation hashing iteratively. [ 6 ] [ 7 ]
The notion of k -independence can be used to differentiate between different collision resolution in hashtables, according to the level of independence required to guarantee constant expected time per operation.
For instance, hash chaining takes constant expected time even with a 2-independent family of hash functions, because the expected time to perform a search for a given key is bounded by the expected number of collisions that key is involved in. By linearity of expectation, this expected number equals the sum, over all other keys in the hash table, of the probability that the given key and the other key collide. Because the terms of this sum only involve probabilistic events involving two keys, 2-independence is sufficient to ensure that this sum has the same value that it would for a truly random hash function. [ 2 ]
Double hashing is another method of hashing that requires a low degree of independence. It is a form of open addressing that uses two hash functions: one to determine the start of a probe sequence, and the other to determine the step size between positions in the probe sequence. As long as both of these are 2-independent, this method gives constant expected time per operation. [ 8 ]
On the other hand, linear probing , a simpler form of open addressing where the step size is always one can be guaranteed to work in constant expected time per operation with a 5-independent hash function, [ 9 ] and there exist 4-independent hash functions for which it takes logarithmic time per operation. [ 10 ]
For Cuckoo hashing the required k-independence is not known as of 2021.
In 2009 it was shown [ 11 ] that O ( log n ) {\displaystyle O(\log n)} -independence suffices, and at least 6-independence is needed.
Another approach is to use Tabulation hashing , which is not 6-independent, but was shown in 2012 [ 12 ] to have other properties sufficient for Cuckoo hashing.
A third approach from 2014 [ 13 ] is to slightly modify the cuckoo hashtable with a so-called stash, which makes it possible to use nothing more than 2-independent hash functions.
Kane , Nelson and David Woodruff improved the Flajolet–Martin algorithm for the Distinct Elements Problem in 2010. [ 14 ] To give an ε {\displaystyle \varepsilon } approximation to the correct answer, they need a log 1 / ε log log 1 / ε {\displaystyle {\tfrac {\log 1/\varepsilon }{\log \log 1/\varepsilon }}} -independent hash function.
The Count sketch algorithm for dimensionality reduction requires two hash functions, one 2-independent and one 4-independent .
The Karloff–Zwick algorithm for the MAX-3SAT problem can be implemented with 3-independent random variables.
The MinHash algorithm can be implemented using a log 1 ϵ {\displaystyle \log {\tfrac {1}{\epsilon }}} -independent hash function as was proven by Piotr Indyk in 1999 [ 15 ] | https://en.wikipedia.org/wiki/K-independent_hashing |
K-selectride is the organoboron compound with the formula KBH(C 4 H 9 ) 3 . It is the potassium salt of tri(sec-butyl)borohydride. The compound is sold as solution in THF. It is a strong reducing agent. Solutions are pyrophoric and highly reactive toward water and protic compounds. It is handled using air-free technique . It is produced by the reaction of tri(sec-butyl)borane with potassium hydride . The reagent is used to reduce ketones to alcohols. [ 1 ] | https://en.wikipedia.org/wiki/K-selectride |
The K-system is an audio level measuring technique proposed by mastering engineer Bob Katz in the paper "An integrated approach to Metering, Monitoring and Levelling". [ 1 ] It proposes a studio monitor calibration system and a set of meter ballistics to help engineers produce consistent sounding music while preserving appropriate dynamic range . [ 2 ]
This sound technology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K-system |
In mathematics , a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix-free Kolmogorov complexity is as low as possible, close to that of a computable set . Solovay proved in 1975 that a set can be K-trivial without being computable.
The Schnorr–Levin theorem says that random sets have a high initial segment complexity. Thus the K-trivials are far from random. This is why these sets are studied in the field of algorithmic randomness , which is a subfield of Computability theory and related to algorithmic information theory in computer science .
At the same time, K-trivial sets are close to computable. For instance, they are all superlow , i.e. sets whose Turing jump is computable from the Halting problem , and form a Turing ideal , i.e. class of sets closed under Turing join and closed downward under Turing reduction .
Let K be the prefix-free Kolmogorov Complexity , i.e. given a string x, K(x) outputs the least length of the input string under a prefix-free universal machine . Such a machine, intuitively, represents a universal programming language with the property that no valid program can be obtained as a proper extension of another valid program. For more background of K, see e.g. Chaitin's constant .
We say a set A of the natural numbers is K-trivial via a constant b ∈ N {\displaystyle \mathbb {N} } if
A set is K-trivial if it is K-trivial via some constant. [ 1 ] [ 2 ]
In the early days of the development of K-triviality, attention was paid to separation of K-trivial sets and computable sets .
Chaitin in his 1976 paper [ 3 ] mainly studied sets such that there exists b ∈ N {\displaystyle \mathbb {N} } with
where C denotes the plain Kolmogorov complexity . These sets are known as C-trivial sets. Chaitin showed they coincide with the computable sets. He also showed that the K-trivials are computable in the halting problem . This class of sets is commonly known as Δ 2 0 {\displaystyle \Delta _{2}^{0}} sets in arithmetical hierarchy .
Robert M. Solovay was the first to construct a noncomputable K-trivial set, while construction of a computably enumerable such A was attempted by Calude , Coles [ 4 ] and other unpublished constructions by Kummer of a K-trivial, and Muchnik junior of a low for K set.
In the context of computability theory, a cost function is a computable function
For a computable approximation ⟨ A s ⟩ {\displaystyle \langle A_{s}\rangle } of Δ 2 0 {\displaystyle \Delta _{2}^{0}} set A , such a function measures the cost c ( n , s ) of changing the approximation to A(n) at stage s. The first cost function construction was due to Kučera and Terwijn. [ 5 ] They built a computably enumerable set that is low for Martin-Löf-randomness but not computable. Their cost function was adaptive, in that the definition of the cost function depends on the computable approximation of the Δ 2 0 {\displaystyle \Delta _{2}^{0}} set being built.
A cost function construction of a K-trivial computably enumerable noncomputable set first appeared in Downey et al. [ 6 ]
We say a Δ 2 0 {\displaystyle \Delta _{2}^{0}} set A obeys a cost function c if there exists a computable approximation of A, ⟨ A s : s ∈ ω ⟩ {\displaystyle \langle A_{s}:s\in \omega \rangle } S = Σ x , s c ( x , s ) [ x < s ∧ x is the least s.t. A s − 1 ( x ) ≠ A s ( x ) ] < ∞ . {\displaystyle S=\Sigma _{x,s}c(x,s)[x<s\wedge {\text{x is the least s.t. }}A_{s-1}(x)\neq A_{s}(x)]<\infty .}
K-trivial sets are characterized [ 7 ] by obedience to the Standard cost function , defined by
and U s {\displaystyle \mathbb {U} _{s}} is the s -th step in a computable approximation of a fixed universal prefix-free machine U {\displaystyle \mathbb {U} } .
In fact the set can be made promptly simple . The idea is to meet the prompt simplicity requirements,
as well as to keep the costs low. We need the cost function to satisfy the limit condition
namely the supremum over stages of the cost for x goes to 0 as x increases. For instance, the standard cost function has this property. The construction essentially waits until the cost is low before putting numbers into A {\displaystyle A} to meet the promptly simple requirements. We define a computable enumeration ⟨ A s : s ∈ ω ⟩ {\displaystyle \langle A_{s}:s\in \omega \rangle } such that
A 0 = ∅ {\displaystyle A_{0}=\emptyset } . At stage s > 0 , for each e < s , if P S e {\displaystyle PS_{e}} has not been met yet and there exists x ≥ 2 e such that x ∈ W e , s ∖ W e , s − 1 {\displaystyle x\in W_{e,s}\backslash W_{e,s-1}} and c ( x , s ) ≤ 2 − e {\displaystyle c(x,s)\leq 2^{-e}} , then we put x into A s {\displaystyle A_{s}} and declare that P S e {\displaystyle PS_{e}} is met. End of construction.
To verify that the construction works, note first that A obeys the cost function since at most one number enters A for the sake of each requirement. The sum S is therefore at most
Secondly, each requirement is met: if W e {\displaystyle W_{e}} is infinite, by the fact that the cost function satisfies the limit condition, some number will eventually be enumerated into A to meet the requirement.
K-triviality turns out to coincide with some computational lowness notions, saying that a set is close to computable. The following notions capture the same class of sets. [ 7 ]
We say that A is low for K if there is b ∈ N {\displaystyle \mathbb {N} } such that
Here K A {\displaystyle K^{A}} is prefix-free Kolmogorov complexity relative to oracle A {\displaystyle A} .
A is low for Martin-Löf-randomness [ 8 ] if whenever Z is Martin-Löf random , it is already Martin-Löf random relative to A .
A is a base for Martin-Löf-randomness if A is Turing reducible to Z for some set Z that is Martin-Löf random relative to A . [ 7 ]
More equivalent characterizations of K-triviality have been studied, such as:
From 2009 on, concepts from analysis entered the stage. This helped solving some notorious problems.
One says that a set Y is a positive density point if every effectively closed class containing Y has positive lower Lebesgue density at Y. Bienvenu, Hölzl, Miller, and Nies [ 9 ] showed that a ML-random is Turing incomplete iff it is a positive density point. Day and Miller [ 10 ] used this for an affirmative answer to the ML-cupping problem: [ 11 ] A is K-trivial iff for every Martin-Löf random set Z such that A⊕Z compute the halting problem , already Z by itself computes the halting problem .
One says that a set Y is a density-one point if every effectively closed class containing Y has Lebesgue density 1 at Y. Any Martin-Löf random set that is not a density-one point computes every K trivial set by Bienvenu, et al. [ 12 ] Day and Miller showed that there is Martin-Löf random set which is a positive density point but not a density one point. Thus there is an incomplete such Martin-Löf random set which computes every K-trivial set. This affirmatively answered the covering problem first asked by Stephan and then published by Miller and Nies. [ 13 ] For a summary see L. Bienvenu, A. Day, N. Greenberg, A. Kucera, J. Miller, A. Nies, and D. Turetsky. [ 14 ]
Variants of K-triviality have been studied: | https://en.wikipedia.org/wiki/K-trivial_set |
K. Andre Mkhoyan (born 1974) is the Ray D. and Mary T. Johnson Chair and Professor in the Department of Chemical Engineering and Materials Science at the University of Minnesota . [ 1 ] He is recognized for advancing both fundamental scientific understanding and diverse applications of scanning transmission electron microscopy (STEM) techniques. He was elected as a Fellow of the Microscopy Society of America in 2024 for "seminal contributions to the understanding of electron beam channeling, quantification of imaging and spectroscopy in STEM , and for his discovery of fundamentally new behavior in crystal point and line defects using STEM." [ 2 ] According to Web of Science, he has produced over 180 published works that have been cited over 9800 times, with an h-index of 44 as of October 25, 2024. [ 3 ]
Andre Mkhoyan was born in 1974 in Yerevan, Armenia . He received his high school diploma from the prestigious Artashes Shahinyan Physics-Mathematics School . In 1996, Mkhoyan graduated with a B.Sc. (Hons.) in Physics from the Yerevan State University . Following graduation, he moved to the United States to pursue a research career specialized in transmission electron microscopy (TEM). After working at Bell Labs as a research scientist in support of the SCALPEL projection electron-beam lithography project, he began graduate studies in Applied and Engineering Physics at Cornell University in 1999. Working under the supervision of Professor John Silcox (1935–2024), Mkhoyan received his M.S. in Engineering Physics in 2003 and Ph.D. in Applied Physics in 2004. His dissertation was titled "Scanning Transmission Electron Microscopy Study of III-V Nitrides." [ 4 ]
In his postdoctoral research studies, Mkhoyan worked with Professor Silcox at Cornell as well as with Dr. Philip E. Batson at the IBM TJ Watson Lab . In this period, he was one of the first people to work on a prototype aberration-corrected STEM on a VG microscope retro-fitted with a NION probe-corrector. He worked extensively on understanding electron beam channeling, spectroscopy and quantification methods during this time. In 2008, Mkhoyan joined the University of Minnesota as an Assistant Professor of Chemical Engineering and Materials Science where he continues to be a professor and lead an electron microscopy research group. He is also the chair for the Electron Microscopy Management Committee at the University of Minnesota.
Mkhoyan has contributed to fundamental studies of electron microscopy physics as well as pioneered challenging applications of high resolution analytical STEM, specifically, multimodal use of EELS and EDX signals in conjunction with annular dark-field imaging to materials science. He has been credited for pushing the boundaries of atomic-resolution analytical STEM for the better understanding of point, line and planar defects , including discoveries of two new line defects [ 5 ] [ 6 ] and interaction mechanisms between dopant atoms and dislocations. [ 7 ] He has worked extensively on development of new methods of STEM-based atomic-resolution imaging and EELS spectroscopy of highly-beam-sensitive zeolites and metal organic frameworks . [ 8 ] [ 9 ] [ 10 ] and atomic-resolution in-situ STEM work. [ 11 ] His research has improved understanding of electron beam channeling and quantification of imaging and EELS spectroscopy in STEM, which includes identification of the factors behind electron beam channeling even in non-periodic crystals [ 12 ] and discovery of new kind of sub-atomic beam channeling. [ 13 ]
Andre Mkhoyan has authored numerous journal articles describing significant advances in STEM, defects in materials, nanoporous materials , complex oxides , and two-dimensional/single-layer materials which includes but is not limited to: | https://en.wikipedia.org/wiki/K._Andre_Mkhoyan |
Potassium aluminium borate (K 2 Al 2 B 2 O 7 ) is an ionic compound composed of potassium ions, aluminium ions, and borate ions. Its crystal form exhibits nonlinear optical properties . The ultraviolet beam at 266 nm can be obtained by fourth harmonic generation (FGH) of 1064 nm Nd:YAG laser radiation through a nonlinear crystal K 2 Al 2 B 2 O 7 (KABO). [ 1 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K2Al2B2O7 |
Dipotassium cyclooctatetraenide , sometimes abbreviated K 2 COT, is an organopotassium compound with the formula K 2 C 8 H 8 . It is a brown solid that is used as a precursor to cyclooctatetraenide complexes, such as uranocene (U(C 8 H 8 ) 2 ). Analogs of K 2 C 8 H 8 are known with ring substituents, with different alkali metals, and with various complexants.
Potassium cyclooctatetraenide is formed by the reaction of cyclooctatetraene with potassium metal:
The reaction entails 2-electron reduction of the polyene and is accompanied by a color change from colorless to brown. [ 1 ]
The structure of K 2 ( diglyme )C 8 H 8 has been characterized by X-ray crystallography of the derivatives with diglyme complexed to the potassium cations. The C 8 H 8 unit is planar with an average C-C distance of 1.40 A. [ 2 ] | https://en.wikipedia.org/wiki/K2C8H8 |
Potassium carbonate is the inorganic compound with the formula K 2 C O 3 . It is a white salt , which is soluble in water and forms a strongly alkaline solution. It is deliquescent , often appearing as a damp or wet solid . Potassium carbonate is mainly used in the production of soap and glass . [ 3 ] Commonly, it can be found as the result of leakage of alkaline batteries . [ 4 ] Potassium carbonate is a potassium salt of carbonic acid . This salt consists of potassium cations K + and carbonate anions CO 2− 3 , and is therefore an alkali metal carbonate.
Potassium carbonate is the primary component of potash and the more refined pearl ash or salt of tartar. Historically, pearl ash was created by baking potash in a kiln to remove impurities. The fine, white powder remaining was the pearl ash. The first patent issued by the US Patent Office was awarded to Samuel Hopkins in 1790 for an improved method of making potash and pearl ash. [ 5 ]
In late 18th-century North America , before the development of baking powder , pearl ash was used as a leavening agent for quick breads . [ 6 ] [ 7 ]
The modern commercial production of potassium carbonate is by reaction of potassium hydroxide with carbon dioxide : [ 3 ]
From the solution crystallizes the sesquihydrate K 2 CO 3 ·1.5H 2 O ("potash hydrate"). Heating this solid above 200 °C (392 °F) gives the anhydrous salt. In an alternative method, potassium chloride is treated with carbon dioxide in the presence of an organic amine to give potassium bicarbonate , which is then calcined : | https://en.wikipedia.org/wiki/K2CO3 |
Potassium dichromate , K 2 Cr 2 O 7 , is a common inorganic chemical reagent, most commonly used as an oxidizing agent in various laboratory and industrial applications. As with all hexavalent chromium compounds, it is acutely and chronically harmful to health. It is a crystalline ionic solid with a very bright, red-orange color. The salt is popular in laboratories because it is not deliquescent , in contrast to the more industrially relevant salt sodium dichromate . [ 6 ]
Potassium dichromate is usually prepared by the reaction of sodium dichromate and potassium chloride . Alternatively, it can be also obtained from potassium chromate by roasting chromite ore with potassium hydroxide . It is soluble in water and in the dissolution process it ionizes:
Potassium dichromate is an oxidising agent in organic chemistry , and is milder than potassium permanganate . It is used to oxidize alcohols . It converts primary alcohols into aldehydes and, under more forcing conditions, into carboxylic acids. In contrast, potassium permanganate tends to give carboxylic acids as the sole products. Secondary alcohols are converted into ketones . For example, menthone may be prepared by oxidation of menthol with acidified dichromate. [ 7 ] Tertiary alcohols cannot be oxidized.
In an aqueous solution the color change exhibited can be used to test for distinguishing aldehydes from ketones. Aldehydes reduce dichromate from the +6 to the +3 oxidation state , changing color from orange to green. This color change arises because the aldehyde can be oxidized to the corresponding carboxylic acid. A ketone will show no such change because it cannot be oxidized further, and so the solution will remain orange.
When heated strongly, it decomposes with the evolution of oxygen.
When an alkali is added to an orange-red solution containing dichromate ions, a yellow solution is obtained due to the formation of chromate ions ( CrO 2− 4 ). For example, potassium chromate is produced industrially using potash :
The reaction is reversible.
Treatment with cold sulfuric acid gives red crystals of chromic anhydride (chromium trioxide, CrO 3 ):
On heating with concentrated acid, oxygen is evolved:
Potassium dichromate has few major applications, as the sodium salt is dominant industrially. The main use is as a precursor to potassium chrome alum , used in leather tanning . [ 6 ] [ 8 ]
Like other chromium(VI) compounds ( chromium trioxide , sodium dichromate ), potassium dichromate has been used to prepare " chromic acid " for cleaning glassware and etching materials. Because of safety concerns associated with hexavalent chromium, this practice has been largely discontinued.
It is used as an ingredient in cement in which it retards the setting of the mixture and improves its density and texture. This usage commonly causes contact dermatitis in construction workers . [ 9 ]
In 1839, Mungo Ponton discovered that paper treated with a solution of potassium dichromate was visibly tanned by exposure to sunlight, the discoloration remaining after the potassium dichromate had been rinsed out. In 1852, Henry Fox Talbot discovered that exposure to ultraviolet light in the presence of potassium dichromate hardened organic colloids such as gelatin and gum arabic , making them less soluble.
These discoveries soon led to the carbon print , gum bichromate , and other photographic printing processes based on differential hardening. Typically, after exposure, the unhardened portion was rinsed away with warm water, leaving a thin relief that either contained a pigment included during manufacture or was subsequently stained with a dye. Some processes depended on the hardening only, in combination with the differential absorption of certain dyes by the hardened or unhardened areas. Because some of these processes allowed the use of highly stable dyes and pigments, such as carbon black , prints with an extremely high degree of archival permanence and resistance to fading from prolonged exposure to light could be produced.
Dichromated colloids were also used as photoresists in various industrial applications, most widely in the creation of metal printing plates for use in photomechanical printing processes.
Chromium intensification or Photochromos uses potassium dichromate together with equal parts of concentrated hydrochloric acid diluted down to approximately 10% v/v to treat weak and thin negatives of black and white photograph roll. This solution reconverts the elemental silver particles in the film to silver chloride . After thorough washing and exposure to actinic light, the film can be redeveloped to its end-point yielding a stronger negative which is able to produce a more satisfactory print.
A potassium dichromate solution in sulfuric acid can be used to produce a reversal negative (that is, a positive transparency from a negative film). This is effected by developing a black and white film but allowing the development to proceed more or less to the end point. The development is then stopped by copious washing and the film then treated in the acid dichromate solution. This converts the silver metal to silver sulfate , a compound that is insensitive to light. After thorough washing and exposure to actinic light, the film is developed again allowing the previously unexposed silver halide to be reduced to silver metal. The results obtained can be unpredictable, but sometimes excellent results are obtained producing images that would otherwise be unobtainable. This process can be coupled with solarisation so that the end product resembles a negative and is suitable for printing in the normal way.
Cr(VI) compounds have the property of tanning animal proteins when exposed to strong light. This quality is used in photographic screen-printing .
In screen-printing a fine screen of bolting silk or similar material is stretched taut onto a frame similar to the way canvas is prepared before painting. A colloid sensitized with a dichromate is applied evenly to the taut screen. Once the dichromate mixture is dry, a full-size photographic positive is attached securely onto the surface of the screen, and the whole assembly exposed to strong light – times vary from 3 minutes to a half an hour in bright sunlight – hardening the exposed colloid. When the positive is removed, the unexposed mixture on the screen can be washed off with warm water, leaving the hardened mixture intact, acting as a precise mask of the desired pattern, which can then be printed with the usual screen-printing process.
Because it is non-hygroscopic, potassium dichromate is a common reagent in classical "wet tests" in analytical chemistry.
The concentration of ethanol in a sample can be determined by back titration with acidified potassium dichromate. Reacting the sample with an excess of potassium dichromate, all ethanol is oxidized to acetic acid :
Full reaction of converting ethanol to acetic acid:
The excess dichromate is determined by titration against sodium thiosulfate . Adding the amount of excess dichromate from the initial amount, gives the amount of ethanol present. Accuracy can be improved by calibrating the dichromate solution against a blank.
One major application for this reaction is in old police breathalyzer tests. When alcohol vapor makes contact with the orange dichromate-coated crystals, the color changes from Cr(VI) orange to Cr(III) green. The degree of the color change is directly related to the level of alcohol in the suspect's breath.
When dissolved in an approximately 35% nitric acid solution it is called Schwerter's solution and is used to test for the presence of various metals, notably for determination of silver purity. Pure silver will turn the solution bright red, sterling silver will turn it dark red, low grade coin silver (0.800 fine) will turn brown (largely due to the presence of copper which turns the solution brown) and even green for 0.500 silver.
Brass turns dark brown, copper turns brown, lead and tin both turn yellow while gold and palladium do not change.
Potassium dichromate paper can be used to test for sulfur dioxide , as it turns distinctively from orange to green. This is typical of all redox reactions where hexavalent chromium is reduced to trivalent chromium. Therefore, it is not a conclusive test for sulfur dioxide. The final product formed is Cr 2 (SO 4 ) 3 .
Potassium dichromate is used to stain certain types of wood by darkening the tannins in the wood. It produces deep, rich browns that cannot be achieved with modern color dyes. It is a particularly effective treatment on mahogany . [ 10 ]
Potassium dichromate occurs naturally as the rare mineral lópezite . It has only been reported as vug fillings in the nitrate deposits of the Atacama Desert of Chile and in the Bushveld igneous complex of South Africa . [ 11 ]
In 2005–06, potassium dichromate was the 11th-most-prevalent allergen in patch tests (4.8%). [ 12 ]
Potassium dichromate is one of the most common causes of chromium dermatitis ; [ 13 ] chromium is highly likely to induce sensitization leading to dermatitis, especially of the hand and forearms, which is chronic and difficult to treat. Toxicological studies have further illustrated its highly toxic nature. With rabbits and rodents, concentrations as low as 14 mg/kg have shown a 50% fatality rate amongst test groups. [ 14 ] Aquatic organisms are especially vulnerable if exposed, and hence responsible disposal according to the local environmental regulations is advised.
As with other Cr(VI) compounds, potassium dichromate is carcinogenic . [ 15 ] The compound is also corrosive and exposure may produce severe eye damage or blindness. [ 16 ] Human exposure further encompasses impaired fertility. | https://en.wikipedia.org/wiki/K2Cr2O7 |
Potassium chromate is the inorganic compound with the formula K 2 CrO 4 . This yellow solid is the potassium salt of the chromate anion. It is a common laboratory chemical, whereas sodium chromate is important industrially.
Two crystalline forms are known, both being very similar to the corresponding potassium sulfate. Orthorhombic β-K 2 CrO 4 is the common form, but it converts to an α-form above 666 °C. [ 1 ] These structures are complex, although the chromate ion adopts the typical tetrahedral geometry. [ 2 ]
It is prepared by treating potassium dichromate with potassium hydroxide :
Or, the fusion of potassium hydroxide and chromium trioxide :
In solution, the behavior of potassium and sodium dichromates are very similar. When treated with lead(II) nitrate, it gives an orange-yellow precipitate, lead(II) chromate.
Unlike the less expensive sodium salt, potassium salt is mainly used for laboratory work in situations where an anhydrous salt is required. [ 1 ] It is as an oxidizing agent in organic synthesis . It is used in qualitative inorganic analysis , e.g. as a colorimetric test for silver ion. It is also used as an indicator in precipitation titrations with silver nitrate and sodium chloride (they can be used as standard as well as titrant for each other) as potassium chromate turns red in the presence of excess of silver ions.
Tarapacaite is the natural, mineral form of potassium chromate. It occurs very rarely and until now is known from only few localities on Atacama Desert . [ citation needed ]
As with other Cr(VI) compounds, potassium chromate is carcinogenic . [ 3 ] The compound is also corrosive and exposure may produce severe eye damage or blindness. [ 4 ] Human exposure further encompasses impaired fertility, heritable genetic damage and harm to unborn children. | https://en.wikipedia.org/wiki/K2CrO4 |
Dipotassium phosphate (also dipotassium hydrogen orthophosphate or potassium phosphate dibasic ) is the inorganic compound with the formula K 2 HPO 4 . (H 2 O) x (x = 0, 3, 6). Together with monopotassium phosphate (KH 2 PO 4 . (H 2 O) x ), it is often used as a fertilizer , food additive , and buffering agent . [ 1 ] It is a white or colorless solid that is soluble in water.
It is produced commercially by partial neutralization of phosphoric acid with two equivalents of potassium chloride : [ 1 ]
As a food additive, dipotassium phosphate is used in imitation dairy creamers , dry powder beverages, mineral supplements, and starter cultures. [ 2 ] It functions as an emulsifier, stabilizer and texturizer; it is also a buffering agent, and chelating agent especially for the calcium in milk products. [ 3 ]
As a food additive , dipotassium phosphate is generally recognized as safe by the United States Food and Drug Administration , [ 4 ] and is commonly used (in conjunction with other inorganic salts) to add taste to bottled water . [ 5 ]
This food ingredient article is a stub . You can help Wikipedia by expanding it .
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K2HPO4 |
Langbeinite is a potassium magnesium sulfate mineral with the chemical formula K 2 Mg 2 (SO 4 ) 3 . Langbeinite crystallizes in the isometric -tetartoidal (cubic) system as transparent colorless or white with pale tints of yellow to green and violet crystalline masses. It has a vitreous luster . The Mohs hardness is 3.5 to 4 and the specific gravity is 2.83. The crystals are piezoelectric . [ 4 ]
The mineral is an ore of potassium and occurs in marine evaporite deposits in association with carnallite , halite , and sylvite . [ 4 ]
It was first described in 1891 for an occurrence in Wilhelmshall, Halberstadt , Saxony-Anhalt , Germany , and named for A. Langbein of Leopoldshall, Germany. [ 4 ] [ 5 ]
Langbeinite gives its name to the langbeinites , a family of substances with the same cubic structure, a tetrahedral anion, and large and small cations.
Related substances include hydrated salts leonite (K 2 Mg(SO 4 ) 2 ·4H 2 O) and picromerite (K 2 Mg(SO 4 ) 2 ·6H 2 O).
This article about a specific sulfate mineral is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K2Mg2(SO4)3 |
Potassium manganate is the inorganic compound with the formula K 2 MnO 4 . This green-colored salt is an intermediate in the industrial synthesis of potassium permanganate ( KMnO 4 ), a common chemical. [ 1 ] Occasionally, potassium manganate and potassium per manganate are confused, but each compound's properties are distinct.
K 2 MnO 4 is a salt, consisting of K + cations and Mn O 2− 4 anions . X-ray crystallography shows that the anion is tetrahedral, with Mn-O distances of 1.66 Å, ca. 0.03 Å longer than the Mn-O distances in KMnO 4 . [ 2 ] It is isostructural with potassium sulfate. The compound is paramagnetic, owing to the presence of one unpaired electron on the Mn(VI) center.
The industrial route entails treatment of MnO 2 with air and potassium hydroxide : [ 1 ]
The transformation gives a green-colored melt. Alternatively, instead of using air, potassium nitrate can be used as the oxidizer:
One can test an unknown substance for the presence of manganese by heating the sample in strong KOH in air. The production of a green coloration indicates the presence of Mn . This green color results from an intense absorption at 610 nm.
In the laboratory, K 2 MnO 4 can be synthesized by heating a solution of KMnO 4 in concentrated KOH solution followed by cooling to give green crystals: [ 3 ]
This reaction illustrates the relatively rare role of hydroxide as a reducing agent. The concentration of K 2 MnO 4 in such solutions can be checked by measuring their absorbance at 610 nm.
The one-electron reduction of permanganate to manganate can also be effected using iodide as the reducing agent:
The conversion is signaled by the color change from purple, characteristic of permanganate, to the green color of manganate. This reaction also shows that manganate(VII) can serve as an electron acceptor in addition to its usual role as an oxygen-transfer reagent. Barium manganate , BaMnO 4 , is generated by the reduction of KMnO 4 with iodide in the presence of barium chloride . Just like BaSO 4 , BaMnO 4 exhibits low solubility in virtually all solvents.
An easy method for preparing potassium manganate in the laboratory involves heating crystals or powder of pure potassium permanganate. Potassium permanganate will decompose into potassium manganate, manganese dioxide and oxygen gas:
This reaction is a laboratory method to prepare oxygen, but produces samples of potassium manganate contaminated with MnO 2 . The former is soluble and the latter is not.
Manganate salts readily disproportionate to permanganate ion and manganese dioxide :
The colorful nature of the disproportionation has led the manganate/manganate(VII) pair to be referred to as a chemical chameleon . This disproportionation reaction, which becomes rapid when [ OH − ] < 1M, follows bimolecular kinetics. [1] | https://en.wikipedia.org/wiki/K2MnO4 |
Potassium oxide ( K 2 O ) is an ionic compound of potassium and oxygen . It is a base . This pale yellow solid is the simplest oxide of potassium. It is a highly reactive compound that is rarely encountered. Some industrial materials, such as fertilizers and cements, are assayed assuming the percent composition that would be equivalent to K 2 O.
Potassium oxide is produced from the reaction of oxygen and potassium; this reaction affords potassium peroxide , K 2 O 2 . Treatment of the peroxide with potassium produces the oxide: [ 5 ]
Alternatively and more conveniently, K 2 O is synthesized by heating potassium nitrate with metallic potassium:
Other possibility is to heat potassium peroxide at 500 °C which decomposes at that temperature giving pure potassium oxide and oxygen.
Potassium hydroxide cannot be further dehydrated to the oxide but it can react with molten potassium to produce it, releasing hydrogen as a byproduct.
K 2 O crystallises in the antifluorite structure . In this motif the positions of the anions and cations are reversed relative to their positions in CaF 2 , with potassium ions coordinated to 4 oxide ions and oxide ions coordinated to 8 potassium. [ 6 ] [ 7 ] K 2 O is a basic oxide and reacts with water violently to produce the caustic potassium hydroxide . It is deliquescent and will absorb water from the atmosphere, initiating this vigorous reaction.
The chemical formula K 2 O (or simply 'K') is used in several industrial contexts: the N-P-K numbers for fertilizers , in cement formulas , and in glassmaking formulas . Potassium oxide is often not used directly in these products, but the amount of potassium is reported in terms of the K 2 O equivalent for whatever type of potash was used, such as potassium carbonate . For example, potassium oxide is about 83% potassium by weight, while potassium chloride is only 52%. Potassium chloride provides less potassium than an equal amount of potassium oxide. Thus, if a fertilizer is 30% potassium chloride by weight, its standard potassium rating, based on potassium oxide, would be only 18.8%.
Media related to Potassium oxide at Wikimedia Commons | https://en.wikipedia.org/wiki/K2O |
Potassium peroxide is an inorganic compound with the molecular formula K 2 O 2 . It is formed as potassium reacts with oxygen in the air, along with potassium oxide (K 2 O) and potassium superoxide (KO 2 ).
Potassium peroxide reacts with water to form potassium hydroxide and oxygen :
Potassium peroxide is a highly reactive, oxidizing white to yellowish solid which, while not flammable itself, reacts violently with flammable materials. It decomposes violently on contact with water . [ 1 ]
The standard enthalpy of formation of potassium peroxide is ΔH f 0 = −496 kJ/mol.
Potassium peroxide is used as an oxidizing agent and bleach (due to the peroxide ), and to purify air. | https://en.wikipedia.org/wiki/K2O2 |
Potassium sulfate (US) or potassium sulphate (UK), also called sulphate of potash (SOP), arcanite , or archaically potash of sulfur , is the inorganic compound with formula K 2 SO 4 , a white water- soluble solid. It is commonly used in fertilizers , providing both potassium and sulfur .
Potassium sulfate (K 2 SO 4 ) has been known since early in the 14th century. It was studied by Glauber , Boyle , and Tachenius . In the 17th century, it was named arcanuni or sal duplicatum , as it was a combination of an acid salt with an alkaline salt. It was also known as vitriolic tartar and Glaser's salt or sal polychrestum Glaseri after the pharmaceutical chemist Christopher Glaser who prepared it and used medicinally. [ 4 ] [ 5 ]
Known as arcanum duplicatum ("double secret") or panacea duplicata in pre-modern medicine , it was prepared from the residue ( caput mortuum ) left over from the production of aqua fortis (nitric acid, HNO 3 ) from nitre (potassium nitrate, KNO 3 ) and oil of vitriol (sulphuric acid, H 2 SO 4 ) via Glauber's process:
The residue was dissolved in hot water, filtered, and evaporated to a cuticle. It was then left to crystallise. It was used as a diuretic and sudorific . [ 6 ]
According to Chambers's Cyclopedia , the recipe was purchased for five hundred thalers by Charles Frederick, Duke of Holstein-Gottorp . Schroder, the duke's physician, wrote wonders of its great uses in hypochondriacal cases, continued and intermitting fevers , stone, scurvy , and more. [ 6 ]
The mineral form of potassium sulfate, arcanite , is relatively rare. Natural resources of potassium sulfate are minerals abundant in the Stassfurt salt . These are cocrystallizations of potassium sulfate and sulfates of magnesium , calcium , and sodium .
Relevant minerals are:
The potassium sulfate can be separated from some of these minerals, like kainite, because the corresponding salt is less soluble in water.
Kieserite , MgSO 4 ·H 2 O, can be combined with a solution of potassium chloride to produce potassium sulfate.
Approximately 1.5 million tons were produced in 1985, typically by the reaction of potassium chloride with sulfuric acid , analogous to the Mannheim process for producing sodium sulfate. [ 7 ] The process involves intermediate formation of potassium bisulfate , an exothermic reaction that occurs at room temperature:
The second step of the process is endothermic, requiring energy input:
Two crystalline forms are known. Orthorhombic β-K 2 SO 4 is the common form, but it converts to α-K 2 SO 4 above 583 °C. [ 7 ] These structures are complex, although the sulfate adopts the typical tetrahedral geometry. [ 8 ]
It does not form a hydrate, unlike sodium sulfate . The salt crystallizes as double six-sided pyramids, classified as rhombic. They are transparent, very hard and have a bitter, salty taste. The salt is soluble in water, but insoluble in solutions of potassium hydroxide ( sp. gr. 1.35), or in absolute ethanol .
The dominant use of potassium sulfate is as a fertilizer . K 2 SO 4 does not contain chloride, which can be harmful to some crops. Potassium sulfate is preferred for these crops, which include tobacco and some fruits and vegetables. Crops that are less sensitive may still require potassium sulfate for optimal growth if the soil accumulates chloride from irrigation water. [ 9 ]
The crude salt is also used occasionally in the manufacture of glass. Potassium sulfate is also used as a flash reducer in artillery propellant charges. It reduces muzzle flash , flareback and blast overpressure.
It is sometimes used as an alternative blast media similar to soda in soda blasting as it is harder and similarly water-soluble. [ 10 ]
Potassium sulfate can also be used in pyrotechnics in combination with potassium nitrate to generate a purple flame .
A 5% solution of potassium sulfate was used in the beginning of the 20th century as a topical mosquito repellent. [ citation needed ]
Potassium hydrogen sulfate (also known as potassium bisulfate), KHSO 4 , is readily produced by reacting K 2 SO 4 with sulfuric acid . It forms rhombic pyramids , which melt at 197 °C (387 °F). It dissolves in three parts of water at 0 °C (32 °F). The solution behaves much as if its two congeners , K 2 SO 4 and H 2 SO 4 , were present side by side of each other uncombined; an excess of ethanol the precipitates normal sulfate (with little bisulfate) with excess acid remaining.
The behavior of the fused dry salt is similar when heated to several hundred degrees; it acts on silicates , titanates , etc., the same way as sulfuric acid that is heated beyond its natural boiling point does. Hence it is frequently used in analytical chemistry as a disintegrating agent. For information about other salts that contain sulfate, see sulfate . | https://en.wikipedia.org/wiki/K2O4S |
Potassium dithionite or potassium hydrosulfite is a potassium salt of dithionous acid .
The compound has UN number UN 1929. As a dithionite, it is closely related to sodium dithionite , which is a commonly used reducing agent and bleaching agent .
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K2O4S2 |
Potassium metabisulfite , K 2 S 2 O 5 , also known as potassium pyrosulfite , is a white crystalline powder with a pungent odour. It is mainly used as an antioxidant or chemical sterilant . [ 1 ] As a disulfite , it is chemically very similar to sodium metabisulfite , with which it is sometimes used interchangeably. Potassium metabisulfite has a monoclinic crystal structure.
Potassium metabisulfite can be prepared by treating a solution of potassium hydroxide with sulfur dioxide . [ 2 ]
It decomposes at 190 °C, yielding potassium sulfite and sulfur dioxide :
It is used as a food additive, also known as E224. [ 3 ] It is restricted in use and may cause allergic reactions in some sensitive persons. [ 4 ]
Potassium metabisulfite is a common wine or must additive, in which it forms sulfur dioxide (SO 2 ). Sulfur dioxide is a disinfectant. It also acts as a potent antioxidant , protecting both the color and delicate flavors of wine.
A high dose would be 3 grams of potassium metabisulfite per six-gallon bucket of must or around 132 milligrams per liter (yielding roughly 75 ppm of SO 2 ) prior to fermentation; then 6 grams per six-gallon bucket (150 ppm of SO 2 ) at bottling. Some countries regulate the SO 2 content of wines. [ 5 ]
Winemaking equipment is sanitized by spraying with a 1% SO 2 (2 tsp potassium metabisulfite per L) solution.
Potassium metabisulfite is sometimes used in the brewing industry to inhibit the growth of wild bacteria and fungi . This step is called 'stabilizing'. It is also used to neutralize monochloramine from tap water. It is used both by homebrewers and commercial brewers alike. It is not used as much for brewing beer , because the wort is almost always boiled, which kills most microorganisms. | https://en.wikipedia.org/wiki/K2O5S2 |
Potassium octachlorodirhenate(III) is an inorganic compound with the formula K 2 Re 2 Cl 8 . This dark blue salt is well known as an early example of a compound featuring quadruple bond between its metal centers. Although the compound has no practical value, its characterization was significant in opening a new field of research into complexes with quadruple bonds. [ 1 ]
Soviet chemists first reported K 2 [Re 2 Cl 8 ] in 1954, [ 2 ] but it was not until 1964 that Cotton and Harris characterized the compound as featuring a short Re–Re bond, the first of its kind discovered. [ 3 ] [ 4 ] The results of this classic study subsequently led to new work into other metals capable of forming metal–metal bonds, such as chromium , molybdenum , tungsten , and technetium . [ 5 ] [ 6 ] [ 7 ]
A high-yield synthesis of the tetrabutylammonium salt involves treating the perrhenate salt with benzoyl chloride followed by HCl:
Octachlorodirhenate(III) is a precursor to other complexes with multiply-bonded rhenium centers as the quadruple bond is quite stable and is often maintained in ligand substitution reactions . For example, upon treatment with concentrated HBr , the complex forms the analogous anion [Re 2 Br 8 ] 2− , which can easily be converted into other dirhenium species. [ 8 ]
In the [Re 2 Cl 8 ] 2− , the Re–Re bond distance is 2.24 Å , the Re–Re–Cl bond angles are 104°, and the Cl–Re–Cl angles are 87°. The chloride ligands are fully eclipsed . Although this geometry results in repulsive interactions between the chloride ions, this conformation allows for maximum δ–δ overlap between the Re(III) centers, a factor which overrides the unfavorable chloride repulsions. The [Re 2 Cl 8 ] 2− anion has a weak electrophilic character. [ 9 ] [ 1 ] With the configuration, Re(III) is well suited to engage in quadruple bonding. Electrons are allocated to give the configuration σ 2 π 4 δ 2 , resulting in a bond order of 4 between the rhenium centers. The brilliant color of the [Re 2 Cl 8 ] 2− arises from the δ→δ* electronic transition. [ 8 ] | https://en.wikipedia.org/wiki/K2Re2Cl8 |
Potassium nonahydridorhenate(VII) is an inorganic compound having the formula K 2 [ Re H 9 ] . This colourless salt is soluble in water but only poorly soluble in most alcohols . This salt contains the nonahydridorhenate(VII) anion , [ReH 9 ] 2− , which is a rare example of a coordination complex bearing only hydride ligands .
The study of rhenium hydrides can be traced to the 1950s and included reports of the "rhenide" anion, supposedly Re − . These reports led to a series of investigations by A. P. Ginsberg and coworkers on the products from the reduction of perrhenate . [ 1 ]
The rhenide anion, Re − , was based on the product of the reduction of perrhenate salts, such as the reduction of potassium perrhenate ( KReO 4 ) by potassium metal. [ 2 ] "Potassium rhenide" was shown to exist as a tetrahydrated complex, with the postulated chemical formula KRe·4H 2 O (potassium rhenide tetrahydrate). [ 3 ] This compound exhibits strongly reducing properties, and slowly yields hydrogen gas when dissolved in water. The lithium and thallous salts were also reported. Later research, however, indicates that the "rhenide" ion is actually a hydridorhenate complex. "Potassium rhenide" was shown to be in fact the potassium nonahydridorhenate(VII), K 2 [ReH 9 ] , containing the nonahydridorhenate(VII) anion, [ReH 9 ] 2− , in which the oxidation state of rhenium is actually +7. [ 4 ] [ 5 ] Other methods of reduction of perrhenate salts yield compounds containing other hydrido- complexes, including ReH 3 (OH) 3 (H 2 O) − . [ 6 ]
[ReH 9 ] 2− is an unusual example of a nonacoordinated complex , its high coordination number being attributed to the small size of the hydride ligand and the high positive charge on the Re(VII) central atom. Its structure consists of a tricapped trigonal prism , [ 7 ] [ 8 ] as determined by neutron crystallography . [ 9 ] [ 10 ] The diamagnetic sodium salt, like the analogous technetium compound, is prepared by treating an ethanol solution of sodium perrhenate , NaReO 4 , with sodium metal . [ 11 ] Via cation exchange , it can be converted to the corresponding tetraethylammonium salt, ([(CH 3 CH 2 ) 4 N] + ) 2 [ReH 9 ] 2− (tetraethylammonium nonahydridorhenate(VII)).
Isostructural with [ReH 9 ] 2− (nonahydridotechnetate(VII)), [TcH 9 ] 2− consists of a trigonal prism with Tc atom in the center and six hydrogen atoms at the corners. Three more hydrogen ligands define a triangle lying parallel to the base and crossing the prism in its center (see figure). Although those hydride ligands are not equivalent, their electronic structure is almost the same. The coordination number of 9 in this complex is the highest known for any rhenium complex.
Recent density functional theory calculations on [ReH 9 ] 2− indicate that this dianion adopts the D 3h ⇌C 4v ⇌D 3h pathway in gas phase and solution, such interconversion originally proposed by Muetterties [ 12 ] featuring a capped square antiprism structure as transition state has very low energy barrier . In K 2 [ReH 9 ] solid, intramolecular motions of [ReH 9 ] 2− include (1) circle-dance mechanism (resembling Matisse's painting Dance (II) ) and (2) three-arm turnstile rotation. [ 13 ] | https://en.wikipedia.org/wiki/K2ReH9 |
Potassium sulfide is an inorganic compound with the formula K 2 S . The colourless solid is rarely encountered, because it reacts readily with water, a reaction that affords potassium hydrosulfide (KSH) and potassium hydroxide (KOH). Most commonly, the term potassium sulfide refers loosely to this mixture, not the anhydrous solid.
It adopts an antifluorite structure , which means that the small K + ions occupy the tetrahedral (F − ) sites in fluorite , and the larger S 2− centers occupy the eight-coordinate sites. Li 2 S , Na 2 S , and Rb 2 S crystallize similarly. [ 3 ]
It can be produced by heating K 2 SO 4 with carbon ( coke ):
In the laboratory, pure K 2 S may be prepared by the reaction of potassium and sulfur in anhydrous ammonia. [ 4 ]
Sulfide is highly basic, consequently K 2 S completely and irreversibly hydrolyzes in water according to the following equation:
For many purposes, this reaction is inconsequential since the mixture of SH − and OH − behaves as a source of S 2− . Other alkali metal sulfides behave similarly. [ 3 ]
Potassium sulfides are formed when black powder is burned and are important intermediates in many pyrotechnic effects, such as senko hanabi and some glitter formulations. [ 5 ] | https://en.wikipedia.org/wiki/K2S |
Potassium metabisulfite , K 2 S 2 O 5 , also known as potassium pyrosulfite , is a white crystalline powder with a pungent odour. It is mainly used as an antioxidant or chemical sterilant . [ 1 ] As a disulfite , it is chemically very similar to sodium metabisulfite , with which it is sometimes used interchangeably. Potassium metabisulfite has a monoclinic crystal structure.
Potassium metabisulfite can be prepared by treating a solution of potassium hydroxide with sulfur dioxide . [ 2 ]
It decomposes at 190 °C, yielding potassium sulfite and sulfur dioxide :
It is used as a food additive, also known as E224. [ 3 ] It is restricted in use and may cause allergic reactions in some sensitive persons. [ 4 ]
Potassium metabisulfite is a common wine or must additive, in which it forms sulfur dioxide (SO 2 ). Sulfur dioxide is a disinfectant. It also acts as a potent antioxidant , protecting both the color and delicate flavors of wine.
A high dose would be 3 grams of potassium metabisulfite per six-gallon bucket of must or around 132 milligrams per liter (yielding roughly 75 ppm of SO 2 ) prior to fermentation; then 6 grams per six-gallon bucket (150 ppm of SO 2 ) at bottling. Some countries regulate the SO 2 content of wines. [ 5 ]
Winemaking equipment is sanitized by spraying with a 1% SO 2 (2 tsp potassium metabisulfite per L) solution.
Potassium metabisulfite is sometimes used in the brewing industry to inhibit the growth of wild bacteria and fungi . This step is called 'stabilizing'. It is also used to neutralize monochloramine from tap water. It is used both by homebrewers and commercial brewers alike. It is not used as much for brewing beer , because the wort is almost always boiled, which kills most microorganisms. | https://en.wikipedia.org/wiki/K2S2O5 |
Potassium pyrosulfate , or potassium disulfate , is an inorganic compound with the chemical formula K 2 S 2 O 7 .
Potassium pyrosulfate is obtained by the thermal decomposition of other salts, most directly from potassium bisulfate : [ 1 ]
Temperatures above 600°C further decompose potassium pyrosulfate to potassium sulfate and sulfur trioxide however: [ 2 ]
Other salts, such as potassium trisulfate , [ 3 ] can also decompose into potassium pyrosulfate.
Potassium pyrosulfate contains the pyrosulfate anion which has a dichromate -like structure . The geometry can be visualized as a tetrahedron with two corners sharing the SO 4 anion's configuration and a centrally bridged oxygen atom. [ 4 ] A semi- structural formula for the pyrosulfate anion is O 3 SOSO 3 2− . The oxidation state of sulfur in this compound is +6.
Potassium pyrosulfate is used in analytical chemistry ; samples are fused with potassium pyrosulfate, (or a mixture of potassium pyrosulfate and potassium fluoride ) to ensure complete dissolution prior to a quantitative analysis . [ 5 ] [ 6 ]
The compound is also present in a catalyst in conjunction with vanadium(V) oxide in the industrial production of sulfur trioxide. [ 7 ] | https://en.wikipedia.org/wiki/K2S2O7 |
Potassium persulfate is the inorganic compound with the formula K 2 S 2 O 8 . Also known as potassium peroxydisulfate , it is a white solid that is sparingly soluble in cold water, but dissolves better in warm water. This salt is a powerful oxidant, commonly used to initiate polymerizations .
The sodium and potassium salts are very similar. In the potassium salt, the O-O distance is 1.495 Å. The individual sulfate groups are tetrahedral, with three short S-O distances near 1.43 and one long S-O bond at 1.65 Å. [ 3 ]
Potassium persulfate can be prepared by electrolysis of a cold solution potassium bisulfate in sulfuric acid at a high current density. [ 1 ] [ 4 ]
It can also be prepared by adding potassium bisulfate (KHSO 4 ) to a solution of the more soluble salt ammonium peroxydisulfate (NH 4 ) 2 S 2 O 8 . In principle it can be prepared by chemical oxidation of potassium sulfate using fluorine . Several million kilograms of the ammonium, sodium, and potassium salts of peroxydisulfate are produced annually.
This salt is used to initiate polymerization of various alkenes leading to commercially important polymers such as styrene-butadiene rubber and polytetrafluoroethylene and related materials. In solution, the dianion dissociates to give radicals: [ 5 ]
It is used in organic chemistry as an oxidizing agent , [ 6 ] for instance in the Elbs persulfate oxidation of phenols and the Boyland–Sims oxidation of anilines .
As a strong yet stable bleaching agent it also finds use in various hair bleaches and lighteners. Such brief and non-continuous use is normally hazard free, however prolonged contact can cause skin irritation. [ 7 ] It has been used as an improving agent for flour with the E number E922, although it is no longer approved for this use within the EU.
The salt is a strong oxidant and is incompatible with organic compounds. Prolonged skin contact can result in irritation. [ 7 ] | https://en.wikipedia.org/wiki/K2S2O8 |
Potassium pentasulfide is the inorganic compound with the formula K 2 S 5 . It is a red-orange solid that dissolves in water. The salt decomposes rapidly in air.
It is one of several polysulfide salts with the general formula M 2 S n , where M = Li, Na, K and n = 2, 3, 4, 5, 6. [ 1 ] The polysulfide salts of potassium and sodium are similar.
The salt is prepared by the addition of elemental sulfur to potassium sulfide . An idealized equation is shown for potassium hydrosulfide:
The structure consists of zigzag chains of S 2− 5 paired with K + ions. [ 2 ]
Various polysulfides K 2 S 2 - K 2 S 6 are components of liver of sulfur . Polysulfides, like sulfides, can induce stress corrosion cracking in carbon steel and stainless steel . | https://en.wikipedia.org/wiki/K2S5 |
Potassium sulfite is the inorganic compound with the formula K 2 SO 3 . It is the salt of potassium cation and sulfite anion. It is a white solid that is highly soluble in water. Potassium sulfite is used for preserving food and beverages . [ 2 ]
Potassium sulfite was first obtained by Georg Ernst Stahl in the early 18th century, [ 3 ] and was therefore known afterwards as Stahl's sulphureous salt . It became the first discovered sulfite and was first properly studied along with other sulfites by French chemists in the 1790s, and it was called sulphite of potash in the early 19th century. [ 4 ] Gilles-François Boulduc also discovered the salt in water of Passy in the 1720s. [ 5 ]
Potassium sulfite is produced by the thermal decomposition of potassium metabisulfite at 190 °C: [ 6 ]
The structure of solid K 2 SO 3 , as assessed by X-ray crystallography . The S-O distances are 1.515 Å, and the O-S-O angles are 105.2° [ 1 ] | https://en.wikipedia.org/wiki/K2SO3 |
Potassium sulfate (US) or potassium sulphate (UK), also called sulphate of potash (SOP), arcanite , or archaically potash of sulfur , is the inorganic compound with formula K 2 SO 4 , a white water- soluble solid. It is commonly used in fertilizers , providing both potassium and sulfur .
Potassium sulfate (K 2 SO 4 ) has been known since early in the 14th century. It was studied by Glauber , Boyle , and Tachenius . In the 17th century, it was named arcanuni or sal duplicatum , as it was a combination of an acid salt with an alkaline salt. It was also known as vitriolic tartar and Glaser's salt or sal polychrestum Glaseri after the pharmaceutical chemist Christopher Glaser who prepared it and used medicinally. [ 4 ] [ 5 ]
Known as arcanum duplicatum ("double secret") or panacea duplicata in pre-modern medicine , it was prepared from the residue ( caput mortuum ) left over from the production of aqua fortis (nitric acid, HNO 3 ) from nitre (potassium nitrate, KNO 3 ) and oil of vitriol (sulphuric acid, H 2 SO 4 ) via Glauber's process:
The residue was dissolved in hot water, filtered, and evaporated to a cuticle. It was then left to crystallise. It was used as a diuretic and sudorific . [ 6 ]
According to Chambers's Cyclopedia , the recipe was purchased for five hundred thalers by Charles Frederick, Duke of Holstein-Gottorp . Schroder, the duke's physician, wrote wonders of its great uses in hypochondriacal cases, continued and intermitting fevers , stone, scurvy , and more. [ 6 ]
The mineral form of potassium sulfate, arcanite , is relatively rare. Natural resources of potassium sulfate are minerals abundant in the Stassfurt salt . These are cocrystallizations of potassium sulfate and sulfates of magnesium , calcium , and sodium .
Relevant minerals are:
The potassium sulfate can be separated from some of these minerals, like kainite, because the corresponding salt is less soluble in water.
Kieserite , MgSO 4 ·H 2 O, can be combined with a solution of potassium chloride to produce potassium sulfate.
Approximately 1.5 million tons were produced in 1985, typically by the reaction of potassium chloride with sulfuric acid , analogous to the Mannheim process for producing sodium sulfate. [ 7 ] The process involves intermediate formation of potassium bisulfate , an exothermic reaction that occurs at room temperature:
The second step of the process is endothermic, requiring energy input:
Two crystalline forms are known. Orthorhombic β-K 2 SO 4 is the common form, but it converts to α-K 2 SO 4 above 583 °C. [ 7 ] These structures are complex, although the sulfate adopts the typical tetrahedral geometry. [ 8 ]
It does not form a hydrate, unlike sodium sulfate . The salt crystallizes as double six-sided pyramids, classified as rhombic. They are transparent, very hard and have a bitter, salty taste. The salt is soluble in water, but insoluble in solutions of potassium hydroxide ( sp. gr. 1.35), or in absolute ethanol .
The dominant use of potassium sulfate is as a fertilizer . K 2 SO 4 does not contain chloride, which can be harmful to some crops. Potassium sulfate is preferred for these crops, which include tobacco and some fruits and vegetables. Crops that are less sensitive may still require potassium sulfate for optimal growth if the soil accumulates chloride from irrigation water. [ 9 ]
The crude salt is also used occasionally in the manufacture of glass. Potassium sulfate is also used as a flash reducer in artillery propellant charges. It reduces muzzle flash , flareback and blast overpressure.
It is sometimes used as an alternative blast media similar to soda in soda blasting as it is harder and similarly water-soluble. [ 10 ]
Potassium sulfate can also be used in pyrotechnics in combination with potassium nitrate to generate a purple flame .
A 5% solution of potassium sulfate was used in the beginning of the 20th century as a topical mosquito repellent. [ citation needed ]
Potassium hydrogen sulfate (also known as potassium bisulfate), KHSO 4 , is readily produced by reacting K 2 SO 4 with sulfuric acid . It forms rhombic pyramids , which melt at 197 °C (387 °F). It dissolves in three parts of water at 0 °C (32 °F). The solution behaves much as if its two congeners , K 2 SO 4 and H 2 SO 4 , were present side by side of each other uncombined; an excess of ethanol the precipitates normal sulfate (with little bisulfate) with excess acid remaining.
The behavior of the fused dry salt is similar when heated to several hundred degrees; it acts on silicates , titanates , etc., the same way as sulfuric acid that is heated beyond its natural boiling point does. Hence it is frequently used in analytical chemistry as a disintegrating agent. For information about other salts that contain sulfate, see sulfate . | https://en.wikipedia.org/wiki/K2SO4 |
Potassium selenide ( K 2 Se ) is an inorganic compound formed from selenium and potassium .
It can be produced by the reaction of selenium and potassium . If the two are combined in liquid ammonia , the purity is higher.
Potassium selenide has a cubic, antifluorite crystal structure .
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K2Se |
Potassium telluride is an inorganic compound with a chemical formula K 2 Te. It is formed from potassium and tellurium , making it a telluride . [ 2 ] Potassium telluride is a white powder. Like rubidium telluride and caesium telluride , it can be used as an ultraviolet detector in space. Its crystal structure is similar to other tellurides , which have an anti - fluorite structure.
Tellurium will react with melting potassium cyanide (KCN) producing potassium telluride. It can also be produced by direct combination of potassium and tellurium, usually in liquid ammonia solvent: [ 3 ]
Adding potassium telluride to water and letting the filtrate stand in air leads to an oxidation reaction that generates potassium hydroxide (KOH) and elemental tellurium: [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/K2Te |
Potassium ferrioxalate, also called potassium trisoxalatoferrate or potassium tris(oxalato)ferrate(III) [ 3 ] is a chemical compound with the formula K 3 [ Fe ( C 2 O 4 ) 3 ] . It often occurs as the trihydrate K 3 [Fe(C 2 O 4 ) 3 ]·3H 2 O . Both are crystalline compounds, lime green in colour. [ 4 ]
The compound is a salt consisting of ferrioxalate anions , [Fe(C 2 O 4 ) 3 ] 3− , and potassium cations K + . The anion is a transition metal oxalate complex consisting of an iron atom in the +3 oxidation state and three bidentate oxalate C 2 O 2− 4 ligands . Potassium is a counterion , balancing the −3 charge of the complex. In solution, the salt dissociates to give the ferrioxalate anion, [Fe(C 2 O 4 ) 3 ] 3− , which appears fluorescent green in color. The salt is available in anhydrous form [ 3 ] as well as a trihydrate . [ 5 ]
The ferrioxalate anion is quite stable in the dark, but it is decomposed by light and high-energy electromagnetic radiation .
The complex can be synthesized by the reaction between iron(III) sulfate , barium oxalate and potassium oxalate : [ 4 ]
As can be read in the reference above, iron(III) sulfate, barium oxalate and potassium oxalate are combined in water and digested for several hours on a steam bath. Oxalate ions from barium oxalate will then replace the sulfate ions in solution, removing them as BaSO 4 which can then be filtered and the pure material can be crystallized.
The structures of the trihydrate and of the anhydrous salt have been extensively studied. [ 5 ] which indicates that the Fe(III) is high spin ; as the low spin complex would display Jahn–Teller distortions . The ammonium and mixed sodium-potassium salts are isomorphous , as are related complexes with Al 3+ , Cr 3+ , and V 3+ .
The ferrioxalate complex displays helical chirality as it can form two non-superimposable geometries. In accordance with the IUPAC convention, the isomer with the left-handed screw axis is assigned the Greek symbol Λ (lambda). Its mirror image with the right-handed screw axis is given the Greek symbol Δ (delta). [ 6 ]
The ferrioxalate anion is sensitive to light and to high-energy electromagnetic radiation, including X-rays and gamma rays . Absorption of a photon causes the decomposition of one oxalate ion to carbon dioxide CO 2 and reduction of the iron(III) atom to iron(II). [ 7 ] This photo-sensitive property is used for chemical actinometry , the measure of luminous flux, and for preparation of blueprints . This light-catalyzed redox reaction once formed the basis of some photographic processes. However due to their insensitivity and ready availability of advanced digital photography, these processes are obsolete.
The trihydrate loses the three water molecules at 113 °C. [ 1 ]
At 296 °C, the anhydrous salt decomposes into the iron(II) complex potassium ferrioxalate, potassium oxalate, and carbon dioxide : [ 1 ]
The discovery of the efficient photolysis of the ferrioxalate anion was a landmark for chemical photochemistry and actinometry . The potassium salt was found to be over 1000 times more sensitive than uranyl oxalate , the compound previously used for these purposes. [ 7 ] [ 8 ]
The synthesis and thermal decomposition of potassium ferrioxalate is a popular exercise for high school, college or undergraduate university students, since it involves the chemistry of transition metal complexes, visually observable photochemistry, and thermogravimetry . [ 9 ]
Before the ready availability of wide ink-jet and laser printers , large-size engineering drawings were commonly reproduced by the cyanotype method.
That was a simple contact-based photographic process that produced a "negative" white-on-blue copy of the original drawing—a blueprint . The process is based on the photolysis of an iron(III) complex which gets converted into an insoluble iron(II) version in areas of the paper that were exposed to light.
The complex used in cyanotype is mainly ammonium ferric citrate , but potassium ferrioxalate is also used. [ 10 ] [ 11 ]
A number of other iron oxalates are known:
See transition metal oxalate complex . | https://en.wikipedia.org/wiki/K3(Fe(C2O4)3) |
Potassium hypomanganate is the inorganic compound with the formula K 3 MnO 4 . Also known as potassium manganate(V) , this bright blue solid is a rare example of a salt with the hypomanganate or manganate(V) anion, where the manganese atom is in the +5 oxidation state. It is an intermediate in the production of potassium permanganate and the industrially most important Mn(V) compound. [ 2 ]
Potassium hypomanganate is oxidized in water to potassium manganate : [ 3 ]
However, it undergoes disproportionation in acidic solutions producing manganese dioxide and potassium permanganate. [ 3 ]
In the absence of moisture, it is stable up to 900 °C. Above that temperature, it decomposes to potassium oxide , manganese(II,III) oxide , and oxygen. [ 4 ]
The solid salt can be produced by the reaction of potassium carbonate and manganese carbonate in the presence of oxygen at 800 °C. [ 3 ] However, in the industrial process of producing potassium permanganate, it is produced by fusing manganese dioxide and potassium hydroxide . The resulting hypomanganate further reacts with water to produce manganate. [ 2 ]
A solution of potassium hypomanganate is produced:
The compound is unstable due to the tendency of the hypomanganate anion to disproportionate in all but the most alkaline solutions. [ 5 ] [ 6 ] | https://en.wikipedia.org/wiki/K3MnO4 |
Potassium nitride is an unstable chemical compound. Several syntheses were erroneously claimed in the 19th century, and by 1894 it was assumed that it did not exist. [ 2 ]
However, a synthesis of this compound was claimed in 2004. It is observed to have the anti- TiI 3 structure below 233 K (−40 °C; −40 °F), although a Li 3 P -type structure should be more stable. Above this temperature, it converts to an orthorhombic phase. This compound was produced by the reaction of potassium metal and liquid nitrogen at 77 K (−196.2 °C; −321.1 °F) under vacuum: [ 1 ]
This compound decomposes back into potassium and nitrogen at room temperature.
This compound is unstable due to steric hindrance .
This article about chemical compounds is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K3N |
Orthonitrate is a tetrahedral anion of nitrogen with the formula NO 3− 4 . It was first identified in 1977 [ 1 ] and is currently known in only two compounds, sodium orthonitrate (Na 3 NO 4 ) and potassium orthonitrate (K 3 NO 4 ). The corresponding oxoacid, orthonitric acid (H 3 NO 4 ), is hypothetical and has never been observed. Sodium and potassium orthonitrate can be prepared by fusion of the nitrate and metal oxide under high temperatures [ 2 ] and ideally high pressures (several GPa ). [ 3 ]
The resulting orthonitrates are white solids which are extremely sensitive to moisture and CO 2 , decomposing within minutes to hydroxides, carbonates, and nitrates upon exposure to air. [ 1 ]
The orthonitrate ion is tetrahedral with N–O bond lengths of 139 pm, which is unexpectedly short, indicating that polar interactions are shortening the bond. [ 4 ] This short bond length parallels that of hypervalent oxyanions containing third-row elements like PO 3− 4 and SO 2− 4 , for which pπ–dπ bonding was previously proposed as the explanation for the short bond length. Since 3d orbitals of nitrogen are much too high in energy to be involved in the case of orthonitrate, the shortness of the N–O bond in orthonitrate indicates that pπ–dπ bonding is likely not the most important explanation for the bond lengths of these heavier anions either. [ 2 ] | https://en.wikipedia.org/wiki/K3NO4 |
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/K3O4P |
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/K3PO4 |
Potassium octachlorodimolybdate (systematically named potassium bis(tetrachloromolybdate)( Mo – Mo )(4−) ) is an inorganic compound with the chemical formula K 4 [Mo 2 Cl 8 ] . It is known as a red-coloured, microcrystalline solid. The anion is of historic interest as one of the earliest illustrations of a quadruple bonding . The salt is usually obtained as the pink-coloured dihydrate .
The compound is prepared in two steps from molybdenum hexacarbonyl : [ 1 ] [ 2 ]
The reaction of the acetate with HCl was first described as providing trimolybdenum compounds, [ 3 ] but subsequent crystallographic analysis confirmed that the salt contains the [Cl 4 Mo≣MoCl 4 ] 4− anion , with D 4h symmetry, in which the two Mo atoms are linked by a quadruple bond. Each Mo atom is bounded with four Cl − ligands by a single bond . Each MoCl 4 group is a regular square pyramid , with an Mo atom at the apex , and four Cl atoms at the vertices of the square base of the pyramid . The Mo–Mo distance is 214 pm. [ 4 ] | https://en.wikipedia.org/wiki/K4Mo2Cl8 |
The K5 Plan ( Khmer : ផែនការក៥ ), K5 Belt or K5 Project , also known as the Bamboo Curtain , [ 1 ] was an attempt between 1985 and 1989 by the government of the People's Republic of Kampuchea to seal Khmer Rouge guerrilla infiltration routes into Cambodia by means of trenches, wire fences, and minefields along virtually the entire Cambodia–Thailand border . [ 2 ]
After the defeat of Democratic Kampuchea in 1979, the Khmer Rouge fled Cambodia quickly. Protected by the Thai state, and with powerful foreign connections, Pol Pot 's virtually intact militia of about 30,000 to 35,000 troops regrouped and reorganized in forested and mountainous zones behind the Thai-Cambodian border. During the early 1980s Khmer Rouge forces showed their strength in Thailand , inside the refugee camps near the border, and were able to receive a steady and abundant supply of military equipment. The weapons came mainly from China and the US and were channeled across Thailand with the cooperation of the Royal Thai Armed Forces . [ 3 ]
From their position of security in hidden military outposts along the Thai border, the Khmer Rouge militias launched a relentless military campaign against the newly established People's Republic of Kampuchea state. Even though the Khmer Rouge was dominant, it fought against the Kampuchean People's Revolutionary Armed Forces (KPRAF) and Vietnam People's Army along with minor non-communist armed factions which had formerly been fighting against the Khmer Rouge between 1975 and 1979. [ citation needed ]
The border war followed a wet season / dry season rhythm. Generally, the heavily armed Vietnamese forces conducted offensive operations during the dry seasons, and the Chinese-backed Khmer Rouge held the initiative during the rainy seasons. In 1982, Vietnam launched a largely unsuccessful offensive against the main Khmer Rouge base at Phnom Malai in the Cardamom Mountains . [ citation needed ]
The major consequence of the border civil war was that the PRK was hampered in its efforts to rebuild the much-damaged nation and consolidate its administration. The new republic's rule was tenuous in the border areas owing to persistent sabotage by the Khmer Rouge of the provincial administrative system through constant guerrilla warfare. [ 2 ]
The architect of the K5 plan was Vietnamese general Lê Đức Anh , commander of the PAVN forces in Cambodia. He formulated five key points for the defence of Cambodia against Khmer Rouge re-infiltration. Letter "K", the first letter of the Khmer alphabet , came from kar karpier , meaning 'defence' in the Khmer language , and number "5" referred to Le Duc Anh's five points in his plan of defence, of which the sealing of the border with Thailand was the second point. [ 2 ] Many workers on the project, however, did not know what "K5" stood for. [ 4 ]
The K5 Plan began on 19 July 1984. [ 5 ] It became a gigantic effort that included clearing long patches of tropical forest by felling a great number of trees, as well as slashing and uprooting tall vegetation.
The purpose was to leave a continuous broad open space all along the Thai border that would be watched and mined. [ citation needed ]
In practice the K5 fence consisted of a roughly 700 km-long, 500 m-wide swath of land along the border with Thailand, where antitank and antipersonnel mines were buried to a density of about 3,000 mines per kilometre of frontage. [ 6 ]
From the environmental viewpoint the massive felling of trees was an ecological disaster , contributing to acute deforestation , the endangerment of species, and leaving behind a vast degraded area . The more remote places, like the Cardamom Mountains had been relatively untouched by man until they became a stronghold of the Khmer Rouge in the 1980s. Presently these mountains are an endangered ecoregion . [ citation needed ]
Unforeseen by the planners of the project, from the military point of view the K5 Plan was also disastrous for the PRK. It did not deter the Khmer Rouge fighters who found ways to cross it, for it was impossible to effectively police the long border. Besides, maintenance was difficult, as the razed jungle left a scruffy undergrowth that, in the tropical climate, would grow again yearly to about a man's height. [ 7 ]
The K5 Plan was counterproductive for the image of the PRK, as a republic bent on reconstructing what the rule of Pol Pot and his Communist Party of Kampuchea had destroyed in Cambodia. Despite the magnitude of the effort, the whole project was ultimately unsuccessful and ended up playing into the hands of the enemies of the new pro- Hanoi republic. Thousands of Cambodian peasants, who despite the Vietnamese invasion had welcomed their release from the Khmer Rouge's interference in traditional farming and the absence of taxes under the PRK government, [ 2 ] became disgruntled.
They were angry at having to abandon their farms in order to dedicate time to clear the jungle, heavy toil they perceived as useless and unfruitful. [ 7 ] Their resentment grew in time as they perceived the forced labor to be, albeit without the killings, very similar to what they had experienced under the Khmer Rouge. [ 8 ] Owing to unsanitary conditions and the abundance of mosquitoes in areas of difficult access, badly fed and badly lodged workers on the K5 project fell victim to malaria and exhaustion. [ 9 ]
Many of the mines remain to this day, making the vast area dangerous. The K5 zone became part of the great landmine problem in Cambodia after the end of the civil war. In 1990 alone, the number of Cambodians that had a leg or foot amputated as a result of an injury caused by a land mine reached around 6,000. [ 10 ] | https://en.wikipedia.org/wiki/K5_Plan |
The KALQ keyboard (dubbed after the order the keys appear in the keyboard, analogous to QWERTY ) is a keyboard layout that has been developed by researchers at the Montana Tech , University of St Andrews and the Max Planck Institute for Informatics as a split-screen keyboard for thumb-typing, which is claimed to allow a 34% increase in speed of typing for the people who use touchscreen . KALQ was released as a free app, albeit a beta, for Android -based smartphones . [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] Although the KALQ project received some buzz in tech media, as of early 2017, the latest public version is dated October 2013, and still labelled a beta.
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KALQ_keyboard |
In information security , a KARMA attack is an attack that exploits a behaviour of some Wi-Fi devices, combined with the lack of access point authentication in numerous WiFi protocols. It is a variant of the evil twin attack. [ 1 ] Details of the attack were first published in 2004 by Dino dai Zovi and Shane Macaulay. [ 2 ]
Vulnerable client devices broadcast a "preferred network list" (PNL), which contains the SSIDs of access points to which they have previously connected and are willing to automatically reconnect without user intervention. [ 3 ] [ 1 ] These broadcasts are not encrypted and hence may be received by any WiFi access point in range. [ 4 ] [ 5 ] The KARMA attack consists in an access point receiving this list and then giving itself an SSID from the PNL, [ 3 ] [ 6 ] thus becoming an evil twin of an access point already trusted by the client. [ 1 ]
Once that has been done, if the client receives the malicious access point's signal more strongly than that of the genuine access point (for example, if the genuine access point is nowhere nearby), and if the client does not attempt to authenticate the access point, then the attack should succeed. If the attack succeeds, then the malicious access point becomes a man in the middle (MITM), which positions it to deploy other attacks against the victim device. [ 4 ]
What distinguishes KARMA from a plain evil twin attack is the use of the PNL, which allows the attacker to know, rather than simply to guess, which SSIDs (if any) the client will automatically attempt to connect to. [ 1 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KARMA_attack |
Potassium aluminium fluoride ( PAF , chemical formula KAlF 4 ) is an inorganic compound .
This compound is used as flux in the smelting of secondary aluminium, to reduce or remove the magnesium content of the melt. The main environmental issue that arises from using PAF is the production of fluoride gases. Calcium hydroxide is widely used to suppress the fluorides produced but in most cases fails to remove it sufficiently.
PAF is also present in a wide range of products for the metals industry as a fluxing agent within additives to help its dispersion within a charge.
It is also used as an insecticide. [ 1 ]
A single natural occurrence has been reported at a burning coal bank at Forestville, Pennsylvania , as an unnamed mineral. [ 2 ] | https://en.wikipedia.org/wiki/KAlF4 |
The KBD algorithm is a cluster update algorithm designed for the fully frustrated Ising model in two dimensions, [ 1 ] or more generally any two dimensional spin glass with frustrated plaquettes arranged in a checkered pattern . [ 2 ] It is discovered in 1990 by Daniel Kandel, Radel Ben-Av, and Eytan Domany, and generalized by P. D. Coddington and L. Han in 1994. [ 3 ] It is the inspiration for cluster algorithms used in quantum monte carlo simulations.
The SW algorithm is the first non-local algorithm designed for efficient simulation of ferromagnetic spin models . [ 4 ] However, it is soon realized that the efficiency of the algorithm cannot be extended to frustrated systems , due to an overly large correlation length of the generated clusters with respect to the underlying spin system. [ 5 ] The KBD algorithm is an attempt to extend the bond-formation rule to the plaquettes of the lattice, such that the generated clusters are informed by the frustration profile, resulting in them being smaller than the SW ones, [ 3 ] thereby making the algorithm more efficient in comparison. However, at the current stage, it is not known whether this algorithm can be generalized for arbitrary spin glass models.
We begin by decomposing the square lattice down into plaquettes arranged in a checkered pattern (such that the plaquettes only overlap vertex-wise but not edge-wise). Since the spin model is fully-frustrated, each plaquette must contain exactly one or three negative interactions. [ 1 ] If the plaquette contains three negative interactions, then no bonds can be formed. However, if the plaquette contains one negative interaction, then two parallel bonds can be formed (perpendicular to the negative edge) with probability p = 1 − e − 4 β {\displaystyle p=1-e^{-4\beta }} , where β {\displaystyle \beta } is the inverse temperature of the spin model.
The bonds will then form clusters on the lattice, on which the spins can be collectively flipped (either with the SW rule or the Wolff rule ). It can be shown that the update satisfies detailed balance , meaning that correctness is guaranteed if the algorithm is used in conjunction with ergodic algorithms like single spin-flip updates .
At zero temperature, or the β → ∞ {\displaystyle \beta \to \infty } limit, all the plaquettes will contain exactly one negative edge. In this case, on each checkered plaquette, the KBD algorithm will always open two parallel bonds perpendicular to the negative edge, meaning that the bond will be closed on the negative edge along with the edge opposite to it. If we were to track the closed bonds in the dual lattice , by drawing a straight/bent line inside each plaquette such that it intersects with the closed bonds, then it can be shown that a path following the lines must form a cycle .
Furthermore, it can be shown that there must be at least two such cycles, and that the cycles cannot intersect. Most importantly, each cycle cannot be contracted to a point in the underlying surface that the lattice is embedded in. [ 6 ] On a periodic lattice (or a torus ), this means that the cycles of closed bonds must wind around the torus in the same direction, from which one can show that the largest cluster (which must be "squeezed" between these cycles) at zero temperature cannot span a finite fraction of the lattice size in the thermodynamic limit . | https://en.wikipedia.org/wiki/KBD_algorithm |
Potassium bromide ( K Br ) is a salt , widely used as an anticonvulsant and a sedative in the late 19th and early 20th centuries, with over-the-counter use extending to 1975 in the US. Its action is due to the bromide ion ( sodium bromide is equally effective). Potassium bromide is used as a veterinary drug, in antiepileptic medication for dogs.
Under standard conditions, potassium bromide is a white crystalline powder. It is freely soluble in water; it is not soluble in acetonitrile . In a dilute aqueous solution, potassium bromide tastes sweet, at higher concentrations it tastes bitter, and tastes salty when the concentration is even higher. These effects are mainly due to the properties of the potassium ion—sodium bromide tastes salty at any concentration. In high concentration, potassium bromide strongly irritates the gastric mucous membrane, causing nausea and sometimes vomiting (a typical effect of all soluble potassium salts). [ citation needed ]
Potassium bromide, a typical ionic salt , is fully dissociated and near pH 7 in aqueous solution. It serves as a source of bromide ions. This reaction is important for the manufacture of silver bromide for photographic film :
Aqueous bromide Br − also forms complexes when reacted with some metal halides such as copper(II) bromide :
A traditional method for the manufacture of KBr is the reaction of potassium carbonate with an iron( III , II ) bromide, Fe 3 Br 8 , made by treating scrap iron under water with excess bromine : [ 4 ]
The anticonvulsant properties of potassium bromide were first noted by Sir Charles Locock at a meeting of the Royal Medical and Chirurgical Society in 1857. Bromide can be regarded as the first effective medication for epilepsy . At the time, it was commonly thought that epilepsy was caused by masturbation. [ 6 ] Locock noted that bromide calmed sexual excitement and thought this was responsible for his success in treating seizures. In the latter half of the 19th century, potassium bromide was used for the calming of seizure and nervous disorders on an enormous scale, with the use by single hospitals being as much as several tons a year (the dose for a given person being a few grams per day). [ 6 ] By the beginning of the 20th century the generic word had become so widely associated with being sedate that bromide came to mean a dull, sedate person or a boring platitude uttered by such a person. [ 7 ]
There was not a better epilepsy drug until phenobarbital in 1912. The British Army has historically been claimed to lace soldiers' tea with bromide to quell sexual arousal and in the Victorian era prisoners in England were compulsorily dosed with the chemical. [ 8 ] [ 9 ]
Bromide compounds, especially sodium bromide , remained in over-the-counter sedatives and headache remedies (such as the original formulation of Bromo-Seltzer ) in the US until 1975, when bromides were outlawed in all over-the-counter medicines, due to chronic toxicity. [ 10 ] Bromide's exceedingly long half life in the body made it difficult to dose without side effects. Medical use of bromides for humans in the US was discontinued at this time, as many better and shorter-acting sedatives were known by then.
Potassium bromide is still used in veterinary medicine to treat epilepsy in dogs , either as first-line treatment or in addition to phenobarbital, when seizures are not adequately controlled with phenobarbital alone. [ 5 ] Use of bromide in cats is limited because it carries a substantial risk of causing lung inflammation (pneumonitis) in them. Why bromides should cause such inflammation in cats, but not in dogs is not clear. [ 11 ]
The use of bromide as a treatment drug for animals means that veterinary medical diagnostic laboratories are able as a matter of routine to measure serum levels of bromide on order of a veterinarian, whereas human medical diagnostic labs in the US do not measure bromide as a routine test.
Potassium bromide is not approved by the US Food and Drug Administration (FDA) for use in humans to control seizures. In Germany, it is still approved as an antiepileptic drug for humans, particularly children and adolescents. [ 12 ] These indications include severe forms of generalized tonic-clonic seizures, early-childhood-related tonic–clonic seizures, and also severe myoclonic seizures during childhood. Adults who have reacted positively to the drug during childhood/adolescence may continue treatment. Potassium bromide tablets are sold under the brand name Dibro-Be mono (Rx-only). The drug has almost complete bioavailability, but the bromide ion has a relatively long half life of 12 days in the blood, [ 6 ] making bromide salts difficult to adjust and dose. Bromide is not known to interfere with the absorption or excretion of any other anticonvulsant, though it does have strong interactions with chloride in the body, the normal body uptake and excretion of which strongly influences bromide's excretion. [ 6 ]
The therapeutic index (ratio of effectiveness to toxicity) for bromide is small. As with other antiepileptics, sometimes even therapeutic doses (3 to 5 grams per day, taking 6 to 8 weeks to reach stable levels) may give rise to intoxication. Often indistinguishable from 'expected' side-effects, these include:
Potassium bromide is transparent from the near ultraviolet to long-wave infrared wavelengths (0.25-25 μm) and has no significant optical absorption lines in its high transmission region.
It is used widely as infrared optical windows and components for general spectroscopy because of its wide spectral range. In infrared spectroscopy , samples are analyzed by grinding with powdered potassium bromide and pressing into a disc. Alternatively, samples may be analyzed as a liquid film (neat, as a solution, or in a mull with Nujol ) between two polished potassium bromide discs. [ 13 ]
Due to its high solubility and hygroscopic nature it must be kept in a dry environment. The refractive index is about 1.55 at 1.0 μm.
In addition to manufacture of silver bromide, potassium bromide is used as a restrainer in black and white developer formulas. It improves differentiation between exposed and unexposed crystals of silver halide, and thus reduces fog. [ 14 ] | https://en.wikipedia.org/wiki/KBr |
Potassium bromate ( KBrO 3 ) is a bromate of potassium and takes the form of white crystals or powder. It is a strong oxidizing agent.
Potassium bromate is produced when bromine is passed through a hot solution of potassium hydroxide . This first forms unstable potassium hypobromite , which quickly disproportionates into bromide and bromate: [ 3 ]
Electrolysis of potassium bromide solutions will also give bromate. Both processes are analogous to those used in the production of chlorates . [ citation needed ]
Potassium bromate is readily separated from the potassium bromide present in both methods owing to its much lower solubility; when a solution containing potassium bromate and bromide is cooled to 0°C, nearly all bromate will precipitate, while nearly all of the bromide will stay in solution. [ 3 ]
As established by X-ray crystallography , the O-Br-O angles are 104.5°, consistent with its pyramidal shape of the anion. The Br-O distances are 1.66 Å. [ 1 ]
Potassium bromate is typically used in the United States as a flour improver ( E number E924). It acts to strengthen the dough and to allow higher rising. It is an oxidizing agent , and under the right conditions, is reduced to bromide in the baking process. [ 4 ] [ 5 ] However, if too much is added, or if the bread is under-baked long or baked at a low enough temperature, then a residual amount remains, which may be harmful if consumed. [ 5 ]
Potassium bromate may be used in the production of malt barley, but under safety conditions prescribed by the U.S. Food and Drug Administration (FDA), including labeling standards for the finished product. [ 6 ] It is a powerful oxidizer ( electrode potential E ⊖ {\displaystyle E^{\ominus }} = 1.5 volts, similar to potassium permanganate ). [ citation needed ]
Potassium bromate is classified as a category 2B carcinogen by the IARC . [ 7 ] The FDA allowed the use of bromate before the Delaney clause of the Food, Drug, and Cosmetic Act – which bans potentially carcinogenic substances – went into effect in 1958. Since 1991, the FDA has urged bakers to not use it, but has not mandated a ban.
Japanese baked goods manufacturers stopped using potassium bromate voluntarily in 1980; however, Yamazaki Baking resumed its use in 2005, claiming it had new production methods to reduce the amount of the chemical which remained in the final product. [ 8 ]
Potassium bromate is banned from food products in the European Union, Argentina, Brazil, [ 9 ] Canada, Nigeria, South Korea, and Peru. It was banned in Sri Lanka in 2001, [ 10 ] China in 2005, [ 11 ] and India in 2016, [ 12 ] but it is allowed in most of the United States. As of May 2023, the U.S. state of New York is considering banning the use of potassium bromate. [ 13 ]
In California , a warning label is required when bromated flour is used. [ 14 ] In October 2023, California enacted a law that banned the manufacture, sale, and distribution of potassium bromate (along with three other additives: brominated vegetable oil , propylparaben , and Red 3 ). The law takes effect in 2027. It was the first U.S. state to ban it. [ 15 ] [ 16 ] [ 17 ] | https://en.wikipedia.org/wiki/KBrO3 |
Potassium bitartrate , also known as potassium hydrogen tartrate , with formula K C 4 H 5 O 6 , is a chemical compound with a number of uses. It is the potassium acid salt of tartaric acid (a carboxylic acid ). Especially in cooking, it is also known as cream of tartar .
It is used as a component of baking powders and baking mixes, as mordant in textile dyeing, as reducer of chromium trioxide in mordants for wool, as a metal processing agent that prevents oxidation, as an intermediate for other potassium tartrates , as a cleaning agent when mixed with a weak acid such as vinegar , and as reference standard pH buffer . Medical uses include as a cathartic , as a diuretic, and as a veterinary laxative and diuretic. [ 1 ]
It is produced as a byproduct of winemaking by purifying the precipitate that is deposited in wine barrels. It arises from the tartaric acid and potassium naturally occurring in grapes.
In culinary applications, potassium bitartrate is valued for its role in stabilizing egg whites, which enhances the volume and texture of meringues and soufflés . Its acidic properties prevent sugar syrups from crystallizing, aiding in the production of smooth confections such as candies and frostings. When combined with sodium bicarbonate , it acts as a leavening agent , producing carbon dioxide gas that helps baked goods rise. Additionally, potassium bitartrate is used to stabilize whipped cream , allowing it to retain its shape for longer periods.
Potassium bitartrate was first characterized by Swedish chemist Carl Wilhelm Scheele (1742–1786). [ 2 ] This was a result of Scheele's work studying fluorite and hydrofluoric acid . [ 3 ]
Scheele may have been the first scientist to publish work on potassium bitartrate, but use of potassium bitartrate has been reported to date back 7000 years to an ancient village in northern Iran. [ 4 ] Modern applications of cream of tartar started in 1768 after it gained popularity when the French started using it regularly in their cuisine. [ 4 ]
In 2021, a connection between potassium bitartrate and canine and feline toxicity of grapes was first proposed. [ 5 ] Since then, it has been deemed likely as the source of grape and raisin toxicity to pets. [ 6 ]
Potassium bitartrate is naturally formed in grapes from the acid dissociation of tartaric acid into bitartrate and tartrate ions. [ 7 ]
Potassium bitartrate has a low solubility in water. It crystallizes in wine casks during the fermentation of grape juice , and can precipitate out of wine in bottles. The rate of potassium bitartrate precipitation depends on the rates of nuclei formation and crystal growth , which varies based on a wine's alcohol, sugar, and extract content. [ 8 ] The crystals ( wine diamonds ) will often form on the underside of a cork in wine-filled bottles that have been stored at temperatures below 10 °C (50 °F), and will seldom, if ever, dissolve naturally into the wine. Over time, crystal formation is less likely to occur due to the decreasing supersaturation of potassium bitartrate, with the greatest amount of precipitation occurring in the initial few days of cooling. [ 8 ]
Historically, it was known as beeswing for its resemblance to the sheen of bees' wings. It was collected and purified to produce the white, odorless, acidic powder used for many culinary and other household purposes.
These crystals also precipitate out of fresh grape juice that has been chilled or allowed to stand for some time. [ 9 ] To prevent crystals from forming in homemade grape jam or jelly , the prerequisite fresh grape juice should be chilled overnight to promote crystallization. The potassium bitartrate crystals are removed by filtering through two layers of cheesecloth . The filtered juice may then be made into jam or jelly. [ 10 ] In some cases they adhere to the side of the chilled container, making filtering unnecessary.
The presence of crystals is less prevalent in red wines than in white wines. This is because red wines have a higher amount of tannin and colouring matter present as well as a higher sugar and extract content than white wines. [ 8 ] Various methods such as promoting crystallization and filtering, removing the active species required for potassium bitartrate precipitation, and adding additives have been implemented to reduce the presence of potassium bitartrate crystals in wine. [ 7 ]
In food, potassium bitartrate is used for:
Additionally, it is used as a component of:
A similar acid salt, sodium acid pyrophosphate , can be confused with cream of tartar because of its common function as a component of baking powder.
Adding cream of tartar to egg whites gives volume to cakes, and makes them more tender. [ 16 ] As cream of tartar is added, the pH decreases to around the isoelectric point of the foaming proteins in egg whites. Foaming properties of egg whites are optimal at this pH due to increased protein-protein interactions. [ 17 ] The low pH also results in a whiter crumb in cakes due to flour pigments that respond to these pH changes. [ 16 ] However, adding too much cream of tartar (>2.4% weight of egg white) can affect the texture and taste of cakes. [ 16 ] The optimal cream of tartar concentration to increase volume and the whiteness of interior crumbs without making the cake too tender, is about 1/4 tsp per egg white. [ 16 ]
As an acid, cream of tartar with heat reduces sugar crystallization in invert syrups by helping to break down sucrose into its monomer components - fructose and glucose in equal parts. [ 18 ] Preventing the formation of sugar crystals makes the syrup have a non-grainy texture, shinier and less prone to break and dry. However, a downside of relying on cream of tartar to thin out crystalline sugar confections (like fudge) is that it can be hard to add the right amount of acid to get the desired consistency.
Cream of tartar is used as a type of acid salt that is crucial in baking powder . [ 18 ] Upon dissolving in batter or dough, the tartaric acid that is released reacts with baking soda to form carbon dioxide that is used for leavening . Since cream of tartar is fast-acting, it releases over 70 percent of carbon dioxide gas during mixing.
Potassium bitartrate can be mixed with an acidic liquid, such as lemon juice or white vinegar, to make a paste-like cleaning agent for metals, such as brass , aluminium , or copper , or with water for other cleaning applications, such as removing light stains from porcelain . [ 19 ] This mixture is sometimes mistakenly made with vinegar and sodium bicarbonate (baking soda), which actually react to neutralize each other, creating carbon dioxide and a sodium acetate solution.
Cream of tartar was often used in traditional dyeing where the complexing action of the tartrate ions was used to adjust the solubility and hydrolysis of mordant salts such as tin chloride and alum .
Cream of tartar, when mixed into a paste with hydrogen peroxide , can be used to clean rust from some hand tools , notably hand files . The paste is applied, left to set for a few hours, and then washed off with a baking soda/water solution. After another rinse with water and thorough drying, a thin application of oil will protect the file from further rusting.
Slowing the set time of plaster of Paris products (most widely used in gypsum plaster wall work and artwork casting) is typically achieved by the simple introduction of almost any acid diluted into the mixing water. A commercial retardant premix additive sold by USG to trade interior plasterers includes at least 40% potassium bitartrate. The remaining ingredients are the same plaster of Paris and quartz -silica aggregate already prominent in the main product. This means that the only active ingredient is the cream of tartar. [ 20 ]
For dyeing hair, potassium bitartrate can be mixed with henna as the mild acid needed to activate the henna.
Cream of tartar has been used internally as a purgative , but this is dangerous because an excess of potassium, or hyperkalemia , may occur. [ 21 ] [ 22 ]
Potassium bitartrate is the United States' National Institute of Standards and Technology 's primary reference standard for a pH buffer . Using an excess of the salt in water, a saturated solution is created with a pH of 3.557 at 25 °C (77 °F). Upon dissolution in water, potassium bitartrate will dissociate into acid tartrate, tartrate, and potassium ions . Thus, a saturated solution creates a buffer with standard pH. Before use as a standard, it is recommended that the solution be filtered or decanted between 22 °C (72 °F) and 28 °C (82 °F). [ 23 ]
Potassium carbonate can be made by burning cream of tartar, which produces " pearl ash ". This process is now obsolete but produced a higher quality (reasonable purity) than " potash " extracted from wood or other plant ashes.
In wine lees, tartaric acid mostly appears as potassium bitartrate (which barely dissolves) and, to a lesser extent, calcium tartrate, all mixed with dead yeast and other solids. Traditionally, you dry and grind the lees, dissolve the potassium bitartrate in hot water (around 70°C), filter out any solids, and then add calcium salts or lime to precipitate it as calcium tartrate. [ 24 ] | https://en.wikipedia.org/wiki/KC4H5O6 |
In quantum foundations , the KCBS pentagram was discovered by Alexander Klyachko , M. Ali Can , Sinem Binicioglu , and Alexander Shumovsky as an example disproving noncontextual hidden variable models .
Let's say we have a pentagram, which is a graph with 5 vertices and 5 edges. Each vertex can be colored either red or blue. An edge is said to match if both of its vertices have the same color. Otherwise, it's a mismatch. In a hidden variable model, the total number of mismatches over all of the edges has to be an even number due to cyclicity, i.e. 0, 2 or 4. So, with a probability mixture over hidden variable assignments, the expectation value of the sum of mismatches over all of the 5 edges has to lie between 0 and 4.
Then, someone hands you a huge number of KCBS pentagrams, but at first, all of the colorings are hidden. You're told you can only uncover 2 vertices at most, and only if they share a common edge. So, for each pentagram, you randomly pick an edge and uncover the colors on its vertices. This random choice is necessary because if the pentagram producers had been able to guess your choice for each pentagram in advance, he could have "conspired" to fool you. You find no matter which edge you choose, you find blue-blue with a probability of 1 − 2 5 {\displaystyle 1-{\frac {2}{\sqrt {5}}}} , red-blue with 1 5 {\displaystyle {\frac {1}{\sqrt {5}}}} , and blue-red with 1 5 {\displaystyle {\frac {1}{\sqrt {5}}}} . So, the expectation value of the sum of mismatches is 2 5 ≈ 4.47 > 4 {\displaystyle 2{\sqrt {5}}\approx 4.47>4} .
How was it done? Each pentagram is a 3D quantum system with an orthonormal basis { | A ⟩ , | B ⟩ , | C ⟩ } {\displaystyle \left\{|A\rangle ,|B\rangle ,|C\rangle \right\}} . Each pentagram is initialized to | C ⟩ {\displaystyle |C\rangle } . Each vertex is assigned a 1D projector projecting to 1 5 | C ⟩ + 1 − 1 5 [ cos ( 4 π n 5 ) | A ⟩ + sin ( 4 π n 5 ) | B ⟩ ] {\displaystyle {\frac {1}{\sqrt {\sqrt {5}}}}|C\rangle +{\sqrt {1-{\frac {1}{\sqrt {5}}}}}\left[\cos \left({\frac {4\pi n}{5}}\right)|A\rangle +\sin \left({\frac {4\pi n}{5}}\right)|B\rangle \right]} , n = 0, ..., 4 .
Adjacent projectors commute. If we project, color the vertex red. Otherwise, color it blue.
This quantum mechanics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KCBS_pentagram |
Potassium chlorate is the inorganic compound with the molecular formula KClO 3 . In its pure form, it is a white solid. After sodium chlorate , it is the second most common chlorate in industrial use. It is a strong oxidizing agent and its most important application is in safety matches . [ 6 ] In other applications it is mostly obsolete and has been replaced by safer alternatives in recent decades. It has been used
On the industrial scale, potassium chlorate is produced by the salt metathesis reaction of sodium chlorate and potassium chloride :
The reaction is driven by the low solubility of potassium chlorate in water. The equilibrium of the reaction is shifted to the right hand side by the continuous precipitation of the product ( Le Chatelier's Principle ). The precursor sodium chlorate is produced industrially in very large quantities by electrolysis of sodium chloride , common table salt. [ 6 ]
The direct electrolysis of KCl in aqueous solution is also used sometimes, in which elemental chlorine formed at the anode reacts with KOH in situ . The low solubility of KClO 3 in water causes the salt to conveniently isolate itself from the reaction mixture by simply precipitating out of solution.
Potassium chlorate can be produced in small amounts by disproportionation in a sodium hypochlorite solution followed by metathesis reaction with potassium chloride: [ 7 ]
It can also be produced by passing chlorine gas into a hot solution of caustic potash: [ 8 ]
According to X-ray crystallography , potassium chlorate is a dense salt-like structure consisting of chlorate and potassium ions in close association.
Potassium chlorate was one key ingredient in early firearms percussion caps (primers). It continues in that application, where not supplanted by potassium perchlorate .
Chlorate-based propellants are more efficient than traditional gunpowder and are less susceptible to damage by water. However, they can be extremely unstable in the presence of sulfur or phosphorus and are much more expensive. Chlorate propellants must be used only in equipment designed for them; failure to follow this precaution is a common source of accidents. Potassium chlorate, often in combination with silver fulminate , is used in trick noise-makers known as "crackers", "snappers", "pop-its", "caps" or "bang-snaps", a popular type of novelty firework.
Another application of potassium chlorate is as the oxidizer in a smoke composition such as that used in smoke grenades . Since 2005, a cartridge with potassium chlorate mixed with lactose and rosin is used for generating the white smoke signaling the election of new pope by a papal conclave . [ 9 ]
High school and college laboratories often use potassium chlorate to generate oxygen gas. [ citation needed ] It is a far cheaper source than a pressurized or cryogenic oxygen tank. Potassium chlorate readily decomposes if heated while in contact with a catalyst , typically manganese(IV) dioxide (MnO 2 ). Thus, it may be simply placed in a test tube and heated over a burner. If the test tube is equipped with a one-holed stopper and hose, warm oxygen can be drawn off. The reaction is as follows:
Heating it in the absence of a catalyst converts it into potassium perchlorate : [ 8 ]
With further heating, potassium perchlorate decomposes to potassium chloride and oxygen:
The safe performance of this reaction requires very pure reagents and careful temperature control. Molten potassium chlorate is an extremely powerful oxidizer and spontaneously reacts with many common materials such as sugar. Explosions have resulted from liquid chlorates spattering into the latex or PVC tubes of oxygen generators and from contact between chlorates and hydrocarbon sealing greases. Impurities in potassium chlorate itself can also cause problems. When working with a new batch of potassium chlorate, it is advisable to take a small sample (~1 gram) and heat it strongly on an open glass plate. Contamination may cause this small quantity to explode, indicating that the chlorate should be discarded.
Potassium chlorate is used in chemical oxygen generators (also called chlorate candles or oxygen candles), employed as oxygen-supply systems of e.g. aircraft, space stations, and submarines, and has been responsible for at least one plane crash . A fire on the space station Mir was traced to oxygen generation candles that use a similar lithium perchlorate. The decomposition of potassium chlorate was also used to provide the oxygen supply for limelights .
Potassium chlorate is used also as a pesticide . In Finland it was sold under trade name Fegabit.
Potassium chlorate can react with sulfuric acid to form a highly reactive solution of chloric acid and potassium sulfate:
The solution so produced is sufficiently reactive that it spontaneously ignites if combustible material (sugar, paper, etc.) is present.
In schools, molten potassium chlorate is used in screaming jelly babies , Gummy bear , Haribo , and Trolli candy demonstration where the candy is dropped into the molten salt.
In chemical labs it is used to oxidize HCl and release small amounts of gaseous chlorine.
Militant groups in Afghanistan also use potassium chlorate extensively as a key component in the production of improvised explosive devices (IEDs). When significant effort was made to reduce the availability of ammonium nitrate fertilizer in Afghanistan, IED makers started using potassium chlorate as a cheap and effective alternative. In 2013, 60% of IEDs in Afghanistan used potassium chlorate, making it the most common ingredient used in IEDs. [ 10 ] Potassium chlorate was also the main ingredient in the car bomb used in the 2002 Bali bombings that killed 202 people.
Potassium chlorate is used to force the blossoming stage of the longan tree, causing it to produce fruit in warmer climates. [ 11 ]
Potassium chlorate should be handled with care. It reacts vigorously, and in some cases spontaneously ignites or explodes, when mixed with many combustible materials. It burns vigorously in combination with virtually any combustible material, even those normally only slightly flammable (including ordinary dust and lint). Mixtures of potassium chlorate and a fuel can ignite by contact with sulfuric acid, so it should be kept away from this reagent. Sulfur should be avoided in pyrotechnic compositions containing potassium chlorate, as these mixtures are prone to spontaneous deflagration . Most sulfur contains trace quantities of sulfur-containing acids, and these can cause spontaneous ignition - "Flowers of sulfur" or "sublimed sulfur", despite the overall high purity, contains significant amounts of sulfur acids. Also, mixtures of potassium chlorate with any compound with ignition promoting properties, such as antimony(III) sulfide , are very dangerous to prepare, as they are extremely shock sensitive. | https://en.wikipedia.org/wiki/KCIO3 |
KCR is a clinical development provider for the biotechnology and pharmaceutical industries. It has three main service areas: Trial Execution, Consulting and Placement.
KCR operates across four main regions: North America, Western Europe, Central Europe, and Eastern Europe , with a main operational hub located in Boston, MA , and other hubs in Berlin , Germany, Warsaw, Poland , Kyiv, Ukraine and Sydney, Australia respectively. KCR employs over 700 staff. [ 1 ]
KCR was established in 1997 as Kiecana Clinical Research. The company provided services for clinical monitoring, clinical project management, safety/ pharmacovigilance , regulatory affairs and quality assurance.
In April 2014, KCR launched KCR Placement, which offers recruitment and outsourcing for pharma and biotech in Europe. [ 2 ] In 2017, KCR opened its headquarters in Boston, US. [ 3 ]
In 2017, KCR, launched an NGO called Human Behind Every Number which provides research, insight and education on the first-hand experiences of patients involved in clinical trials . [ 4 ] In March 2018, KCR and The Story, received an iF Design Award for their work on the NGO's website. [ 5 ] [ 6 ]
As of 2020, KCR employs over 700 life science professionals and offers end-to-end study execution and consulting services in oncology , immunology , CNS and vaccines . [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/KCR_CRO |
Calcium chloride is an inorganic compound , a salt with the chemical formula CaCl 2 . It is a white crystalline solid at room temperature, and it is highly soluble in water. It can be created by neutralising hydrochloric acid with calcium hydroxide .
Calcium chloride is commonly encountered as a hydrated solid with generic formula CaCl 2 · n H 2 O , where n = 0, 1, 2, 4, and 6. These compounds are mainly used for de-icing and dust control. Because the anhydrous salt is hygroscopic and deliquescent , it is used as a desiccant . [ 10 ]
Calcium chloride was apparently discovered in the 15th century but wasn't studied properly until the 18th century. [ 11 ] It was historically called "fixed sal ammoniac " ( Latin : sal ammoniacum fixum [ 12 ] ) because it was synthesized during the distillation of ammonium chloride with lime and was nonvolatile (while the former appeared to sublime ); in more modern times (18th–19th cc.) it was called "muriate of lime" ( Latin : murias calcis, calcaria muriatica [ 12 ] ). [ 13 ]
By depressing the freezing point of water, calcium chloride is used to prevent ice formation and is used to de-ice . This application consumes the greatest amount of calcium chloride. Calcium chloride is relatively harmless to plants and soil. As a de-icing agent, it is much more effective at lower temperatures than sodium chloride . When distributed for this use, it usually takes the form of small, white spheres a few millimeters in diameter, called prills . Solutions of calcium chloride can prevent freezing at temperatures as low as −52 °C (−62 °F), making it ideal for filling agricultural implement tires as a liquid ballast, aiding traction in cold climates. [ 14 ]
It is also used in domestic and industrial chemical air dehumidifiers . [ 15 ]
The second largest application of calcium chloride exploits its hygroscopic nature and the tackiness of its hydrates; calcium chloride is highly hygroscopic and its hydration is an exothermic process . A concentrated solution keeps a liquid layer on the surface of dirt roads , which suppresses the formation of dust. It keeps the finer dust particles on the road, providing a cushioning layer. If these are allowed to blow away, the large aggregate begins to shift around and the road breaks down. Using calcium chloride reduces the need for grading by as much as 50% and the need for fill-in materials as much as 80%. [ 16 ]
In the food industry, calcium chloride is frequently employed as a firming agent in canned vegetables, particularly for canned tomatoes and cucumber pickles. [ 17 ] [ 18 ] [ 19 ] [ 20 ] It is also used in firming soybean curds into tofu and in producing a caviar substitute from vegetable or fruit juices . [ 21 ] [ 22 ] [ 23 ] It is also used to enhance the texture of various other products, such as whole apples, whole hot peppers, whole and sliced strawberries, diced tomatoes, and whole peaches. [ 24 ] [ 25 ]
The firming effect of calcium chloride can be attributed to several mechanisms: [ 24 ]
Calcium chloride's freezing-point depression properties are used to slow the freezing of the caramel in caramel-filled chocolate bars. [ citation needed ] Also, it is frequently added to sliced apples to maintain texture. [ 26 ]
In brewing beer, calcium chloride is sometimes used to correct mineral deficiencies in the brewing water. It affects flavor and chemical reactions during the brewing process, and can also affect yeast function during fermentation. [ 27 ] [ 28 ] [ 29 ] [ 30 ] [ 31 ]
In cheesemaking , calcium chloride is sometimes added to processed (pasteurized/homogenized) milk to restore the natural balance between calcium and protein in casein . It is added before the coagulant. [ 32 ]
Calcium chloride is also commonly used as an " electrolyte " in sports drinks and other beverages; as a food additive used in conjunction with other inorganic salts it adds taste to bottled water . [ 33 ] [ 34 ] [ 35 ]
The average intake of calcium chloride as food additives has been estimated to be 160–345 mg/day. [ 36 ] Calcium chloride is permitted as a food additive in the European Union for use as a sequestrant and firming agent with the E number E509 . [ 37 ] It is considered as generally recognized as safe (GRAS) by the U.S. Food and Drug Administration. [ 38 ] Its use in organic crop production is generally prohibited under the US National Organic Program . [ 39 ]
The elemental calcium content in calcium chloride hexahydrate (CaCl 2 ·6H 2 O) is approximately 18.2%. This means that for every gram of calcium chloride hexahydrate, there are about 182 milligrams of elemental calcium.
For anhydrous calcium chloride (CaCl 2 ), the elemental calcium content is almost twice higher, that is around 36.1% (for every gram of anhydrous calcium chloride there are about 361 milligrams of elemental calcium).
Calcium chloride has a very salty taste and can cause mouth and throat irritation at high concentrations, so it is typically not the first choice for long-term oral supplementation (as a calcium supplement ). [ 40 ] [ 41 ] Calcium chloride, characterized by its low molecular weight and high water solubility, readily breaks down into calcium and chloride ions when exposed to water. These ions are efficiently absorbed from the intestine. [ 42 ] Calcium chloride has the potential to release heat energy upon dissolution in water. This release of heat can lead to trauma and burns in the mouth, throat, esophagus , and stomach. In fact, there have been reported cases of stomach necrosis resulting from burns caused by accidental ingestions of big amounts of undissolved calcium chloride. [ 43 ] [ 44 ]
The extremely salty taste of calcium chloride is used to flavor pickles without increasing the food's sodium content. [ 45 ]
Calcium chloride is used to prevent cork spot and bitter pit on apples by spraying on the tree during the late growing season. [ 46 ]
Drying tubes are frequently packed with calcium chloride. Kelp is dried with calcium chloride for use in producing sodium carbonate . Anhydrous calcium chloride has been approved by the FDA as a packaging aid to ensure dryness (CPG 7117.02). [ 47 ]
The hydrated salt can be dried for re-use but will dissolve in its own water of hydration if heated quickly and form a hard amalgamated solid when cooled.
Similarly, CaCl 2 is used as a flux and electrolyte in the FFC Cambridge electrolysis process for titanium production, where it ensures the proper exchange of calcium and oxygen ions between the electrodes.
Calcium chloride infusions may be used as an intravenous therapy to prevent hypocalcemia . [ 48 ] [ 49 ] [ 50 ] [ 51 ] [ 52 ]
Calcium chloride is a highly soluble calcium salt. Hexahydrate calcium chloride (CaCl 2 ·6H 2 O) has solubility in water of 811 g/L at 25 °C. [ 1 ] Calcium chloride when taken orally completely dissociates into calcium ions (Ca 2+ ) in the gastrointestinal tract, resulting in readily bioavailable calcium. The high concentration of calcium ions facilitates efficient absorption in the small intestine. [ 42 ] [ 53 ] However, the use of calcium chloride as a source of calcium taken orally is less common compared to other calcium salts because of potential adverse effects such as gastrointestinal irritation and discomfort. [ 53 ] [ 54 ] [ 55 ]
When tasted, calcium chloride exhibits a distinctive bitter flavor alongside its salty taste. The bitterness is attributable to the calcium ions and their interaction with human taste receptors: certain members of the TAS2R family of bitter taste receptors respond to calcium ions; the bitter perception of calcium is thought to be a protective mechanism to avoid ingestion of toxic substances, as many poisonous compounds taste bitter. While chloride ions (Cl⁻) primarily contribute to saltiness, at higher concentrations, they can enhance the bitter sensation. The combination of calcium and chloride ions intensifies the overall bitterness. At lower concentrations, calcium chloride may taste predominantly salty. The salty taste arises from the electrolyte nature of the compound, similar to sodium chloride (table salt). As the concentration increases, the bitter taste becomes more pronounced: the increased presence of calcium ions enhances the activation of bitterness receptors. [ 56 ] [ 57 ] [ 58 ]
Calcium chloride is used in concrete mixes to accelerate the initial setting, but chloride ions lead to corrosion of steel rebar , so it should not be used in reinforced concrete . [ 59 ] The anhydrous form of calcium chloride may also be used for this purpose and can provide a measure of the moisture in concrete. [ 60 ]
Calcium chloride is included as an additive in plastics and in fire extinguishers , in blast furnaces as an additive to control scaffolding (clumping and adhesion of materials that prevent the furnace charge from descending), and in fabric softener as a thinner. [ citation needed ]
The exothermic dissolution of calcium chloride is used in self-heating cans and heating pads . [ citation needed ]
Calcium chloride is used as a water hardener in the maintenance of hot tub water, as insufficiently hard water can lead to corrosion and foaming. [ citation needed ]
In the oil industry , calcium chloride is used to increase the density of solids-free brines . It is also used to provide inhibition of swelling clays in the water phase of invert emulsion drilling fluids. [ citation needed ]
Calcium chloride ( CaCl 2 ) acts as flux material , decreasing the melting point, in the Davy process for the industrial production of sodium metal through the electrolysis of molten NaCl . [ citation needed ]
Calcium chloride is also used in the production of activated charcoal . [ citation needed ]
Calcium chloride can be used to precipitate fluoride ions from water as insoluble CaF 2 . [ citation needed ]
Calcium chloride is also an ingredient used in ceramic slipware . It suspends clay particles so that they float within the solution, making it easier to use in a variety of slipcasting techniques. [ citation needed ]
For watering plants to use as a fertilizer, a moderate concentration of calcium chloride is used to avoid potential toxicity: 5 to 10 mM (millimolar) is generally effective and safe for most plants—that is 0.55–1.11 grams (0.019–0.039 oz) of anhydrous calcium chloride ( CaCl 2 ) per liter of water or 1.10–2.19 grams (0.039–0.077 oz) of calcium chloride hexahydrate ( CaCl 2 ·6 H 2 O ) per liter of water. [ 61 ] [ 62 ] Calcium chloride solution is used immediately after preparation to prevent potential alterations in its chemical composition. [ 63 ] [ 64 ] Besides that, calcium chloride is highly hygroscopic, meaning it readily absorbs moisture from the air. [ 65 ] If the solution is left standing, it can absorb additional water vapor, leading to dilution and a decrease in the intended concentration. [ 65 ] Prolonged standing may lead to the precipitation of calcium hydroxide or other insoluble calcium compounds, reducing the availability of calcium ions in the solution [ 66 ] and reducing the effectiveness of the solution as a calcium source for plants. [ 66 ] Nutrient solutions can become a medium for microbial growth if stored for extended periods. [ 67 ] Microbial contamination may alter the composition of the solution and potentially introduce pathogens to the plants. [ 67 ] When dissolved in water, calcium chloride can undergo hydrolysis, especially over time, which can lead to the formation of small amounts of hydrochloric acid and calcium hydroxide: Ca + 2 +2 H 2 O ⇌ Ca(OH) 2 +2 H + . This reaction can lower the pH of the solution, making it more acidic. [ 68 ] Acidic solutions may harm plant tissues and disrupt nutrient uptake. [ 69 ]
Calcium chloride dihydrate (20 percent by weight) dissolved in ethanol (95 percent ABV) has been used as a sterilant for male animals. The solution is injected into the testes of the animal. Within one month, necrosis of testicular tissue results in sterilization. [ 70 ] [ 71 ] [ non-primary sources needed ]
Cocaine producers in Colombia import tons of calcium chloride to recover solvents that are on the INCB Red List and are more tightly controlled. [ 72 ]
Although the salt is non-toxic in small quantities when wet, the strongly hygroscopic properties of non-hydrated calcium chloride present some hazards. It can act as an irritant by desiccating moist skin. Solid calcium chloride dissolves exothermically , and burns can result in the mouth and esophagus if it is ingested. Ingestion of concentrated solutions or solid products may cause gastrointestinal irritation or ulceration . [ 73 ]
Consumption of calcium chloride can lead to hypercalcemia . [ 74 ]
Calcium chloride dissolves in water, producing chloride and the aquo complex [Ca(H 2 O) 6 ] 2+ . In this way, these solutions are sources of "free" calcium and free chloride ions. This description is illustrated by the fact that these solutions react with phosphate sources to give a solid precipitate of calcium phosphate :
Calcium chloride has a very high enthalpy change of solution , indicated by considerable temperature rise accompanying dissolution of the anhydrous salt in water. This property is the basis for its largest-scale application.
Aqueous solutions of calcium chloride tend to be slightly acidic due to the influence of the chloride ions on the hydrogen ion concentration in water. The slight acidity of calcium chloride solutions is primarily due to the increased ionic strength of the solution, which can influence the activity of hydrogen ions and lower the pH slightly. The pH of calcium chloride in aqueous solution is the following: [ 75 ] [ 76 ]
Molten calcium chloride can be electrolysed to give calcium metal and chlorine gas:
In much of the world, calcium chloride is derived from limestone as a by-product of the Solvay process , which follows the net reaction below: [ 10 ]
North American consumption in 2002 was 1,529,000 tonnes (3.37 billion pounds). [ 77 ] In the US, most calcium chloride is obtained by purification from brine . As with most bulk commodity salt products, trace amounts of other cations from the alkali metals and alkaline earth metals ( groups 1 and 2) and other anions from the halogens ( group 17) typically occur. [ 10 ]
Calcium chloride occurs as the rare evaporite minerals sinjarite (dihydrate) and antarcticite (hexahydrate). [ 78 ] [ 79 ] [ 80 ] Another natural hydrate known is ghiaraite – a tetrahydrate. [ 81 ] [ 80 ] The related minerals chlorocalcite (potassium calcium chloride, KCaCl 3 ) and tachyhydrite (calcium magnesium chloride, Ca Mg 2 Cl 6 ·12 H 2 O ) are also very rare. [ 82 ] [ 83 ] [ 80 ] The same is true for rorisite, CaClF (calcium chloride fluoride). [ 84 ] [ 80 ] | https://en.wikipedia.org/wiki/KCaCl3 |
Potassium chloride ( KCl , or potassium salt ) is a metal halide salt composed of potassium and chlorine . It is odorless and has a white or colorless vitreous crystal appearance. The solid dissolves readily in water, and its solutions have a salt -like taste. Potassium chloride can be obtained from ancient dried lake deposits. [ 7 ] KCl is used as a salt substitute for table salt (NaCl), a fertilizer, [ 8 ] as a medication , in scientific applications, in domestic water softeners (as a substitute for sodium chloride salt), as a feedstock , and in food processing , where it may be known as E number additive E508 .
It occurs naturally as the mineral sylvite , which is named after salt's historical designations sal degistivum Sylvii and sal febrifugum Sylvii , [ 9 ] and in combination with sodium chloride as sylvinite . [ 10 ]
The majority of the potassium chloride produced is used for making fertilizer , called potash , since the growth of many plants is limited by potassium availability. [ 11 ] [ 12 ] The term "potash" refers to various mined and manufactured salts that contain potassium in water-soluble form. Potassium chloride sold as fertilizer is known as "muriate of potash"—it is the common name for potassium chloride ( KCl ) used in agriculture. [ 13 ] [ 14 ] [ 15 ] [ 16 ] The vast majority of potash fertilizer worldwide is sold as muriate of potash. [ 17 ] [ 18 ] The dominance of muriate of potash in the fertilizer market is due to its high potassium content (approximately 60% K 2 O equivalent) and relative affordability compared to other potassium sources like sulfate of potash ( potassium sulfate ). [ 16 ] [ 19 ] Potassium is one of the three primary macronutrients essential for plant growth, alongside nitrogen and phosphorus. Potassium plays a vital role in various plant physiological processes, including enzyme activation, photosynthesis, protein synthesis, and water regulation. [ 20 ] [ 21 ] For watering plants, a moderate concentration of potassium chloride (KCl) is used to avoid potential toxicity: 6 mM (millimolar) is generally effective and safe for most plants, that is approximately 0.4 grams (0.014 oz) per liter of water. [ 22 ] [ 23 ]
Potassium is vital in the human body , and potassium chloride by mouth is the standard means to treat low blood potassium , although it can also be given intravenously. It is on the World Health Organization's List of Essential Medicines . [ 24 ] It is also an ingredient in Oral Rehydration Therapy (ORT)/solution (ORS) to reduce hypokalemia caused by diarrhoea. [ 25 ] This is another medicine on the WHO's List of Essential Medicines . [ 24 ]
Potassium chloride contains 52% of elemental potassium by mass. [ 26 ]
Overdose causes hyperkalemia which can disrupt cell signaling to the extent that the heart will stop, reversibly in the case of some open heart surgeries . [ 27 ] [ 28 ] [ 29 ]
Potassium chloride can be used as a salt substitute for food , but because not everyone likes its flavor , it is often mixed with ordinary table salt (sodium chloride) to improve the taste , to form low sodium salt . The addition of 1 ppm of thaumatin considerably reduces this bitterness. [ 30 ] Complaints of bitterness or a chemical or metallic taste are also reported with potassium chloride used in food. [ 31 ]
The World Health Organization guideline Use of lower-sodium salt substitutes strongly recommends reducing sodium intake to less than 2 g/day and conditionally recommends replacing regular table salt with lower-sodium salt substitutes that contain potassium. This recommendation is intended for adults (not pregnant women or children) in general populations, excluding individuals with kidney impairments or with other circumstances or conditions that might compromise potassium excretion. [ 32 ] [ 33 ] [ 34 ]
In the United States, potassium chloride is used as the final drug in the three-injection sequence of lethal injection as a form of capital punishment . It induces cardiac arrest , ultimately killing the person. [ 35 ]
As a chemical feedstock , the salt is used for the manufacture of potassium hydroxide and potassium metal. It is also used in medicine, lethal injections , scientific applications, food processing , soaps , and as a sodium-free substitute for table salt for people concerned about the health effects of sodium. [ citation needed ]
It is used as a supplement in animal feed to boost the potassium level in the feed. As an added benefit, it is known to increase milk production. [ citation needed ]
It is sometimes used in solution as a completion fluid in petroleum and natural gas operations, as well as being an alternative to sodium chloride in household water softener units. [ citation needed ]
Glass manufacturers use granular potash as a flux , lowering the temperature at which a mixture melts. Because potash imparts excellent clarity to glass, it is commonly used in eyeglasses, glassware, televisions, and computer monitors. [ citation needed ]
Because natural potassium contains a tiny amount of the isotope potassium-40 , potassium chloride is used as a beta radiation source to calibrate radiation monitoring equipment . It also emits a relatively low level of 511 keV gamma rays from positron annihilation, which can be used to calibrate medical scanners. [ citation needed ]
Potassium chloride is used in some de-icing products designed to be safer for pets and plants, though these are inferior in melting quality to calcium chloride . It is also used in various brands of bottled water . [ citation needed ]
Potassium chloride was once used as a fire extinguishing agent , and in portable and wheeled fire extinguishers . Known as Super-K dry chemical, it was more effective than sodium bicarbonate -based dry chemicals and was compatible with protein foam . This agent fell out of favor with the introduction of potassium bicarbonate ( Purple-K ) dry chemical in the late 1960s, which was much less corrosive , as well as more effective. It is rated for B and C fires. [ citation needed ]
Along with sodium chloride and lithium chloride , potassium chloride is used as a flux for the gas welding of aluminium . [ citation needed ]
Potassium chloride is also an optical crystal with a wide transmission range from 210 nm to 20 μm. While cheap, KCl crystals are hygroscopic . This limits its application to protected environments or short-term uses such as prototyping. Exposed to free air, KCl optics will "rot". Whereas KCl components were formerly used for infrared optics , they have been entirely replaced by much tougher crystals such as zinc selenide . [ citation needed ]
Potassium chloride is used as a scotophor with designation P10 in dark-trace CRTs , e.g. in the Skiatron . [ citation needed ]
The typical amounts of potassium chloride found in the diet appear to be generally safe. [ 36 ] In larger quantities, however, potassium chloride is toxic. The LD 50 of orally ingested potassium chloride is approximately 2.5 g/kg, or 190 grams (6.7 oz) for a body mass of 75 kilograms (165 lb). In comparison, the LD 50 of sodium chloride (table salt) is 3.75 g/kg.
Intravenously, the LD 50 of potassium chloride is far smaller, at about 57.2 mg/kg to 66.7 mg/kg; this is found by dividing the lethal concentration of positive potassium ions (about 30 to 35 mg/kg) [ 37 ] by the proportion by mass of potassium ions in potassium chloride (about 0.52445 mg K + /mg KCl). [ 38 ]
KCl is soluble in a variety of polar solvents.
Solutions of KCl are common standards, for example for calibration of the electrical conductivity of (ionic) solutions, since KCl solutions are stable, allowing for reproducible measurements. In aqueous solution , it is essentially fully ionized into solvated K + and Cl − ions.
Although potassium is more electropositive than sodium , KCl can be reduced to the metal by reaction with metallic sodium at 850 °C because the more volatile potassium can be removed by distillation (see Le Chatelier's principle ):
This method is the main method for producing metallic potassium. Electrolysis (used for sodium) fails because of the high solubility of potassium in molten KCl. [ 10 ]
Potassium chlorides with formulas other than KCl have been predicted to become stable under pressures of 20 GPa or more. [ 40 ] Among these, two phases of KCl 3 were synthesized and characterized. At 20-40 GPa, a trigonal structure containing K + and Cl 3 − is obtained; above 40 GPa this gives way to a phase isostructural with the intermetallic compound Cr 3 Si. [ citation needed ]
Under ambient conditions, the crystal structure of potassium chloride is like that of NaCl. It adopts a face-centered cubic structure known as the B1 phase with a lattice constant of roughly 6.3 Å. Crystals cleave easily in three directions. Other polymorphic and hydrated phases are adopted at high pressures. [ 41 ]
Some other properties are
As with other compounds containing potassium, KCl in powdered form gives a lilac flame .
Potassium chloride is extracted from minerals sylvite , carnallite , and potash . It is also extracted from salt water and can be manufactured by crystallization from solution, flotation or electrostatic separation from suitable minerals. It is a by-product of the production of nitric acid from potassium nitrate and hydrochloric acid .
Most potassium chloride is produced as agricultural and industrial-grade potash in Saskatchewan, Canada , Russia, and Belarus. Saskatchewan alone accounted for over 25% of the world's potash production in 2017. [ 42 ]
Potassium chloride is inexpensively available and is rarely prepared intentionally in the laboratory. It can be generated by treating potassium hydroxide (or other potassium bases) with hydrochloric acid :
This conversion is an acid-base neutralization reaction . The resulting salt can then be purified by recrystallization. Another method would be to allow potassium to burn in the presence of chlorine gas, also a very exothermic reaction: | https://en.wikipedia.org/wiki/KCl |
Potassium hypochlorite is a chemical compound with the chemical formula K O Cl , also written as KClO. It is the potassium salt of hypochlorous acid . It consists of potassium cations ( K + ) and hypochlorite anions ( − OCl ). It is used in variable concentrations, often diluted in water solution. Its aqueous solutions are colorless liquids (light yellow when impure) that have a strong chlorine smell. [ 1 ] It is used as a biocide and disinfectant . [ 1 ]
Potassium hypochlorite is produced by the disproportionation reaction of chlorine with a solution of potassium hydroxide : [ 2 ]
This is the traditional method, first used by Claude Louis Berthollet in 1789. [ 3 ]
Another production method is electrolysis of potassium chloride solution.
With both methods, the reaction mixture must be kept cold to prevent formation of potassium chlorate .
Potassium hypochlorite is used for sanitizing surfaces as well as disinfecting drinking water . Because its degradation leaves behind potassium chloride rather than sodium chloride , its use has been promoted in agriculture , where addition of potassium to soil is desired. [ 4 ]
Potassium hypochlorite was first produced in 1789 by Claude Louis Berthollet in his laboratory located in Javel in Paris, France, by passing chlorine gas through a solution of potash lye . The resulting liquid, known as " Eau de Javel " ("Javel water"), was a weak solution of potassium hypochlorite. Due to production difficulties, the product was then modified using sodium instead of potassium , giving rise to sodium hypochlorite , widely used today as a disinfectant .
Like sodium hypochlorite , potassium hypochlorite is an irritant. It can cause severe damage on contact with the skin, eyes, and mucous membranes . [ 5 ] Inhalation of a mist of KOCl can cause bronchus and lung irritation, difficulty breathing, and in severe cases pulmonary edema . Ingestion of strong concentrations can be lethal. [ 6 ] Symptoms of contact or inhalation can be delayed. [ 1 ]
Potassium hypochlorite is not considered to cause a fire or explosive hazards by itself. [ 6 ] However, it can react explosively with numerous chemicals, including urea , ammonium salts , methanol , acetylene , and many organic compounds . Heating and acidification can produce toxic chlorine gas. [ 7 ] Containers may explode upon exposure to heat. [ 1 ] Potassium hypochlorite forms highly explosive NCl 3 upon contact with urea or ammonia . [ 1 ] | https://en.wikipedia.org/wiki/KClO |
Potassium chlorate is the inorganic compound with the molecular formula KClO 3 . In its pure form, it is a white solid. After sodium chlorate , it is the second most common chlorate in industrial use. It is a strong oxidizing agent and its most important application is in safety matches . [ 6 ] In other applications it is mostly obsolete and has been replaced by safer alternatives in recent decades. It has been used
On the industrial scale, potassium chlorate is produced by the salt metathesis reaction of sodium chlorate and potassium chloride :
The reaction is driven by the low solubility of potassium chlorate in water. The equilibrium of the reaction is shifted to the right hand side by the continuous precipitation of the product ( Le Chatelier's Principle ). The precursor sodium chlorate is produced industrially in very large quantities by electrolysis of sodium chloride , common table salt. [ 6 ]
The direct electrolysis of KCl in aqueous solution is also used sometimes, in which elemental chlorine formed at the anode reacts with KOH in situ . The low solubility of KClO 3 in water causes the salt to conveniently isolate itself from the reaction mixture by simply precipitating out of solution.
Potassium chlorate can be produced in small amounts by disproportionation in a sodium hypochlorite solution followed by metathesis reaction with potassium chloride: [ 7 ]
It can also be produced by passing chlorine gas into a hot solution of caustic potash: [ 8 ]
According to X-ray crystallography , potassium chlorate is a dense salt-like structure consisting of chlorate and potassium ions in close association.
Potassium chlorate was one key ingredient in early firearms percussion caps (primers). It continues in that application, where not supplanted by potassium perchlorate .
Chlorate-based propellants are more efficient than traditional gunpowder and are less susceptible to damage by water. However, they can be extremely unstable in the presence of sulfur or phosphorus and are much more expensive. Chlorate propellants must be used only in equipment designed for them; failure to follow this precaution is a common source of accidents. Potassium chlorate, often in combination with silver fulminate , is used in trick noise-makers known as "crackers", "snappers", "pop-its", "caps" or "bang-snaps", a popular type of novelty firework.
Another application of potassium chlorate is as the oxidizer in a smoke composition such as that used in smoke grenades . Since 2005, a cartridge with potassium chlorate mixed with lactose and rosin is used for generating the white smoke signaling the election of new pope by a papal conclave . [ 9 ]
High school and college laboratories often use potassium chlorate to generate oxygen gas. [ citation needed ] It is a far cheaper source than a pressurized or cryogenic oxygen tank. Potassium chlorate readily decomposes if heated while in contact with a catalyst , typically manganese(IV) dioxide (MnO 2 ). Thus, it may be simply placed in a test tube and heated over a burner. If the test tube is equipped with a one-holed stopper and hose, warm oxygen can be drawn off. The reaction is as follows:
Heating it in the absence of a catalyst converts it into potassium perchlorate : [ 8 ]
With further heating, potassium perchlorate decomposes to potassium chloride and oxygen:
The safe performance of this reaction requires very pure reagents and careful temperature control. Molten potassium chlorate is an extremely powerful oxidizer and spontaneously reacts with many common materials such as sugar. Explosions have resulted from liquid chlorates spattering into the latex or PVC tubes of oxygen generators and from contact between chlorates and hydrocarbon sealing greases. Impurities in potassium chlorate itself can also cause problems. When working with a new batch of potassium chlorate, it is advisable to take a small sample (~1 gram) and heat it strongly on an open glass plate. Contamination may cause this small quantity to explode, indicating that the chlorate should be discarded.
Potassium chlorate is used in chemical oxygen generators (also called chlorate candles or oxygen candles), employed as oxygen-supply systems of e.g. aircraft, space stations, and submarines, and has been responsible for at least one plane crash . A fire on the space station Mir was traced to oxygen generation candles that use a similar lithium perchlorate. The decomposition of potassium chlorate was also used to provide the oxygen supply for limelights .
Potassium chlorate is used also as a pesticide . In Finland it was sold under trade name Fegabit.
Potassium chlorate can react with sulfuric acid to form a highly reactive solution of chloric acid and potassium sulfate:
The solution so produced is sufficiently reactive that it spontaneously ignites if combustible material (sugar, paper, etc.) is present.
In schools, molten potassium chlorate is used in screaming jelly babies , Gummy bear , Haribo , and Trolli candy demonstration where the candy is dropped into the molten salt.
In chemical labs it is used to oxidize HCl and release small amounts of gaseous chlorine.
Militant groups in Afghanistan also use potassium chlorate extensively as a key component in the production of improvised explosive devices (IEDs). When significant effort was made to reduce the availability of ammonium nitrate fertilizer in Afghanistan, IED makers started using potassium chlorate as a cheap and effective alternative. In 2013, 60% of IEDs in Afghanistan used potassium chlorate, making it the most common ingredient used in IEDs. [ 10 ] Potassium chlorate was also the main ingredient in the car bomb used in the 2002 Bali bombings that killed 202 people.
Potassium chlorate is used to force the blossoming stage of the longan tree, causing it to produce fruit in warmer climates. [ 11 ]
Potassium chlorate should be handled with care. It reacts vigorously, and in some cases spontaneously ignites or explodes, when mixed with many combustible materials. It burns vigorously in combination with virtually any combustible material, even those normally only slightly flammable (including ordinary dust and lint). Mixtures of potassium chlorate and a fuel can ignite by contact with sulfuric acid, so it should be kept away from this reagent. Sulfur should be avoided in pyrotechnic compositions containing potassium chlorate, as these mixtures are prone to spontaneous deflagration . Most sulfur contains trace quantities of sulfur-containing acids, and these can cause spontaneous ignition - "Flowers of sulfur" or "sublimed sulfur", despite the overall high purity, contains significant amounts of sulfur acids. Also, mixtures of potassium chlorate with any compound with ignition promoting properties, such as antimony(III) sulfide , are very dangerous to prepare, as they are extremely shock sensitive. | https://en.wikipedia.org/wiki/KClO3 |
Potassium perchlorate is the inorganic salt with the chemical formula K Cl O 4 . Like other perchlorates , this salt is a strong oxidizer when the solid is heated at high temperature although it usually reacts very slowly in solution with reducing agents or organic substances. This colorless crystalline solid is a common oxidizer used in fireworks , ammunition percussion caps , and explosive primers , and is used variously in propellants , flash compositions , stars, and sparklers . It has been used as a solid rocket propellant, although in that application it has mostly been replaced by the more performant ammonium perchlorate .
KClO 4 has a relatively low solubility in water (1.5 g in 100 mL of water at 25 °C). [ 1 ]
Potassium perchlorate is prepared industrially by treating an aqueous solution of sodium perchlorate with potassium chloride . This single precipitation reaction exploits the low solubility of KClO 4 , which is about 1/100 as much as the solubility of NaClO 4 (209.6 g/100 mL at 25 °C). [ 8 ]
It can also be produced by bubbling chlorine gas through a solution of potassium chlorate and potassium hydroxide , [ citation needed ] and by the reaction of perchloric acid with potassium hydroxide; however, this is not used widely due to the dangers of perchloric acid.
Another preparation involves the electrolysis of a potassium chlorate solution, causing KClO 4 to form and precipitate at the anode . This procedure is complicated by the low solubility of both potassium chlorate and potassium perchlorate, the latter of which may precipitate onto the electrodes and impede the current.
KClO 4 is an oxidizer in the sense that it exothermically "transfers oxygen " to combustible materials, greatly increasing their rate of combustion relative to that in air . Thus, it reacts with glucose to give carbon dioxide , water molecules and potassium chloride :
The conversion of solid glucose into hot gaseous CO 2 is the basis of the explosive force of this and other such mixtures. With sugar , KClO 4 yields a low explosive, provided a necessary confinement. Otherwise such mixtures simply deflagrate with an intense purple flame characteristic of potassium . Flash compositions used in firecrackers usually consist of a mixture of aluminium powder and potassium perchlorate. This mixture, sometimes called flash powder, is also used in ground and air fireworks .
As an oxidizer, potassium perchlorate can be used safely in the presence of sulfur , whereas potassium chlorate cannot. The greater reactivity of chlorate is typical – perchlorates are kinetically poorer oxidants. Chlorate produces chloric acid ( HClO 3 ), which is highly unstable and can lead to premature ignition of the composition. Correspondingly, perchloric acid ( HClO 4 ) is quite stable. [ 9 ]
For a commercial use, potassium perchlorate is mixed 50/50 with potassium nitrate to fabricate Pyrodex , a black powder substitute , and when not compressed within a muzzle loading firearm or in a cartridge, burns at a sufficiently slow rate to prevent it from being categorized with the black powder as a "low explosive", and to demote it as "flammable" material.
Potassium perchlorate can be used as an antithyroid agent used to treat hyperthyroidism , usually in combination with one other medication. This application exploits the similar ionic radius and hydrophilicity of perchlorate and iodide .
The administration of known goitrogen substances can also be used as a prevention in reducing the biological uptake of iodine , (whether it is the nutritional non-radioactive iodine-127 or radioactive iodine, most commonly iodine-131 ( half-life = 8.02 days), as the body cannot discern between different iodine isotopes ). Perchlorate ions, a common water contaminant in the USA due to the aerospace industry , has been shown to reduce iodine uptake and thus is classified as a goitrogen . Perchlorate ion is a competitive inhibitor of the process by which iodide is actively accumulated into the thyroid follicular cells. Studies involving healthy adult volunteers determined that at levels above 7 micrograms per kilogram per day (μg/(kg·d)), perchlorate begins to temporarily inhibit the thyroid gland's ability to absorb iodine from the bloodstream ("iodide uptake inhibition", thus perchlorate is a known goitrogen). [ 10 ] The reduction of the iodide pool by perchlorate has a dual effect – reduction of excess hormone synthesis and hyperthyroidism , on the one hand, and reduction of thyroid inhibitor synthesis and hypothyroidism on the other. Perchlorate remains very useful as a single dose application in tests measuring the discharge of radioiodide accumulated in the thyroid as a result of many different disruptions in the further metabolism of iodide in the thyroid gland. [ 11 ]
Treatment of thyrotoxicosis (including Graves' disease ) with 600-2,000 mg potassium perchlorate (430-1,400 mg perchlorate) daily for periods of several months, or longer, was once a common practice, particularly in Europe, [ 10 ] [ 12 ] and perchlorate use at lower doses to treat thyroid problems continues to this day. [ 13 ] Although 400 mg of potassium perchlorate divided into four or five daily doses was used initially and found effective, higher doses were introduced when 400 mg/d was discovered not to control thyrotoxicosis in all subjects. [ 10 ] [ 11 ]
Current regimens for treatment of thyrotoxicosis (including Graves' disease), when a patient is exposed to additional sources of iodine, commonly include 500 mg potassium perchlorate twice per day for 18–40 days. [ 10 ] [ 14 ]
Prophylaxis with perchlorate-containing water at concentrations of 17 ppm , corresponding to 0.5 mg/(kg·d) intake for a person of 70 kg consuming 2 litres of water per day, was found to reduce the baseline of radioiodine uptake by 67% [ 10 ] This is equivalent to ingesting a total of just 35 mg of perchlorate ions per day. In another related study were subjects drank just 1 litre of perchlorate-containing water per day at a concentration of 10 ppm, i.e. daily 10 mg of perchlorate ions were ingested, an average 38% reduction in the uptake of Iodine was observed. [ 15 ]
However, when the average perchlorate absorption in perchlorate plant workers subjected to the highest exposure has been estimated as approximately 0.5 mg/(kg·d), as in the above paragraph, a 67% reduction of iodine uptake would be expected. Studies of chronically exposed workers though have thus far failed to detect any abnormalities of thyroid function, including the uptake of iodine. [ 16 ] This may well be attributable to sufficient daily exposure, or intake, of stable iodine-127 among these workers and the short 8 hr biological half life of perchlorate in the body. [ 10 ]
To completely block the uptake of iodine-131 (half-life = 8.02 days) by the purposeful addition of perchlorate ions to a public water supply, aiming at dosages of 0.5 mg/(kg·d), or a water concentration of 17 ppm, would therefore be grossly inadequate at truly reducing a radio-iodine uptake. Perchlorate ion concentrations in a region water supply, would need to be much higher, at least 7.15 mg/kg of body weight per day or a water concentration of 250 ppm , assuming people drink 2 liters of water per day, to be truly beneficial to the population at preventing bioaccumulation when exposed to an iodine-131 contamination, [ 10 ] [ 14 ] independent of the availability of iodate or iodide compounds.
The distribution of perchlorate tablets, or the addition of perchlorate to the water supply, would need to continue for 80–90 days (~10 half-life of 8.02 days) after the release of iodine-131. After this time, the radioactive iodine-131 would have decayed to less than 1/1000 of its initial activity at which time the danger from the biological uptake of iodine-131 is essentially over. [ 17 ]
So, perchlorate administration could represent a possible alternative to iodide tablets distribution in case of a large-scale nuclear accident releasing important quantities of iodine-131 in the atmosphere. However, the advantages are not always clear and would depend on the extent of a hypothetical nuclear accident. As for the stable iodide intake to rapidly saturate the thyroid gland before it accumulates radioactive iodine-131, a careful cost-benefit analysis has to be first done by the nuclear safety authorities. Indeed, blocking the thyroid activity of a whole population for three months can also have negative consequences for the human health, especially for young children.
So, the decision of perchlorate, or stable iodine, administration cannot be left to the individual initiative and falls under the authority of the government in case of a major nuclear accident.
Injecting perchlorate or iodide directly in the public drinking water is also probably as restrictive as tablets distribution. | https://en.wikipedia.org/wiki/KClO4 |
KDE Frameworks is a collection of libraries and software frameworks readily available to any Qt -based software stacks or applications on multiple operating systems . [ 6 ] Featuring frequently needed functionality solutions like hardware integration, file format support, additional graphical control elements , plotting functions, and spell checking , the collection serves as the technological foundation for KDE Plasma and KDE Gear . It is distributed under the GNU Lesser General Public License (LGPL). [ 7 ]
KDE Frameworks is based on Qt, which enables a more widespread use of QML , a simpler JavaScript -based declarative programming language, for the design of user interfaces. The graphics rendering engine used by QML allows for more fluid user interfaces across different devices. [ 8 ]
Since the split of the KDE Software Compilation into KDE Frameworks 5, KDE Plasma 5 and KDE Applications , each sub-project can pick its own development pace. KDE Frameworks are released on a monthly basis [ 9 ] and use Git . [ 10 ] [ 11 ]
It should be possible to install KDE Frameworks alongside the KDE Platform 4 so apps can use either one. [ 12 ]
Platform releases are those which begin a series (version number X.0). Only these major releases are allowed to break binary compatibility with the predecessor. Releases in the minor series (X.1, X.2, ...) will guarantee binary portability ( API & ABI ). This means, for instance, that software that was developed for KDE 3.0 will work on all (future) KDE 3 releases; however, an application developed for KDE 2 is not guaranteed to be able to make use of the KDE 3 libraries. KDE major version numbers mainly follow the Qt release cycle, meaning that KDE SC 4 is based on Qt 4, while KDE 3 was based on Qt 3.
The repository of each framework should contain a file named metainfo.yaml . [ 13 ] This file documents the maintainer of the framework, the type, the supported operating system and other information. The currently supported platforms are Linux, Microsoft Windows, macOS and Android.
The Frameworks have a clear dependency structure, divided into "categories" and "tiers". The "categories" refer to runtime dependencies:
The KDE Frameworks bundle consists of over 70 packages. These existed as a single large package, called kdelibs, in KDE SC 4 . Kdelibs was split into several individual frameworks, some of which are no longer part of KDE but were integrated into Qt 5.2. [ 14 ]
KDE Frameworks are grouped in four different tiers according to dependency on other libraries. [ 15 ] [ 16 ]
The following image formats have read and write support:
Attica is a Qt library that implements the Open Collaboration Services API version 1.6. It grants easy access to the services such as querying information about persons and contents.
Further documentation:
to specify information in "data units"; i.e., the natural units of the data being plotted. KPlotWidget automatically converts everything to screen pixel units. KPlotWidget draws X and Y axes with tick marks and tick labels. It automatically determines how many tick marks to use and where they should be, based on the data limits specified for the plot. You change the limits by calling `setLimits(double x1, double x2, double y1, double y2)`. Data to be plotted are stored using the KPlotObject class. KPlotObject consists of a QList of QPointF's, each specifying the X,Y coordinates of a data point. KPlotObject also specifies the "type" of data to be plotted (POINTS or CURVE or POLYGON or LABEL).
The core of Kross provides the framework to deal transparently with interpreter-back-ends and offers abstract functionality to deal with scripts.
Kirigami is a QML application framework [ 18 ] developed by Marco Martin [ 19 ] that enables developers to write applications that run natively on Android, iOS, Windows, Plasma Mobile and any classic Linux desktop environment without code adjustments.
It is used by various applications, for example Linus Torvalds and Dirk Hohndels' scuba diving application Subsurface, the messenger client Banji, [ 20 ] the Kaidan messenger, [ 21 ] Vvave music player and the KDE software center Discover.
Linux distribution use some package management system to package the software they distribute. Debian for example distributes KGlobalAccel under the package name libkf5globalaccel , [ 22 ] while Fedora Linux distributes it under the name kf5-kglobalaccel . [ 23 ]
While being mainly written in C++, there are many bindings for other programming languages available: [ 24 ] [ 25 ]
These and other bindings use the following technologies:
Many bindings weren't updated to Qt5 and KF5 or only later in the release cycle.
The 5.0 release was preceded by a technology preview, two alpha releases, and three beta releases. [ 27 ] [ 28 ] [ 29 ]
The source code of KDE Frameworks has been around since KDElibs 1. The first release as KDE Frameworks was with version 5, to account for the fact that the code base was that of KDE Platform version 4 (the only major version of KDE Platform ).
The transition from KDE Platform to KDE Frameworks began in August 2013, guided by top KDE technical contributors. [ 8 ]
After the initial release of KDE Frameworks 5.0, the developers focused on adding new features to the components in KDE Frameworks 5, [ 30 ] an example being better integration of Firefox into KDE. [ 31 ]
The major improvement of Frameworks 5 is its modularization. In earlier KDE versions, the libraries were bundled as a single large package. In Frameworks, the libraries were split into individual smaller packages. This facilitates utilization of the libraries by other Qt-based software, since dependencies can be kept at a minimum. [ 8 ]
While KDE 4 was based on version 4 of the Qt widget toolkit, Frameworks 5 is based on version 5.
As part of the KDE project's 'MegaRelease 6', on February 28, 2024, KDE Frameworks 6 was released, upgrading it to a Qt 6 base. [ 32 ]
During KDE SC 4, the then so called KDE Platform consisted of all libraries and services needed for KDE Plasma and the applications. Starting with Qt 5, this platform was transformed into a set of modules that is now referred to as KDE Frameworks. These modules include: Solid , Nepomuk , Phonon , etc. and are licensed either under the LGPL, BSD license, MIT License or X11 license. [ 33 ]
Besides the KDE Software Compilation , there are other adopters such as the desktop environments LXQt , MoonLightDE or Hawaii.
Version 3.0 of Krita , the raster graphics editor of the Calligra Suite , which was released on May 31, 2016, depends on KDE Frameworks 5 and Qt 5.2.
With Kirigami, there is also increased usage by applications such as Amarok , Avogadro , Trojitá or Subsurface . | https://en.wikipedia.org/wiki/KDE_Frameworks |
The KDE Gear is a set of applications and supporting libraries that are developed by the KDE community , [ 3 ] primarily used on Linux -based operating systems but mostly multiplatform, and released on a common release schedule.
The bundle is composed of over 200 applications. Examples of prominent applications in the bundle include the file manager Dolphin , document viewer Okular , text editor Kate , archiving tool Ark and terminal emulator Konsole . [ 4 ]
Previously the KDE Applications Bundle was part of the KDE Software Compilation .
Software that is not part of the official KDE Applications bundle can be found in the "Extragear" section. They release on their own schedule and feature their own versioning numbers. There are many standalone applications like Krita or Amarok that are mostly designed to be portable between operating systems and deployable independent of a particular workspace or desktop environment. Some brands consist of multiple applications, such as Calligra Office Suite . There are several options for obtaining and installing KDE applications under Linux. Moreover, most of the KDE platform and applications have been ported to OpenBSD and NetBSD .
KDE SDK [ 5 ] [ 6 ] is a collection of two dozen distinct integrated (both within the SDK but also with other KDE applications, e.g. many work with Dolphin, the default file manager) applications and components that work with/are part of KDevelop, [ 7 ] and is suitable for general purpose software development in a range of languages. It provides the tooling used to engineer KDE, and is particularly rich in tools to support Qt and C++ development, as well as the more fashionable Rust, Python, etc.
Various other packages are being built for testing on Android, although plans for some of the core parts of the SDK (e.g. Kate) have not been announced.
[ 32 ]
KDebugSettings [ 43 ]
Dferry D-Bus library and tools [ 45 ] CuteHMI Open-source HMI (Human Machine Interface) software written in C++ and QML.
Unmaintained Applications [ 67 ]
The KDE Applications Bundle is released every four months and has bugfix releases in each intervening month. A date-based version scheme is used, which is composed of the year and month. A third digit is used for bugfix releases. [ 78 ]
With the April 2021 release, the KDE Applications Bundle has been renamed to KDE Gear. [ 3 ] | https://en.wikipedia.org/wiki/KDE_Gear |
KDE Platform 4 was a collection of libraries and software frameworks by KDE that served as technological foundation for KDE Software Compilation 4 distributed under the GNU Lesser General Public License (LGPL). KDE Platform 4 was the successor to KDElibs and the predecessor of KDE Frameworks . KDE Platform 4 is the only version of KDE Platform, and in 2013 it was replaced by KDE Frameworks 5 .
KParts is the component framework for the KDE Plasma desktop environment . An individual component is called a KPart . KParts are analogous to Bonobo components in GNOME and ActiveX controls in Microsoft's Component Object Model . Konsole is available as a KPart and is used in applications like Konqueror and Kate .
Example uses of KParts:
Solid is a device integration framework for KDE Platform 4 and its successor, KDE Frameworks . It functions on similar principles to KDE's multimedia pillar Phonon ; rather than managing hardware on its own, it makes existing solutions accessible through a single API. The current solution uses udev , NetworkManager and BlueZ (the official Linux Bluetooth stack). However, any and all parts can be replaced without breaking the application, making applications using Solid extremely flexible and portable. [ 5 ] [ 6 ] Work is underway to build a Solid backend for the Windows port of KDE based on Windows Management Instrumentation . [ 7 ] | https://en.wikipedia.org/wiki/KDE_Platform_4 |
KEGG ( Kyoto Encyclopedia of Genes and Genomes ) is a collection of databases dealing with genomes , biological pathways , diseases , drugs , and chemical substances . KEGG is utilized for bioinformatics research and education, including data analysis in genomics , metagenomics , metabolomics and other omics studies, modeling and simulation in systems biology , and translational research in drug development .
The KEGG database project was initiated in 1995 by Minoru Kanehisa , professor at the Institute for Chemical Research, Kyoto University , under the then ongoing Japanese Human Genome Program . [ 1 ] [ 2 ] Foreseeing the need for a computerized resource that can be used for biological interpretation of genome sequence data , he started developing the KEGG PATHWAY database. It is a collection of manually drawn KEGG pathway maps representing experimental knowledge on metabolism and various other functions of the cell and the organism . Each pathway map contains a network of molecular interactions and reactions and is designed to link genes in the genome to gene products (mostly proteins ) in the pathway. This has enabled the analysis called KEGG pathway mapping, whereby the gene content in the genome is compared with the KEGG PATHWAY database to examine which pathways and associated functions are likely to be encoded in the genome.
According to the developers, KEGG is a "computer representation" of the biological system . [ 3 ] It integrates building blocks and wiring diagrams of the system—more specifically, genetic building blocks of genes and proteins, chemical building blocks of small molecules and reactions, and wiring diagrams of molecular interaction and reaction networks. This concept is realized in the following databases of KEGG, which are categorized into systems, genomic, chemical, and health information. [ 4 ]
The KEGG PATHWAY database, the wiring diagram database, is the core of the KEGG resource. It is a collection of pathway maps integrating many entities including genes, proteins, RNAs, chemical compounds, glycans, and chemical reactions, as well as disease genes and drug targets, which are stored as individual entries in the other databases of KEGG. The pathway maps are classified into the following sections:
The metabolism section contains aesthetically drawn global maps showing an overall picture of metabolism, in addition to regular metabolic pathway maps. The low-resolution global maps can be used, for example, to compare metabolic capacities of different organisms in genomics studies and different environmental samples in metagenomics studies. In contrast, KEGG modules in the KEGG MODULE database are higher-resolution, localized wiring diagrams, representing tighter functional units within a pathway map, such as subpathways conserved among specific organism groups and molecular complexes. KEGG modules are defined as characteristic gene sets that can be linked to specific metabolic capacities and other phenotypic features, so that they can be used for automatic interpretation of genome and metagenome data.
Another database that supplements KEGG PATHWAY is the KEGG BRITE database. It is an ontology database containing hierarchical classifications of various entities including genes, proteins, organisms, diseases, drugs, and chemical compounds. While KEGG PATHWAY is limited to molecular interactions and reactions of these entities, KEGG BRITE incorporates many different types of relationships.
Several months after the KEGG project was initiated in 1995, the first report of the completely sequenced bacterial genome was published. [ 5 ] Since then all published complete genomes are accumulated in KEGG for both eukaryotes and prokaryotes . The KEGG GENES database contains gene/protein-level information and the KEGG GENOME database contains organism-level information for these genomes. The KEGG GENES database consists of gene sets for the complete genomes, and genes in each set are given annotations in the form of establishing correspondences to the wiring diagrams of KEGG pathway maps, KEGG modules, and BRITE hierarchies.
These correspondences are made using the concept of orthologs . The KEGG pathway maps are drawn based on experimental evidence in specific organisms but they are designed to be applicable to other organisms as well, because different organisms, such as human and mouse, often share identical pathways consisting of functionally identical genes, called orthologous genes or orthologs. All the genes in the KEGG GENES database are being grouped into such orthologs in the KEGG ORTHOLOGY (KO) database. Because the nodes (gene products) of KEGG pathway maps, as well as KEGG modules and BRITE hierarchies, are given KO identifiers, the correspondences are established once genes in the genome are annotated with KO identifiers by the genome annotation procedure in KEGG. [ 4 ]
The KEGG metabolic pathway maps are drawn to represent the dual aspects of the metabolic network: the genomic network of how genome-encoded enzymes are connected to catalyze consecutive reactions and the chemical network of how chemical structures of substrates and products are transformed by these reactions. [ 6 ] A set of enzyme genes in the genome will identify enzyme relation networks when superimposed on the KEGG pathway maps, which in turn characterize chemical structure transformation networks allowing interpretation of biosynthetic and biodegradation potentials of the organism. Alternatively, a set of metabolites identified in the metabolome will lead to the understanding of enzymatic pathways and enzyme genes involved.
The databases in the chemical information category, which are collectively called KEGG LIGAND, are organized by capturing knowledge of the chemical network. In the beginning of the KEGG project, KEGG LIGAND consisted of three databases: KEGG COMPOUND for chemical compounds, KEGG REACTION for chemical reactions, and KEGG ENZYME for reactions in the enzyme nomenclature. [ 7 ] Currently, there are additional databases: KEGG GLYCAN for glycans [ 8 ] and two auxiliary reaction databases called RPAIR (reactant pair alignments) and RCLASS (reaction class). [ 9 ] KEGG COMPOUND has also been expanded to contain various compounds such as xenobiotics , in addition to metabolites.
In KEGG, diseases are viewed as perturbed states of the biological system caused by perturbants of genetic factors and environmental factors, and drugs are viewed as different types of perturbants. [ 10 ] The KEGG PATHWAY database includes not only the normal states but also the perturbed states of the biological systems. However, disease pathway maps cannot be drawn for most diseases because molecular mechanisms are not well understood. An alternative approach is taken in the KEGG DISEASE database, which simply catalogs known genetic factors and environmental factors of diseases. These catalogs may eventually lead to more complete wiring diagrams of diseases.
The KEGG DRUG database contains active ingredients of approved drugs in Japan, the US, and Europe. They are distinguished by chemical structures and/or chemical components and associated with target molecules, metabolizing enzymes , and other molecular interaction network information in the KEGG pathway maps and the BRITE hierarchies. This enables an integrated analysis of drug interactions with genomic information. Crude drugs and other health-related substances, which are outside the category of approved drugs, are stored in the KEGG ENVIRON database. The databases in the health information category are collectively called KEGG MEDICUS, which also includes package inserts of all marketed drugs in Japan.
In July 2011 KEGG introduced a subscription model for FTP download due to a significant cutback of government funding. KEGG continues to be freely available through its website, but the subscription model has raised discussions about sustainability of bioinformatics databases. [ 11 ] [ 12 ] | https://en.wikipedia.org/wiki/KEGG |
KENTORT II is an above-ground shale oil extraction process developed by the Center for Applied Energy Research of the University of Kentucky . It is a hot recycled solids fluidized bed retorting process developed since 1982 for processing the eastern United States Devonian oil shales . [ 1 ] [ 2 ] The concept of this process was initiated in 1986 in the test unit. [ 3 ]
The KENTORT II retort consists of four fluidized bed vessels, configured in cascade. The raw oil shale is fed to the pyrolysis vessel the pyrolysis section, where it is fluidized by a mixture of steam and product oil shale gas from the gasification section below. Heat is transferred to the raw oil shale by a combination of fluidizing gas and recirculating hot spent shale from the gasification section. The pyrolysis takes place at 500 °C (930 °F) to 550 °C (1,020 °F). [ 3 ] [ 4 ]
The pyrolyzed oil shale moves by gravity downward to the gasification section. Gasification, which takes place at 750 °C (1,380 °F) to 850 °C (1,560 °F), converts remained carbon in the spent shale ( char ) to product oil shale gas. Steam from the cooling zone is used for fluidizing the sent shale while heat transferred by hot solids (oil shale ash) from the combustion section. The spent shale moves to the combustion section where it is burnt to heat the process, while oil shale ash moves to the cooling section before its removal from the retort. [ 3 ] | https://en.wikipedia.org/wiki/KENTORT_II |
The Industrial & Systems Engineering Program offers a Bachelor of Science degree in industrial engineering at the King Fahd University of Petroleum & Minerals (KFUPM) in the Kingdom of Saudi Arabia. With a total of 133 credit hours, the program covers the major areas of industrial engineering, such as operations research , production planning, inventory control, methods engineering , quality control , facility location , manufacturing , and facility layout.
The Industrial & Systems Engineering (ISE) program in the Systems Engineering Department was first introduced in 1984 and has been revised in 1996 based on the Accreditation Board for Engineering and Technology ( ABET ) recommendation after their first visit in 1993. The revision made in 1996 came after when the number of credit hours of the Bachelor of Science (B.Sc) was reduced from 141 to 133 credit hours. The program has received ABET accreditation extension in 2010.
The ISE program has a total of 50 credit hours on required ISE courses, with the following descriptions: | https://en.wikipedia.org/wiki/KFUPM_Program_of_Industrial_and_Systems_Engineering |
Monopotassium phosphate ( MKP ) (also, potassium dihydrogen phosphate , KDP , or monobasic potassium phosphate ) is the inorganic compound with the formula KH 2 PO 4 . Together with dipotassium phosphate (K 2 HPO 4 . (H 2 O) x ) it is often used as a fertilizer , food additive , and buffering agent . The salt often cocrystallizes with the dipotassium salt as well as with phosphoric acid . [ 7 ]
Single crystals are paraelectric at room temperature. At temperatures below −150 °C (−238 °F), they become ferroelectric .
Monopotassium phosphate can exist in several polymorphs . At room temperature it forms paraelectric crystals with tetragonal symmetry. Upon cooling to −150 °C (−238 °F) it transforms to a ferroelectric phase of orthorhombic symmetry, and the transition temperature shifts up to −50 °C (−58 °F) when hydrogen is replaced by deuterium. [ 8 ] Heating to 190 °C (374 °F) changes its structure to monoclinic. [ 9 ] When heated further, MKP decomposes, by loss of water, to potassium metaphosphate, KPO 3 , at 400 °C (752 °F).
Monopotassium phosphate is produced by the action of phosphoric acid on potassium carbonate . It can then be crystallized into boules, large crystals by dissolving the KDP in hot water and salt, creating a growth solution, placing a seed crystal in the solution and then cooling the solution, done in a holden-type crystallizer, in what is known as solution growth. [ 10 ] [ 11 ] [ 12 ]
Fertilizer-grade MKP powder contains the equivalent of 52% P 2 O 5 and 34% K 2 O , and is labeled NPK 0-52-34. MKP powder is often used as a nutrient source in the greenhouse trade and in hydroponics .
Crystals of MKP are used in optical modulators and for non-linear optics such as second-harmonic generation (SHG). Potassium dideuterium phosphate (KDP), with slightly different properties, is also used in nonlinear frequency conversion of laser light. The replacement of protons with deuterons in the crystal shifts the third overtone of the strong OH molecular stretch to longer wavelengths, moving it mostly out of the range of the fundamental line at approximately 1064 nm of neodymium-based lasers . Regular KDP has absorbances at this wavelength of approximately 4.7–6.3% per cm of thickness while highly deuterated KDP has absorbances of typically less than 0.8% per cm.
Monopotassium phosphate is also used as an ingredient in sports drinks such as Gatorade and Powerade .
In medicine, monopotassium phosphate is used for phosphate substitution in hypophosphatemia . [ 13 ] | https://en.wikipedia.org/wiki/KH2PO4 |
Potassium formate , HCO 2 K, HCOOK, or KHCO 2 , is the potassium salt of formic acid . This strongly hygroscopic white solid [ 2 ] is an intermediate in the formate potash process for the production of potassium. [ 3 ] Potassium formate has also been studied as a potential environmentally friendly deicing salt for use on roads. [ 4 ] [ 5 ] It has also been suggested for use in a less corrosive liquid desiccant . [ 6 ] A 52% solution of potassium formate has a freezing point of −60 °C (−76 °F). [ 7 ] Potassium formate brines are sometimes used for heat transfer, despite being much more corrosive than many other liquid coolants, especially to zinc and aluminum but even to many steels, [ 8 ] though some formulations are compatible with aluminum and steels. [ 9 ]
Since 1995, potassium formate has been increasingly used in aqueous drilling fluids to increase density, stabilize the hole, and improve drilling performance. [ 10 ] [ 11 ] [ 12 ]
This article about an organic compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KHCO2 |
6.351 (carbonic acid) [ 2 ]
Potassium bicarbonate ( IUPAC name : potassium hydrogencarbonate , also known as potassium acid carbonate ) is the inorganic compound with the chemical formula KHCO 3 . It is a white solid. [ 1 ]
It is manufactured by treating an aqueous solution of potassium carbonate or potassium hydroxide with carbon dioxide : [ 1 ]
Decomposition of the bicarbonate occurs between 100 and 120 °C (212 and 248 °F):
This reaction is employed to prepare high purity potassium carbonate.
This compound is a source of carbon dioxide for leavening in baking. It can substitute for baking soda (sodium bicarbonate) for those with a low-sodium diet , [ 4 ] and it is an ingredient in low-sodium baking powders . [ 5 ] [ 6 ]
As an inexpensive, nontoxic base , it is widely used in diverse application to regulate pH or as a reagent . Examples include as buffering agent in medications, an additive in winemaking .
Potassium bicarbonate is often added to bottled water to improve taste, [ 7 ] and is also used in club soda .
Higher potassium intake may prevent development of kidney stone disease . [ 8 ] Higher potassium intake is associated with a reduced risk of stroke . [ 9 ]
Potassium bicarbonate is used as a fire suppression agent ("BC dry chemical") in some dry chemical fire extinguishers , as the principal component of the Purple-K dry chemical, and in some applications of condensed aerosol fire suppression . It is the only dry chemical fire suppression agent recognized by the U.S. National Fire Protection Association for firefighting at airport crash rescue sites. It is about twice as effective in fire suppression as sodium bicarbonate . [ 10 ]
Potassium bicarbonate has widespread use in crops, especially for neutralizing acidic soil . [ 11 ]
Potassium bicarbonate is an effective fungicide against powdery mildew and apple scab , allowed for use in organic farming . [ 12 ] [ 13 ] [ 14 ] [ 15 ]
Potassium bicarbonate is a contact killer for Spanish moss when mixed 1 ⁄ 4 cup per gallon . [ 16 ]
The word saleratus , from Latin sal æratus meaning "aerated salt", first used in the nineteenth century, refers to both potassium bicarbonate and sodium bicarbonate. [ 17 ] | https://en.wikipedia.org/wiki/KHCO3 |
Potassium bifluoride is the inorganic compound with the formula K[HF 2 ] . This colourless salt consists of the potassium cation ( K + ) and the bifluoride anion ( [HF 2 ] − ). The salt is used as an etchant for glass. Sodium bifluoride is related and is also of commercial use as an etchant as well as in cleaning products. [ 3 ]
The salt was prepared by Edmond Frémy by treating potassium carbonate or potassium hydroxide with hydrofluoric acid:
With one more equivalent of HF, K[H 2 F 3 ] ( CAS RN 12178-06-2, m.p. 71.7 °C [ 4 ] ) is produced:
Thermal decomposition of K[HF 2 ] gives hydrogen fluoride :
The industrial production of fluorine entails the electrolysis of molten K[HF 2 ] and K[H 2 F 3 ] . [ 3 ] The electrolysis of K[HF 2 ] was first used by Henri Moissan in 1886. | https://en.wikipedia.org/wiki/KHF2 |
Potassium bisulfate ( potassium bisulphate ) is an inorganic compound with the chemical formula KHSO 4 and is the potassium acid salt of sulfuric acid . It is a white, water-soluble solid.
More than 1 million tons were produced in 1985 as the initial stage in the Mannheim process for producing potassium sulfate. The relevant conversion is the exothermic reaction of potassium chloride and sulfuric acid: [ 1 ] [ 2 ]
Potassium bisulfate is a by-product in the production of nitric acid from potassium nitrate and sulfuric acid: [ 3 ]
Thermal decomposition of potassium bisulfate forms potassium pyrosulfate : [ 1 ]
Above 600 °C potassium pyrosulfate converts to potassium sulfate and sulfur trioxide : [ 4 ]
Potassium bisulfate is commonly used to prepare potassium bitartrate for winemaking . [ 5 ] Potassium bisulfate is also used as a disintegrating agent in analytical chemistry or as a precursor to prepare potassium persulfate , a powerful oxidizing agent . [ 6 ]
Mercallite , the mineralogical form of potassium bisulfate, occurs very rarely. [ 7 ] Misenite is another more complex form of potassium bisulfate with the formula K 8 H 6 (SO 4 ) 7 . | https://en.wikipedia.org/wiki/KHSO4 |
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