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KICTANet Trust [ 1 ] is a multistakeholder think tank for Information and communications technology policy formulation whose work spans Stakeholder engagement, capacity building, research, and policy advocacy. [ 2 ] The network was initially designed to welcome multistakeholder participation due to the ‘perceived strength and effectiveness in joint collaborative policy advocacy activities, which would be based on pooling skills and resources ,’ [ 3 ] as opposed to wasting resources in ‘competing, overlapping advocacy ’. [ 4 ] Its operating slogan was, ‘let’s talk, though we may not agree’. [ 5 ] Tina James, who worked with CATIA when it supported the creation of KICTANet, points out: ‘the creation of KICTANet was just the right process at the right time.' [ 6 ]
With government and other stakeholders apparently relying on it, KICTANet therefore continued after the ICT policy was adopted, leading to ‘quite a lot of successes’ like the 2010 Kenya ICT Master Plan, as well as the regulatory approval of M-Pesa and Voice over Internet Protocol (VOIP) services in the country. [ 7 ] It also, for instance, participated in discussions that led to the drafting and passing of the National Cybersecurity Strategy (2014) and coordinated public participation in consultations like the 2014 African Union Convention on Cybersecurity. [ 8 ] By managing a website and mailing list with over 1000 participants from diverse stakeholder groups, [ 9 ] it has been described as ‘the biggest convener of ICT stakeholders in Kenya ’. [ 8 ]
Over the years, KICTAnet has contributed to the development of various ICT laws in Kenya, among them the Kenya Information & Communications Act 2013, [ 10 ] Kenya Data Protection Act 2019, [ 11 ] [ 12 ] Kenya Computer Misuse & Cybercrimes Act 2018, [ 13 ] Kenya ICT Policy 2006, Kenya ICT Policy 2019, [ 14 ] and the Kenya Data Protection Policy 2019. KICTANet's work has accelerated the uptake of ICTs in the African region and contributed to the achievement of the Sustainable Development Goals .
KICTANet has played a major advocacy role in the liberalization of the voice of the internet, and such other processes as the Freedom of Information Bills, the Independent Communications Commission of Kenya Bill, and the Media Council Bill. [ 15 ]
KICTANet has been the convener of the Kenya IGF [ 16 ] and the East African IGF. It was also one of the organizers of the global IGF held in Nairobi, Kenya in 2011. [ 17 ]
In 2016, KICTANet was registered as a Trust governed by a board of Trustees which includes a convenor (Chief Executive Officer), a chair, a treasurer, and a secretary. The current convenor and Chief Executive Officer is Ms Grace Githaiga . [ 18 ] [ 19 ] | https://en.wikipedia.org/wiki/KICTANet |
Potassium iodate ( K I O 3 ) is an ionic inorganic compound with the formula KIO 3 . It is a white salt that is soluble in water. [ 1 ]
It can be prepared by reacting a potassium-containing base such as potassium hydroxide with iodic acid , for example: [ 1 ]
It can also be prepared by adding iodine to a hot, concentrated solution of potassium hydroxide: [ 1 ]
Or by fusing potassium iodide with potassium chlorate , bromate or perchlorate , the melt is extracted with water and potassium iodate is isolated from the solution by crystallization: [ 2 ]
The analogous reaction with potassium hypochlorite is also possible: [ 3 ]
KI + 3KOCl → 3KCl + KIO 3
Conditions/substances to avoid include: heat , shock , friction , [ 4 ] combustible materials, [ 1 ] reducing materials, aluminium , [ 4 ] organic compounds , [ 1 ] carbon , hydrogen peroxide and sulfides . [ 4 ]
Potassium iodate is sometimes used for iodination of table salt to prevent iodine deficiency . In the US, iodized salt contains antioxidants , because atmospheric oxygen can oxidize wet iodide to iodine; other countries simply use potassium iodate instead. [ 5 ] Salt mixed with ferrous fumarate and potassium iodate, "double fortified salt", are used to address both iron and iodine deficiencies. [ 6 ] Potassium iodate is also used to provide iodine in some baby formula . [ 7 ]
Like potassium bromate , potassium iodate is occasionally used as a maturing agent in baking. [ 8 ]
Potassium iodate may be used to protect against accumulation of radioactive iodine in the thyroid by saturating the body with a stable source of iodine prior to exposure. [ 9 ] Approved by the World Health Organization for radiation protection, potassium iodate (KIO 3 ) is an alternative to potassium iodide (KI) , which has poor shelf life in hot and humid climates . [ 10 ] The UK , Singapore , United Arab Emirates , and the U.S. states Idaho and Utah all maintain potassium iodate tablets towards this end. [ citation needed ] Following the September 11 attacks , the government of Ireland issued potassium iodate tablets to all households for a similar purpose. [ 11 ]
Potassium iodate is not approved by the U.S. Food and Drug Administration (FDA) for use as a thyroid blocker , and the FDA has taken action against US websites that promote this use. [ 13 ] [ 14 ]
Potassium iodate is an oxidizing agent and as such it can form explosive mixtures when combined with organic compounds. [ 1 ] | https://en.wikipedia.org/wiki/KIO3 |
Potassium periodate is an inorganic salt with the molecular formula KIO 4 . It is composed of a potassium cation and a periodate anion and may also be regarded as the potassium salt of periodic acid . Note that the pronunciation is per-iodate, not period-ate.
Unlike other common periodates, such as sodium periodate and periodic acid , it is only available in the meta periodate form; the corresponding potassium ortho periodate (K 5 IO 6 ) has never been reported.
Potassium periodate can be prepared by the oxidation of an aqueous solution of potassium iodate by chlorine and potassium hydroxide . [ 1 ]
It can also be generated by the electrochemical oxidation of potassium iodate , however the low solubility of KIO 3 makes this approach of limited use.
Potassium periodate decomposes at 582 °C to form potassium iodate and oxygen .
The low solubility of KIO 4 makes it useful for the determination of potassium [ citation needed ] and cerium . [ 2 ]
It is slightly soluble in water (one of the less soluble of potassium salts, owing to a large anion), giving rise to a solution that is slightly alkaline . On heating (especially with manganese(IV) oxide as catalyst), it decomposes to form potassium iodate, releasing oxygen gas.
KIO 4 forms tetragonal crystals of the Scheelite type ( space group I 4 1 / a ). [ 3 ] | https://en.wikipedia.org/wiki/KIO4 |
KISS , an acronym for " Keep it simple, stupid! ", is a design principle first noted by the U.S. Navy in 1960. [ 1 ] [ 2 ] First seen partly in American English by at least 1938, KISS implies that simplicity should be a design goal. The phrase has been associated with aircraft engineer Kelly Johnson . [ 3 ] The term "KISS principle" was in popular use by 1970. [ 4 ] Variations on the phrase (usually as some euphemism for the more churlish "stupid") include "keep it super simple", "keep it simple, silly", "keep it short and simple", "keep it short and sweet", "keep it simple and straightforward", [ 5 ] "keep it small and simple", "keep it simple, soldier", [ 6 ] "keep it simple, sailor", "keep it simple, sweetie", [ 7 ] "keep it stupidly simple", or "keep it sweet and simple".
The acronym was reportedly coined by Kelly Johnson , lead engineer at the Lockheed Skunk Works (creators of the Lockheed U-2 and SR-71 Blackbird spy planes, among many others). [ 3 ] However, the variant "Keep it Short and Simple" is attested from a 1938 issue of the Minneapolis Star . [ 8 ]
While popular usage has transcribed it for decades as "Keep it simple, stupid", Johnson transcribed it simply as "Keep it simple stupid" (no comma), and this reading is still used by many authors. [ 9 ]
The principle is best exemplified by the story of Johnson handing a team of design engineers a handful of tools, with the challenge that the jet aircraft they were designing must be repairable by an average mechanic in the field under combat conditions with only these tools. Hence, the "stupid" refers to the relationship between the way things break and the sophistication available to repair them.
The acronym has been used by many in the U.S. military , especially the U.S. Navy and United States Air Force , and in the field of software development .
The principle most probably finds its origins in similar minimalist concepts, such as:
Heath Robinson contraptions and Rube Goldberg's machines , intentionally overly-complex solutions to simple tasks or problems, are humorous examples of "non-KISS" solutions.
Master animator Richard Williams explains the KISS principle in his book The Animator's Survival Kit , and Disney's Nine Old Men write about it in Disney Animation: The Illusion of Life , a considerable work of the genre. The problem faced is that inexperienced animators may "over-animate" in their works, that is, a character may move too much and do too much. Williams urges animators to "KISS".
In the Filipino neo-noir film Segurista , KISS is invoked by Mrs Librada (played by Liza Lorena ) as an approach to selling insurance . [ 13 ]
In the American version of The Office , Michael Scott's advice to Dwight Schrute before making any decision is KISS (Keep it Simple, Stupid). | https://en.wikipedia.org/wiki/KISS_principle |
In biochemistry, the KIX domain (kinase-inducible domain (KID) interacting domain) or CREB binding domain is a protein domain of the eukaryotic transcriptional coactivators CBP and P300 . It serves as a docking site for the formation of heterodimers between the coactivator and specific transcription factors . Structurally, the KIX domain is a globular domain consisting of three α-helices and two short 3 10 -helices.
The KIX domain was originally discovered in 1996 as the specific and minimal region in CBP that binds and interacts with phosphorylated CREB to activate transcription. [ 2 ] It was thus first termed CREB-binding domain. However, when it was later discovered that it also binds many other proteins, the more general name KIX domain became favoured. The KIX domain contains two separate binding sites: the "c-Myb site", named after the oncoprotein c-Myb , and the "MLL site", named after the proto-oncogene MLL (Mixed Lineage Leukemia, KMT2A ). [ 3 ]
The paralogous coactivators CBP ( CREBBP ) and P300 ( EP300 ) are recruited to DNA -bound transcription factors to activate transcription. Coactivators can associate with promoters and enhancers in the DNA only indirectly through protein-protein contacts with transcription factors . CBP and P300 activate transcription synergistically in two ways: first, by remodelling and relaxing chromatin through their intrinsic histone acetyltransferase activity, and second, by recruiting the basal transcription machinery, such as RNA polymerase II . [ 4 ]
The KIX domain belongs to the proposed GACKIX domain superfamily . GACKIX comprises structurally and functionally highly homologous domains in related proteins. It is named after the protein GAL11 / ARC105 ( MED15 ), the plant protein CBP-like, and the KIX domain from CBP and P300. [ 5 ] Additional instances include RECQL5 and related plant proteins. [ 6 ] [ 7 ] All of these contain a KIX domain or KIX-related domain that interacts with the transactivation domain of many different transcription factors. The distinction between a KIX domain, a KIX-related domain and a GACKIX domain is subject to an ongoing debate and not clearly defined.
Aside from the KIX domain, CBP and P300 contain many other protein binding domains that should not be confused (numbers are aa numberings):
All three CH (cysteine/histidine-rich) domains are zinc fingers . [ 9 ]
Human and animal proteins:
Yeast proteins:
Viral proteins: | https://en.wikipedia.org/wiki/KIX_domain |
In the statistical mechanics of quantum mechanical systems and quantum field theory , the properties of a system in thermal equilibrium can be described by a mathematical object called a Kubo–Martin–Schwinger ( KMS ) state : a state satisfying the KMS condition .
Ryogo Kubo introduced the condition in 1957, [ 1 ] Paul C. Martin [ de ] and Julian Schwinger used it in 1959 to define thermodynamic Green's functions , [ 2 ] and Rudolf Haag , Marinus Winnink and Nico Hugenholtz used the condition in 1967 to define equilibrium states and called it the KMS condition. [ 3 ]
The simplest case to study is that of a finite-dimensional Hilbert space , in which one does not encounter complications like phase transitions or spontaneous symmetry breaking . The density matrix of a thermal state is given by
where H is the Hamiltonian operator and N is the particle number operator (or charge operator, if we wish to be more general) and
is the partition function . We assume that N commutes with H, or in other words, that particle number is conserved .
In the Heisenberg picture , the density matrix does not change with time, but the operators are time-dependent. In particular, translating an operator A by τ into the future gives the operator
A combination of time translation with an internal symmetry "rotation" gives the more general
A bit of algebraic manipulation shows that the expected values
for any two operators A and B and any real τ (we are working with finite-dimensional Hilbert spaces after all). We used the fact that the density matrix commutes with any function of ( H − μ N ) and that the trace is cyclic.
As hinted at earlier, with infinite dimensional Hilbert spaces, we run into a lot of problems like phase transitions, spontaneous symmetry breaking, operators that are not trace class , divergent partition functions, etc..
The complex functions of z , ⟨ α z μ ( A ) B ⟩ {\displaystyle \left\langle \alpha _{z}^{\mu }(A)B\right\rangle } converges in the complex strip − β < ℑ z < 0 {\displaystyle -\beta <\Im {z}<0} whereas ⟨ B α z μ ( A ) ⟩ {\displaystyle \left\langle B\alpha _{z}^{\mu }(A)\right\rangle } converges in the complex strip 0 < ℑ z < β {\displaystyle 0<\Im {z}<\beta } if we make certain technical assumptions like the spectrum of H − μ N is bounded from below and its density does not increase exponentially (see Hagedorn temperature ). If the functions converge, then they have to be analytic within the strip they are defined over as their derivatives,
and
exist.
However, we can still define a KMS state as any state satisfying
with ⟨ α z μ ( A ) B ⟩ {\displaystyle \left\langle \alpha _{z}^{\mu }(A)B\right\rangle } and ⟨ B α z μ ( A ) ⟩ {\displaystyle \left\langle B\alpha _{z}^{\mu }(A)\right\rangle } being analytic functions of z within their domain strips.
⟨ α τ μ ( A ) B ⟩ {\displaystyle \left\langle \alpha _{\tau }^{\mu }(A)B\right\rangle } and ⟨ B α τ + i β μ ( A ) ⟩ {\displaystyle \left\langle B\alpha _{\tau +i\beta }^{\mu }(A)\right\rangle } are the boundary distribution values of the analytic functions in question.
This gives the right large volume, large particle number thermodynamic limit. If there is a phase transition or spontaneous symmetry breaking, the KMS state is not unique.
The density matrix of a KMS state is related to unitary transformations involving time translations (or time translations and an internal symmetry transformation for nonzero chemical potentials) via the Tomita–Takesaki theory .
This quantum mechanics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KMS_state |
Potassium permanganate is an inorganic compound with the chemical formula KMnO 4 . It is a purplish-black crystalline salt, which dissolves in water as K + and MnO − 4 ions to give an intensely pink to purple solution.
Potassium permanganate is widely used in the chemical industry and laboratories as a strong oxidizing agent , and also as a medication for dermatitis , for cleaning wounds , and general disinfection . It is on the World Health Organization's List of Essential Medicines . [ 5 ] In 2000, worldwide production was estimated at 30,000 tons. [ 5 ]
Potassium permanganate is the potassium salt of the tetrahedral transition metal oxo complex permanganate , in which four O 2− ligands are bound to a manganese(VII) center. [ citation needed ]
KMnO 4 forms orthorhombic crystals with constants: a = 910.5 pm , b = 572.0 pm, c = 742.5 pm. The overall motif is similar to that for barium sulfate , with which it forms solid solutions . [ 6 ] In the solid (as in solution), each MnO − 4 centre is tetrahedral. The Mn–O distances are 1.62 Å. [ 7 ]
The purplish-black color of solid potassium permanganate, and the intensely pink to purple color of its solutions, is caused by its permanganate anion, which gets its color from a strong charge-transfer absorption band caused by excitation of electrons from oxo ligand orbitals to empty orbitals of the manganese(VII) center. [ 8 ]
Potassium permanganate functions as a strong oxidising agent . [ 9 ] Through this mechanism it results in disinfection , astringent effects, and decreased smell. [ 9 ]
Potassium permanganate is used for a number of skin conditions . [ 10 ] This includes fungal infections of the foot , impetigo , pemphigus , superficial wounds, dermatitis , and topical ulcers. [ 11 ] [ 10 ] Radioactive contamination of the skin can be cleaned with potassium permanganate and vigorous scrubbing. For topical ulcers it is used together with procaine benzylpenicillin . [ 10 ] Typically it is used in skin conditions that produce a lot of liquid. [ 11 ] It can be applied as a soaked dressing or a bath. [ 12 ] It can be used in children and adults. [ 13 ] Petroleum jelly may be used on the nails before soaking to prevent their discoloration. [ 14 ] For treating eczema, it is recommended using for only a few days at a time due to the possibility of it irritating the skin. [ 15 ]
The U.S. Food and Drug Administration does not recommend its use in the crystal or tablet form. It should only be used in a diluted liquid form. [ 16 ]
Potassium permanganate was first made in the 1600s and came into common medical use at least as early as the 1800s. [ 17 ] During World War I Canadian soldiers were given potassium permanganate (to be applied mixed with an ointment) in an effort to prevent sexually transmitted infections . [ 18 ] Some have attempted to bring about an abortion by putting it in the vagina, though this is not effective. [ 19 ] [ 20 ] [ 16 ] Other historical uses have included an effort to wash out the stomach in those with strychnine or picrotoxin poisoning. [ 21 ]
Side effects from topical use may include irritation of the skin and discoloration of clothing. [ 22 ] A harsh burn on a child from an undissolved tablet has been reported. [ 15 ] Higher concentration solutions can result in chemical burns . [ 23 ] Therefore, the British National Formulary recommends 100 mg be dissolved in a liter of water before use to form a 1:10,000 (0.01%) solution. [ 15 ] [ 24 ] [ 13 ] Wrapping the dressings soaked with potassium permanganate is not recommended. [ citation needed ]
Potassium permanganate is toxic if taken by mouth. [ 25 ] Side effects may include nausea, vomiting, and shortness of breath may occur. [ 26 ] If a sufficiently large amount (about 10 grams) is eaten death may occur. [ 26 ]
Concentrated solutions when drunk have resulted in acute respiratory distress syndrome or swelling of the airway. [ 27 ] Recommended measures for those who have ingested potassium permanganate include gastroscopy . [ 27 ] Activated charcoal or medications to cause vomiting are not recommended. While medications like ranitidine and acetylcysteine may be used in toxicity, evidence for this use is poor. [ 27 ]
In the United States the FDA requires tablets of the medication to be sold by prescription . [ 16 ] Potassium permanganate, however, does not have FDA approved uses and therefore non medical grade potassium permanganate is sometimes used for medical purposes. [ citation needed ]
It is available under a number of brand names including Permasol, Koi Med Tricho-Ex, and Kalii permanganas RFF. [ 28 ] It is occasionally called "Condy's crystals". [ 29 ]
Potassium permanganate may be used to prevent the spread of glanders among horses. [ 30 ]
Almost all applications of potassium permanganate exploit its oxidizing properties. [ 31 ] As a strong oxidant that does not generate toxic byproducts, KMnO 4 has many niche uses. [ citation needed ]
Potassium permanganate is used extensively in the water treatment industry. It is used as a regeneration chemical to remove iron and hydrogen sulfide (rotten egg smell) from well water via a "manganese greensand" filter. "Pot-Perm" is also obtainable at pool supply stores and is used additionally to treat wastewater. Historically it was used to disinfect drinking water [ 32 ] [ 33 ] and can turn the water pink. [ 34 ] Modern hiking and survivalist guides advise against using potassium permanganate in the field because it is difficult to dose correctly. [ 35 ] It currently finds application in the control of nuisance organisms such as zebra mussels in fresh water collection and treatment systems. [ 36 ]
A major application of KMnO 4 is as a reagent for the synthesis of organic compounds. [ 37 ] Significant amounts are required for the synthesis of ascorbic acid , chloramphenicol , saccharin , isonicotinic acid , and pyrazinoic acid . [ 31 ]
KMnO 4 is used in qualitative organic analysis to test for the presence of unsaturation . It is sometimes referred to as Baeyer's reagent after the German organic chemist Adolf von Baeyer . The reagent is an alkaline solution of potassium permanganate. Reaction with double or triple bonds ( R 2 C=CR 2 or R−C≡C−R ) causes the color to fade from purplish-pink to brown. Aldehydes and formic acid (and formates ) also give a positive test. [ 38 ] The test is antiquated.
KMnO 4 solution is a common thin layer chromatography (TLC) stain for the detection of oxidizable functional groups, such as alcohols, aldehydes, alkenes, and ketones. Such compounds result in a white to orange spot on TLC plates. [ 39 ] [ 40 ] [ 41 ]
Potassium permanganate can be used to quantitatively determine the total oxidizable organic material in an aqueous sample. The value determined is known as the permanganate value. In analytical chemistry , a standardized aqueous solution of KMnO 4 is sometimes used as an oxidizing titrant for redox titrations ( permanganometry ). As potassium permanganate is titrated, the solution becomes a light shade of purple, which darkens as excess of the titrant is added to the solution. In a related way, it is used as a reagent to determine the Kappa number of wood pulp. For the standardization of KMnO 4 solutions, reduction by oxalic acid is often used. [ 42 ] In agricultural chemistry, it is used for estimation of active carbon in soil. [ 43 ]
Aqueous, acidic solutions of KMnO 4 are used to collect gaseous mercury in flue gas during stationary source emissions testing. [ 44 ]
In histology , potassium permanganate was used as a bleaching agent. [ 45 ] [ 46 ]
Ethylene absorbents extend storage time of bananas even at high temperatures. This effect can be exploited by packing bananas in polyethylene together with potassium permanganate. By removing ethylene by oxidation, the permanganate delays the ripening, increasing the fruit's shelf life up to 4 weeks without the need for refrigeration. [ 47 ] [ 48 ] [ 49 ]
The chemical reaction, in which ethylene (C 2 H 4 ) is oxidised by potassium permanganate (KMnO 4 ) to carbon dioxide (CO 2 ), manganese oxide (MnO 2 ) and potassium hydroxide (KOH), in the presence of water, is presented as follows: [ 50 ]
3 C 2 H 4 + 12 KMnO 4 + 2 H 2 O → 6 CO 2 + 2 H 2 O + 12 MnO 2 + 12 KOH
Potassium permanganate is sometimes included in survival kits: as a hypergolic fire starter (when mixed with glycerol antifreeze from a car radiator); [ 51 ] [ 52 ] [ 53 ] as a water sterilizer; and for creating distress signals on snow. [ 54 ]
Potassium permanganate is added to "plastic sphere dispensers" to create backfires, burnouts, and controlled burns . Polymer spheres resembling ping-pong balls containing small amounts of permanganate are injected with ethylene glycol and projected towards the area where ignition is desired, where they spontaneously ignite seconds later. [ 55 ] [ 56 ] Both handheld [ 56 ] helicopter- [ 55 ] unmanned aircraft systems (UAS) or boat-mounted [ 56 ] plastic sphere dispensers are used.
Potassium permanganate is one of the principal chemicals used in the film and television industries to "age" props and set dressings. Its ready conversion to brown MnO 2 creates "hundred-year-old" or "ancient" looks on hessian cloth (burlap), ropes, timber and glass. [ 57 ]
Potassium permanganate can be used to oxidize cocaine paste to purify it and increase its stability. This led to the Drug Enforcement Administration launching Operation Purple in 2000, with the goal of monitoring the world supply of potassium permanganate; however, potassium permanganate derivatives and substitutes were soon used thereafter to avoid the operation. [ 58 ]
Potassium permanganate is used as an oxidizing agent in the synthesis of cocaine and methcathinone . [ 59 ]
Potassium permanganate is one of a number of possible treatments for Ichthyophthirius multifiliis (commonly known as "ich"), a parasite that infects and usually kills freshwater aquarium fish.
In 1659, Johann Rudolf Glauber fused a mixture of the mineral pyrolusite (manganese dioxide, MnO 2 ) and potassium carbonate to obtain a material that, when dissolved in water, gave a green solution ( potassium manganate ) which slowly shifted to violet and then finally red. [ 60 ] The reaction that produced the color changes that Glauber observed in his solution of potassium permanganate and potassium manganate (K 2 MnO 4 ) is now known as the " chemical chameleon ". [ 61 ] This report represents the first description of the production of potassium permanganate. [ 62 ] Just under 200 years later, London chemist Henry Bollmann Condy had an interest in disinfectants; he found that fusing pyrolusite with sodium hydroxide (NaOH) and dissolving it in water produced a solution with disinfectant properties. He patented this solution, and marketed it as 'Condy's Fluid'. Although effective, the solution was not very stable. This was overcome by using potassium hydroxide (KOH) rather than NaOH. This was more stable, and had the advantage of easy conversion to the equally effective potassium permanganate crystals. This crystalline material was known as 'Condy's crystals' or 'Condy's powder'. Potassium permanganate was comparatively easy to manufacture, so Condy was subsequently forced to spend considerable time in litigation to stop competitors from marketing similar products. [ 63 ] According to Varlam Shalamov , potassium permanganate solution was used as a catch-all treatment for dysentery, frostbite and ulcers in the Gulag camps of Kolyma.
Early photographers used it as a component of flash powder . It is now replaced with other oxidizers, due to the instability of permanganate mixtures. [ citation needed ]
Potassium permanganate is produced industrially from manganese dioxide , which also occurs as the mineral pyrolusite . In 2000, worldwide production was estimated at 30,000 tonnes. [ 31 ] The MnO 2 is fused with potassium hydroxide and heated in air or with another source of oxygen, like potassium nitrate or potassium chlorate . [ 31 ] This process gives potassium manganate :
With sodium hydroxide, the end product is not sodium manganate but a Mn(V) compound, which is one reason why the potassium permanganate is more commonly used than sodium permanganate . Furthermore, the potassium salt crystallizes better. [ 31 ]
The potassium manganate is then converted into permanganate by electrolytic oxidation in alkaline media:
Although of no commercial importance, potassium manganate can be oxidized by chlorine or by disproportionation under acidic conditions. [ 64 ] The chlorine oxidation reaction is
and the acid-induced disproportionation reaction may be written as
A weak acid such as carbonic acid is sufficient for this reaction:
Permanganate salts may also be generated by treating a solution of Mn 2+ ions with strong oxidants such as lead dioxide (PbO 2 ), sodium bismuthate (NaBiO 3 ), or peroxydisulfate . Tests for the presence of manganese exploit the vivid violet color of permanganate produced by these reagents.
Dilute solutions of KMnO 4 convert alkenes into diols . This behaviour is also used as a qualitative test for the presence of double or triple bonds in a molecule, since the reaction decolorizes the initially purple permanganate solution and generates a brown precipitate (MnO 2 ). In this context, it is sometimes called Baeyer's reagent . However, bromine serves better in measuring unsaturation (double or triple bonds) quantitatively, since KMnO 4 , being a very strong oxidizing agent , can react with a variety of groups.
Under acidic conditions, the alkene double bond is cleaved to give the appropriate carboxylic acid : [ 65 ]
Potassium permanganate oxidizes aldehydes to carboxylic acids, illustrated by the conversion of n - heptanal to heptanoic acid: [ 66 ]
Even an alkyl group (with a benzylic hydrogen) on an aromatic ring is oxidized, e.g. toluene to benzoic acid . [ 67 ]
Glycols and polyols are highly reactive toward KMnO 4 . For example, addition of potassium permanganate to an aqueous solution of sugar and sodium hydroxide produces the chemical chameleon reaction, which involves dramatic color changes associated with the various oxidation states of manganese . A related vigorous reaction is exploited as a fire starter in survival kits. For example, a mixture of potassium permanganate and glycerol or pulverized glucose ignites readily. [ 51 ] Its sterilizing properties are another reason for inclusion of KMnO 4 in a survival kit. [ citation needed ]
Treating a mixture of aqueous potassium permanganate with a quaternary ammonium salt results in ion exchange, precipitating the quat salt of permanganate. Solutions of these salts are sometimes soluble in organic solvents: [ 68 ]
Similarly, addition of a crown ether also gives a lipophilic salt. [ 69 ]
Permanganate reacts with concentrated hydrochloric acid to give chlorine and manganese(II):
In neutral solution, permanganate slowly reduces to manganese dioxide (MnO 2 ). This is the material that stains one's skin when handling KMnO 4 .
KMnO 4 reduces in alkaline solution to give green K 2 MnO 4 : [ 70 ]
This reaction illustrates the relatively rare role of hydroxide as a reducing agent.
Addition of concentrated sulfuric acid to potassium permanganate gives Mn 2 O 7 . [ 71 ] Although no reaction may be apparent, the vapor over the mixture will ignite paper impregnated with alcohol. Potassium permanganate and sulfuric acid react to produce some ozone , which has a high oxidizing power and rapidly oxidizes the alcohol, causing it to combust. As the reaction also produces explosive Mn 2 O 7 , this should only be attempted with great caution. [ 72 ] [ 73 ]
Solid potassium permanganate decomposes when heated:
It is a redox reaction.
Potassium permanganate poses risks as an oxidizer . [ 74 ] Contact with skin can cause skin irritation and in some cases severe allergic reaction. It can also result in discoloration and clothing stains. [ 75 ] | https://en.wikipedia.org/wiki/KMnO4 |
Potassium nitrite (distinct from potassium nitrate ) is the inorganic compound with the chemical formula K N O 2 . It is an ionic salt of potassium ions K + and nitrite ions NO 2 − , which forms a white or slightly yellow, hygroscopic crystalline powder that is soluble in water. [ 1 ]
It is a strong oxidizer and may accelerate the combustion of other materials. Like other nitrite salts such as sodium nitrite , potassium nitrite is toxic if swallowed, and laboratory tests suggest that it may be mutagenic or teratogenic . Gloves and safety glasses are usually used when handling potassium nitrite.
Nitrite is present at trace levels in soil, natural waters, plant and animal tissues, and fertilizer. [ 2 ] The pure form of nitrite was first made by the Swedish chemist Carl Wilhelm Scheele working in the laboratory of his pharmacy in the market town of Köping . He heated potassium nitrate at red heat for half an hour and obtained what he recognized as a new “salt.” The two compounds (potassium nitrate and nitrite) were characterized by Péligot and the reaction was established as:
Potassium nitrite can be obtained by the reduction of potassium nitrate. The production of potassium nitrite by absorption of nitrogen oxides in potassium hydroxide or potassium carbonate is not employed on a large scale because of the high price of these alkalies. Furthermore, the fact that potassium nitrite is highly soluble in water makes the solid difficult to recover.
The mixing of cyanamide and KNO 2 produces changes from white solids to yellow liquid and then to orange solid, forming cyanogen and ammonia gases. No external energy is used and the reactions are carried out with a small amount of O 2 . [ 3 ]
Potassium nitrite forms potassium nitrate when heated in the presence of oxygen from 550 °C to 790 °C. The rate of reaction increases with temperature, but the extent of reaction decreases. At 550 °C and 600 °C the reaction is continuous and eventually goes to completion. From 650 °C to 750 °C, as the case of decomposition of potassium nitrate is, the system attains equilibrium . At 790 °C, a rapid decrease in volume is first observed, followed by a period of 15 minutes during which no volume changes occur. This is then followed by an increase in volume due primarily to the evolution of nitrogen, which is attributed to the decomposition of potassium nitrite. [ 4 ]
Potassium nitrite reacts at an extremely slow rate with a liquid ammonia solution of potassium amide at room temperatures, and in the presence of ferric oxide or cobaltic oxide , to form nitrogen and potassium hydroxide .
Interest in a medical role for inorganic nitrite was first aroused because of the spectacular success of organic nitrites and related compounds in the treatment of angina pectoris . While working with Butter at the Edinburgh Royal Infirmary in the 1860s, Brunton noted that the pain of angina could be lessened by venesection and wrongly concluded that the pain must be due to elevated blood pressure. As a treatment for angina, the reduction of circulating blood by venesection was inconvenient. Therefore, he decided to try the effect on a patient of inhaling amyl nitrite , a recently synthesized compound and one that his colleague had shown lowered blood pressure in animals. Pain associated with an anginal attack disappeared rapidly, and the effect lasted for several minutes, generally long enough for the patient to recover by resting. For a time, amyl nitrite was the favored treatment for angina, but due to its volatility, it was replaced by chemically related compounds that had the same effect. [ 2 ]
The effect of potassium nitrite on the nervous system, brain, spinal cord, pulse, arterial blood pressure, and respiration of healthy human volunteers was noted, as was the variability between individuals. The most significant observation was that even a small dose of <0.5 grains (≈30 mg) given by mouth caused, at first, an increase in arterial blood pressure , followed by a moderate decrease. With larger doses, pronounced hypotension ensued. They also noted that potassium nitrite, however administered, had a profound effect on the appearance and oxygen-carrying capacity of the blood. They compared the biological action of potassium nitrite with that of amyl and ethyl nitrites and concluded that the similarity of action depends on the conversion of organic nitrites to nitrous acid . [ 2 ]
Solutions of acidified nitrite have been used successfully to generate NO and to induce vasorelaxation in isolated blood vessel studies, and the same reaction mechanism has been proposed to explain the biological action of nitrite . [ 2 ]
Potassium nitrite is used in the manufacturing of heat transfer salts. As food additive E249 , potassium nitrite is a preservative similar to sodium nitrite and is approved for usage in the EU, [ 5 ] USA, [ 6 ] Australia and New Zealand [ 7 ] (where it is listed under its INS number 249).
Potassium nitrite is also used by modern luthiers to darken the tone and possibly improve the acoustic characteristics of violins , used after completing the box and before varnishing . The KNO2 is applied then exposed to sunlight .
When reacting with acids, potassium nitrite forms toxic nitrous oxides. Fusion with ammonium salts results in effervescence and ignition . Reactions with reducing agents can result in fires and explosions. [ 8 ]
Potassium nitrite is stored with other oxidizing agents but separated from flammables, combustibles, reducing agents , acids, cyanides , ammonium compounds, amides, and other nitrogenous salts in a cool, dry, well ventilated location. [ 8 ] | https://en.wikipedia.org/wiki/KNO2 |
Potassium nitrate is a chemical compound with a sharp, salty, bitter taste and the chemical formula K N O 3 . It is a potassium salt of nitric acid . This salt consists of potassium cations K + and nitrate anions NO − 3 , and is therefore an alkali metal nitrate . It occurs in nature as a mineral, niter (or nitre outside the United States). [ 5 ] It is a source of nitrogen , and nitrogen was named after niter. Potassium nitrate is one of several nitrogen-containing compounds collectively referred to as saltpetre (or saltpeter in the United States). [ 5 ]
Major uses of potassium nitrate are in fertilizers , tree stump removal , rocket propellants and fireworks . It is one of the major constituents of traditional gunpowder (black powder). [ 6 ] In processed meats , potassium nitrate reacts with hemoglobin and myoglobin generating a red color. [ 7 ]
Nitre, or potassium nitrate, because of its early and global use and production, has many names.
As for nitrate, Egyptian and Hebrew words for it had the consonants n-t-r, indicating likely cognation in the Greek nitron , which was Latinised to nitrum or nitrium . Thence Old French had niter and Middle English nitre . By the 15th century, Europeans referred to it as saltpetre , [ 8 ] specifically Indian saltpetre (Chilean saltpetre is sodium nitrate [ 9 ] ) and later as nitrate of potash, as the chemistry of the compound was more fully understood.
The Arabs called it "Chinese snow" ( Arabic : ثلج الصين , romanized : thalj al-ṣīn ) as well as bārūd ( بارود ), a term of uncertain origin that later came to mean gunpowder . It was called "Chinese salt" by the Iranians/Persians [ 10 ] [ 11 ] [ 12 ] or "salt from Chinese salt marshes" ( Persian : نمک شوره چينی namak shūra chīnī ). [ 13 ] : 335 [ 14 ] The Tiangong Kaiwu , published in the 17th century by members of the Qing dynasty , detailed the production of gunpowder and other useful products from nature.
In Mauryan India saltpeter manufacturers formed the Nuniya & Labana caste . [ 15 ] Saltpeter finds mention in Kautilya's Arthashastra (compiled 300BC – 300AD), which mentions using its poisonous smoke as a weapon of war, [ 16 ] although its use for propulsion did not appear until medieval times.
A purification process for potassium nitrate was outlined in 1270 by the chemist and engineer Hasan al-Rammah of Syria in his book al-Furusiyya wa al-Manasib al-Harbiyya ( The Book of Military Horsemanship and Ingenious War Devices ). In this book, al-Rammah describes first the purification of barud (crude saltpeter mineral) by boiling it with minimal water and using only the hot solution, then the use of potassium carbonate (in the form of wood ashes ) to remove calcium and magnesium by precipitation of their carbonates from this solution, leaving a solution of purified potassium nitrate, which could then be dried. [ 17 ] This was used for the manufacture of gunpowder and explosive devices. The terminology used by al-Rammah indicated the gunpowder he wrote about originated in China. [ 18 ]
At least as far back as 1845, nitratite deposits were exploited in Chile and California.
Major natural sources of potassium nitrate were the deposits crystallizing from cave walls and the accumulations of bat guano in caves. [ 19 ] Extraction is accomplished by immersing the guano in water for a day, filtering, and harvesting the crystals in the filtered water. Traditionally, guano was the source used in Laos for the manufacture of gunpowder for Bang Fai rockets. [ 20 ]
Calcium nitrate , or lime saltpetre, was discovered on the walls of stables, from the urine of barnyard animals. [ 9 ]
Potassium nitrate was produced in a nitrary or " saltpetre works ". [ 21 ] The process involved burial of excrements (human or animal) in a field beside the nitraries, watering them and waiting until leaching allowed saltpeter to migrate to the surface by efflorescence . Operators then gathered the resulting powder and transported it to be concentrated by ebullition in the boiler plant. [ 22 ] [ 23 ]
Besides " Montepellusanus ", during the thirteenth century (and beyond) the only supply of saltpeter across Christian Europe (according to "De Alchimia" in 3 manuscripts of Michael Scot, 1180–1236) was "found in Spain in Aragon in a certain mountain near the sea". [ 13 ] : 89, 311 [ 24 ]
In 1561, Elizabeth I , Queen of England and Ireland, who was at war with Philip II of Spain , became unable to import saltpeter (of which the Kingdom of England had no home production), and had to pay "300 pounds gold" to the German captain Gerrard Honrik for the manual "Instructions for making saltpeter to growe" (the secret of the " Feuerwerkbuch " -the nitraries-). [ 25 ]
A nitre bed is a similar process used to produce nitrate from excrement. Unlike the leaching-based process of the nitrary, however, one mixes the excrements with soil and waits for soil microbes to convert amino-nitrogen into nitrates by nitrification . The nitrates are extracted from soil with water and then purified into saltpeter by adding wood ash. The process was discovered in the early 15th century and was very widely used until the Chilean mineral deposits were found. [ 26 ]
The Confederate side of the American Civil War had a significant shortage of saltpeter. As a result, the Nitre and Mining Bureau was set up to encourage local production, including by nitre beds and by providing excrement to government nitraries. On November 13, 1862, the government advertised in the Charleston Daily Courier for 20 or 30 "able bodied Negro men" to work in the new nitre beds at Ashley Ferry, S.C. The nitre beds were large rectangles of rotted manure and straw, moistened weekly with urine, "dung water", and liquid from privies, cesspools and drains, and turned over regularly. The National Archives published payroll records that account for more than 29,000 people compelled to such labor in the state of Virginia. The South was so desperate for saltpeter for gunpowder that one Alabama official reportedly placed a newspaper ad asking that the contents of chamber pots be saved for collection. In South Carolina, in April 1864, the Confederate government forced 31 enslaved people to work at the Ashley Ferry Nitre Works, outside Charleston. [ 27 ]
Perhaps the most exhaustive discussion of the niter-bed production is the 1862 LeConte text. [ 28 ] He was writing with the express purpose of increasing production in the Confederate States to support their needs during the American Civil War . Since he was calling for the assistance of rural farming communities, the descriptions and instructions are both simple and explicit. He details the "French Method", along with several variations, as well as a "Swiss method". N.B. Many references have been made to a method using only straw and urine, but there is no such method in this work.
Turgot and Lavoisier created the Régie des Poudres et Salpêtres a few years before the French Revolution . Niter-beds were prepared by mixing manure with either mortar or wood ashes, common earth and organic materials such as straw to give porosity to a compost pile typically 4 feet (1.2 m) high, 6 feet (1.8 m) wide, and 15 feet (4.6 m) long. [ 28 ] The heap was usually under a cover from the rain, kept moist with urine , turned often to accelerate the decomposition, then finally leached with water after approximately one year, to remove the soluble calcium nitrate which was then converted to potassium nitrate by filtering through potash .
Joseph LeConte describes a process using only urine and not dung, referring to it as the Swiss method . Urine is collected directly, in a sandpit under a stable. The sand itself is dug out and leached for nitrates which are then converted to potassium nitrate using potash, as above. [ 29 ]
From 1903 until the World War I era, potassium nitrate for black powder and fertilizer was produced on an industrial scale from nitric acid produced using the Birkeland–Eyde process , which used an electric arc to oxidize nitrogen from the air. During World War I the newly industrialized Haber process (1913) was combined with the Ostwald process after 1915, allowing Germany to produce nitric acid for the war after being cut off from its supplies of mineral sodium nitrates from Chile (see nitratite ).
Potassium nitrate can be made by combining ammonium nitrate and potassium hydroxide .
An alternative way of producing potassium nitrate without a by-product of ammonia is to combine ammonium nitrate, found in instant ice packs , [ 30 ] and potassium chloride , easily obtained as a sodium-free salt substitute .
Potassium nitrate can also be produced by neutralizing nitric acid with potassium hydroxide. This reaction is highly exothermic.
On industrial scale it is prepared by the double displacement reaction between sodium nitrate and potassium chloride.
Potassium nitrate has an orthorhombic crystal structure at room temperature, [ 31 ] which transforms to a trigonal system at 128 °C (262 °F). On cooling from 200 °C (392 °F), another trigonal phase forms between 124 °C (255 °F) and 100 °C (212 °F). [ 32 ] [ 33 ]
Sodium nitrate is isomorphous with calcite , the most stable form of calcium carbonate , whereas room-temperature potassium nitrate is isomorphous with aragonite , a slightly less stable polymorph of calcium carbonate. The difference is attributed to the similarity in size between nitrate ( NO − 3 ) and carbonate ( CO 2− 3 ) ions and the fact that the potassium ion ( K + ) is larger than sodium ( Na + ) and calcium ( Ca 2+ ) ions. [ 34 ]
In the room-temperature structure of potassium nitrate, each potassium ion is surrounded by 6 nitrate ions. In turn, each nitrate ion is surrounded by 6 potassium ions. [ 31 ]
Potassium nitrate is moderately soluble in water, but its solubility increases with temperature. The aqueous solution is almost neutral, exhibiting pH 6.2 at 14 °C (57 °F) for a 10% solution of commercial powder. It is not very hygroscopic , absorbing about 0.03% water in 80% relative humidity over 50 days. It is insoluble in alcohol and is not poisonous; it can react explosively with reducing agents , but it is not explosive on its own. [ 2 ]
Between 550–790 °C (1,022–1,454 °F), potassium nitrate reaches a temperature-dependent equilibrium with potassium nitrite : [ 35 ]
Potassium nitrate has a wide variety of uses, largely as a source of nitrate.
Historically, nitric acid was produced by combining sulfuric acid with nitrates such as saltpeter. In modern times this is reversed: nitrates are produced from nitric acid produced via the Ostwald process .
The most famous use of potassium nitrate is probably as the oxidizer in blackpowder . From the most ancient times until the late 1880s, blackpowder provided the explosive power for all the world's firearms. After that time, small arms and large artillery increasingly began to depend on cordite , a smokeless powder . Blackpowder remains in use today in black powder rocket motors , but also in combination with other fuels like sugars in " rocket candy " (a popular amateur rocket propellant). It is also used in fireworks such as smoke bombs . [ 36 ] It is also added to cigarettes to maintain an even burn of the tobacco [ 37 ] and is used to ensure complete combustion of paper cartridges for cap and ball revolvers. [ 38 ] It can also be heated to several hundred degrees to be used for niter bluing , which is less durable than other forms of protective oxidation, but allows for specific coloration of steel parts, such as screws, pins, and other small parts of firearms.
Potassium nitrate has been a common ingredient of salted meat since antiquity [ 39 ] or the Middle Ages . [ 40 ] The widespread adoption of nitrate use is more recent and is linked to the development of large-scale meat processing. [ 6 ] The use of potassium nitrate has been mostly discontinued because it gives slow and inconsistent results compared with sodium nitrite preparations such as "Prague powder" or pink " curing salt ". Even so, potassium nitrate is still used in some food applications, such as salami, dry-cured ham, charcuterie , and (in some countries) in the brine used to make corned beef (sometimes together with sodium nitrite). [ 41 ] In the Shetland Islands (UK) it is used in the curing of mutton to make reestit mutton , a local delicacy. [ 42 ] When used as a food additive in the European Union, [ 43 ] the compound is referred to as E252 ; it is also approved for use as a food additive in the United States [ 44 ] and Australia and New Zealand [ 45 ] (where it is listed under its INS number 252). [ 2 ]
Since October 2015, WHO classifies processed meat as Group 1 carcinogen (based on epidemiological studies, convincingly carcinogenic to humans). [ 46 ]
In April 2023 the French Court of Appeals of Limoges confirmed that food-watch NGO Yuka was legally legitimate in describing Potassium Nitrate E249 to E252 as a "cancer risk", and thus rejected an appeal by the French charcuterie industry against the organisation. [ 47 ]
Potassium nitrate is used in fertilizers as a source of nitrogen and potassium – two of the macronutrients for plants. When used by itself, it has an NPK rating of 13-0-44. [ 48 ] [ 49 ]
Potassium nitrate was once thought to induce impotence , and is still rumored to be in institutional food (such as military fare). There is no scientific evidence for such properties. [ 65 ] [ 66 ] In Bank Shot , El ( Joanna Cassidy ) propositions Walter Ballantine ( George C. Scott ), who tells her that he has been fed saltpeter in prison. [ citation needed ] In One Flew Over the Cuckoo's Nest , Randle is asked by the nurses to take his medications, but not knowing what they are, he mentions he does not want anyone to "slip me saltpeter". He then proceeds to imitate the motions of masturbation.
In 1776 , John Adams asks his wife Abigail to make saltpeter for the Continental Army. She, eventually, is able to do so in exchange for pins for sewing. [ 67 ]
In the Star Trek episode " Arena ", Captain Kirk injures a gorn using a rudimentary cannon that he constructs using potassium nitrate as a key ingredient of gunpowder . [ citation needed ]
In 21 Jump Street , Jenko, played by Channing Tatum , gives a rhyming presentation about potassium nitrate for his chemistry class. [ citation needed ]
In Eating Raoul , Paul hires a dominatrix to impersonate a nurse and trick Raoul into consuming saltpeter in a ploy to reduce his sexual appetite for his wife. [ citation needed ]
In The Simpsons episode " El Viaje Misterioso de Nuestro Jomer (The Mysterious Voyage of Our Homer) ", Mr. Burns is seen pouring saltpeter into his chili entry, titled Old Elihu's Yale-Style Saltpeter Chili. [ citation needed ]
In the Sharpe novel series by Bernard Cornwell , numerous mentions are made of an advantageous supply of saltpeter from India being a crucial component of British military supremacy in the Napoleonic Wars. In Sharpe's Havoc , the French Captain Argenton laments that France needs to scrape its supply from cesspits . [ citation needed ]
In the Dr. Stone anime and manga series, the struggle for control over a natural saltpeter source from guano features prominently in the plot. [ citation needed ]
In the farming lore from the Corn Belt of the 1800s, drought-killed corn [ 68 ] in manured fields could accumulate saltpeter to the extent that upon opening the stalk for examination it would "fall as a fine powder upon the table". [ 69 ]
In the Slovenian short story Martin Krpan from Vrh pri Sveti Trojici , the titular character and Slovene folk hero Martin Krpan illegally smuggles "English salt" for a living. The exact nature of "English salt" is a matter of debate, but it may have been a euphemism for potassium nitrate (saltpeter) due to its role in manufacturing gunpowder . [ citation needed ]
In Dexter: Original Sin 's first episode, Dexter's first victim uses potassium nitrate to kill her victims. | https://en.wikipedia.org/wiki/KNO3 |
Potassium superoxide is an inorganic compound with the formula K O 2 . [ 6 ] It is a yellow paramagnetic solid that decomposes in moist air. It is a rare example of a stable salt of the superoxide anion. It is used as a CO 2 scrubber, H 2 O dehumidifier, and O 2 generator in rebreathers , spacecraft , submarines , and spacesuits .
Potassium superoxide is produced by burning molten potassium in an atmosphere of excess oxygen . [ 7 ]
The salt consists of K + and O − 2 ions, linked by ionic bonding. The O–O distance is 1.28 Å. [ 2 ]
Potassium superoxide is a source of superoxide, which is an oxidant and a nucleophile, depending on its reaction partner. [ 8 ]
Upon contact with water, it undergoes disproportionation to potassium hydroxide , oxygen, and hydrogen peroxide:
It reacts with carbon dioxide, releasing oxygen:
Theoretically, 1 kg of KO 2 absorbs 0.310 kg of CO 2 while releasing 0.338 kg of O 2 . One mole of KO 2 absorbs 0.5 moles of CO 2 and releases 0.75 moles of oxygen.
Potassium superoxide finds only niche uses as a laboratory reagent. Because it reacts with water, KO 2 is often studied in organic solvents. Since the salt is poorly soluble in nonpolar solvents, crown ethers are typically used. The tetraethylammonium salt is also known. Representative reactions of these salts involve using superoxide as a nucleophile , e.g., in converting alkyl bromides to alcohols and acyl chlorides to diacyl peroxides . [ 10 ]
Ion exchange with tetramethylammonium hydroxide gives tetramethylammonium superoxide, a yellow solid. [ 11 ]
The Russian Space Agency has successfully used potassium superoxide in chemical oxygen generators for its spacesuits and Soyuz spacecraft . Potassium superoxide was also used in a rudimentary life support system for five mice as part of the Biological Cosmic Ray Experiment on Apollo 17. [ 12 ]
KO 2 has also been used in canisters for rebreathers for firefighting and mine rescue , and in cartridges for chemical oxygen generators on submarines. A flash fire caused by dropping such a cartridge into seawater contributed to the Kursk disaster . This highly exothermic reaction with water is also the reason why potassium superoxide has had only limited use in scuba rebreathers . | https://en.wikipedia.org/wiki/KO2 |
Potassium titanyl phosphate ( KTP ) is an inorganic compound with the formula K + [TiO] 2+ PO 3− 4 . It is a white solid. KTP is an important nonlinear optical material that is commonly used for frequency-doubling diode-pumped solid-state lasers such as Nd:YAG and other neodymium -doped lasers . [ 1 ]
The compound is prepared by the reaction of titanium dioxide with a mixture of KH 2 PO 4 and K 2 HPO 4 near 1300 K. The potassium salts serve both as reagents and flux. [ 2 ]
The material has been characterized by X-ray crystallography . KTP has an orthorhombic crystal structure . It features octahedral Ti(IV) and tetrahedral phosphate sites. Potassium has a high coordination number. All heavy atoms (Ti, P, K) are linked exclusively by oxides, which interconnect these atoms. [ 2 ]
Crystals of KTP are highly transparent for wavelengths between 350 and 2700 nm with a reduced transmission out to 4500 nm where the crystal is effectively opaque. Its second-harmonic generation (SHG) coefficient is about three times higher than KDP . It has a Mohs hardness of about 5. [ 3 ]
KTP is also used as an optical parametric oscillator for near IR generation up to 4 μm. It is particularly suited to high power operation as an optical parametric oscillator due to its high damage threshold and large crystal aperture. The high degree of birefringent walk-off between the pump signal and idler beams present in this material limit its use as an optical parametric oscillator for very low power applications.
The material has a relatively high threshold to optical damage (~15 J/cm 2 ), an excellent optical nonlinearity and excellent thermal stability in theory. In practice, KTP crystals need to have stable temperature to operate if they are pumped with 1064 nm ( infrared , to output 532 nm green). However, it is prone to photochromic damage (called grey tracking) during high-power 1064 nm second-harmonic generation which tends to limit its use to low- and mid-power systems.
Other such materials include potassium titanyl arsenate (KTiOAsO 4 ).
It is used to produce "greenlight" to perform some laser prostate surgery . KTP crystals coupled with Nd:YAG or Nd:YVO 4 crystals are commonly found in green laser pointers . [ 4 ]
KTP is also used as an electro-optic modulator , optical waveguide material, and in directional couplers .
Periodically poled potassium titanyl phosphate ( PPKTP ) consists of KTP with switched domain regions within the crystal for various nonlinear optic applications and frequency conversion. It can be wavelength tailored for efficient second-harmonic generation , sum-frequency generation , and difference frequency generation. The interactions in PPKTP are based upon quasi-phase-matching , achieved by periodic poling of the crystal, whereby a structure of regularly spaced ferroelectric domains with alternating orientations are created in the material.
PPKTP is commonly used for Type 1 & 2 frequency conversions for pump wavelengths of 730–3500 nm.
Other materials used for periodic poling are wide band gap inorganic crystals like lithium niobate (resulting in periodically poled lithium niobate, PPLN), lithium tantalate , and some organic materials.
Other materials used for laser frequency doubling are | https://en.wikipedia.org/wiki/KO5PTi |
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/KOCl |
KORE Wireless Group specializes in Internet of Things (IoT) systems. It is headquartered in Atlanta, Georgia . [ 4 ] In March 2021, KORE and Cerberus Telecom Acquisition Corp. announced a definitive merger agreement. Upon completion of the transaction, the combined company, which has a pro forma valuation of $1.04 billion, [ 5 ] expects to be listed on the New York Stock Exchange under the ticker symbol “KORE”. [ 6 ] [ 7 ]
KORE was founded in 2002 by Chris Scatliff by acquiring Zero Gravity Wireless, a Microcell reseller and support software developer. With Alex Brisbourne and William Greenberg as part of the founding team, KORE was repositioned as a provider of Machine-to-Machine connectivity. [ citation needed ]
Following the acquisition of Microcell by Rogers Wireless , KORE expanded its wholesale agreement to provide M2M and Mobile Virtual Network Operator (MVNO) footprint in Canada. [ 8 ]
Wireless Matrix Corp selected KORE to provide the platform for fleet management across North America. [ 9 ] [ 10 ]
In 2010 Geotab selected KORE to enable it to expand its European fleet management products. [ 11 ] KORE signed an agreement with both Vodafone and Iridium Communications to expand its MVNO M2M service to more than 180 countries in March 2011. [ 12 ]
After launching M2M consulting company KORE Systems, the company then acquired all assets of nPhase from Verizon Wireless . [ citation needed ]
In May 2013, KORE became a founding member of the International M2M Council, with KORE's then COO Alex Brisbourne joining the Council's Board of Governors. [ 13 ] In November 2013, Inmarsat appointed KORE as its M2M distribution partner, [ 14 ]
In March 2014, KORE acquired Jazz Wireless Data to further enhance its service portfolio. [ 15 ] [ 16 ]
In November 2014, KORE announced that ABRY Partners would invest in KORE and simultaneously announced that KORE would acquire RacoWireless . [ 17 ]
In April 2016, KORE acquired Wyless Group. Wyless Group, founded in 2003 by Christopher Lowery, a UK telecoms entrepreneur, had operating subsidiaries in UK, USA, Europe, Latin America and Asia. [ 18 ]
In December 2018, KORE announced its acquisition of Aspider. [ 19 ]
In December 2019, KORE announced its acquisition of Integron, an IoT solutions and managed services provider. [ 20 ]
In February 2022, KORE acquired Business Mobility Partners and SIMON IoT. [ 21 ]
In June 2023, KORE acquired the IoT and Wireless Business unit from Twilio. [ 22 ] | https://en.wikipedia.org/wiki/KORE_Wireless |
Potassium hexafluorophosphate is a chemical compound with the formula KPF 6 . This colourless salt consists of potassium cations and hexafluorophosphate anions . It is prepared from phosphorus pentachloride : [ 2 ]
This exothermic reaction is conducted in liquid hydrogen fluoride . The salt is stable in a hot alkaline aqueous solution, from which it can be recrystallized. The sodium and ammonium salts are more soluble in water whereas the rubidium and caesium salts are less so.
KPF 6 is a common laboratory source of the hexafluorophosphate anion, a non-coordinating anion that confers lipophilicity to its salts. These salts are often less soluble than the closely related tetrafluoroborates . | https://en.wikipedia.org/wiki/KPF6 |
Potassium phosphate is a generic term for the salts of potassium and phosphate ions including: [ 1 ]
As food additives , potassium phosphates have the E number E340.
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KPO4 |
In probability theory , the KPZ fixed point is a Markov field and conjectured to be a universal limit of a wide range of stochastic models forming the universality class of a non-linear stochastic partial differential equation called the KPZ equation . Even though the universality class was already introduced in 1986 with the KPZ equation itself, the KPZ fixed point was not concretely specified until 2021 when mathematicians Konstantin Matetski , Jeremy Quastel and Daniel Remenik gave an explicit description of the transition probabilities in terms of Fredholm determinants . [ 1 ]
All models in the KPZ class have in common, that they have a fluctuating height function or some analogue function, that can be thought of as a function, that models the growth of the model by time. The KPZ equation itself is also a member of this class and the canonical model of modelling random interface growth. The strong KPZ universality conjecture conjectures that all models in the KPZ universality class converge under a specific scaling of the height function to the KPZ fixed point and only depend on the initial condition.
Matetski-Quastel-Remenik constructed the KPZ fixed point for the ( 1 + 1 ) {\displaystyle (1+1)} -dimensional KPZ universality class (i.e. one space and one time dimension) on the polish space of upper semicontinous functions (UC) with the topology of local UC convergence. They did this by studying a particular model of the KPZ universality class the TASEP („Totally Asymmetric Simple Exclusion Process“) with general initial conditions and the random walk of its associated height function. They achieved this by rewriting the biorthogonal function of the correlation kernel, that appears in the Fredholm determinant formula for the multi-point distribution of the particles in the Weyl chamber . Then they showed convergence to the fixed point. [ 1 ]
Let h ( t , x → ) {\displaystyle h(t,{\vec {x}})} denote a height function of some probabilistic model with ( t , x → ) ∈ R × R d {\displaystyle (t,{\vec {x}})\in \mathbb {R} \times \mathbb {R} ^{d}} denoting space-time. So far only the case for d = 1 {\displaystyle d=1} , also noted as ( 1 + 1 ) {\displaystyle (1+1)} , was deeply studied, therefore we fix this dimension for the rest of the article. In the KPZ universality class exist two equilibrium points or fixed points, the trivial Edwards-Wilkinson (EW) fixed point and the non-trivial KPZ fixed point . The KPZ equation connects them together.
The KPZ fixed point is rather defined as a height function h ( t , x → ) {\displaystyle {\mathfrak {h}}(t,{\vec {x}})} and not as a particular model with a height function.
The KPZ fixed point ( h ( t , x ) ) t ≥ 0 , x ∈ R {\displaystyle ({\mathfrak {h}}(t,x))_{t\geq 0,x\in \mathbb {R} }} is a Markov process, such that the n-point distribution for x 1 < x 2 < ⋯ < x n ∈ R {\displaystyle x_{1}<x_{2}<\cdots <x_{n}\in \mathbb {R} } and t > 0 {\displaystyle t>0} can be represented as
where a 1 , … , a n ∈ R {\displaystyle a_{1},\dots ,a_{n}\in \mathbb {R} } and K {\displaystyle K} is a trace class operator called the extended Brownian scattering operator and the subscript means that the process in h ( 0 , ⋅ ) {\displaystyle {\mathfrak {h}}(0,\cdot )} starts. [ 1 ]
The KPZ conjecture conjectures that the height function h ( t , x → ) {\displaystyle h(t,{\vec {x}})} of all models in the KPZ universality at time t {\displaystyle t} fluctuate around the mean with an order of t 1 / 3 {\displaystyle t^{1/3}} and the spacial correlation of the fluctuation is of order t 2 / 3 {\displaystyle t^{2/3}} . This motivates the so-called 1:2:3 scaling which is the characteristic scaling for the KPZ fixed point. The EW fixed point has also a scaling the 1:2:4 scaling . The fixed points are invariant under their associated scaling.
The 1:2:3 scaling of a height function is for ε > 0 {\displaystyle \varepsilon >0}
where 1:3 and 2:3 stand for the proportions of the exponents and C ε {\displaystyle C_{\varepsilon }} is just a constant. [ 2 ]
The strong conjecture says, that all models in the KPZ universality class converge under 1:2:3 scaling of the height function if their initial conditions also converge, i.e.
with initial condition
where c 1 , c 2 , c 3 {\displaystyle c_{1},c_{2},c_{3}} are constants depending on the model. [ 3 ]
If we remove the growth term in the KPZ equation, we get
which converges under the 1:2:4 scaling
to the EW fixed point. The weak conjecture says now, that the KPZ equation is the only Heteroclinic orbit between the KPZ and EW fixed point.
If one fixes the time dimension and looks at the limit
then one gets the Airy process ( A ( x ) ) x ∈ R {\displaystyle ({\mathcal {A}}(x))_{x\in \mathbb {R} }} which also occurs in the theory of random matrices . [ 4 ] | https://en.wikipedia.org/wiki/KPZ_fixed_point |
KREEP , an acronym built from the letters K (the atomic symbol for potassium ), REE ( rare-earth elements ) and P (for phosphorus ), is a geochemical component of some lunar impact breccia and basaltic rocks. Its most significant feature is somewhat enhanced concentration of a majority of so-called "incompatible" elements [ 1 ] (those that are concentrated in the liquid phase during magma crystallization ) and the heat -producing elements, namely radioactive uranium , thorium , and potassium (due to presence of the radioactive 40 K ). [ 2 ]
The typical composition of KREEP includes about one percent, by mass, of potassium and phosphorus oxides, 20 to 25 parts per million of rubidium , and a concentration of the element lanthanum that is 300 to 350 times the concentrations found in carbonaceous chondrites . [ 3 ] Most of potassium, phosphorus and rare-earth elements in KREEP basalts are incorporated in the grains of the phosphate minerals apatite and merrillite . [ 4 ]
Indirectly, it has been deduced that the origin of KREEP is contained in the origin of the Moon. This is now commonly thought to be the result of a rocky object the size of Mars that struck the Earth about 4.5 billion (4.5×10 9 ) years ago. [ 5 ] This collision threw a large amount of broken rock into orbit around the Earth. This ultimately gathered together to form the Moon . [ 6 ]
Given the high energy such a collision would involve, it has been deduced that a large portion of the Moon would have been liquified, and this
formed a lunar magma ocean . As the crystallization of this liquid rock proceeded, minerals such as olivine and pyroxene precipitated and sank to the bottom to form the lunar mantle .
After the solidification was about 75% complete, the material anorthositic plagioclase began to crystallize, and because of its low density, it floated, forming a solid crust. Hence, elements that are usually incompatible (i.e., those that usually partition in the liquid phase) would have been progressively concentrated into the magma. Thus a KREEP-rich magma was formed that was sandwiched at first between the crust and mantle. The evidence for these processes comes from the highly anorthositic composition of the crust of the lunar highlands, as well as the presence of the rocks rich in KREEP. [ 7 ]
Before the mission of Lunar Prospector lunar satellite , it was commonly thought that these KREEP materials had been formed in a widespread layer beneath the crust. However, the measurements from the gamma-ray spectrometer on-board this satellite showed that the KREEP-containing rocks are primarily concentrated underneath the Oceanus Procellarum and the Mare Imbrium . This is a unique lunar geological province that is now known as the Procellarum KREEP Terrane .
Basins far from this province that dug deeply into the crust (and possibly the mantle), such as the Mare Crisium , the Mare Orientale , and the South Pole–Aitken basin , show only little or no enhancements of KREEP within their rims or ejecta. The enhancement of heat-producing radioactive elements within the crust (and/or the mantle) of the Procellarum KREEP Terrane is almost certainly responsible for the longevity and intensity of mare volcanism on the nearside of the Moon. [ 8 ]
KREEP might be of interest in lunar mining if a lunar base were to be established. Potassium and phosphorus are important for plant growth ( NPK fertilizer is used on earth) whereas uranium and thorium are potential fuels for nuclear power . However, the relatively low concentrations of the desired materials compared to earthbound ores may make extraction difficult. | https://en.wikipedia.org/wiki/KREEP |
KRP stands for kinesin related proteins . bimC is a subfamily of KRPs and its function is to separate the duplicated centrosomes during mitosis .
Kinesin-13 MCAK (Mitotic Centromere-Associated Kinesin) is a KRP that is involved in resolving errors during mitosis involving kinetochore-microtubules. This process is associated with Aurora B Protein Kinase. When Aurora B's function is disrupted, MCAK ability to locate centromeres, which play a critical role in separation of chromosomes during mitosis, was suppressed. [ 1 ] There are other environments in which MCAK's function is impaired, absent impact on its associated kinase. For example, alpha-tubulin detyrosination has been demonstrated to impact MCAK's mitotic repair capabilities, suggesting a potential cause of chromosomal instability. [ 2 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KRP_(biochemistry) |
KS Steel is a permanent magnetic steel with three times the magnetic reluctance of tungsten steel , which was developed in 1917 by the Japanese scientist and inventor Kotaro Honda . "KS" stands for Kichizaemon Sumitomo , the head of the family-run conglomerate, who provided financial support for the research leading to KS Steel's invention. Honda would go on to invent NKS steel in 1933 whose magnetic resistance is several times higher than that of KS Steel. [ 1 ]
After World War one, when Japan had to cope with painful restrictions on imports of materials from foreign countries such as Germany, physicist Kotaro Honda was motivated to study alloys due to the need of a domestic steel production. He opened up his RIKEN-Honda Laboratory at Tohoku Imperial University in 1922 after he invented KS steel in 1917; it is a permanent magnetic steel with three times the magnetic resistance of tungsten steel . [ 2 ] The initials KS in the name of the steel come from Kichizaemon Sumitomo, who was the head of the family that provided financial support for the research leading to the invention.
The composition of KS steel is 0.4–0.8 percent carbon ; 30–40 percent cobalt ; 5–9 percent tungsten ; and 1.5–3 percent chromium . KS steel is best tempered when heated to 950 °C and then quenched in heavy oil. The residual magnetism is reduced by only 6 percent when artificially aged. [ 3 ] The yield strength of KS steel is above 500 and tensile strength is above 620 and elongation is above 14. The maximum energy product (BH)max of KS steel is 30 kJ/m^3. [ 4 ]
This alloy-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KS_Steel |
KT5720 is a kinase inhibitor with specificity towards protein kinase A . [ 1 ] It is a semi-synthetic derivative of K252a [ 2 ] and analog of staurosporine .
KT5720 is an antagonist of protein kinase A . Protein kinase A (PKA) is a group of kinases that are cAMP-dependent that primarily phosphorylate serine or threonine residues in target proteins. PKA is a tetramer consisting of two catalytic subunits and two regulatory subunits, with the later holding the catalytic subunits in an inactive state. The binding of two cAMP molecules to each regulatory subunit causes an allosteric change that detaches the regulatory subunits from the catalytic subunits. [ 3 ] This exposes the ATP-binding site of the kinase. KT5720 binds competitively to the ATP-binding site of the catalytic subunit of PKA and its effects are dependent on the cellular concentration of ATP . [ 4 ]
There have been several studied effects on the inhibition of PKA through the binding of KT5720. KT5720 has been shown to effect dorsal root ganglion neurons through the inhibition of PKA. It reduced intracellular concentration of calcium ions as well as decrease the H-current in the HCN channels which decreased the excitability of rat neurons. [ 5 ] Additionally, there is evidence to suggest that the inhibition of KT5720 affects endothelial cell response to irradiation. It has been shown to decrease irradiation-induced apoptosis in human pulmonary microvascular endothelial cells. [ 6 ]
The purported target of KT5720 is PKA, however, it has displayed effects on other proteins. KT5720 has been shown to inhibit other protein kinases such as phosphorylase kinase (PHK) and pyruvate dehydrogenase kinase 1 (PDK1). One study determined that the IC 50 was 11nM and 300nM for PHK and PDK1, respectively. This was significantly lower than the IC 50 for PKA, determined to be 3.3µM in the same study. [ 7 ] This establishes that KT5720 can significantly affect other kinases, however, it cannot be used to determined the absolute specificity of KT5720 due to differing ATP concentrations in vitro and in vivo.
KT5720 has also been shown to affect platelet aggregation in rabbits. It's mechanism of action favored the inhibition of certain molecules such as serotonin but did not inhibit other platelets aggregation factors such as thrombin and collagen. [ 8 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KT5720 |
KT Freetel Co., Ltd. (Korea Telecom Freetel, Korean : 주식회사케이티프리텔 ) was a South Korean telecommunications firm, now merged into Korea Telecom , specializing in cellular, or mobile, phones. Since 1999, it has also developed extensive overseas operations. The company is credited with developing customized ring back tones . On 1 June 2009, KTF was merged with KT .
In 2003, KTF received an order from PT Mobile-8 Telecom of Indonesia for a comprehensive consulting service. KTF also signed a contract for the export of its CDMA network management system and invested $10 million in the Indonesian mobile provider.
KTF commercialized the world first nationwide HSDPA service with the brand of "SHOW" on 1 March 2007.
In India, the firm completed the first stage of its contract with Reliance for $2.65 million worth of the CDMA network construction.
KTF also holds a 25% stake in CEC Mobile of China , after investing a sum of 4.5 billion won in 2002. The two major shareholders of KTF are KT (52.99%) and NTT DoCoMo (10.03%). KTF sponsors a professional StarCraft team.
KT officially declared the merger on January 14 2009. [ citation needed ] KFTC approved merge on February 25, 2009. [ citation needed ] The Korea Communications Commission finally approved the merger on Mar 18 2009. [ citation needed ]
A special meeting of shareholders was held on Mar 27 2009. [ citation needed ] KT finished the merge on May 31, 2009. [ citation needed ] | https://en.wikipedia.org/wiki/KTF |
In statistical mechanics , the Kosterlitz–Thouless–Halperin–Nelson–Young ( KTHNY ) theory describes the process of melting of crystals in two dimensions (2D). The name is derived from the initials of the surnames of John Michael Kosterlitz , David J. Thouless , [ 1 ] [ 2 ] Bertrand Halperin , David R. Nelson , [ 3 ] [ 4 ] and A. Peter Young, [ 5 ] who developed the theory in the 1970s. It is, beside the Ising model in 2D and the XY model in 2D, [ 6 ] [ 7 ] one of the few theories, which can be solved analytically and which predicts a phase transition at a temperature T > 0 {\displaystyle T>0} .
Melting of 2D crystals is mediated by the dissociation of topological defects , which destroy the order of the crystal. In 2016, Michael Kosterlitz and David Thouless were awarded with the Nobel prize in physics for their idea, how thermally excited pairs of virtual dislocations induce a softening (described by renormalization group theory ) of the crystal during heating. The shear elasticity disappears simultaneously with the dissociation of the dislocations, indicating a fluid phase. [ 8 ] [ 9 ] Based on this work, David Nelson and Bertrand Halperin showed, that the resulting hexatic phase is not yet an isotropic fluid. Starting from a hexagonal crystal (which is the densest packed structure in 2D), the hexatic phase has a six-folded director field, similar to liquid crystals. Orientational order only disappears due to the dissociations of a second class of topological defects, named disclinations . Peter Young calculated the critical exponent of the diverging correlations length at the transition between crystalline and hexatic.
KTHNY theory predicts two continuous phase transitions , thus latent heat and phase coexistence is ruled out. The thermodynamic phases can be distinguished based on discrete versus continuous translational and orientational order. One of the transitions separates a solid phase with quasi-long range translational order and perfect long ranged orientational order from the hexatic phase. The hexatic phase shows short ranged translational order and quasi-long ranged orientational order. The second phase transition separates the hexatic phase from the isotropic fluid, where both, translational and orientational order is short ranged. The system is dominated by critical fluctuations, since for continuous transitions, the difference of energy between the thermodynamic phases disappears in the vicinity of the transition. This implies, that ordered and disordered regions fluctuate strongly in space and time. The size of those regions grows strongly near the transitions and diverges at the transition itself. At this point, the pattern of symmetry broken versus symmetric domains is fractal . Fractals are characterized by a scaling invariance – they appear similar on an arbitrary scale or by arbitrarily zooming in (this is true on any scale larger than the atomic distance). The scale invariance is the basis to use the renormalization group theory to describe the phase transitions. Both transitions are accompanied by spontaneous symmetry breaking . Unlike for melting in three dimensions, translational and orientational symmetry breaking does not need to appear simultaneously in 2D, since two different types of topological defects destroy the different types of order.
Michael Kosterlitz and David Thouless tried to resolve a contradiction about 2D crystals: on one hand side, the Mermin-Wagner theorem claims that symmetry breaking of a continuous order-parameter cannot exist in two dimensions. This implies, that perfect long range positional order is ruled out in 2D crystals. On the other side, very early computer simulations of Berni Alder and Thomas E. Wainwright indicated crystallization in 2D. The KTHNY theory shows implicitly that periodicity is not a necessary criterion for a solid (this is already indicated by the existence of amorphous solids like glasses). Following M. Kosterlitz, a finite shear elasticity defines a 2D solid, including quasicrystals in this description.
All three thermodynamic phases and their corresponding symmetries can be visualized using the structure factor : S ( q → ) = 1 N ⟨ ∑ i j e − i q → ( r → i − r → j ) ⟩ {\displaystyle S({\vec {q}})={\frac {1}{N}}\langle \sum _{ij}e^{-i{\vec {q}}({\vec {r}}_{i}-{\vec {r}}_{j})}\rangle } . The double sum runs over all positions of particle pairs i and j and the brackets denote an average about various configurations. The isotropic phase is characterized by concentric rings at q = 2 π / a {\displaystyle q=2\pi /a} , if a = 1 / ρ {\displaystyle a=1/{\sqrt {\rho }}} is the average particle distance calculated by the 2D particle density ρ {\displaystyle \rho } . The (closed packed) crystalline phase is characterized by six-fold symmetry based on the orientational order. Unlike in 3D, where the peaks are arbitrarily sharp ( δ {\displaystyle \delta } -peaks), the 2D peaks have a finite width described with a Lorenz-curve. This is due to the fact, that the translational order is only quasi-long ranged as predicted by the Mermin-Wagner theorem. The hexatic phase is characterized by six segments, which reflect the quasi-long ranged orientational order. The structure factor of Figure 1 is calculated from the positions of a colloidal monolayer (crosses at high intensity are artefacts from the Fourier transformation due to the finite (rectangular) field of view of the ensemble).
To analyse melting due to the dissociation of dislocations, one starts with the energy H l o c {\displaystyle H_{loc}} as function of distance between two dislocations. An isolated dislocation in 2D is a local distortions of the six-folded lattice, where neighbouring particles have five- and seven nearest neighbours, instead of six. It is important to note, that dislocations can only be created in pairs, due to topological reasons. A bound pair of dislocations is a local configuration with 5-7-7-5 neighbourhood.
The double sum runs over all positions of defect pairs k {\displaystyle k} and l {\displaystyle l} , Δ r → k , l = r → k − r → l {\displaystyle \Delta {\vec {r}}_{k,l}={\vec {r}}_{k}-{\vec {r}}_{l}} measures the distance between the dislocations. b → {\displaystyle {\vec {b}}} is the Burgers vector and denotes the orientation of the dislocation at position Orte r → k {\displaystyle {\vec {r}}_{k}} . The second term in the brackets brings dislocations to arrange preferentially antiparallel due to energetic reasons. Its contribution is small and can be neglected for large distance between defects. The main contribution stems from the logarithmic term (the first one in the brackets) which describes, how the energy of a dislocation pair diverges with increasing distance. Since the shortest distance between two dislocations is given approximatively by the average particle distance a {\displaystyle a} , the scaling of distances with a {\displaystyle a} prevents the logarithm ln Δ r → k , l a {\displaystyle \ln {\frac {\Delta {\vec {r}}_{k,l}}{a}}} to become negative. The strength of the interaction is proportional to Young's modulus Y {\displaystyle Y} given by the stiffness of the crystal lattice. To create a dislocation from an undisturbed lattice, a small displacement on a scale smaller than the average particle distance a {\displaystyle a} is needed. The discrete energy associated with this displacement is usually called core energy Energie E c {\displaystyle E_{c}} and has to be counted for each of the N l o c {\displaystyle N_{loc}} dislocations individually (last term).
An easy argument for the dominating logarithmic term is, that the magnitude of the strain induced by an isolated dislocation decays according to ∝ 1 r {\displaystyle \propto {\frac {1}{r}}} with distance. Assuming Hooke's approximation , the associated stress is linear with the strain. Integrating the strain ~1/r gives the energy proportional to the logarithm . The logarithmic distance dependence of the energy is the reason, why KTHNY-theory is one of the few theories of phase transitions which can be solved analytically: in statistical physics one has to calculate partition functions , e.g. the probability distribution for all possible configurations of dislocation pairs given by the Boltzmann distribution e H l o c k B T {\displaystyle e^{\frac {H_{loc}}{k_{B}T}}} . Here, k B T {\displaystyle k_{B}T} is the thermal energy with Boltzmann constant k B {\displaystyle k_{B}} . For the majority of problems in statistical physics one can hardly solve the partition function due to the enormous amount of particles and degrees of freedoms. This is different in KTHNY theory due to the logarithmic energy functions of dislocations H l o c {\displaystyle H_{loc}} and the e-function from the Boltzmann factor as inverse which can be solved easily.
We want to calculate the mean squared distance between two dislocations considering only the dominant logarithmic term for simplicity:
This mean distance ⟨ r 2 ⟩ → 0 {\displaystyle \langle r^{2}\rangle \to 0} tends to zero for low temperatures – dislocations will annihilate and the crystal is free of defects. The expression diverges ⟨ r 2 ⟩ → ∞ {\displaystyle \langle r^{2}\rangle \to \infty } , if the denominator tends to zero. This happens, when Y ⋅ a 4 π k B T = 4 {\displaystyle {\frac {Y\cdot a}{4\pi k_{B}T}}=4} . A diverging distance of dislocations implies, that they are dissociated and do not form a bound pair. The crystal is molten, if several isolated dislocations are thermally excited and the melting temperature T m {\displaystyle T_{m}} is given by Young's modulus:
The dimensionless quantity 16 π {\displaystyle 16\pi } is a universal constant for melting in 2D and is independent of details of the system under investigation.
This example investigated only an isolated pair of dislocations. In general, a multiplicity of dislocations will appear during melting. The strain field of an isolated dislocation will be shielded and the crystal will get softer in the vicinity of the phase transition; Young's modulus will decrease due to dislocations. In KTHNY theory, this feedback of dislocations on elasticity, and especially on Young's modulus acting as coupling constant in the energy function, is described within the framework of renormalization group theory .
If a 2D crystal is heated, virtual dislocation pairs will be excited due to thermal fluctuations in the vicinity of the phase transition. Virtual means, that the average thermal energy is not large enough to overcome (two times) the core-energy and to dissociate (unbind) dislocation pairs. Nonetheless, dislocation pairs can appear locally on very short time scales due to thermal fluctuations, before they annihilate again. Although they annihilate, they have a detectable impact on elasticity: they soften the crystal. The principle is completely analogue to calculating the bare charge of the electron in quantum electrodynamics (QED). In QED, the charge of the electron is shielded due to virtual electron-positron pairs due to quantum fluctuations of the vacuum. Roughly spoken one can summarize: If the crystal is softened due to the presence of virtual pairs of dislocation, the probability (fugacity) y {\displaystyle y} for creating additional virtual dislocations is enhanced, proportional to the Boltzmann factor of the core-energy of a dislocation y = e E C k B T {\displaystyle y=e^{\frac {E_{C}}{k_{B}T}}} . If additional (virtual) dislocations are present, the crystal will get additionally softer. If the crystal is additionally softer, the fugacity will increase further... and so on and so forth.
David Nelson, Bertrand Halperin and independently Peter Young formulated this in a mathematically precise way, using renormalization group theory for the fugacity and the elasticity: In the vicinity of the continuous phase transition, the system becomes critical – this means that it becomes self-similar on all length scales ≫ a {\displaystyle \gg a} . Executing a transformation of all length scales by a factor of l {\displaystyle l} , the energy E → E ( l ) {\displaystyle E\to E(l)} and fugacity y → y ( l ) {\displaystyle y\to y(l)} will depend on this factor, but the system has to appear identically, simultaneously due to the self similarity. Especially the energy function (Hamiltonian) of the dislocations have to be invariant in structure. The softening of the system after a length scale transformation (zooming out to visualize a larger area implies to count more dislocations) is now covered in a renormalized (reduced) elasticity. The recursion relation for elasticity and fugacity are:
Similar recursion relations can be derived for the shear modulus and the bulk modulus. I 0 {\displaystyle I_{0}} and I 1 {\displaystyle I_{1}} are Bessel functions , respectively. Depending on the starting point, the recursion relation can run into two directions. y → 0 {\displaystyle y\to 0} implies no defects, the ensemble is crystalline. y → ∞ {\displaystyle y\to \infty } , implies arbitrary many defects, the ensemble is fluid. The recursion relation have a fix-point at y = 0 {\displaystyle y=0} with E R / k B T = 16 π {\displaystyle E_{R}/k_{B}T=16\pi } . Now, E R {\displaystyle E_{R}} is the renormalized value instead of the bare one. Figure 2 shows Youngs’modulus as function of the dimensionless control parameter Γ {\displaystyle \Gamma } . It measures the ratio of the repelling energy between two particles and the thermal energy (which was constant in this experiment). It can be interpreted as pressure or inverse temperature. The black curve is a thermodynamic calculation of a perfect hexagonal crystal at T = 0 {\displaystyle T=0} . The blue curve is from computer simulations and shows a reduced elasticity due to lattice vibrations at T > 0 {\displaystyle T>0} . The red curve is the renormalization following the recursion relations, Young's modulus disappears discontinuously to zero at 16 π {\displaystyle 16\pi } . Turquoise symbols are from measurements of elasticity in a colloidal monolayer, and confirm the melting point at Y R = 16 π {\displaystyle Y_{R}=16\pi } .
The system enters the hexatic phase after the dissociation of dislocations. To reach the isotropic fluid, dislocations (5-7-pairs) have to dissociate into disclinations , consisting of isolated 5-folded and isolated 7-folded particles. Similar arguments for the interaction of disclinations compared to dislocations can be used. Again, disclinations can only be created as pairs due to topological reasons. Starting with the energy H c l i {\displaystyle H_{cli}} as function of distance between two disclinations one finds:
The logarithmic term is again dominating. The sign of the interaction gives attraction or repulsion for the winding numbers + π / 3 {\displaystyle +\pi /3} and − π / 3 {\displaystyle -\pi /3} of the five- and seven-folded disclinations in a way that charges with opposite sign have attraction. The overall strength is given by the stiffness against twist. The coupling constant F A {\displaystyle F_{A}} is called Frank's constant, following the theory of liquid crystals . E s {\displaystyle E_{s}} is the discrete energy of a dislocation to dissociate into two disclinations. The squared distance of two disclinations can be calculated the same way, as for dislocations, only the prefactor, denoting the coupling constant, has to be changed accordingly. It diverges for F A ⋅ π 36 = 4 {\displaystyle {\frac {F_{A}\cdot \pi }{36}}=4} . The system is molten from the hexatic phase into the isotropic liquid, if unbound disclinations are present. This transition temperature T i {\displaystyle T_{i}} is given by Frank's constant:
72 / π {\displaystyle 72/\pi } is again a universal constant. Figure 3 shows measurements of the orientational stiffness of a colloidal monolayer; Frank's constant drops below this universal constant at T i {\displaystyle T_{i}} .
Typically, Kosterlitz–Thouless transitions have a continuum of critical points which can be characterised by self-similar grains of disordered and ordered regions. In second order phase transitions, the correlation length measuring the size of those regions diverges algebraically:
Here, T c {\displaystyle T_{c}} is the transition temperature and ν {\displaystyle \nu } is a critical exponent. Another special feature of Kosterlitz–Thouless transitions is, that translational and orientational correlation length in 2D diverge exponentially (see also hexatic phase for the definition of those correlation functions):
The critical exponent becomes ν ¯ = 0,369 63 … {\displaystyle {\bar {\nu }}=0{,}36963\dots } for the diverging translational correlation length at the hexatic – crystalline transition. D. Nelson and B. Halperin predicted, that Frank's constant diverges exponentially with ν ¯ {\displaystyle {\bar {\nu }}} at T m {\displaystyle T_{m}} , too. The red curve shows a fit of experimental data covering the critical behaviour; the critical exponent is measured to be ν ¯ = 0 , 35 ± 0 , 02 {\displaystyle {\bar {\nu }}=0{,}35\pm 0{,}02} . This value is compatible with the prediction of KTHNY theory within the error bars. The orientational correlation length at the hexatic – isotropic transition is predicted to diverge with an exponent ν = 0 , 5 {\displaystyle \nu =0{,}5} . This rational value is compatible with mean-field-theories and implies that a renormalization of Frank's constant is not necessary. The increasing shielding of orientational stiffness due to disclinations has not to be taken into account – this is already done by dislocations which are frequently present at T i {\displaystyle T_{i}} . Experiments measured a critical exponent of ν = 0 , 5 ± 0 , 03 {\displaystyle \nu =0{,}5\pm 0{,}03} .
KTHNY-theory has been tested in experiment [ 10 ] [ 11 ] [ 12 ] and in computer simulations. [ 13 ] For short range particle interaction (hard discs), simulations found a weakly first order transition for the hexatic – isotropic transition, slightly beyond KTHNY-theory. [ 14 ] | https://en.wikipedia.org/wiki/KTHNY_theory |
kT (also written as k B T ) is the product of the Boltzmann constant , k (or k B ), and the temperature , T . This product is used in physics as a scale factor for energy values in molecular -scale systems (sometimes it is used as a unit of energy), as the rates and frequencies of many processes and phenomena depend not on their energy alone, but on the ratio of that energy and kT , that is, on E / kT (see Arrhenius equation , Boltzmann factor ). For a system in equilibrium in canonical ensemble , the probability of the system being in state with energy E is proportional to e − Δ E k T . {\displaystyle e^{\frac {-\Delta E}{kT}}.} [ 2 ]
More fundamentally, kT is the amount of heat required to increase the thermodynamic entropy of a system by k .
In physical chemistry , as kT often appears in the denominator of fractions (usually because of Boltzmann distribution ), sometimes β = 1 / kT is used instead of kT , turning e − Δ E k T {\displaystyle e^{\frac {-\Delta E}{kT}}} into e −βΔ E . [ 2 ]
RT is the product of the molar gas constant , R , and the temperature , T . This product is used in physics and chemistry as a scaling factor for energy values in macroscopic scale (sometimes it is used as a pseudo-unit of energy), as many processes and phenomena depend not on the energy alone, but on the ratio of energy and RT , i.e. E / RT . The SI units for RT are joules per mole ( J / mol ).
It differs from kT only by a factor of the Avogadro constant , N A . Its dimension is energy or ML 2 T −2 , expressed in SI units as joules (J):
This thermodynamics -related article is a stub . You can help Wikipedia by expanding it .
This article about statistical mechanics is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KT_(energy) |
Potassium titanyl phosphate ( KTP ) is an inorganic compound with the formula K + [TiO] 2+ PO 3− 4 . It is a white solid. KTP is an important nonlinear optical material that is commonly used for frequency-doubling diode-pumped solid-state lasers such as Nd:YAG and other neodymium -doped lasers . [ 1 ]
The compound is prepared by the reaction of titanium dioxide with a mixture of KH 2 PO 4 and K 2 HPO 4 near 1300 K. The potassium salts serve both as reagents and flux. [ 2 ]
The material has been characterized by X-ray crystallography . KTP has an orthorhombic crystal structure . It features octahedral Ti(IV) and tetrahedral phosphate sites. Potassium has a high coordination number. All heavy atoms (Ti, P, K) are linked exclusively by oxides, which interconnect these atoms. [ 2 ]
Crystals of KTP are highly transparent for wavelengths between 350 and 2700 nm with a reduced transmission out to 4500 nm where the crystal is effectively opaque. Its second-harmonic generation (SHG) coefficient is about three times higher than KDP . It has a Mohs hardness of about 5. [ 3 ]
KTP is also used as an optical parametric oscillator for near IR generation up to 4 μm. It is particularly suited to high power operation as an optical parametric oscillator due to its high damage threshold and large crystal aperture. The high degree of birefringent walk-off between the pump signal and idler beams present in this material limit its use as an optical parametric oscillator for very low power applications.
The material has a relatively high threshold to optical damage (~15 J/cm 2 ), an excellent optical nonlinearity and excellent thermal stability in theory. In practice, KTP crystals need to have stable temperature to operate if they are pumped with 1064 nm ( infrared , to output 532 nm green). However, it is prone to photochromic damage (called grey tracking) during high-power 1064 nm second-harmonic generation which tends to limit its use to low- and mid-power systems.
Other such materials include potassium titanyl arsenate (KTiOAsO 4 ).
It is used to produce "greenlight" to perform some laser prostate surgery . KTP crystals coupled with Nd:YAG or Nd:YVO 4 crystals are commonly found in green laser pointers . [ 4 ]
KTP is also used as an electro-optic modulator , optical waveguide material, and in directional couplers .
Periodically poled potassium titanyl phosphate ( PPKTP ) consists of KTP with switched domain regions within the crystal for various nonlinear optic applications and frequency conversion. It can be wavelength tailored for efficient second-harmonic generation , sum-frequency generation , and difference frequency generation. The interactions in PPKTP are based upon quasi-phase-matching , achieved by periodic poling of the crystal, whereby a structure of regularly spaced ferroelectric domains with alternating orientations are created in the material.
PPKTP is commonly used for Type 1 & 2 frequency conversions for pump wavelengths of 730–3500 nm.
Other materials used for periodic poling are wide band gap inorganic crystals like lithium niobate (resulting in periodically poled lithium niobate, PPLN), lithium tantalate , and some organic materials.
Other materials used for laser frequency doubling are | https://en.wikipedia.org/wiki/KTiOPO4 |
Prasterone sulfate (brand names Astenile , Mylis , Teloin , others), also known as dehydroepiandrosterone sulfate ( DHEA-S ), is a naturally occurring androstane steroid which is marketed and used in Japan and other countries as a labor inducer in the treatment of insufficient cervical ripening and dilation during childbirth . [ 3 ] [ 1 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] It is the C3β sulfate ester of prasterone (dehydroepiandrosterone; DHEA), and is known to act as a prohormone of DHEA and by extension of androgens and estrogens , [ 10 ] although it also has its own activity as a neurosteroid . [ 11 ] Prasterone sulfate is used medically as the sodium salt via injection and is referred to by the name sodium prasterone sulfate ( JAN Tooltip Japanese Accepted Name ). [ 9 ] [ 12 ]
Prasterone sulfate is available in Japan , Italy , Portugal , Argentina , and China . [ 9 ] [ 13 ] Brand names include Astenile, Dastonil, Di Luo An, Dinistenile, Levospa, Mylis, Sinsurrene, and Teloin. [ 9 ] [ 13 ]
This article about a steroid is a stub . You can help Wikipedia by expanding it .
This drug article relating to the genito-urinary system is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KYH3102 |
In infrared astronomy , the K band is an atmospheric transmission window centered on 2.2 μm (in the near-infrared 136 THz range). [ 1 ] [ 2 ] HgCdTe -based detectors are typically preferred for observing in this band. [ 3 ]
Photometric systems used in astronomy are sets of filters or detectors that have well-defined windows of absorption, based around a central peak detection frequency and where the edges of the detection window are typically reported where sensitivity drops below 50% of peak. Various organizations have defined systems with various peak frequencies and cutoffs in the K band, including K ′ , and K S , and K dark . [ 4 ]
This astronomy -related article is a stub . You can help Wikipedia by expanding it .
This physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K_band_(infrared) |
K correction converts measurements of astronomical objects into their respective rest frames . The correction acts on that object's observed magnitude (or equivalently, its flux ). Because astronomical observations often measure through a single filter or bandpass, observers only measure a fraction of the total spectrum , redshifted into the frame of the observer. For example, to compare measurements of stars at different redshifts viewed through a red filter, one must estimate K corrections to these measurements in order to make comparisons. If one could measure all wavelengths of light from an object (a bolometric flux), a K correction would not be required, nor would it be required if one could measure the light emitted in an emission line .
Carl Wilhelm Wirtz (1918), [ 1 ] who referred to the correction as a Konstanten k (German for "constant") - correction dealing with the effects of redshift of in his work on Nebula. English-speaking claim for the origin of the term "K correction" is Edwin Hubble , who supposedly arbitrarily chose K {\displaystyle K} to represent the reduction factor in magnitude due to this same effect and who may not have been aware / given credit to the earlier work. [ 2 ] [ 3 ]
The K-correction can be defined as follows
I.E. the adjustment to the standard relationship between absolute and apparent magnitude required to correct for the redshift effect. [ 4 ] Here, D L is the luminosity distance measured in parsecs .
The exact nature of the calculation that needs to be applied in order to perform a K correction depends upon the type of filter used to make the observation and the shape of the object's spectrum. If multi-color photometric measurements are available for a given object thus defining its spectral energy distribution ( SED ), K corrections then can be computed by fitting it against a theoretical or empirical SED template. [ 5 ] It has been shown that K corrections in many frequently used broad-band filters for low-redshift galaxies can be precisely approximated using two-dimensional polynomials as functions of a redshift and one observed color . [ 6 ] This approach is implemented in the K corrections calculator web-service. [ 7 ] | https://en.wikipedia.org/wiki/K_correction |
The K factor or characterization factor is defined from Rankine boiling temperature °R=1.8Tb[k] and relative to water density ρ at 60°F:
K(UOP) = 1.8 T b 3 / ρ {\displaystyle {\sqrt[{3}]{1.8Tb}}/\rho }
The K factor is a systematic way of classifying a crude oil according to its paraffinic , naphthenic , intermediate or aromatic nature. 12.5 or higher indicate a crude oil of predominantly paraffinic constituents, while 10 or lower indicate a crude of more aromatic nature. The K(UOP) is also referred to as the UOP K factor or just UOPK. [ 1 ]
This chemical process -related article is a stub . You can help Wikipedia by expanding it .
This article related to natural gas, petroleum or the petroleum industry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/K_factor_(crude_oil_refining) |
In genetics , the K a /K s ratio , also known as ω or d N / d S ratio , [ a ] is used to estimate the balance between neutral mutations , purifying selection and beneficial mutations acting on a set of homologous protein-coding genes . It is calculated as the ratio of the number of nonsynonymous substitutions per non-synonymous site (K a ), in a given period of time, to the number of synonymous substitutions per synonymous site (K s ), in the same period. The latter are assumed to be neutral, so that the ratio indicates the net balance between deleterious and beneficial mutations. Values of K a /K s significantly above 1 are unlikely to occur without at least some of the mutations being advantageous. If beneficial mutations are assumed to make little contribution, then K a /K s estimates the degree of evolutionary constraint .
Selection acts on variation in phenotypes, which are often the result of mutations in protein -coding genes . The genetic code is written in DNA sequences as codons , groups of three nucleotides . Each codon represents a single amino acid in a protein chain. However, there are more codons (64) than amino acids found in proteins (20), so many codons are effectively synonyms. For example, the DNA codons TTT and TTC both code for the amino acid Phenylalanine , so a change from the third T to C makes no difference to the resulting protein. On the other hand, the codon GAG codes for Glutamic acid while the codon GTG codes for Valine , so a change from the middle A to T does change the resulting protein, for better or (more likely) worse, [ b ] so the change is not a synonym. These changes are illustrated in the tables below.
The K a /K s ratio measures the relative rates of synonymous and nonsynonymous substitutions at a particular site.
Methods for estimating K a and K s use a sequence alignment of two or more nucleotide sequences of homologous genes that code for proteins (rather than being genetic switches, controlling development or the rate of activity of other genes). Methods can be classified into three groups: approximate methods, maximum-likelihood methods , and counting methods. However, unless the sequences to be compared are distantly related (in which case maximum-likelihood methods prevail), the class of method used makes a minimal impact on the results obtained; more important are the assumptions implicit in the chosen method. [ 1 ] : 498
Approximate methods involve three basic steps: (1) counting the number of synonymous and nonsynonymous sites in the two sequences, or estimating this number by multiplying the sequence length by the proportion of each class of substitution;
(2) counting the number of synonymous and nonsynonymous substitutions; and (3) correcting for multiple substitutions.
These steps, particularly the latter, require simplistic assumptions to be made if they are to be achieved computationally; for reasons discussed later, it is impossible to exactly determine the number of multiple substitutions. [ 1 ]
The maximum-likelihood approach uses probability theory to complete all three steps simultaneously. [ 1 ] It estimates critical parameters, including the divergence between sequences and the transition/transversion ratio, by deducing the most likely values to produce the input data. [ 1 ]
In order to quantify the number of substitutions, one may reconstruct the ancestral sequence and record the inferred changes at sites (straight counting – likely to provide an underestimate); fitting the substitution rates at sites into predetermined categories ( Bayesian approach; poor for small data sets); and generating an individual substitution rate for each codon (computationally expensive). Given enough data, all three of these approaches will tend to the same result. [ 2 ]
The K a /K s ratio is used to infer the direction and magnitude of natural selection acting on protein coding genes. A ratio greater than 1 implies positive or Darwinian selection (driving change); less than 1 implies purifying or stabilizing selection (acting against change); and a ratio of exactly 1 indicates neutral (i.e. no) selection. However, a combination of positive and purifying selection at different points within the gene or at different times along its evolution may cancel each other out. The resulting averaged value can mask the presence of one of the selections and lower the seeming magnitude of another selection.
Of course, it is necessary to perform a statistical analysis to determine whether a result is significantly different from 1, or whether any apparent difference may occur as a result of a limited data set. The appropriate statistical test for an approximate method involves approximating dN − dS with a normal approximation, and determining whether 0 falls within the central region of the approximation. More sophisticated likelihood techniques can be used to analyse the results of a Maximum Likelihood analysis, by performing a chi-squared test to distinguish between a null model (K a /K s = 1) and the observed results. [ 1 ]
The K a /K s ratio is a more powerful test of the neutral model of evolution than many others available in population genetics as it requires fewer assumptions. [ 1 ]
There is often a systematic bias in the frequency at which various nucleotides are swapped, as certain mutations are more probable than others. [ 1 ] For instance, some lineages may swap C to T more frequently than they swap C to A. In the case of the amino acid Asparagine , which is coded by the codons AAT or AAC, a high C->T exchange rate will increase the proportion of synonymous substitutions at this codon, whereas a high C→A exchange rate will increase the rate of non-synonymous substitutions. Because it is rather common for transitions (T↔C & A↔G) to be favoured over transversions (other changes), [ 1 ] models must account for the possibility of non-homogeneous rates of exchange. [ 3 ] Some simpler approximate methods, such as those of Miyata & Yasunaga and Nei & Gojobori, neglect to take these into account, which generates a faster computational time at the expense of accuracy; these methods will systematically overestimate N and underestimate S. [ 1 ]
Further, there may be a bias in which certain codons are preferred in a gene, as a certain combination of codons may improve translational efficiency. [ 1 ] A 2022 study reported that synonymous mutations in representative yeast genes are mostly strongly non-neutral, which calls into question the assumptions underlying use of the K a /K s ratio. [ 4 ]
In addition, as time progresses, it is possible for a site to undergo multiple modifications. For instance, a codon may switch from AAA→AAC→AAT→AAA. There is no way of detecting multiple substitutions at a single site, thus the estimate of the number of substitutions is always an underestimate. In addition, in the example above two non-synonymous and one synonymous substitution occurred at the third site; however, because substitutions restored the original sequence, there is no evidence of any substitution. As the divergence time between two sequences increases, so too does the amount of multiple substitutions. Thus "long branches" in a dN/dS analysis can lead to underestimates of both dN and dS, and the longer the branch, the harder it is to correct for the introduced noise. [ 3 ] Of course, the ancestral sequence is usually unknown, and two lineages being compared will have been evolving in parallel since their last common ancestor. This effect can be mitigated by constructing the ancestral sequence; the accuracy of this sequence is enhanced by having a large number of sequences descended from that common ancestor to constrain its sequence by phylogenetic methods. [ 1 ]
Methods that account for biases in codon usage and transition/transversion rates are substantially more reliable than those that do not. [ 1 ]
Although the K a /K s ratio is a good indicator of selective pressure at the sequence level, evolutionary change can often take place in the regulatory region of a gene which affects the level, timing or location of gene expression. K a /K s analysis will not detect such change. It will only calculate selective pressure within protein coding regions. In addition, selection that does not cause differences at an amino acid level—for instance, balancing selection —cannot be detected by these techniques. [ 1 ]
Another issue is that heterogeneity within a gene can make a result hard to interpret. For example, if K a /K s = 1, it could be due to relaxed selection, or to a chimera of positive and purifying selection at the locus. A solution to this limitation would be to apply K a /K s analysis across many species at individual codons.
The K a /K s method requires a rather strong signal in order to detect selection.
In order to detect selection between lineages, then the selection, averaged over all sites in the sequence, must produce a K a /K s greater than one—quite a feat if regions of the gene are strongly conserved.
In order to detect selection at specific sites, then the K a /K s ratio must be greater than one when averaged over all included lineages at that site—implying that the site must be under selective pressure in all sampled lineages.
This limitation can be moderated by allowing the K a /K s rate to take multiple values across sites and across lineages; the inclusion of more lineages also increases the power of a sites-based approach. [ 1 ]
Further, the method lacks the capability to distinguish between positive and negative nonsynonymous substitutions. Some amino acids are chemically similar to one another, whereas other substitutions may place an amino acid with wildly different properties to its precursor. In most situations, a smaller chemical change is more likely to allow the protein to continue to function, and a large chemical change is likely to disrupt the chemical structure and cause the protein to malfunction. However, incorporating this into a model is not straightforward as the relationship between a nucleotide substitution and the effects of the modified chemical properties is very difficult to determine. [ 1 ]
An additional concern is that the effects of time must be incorporated into an analysis, if the lineages being compared are closely related; this is because it can take a number of generations for natural selection to "weed out" deleterious mutations from a population, especially if their effect on fitness is weak. [ 5 ] [ 6 ] [ 7 ] [ 8 ] This limits the usefulness of the K a /K s ratio for comparing closely related populations.
Additional information can be gleaned by determining the K a /K s ratio at specific codons within a gene sequence. For instance, the frequency-tuning region of an opsin may be under enhanced selective pressure when a species colonises and adapts to new environment, whereas the region responsible for initializing a nerve signal may be under purifying selection. In order to detect such effects, one would ideally calculate the K a /K s ratio at each site. However this is computationally expensive and in practise, a number of K a /K s classes are established, and each site is assigned to the best-fitting class. [ 1 ]
The first step in identifying whether positive selection acts on sites is to compare a test where the K a /K s ratio is constrained to be < 1 in all sites to one where it may take any value, and see if permitting K a /K s to exceed 1 in some sites improves the fit of the model. If this is the case, then sites fitting into the class where K a /K s > 1 are candidates to be experiencing positive selection. This form of test can either identify sites that further laboratory research can examine to determine possible selective pressure; or, sites believed to have functional significance can be assigned into different K a /K s classes before the model is run. [ 1 ] | https://en.wikipedia.org/wiki/Ka/Ks_ratio |
KaPPA-View4 is a metabolic pathway database containing data about metabolic regulation from 'omics' data. [ 1 ]
This Biological database -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/KaPPA-View4 |
Ka'abas also spelt Ka'bas ( Arabic : الكعبات) are the plural term used to describe houses of worship mainly located in the Arabian Peninsula that are cubic in shape and resemble the Kaaba structure from Mecca . They are mainly dedicated to various gods from the Arabian pantheon, although the term has been used to describe some Christian churches built in a similar style in the Arabian Peninsula.
A typical Kaaba building is shaped like a cube or block and functions as a place for the devotees of a particular god or goddess to worship in. [ 1 ] [ 2 ] The name "Kaaba" was used by ancient Arabians to describe and label these sites because of their resemblance to the Kaaba at Mecca and the purpose of doing pilgrimage to them. [ 1 ] [ 2 ] They were located throughout the Arabian Peninsula , although some of them even appeared in Persia and the region of Mesopotamia . [ a ]
Here is a list of some of these Kaaba structures that are mentioned in the writings of Muslim scholars and historians.
Most of the Kaabas dedicated to pagan gods in the Arabian Peninsula were destroyed after Islam. [ 3 ] [ 7 ] Among the destroyed Kaabas include that of the Kaaba of al-Lat that was worshipped by the Thaqif. [ 7 ]
Some said that the Kaaba of Najran in the ancient city of Al-Okhdood became a church after the Aksumites entered Najran as a relief for their Christian brethren who had been persecuted by Dhu Nuwas . The Kaaba of Najran still survives today, although in ruins, and is part of an archaeological site.
The traveller Yaqut al-Hamawi mentions that the Kaaba of Dhu al-Khalasa was converted into a mosque. [ 4 ] The site of the Kaaba of al-Lat is also now where the Abd Allah ibn al-Abbas Mosque stands. [ 10 ] | https://en.wikipedia.org/wiki/Kaabas |
In organophosphorus chemistry , the Kabachnik–Fields reaction is a three-component organic reaction forming α-aminomethylphosphonates from an amine , a carbonyl compound , and a dialkyl phosphonate , (RO) 2 P(O)H (that are also called dialkylphosphites). [ 1 ] Aminophosphonates are synthetic targets of some importance as phosphorus analogues of α- amino acids (a bioisostere ). This multicomponent reaction was independently discovered by Martin Kabachnik [ ru ] [ 2 ] [ 3 ] and Ellis K. Fields [ 4 ] in 1952. The reaction is very similar to the two-component Pudovik reaction , which involves condensation of the phosphite and a preformed imine .
The first step in this reaction is the formation of an imine , followed by a hydrophosphonylation step where the phosphonate P–H bond across the C=N double bond. [ 5 ] The starting carbonyl component is usually an aldehyde and sometimes a ketone . The reaction can be accelerated with a combination of dehydrating reagent and Lewis acid .
Enantioselective variants of the Kabachnik–Fields reaction have been developed, for example employing α-methylbenzylamine provides a chiral, non-racemic α-aminophosphonate. [ 6 ] | https://en.wikipedia.org/wiki/Kabachnik–Fields_reaction |
The Kabat numbering scheme is a scheme for the numbering of amino acid residues in antibodies based upon variable regions. The scheme is useful when comparing these variable regions between antibodies. [ 1 ] Its foundations were laid by the American biomedical scientist Elvin A. Kabat , who started collecting and aligning amino acid sequences of human and mouse Bence Jones proteins and immunoglobulin light chains in 1969.
Another numbering scheme is the Chothia numbering system .
The basis for the Kabat numbering scheme was laid out by a 1970s paper aligning 77 Bence Jones protein sequences. This analysis showed signals of "10 invariant and almost invariant glycines" as well as signals of hypervariable regions. [ 2 ] Kabat produced the first numbering scheme in 1970. [ 2 ]
The KabatMan (Kabat Sequence Database) is a database collecting antibody sequences. [ 3 ] | https://en.wikipedia.org/wiki/Kabat_numbering_scheme |
In ergodic theory , Kac's lemma , demonstrated by mathematician Mark Kac in 1947, [ 1 ] is a lemma stating that in a measure space the orbit of almost all the points contained in a set A {\displaystyle A} of such space, whose measure is μ ( A ) {\displaystyle \mu (A)} , return to A {\displaystyle A} within an average time inversely proportional to μ ( A ) {\displaystyle \mu (A)} . [ 2 ]
The lemma extends what is stated by Poincaré recurrence theorem , in which it is shown that the points return in A {\displaystyle A} infinite times. [ 3 ]
In physics , a dynamical system evolving in time may be described in a phase space , that is by the evolution in time of some variables. If this variables are bounded , that is having a minimum and a maximum, for a theorem due to Liouville , a measure can be defined in the space, having a measure space where the lemma applies. As a consequence, given a configuration of the system (a point in the phase space) the average return period close to this configuration (in the neighbourhood of the point) is inversely proportional to the considered size of volume surrounding the configuration.
Normalizing the measure space to 1, it becomes a probability space and the measure P ( A ) {\displaystyle P(A)} of its set A {\displaystyle A} represents the probability of finding the system in the states represented by the points of that set. In this case the lemma implies that the smaller is the probability to be in a certain state (or close to it), the longer is the time of return near that state. [ 4 ]
In formulas, if A {\displaystyle A} is the region close to the starting point and T R {\displaystyle T_{R}} is the return period, its average value is:
⟨ T R ⟩ = τ / P ( A ) {\displaystyle \langle T_{R}\rangle =\tau /P(A)}
Where τ {\displaystyle \tau } is a characteristic time of the system in question.
Note that since the volume of A {\displaystyle A} , therefore P ( A ) {\displaystyle P(A)} , depends exponentially on the n {\displaystyle n} variables in the system ( A = ϵ n {\displaystyle A=\epsilon ^{n}} , with ϵ {\displaystyle \epsilon } infinitesimal side, therefore less than 1, of the volume in n {\displaystyle n} dimensions), [ 5 ] P ( A ) {\displaystyle P(A)} decreases very rapidly as the variables of the system increase and consequently the return period increases exponentially. [ 6 ]
In practice, as the variables needed to describe the system increase, the return period increases rapidly. [ 7 ] | https://en.wikipedia.org/wiki/Kac's_lemma |
In statistical mechanics , the Kac ring is a toy model [ 1 ] introduced by Mark Kac in 1956 [ 2 ] [ 3 ] to explain how the second law of thermodynamics emerges from time-symmetric interactions between molecules (see reversibility paradox ). Although artificial, [ 4 ] the model is notable as a mathematically transparent example of coarse-graining [ 5 ] and is used as a didactic tool [ 6 ] in non-equilibrium thermodynamics .
The Kac ring consists of N equidistant points in a circle. Some of these points are marked . The number of marked points is M , where 0 < 2 M < N {\displaystyle 0<2M<N} . Each point represents a site occupied by a ball, which is black or white . After a unit of time, each ball moves to a neighboring point counterclockwise. Whenever a ball leaves a marked site, it switches color from black to white and vice versa. (If, however, the starting point is not marked, the ball completes its move without changing color.)
An imagined observer can only measure coarse-grained (or macroscopic ) quantities: the ratio
and the overall color
where B , W denote the total number of black and white balls respectively. Without the knowledge of detailed ( microscopic ) configuration, any distribution of M marks is considered equally likely. This assumption of equiprobability is comparable to Stosszahlansatz , which leads to Boltzmann equation . [ 7 ]
Let η k ( t ) {\displaystyle \eta _{k}(t)} denote the color of a ball at point k and time t with a convention
The microscopic dynamics can be mathematically formulated as
where
and k − 1 {\displaystyle k-1} is taken modulo N . In analogy to molecular motion, the system is time-reversible. Indeed, if balls would move clockwise (instead of counterclockwise) and marked points changed color upon entering them (instead of leaving), the motion would be equivalent, except going backward in time. Moreover, the evolution of η k ( t ) {\displaystyle \eta _{k}(t)} is periodic , where the period is at most 2 N {\displaystyle 2N} . (After N steps, each ball visits all M marked points and changes color by a factor ( − 1 ) M {\displaystyle (-1)^{M}} .) Periodicity of the Kac ring is a manifestation of more general Poincaré recurrence . [ 6 ]
Assuming that all balls are initially white,
where X = X ( k , t ) {\displaystyle X=X(k,t)} is the number of times the ball will leave a marked point during its journey. When marked locations are unknown (and all possibilities equally likely), X becomes a random variable . Considering the limit when N approaches infinity but t , i , and μ remain constant, the random variable X converges to the binomial distribution , i.e.: [ 5 ]
Hence, the overall color after t steps will be
Since 0 < 1 − 2 μ < 1 {\displaystyle 0<1-2\mu <1} the overall color will, on average, converge monotonically and exponentially to 50% grey (a state that is analogical to thermodynamic equilibrium ). An identical result is obtained for a ring rotating clockwise. Consequently, the coarse-grained evolution of the Kac ring is irreversible.
It is also possible to show that the variance approaches zero: [ 5 ]
Therefore, when N is huge (of order 10 23 ), the observer has to be extremely lucky (or patient) to detect any significant deviation from the ensemble averaged behavior. | https://en.wikipedia.org/wiki/Kac_ring |
The Kac–Bernstein theorem is one of the first characterization theorems of mathematical statistics . If the random variables ξ {\displaystyle \xi } and η {\displaystyle \eta } are independent and normally distributed with the same variance, then their sum and difference are also independent. The Kac–Bernstein theorem states that the independence of the sum and difference of two independent random variables characterizes the normal distribution (the Gauss distribution). This theorem was proved independently by Polish-American mathematician Mark Kac and Soviet mathematician Sergei Bernstein .
Let ξ {\displaystyle \xi } and η {\displaystyle \eta } be independent random variables. If ξ + η {\displaystyle \xi +\eta } and ξ − η {\displaystyle \xi -\eta } are independent then ξ {\displaystyle \xi } and η {\displaystyle \eta } have normal distributions (the Gaussian distribution).
A generalization of the Kac–Bernstein theorem is the Darmois–Skitovich theorem , in which instead of sum and difference linear forms from n independent random variables are considered. | https://en.wikipedia.org/wiki/Kac–Bernstein_theorem |
In mathematics , the Kadison–Singer problem , posed in 1959, was a problem in functional analysis about whether certain extensions of certain linear functionals on certain C*-algebras were unique. The uniqueness was proved in 2013.
The statement arose from work on the foundations of quantum mechanics done by Paul Dirac in the 1940s and was formalized in 1959 by Richard Kadison and Isadore Singer . [ 1 ] The problem was subsequently shown to be equivalent to numerous open problems in pure mathematics, applied mathematics, engineering and computer science. [ 2 ] [ 3 ] Kadison, Singer, and most later authors believed the statement to be false, [ 2 ] [ 3 ] but, in 2013, it was proven true by Adam Marcus , Daniel Spielman and Nikhil Srivastava , [ 4 ] who received the 2014 Pólya Prize for the achievement.
The solution was made possible by a reformulation provided by Joel Anderson, who showed in 1979 that his "paving conjecture", which only involves operators on finite-dimensional Hilbert spaces, is equivalent to the Kadison–Singer problem. Nik Weaver provided another reformulation in a finite-dimensional setting, and this version was proved true using random polynomials. [ 5 ]
Consider the separable Hilbert space ℓ 2 and two related C*-algebras: the algebra B {\displaystyle B} of all continuous linear operators from ℓ 2 to ℓ 2 , and the algebra D {\displaystyle D} of all diagonal continuous linear operators from ℓ 2 to ℓ 2 .
A state on a C*-algebra A {\displaystyle A} is a continuous linear functional φ : A → C {\displaystyle \varphi :A\to \mathbb {C} } such that φ ( I ) = 1 {\displaystyle \varphi (I)=1} (where I {\displaystyle I} denotes the algebra's multiplicative identity ) and φ ( T ) ≥ 0 {\displaystyle \varphi (T)\geq 0} for every T ≥ 0 {\displaystyle T\geq 0} . Such a state is called pure if it is an extremal point in the set of all states on A {\displaystyle A} (i.e. if it cannot be written as a convex combination of other states on A {\displaystyle A} ).
By the Hahn–Banach theorem , any functional on D {\displaystyle D} can be extended to B {\displaystyle B} . Kadison and Singer conjectured that, for the case of pure states, this extension is unique. That is, the Kadison–Singer problem consisted in proving or disproving the following statement:
This claim is in fact true.
The Kadison–Singer problem has a positive solution if and only if the following "paving conjecture" is true: [ 6 ]
Here P A j {\displaystyle P_{A_{j}}} denotes the orthogonal projection on the space spanned by the standard unit vectors corresponding to the elements of A j {\displaystyle A_{j}} , so that the matrix of P A j T P A j {\displaystyle P_{A_{j}}TP_{A_{j}}} is obtained from the matrix of T {\displaystyle T} by replacing all rows and columns that don't correspond to the indices in A j {\displaystyle A_{j}} by 0. The matrix norm ‖ ⋅ ‖ {\displaystyle \|\cdot \|} is the spectral norm , i.e. the operator norm with respect to the Euclidean norm on C n {\displaystyle \mathbb {C} ^{n}} .
Note that in this statement, k {\displaystyle k} may only depend on ε {\displaystyle \varepsilon } , not on n {\displaystyle n} .
The following " discrepancy " statement, again equivalent to the Kadison–Singer problem because of previous work by Nik Weaver, [ 7 ] was proven by Marcus/Spielman/Srivastava using a technique of random polynomials:
This statement implies the following:
Here the "discrepancy" becomes visible when α is small enough: the quadratic form on the unit sphere can be split into two roughly equal pieces, i.e. pieces whose values don't differ much from 1/2 on the unit sphere.
In this form, the theorem can be used to derive statements about certain partitions of graphs. [ 5 ] | https://en.wikipedia.org/wiki/Kadison–Singer_problem |
The Kadowaki–Woods ratio is the ratio of A , the quadratic term of the resistivity and γ 2 , the square of the linear term of the specific heat . This ratio is found to be a constant for transition metals , and for heavy- fermion compounds, although at different values.
In 1968 M. J. Rice pointed out [ 1 ] that the coefficient A should vary predominantly as the square of the linear electronic specific heat coefficient γ; in particular he showed that the ratio A/γ 2 is material independent for the pure 3d, 4d and 5d transition metals. Heavy-fermion compounds are characterized by very large values of A and γ. Kadowaki and Woods [ 2 ] showed that A/γ 2 is material-independent within the heavy-fermion compounds, and that it is about 25 times larger than in aforementioned transition metals.
It was shown by K. Miyake, T. Matsuura and C.M. Varma [ 3 ] that local Fermi liquids , quasiparticle mass and lifetime are linked consistent with the A/γ 2 ratio. This suggest that the Kadowaki-Woods ratio reflects a relation between quasiparticle mass and lifetime renormalisation as a function of electron-electron interaction strength.
According to the theory of electron-electron scattering [ 4 ] [ 5 ] [ 6 ] the ratio A/γ 2 contains indeed several non-universal factors, including the square of the strength of the effective electron-electron interaction. Since in general the interactions differ in nature from one group of materials to another, the same values of A/γ 2 are only expected within a particular group. In 2005 Hussey [ 7 ] proposed a re-scaling of A/γ 2 to account for unit cell volume, dimensionality, carrier density and multi-band effects. In 2009 Jacko, Fjaerestad, and Powell [ 8 ] demonstrated f dx (n)A/γ 2 to have the same value in transition metals, heavy fermions, organics and oxides with A varying over 10 orders of magnitude, where f dx (n) may be written in terms of the dimensionality of the system, the electron density and, in layered systems, the interlayer spacing or the interlayer hopping integral.
This condensed matter physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kadowaki–Woods_ratio |
Kaede is a photoactivatable fluorescent protein naturally originated from a stony coral , Trachyphyllia geoffroyi . Its name means "maple" in Japanese . With the irradiation of ultraviolet light (350–400 nm), Kaede undergoes irreversible photoconversion from green fluorescence to red fluorescence.
Kaede is a homotetrameric protein with the size of 116 kDa . The tetrameric structure was deduced as its primary structure is only 28 kDa. This tetramerization possibly makes Kaede have a low tendency to form aggregates when fused to other proteins.
The property of photoconverted fluorescence Kaede protein was serendipitously discovered and first reported by Ando et al. in Proceedings of the United States National Academy of Sciences . [ 1 ] An aliquot of Kaede protein was discovered to emit red fluorescence after being left on the bench and exposed to sunlight. Subsequent verification revealed that Kaede, which is originally green fluorescent, after exposure to UV light is photoconverted, becoming red fluorescent. It was then named Kaede.
The property of photoconversion in Kaede is contributed by the tripeptide , His 62 - Tyr 63 - Gly 64 , that acts as a green chromophore that can be converted to red. [ 2 ] Once Kaede is synthesized, a chromophore, 4-(p-hydroxybenzylidene)-5-imidazolinone, derived from the tripeptide mediates green fluorescence in Kaede. When exposed to UV, Kaede protein undergoes unconventional cleavage between the amide nitrogen and the α carbon (Cα) at His62 via a formal β-elimination reaction. Followed by the formation of a double bond between His62-Cα and –Cβ, the π-conjugation is extended to the imidazole ring of His62. A new chromophore, 2-[(1E)-2-(5-imidazolyl)ethenyl]-4-(p-hydroxybenzylidene)-5-imidazolinone, is formed with the red-emitting property.
The cleavage of the tripeptide was analysed by SDS-PAGE analysis. Unconverted green Kaede shows one band at 28 kDa, whereas two bands at 18 kDa and 10 kDa are observed for converted red Kaede, indicating that the cleavage is crucial for the photoconversion. [ citation needed ]
A shifting of the absorption and emission spectrum in Kaede is caused by the cleavage of the tripeptide. Before the photoconversion, Kaede displays a major absorption wavelength maximum at 508 nm, accompanied with a slight shoulder at 475 nm. When it is excited at 480 nm, green fluorescence is emitted with a peak of 518 nm.
When Kaede is irradiated with UV or violet light, the major absorption peak shifts to 572 nm. When excited at 540 nm, Kaede showed an emission maximum at 582 nm with a shoulder at 627 nm and the 518-nm peak. Red fluorescence is emitted after this photoconversion.
The photoconversion in Kaede is irreversible. Exposure in dark or illumination at 570 nm cannot restore its original green fluorescence. A reduced fluorescence is observed in red, photoconverted Kaede when it is intensively exposed to 405 nm light, followed by partial recover after several minutes.
As all other fluorescent proteins, Kaede can be the regional optical markers for gene expression and protein labeling for the study of cell behaviors. [ 3 ]
One of the most useful applications is the visualization of neurons . Delineation of an individual neuron is difficult due to the long and thin processes which entangle with other neurons. Even when cultured neurons are labeled with fluorescent proteins, they are still difficult to identify individually because of the dense package.
In the past, such visualization could be done conventionally by filling neurons with Lucifer yellow or sulforhodamine , which is a laborious technique.[1] After the discovery of Kaede protein, it was found to be useful in delineating individual neurons. The neurons are transfected by Kaede protein cDNA , and are UV irradiated. The red, photoconverted Kaede protein has free diffusibility in the cell except for the nucleus, and spreads over the entire cell including dendrites and axon. This technique help disentangle the complex networks established in a dense culture. Besides, by labeling neurons with different colors by UV irradiating with different duration times, contact sites between the red and green neurons of interest are allowed to be visualized. [ 1 ]
The ability of visualization of individual cells is also a powerful tool to identify the precise morphology and migratory behaviors of individual cells within living cortical slices. By Kaede protein, a particular pair of daughter cells in neighboring Kaede-positive cells in the ventricular zone of mouse brain slices can be followed. The cell-cell borders of daughter cells are visualized and the position and distance between two or more cells can be described. [ 4 ]
As the change in the fluorescent colour is induced by UV light, marking of cells and subcellular structures is efficient even when only a partial photoconversion is induced.
Due to the special property of photo-switchable fluorescence, Kaede protein possesses several advantages as an optical cell marker .
After the photoconversion, the photoconverted Kaede protein emits bright and stable red fluorescence. This fluorescence can last for months without anaerobic conditions. As this red state of Kaede is bright and stable compared to the green state, and because the unconverted green Kaede emits very low intensity of red fluorescence, the red signals provides contrast. [ 1 ]
Besides, before the photoconversion, Kaede emits bright green fluorescence which enables the visualization of the localization of the non-photoacivated protein. This is superior to other fluorescent proteins such as PA-GFP and KFP1, which only show low fluorescence before photoactivation. [ 3 ]
In addition, as both green and red fluorescence of Kaede are excited by blue light at 480 nm for observation, this light will not induce photoconversion. Therefore, illumination lights for observation and photoconversion can be separated completely.
In spite of the usefulness in cell tracking and cell visualization of Kaede, there are some limitations.
Although Kaede will shift to red upon the exposure of UV or violet light and display a 2,000-fold increase in red-to-green fluorescence ratio, using both the red and green fluorescence bands can cause problems in multilabel experiments. The tetramerization of Kaede may disturb the localization and trafficking of fusion proteins. This limits the usefulness of Kaede as a fusion protein tag.
The photoconversion property of Kaede does not only contribute to the application on protein labeling and cell tracking, it is also responsible for the vast variation in the colour of stony corals, Trachyphyllia geoffroyi . Under sunlight, due to the photoconversion of Kaede, the tentacles and disks will turn red. As green fluorescent Kaede is synthesized continuously, these corals appear green again as more unconverted Kaede is created. By the different proportion of photoconverted and unconverted Kaede, great diversity of colour is found in corals. | https://en.wikipedia.org/wiki/Kaede_(protein) |
Kaeser Compressors, Inc. manufactures compressed air and vacuum products, including rotary screw compressors , oil-less reciprocating compressors, rotary lobe blowers, rotary screw blowers, high-speed turbo blowers, refrigerated and desiccant dryers, filters, condensate management systems and other related products. The company provides service, rentals, and consulting services. Kaeser Compressors, Inc. is a US affiliate of Kaeser Kompressoren headquartered in Coburg, Germany .
Carl Kaeser, Sr. founded the Kaeser organization as an engineering workshop that produced car and engine parts in 1919. Soon after, the factory was reconditioning engines, producing gears and building special purpose machines for the local glass industry. It wasn’t until the post-war need for compressed air in the rebuilding of Germany that the company began manufacturing and developing air compressors. The company grew rapidly after turning out its first reciprocating compressor in 1948, and by 1960 had outgrown its facility of 38 years and moved to a new location in Coburg, Germany.
Under the leadership of Carl Kaeser, Jr., Kaeser engineers developed a rotary screw compressor that featured the "Sigma Profile" air-end in the early 1970s. The first compressor to incorporate the Sigma Profile was delivered in 1975.
Now represented in every major industrialized country in the world, Kaeser established its first subsidiary in Switzerland by the late 1970s. The US subsidiary is the largest. Reiner Mueller started the US subsidiary in Fredericksburg, VA in 1982. Fredericksburg is near to several transport centers, and remains home to the US headquarters. The 22.5-acre (91,000 m 2 ) site includes a 155,176-square-foot (14,416.3 m 2 ) facility. Reiner Mueller retired in December 2008, and his son Frank assumed leadership in January 2009.
Carl Kaeser, Jr., who started with Kaeser Kompressoren in 1937, worked until the day he died in 2009. Thomas Kaeser assumed leadership of Kaeser Kompressoren after his father, Carl, died at the age of 95.
Kaeser’s manufacturing facilities in Europe consist of a group headquarters in Coburg, Germany that produces rotary screw, reciprocating, and portable compressors, and a plant in Gera, Germany that produces refrigeration dryers and rotary blowers. Also, the company has a sheet metal plant near Coburg in Sonnefeld.
When developing the Sigma Profile in the nineteen seventies, the Kaeser engineering team was faced with overcoming the disadvantages that previous screw designs presented to the market. Those previous designs included an energy-consuming symmetrical profile, and an asymmetric design introduced in 1962 that was an improvement over the symmetrical design but still consumed more energy than a reciprocating compressor. Kaeser engineers introduced the Sigma Profile with a five-to-six lobe asymmetrical design. The design required closer tolerances between the rotors and the housing, resulting in fewer air back-flow losses.
Kaeser’s design philosophy remains to develop larger, slower running air-ends. Air-ends turning at slower speeds deliver more compressed air for the same drive power (up to 20% more efficient than conventional screw designs). Oil flooding at the point of compression provides cleaning, lubrication and cooling, which contributes to air-end efficiency.
Sigma Profile air-ends are now found in a range of compressors from 3 to 650 hp (2.2 to 484.7 kW). Kaeser continues to refine and improve the air-end design up to 1000 hp.
Kaeser's screw compressor rotors and air-end castings are created in climate-controlled environments. Precision milling machines mill the screw compressor rotors to fine tolerances, and CNC machining centers with pallet changing systems allow for 24-hour automatic machining of the air-end castings. A 3D coordinate-measuring machine automatically checks the critical dimensions of the air-end casing. CNC profile grinders finish the rotors to micrometre tolerances following solution hardening of the milled rotors within controlled atmosphere heat treating ovens. | https://en.wikipedia.org/wiki/Kaeser_Compressors |
Kaffe is a discontinued " clean room design " ( reverse engineering ) version of a Java Virtual Machine . It comes with a subset of the Java Platform, Standard Edition (Java SE), Java API , and tools needed to provide a Java runtime environment. Like most other Free Java virtual machines , Kaffe uses GNU Classpath as its class library .
Kaffe, first released in 1996, was the original open-source Java implementation. Initially developed as part of another project, it grew so popular that developers Tim Wilkinson and Peter Mehlitz founded Transvirtual Technologies, Inc. with Kaffe as the company's flagship product. In July 1998, Transvirtual released Kaffe OpenVM under a GNU General Public License .
Kaffe is a lean and portable virtual machine , although it is significantly slower than commercial implementations. [ 3 ] When compared to the reference implementation of the Java Virtual Machine written by Sun Microsystems , Kaffe was significantly smaller; it thus appeals to embedded system developers . [ unbalanced opinion? ] It comes with just-in-time compilers for many of the CPU architectures , and has been ported to more than 70 system platforms in total. It runs on devices ranging from embedded SuperH devices to IBM zSeries mainframe computers , and it will even run on a PlayStation 2 .
Unlike other implementations, in the past Kaffe used GNU Multi-Precision Library (GMP) to support arbitrary precision arithmetic. This feature has been removed from release 1.1.9, causing protests from people that claim they used Kaffe for the sole reason of GMP arithmetic being faster than the typical pure java implementation, available in other distributions. [ 4 ] [ unreliable source? ] The capability was removed to reduce the maintenance work, expecting that interested people will integrate GMP support into GNU Classpath or OpenJDK . Subsequently, GNU Classpath introduced GMP support in version 0.98.
This software article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kaffe |
In solid-state physics , the kagome metal or kagome magnet is a type of ferromagnetic quantum material . The atomic lattice in a kagome magnet has layered overlapping triangles and large hexagonal voids, akin to the kagome pattern in traditional Japanese basket-weaving . [ 1 ] [ 2 ] [ 3 ] [ 4 ] This geometry induces a flat electronic band structure with Dirac crossings , in which the low-energy electron dynamics correlate strongly . [ 5 ]
Electrons in a kagome metal experience a "three-dimensional cousin of the quantum Hall effect ": magnetic effects require electrons to flow around the kagome triangles, akin to superconductivity . [ 5 ] This phenomenon occurs in many materials at low temperatures and high external field, but, unlike superconductivity, materials are known in which the effect remains under standard conditions . [ 5 ] [ 6 ]
The first room-temperature, vanishing-external-field kagome magnet discovered was the intermetallic Fe 3 Sn 2 , as shown in 2011. [ 7 ] Many others have since been found. Kagome magnets occur in a variety of crystal and magnetic structures, generally featuring a 3 d - transition-metal kagome lattice with in-plane period ~5.5 Å. Examples include antiferromagnet Mn 3 Sn , paramagnet CoSn , ferrimagnet TbMn 6 Sn 6 , hard ferromagnet (and Weyl semimetal ) Co 3 Sn 2 S 2 , and soft ferromagnet Fe 3 Sn 2 . Until 2019, all known kagome materials contained the heavy element tin , which has a strong spin–orbit coupling , but potential kagome materials under study (as of 2019 [update] ) included magnetically doped Weyl-semimetal Co 2 MnGa , [ 8 ] and the class AV 3 Sb 5 (A = Cs, Rb, K). [ 9 ] Although most research on kagome magnets has been performed on Fe 3 Sn 2 , it has since been discovered that FeSn in fact exhibits a structure much closer to the ideal kagome lattice. [ 10 ]
A kagome lattice harbors massive Dirac fermions , Berry curvature, band gaps, and spin–orbit activity, all of which are conducive to the Hall Effect and zero-energy-loss electric currents. [ 6 ] [ 11 ] [ 12 ] These behaviors are promising for the development of technologies in quantum computing, spin superconductors, and low power electronics. [ 5 ] [ 6 ] CsV 3 Sb 5 in particular exhibits numerous exotic properties, including superconductivity, [ 13 ] topological states, and more. [ vague ] [ 14 ] [ 15 ] [ 16 ] [ 17 ] Magnetic skyrmionic bubbles have been found in Kagome metals over a wide temperature range. For example, they were observed in Fe 3 Sn 2 at ~200-600 K using LTEM but with high critical field ~0.8 T. [ 18 ] | https://en.wikipedia.org/wiki/Kagome_metal |
The Kahn–Kalai conjecture , also known as the expectation threshold conjecture or more recently the Park-Pham Theorem , was a conjecture in the field of graph theory and statistical mechanics , proposed by Jeff Kahn and Gil Kalai in 2006. [ 1 ] [ 2 ] It was proven in a paper published in 2024. [ 3 ]
This conjecture concerns the general problem of estimating when phase transitions occur in systems. [ 1 ] For example, in a random network with N {\displaystyle N} nodes, where each edge is included with probability p {\displaystyle p} , it is unlikely for the graph to contain a Hamiltonian cycle if p {\displaystyle p} is less than a threshold value ( log N ) / N {\displaystyle (\log N)/N} , but highly likely if p {\displaystyle p} exceeds that threshold. [ 4 ]
Threshold values are often difficult to calculate, but a lower bound for the threshold, the "expectation threshold", is generally easier to calculate. [ 1 ] The Kahn–Kalai conjecture is that the two values are generally close together in a precisely defined way, namely that there is a universal constant K {\displaystyle K} for which the ratio between the two is less than K log l ( F ) {\displaystyle K\log {l({\mathcal {F}})}} where l ( F ) {\displaystyle l({\mathcal {F}})} is the size of a largest minimal element of an increasing family F {\displaystyle {\mathcal {F}}} of subsets of a power set. [ 3 ]
Jinyoung Park and Huy Tuan Pham announced a proof of the conjecture in 2022; it was published in 2024. [ 4 ] [ 3 ] | https://en.wikipedia.org/wiki/Kahn–Kalai_conjecture |
KaiC is a gene belonging to the KaiABC gene cluster (with KaiA , and KaiB ) that, together, regulate bacterial circadian rhythms , specifically in cyanobacteria . KaiC encodes the KaiC protein, which interacts with the KaiA and KaiB proteins in a post-translational oscillator (PTO). The PTO is cyanobacteria master clock that is controlled by sequences of phosphorylation of KaiC protein. [ 1 ] [ 2 ] Regulation of KaiABC expression and KaiABC phosphorylation is essential for cyanobacteria circadian rhythmicity , and is particularly important for regulating cyanobacteria processes such as nitrogen fixation , photosynthesis , and cell division . [ 3 ] Studies have shown similarities to Drosophila , Neurospora , and mammalian clock models in that the kaiABC regulation of the cyanobacteria slave circadian clock is also based on a transcription translation feedback loop (TTFL). [ 4 ] KaiC protein has both auto-kinase and auto-phosphatase activity and functions as the circadian regulator in both the PTO and the TTFL. KaiC has been found to not only suppress kaiBC when overexpressed, but also suppress circadian expression of all genes in the cyanobacterial genome . [ 5 ]
Though the KaiABC gene cluster has been found to exist only in cyanobacteria, evolutionarily KaiC contains homologs that occur in Archaea and Pseudomonadota . It is the oldest circadian gene that has been discovered in prokaryotes. KaiC has a double-domain structure and sequence that classifies it as part of the RecA gene family of ATP-dependent recombinases . [ 3 ] Based on a number of single-domain homologous genes in other species, KaiC is hypothesized to have horizontally transferred from Bacteria to Archaea, eventually forming the double-domain KaiC through duplication and fusion . KaiC' s key role in circadian control and homology to RecA suggest its individual evolution before its presence in the KaiABC gene cluster. [ 4 ]
Masahiro Ishiura, Takao Kondo , Susan S. Golden , Carl H. Johnson , and their colleagues discovered the gene cluster in 1998 and named the gene cluster kaiABC, as "kai" means “cycle” in Japanese. They generated 19 different clock mutants that were mapped to kaiA, kaiB, and kaiC genes, and successfully cloned the gene cluster in the cyanobacteria Synechococcus elongatus . Using a bacterial luciferase reporter to monitor the expression of clock-controlled gene psbAI in Synechococcus, they investigated and reported on the rescue to normal rhythmicity of long-period clock mutant C44a (with a period of 44 hours) by kaiABC. They inserted wild-type DNA through a pNIBB7942 plasmid vector into the C44a mutant, and generated clones that restored normal period (a period of 25 hours). They were eventually able to localize the gene region causing this rescue, and observed circadian rhythmicity in upstream promotor activity of kaiA and kaiB, as well as in the expression of kaiA and kaiBC messenger RNA . They determined abolishing any of the three kai genes would cause arrhythmicity in the circadian clock and reduce kaiBC promoter activity. [ 3 ] KaiC was later found to have both autokinase and autophosphatase activity. [ 1 ] These findings suggested that circadian rhythm was controlled by a TTFL mechanism, which is consistent with other known biological clocks. [ 6 ]
In 2000, S. elongatus was observed in constant dark (DD) and constant light (LL). In DD, transcription and translation halted due to the absence of light but the circadian mechanism showed no significant phase shift after transitioning to constant light. [ 7 ] In 2005, after closer examination of the KaiABC protein interactions, the phosphorylation of KaiC proved to oscillate with daily rhythms in the absence of light. [ 8 ] In addition to the TTFL model, the PTO model was hypothesized for the KaiABC phosphorylation cycle. [ 6 ]
Also in 2005, Nakajima et al. lysed S. elongatus and isolated KaiABC proteins. In test tubes containing only KaiABC proteins and ATP , in vitro phosphorylation of KaiC oscillated with a near 24 hour period with a slightly smaller amplitude than in vivo oscillation, proving that the KaiABC proteins are sufficient for circadian rhythm solely in the presence of ATP. [ 9 ] Combined with the TTFL model, KaiABC as a circadian PTO was shown to be the fundamental clock regulator in S. elongatus [ 6 ]
On Synechococcus elongatus' singular circular chromosome, the protein-coding gene kaiC is located at position 380696-382255 (its locus tag is syc0334_d). The gene kaiC has paralogs [ dubious – discuss ] kaiB (located 380338..380646) and kaiA (located 379394..380248). kaiC encodes the protein KaiC (519 amino acids ). KaiC acts as a non-specific transcription regulator that represses transcription of the kaiBC promoter. Its crystal structure has been solved at 2.8 Å resolution; it is a homohexameric complex (approximately 360 kDa ) with a double-doughnut structure and a central pore which is open at the N-terminal ends and partially sealed at the C-terminal ends due to the presence of six arginine residues. [ 5 ] The hexamer has twelve ATP molecules between the N- (CI) and C-terminal (CII) domains, which demonstrate ATPase activity. [ 10 ] The CI and CII domains are linked by the N-terminal region of the CII domain. The last 20 residues from the C-terminal of the CII domain protrude from the doughnut to form what is called the A-loop. [1] Interfaces on KaiC's CII domain are sites for both auto-kinase and auto-phosphatase activity, both in vitro and in vivo . [ 11 ] [ 12 ] KaiC has two P loops or Walker’s motif As ( ATP -/ GTP -binding motifs) in the CI and CII domains; the CI domain also contains two DXXG (X represents any amino acid) motifs that are highly conserved among the GTPase super-family. [ 13 ]
KaiC shares structural similarities to several other proteins with hexameric rings, including RecA , DnaB and ATPases . The hexameric rings of KaiC closely resembles RecA, with 8 α-helices surrounding a twisted β-sheet made up of 7 strands. This structure favours the binding of a nucleotide at the carboxy-end of the β-sheet. KaiC’s structural similarities to these proteins suggests a role for KaiC in transcription regulation. Further, the diameter of the rings in KaiC are suitable to accommodate single stranded DNA . Additionally, the surface potential at the CII ring and the C-terminal channel opening is mostly positive. The compatibility of the diameter as well as the surface potential charge suggests that DNA may be able to bind to the C-terminal channel opening. [ 14 ]
Kai proteins regulate genome-wide gene expression. [ 8 ] Protein KaiA enhances the phosphorylation of protein KaiC by binding to the A loop of the CII domain to promote auto-kinase activity during subjective day. [ 15 ] Phosphorylation at subunits occurs in an ordered manner, beginning with phosphorylation of Threonine 432 (T432) followed by Serine 431 (S431) on the CII domain. This leads to tight stacking of the CII domain to the CI domain. [ 16 ] KaiB then binds to the exposed B loop on the CII domain of KaiC and sequesters KaiA from the C-terminals during subjective night, which inhibits phosphorylation and stimulates auto-phosphatase activity. [2] Dephosphorylation of T432 occurs followed by S431, returning KaiC to its original state. [ 16 ] [ 12 ]
Disruption of KaiC’s CI domain results both in arrhythmia of kaiBC expression and a reduction of ATP-binding activity; this, along with in vitro autophosphorylation of KaiC indicate that ATP binding to KaiC is crucial for Synechococcus circadian oscillation. [ 13 ] The phosphorylation status of KaiC has been correlated with Synechococcus clock speed in vivo . [ 12 ] Additionally, overexpression of KaiC has been shown to strongly repress the kaiBC promoter, while kaiA overexpression has experimentally enhanced the kaiBC promoter. [ 5 ] These positive and negative binding elements mirror a feedback mechanism of rhythm generation conserved across many different species. [ 17 ]
KaiC phosphorylation oscillates with a period of approximately 24 hours when placed in vitro with the three recombinant Kai proteins, incubated with ATP. The circadian rhythm of KaiC phosphorylation persists in constant darkness, regardless of Synechococcus transcription rates . This oscillation rate is thought to be controlled by the ratio of phosphorylated to unphosphorylated KaiC protein. KaiC phosphorylation ratio is a main factor in the activation of kaiBC promoter as well. The kaiBC operon is transcribed in a circadian fashion and precedes KaiC build up by about 6 hours, [ 18 ] a lag thought to play a role in feedback loops.
kaiA , kaiB , and kaiC have been shown to be essential genetic components in Synechococcus elongatus for circadian rhythms. [ 18 ] Experiments have also shown that KaiC enhances the KaiA-KaiB interaction in yeast cells and in vitro. This implies that there may be the formation of a heteromultimeric complex composed of the three Kai proteins with KaiC serving as a bridge between KaiA and KaiB. Alternatively, KaiC may form a heterodimer with KaiA or KaiB to induce a conformational change. [ 19 ] Variations in the C-terminal region of each of their proteins suggest functional divergence between the Kai clock proteins, [ 8 ] however there are critical interdependencies between the three paralogs.
Cyanobacteria are the simplest organisms with a known mechanism for the generation of circadian rhythms . [ 18 ] KaiC ATPase activity is temperature compensated from 25 to 50 degrees Celsius [ 20 ] and has a Q10 of about 1.1 (Q10 values around 1 indicate temperature compensation). Because the period of KaiC phosphorylation is temperature compensated and agrees with in vivo circadian rhythms, KaiC is thought to be the mechanism for basic circadian timing in Synechococcus . [ 21 ] ∆kaiABC individuals, one of the more common mutants, grow just as well as wild type individuals but they lack rhythmicity. This is evidence that the kaiABC gene cluster is not necessary for growth. [ 5 ]
In addition to the PTO regulating the autokinase and autophosphatase activities of KaiC, there is also evidence for a TTFL, similar to other eukaryotes, that governs the circadian rhythm in outputs of the clock. [ 22 ] By studying the structure and the activities of KaiC, several roles of KaiC in the TTFL were suggested. The similar structures of KaiC to the RecA/DnaB superfamily suggested a possible role for KaiC in direct DNA binding and promoting of transcription. [ 14 ] KaiC knock-out(KO) experiments determined KaiC to be a negative regulator of the kaiBC promoter sequence but it was found working through a separate, SasA/RpaA pathway, as KaiC was found to be not a transcription factor. [ 23 ] However, elimination of the PTO did not fully eliminate the rhythmicity in kaiBC promoter activities, suggesting that the PTO is not necessary in generating rhythms in the TTFL. [ 24 ] In truth, the activities of KaiC outside of the PTO is still relatively unknown.
Recent experiments have found that the oscillations in the cell cycle and circadian rhythms of Synechococcus are linked together through a one way mechanism. The circadian clock gates cells division, only allowing it to proceed at certain phases. The cell cycle does not appear to have any effect on the circadian clock, though. When binary fission occurs, the daughter cells inherit the mother cell's circadian clock and are in phase with the mother cell. The circadian gating of cell division may be a protective feature to prevent division at a vulnerable phase.
Phases in which KaiC has high ATPase activity do not allow for cell division to take place. In mutants with constantly elevated KaiC ATPase activity, the protein CikA is absent. CikA is a major factor in the input pathway and causes KaiC-dependent cell elongation. [ 25 ]
The recreation of a circadian oscillator in vitro in the presence of only KaiA, KaiB, KaiC, and ATP has sparked interest in the relationship between cellular biochemical oscillators and their associated transcription-translation feedback loops (TTFLs). TTFLs have long been assumed to be the core of circadian rhythmicity, but that claim is now being tested again due to the possibility that the biochemical oscillators could constitute the central mechanism of the clock system, regulating and operating within TTFLs that control output and restore proteins essential to the oscillators in organisms, such as the KaiABC system in Synechococcus . [ 26 ] Two models have been proposed to describe the relationship between the biochemical and TTFL regulation of circadian rhythms: a master/slave oscillator system with the TTFL oscillator synchronizing to the biochemical oscillator and an equally weighted coupled oscillator system in which both oscillators synchronize and influence the other oscillator. Both are coupled oscillator models that account for the high stability of the timing mechanism within Synechococcus . The biochemical oscillator relies on redundant molecular interactions based on the law of mass action , whereas the TTFL relies on cellular machinery that mediates translation, transcription, and degradation of mRNA and proteins. The different types of interactions driving the two oscillators allows the circadian clock to be resilient to changes within the cell, such as metabolic fluctuation, temperature changes, and cell division. [ 27 ]
Though the period of the circadian clock is temperature compensated, the phosphorylation of KaiC can be stably entrained to a temperature cycle. The phosphorylation of KaiC was successfully entrained in vitro to temperature cycles with periods between 20 and 28 hours using temperature steps from 30 °C to 45 °C and vice versa. The results reflect a phase-dependent shift in the phase of the KaiC phosphorylation rhythms. The period of the circadian clock was not changed, reinforcing the temperature compensation of the clock mechanism. [ 28 ]
A 2012 study out of Vanderbilt University shows evidence that KaiC acts as a phospho-transferase that hands back phosphates to ADP on the T432 (threonine residue at position 432) and S431 (serine residue 431) indicating that KaiC effectively serves as an ATP synthase . [ 10 ]
Various KaiC mutants have been identified and their phenotypes studied. Many mutants show a change in the period of their circadian rhythms.
[ 9 ] [ 29 ] | https://en.wikipedia.org/wiki/KaiC |
Kai Simons is a Finnish professor of biochemistry and cell biology and physician, living and working in Germany. He introduced the concept of lipid rafts , and coined the term trans-Golgi network . He is the co-founder and co-organizer of the European Molecular Biology Laboratory and European Molecular Biology Organization , and initiated the foundation of Max Planck Institute of Molecular Cell Biology and Genetics .
Kai Simons is the son of a physics professor. His father convinced him to study medicine, though he originally wanted to study physics. [ 2 ] While studying at the University of Helsinki , Simons spent a summer internship in the Stockholm laboratory of Bengt Samuelsson [ 3 ] There, he studied mechanisms of vitamin B12 absorption. [ 2 ] He worked with other students to organize a campaign to fight taeniasis , a disease common in eastern Finland where eating raw fish is popular. [ 3 ]
After completing his MD in 1964, he began a postdoctoral fellowship at Rockefeller University in New York City , where he worked between 1966 and 1967 on blood serum protein polymorphism. [ 2 ]
Simons returned to Helsinki in 1967, where he began working as a junior investigator for the Finnish Medical Research Council at the University of Helsinki . [ 3 ] [ 4 ] He became a group leader in 1972 and was a biochemistry professor in 1971–79 at the medical faculty of this university [ 4 ] At first, he continued his work on serum proteins. Next, together with Leevi Kääriäinen and Ossi Renkonen , he started a research team – later joined by Ari Helenius , his first PhD student and later a post doctoral researcher who became Simons' brother-in-law. After a one-month stay in MRC Laboratory for Molecular Biology in Cambridge , the group started investigating a Semliki Forest virus , introduced to Simons by Kääriäinen. [ 2 ]
In 1975 Simons went to Heidelberg , Germany, as one of the EMBL group leaders. Together with Ari Helenius he helped to develop EMBL, headed at this time by John Kendrew . [ 2 ] In years 1982–1998 Simons was a coordinator of the Cell Biology Program there. [ 4 ] During this time he for the first time he introduced the concept of lipid rafts , [ 5 ] as well as coined the term trans-Golgi network and proposed its role in protein and lipid sorting. [ 6 ]
In 1999 he took part in setting up ELSO (later incorporated into EMBO ), which later he presided over. [ 7 ]
He was one of the initiators of establishing and building Max Planck Institute of Molecular Cell Biology and Genetics in Dresden (Germany), where he moved. Formally from 1998 (beginning of MPI-CBG construction) and from 2000 he was one of five institute's directors and also a group leader there. [ 2 ] He was a director (1998–2006) and a group leader (until 2012). [ 8 ] [ 9 ] Since 2006 he is a "director emeritus". [ 8 ]
He is the co-founder and co-owner of Lipotype GmbH. [ 10 ] >
In 2012 he started-up a biotech company Lipotype GmbH, where he is a CEO. [ 10 ]
Early in his career, Simons pursued research in the field of medical biochemistry. Both his master's thesis and postgraduate research focused on vitamin B12 absorption. [ 2 ] [ 11 ] [ 12 ] After returning from his post-doc scholarship he continued research on vitamin B12 as well as on blood plasma proteins , but soon started investigating Semliki Forest virus , focusing on its membrane and its lipid composition and their role in the virus budding and its transport, as the model for lipid and protein secretion . [ 2 ] [ 13 ] [ 14 ] [ 15 ] [ 16 ] During this period, Simons also investigated the application of detergents in biochemistry with a special attention to their role in biological membrane research. [ 17 ]
The virus lifecycle and how it uses components of vesicular pathways while shuttling to the cell surface, turned Simons' attention toward vesicular transport pathways and cell polarization . Applying epithelial model cells – MDCK (Madin-Darby canine kidney), he investigated lipid transport, protein sorting and their role in polarizing cells. [ 2 ] [ 18 ] [ 19 ]
In these studies, he described the role of the trans-Golgi network (TGN) in protein and lipid sorting according to their destination. [ 6 ] [ 2 ] In his works from 1988, together with Gerit van Meer , [ 20 ] [ 21 ] Simons proposed the existence of lipid microdomains in cell membranes for the first time. [ 2 ] Such microdomains differ in their composition from the surrounding membrane and have special functions. Simons coined the term ' lipid rafts ' to describe these microdomains. This concept was developed over the years to be presented more fully in 1997 in Nature journal by Simons and Ikonen. [ 5 ] This paper became one of the most frequently cited works in the field of membrane research. Other Simons' paper, on role of lipid rafts in the signal transduction [ 22 ] is second highest cited work and Simons is fourth highest cited scientist in the field of signal transduction. Kai Simons was also recognized by ISI Web of Knowledge , as one of the most cited scientist ever.
In subsequent years, Simons continued to work on the role of lipid rafts, and more generally lipids, in cell polarization and protein sorting. [ 23 ] He was interested also in the role of lipids and protein sorting in neurodegenerative diseases , especially in Alzheimer's disease . [ 24 ] [ 25 ]
His scientific record includes more than 350 scientific articles , mostly in the field of biochemistry, molecular organization of the cell, and biochemistry and physiology of a cell membrane.
Considering his work from years 1996–2007 tracked until May 2009, Simons was 12. in the list of the most frequently cited scientists in the field cell biology with 90 articles and 16,299 citations. [ 26 ]
Kai Simons honours and awards include: [ 4 ] [ 27 ]
Kai Simons was and is also a member of numerous societies, committees and organisations, as well as an editor for several scientific journals. [ 4 ]
He is married to Carola Simons and a father of three. [ 3 ] | https://en.wikipedia.org/wiki/Kai_Simons |
Kaidā glyphs ( カイダー字 , Kaidā ji ) are a set of pictograms once used in the Yaeyama Islands of southwestern Japan . The word kaidā was taken from Yonaguni , and most studies on the pictographs focused on Yonaguni Island . However, there is evidence for their use in Yaeyama's other islands, most notably on Taketomi Island . [ 1 ] They were used primarily for tax notices, thus were closely associated with the poll tax imposed on Yaeyama by Ryūkyū on Okinawa Island , which was in turn dominated by Satsuma Domain on Southern Kyushu.
Sudō (1944) hypothesized that the etymology of kaidā was kariya ( 仮屋 ) , which meant "government office" in Satsuma Domain. This term was borrowed by Ryūkyū on Okinawa and also by the bureaucrats of Yaeyama ( karja: in Modern Ishigaki). Standard Japanese /j/ regularly corresponds to /d/ in Yonaguni , and /r/ is often dropped when surrounded by vowels. This theory is in line with the primary impetus for Kaidā glyphs, taxation. [ 2 ]
Immediately after conquering Ryūkyū, Satsuma conducted a land survey in Okinawa in 1609 and in Yaeyama in 1611. By doing so, Satsuma decided the amount of tribute to be paid annually by Ryūkyū. Following that, Ryūkyū imposed a poll tax on Yaeyama in 1640. A fixed quota was allocated to each island and then was broken up into each community. Finally, quotas were set for the individual islanders, adjusted only by age and gender. Community leaders were notified of quotas in the government office on Ishigaki. They checked the calculation using warazan ( barazan in Yaeyama), a straw-based method of calculation and recording numerals that was reminiscent of Incan Quipu . After that, the quota for each household was written on a wooden plate called itafuda or hansatsu ( 板札 ) . That was where Kaidā glyphs were used. Although sōrō -style Written Japanese had the status of administrative language, the remote islands had to rely on pictograms to notify illiterate peasants. According to a 19th-century document cited by the Yaeyama rekishi (1954), an official named Ōhama Seiki designed "perfect ideographs" for itafuda in the early 19th century although it suggests the existence of earlier, "imperfect" ideographs. [ 3 ] Sudō (1944) recorded an oral history on Yonaguni: 9 generations ago, an ancestor of the Kedagusuku lineage named Mase taught Kaidā glyphs and warazan to the public. Sudō dated the event to the second half of the 17th century. [ 2 ]
According to Ikema (1959), Kaidā glyphs and warazan were evidently accurate enough to make corrections to official announcements. The poll tax was finally abolished in 1903. They were used until the introduction of the nationwide primary education system rapidly lowered the illiteracy rate during the Meiji period . [ 4 ] They are currently used on Yonaguni and Taketomi for folk art, T-shirts, and other products, more for their artistic value than as a record-keeping system.
Kaidā glyphs consist of
As for numerals, similar systems called sūchūma can be found in Okinawa and Miyako and appear to have their roots in the Suzhou numerals . [ 5 ]
The first non-Yaeyama author to comment on kaidā glyphs was Gisuke Sasamori , who left copies of many short kaidā texts in his Nantō Tanken (南島探検, Exploration of the Southern Islands ), a record of his 1893 visit to Okinawa Prefecture which also mentions the hard labor imposed on the islanders by the regime. Yasusada Tashiro collected various numeral systems found in Okinawa and Miyako and donated them to the Tokyo National Museum in 1887. A paper on sūchūma by British Japanologist Basil Chamberlain (1898) [ 6 ] appears to have been based on Tashiro's collection. [ 5 ]
In 1915 the mathematics teacher Kiichi Yamuro (矢袋喜一) included many more examples of kaidā glyphs, barazan knotted counting ropes, and local number words (along with a reproduction of Sasamori's records) in his book on Old Ryukyuan Mathematics (琉球古来の数学). Although Yamuro did not visit Yonaguni by himself, his records suggest that kaidā glyphs were still in daily use in the 1880s. Anthropologist Tadao Kawamura , who made his anthropological study of the islands in the 1930s, noted "they were in use until recently." He showed how kaidā glyphs were used in sending packages. [ 7 ] Sudō (1944) showed how business transactions were recorded on leaves using kaidā glyphs. He also proposed an etymology for kaidā. [ 2 ] | https://en.wikipedia.org/wiki/Kaidā_glyphs |
Kaikō ( かいこう , "Ocean Trench") [ 4 ] was a remotely operated underwater vehicle (ROV) built by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) for exploration of the deep sea . Kaikō was the second of only five vessels ever to reach the bottom of the Challenger Deep , as of 2019. Between 1995 and 2003, this 10.6 ton unmanned submersible conducted more than 250 dives, collecting 350 biological species (including 180 different bacteria), some of which could prove to be useful in medical and industrial applications. [ 3 ] On 29 May 2003, Kaikō was lost at sea off the coast of Shikoku Island during Typhoon Chan-Hom , when a secondary cable connecting it to its launcher at the ocean surface broke. [ 2 ]
Another ROV, Kaikō7000II , served as the replacement for Kaikō until 2007. At that time, JAMSTEC researchers began sea trials for the permanent replacement ROV, ABISMO ( A utomatic B ottom I nspection and S ampling Mo bile).
Bathymetric data obtained during the course of the expedition (December 1872 – May 1876) of the British Royal Navy survey ship HMS Challenger enabled scientists to draw maps, [ 5 ] which provided a rough outline of certain major submarine terrain features , such as the edge of the continental shelves and the Mid-Atlantic Ridge . This discontinuous set of data points was obtained by the simple technique of taking soundings by lowering long lines from the ship to the seabed . [ 6 ]
Among the many discoveries of the Challenger expedition was the identification of the Challenger Deep. This depression, located at the southern end of the Mariana Trench near the Mariana Islands group, is the deepest surveyed point of the World Ocean . The Challenger scientists made the first recordings of its depth on 23 March 1875 at station 225 . The reported depth was 4,475 fathoms (8184 meters) based on two separate soundings.
On 23 January 1960, Don Walsh and Jacques Piccard were the first men to descend to the bottom of the Challenger Deep in the Trieste bathyscaphe . Though the initial report claimed the bathyscaphe had attained a depth of 37,800 feet, [ 7 ] the maximum recorded depth was later calculated to be 10,911 metres (35,797 ft). At this depth, the water column above exerts a barometric pressure of 108.6 megapascals (15,750 psi), over one thousand times the standard atmospheric pressure at sea level. Since then, only two manned vessels have returned to the Challenger Deep: the Deepsea Challenger , which was piloted by director James Cameron on March 26, 2012, to the bottom of the trench.; [ 8 ] and the Limiting Factor, piloted by Victor Vescovo in 2019.
In March 1995, Kaikō became the second vessel ever to reach the bottom of the Challenger Deep , and the first craft to visit this location since the Trieste mission. [ 3 ] [ 9 ] The maximum depth measured on that dive was 10,911.4 meters, [ 1 ] [ 9 ] [ 10 ] marking the deepest dive for an unmanned submersible to date. On 31 May 2009, Nereus became the third vessel to visit the bottom of the Challenger Deep , reaching a maximum recorded depth of 10,902 meters. [ 9 ] [ 11 ]
RV Kairei ( かいれい ) is a deep sea research vessel that served as the support ship for Kaikō , and for its replacement ROV, Kaikō7000II . It now serves as the support ship for ABISMO . Kairei uses ABISMO to conduct surveys and observations of oceanic plateaus , abyssal plains , oceanic basins , submarine volcanoes , hydrothermal vents , oceanic trenches and other underwater terrain features to a maximum depth of 11,000 meters. Kairei also conducts surveys of the structure of deep sub-bottoms with complicated geographical shapes in subduction zones using its on-board multi-channel reflection survey system. [ 12 ]
In February 1996, Kaikō returned to Challenger Deep, this time collecting sediment and microorganisms from the seabed at a depth of 10,898 meters. Among the novel organisms identified and collected was Moritella yayanosii [ 13 ] and Shewanella benthica . [ 14 ] These two species of bacteria appear to be obligately barophilic. The optimal pressure conditions for growth of S. benthica is 70 Megapascals (MPa) , while M. yayanosii grows best at 80 MPa; no growth at all was detected at pressures of less than 50 MPa with either strain. [ 14 ] Both species appear to contain high levels of docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA), omega-3 fatty acids which could prove to be useful in the treatment of hypertension and even cancer . [ 3 ]
In December 1997, Kaikō located the wreck of Tsushima Maru on the sea floor off the coast of Okinawa . Tsushima Maru was an unmarked Japanese passenger/cargo ship that was sunk during World War II by USS Bowfin , a United States Navy submarine .
In May 1998, Kaikō returned again to Challenger Deep, this time collecting specimens of Hirondellea gigas . Hirondellea gigas (Birstein and Vinagradov, 1955) is a crustacean of the Uristidae family of marine amphipods . [ 15 ]
In October 1999, Kaikō performed a robotic mechanical operation at a depth of 2,150 meters off the coast of Okinawa near the Ryukyu Trench , connecting measuring equipment with underwater cables on the sea floor. On this mission, another bacterial species, Shewanella violacea , was discovered at a depth of 5,110 meters. [ 16 ] This organism is notable for its brilliant violet-colored pigment . Certain compounds found in S. violacea may have applications in the cosmetics industry (development of products for lightening of skin tone) and also in the semiconductor industry (development of chemicals to be used in production of semiconductors). [ 3 ]
In late November 1999, Kaikō located the wreckage of H-2 No. 8, a NASDA rocket ( satellite launch system ), on the sea floor at a depth of 2,900 meters off the Ogasawara Islands . H-2 flight F8 was conducted on 15 November 1999. The rocket, which was carrying a Multi-Functional Transport Satellite (MTSAT) payload, self-destructed after experiencing an engine malfunction shortly after it was launched.
In August 2000, Kaikō discovered hydrothermal vents and their associated deep sea communities at a depth of 2,450 meters near the Central Indian Ridge . The Central Indian Ridge is a divergent tectonic plate boundary between the African Plate and the Indo-Australian Plate located in the western Indian Ocean .
On 29 May 2003, Kaikō was lost at sea during Typhoon Chan-Hom , when a steel secondary cable connecting it to its launcher at the surface broke off the coast of Shikoku Island . [ 2 ]
In May 2004, JAMSTEC resumed its research operations, using a converted ROV as its vehicle. The ROV, formerly known as UROV 7K , was rechristened Kaikō7000II . The 7000 designation indicates that this vessel is rated for diving to a maximum depth of 7,000 meters.
While the temporary replacement ROV ( Kaikō7000II ) has a remarkable performance record, it is only rated to 7,000 meters and cannot reach the deepest oceanic trenches. For this reason, JAMSTEC engineers began work on a new 11,000-meter class of ROV in April 2005. [ 2 ] [ 17 ] The project is called ABISMO (Automatic Bottom Inspection and Sampling Mobile), which translates to abyss in Spanish. Initial sea trials of ABISMO were conducted in 2007. The craft successfully reached a planned depth of 9,760-meters, the deepest part of Izu–Ogasawara Trench , where it collected core samples of sediment from the seabed. [ 2 ] [ 17 ] | https://en.wikipedia.org/wiki/Kaikō_ROV |
The Kaimingjie germ weapon attack ( simplified Chinese : 开明街鼠疫灾难 ; traditional Chinese : 開明街鼠疫災難 ; lit. 'Kaiming Street Plague Disaster') was a secret biological warfare attack launched by Japan in October 1940 against the Kaiming Street area of Ningbo , Zhejiang , China . [ 1 ] A joint operation of the Imperial Japanese Army 's Unit 731 and Unit 1644 , [ 1 ] this attack was operated by military planes taking off from Jianqiao Airport in Hangzhou , [ 2 ] : 89 which airdropped wheat, corn, cotton scraps, and sand infected with plague fleas to target locations. [ 1 ] From September 1940, Ningbo, Quzhou , and other places were subjected to various forms of biological warfares until the end of October 1940, when the attacks triggered a plague epidemic in Ningbo. [ 3 ]
After the outbreak of the plague, the city authorities in Ningbo built a 4.3-meter-high isolation wall around the epidemic area, segregating patients and suspected cases, and eventually burned down the Kaiming Street area to eradicate the disease. [ 4 ] Until the 1960s, this burned area was still referred to as the "plague field". [ 5 ] According to the doctoral thesis of Junichi Kaneko, a military doctor of Unit 731, on October 27, 1940, Unit 731 spread 2 kilograms of plague bacteria over Ningbo, Zhejiang, using aircraft, resulting in a total of 1,554 deaths from the first- and second-round infections. [ 6 ] [ 7 ]
In June 1925, Japan signed the Geneva Protocol , which committed Japan to refrain from using biological and chemical weapons in warfare. [ 8 ] The development of Japan's biological weapons was highly secretive and led by Shiro Ishii . He planned and raised funds for Japan's biological weapons program. [ 9 ] [ 10 ] In 1939, the Imperial Japanese Army established Unit 1644 in Nanjing to conduct research on biological and chemical weapons. Units 1644 and 731 studied the effects of various chemicals and pathogens that could be used as biological weapons on soldiers and civilians and developed weapons to further expand the Japanese Empire's territory in Asia. [ 10 ]
After the failure of the rapid decisive victory plan in the war against China, the Japanese military began using bacteriological weapons. [ 8 ] In the summer of 1939, during the Battle of Khalkhin Gol , the Imperial Japanese Army used biological and chemical weapons against Soviet and Mongolian troops. [ 11 ] On June 13, large quantities of white powder were airdropped in the vicinity of Lihai, Shaoxing. On June 15, chemical tests conducted by the local river police did not reveal any abnormalities, but subsequent bacterial culture tests revealed turbidity in one test tube and cotton-like floating substances in another, with pathogens such as tetanus and diphtheria observed under a microscope. Within days after the airdrop, the weather in Shaoxing was clear and sunny, with abundant sunlight, which was not conducive to bacterial growth, so no epidemic outbreak occurred. This is the earliest recorded instance of the Japanese military's bacteriological weapon attack in Zhejiang. [ 12 ]
Before 1937, Zhejiang cities such as Ningbo , Jinhua , and Quzhou in Zhejiang did not experience a plague epidemic. [ 13 ] However, people may have been aware of the plague near Ningbo in Shanghai in 1910. The incubation period of the plague is 2 to 8 days. At the time of the outbreak, sulfa drugs, streptomycin, and other antibiotics had not yet been invented, so residents of Ningbo could not have access to antibiotics and were primarily treated with serum. Without treatment, the mortality rate of the plague was almost 100%, and there was not enough serum supply prepared in advance. [ 11 ]
After the outbreak of the Second Sino-Japanese War in 1937, Ningbo became one of the important seaports for China to obtain international aid supplies, with a daily throughput of over 10,000 tons of goods. [ 2 ] : 87–88 As a port city with a population of 260,000, Ningbo had numerous streets, dense housing, crowded residents, relatively poor sanitary conditions, high population mobility, and frequent goods entering and leaving, making it easy for the plague to spread and proliferate through people and goods transmission. [ 2 ] : 87–88 Kaiming Street is a north-south urban main road in Ningbo and is the main commercial centre of the old city. [ 14 ] : 196
Since the first Japanese air raid on Lishe Airport on August 16, 1937, the Japanese military had directly attacked Ningbo at least 7 times. On 17 July 1940, the Japanese military first invaded Zhenhai , but were driven out by the Chinese army on the 22. The Japanese military again bombed Ningbo on 5 and 10 September of the same year. [ 6 ]
In June 1940, the Imperial Japanese Army headquarters formally discussed the use of biological weapons and issued orders to begin biological warfare. On 5 June 1940, discussions on the implementation of bacteriological warfare were held by Colonel Kozo Aramaki from the Operations Department of the Imperial Japanese Army General Staff, Major Kumaomi Imoto from the China Expeditionary Army Staff, and Lieutenant Colonel Tomosada Masuda, acting commander of Unit 1644 in Nanjing. It was decided during the discussions that the main cities in Zhejiang would be targeted, and the method of operation would involve dispersing bacterial liquids from aircraft and air-dropping fleas infected with plague. On August 6, a heavily guarded train departed from the barracks of Unit 731 in Pingfang , bound for Hangzhou . The train was loaded with 700 aerial bombs, 20 vehicles, 70 kilograms of Salmonella typhi , 50 kilograms of Vibrio cholerae , and 5 kilograms of plague fleas . Shiro Ishii was the overall director of this operation. [ 3 ]
On September 10, 1940, negotiations were held in Hangzhou between the Central China Expeditionary Army and the Nara Unit, responsible for bacteriological warfare and composed of personnel from Unit 731 and Unit 1644, to select the targets for the attacks: Ningbo and Quzhou , with Jinhua as a backup, to coincide with the blockade of Ningbo Port by the Imperial Japanese Navy since July 1940. [ 2 ] : 87–88 The Japanese army also referred to this operation as the "Operation Hangzhou.". [ 2 ] : 89 According to the plan, aircraft would take off from Hangzhou Jianqiao Airport and drop ceramic bacteriological bombs developed by Shiro Ishii himself, along with cotton, shredded cloth, and other materials to protect the fleas. [ 12 ] Corn and cloth were infested with fleas carrying pathogens of cholera and plague to infect rats, which would then transmit the diseases to human hosts. [ 9 ]
During the three-month-long bacteriological warfare, six areas including Ningbo were subjected to various forms of bacteriological attacks. In Quzhou, the Japanese employed aircraft to scatter grain and wheat seeds carrying bacteria; in Ningbo, aircraft were used to spread bacterium-laden grains and cotton within or around the city; in Jinhua , explosions from bombs dropped by aircraft produced a pale yellow smoke; in Yushan , a plan was implemented to release bacteria among ordinary residents, with pathogens being introduced into residents' water pools, wells, and even placed hundreds of seemingly abandoned desserts and fruits injected with large quantities of typhoid and paratyphoid bacteria by the Imperial Japanese Army at doorsteps and treesides, deceiving local residents who lacked food to consume. [ 3 ]
On 4 October 1940, wheat and barley items dropped by Japanese aircraft were found in Quzhou. [ 13 ] That afternoon, the county magistrate ordered the residents of Quzhou to gather and burn the air-dropped items. Starting from 10 October, the area began to see deaths from the diseases. [ 15 ] From 18 September to 8 October, the Japanese launched a total of six attacks on Ningbo, none of which resulted in a plague outbreak. Despite fleas being dropped in Quzhou on 4 October, there were no apparent effects by the end of October. [ 2 ] : 97 On 22 October, Japanese military aircraft flew over Ningbo and dropped wheat and other items. [ 16 ] The airstrikes in Quzhou did not attract the attention of the provincial government, which instead focused on a plague outbreak in Qiyuan, not associated with the Imperial Japanese Army. [ 12 ]
At around 7 a.m. on 27 October, air raid sirens sounded in downtown Ningbo, and Japanese military aircraft flew over the streets of the city, dropping leaflets instead of bombs. According to eyewitness Hu Xianzhong, the leaflets depicted flags of Japan, Germany, and Italy, and a cartoon depicting "Sino-Japanese friendship," claiming that Chongqing was suffering from famine and hardship while the Japanese people were well-fed and had surplus food to help them. Around 2 p.m., Japanese aircraft reappeared and air-dropped barley, millet, flour, and clusters of cotton balls. [ 6 ] Archibald Crouch , an American missionary in Ningbo, noted in his diary that while Japanese aircraft usually flew in groups when arriving in Ningbo, this time there was only one aircraft, which was unusual, and observed that after the aircraft passed, it seemed to release a cloud that dispersed downward. Local residents had no experience of a plague outbreak, and no one mentioned that this was a biological weapons attack that day. [ 11 ]
In 1940, Ningbo had yet to have piped water , so it was common for households to collect rainwater in one or two large jars placed under the eaves of their courtyards for drinking and cooking. On the evening of 27 October, heavy rain in Ningbo washed wheat grains from rooftops into these water jars. Some poultry that consumed the wheat grains died the following day. [ 17 ] People noticed a sudden increase in fleas in Donghou Street and Kaiming Street, [ 18 ] but there were no reports of deaths among rodents . Rumours circulated that the Japanese air raid was actually a biological weapons attack. [ 11 ]
On 30 October, according to the local Chinese-language newspaper Shishi Gongbao , an acute disease outbreak was reported in Kaiming Street of Ningbo, spreading severely. Within just three days, over 10 deaths were reported. [ 19 ] Subsequently, people from neighbouring establishments such as Wang Shunxing's bakery, Hu Yuanxing's dominoes shop, Yuan Tai Hotel, Bao Changxiang underwear shop on East Zhongshan Road, and the vicinity of Donghou Street, all experienced fatalities. [ 17 ] Infected individuals exhibited symptoms including high fever, headache, dizziness, staggering gait, sometimes confusion, swelling and pain in the lymph nodes, [ 17 ] and diarrhoea before death. [ 20 ] Initially, people mistook it for bubos or malignant malaria . [ 21 ] People sought quinine from hospitals, but it proved ineffective. [ 6 ] On the morning of 1 November, nearly ten households in Kaiming Street, East Main Road, Donghou Street, and Taiping Alley reported deaths, with an increasing number suffering from colds and fever. Nine people succumbed to the disease on that day alone. [ 6 ]
On 1 November, the government of Yin County invited physicians to form a prevention and control committee, with Zhang Fangqing, the director of the Central Hospital, appointed as the head of the Medical Affairs Department, and Sun Jinshi as the attending physician. Based on Sun Jinshi's preliminary diagnosis of patient symptoms, they suspected plague , with the majority of patients suffering from septicemic plague , and a minority from bubonic plague , with no cases of pneumonic plague detected. [ 21 ] Ding Licheng, the director of Hwa Mei Hospital , stated that it was still uncertain whether it was a genuine plague. [ 19 ]
On the evening of 2 November, the county government imposed a blockade and isolation on the area and conducted routine disinfection of households. As a preventive measure, bed sheets and cloth were burned, and officials promptly began vaccinations. [ 9 ] Wang Shunxing's bakery, Hu Yuanxing's dominoes shop, Yuan Tai Hotel, Bao Changxiang underwear shop on East Zhongshan Road, and the vicinity of Donghou Street, all experienced fatalities. [ 17 ]
By November 3, 16 deaths had occurred, followed by another 7 on the next day. The highest recorded death toll in a single day was 20. Wails echoed along Kaiming Street, with mourners clad in mourning attire abound. [ 17 ] Ding Licheng, the director of Hua Mei Hospital, obtained samples through lymph node puncture fluid examination, [ 18 ] and had the plague bacillus detected by Hua Mei's examiner Xu Guofang, followed by multiple tests and rechecks by the provincial health department. [ 17 ] On 4 November, Ding Licheng issued a statement to the Shishi Gongbao , officially declaring the epidemic as "plague." [ 18 ] [ 17 ]
From 4 November onwards, [ 3 ] an isolation zone spanning over 5000 square metres around the affected area was demarcated. [ 17 ] Considering the inconvenience of transporting patients to Dayuwangmiao, due to its distance from the outbreak site, a Class A Isolation Hospital was established in Tongshun Store within the isolation zone to admit patients exhibiting clear symptoms. Additionally, a Class B Isolation Hospital was established at Kaiming Lecture Hall on Kaiming Street adjacent to the outbreak area to accommodate individuals suspected of being infected. [ 18 ] On 5 November, the local newspaper Shishi Gongbao issued an official announcement titled Great Disaster: All Citizens Unite to Eradicate the Plague , [ 17 ] along with the publication of the first epidemic prevention special edition. Subsequently, daily updates on epidemic prevention measures continued to be featured. [ 5 ]
The county secretary, Zhang Hongbin, assumed temporary control of the county government, [ 18 ] and on 6 November, the Yin County Epidemic Prevention Office was established, concurrently forming a team to search for fugitive patients. [ 2 ] : 93 Township governments under the county also issued a notice refusing to accommodate residents from the affected area. [ 17 ] Schools, public places, hotels, and restaurants ceased operations one after another. From that day onwards, families were prohibited from burying bodies privately, and all deceased patients were required to be buried deep in Laolongwan in the southwest suburbs. [ 3 ] [ 21 ]
Starting on 7 November, three quarantine hospitals—designated as Class A, Class B, and Class C—were established. Class A was tasked with treating confirmed plague patients, while Part B oversaw asymptomatic residents under observation within the affected area. Part C dealt with suspected patients both inside and outside the epidemic area. The Class A and Class C hospitals were located at Tongshun Store and Kaiming Hermitage. The Class B hospital was within the Yongyao Power Building. [ 18 ] Residents' clothing, miscellaneous items, and furniture were disinfected and transported by stretcher teams. [ 22 ]
To address the issue of handling materials within the epidemic area, a property registration office was established to register all houses and items within the epidemic area. For valuable or movable items, disinfection was mandatory before removal from the epidemic area. Two large stoves were constructed on the open ground of Kaiming Lane in the southwest corner of the epidemic area for boiling and disinfection purposes. Disinfection personnel wore protective clothing and hats, and based on the household information in the registration book, items were removed for disinfection house by house, with family members responsible for collection. [ 21 ]
On 8 November, the Yin County government held its second epidemic prevention meeting, mandating that residents within the epidemic area and other relevant individuals must receive preventive injections of the plague vaccine. To facilitate this, the county government established a dedicated vaccination team, covering an area from the epidemic area centred around Kaiming Street, extending east to Qizha Street, south to Daliang Street, west to the North and South Main Roads, and north to Cangshui Street in the city centre. All residents, including primary and secondary school students, were required to receive the vaccination. [ 5 ] On 10 November, Chen Wanli, Director of the Zhejiang Provincial Health Bureau, led the 17th Epidemic Prevention Team of the National Health Administration to Ningbo with the vaccines. [ 3 ] In total, 23,343 individuals received the injections. [ 5 ]
From 8 November onwards, [ 3 ] a wall measuring over one yard high was erected around the perimeter of the epidemic area. The wall's surface was plastered with mud and covered with arched white iron sheets on the top. Additionally, a three-foot wide and four-foot deep isolation trench was dug outside the wall to prevent the spread of the epidemic, ensuring that plague-infested fleas could not escape. To prevent the spread of the disease, the disinfection team implemented a series of measures. They primarily sealed the cracks along the street walls with white paper and sprayed lime water along the way. Shops and houses were sealed and subjected to 12 hours of sulphur fumigation for disinfection. Furthermore, ceilings and floors were pried open and filled with lime water to thoroughly remove the bodies of dead rats. Additionally, all domestic animals such as dogs and cats within the epidemic area were culled. [ 17 ]
On 14 November, the search team for escaped patients successfully apprehended 14 individuals. [ 2 ] : 93 Subsequently, a total of 38 residents who had fled the epidemic area were gradually recovered. Shockingly, the number of deaths among those who escaped the area reached as high as 32 individuals. [ 17 ] From 15 November onwards, concerns about personal safety were openly expressed by those responsible for sealing off and isolating the area. Since 23 November, there had been public complaints and protests against the isolation measures. Local media also began questioning the authenticity of the epidemic, with those raising doubts and objections being officially rebutted and condemned. However, there were few who questioned the isolation measures themselves, indicating community understanding of the corresponding risks and support for such actions. [ 11 ]
The epidemic area comprised over 200 houses, mostly of brick and wood construction. Along East Main Road and Kaiming Street, the street-facing houses typically had three or pseudo-three floors, while those within the alleys were mostly two or single-storey buildings. To thoroughly eradicate the source of the epidemic, experts concluded that the area was relatively concentrated and situated in a bustling urban district. Additionally, beneath these houses, there used to be a small river that was purchased and filled in by homeowners during the expansion of East Main Road. However, in some areas, remnants of the river remained, filled with debris, making it challenging to disinfect using conventional methods. [ 21 ]
At the 19th anti-epidemic meeting held on 28 November, due to the poor condition of the houses in the epidemic area and its low-lying location, which made it an ideal breeding ground for rats and fleas, the county government decided to burn down the epidemic area. The burning operation commenced at 7 p.m. on 30 November and was overseen by officials from the Provincial Health Department and local residents of Ningbo. Prior to the burning, nearby streets were closed to traffic, and surrounding buildings were protected by the fire brigade. Except for valuable items that could be disinfected and removed, all other belongings within the epidemic area were incinerated. [ 5 ] Provincial Health Department Director Chen Wanli inspected the area and approved the decision. [ 21 ]
On 30 November 1940, the authorities of Yin County carried out their plan to burn down all the houses in the epidemic area. [ 18 ] Several points were selected within the epidemic area as ignition points, where straw was laid down, soaked with petrol, and designated routes were established for the fire setters. The perimeter was tightly guarded by military and police forces, and the entire city's fire brigade was mobilized to protect the safety of buildings outside the epidemic area. [ 21 ] At around six or seven in the evening, [ 21 ] [ 6 ] fires were simultaneously ignited at 11 locations within the epidemic area, and flames shot up into the sky, lasting for a full four hours. All the residences, shops, and factories within the epidemic area were engulfed by the blaze. A total of 115 households, comprising 137 houses, and 5000 square meters of buildings were reduced to rubble overnight. [ 6 ] The fire spread to the houses across East Avenue, blackening their outer walls and sending sparks flying. The fire brigade then aimed their hoses at these row houses and activated the water pumps. In North Taiping Lane, where the road was narrow, houses were specifically protected by sprinkler heads. [ 21 ]
The specific areas burned included 224 to 268 East Zhongshan Road, Jiang Zhongji to Jiuhe Xiang Smoke Shop, 64 to 98 Kaiming Street, 139, 133, 129, 128, 127, 126, 125, 124, 123, 122, 121, 120, 118, 130 (Tongshun Store), 131, 134, 136 (Wang Renlin), 138, 132, 140, 141 (Xu Shenglai), 142, and 143 Donghou Street. Additionally, there were 8 upstairs houses, 5 front and back small coverings, and 3 high-level flat-roofed houses in the Kaiming Street temple, and 28 third-floor market houses and 3 second-floor market houses in Taiping Lane. [ 23 ] Until the 1960s, this burned area was still referred to as the "plague field." [ 5 ] After the Imperial Japanese Army entered Ningbo in 1941, they demolished the isolation walls. [ 21 ]
In October to November 1940, Chen Wanli from the Zhejiang Provincial Health Department and others involved in the prevention and control of the plague in Zhejiang, such as Liu Jingbang, did not believe that the plague in Ningbo at that time was caused by Japanese biological weapons. [ 19 ]
On 5 November, the Shishi Gongbao published an article titled "Investigating the Origin of the Disease," which rejected the speculation of Japanese biological weapons and put forward the "local origin" theory. The article pointed out that a similar plague event occurred in the Donghou Street area of Kaiming Street, which was initially suspected to be caused by enemy aircraft spreading poison. However, based on factual inference, several factors may have contributed to the outbreak: the Donghou Street area used to have a city moat, which was filled with garbage when the riverbed was filled. In the garbage pile, dead rats were inevitably mixed in. Due to the long decomposition of dead rats or the breeding of toxins in the garbage, once they entered the human body, it would trigger a plague-like outbreak. From this report, it can be inferred that the source of the plague in Ningbo this time was similar to the Qingyuan plague in 1938, both originating locally due to "rotting dead rats" or "garbage brewing toxins" leading to the occurrence of the plague. [ 24 ]
On 28 November 1940, the Japanese bombed Jinhua, scattering granular particles resembling fish eggs, which were confirmed to contain Yersinia pestis . [ 13 ] On 5 December, Huang Shaohong , the Chairman of the Zhejiang Provincial Government, telegraphed all county magistrates, instructing them to immediately report any outbreaks and establish epidemic prevention committees to promptly seal off affected areas and isolate patients. [ 12 ] He also reported the finding to Chiang Kai-shek via telegram, asserting that his province was under the attack of Japanese biological weapons. [ 13 ]
On 29 November 1940, the Shishi Gongbao reported that Japanese aircraft attacked Jinhua on 28 November 28, and in addition to releasing poison gas, also dispersed Gram-negative bacilli, attempting to attack civilians. By December 3, the Shishi Gongbao suggested that the source of the plague in Ningbo was "enemy aircraft spreading poison," but stopped short of making a definitive statement, only stating that "the enemy's intentions are sinister, and poisoning is possible." However, Ningbo health officials remained divided on whether the epidemic in Ningbo originated from Japanese biological weapons. [ 24 ]
On 10 December 1940, Chen Wanli reported to the Nationalist Government, stating, "About a week before the onset of the illness, enemy aircraft dropped about 2 liters of wheat over the epidemic area. Whether this is related to the epidemic is yet to be determined." By mid-December, Chen Wanli, Liu Jingbang, and Ke Zhuguang confirmed that the plague in Qu County and Jinhua was the result of "enemy aircraft spreading poison." Huang Shaoheng, Chairman of the Zhejiang Provincial Government, pointed out in his report to the Nationalist Government that there was a strong correlation between the Ningbo plague and the suspected Japanese aircraft dissemination, citing evidence of Japanese aircraft dispersing plague bacilli in Jinhua, which could prove Japan's use of bacteriological warfare. [ 24 ] While Zhejiang's provincial government introduced a law to manage airdrops from Japanese aircraft, [ 25 ] Chen Wanli and other Zhejiang health officials were disbelieved by the experts of National Health Administration, including Robert Pollitzer . [ 24 ]
In December 1940, the National Health Administration convened a national health technology conference in Chongqing to discuss the plague in Ningbo. [ 26 ] During the meeting, Chen Wengui, a microbiologist, who attended the meeting, pointed out that the Japanese had conducted bacteriological warfare in China, but he was accused of being overly sensitive by the conference chairman. [ 26 ] During the Zhejiang Plague Consultation Conference chaired by Jin Baoshan, Robert Pollitzer expressed skepticism about the theory of bacteriological warfare causing the plague. [ 19 ]
The Nationalist Government received accusations stating that the epidemic was not the plague and that burning down houses was unnecessary. [ 21 ] In January 1941, Jin Baoshan dispatched the Director of the Epidemic Prevention Department, Rong Qirong, and others to investigate in Zhejiang. [ 20 ] Before arriving in Ningbo, Pollitzer had already confirmed the situation of blood smears at the provincial health department and verified the conditions of the disease and its onset. The investigation proposed two theories: one was that the epidemic originated from elsewhere and spread to Ningbo, as there had been a plague outbreak in Qingyuan, southern Zhejiang; the other was that Japanese aircraft had spread fleas and other substances by dropping wheat and grains. [ 21 ] However, the transport from Qingyuan to Ningbo was extremely inconvenient, and no outbreaks occurred along the way. The areas where Japanese aircraft dropped the most wheat and grains also had the highest death tolls. Additionally, strange fleas were found in the epidemic area, slightly smaller in size and red in color, distinct from local fleas. [ 21 ] After the investigation, Rong Qirong supported Pollitzer's judgment, believing there was not enough scientific evidence for biological warfare. [ 19 ]
On 5 March 1941, Chen Wanli, the highest health official of Zhejiang, informed Yu Jimin , the Magistrate of Yin County, requesting the submission of post-growing photographs of airdropped wheat as evidence, to be forwarded to Chongqing for verification. He also mentioned that detailed records of plague cases from the previous year and investigations related to patient onset needed to be provided urgently in response to central government requests. Chen Wanli further instructed Zhang, the director of the Yin County Health Bureau, to submit detailed records of plague cases from the previous year and to send a copy of the plague patient investigation form. He emphasized that all documents needed to be submitted within ten days for transmission to the central authorities, including information on the isolation status of all patients and the entire period of quarantine work. [ 27 ]
On 4 November 1941, using the same method, the Japanese attacked Changde , resulting in 2810 being infected with the plague. Immediately after the attack, Chen Wengui led a team to investigate. He performed autopsies on the bodies and injected lymph node puncture blood from patients into guinea pigs, which died five days later. By observing patient samples and conducting pathological analysis, it was concluded that the patients died from sepsis caused by Yersinia pestis. Chen Wengui compiled the evidence gathered into the "Investigation Report on the Plague in Changde, Hunan," confirming Japanese bacteriological warfare. However, the Nationalist government, considering the matter's impact on international credibility, altered the report. It was not until 1950 that the report resurfaced from the archives. [ 26 ]
The Japanese military monitored the local media reports and regularly dispatched military aircraft to surveil the situation. [ 11 ] The air raids resulted in a plague outbreak, leading to the success of bacteriological warfare attacks by rapidly disseminating a certain bacterial vector through aircraft. This development pleased Shiro Ishii. Ishii concluded that for successful attacks, bacteria should not be dispersed from high altitudes; instead, fleas and pathogens should be released together. Additionally, Shiro Ishii specifically filmed the Ningbo plague as a documentary to publicise his achievements. [ 2 ] : 97–98 On 25 November 1940, the Imperial Japanese Army instructed to terminate the experiments, with all participants instructed to return to their original units and maintain secrecy. [ 2 ] : 99 By the end of 1940, the Emperor ordered the expansion of Unit 731, increasing its personnel to 3,000 and establishing the Hailar Detachment, Sunwu Detachment, Hailin Detachment, and Linkou Detachment. Starting from 1940, an annual budget of 10 million yen was allocated to Unit 731. Shiro Ishii, the commander of Unit 731, was promoted to Major General on 1 March 1941. [ 2 ] : 100
In April 1941, following the Japanese occupation of Ningbo, a further investigation into the effectiveness of the plague attack in Ningbo was launched. The Kwantung Army transferred five researchers from Unit 731 to Nanjing to collaborate with Unit 1644 in investigating the effectiveness of the plague attack in Ningbo. In early May, eleven senior Japanese generals visited the vicinity of the epidemic area to meet with Jin Tirong, who was responsible for epidemic prevention work in 1940. They extensively queried the occurrence of the plague in Ningbo, including when and where it first occurred, which household was initially affected, whether there was aircraft dispersal of wheat, and whether there were accusations from the local population against the Japanese military, among other details. This questioning lasted for about two hours, and the contents were meticulously recorded. [ 2 ] : 91–92
According to the doctoral thesis of Junichi Kaneko, a military doctor of Unit 731, on 27 October 1940, Unit 731 scattered 2 kilograms of plague bacteria over Ningbo, Zhejiang Province, using aircraft. [ 6 ] [ 7 ] According to the data shown in the thesis's charts, the plague began to spread in Ningbo on 30 October, with 3 cases reported on the 31st, increasing to 9 cases on 1 November, peaking at 13 cases on the 6th, 10 cases on the 8th, 8 cases on the 9th, and 7 cases on the 12, gradually declining thereafter until the last case on 7 December, lasting a total of 39 days with 112 reported cases. Patients who escaped from the epidemic area created conditions for a "second infection." According to research conducted by the Japanese military in Ningbo, it was found that 1450 people died in the second round of infections. [ 2 ] : 93–94
On 15 October 2011, representatives of the Tokyo-based citizen organization "Revealing the Truth of Unit 731's Bacterial Warfare" and five others, including Professor Matsamura Takao from Keio University and Wang Xuan, a descendant of victims of bacterial warfare in China, held a press conference in Tokyo. They urged the Japanese government to disclose information on bacterial warfare and face up to historical truths. The organization discovered the first part of a classified military report from the Army Medical School's Epidemic Research Institute, titled "Estimation of PX's Effectiveness," at the Kansai Branch of the National Diet Library in Kyoto . This report directly documented Japan's conduct of bacterial warfare in China, challenging the Japanese government's claim of "no evidence" in response to Chinese accusations of Unit 731's bacterial warfare. [ 28 ]
The cover of the report bears the words " Military Secret " and contains the name of a senior military doctor who graduated from Teikyo University and recorded the content on December 14, 1943. The report explains that "PX" refers to fleas infected with Yersinia pestis , and it calculates the effectiveness of spreading bacteria bombs on the battlefield. The report lists the quantities of PX used and the number of infected individuals in various locations in China, including Nong'an , Quzhou , Ningbo, Changde , Guangxin , Guangfeng and Yushan . It states that over 26,000 people were infected once or twice, defining PX as "the best bacterial bomb, capable of causing psychological and economic panic." [ 29 ]
On 25 December 1949, the Soviet Union began the trial of Japanese prisoners of war involved in bacteriological warfare in Khabarovsk. During the Khabarovsk trial, Japanese prisoners admitted to the events of the "aerial dissemination of pathogens" that took place in Ningbo in 1940. Susumu Hatano testified that the experiment in Ningbo was the first actual field test and, because it was conducted on enemy territory, the results were inconclusive. However, the Japanese military drew conclusions about the bacteriological warfare experiment based on information recorded in Ningbo newspapers and laboratory test data. [ 24 ]
On 29 December 1949, a forensic medical examination committee composed of six medical biologists, including academician Zhukov-Verezhnikov, from the Soviet Academy of Medical Sciences, studied all the materials related to the criminal case against Japanese prisoners charged with preparing and using bacteriological weapons. The committee confirmed that the experiments and production conducted by the Japanese Kwantung Army's Unit 731, Unit 100, and Unit 1644 of the Japanese Expeditionary Forces in China were aimed at exploring and manufacturing bacteriological weapons, as well as researching methods for their use. The committee also confirmed that in 1940, under the leadership of Shiro Ishii, a combat expedition equipped with large quantities of bacillus anthracis, vibrio cholerae, and plague-infected fleas was sent to Ningbo. The aerial dissemination of plague-infected fleas by aircraft resulted in a plague epidemic in the Ningbo area. [ 19 ]
After news of the Khabarovsk trial reached China, the Zhejiang Daily published a news article on 7 February 1950, stating that personnel from the Zhejiang Provincial Health Department, including Wang Yuzhen, Zheng Jie'an, Yu Hanjie, and Jin Qiu, submitted a written report in support of the Soviet Union's trial of Japanese bacteriological warfare criminals. The report criticized the Zhejiang Health Department at the time for not taking action when the Japanese military continuously disseminated plague bacteria in various areas of Zhejiang, instead covering up for the Imperial Japanese Army. [ 24 ]
After the war, the activities of Unit 731 remained confidential and did not appear in the Tokyo Trials . [ 30 ] It wasn't until the publication of The Devil's Gluttony in 1981 that the unit's activities were first revealed to the public. In the first half of the 20th century, including during World War II, dozens of lawsuits for wartime compensation were filed against the Japanese government and companies associated with Japanese aggression. However, almost all of these lawsuits were rejected by Japanese courts. [ 31 ] Nevertheless, the Japanese government has never formally acknowledged that the Japanese military conducted bacteriological warfare. [ 31 ]
In 1996, a group of Japanese anti-war activists came to China to investigate the victims of bacteriological warfare and expressed their willingness to help the victims sue the Japanese government for its crimes. [ 6 ] Subsequently, in 1997 and 1999, a total of 180 plaintiffs from Zhejiang (Quzhou, Ningbo, Jiangshan, Yiwu), and Hunan (Changde) filed lawsuits against Japan, demanding that the Japanese government acknowledge its crimes of bacteriological warfare in China and apologise and compensate the victims. [ 6 ] [ 30 ]
During the five-year trial, veterans of Unit 731 admitted to participating in live dissections, cultivating agents such as anthrax, typhoid, and cholera, and releasing plague-infected fleas into villages. Plaintiffs from China flew to Japan to testify, describing how Japanese planes flew low and dropped infected wheat, rice, or cotton, leading to mysterious disease outbreaks in villages. [ 32 ] Despite a series of confessions from former soldiers, the Japanese government acknowledged the unit's existence but still refused to disclose the scope of scientists' activities. During the debates in the Tokyo District Court , Chinese bacteriologist Huang Ketai pointed out that unlike previous epidemics, the Ningbo plague in 1940 occurred in winter rather than summer and was carried by fleas that were not native to the region, killing humans without affecting mice. [ 33 ]
In 2002, based on 28 hearings and a large amount of evidence, the Tokyo District Court wrote a written summary confirming for the first time that the Japanese military conducted bacteriological warfare . However, many plaintiffs were angry at the rejection of their compensation claims and appealed. [ 32 ] In 2005, the Tokyo High Court upheld the ruling of the Tokyo District Court in 2002 and rejected the request for an apology from the Japanese government for its biological warfare in China before and during World War II. [ 31 ] The Japanese Supreme Court subsequently rejected the appeal, stating that international law prohibits foreign citizens from directly seeking compensation from the Japanese government. [ 34 ]
On 3 September 1995, the Ningbo Municipal People's Government erected a monument on the pedestrian walkway of Kaiming Street, inscribed with the words "Site of the Plague Field in Ningbo Infected by the Bacteriological Warfare of the Japanese Invaders," with the central inscription reading "Never Forget National Humiliation , Strive to Strengthen the Nation." It was signed by "Various sectors of Ningbo City on the 50th anniversary of the victory of the War of Resistance Against the Japanese ." In 2005, the monument was relocated to the original site of the bacteriological epidemic area on the west side of Tianyi Haoting. The new monument's front is engraved with the words "Do Not Forget National Humiliation, Strive to Strengthen the Nation," with bacteriological warfare historical materials and a list of victims carved on both sides. [ 35 ]
In 2009, the Publicity Department of Haishu District Committee, the District Radio, Television, and News Bureau, the District Cultural Relics Management Office, and the Ningbo New Fourth Army Historical Research Association jointly established the "Ningbo Kaiming Street Plague Disaster Exhibition Hall" on the second floor of the Tianyi Business Circle Party and Mass Service Center. The curved wall on the right side of the entrance of the exhibition hall lists the names of all the victims. In the centre of the hall, there is a sand table displaying a model of the buildings in the Kaiming Street epidemic area, reconstructed according to the "Epidemic Area Map" provided by the family of the victim Hu Dingyang. [ 17 ] | https://en.wikipedia.org/wiki/Kaimingjie_germ_weapon_attack |
Kainosymmetry (from Greek καινός "new") describes the first atomic orbital of each azimuthal quantum number (ℓ). Such orbitals include 1s, 2p, 3d, 4f, 5g, and so on. The term kainosymmetric was coined by Sergey Shchukarev [ ru ] . Pekka Pyykkö referred to such orbitals as primogenic instead. [ 1 ] Such orbitals are much smaller than all other orbitals with the same ℓ and have no radial nodes, giving the elements that fill them special properties. [ 2 ] [ 3 ] [ 4 ] They are usually less metallic than their heavier homologues, prefer lower oxidation states , and have smaller atomic and ionic radii . [ 4 ]
Contractions such as the scandide contraction and lanthanide contraction may be considered to be a general incomplete shielding effect in terms of how they impact the properties of the succeeding elements. The kainosymmetric 2p, 3d, and 4f orbitals screen the nuclear charge incompletely, and therefore the valence electrons that fill immediately after the completion of such a core subshell are more tightly bound by the nucleus than would be expected. 1s is an exception, providing nearly complete shielding. This is in particular the reason why sodium has a first ionisation energy of 495.8 kJ/mol that is only slightly smaller than that of lithium , 520.2 kJ/mol, and why lithium acts as less electronegative than sodium in simple σ-bonded alkali metal compounds; sodium suffers an incomplete shielding effect from the preceding 2p elements, but lithium essentially does not. [ 2 ]
Kainosymmetry also explains the specific properties of the 1s, 2p, 3d, and 4f elements. The 1s elements hydrogen and helium are extremely different from all others, because 1s is the only orbital that is completely unscreened from the nucleus, and there is no other orbital of similar energy for it to hybridise with (it also does not polarise easily). The 1s orbital of hydrogen binds to both (n−1)d and ns orbitals of transition elements , while most other ligands bind only to (n−1)d. [ 5 ] The 2p subshell is small and of a similar radial extent as the 2s subshell, which facilitates orbital hybridisation . This does not work as well for the heavier p elements: for example, silicon in silane (SiH 4 ) shows approximate sp 2 hybridisation, whereas carbon in methane (CH 4 ) shows an almost ideal sp 3 hybridisation. The bonding in these nonorthogonal heavy p element hydrides is weakened; this situation worsens with more electronegative substituents as they magnify the difference in energy between the s and p subshells. The heavier p elements are often more stable in their higher oxidation states in organometallic compounds than in compounds with electronegative ligands. This follows Bent's rule : s character is concentrated in the bonds to the more electropositive substituents, while p character is concentrated in the bonds to the more electronegative substituents. Furthermore, the 2p elements prefer to participate in multiple bonding (observed in O=O and N≡N) to eliminate Pauli repulsion from the otherwise close s and p lone pairs: their π bonds are stronger and their single bonds weaker. (See double bond rule .) The small size of the 2p shell is also responsible for the extremely high electronegativities of the 2p elements. [ 2 ]
The 3d elements show the opposite effect; the 3d orbitals are smaller than would be expected, with a radial extent similar to the 3p core shell, which weakens bonding to ligands because they cannot overlap with the ligands' orbitals well enough. These bonds are therefore stretched and therefore weaker compared to the homologous ones of the 4d and 5d elements (the 5d elements show an additional d-expansion due to relativistic effects). This also leads to low-lying excited states, which is probably related to the well-known fact that 3d compounds are often coloured (the light absorbed is visible). This also explains why the 3d contraction has a stronger effect on the following elements than the 4d or 5d ones do. As for the 4f elements, the difficulty that 4f has in being used for chemistry is also related to this, as are the strong incomplete screening effects; the 5g elements may show a similar contraction, but it is likely that relativistic effects will partly counteract this, as they would tend to cause expansion of the 5g shell. [ 2 ]
Another consequence is the increased metallicity of the following elements in a block after the first kainosymmetric orbital, along with a preference for higher oxidation states. This is visible comparing H and He (1s) with Li and Be (2s); N–F (2p) with P–Cl (3p); Fe and Co (3d) with Ru and Rh (4d); and Nd–Dy (4f) with U–Cf (5f). As kainosymmetric orbitals appear in the even rows (except for 1s), this creates an even–odd difference between periods from period 2 onwards: elements in even periods are smaller and have more oxidising higher oxidation states (if they exist), whereas elements in odd periods differ in the opposite direction. [ 4 ]
The difference between kainosymmetric elements and subsequent ones has been called the first-row anomaly . [ 5 ] It has been used to argue that helium should be placed over beryllium in the periodic table rather than over neon , on the grounds that this would constitute the most extreme case of the first-row anomaly. [ 6 ] | https://en.wikipedia.org/wiki/Kainosymmetry |
A kairomone is a semiochemical released by an organism that mediates interspecific interactions in a way that benefits a different species at the expense of the emitter. [ 1 ] Derived from the Greek καιρός , meaning " opportune moment" [ 2 ] [ 3 ] [ 4 ] , it serves as a form of "eavesdropping", enabling the receiver to gain an advantage, such as locating food or evading predators, even if it poses a risk to the emitter. Unlike allomones , which benefit the producer at the receiver's cost, or synomones, which are mutually beneficial, kairomones favor only the recipient. Primarily studied in entomology , kairomones can play key roles in predator-prey dynamics, mate attraction, and even applications in pest control. [ 1 ] [ 5 ]
An example of this can be found in the Ponderosa Pine tree ( Pinus ponderosa ), which produces a terpene called myrcene when it is damaged by the Western pine beetle . Instead of deterring the insect, it acts synergistically with aggregation pheromones which in turn act to lure more beetles to the tree. [ 6 ]
Specialist predatory beetles find bark beetles (their prey) using the pheromones the bark beetles produce. In this case the chemical substance produced is both a pheromone (communication between bark beetles) and a kairomone (eavesdropping). This was discovered accidentally when the predatory beetles and other enemies were attracted to insect traps baited with bark beetle pheromones. [ 5 ]
Pheromones of different kinds may be exploited as kairomones by receivers. The German wasp, Vespula germanica , is attracted to a pheromone produced by male Mediterranean fruit flies ( Ceratitis capitata ) when the males gather for a mating display, causing the death of some. In contrast, it is the alarm pheromone (used to communicate the presence of a threat) of an ant ( Iridomyrmex purpureus ) that a spider predator is attracted to. [ 1 ]
Birds and reptiles secrete uric acid, a metabolite that can be considered a kairomone. This compound can be used by the lone star tick ( Amblyomma americanum ) to locate its hosts. Instead of being attracted to the source, the tick's response is arrestment, ensuring it remains in areas where hosts are likely to pass. Furthermore, A. americanum responds strongly to excreta from fed ticks, suggesting it uses multiple signals to identify promising feeding locations. Unlike A. americanum , the tick Dermacentor variabilis , which prefers mammalian hosts, does not respond to uric acid. [ 7 ]
Some prey make use of chemicals originating from predators, using these cues as an indicator of the level of predation risk and changing their morphology if need be. Changes in morphology caused by predator presence is known as predator-induced polyphenism , and occurs across a variety of animals. For example, Daphnia cucullata show formation of "helmets" when exposed to predators or the water they have lived in. Their predators include cladocerans (such as Leptodora kindtii ) and larvae of Chaoborus flavicans , a midge . They respond to these kairomones by doubling the size of their helmets, a protective structure. These changes in morphology make them safer from predators. [ 9 ]
Mice are instinctively afraid of the smell of their natural predators , including cats and rats, even if they have been isolated from predators for hundreds of generations. [ 10 ] When the chemical cues responsible for the fear response were purified from cat saliva and rat urine, two homologous protein signals were identified: Fel d 4 ( Felis domesticus allergen 4), the product of the cat Mup gene, and Rat n 1 ( Rattus norvegicus allergen 1), the product of the rat Mup13 gene. [ 11 ] [ 12 ] [ 13 ] Mice are fearful of these major urinary proteins (Mups) even when they are produced in bacteria, while mutant animals that are unable to detect the Mups show no fear of rats, demonstrating their importance in triggering fear responses. [ 11 ] [ 14 ] It is not known exactly how Mups from different species initiate disparate behaviours, but mouse Mups and predator Mups have been shown to activate unique patterns of sensory neurons in the nose of recipient mice. This implies the mouse perceives them differently, via distinct neural circuits . [ 11 ] [ 12 ] The pheromone receptors responsible for Mup detection are also unknown, though they are thought be members of the V2R receptor class. [ 12 ] [ 15 ]
The urine of canids , such as wolves , contains sulfur-bearing pyrazine analogues that have been identified as kairomones. [ 16 ] These interspecific chemical signals alert potential prey to the presence of a predator, eliciting avoidance and freezing behaviors in species such as mice, deer, and cattle. [ 16 ] [ 17 ] Other carnivores, such as coyotes, may detect wolf kairomones and avoid areas marked with wolf urine. [ 16 ]
Kairomones are also used by some animals to identify the location of viable mates. For example, by feeding on vascular plants, female Melolontha melolontha stimulate the release of green leaf volatiles (GLVs). These kairomones mix with the females' own pheromones, enhancing their ability to attract males of the species. [ 18 ] [ 19 ]
Like pheromones (communication chemicals used within a species), kairomones can be utilized as an 'attracticide' to lure a pest species to a location containing pesticide . However, they might also be used to lure desired species. Kairomones produced by the hosts of parasitic wasps have been used in an attempt to attract them and keep them around in crops where they reduce herbivory, but this could instead result in fewer attacks on the herbivorous pest if the applied kairomone distracts them from finding real hosts. [ 1 ] For example, studies have shown that kairomones are effective in attracting female African sugarcane borers to deposit eggs on dead leaf material. [ 20 ]
Recent discoveries have highlighted that predators are attracted to the odour of co-existing predators. [ 21 ]
Kairomones have been extensively studied, and some are in successful usage, in Florida's Anastrepha suspensa eradication zone in support of the citrus , and various other orchard industries there. [ 22 ] | https://en.wikipedia.org/wiki/Kairomone |
The Kaiser effect is a phenomenon observed in geology and material science that describes a pattern of acoustic emission (AE) or seismicity in a body of rock or other material subjected to repeated cycles of mechanical stress .
In material that exhibits an initial seismic response under a certain load, the Kaiser effect describes the absence of acoustic emission or seismic events until that load is exceeded. The Kaiser effect results from discontinuities (fractures) created in material during previous steps that do not move, expand, or propagate until the former stress is exceeded. [ 1 ] [ 2 ] [ 3 ]
The Kaiser effect is named after Joseph Kaiser, who first studied this behavior in materials in the 1950s. [ 4 ] He discovered the phenomenon when he was studying AE response of metals, finding that the materials retain a "memory" of previously applied stresses. [ 5 ] Kaiser found that a stressed metal sample is giving zero AE if the applied stress is less than the previously applied maximum stress. [ 6 ] Similar effect was also found in rock samples deformed in the course of acoustic emission, particularly as a result of cyclic thermal loadings of carboniferous sandstone and mudstone samples. [ 7 ] The Kaiser effect became useful in estimating complete stress tensors based on a capacity to determine reliably the magnitudes of the preceding normal stresses applied to the specimen in various directions. [ 8 ]
Induced seismicity associated with fluid pumping in boreholes and wells often exhibits the Kaiser effect, whereby seismicity may be observed shortly following an initial fluid injection, but further seismicity is limited if the fluid flow remains at a constant pressure . [ 9 ] If the fluid pressure at the injection site is later increased, renewed seismicity may be observed due to the greater ease of fracturing caused by higher pore fluid pressure in the rock.
The Kaiser effect has also been observed in relation to recharge of magma chambers below active volcanic systems. [ 10 ]
This technology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kaiser_effect_(material_science) |
Kaizen ( Japanese : 改善 , "improvement") is a concept referring to business activities that continuously improve all functions and involve all employees from the CEO to the assembly line workers. Kaizen also applies to processes, such as purchasing and logistics , that cross organizational boundaries into the supply chain . [ 1 ] Kaizen aims to eliminate waste and redundancies . Kaizen may also be referred to as zero investment improvement (ZII) due to its utilization of existing resources. [ 2 ]
After being introduced by an American , Kaizen was first practiced in Japanese businesses after World War II , and most notably as part of The Toyota Way . It has since spread throughout the world and has been applied to environments outside of business and productivity. [ 3 ]
In 1947, Edwards Deming , an American statistician, went to Japan to help enhance their production processes. He stressed that quality should be prioritized at every stage of production, achieved through statistical process control. Deming is particularly recognized for his PDCA cycle—Plan, Do, Check, Act —which advises stopping production when deviations occur to identify and resolve issues before continuing. During his time in Japan, he trained hundreds of engineers, managers and executives in his approach. [ 4 ]
Deming developed his concepts into what he termed "total quality management," which eventually laid the groundwork for Toyota's Toyota Production System focused on just-in-time manufacturing. [ 5 ]
The Japanese word kaizen means 'improvement' or 'change for better' (from 改 kai - change, revision; and 善 zen - virtue, goodness) without the inherent meaning of either 'continuous' or 'philosophy' in Japanese dictionaries or in everyday use. The word refers to any improvement, one-time or continuous, large or small, in the same sense as the English word improvement . [ 6 ] However, given the common practice in Japan of labeling industrial or business improvement techniques with the word kaizen , particularly the practices spearheaded by Toyota, the word kaizen in English is typically applied to measures for implementing continuous improvement , especially those with a "Japanese philosophy". The discussion below focuses on such interpretations of the word, as frequently used in the context of modern management discussions. Two kaizen approaches have been distinguished: [ 7 ]
Point kaizen ( 現場改善 , Genba kaizen ) is one of the most commonly implemented types of kaizen. [ 8 ] It happens very quickly and usually without much planning. As soon as something is found broken or incorrect, quick and immediate measures are taken to correct the issues. [ 9 ] They are typically done at the individual level. [ 10 ] Although these measures are generally small, isolated and easy to implement, they can have a significant impact.
In some cases, it is also possible that the positive effects of point kaizen in one area can reduce or eliminate benefits of point kaizen in some other area.
Examples of point kaizen include a shop inspection by a supervisor who finds broken materials or other small issues, and then asks the owner of the shop to perform a quick kaizen ( 5S ) to rectify those issues, or a line worker who notices a potential improvement in efficiency by placing the materials needed in another order or closer to the production line in order to minimize downtime.
System kaizen is accomplished in an organized manner and is devised to address system-level problems in an organization or any production factory.
It is an upper-level strategic planning method for a short period of time.
Line kaizen refers to communication of improvements between the upstream and downstream of a process. This can be extended in several ways.
This is the next upper level of line kaizen, in that several lines are connected together. In modern terminologies, this can also be described as a value stream, where instead of traditional departments, the organization is structured into product lines or families and value streams. It can be visualized as changes or improvements made to one line being implemented to multiple other lines or processes.
Cube kaizen describes the situation where all the points of the planes are connected to each other and no point is disjointed from any other. This would resemble a situation where Lean has spread across the entire organization. Improvements are made up and down through the plane, or upstream or downstream, including the complete organization, suppliers and customers. This might require some changes in the standard business processes as well.
The 5S are primarily aimed at the workshop workplaces, whereby the workplace is understood as the place where the value-adding processes in the company take place.
These are the seven most important factors that must be checked again and again:
The original 5M method was expanded to include the last two factors, as the influence of management in the system and measurability are of a certain scope. (See also the Ishikawa diagram as a graphical representation of the 7Ms).
The 7W checklist possibly goes back to Cicero as an original tool for rhetoric:
Related to the 7W questionnaire is the principle of "Go to the source" (Genchi Genbutsu). This means asking "Why?" 5 times in the event of undesirable results or errors in order to find a solution. Furthermore, managers should get an idea of the situation on site, for example a production process, and not make decisions from afar.
The W questions are used in a wide variety of areas, for example when analyzing texts, [ 11 ] as an aid in defining projects [ 12 ] as well as in work analysis [ 13 ] and, as a result, in defining work content.
In the field of quality management , this principle is used in failure mode and effects analysis to identify potential weaknesses.
The three Mu form the basis for the loss philosophy of the Toyota Production System (TPS). In the context of this loss philosophy, the three Mu are seen as negative focal points of the loss potential and should therefore be avoided.
The seven types of waste (seven Muda) as typical sources of loss.
The waste itself ( Muda ) is the obvious cause of losses. A distinction is made between seven types of waste that occur almost everywhere in the company.
JIT is now standard throughout the automotive industry. It is used, for example, for interior parts (seats, airbags, steering wheels, dashboards) or painted parts. The generally higher transportation and handling costs caused by JIT or JIS are offset by savings in inventory, storage or floor space costs.
For more information, see the article Total productive maintenance .
Kaizen is a daily process, the purpose of which goes beyond simple productivity improvement. It is also a process that, when done correctly, humanizes the workplace, eliminates overly hard work ( muri ), and teaches people how to perform experiments on their work using the scientific method and how to learn to spot and eliminate waste in business processes. In all, the process suggests a humanized approach to workers and to increasing productivity: "The idea is to nurture the company's people as much as it is to praise and encourage participation in kaizen activities." [ 14 ] Successful implementation requires "the participation of workers in the improvement." [ 15 ] People at all levels of an organization participate in kaizen, from the CEO down to janitorial staff, as well as external stakeholders when applicable. Kaizen is most commonly associated with manufacturing operations, as at Toyota, but has also been used in non-manufacturing environments. [ 16 ] The format for kaizen can be individual, suggestion system, small group, or large group. At Toyota, it is usually a local improvement within a workstation or local area and involves a small group in improving their own work environment and productivity. This group is often guided through the kaizen process by a line supervisor; sometimes this is the line supervisor's key role. Kaizen on a broad, cross-departmental scale in companies generates total quality management and frees human efforts through improving productivity using machines and computing power. [ citation needed ]
While kaizen (at Toyota) usually delivers small improvements, the culture of continual aligned small improvements and standardization yields large results in terms of overall improvement in productivity. This philosophy differs from the " command and control " improvement programs (e.g., Business Process Improvement ) of the mid-20th century. Kaizen methodology includes making changes and monitoring results, then adjusting. Large-scale pre-planning and extensive project scheduling are replaced by smaller experiments, which can be rapidly adapted as new improvements are suggested. [ citation needed ]
In modern usage, it is designed to address a particular issue over the course of a week and is referred to as a "kaizen blitz" or "kaizen event". [ 17 ] [ 18 ] These are limited in scope, and issues that arise from them are typically used in later blitzes. [ citation needed ] A person who makes a large contribution in the successful implementation of kaizen during kaizen events is awarded the title of "Zenkai". In the 21st century, business consultants in various countries have engaged in widespread adoption and sharing of the kaizen framework as a way to help their clients restructure and refocus their business processes .
The small-step work improvement approach was developed in the USA under Training Within Industry program (TWI Job Methods). [ 19 ] Instead of encouraging large, radical changes to achieve desired goals, these methods recommended that organizations introduce small improvements, preferably ones that could be implemented on the same day. The major reason was that during WWII there was neither time nor resources for large and innovative changes in the production of war equipment. [ 20 ] The essence of the approach came down to improving the use of the existing workforce and technologies.
As part of the aid to allied nations after the war, not directly including the Marshall Plan after World War II , American occupation forces brought in experts to help with the rebuilding of Japanese industry while the Civil Communications Section (CCS) developed a management training program that taught statistical control methods as part of the overall material. Homer Sarasohn and Charles Protzman developed and taught this course in 1949–1950. Sarasohn recommended W. Edwards Deming for further training in statistical methods.
The Economic and Scientific Section (ESS) group was also tasked with improving Japanese management skills and Edgar McVoy was instrumental in bringing Lowell Mellen to Japan to properly install the Training Within Industry (TWI) programs in 1951. The ESS group had a training film to introduce TWI's three "J" programs: Job Instruction, Job Methods and Job Relations. Titled "Improvement in Four Steps" ( Kaizen eno Yon Dankai ), it thus introduced kaizen to Japan.
For the pioneering, introduction, and implementation of kaizen in Japan, the Emperor of Japan awarded the Order of the Sacred Treasure to Dr. Deming in 1960. Subsequently, the Union of Japanese Scientists and Engineers (JUSE) instituted the annual Deming Prizes for achievement in quality and dependability of products. On October 18, 1989, JUSE awarded the Deming Prize to Florida Power & Light Co. (FPL), based in the US, for its exceptional accomplishments in process and quality-control management, making it the first company outside Japan to win the Deming Prize. [ 21 ]
Kaoru Ishikawa took up this concept to define how continuous improvement or kaizen can be applied to processes, as long as all the variables of the process are known. [ 22 ]
The Toyota Production System is known for kaizen, where all line personnel are expected to stop their moving production line in case of any abnormality, and, along with their supervisor, suggest an improvement to resolve the abnormality which may initiate a kaizen. This feature is called Jidoka or "autonomation".
The cycle of kaizen activity can be defined as: Plan → Do → Check → Act. This is also known as the Shewhart cycle , Deming cycle, or PDCA .
Another technique used in conjunction with PDCA is the five whys , which is a form of root cause analysis in which the user asks a series of five "why" questions about a failure that has occurred, basing each subsequent question on the answer to the previous. [ 24 ] [ 25 ] There are normally a series of causes stemming from one root cause, [ 26 ] and they can be visualized using fishbone diagrams or tables. The five whys can be used as a foundational tool in personal improvement. [ 27 ]
Masaaki Imai made the term famous in his book Kaizen: The Key to Japan's Competitive Success . [ 1 ]
In the Toyota Way Fieldbook , Liker and Meier discuss the kaizen blitz and kaizen burst (or kaizen event) approaches to continuous improvement. A kaizen blitz, or rapid improvement, is a focused activity on a particular process or activity. The basic concept is to identify and quickly remove waste. Another approach is that of the kaizen burst, a specific kaizen activity on a particular process in the value stream . [ 28 ]
In the 1990s, Professor Iwao Kobayashi published his book 20 Keys to Workplace Improvement and created a practical, step-by-step improvement framework called "the 20 Keys". He identified 20 operations focus areas which should be improved to attain holistic and sustainable change. He went further and identified the five levels of implementation for each of these 20 focus areas. Four of the focus areas are called Foundation Keys. According to the 20 Keys, these foundation keys should be launched ahead of the others in order to form a strong constitution in the company. The four foundation keys are: | https://en.wikipedia.org/wiki/Kaizen |
In mathematics , a Kakeya set , or Besicovitch set , is a set of points in Euclidean space which contains a unit line segment in every direction. For instance, a disk of radius 1/2 in the Euclidean plane , or a ball of radius 1/2 in three-dimensional space, forms a Kakeya set. Much of the research in this area has studied the problem of how small such sets can be. Besicovitch showed that there are Besicovitch sets of measure zero .
A Kakeya needle set (sometimes also known as a Kakeya set) is a (Besicovitch) set in the plane with a stronger property, that a unit line segment can be rotated continuously through 180 degrees within it, returning to its original position with reversed orientation. Again, the disk of radius 1/2 is an example of a Kakeya needle set.
The Kakeya needle problem asks whether there is a minimum area of a region D {\displaystyle D} in the plane, in which a needle of unit length can be turned through 360°. This question was first posed, for convex regions, by Sōichi Kakeya ( 1917 ). The minimum area for convex sets is achieved by an equilateral triangle of height 1 and area 1/ √ 3 , as Pál showed. [ 1 ]
Kakeya seems to have suggested that the Kakeya set D {\displaystyle D} of minimum area, without the convexity restriction, would be a three-pointed deltoid shape. However, this is false; there are smaller non-convex Kakeya sets.
Besicovitch was able to show that there is no lower bound > 0 for the area of such a region D {\displaystyle D} , in which a needle of unit length can be turned around. That is, for every ε > 0 {\displaystyle \varepsilon >0} , there is region of area ε {\displaystyle \varepsilon } within which the needle can move through a continuous motion that rotates it a full 360 degrees. [ 3 ] This built on earlier work of his, on plane sets which contain a unit segment in each orientation. Such a set is now called a Besicovitch set . Besicovitch's work from 1919 showed such a set could have arbitrarily small measure , although the problem may have been considered by analysts before that.
One method of constructing a Besicovitch set (see figure for corresponding illustrations) is known as a "Perron tree", named after Oskar Perron who was able to simplify Besicovitch's original construction. [ 4 ] The precise construction and numerical bounds are given in Besicovitch's popularization. [ 2 ]
The first observation to make is that the needle can move in a straight line as far as it wants without sweeping any area. This is because the needle is a zero width line segment. The second trick of Pál , known as Pál joins , [ 5 ] describes how to move the needle between any two locations that are parallel while sweeping negligible area. The needle will follow the shape of an "N". It moves from the first location some distance r {\displaystyle r} up the left of the "N", sweeps out the angle to the middle diagonal, moves down the diagonal, sweeps out the second angle,
and them moves up the parallel right side of the "N" until it reaches the required second location. The only non-zero area regions swept are the two triangles of height one and the angle at the top of the "N". The swept area is proportional to this angle which is proportional to 1 / r {\displaystyle 1/r} .
The construction starts with any triangle with height 1 and some substantial angle at the top through which the needle can easily sweep. The goal is to do many operations on this triangle to make its area smaller while keeping the directions through which the needle can sweep the same.
First, consider dividing the triangle into two and translating the pieces over each other so that their bases overlap in a way that minimizes the total area.
The needle is able to sweep out the same directions by sweeping out those given by the first triangle, jumping over to the second, and then sweeping out the directions given by the second. The needle can jump triangles using the "N" technique because the two lines at which the original triangle was cut are parallel.
Now, we divide our triangle into 2 n subtriangles. The figure shows eight.
For each consecutive pair of triangles, perform the same overlapping operation we described before to get half as many new shapes, each consisting of two overlapping triangles. Next, overlap consecutive pairs of these new shapes by shifting them so that their bases overlap in a way that minimizes the total area. Repeat this n times until there is only one shape. Again, the needle is able to sweep out the same directions by sweeping those out in each of the
2 n subtriangles in order of their direction. The needle can jump consecutive triangles using the "N" technique because the two lines at which these triangle were cut are parallel.
What remains is to compute the area of the final shape. Due to difficulty and length constraints the final argument cannot be fully included. Instead, an example will be shown.
Looking at the figure, it can be seen that the 2 n subtriangles overlap a lot. All of them overlap at the bottom, half of them at the bottom of the left branch, a quarter of them at the bottom of the left left branch, and so on.
Suppose that the area of each shape created with i merging operations from 2 i subtriangles is bounded by A i .
Before merging two of these shapes, they have area bounded be 2 A i .
Then, move the two shapes together such that that they overlap as much as possible.
In the worst case, these two regions are
two 1 by ε rectangles perpendicular to each other so that they overlap at an area of only ε 2 . But the two shapes that we have constructed, if long and skinny, point in much of the same direction because they are made from consecutive groups of subtriangles.
The handwaving states that they over lap by at least 1% of their area. Then the merged area would be bounded by A i+1 = 1.99 A i . The area of the original triangle is bounded by 1. Hence, the area of each subtriangle is bounded by A 0 = 2 -n and the final shape has area bounded by A n = 1.99 n × 2 -n . In actuality, a careful summing up of all areas that do not overlap gives that the area of the final region is much bigger, namely, 1/n .
As n grows, this area shrinks to zero.
A Besicovitch set can be created by combining six rotations of a Perron tree created from an equilateral triangle.
A similar construction can be made with parallelograms.
There are other methods for constructing Besicovitch sets of measure zero aside from the 'sprouting' method.
For example, Kahane uses Cantor sets to construct a Besicovitch set of measure zero in the two-dimensional plane. [ 6 ]
In 1941, H. J. Van Alphen [ 7 ] showed that there are arbitrary small Kakeya needle sets inside a circle with radius 2 + ε (arbitrary ε > 0). Simply connected Kakeya needle sets with smaller area than the deltoid were found in 1965. Melvin Bloom and I. J. Schoenberg independently presented Kakeya needle sets with areas approaching to π 24 ( 5 − 2 2 ) {\displaystyle {\tfrac {\pi }{24}}(5-2{\sqrt {2}})} , the Bloom-Schoenberg number . Schoenberg conjectured that this number is the lower bound for the area of simply connected Kakeya needle sets. However, in 1971, F. Cunningham [ 8 ] showed that, given ε > 0, there is a simply connected Kakeya needle set of area less than ε contained in a circle of radius 1.
Although there are Kakeya needle sets of arbitrarily small positive measure and Besicovitch sets of measure 0, there are no Kakeya needle sets of measure 0.
The same question of how small these Besicovitch sets could be was then posed in higher dimensions, giving rise to a number of conjectures known collectively as the Kakeya conjectures , and have helped initiate the field of mathematics known as geometric measure theory . In particular, if there exist Besicovitch sets of measure zero, could they also have s-dimensional Hausdorff measure zero for some dimensions less than the dimension of the space in which they lie? This question gives rise to the following conjecture:
This is known to be true for n = 1, 2 but only partial results are known in higher dimensions.
In February 2025, a claimed proof for the case n = 3 was posted on arXiv by Hong Wang and Joshua Zahl. [ 9 ] The Kakeya conjecture in three dimensions is described as "one of the most sought-after open problems in geometric measure theory", and the claimed proof is considered to be a breakthrough. [ 10 ] [ 11 ] [ 12 ]
A modern way of approaching this problem is to consider a particular type of maximal function , which we construct as follows: Denote S n −1 ⊂ R n to be the unit sphere in n -dimensional space. Define T e δ ( a ) {\displaystyle T_{e}^{\delta }(a)} to be the cylinder of length 1, radius δ > 0, centered at the point a ∈ R n , and whose long side is parallel to the direction of the unit vector e ∈ S n −1 . Then for a locally integrable function f , we define the Kakeya maximal function of f to be
where m denotes the n -dimensional Lebesgue measure . Notice that f ∗ δ {\displaystyle f_{*}^{\delta }} is defined for vectors e in the sphere S n −1 .
Then there is a conjecture for these functions that, if true, will imply the Kakeya set conjecture for higher dimensions:
Some results toward proving the Kakeya conjecture are the following:
Somewhat surprisingly, these conjectures have been shown to be connected to a number of questions in other fields, notably in harmonic analysis . For instance, in 1971, Charles Fefferman was able to use the Besicovitch set construction to show that in dimensions greater than 1, truncated Fourier integrals taken over balls centered at the origin with radii tending to infinity need not converge in L p norm when p ≠ 2 (this is in contrast to the one-dimensional case where such truncated integrals do converge). [ 20 ]
Analogues of the Kakeya problem include considering sets containing more general shapes than lines, such as circles.
A generalization of the Kakeya conjecture is to consider sets that contain, instead of segments of lines in every direction, but, say, portions of k -dimensional subspaces. Define an ( n , k )-Besicovitch set K to be a compact set in R n containing a translate of every k -dimensional unit disk which has Lebesgue measure zero. That is, if B denotes the unit ball centered at zero, for every k -dimensional subspace P , there exists x ∈ R n such that ( P ∩ B ) + x ⊆ K . Hence, a ( n , 1)-Besicovitch set is the standard Besicovitch set described earlier.
In 1979, Marstrand [ 25 ] proved that there were no (3, 2)-Besicovitch sets. At around the same time, however, Falconer [ 26 ] proved that there were no ( n , k )-Besicovitch sets for 2 k > n . The best bound to date is by Bourgain, [ 27 ] who proved in that no such sets exist when 2 k −1 + k > n .
In 1999, Wolff posed the finite field analogue to the Kakeya problem, in hopes that the techniques for solving this conjecture could be carried over to the Euclidean case.
Zeev Dvir proved this conjecture in 2008, showing that the statement holds for c n = 1/ n !. [ 28 ] [ 29 ] In his proof, he observed that any polynomial in n variables of degree less than | F | vanishing on a Kakeya set must be identically zero. On the other hand, the polynomials in n variables of degree less than | F | form a vector space of dimension
Therefore, there is at least one non-trivial polynomial of degree less than | F | that vanishes on any given set with less than this number of points. Combining these two observations shows that Kakeya sets must have at least | F | n / n ! points.
It is not clear whether the techniques will extend to proving the original Kakeya conjecture but this proof does lend credence to the original conjecture by making essentially algebraic counterexamples unlikely. Dvir has written a survey article on progress on the finite field Kakeya problem and its relationship to randomness extractors . [ 30 ] | https://en.wikipedia.org/wiki/Kakeya_set |
The Kakhovka Irrigation System ( Ukrainian : Каховська зрошувальна система ; Russian : Каховская оросительная система ) is an irrigation system in southern Ukraine . With a total irrigation area of 780,000 hectares (1,900,000 acres), it is the largest irrigation system in the entire country. [ 1 ]
In 1951, construction began for the Kakhovka Hydroelectric Power Plant , which created the Kakhovka Reservoir and provided a water source for local irrigation. [ 2 ] By 1967, construction for an irrigation system began, and different sections began operation throughout the 1970s. [ 3 ]
The irrigation system all begin at the Kakhovka Reservoir , where it flows south before diverging into different areas. The entire system includes many interconnected canals, such as the Kakhovka Canal , and it provides water for crops across much of Kherson Oblast . [ citation needed ]
Because of the vast size of the irrigation system, there are 16 pumping stations throughout the canals. [ 4 ] This includes a main pumping station, which is sized 138 metres (453 ft) by 34 metres (112 ft). [ 5 ] | https://en.wikipedia.org/wiki/Kakhovka_Irrigation_System |
Kakutani's theorem is a result in geometry named after Shizuo Kakutani . It states that every convex body in 3- dimensional space has a circumscribed cube , i.e. a cube all of whose faces touch the body. [ 1 ] The result was further generalized by Yamabe and Yujobô to higher dimensions, [ 2 ] and by Floyd to other circumscribed parallelepipeds . [ 3 ]
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kakutani's_theorem_(geometry) |
In measure theory , a branch of mathematics , Kakutani's theorem is a fundamental result on the equivalence or mutual singularity of countable product measures . It gives an " if and only if " characterisation of when two such measures are equivalent, and hence it is extremely useful when trying to establish change-of-measure formulae for measures on function spaces . The result is due to the Japanese mathematician Shizuo Kakutani . Kakutani's theorem can be used, for example, to determine whether a translate of a Gaussian measure μ {\displaystyle \mu } is equivalent to μ {\displaystyle \mu } (only when the translation vector lies in the Cameron–Martin space of μ {\displaystyle \mu } ), or whether a dilation of μ {\displaystyle \mu } is equivalent to μ {\displaystyle \mu } (only when the absolute value of the dilation factor is 1, which is part of the Feldman–Hájek theorem ).
For each n ∈ N {\displaystyle n\in \mathbb {N} } , let μ n {\displaystyle \mu _{n}} and ν n {\displaystyle \nu _{n}} be measures on the real line R {\displaystyle \mathbb {R} } , and let μ = ⨂ n ∈ N μ n {\displaystyle \mu =\bigotimes _{n\in \mathbb {N} }\mu _{n}} and ν = ⨂ n ∈ N ν n {\displaystyle \nu =\bigotimes _{n\in \mathbb {N} }\nu _{n}} be the corresponding product measures on R ∞ {\displaystyle \mathbb {R} ^{\infty }} . Suppose also that, for each n ∈ N {\displaystyle n\in \mathbb {N} } , μ n {\displaystyle \mu _{n}} and ν n {\displaystyle \nu _{n}} are equivalent (i.e. have the same null sets). Then either μ {\displaystyle \mu } and ν {\displaystyle \nu } are equivalent, or else they are mutually singular. Furthermore, equivalence holds precisely when the infinite product
has a nonzero limit; or, equivalently, when the infinite series
converges. | https://en.wikipedia.org/wiki/Kakutani's_theorem_(measure_theory) |
In mathematical analysis , the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions . It provides sufficient conditions for a set-valued function defined on a convex , compact subset of a Euclidean space to have a fixed point , i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization of the Brouwer fixed point theorem . The Brouwer fixed point theorem is a fundamental result in topology which proves the existence of fixed points for continuous functions defined on compact, convex subsets of Euclidean spaces. Kakutani's theorem extends this to set-valued functions.
The theorem was developed by Shizuo Kakutani in 1941, [ 1 ] and was used by John Nash in his description of Nash equilibria . [ 2 ] It has subsequently found widespread application in game theory and economics . [ 3 ]
Kakutani's theorem states: [ 4 ]
The function: φ ( x ) = [ 1 − x / 2 , 1 − x / 4 ] {\displaystyle \varphi (x)=[1-x/2,~1-x/4]} , shown on the figure at the right, satisfies all Kakutani's conditions, and indeed it has many fixed points: any point on the 45° line (dotted line in red) which intersects the graph of the function (shaded in grey) is a fixed point, so in fact there is an infinity of fixed points in this particular case. For example, x = 0.72 (dashed line in blue) is a fixed point since 0.72 ∈ [1 − 0.72/2, 1 − 0.72/4].
The function:
satisfies all Kakutani's conditions, and indeed it has a fixed point: x = 0.5 is a fixed point, since x is contained in the interval [0,1].
The requirement that φ ( x ) be convex for all x is essential for the theorem to hold.
Consider the following function defined on [0,1]:
The function has no fixed point. Though it satisfies all other requirements of Kakutani's theorem, its value fails to be convex at x = 0.5.
Consider the following function defined on [0,1]:
The function has no fixed point. Though it satisfies all other requirements of Kakutani's theorem, its graph is not closed; for example, consider the sequences x n = 0.5 - 1/ n , y n = 3/4.
Some sources, including Kakutani's original paper, use the concept of upper hemicontinuity while stating the theorem:
This statement of Kakutani's theorem is completely equivalent to the statement given at the beginning of this article.
We can show this by using the closed graph theorem for set-valued functions, [ 5 ] which says that for a compact Hausdorff range space Y , a set-valued function φ : X →2 Y has a closed graph if and only if it is upper hemicontinuous and φ ( x ) is a closed set for all x . Since all Euclidean spaces are Hausdorff (being metric spaces ) and φ is required to be closed-valued in the alternative statement of the Kakutani theorem, the Closed Graph Theorem implies that the two statements are equivalent.
The Kakutani fixed point theorem can be used to prove the minimax theorem in the theory of zero-sum games . This application was specifically discussed by Kakutani's original paper. [ 1 ]
Mathematician John Nash used the Kakutani fixed point theorem to prove a major result in game theory . [ 2 ] Stated informally, the theorem implies the existence of a Nash equilibrium in every finite game with mixed strategies for any finite number of players. This work later earned him a Nobel Prize in Economics . In this case:
In general equilibrium theory in economics, Kakutani's theorem has been used to prove the existence of set of prices which simultaneously equate supply with demand in all markets of an economy. [ 6 ] The existence of such prices had been an open question in economics going back to at least Walras . The first proof of this result was constructed by Lionel McKenzie . [ 7 ]
In this case:
Kakutani's fixed-point theorem is used in proving the existence of cake allocations that are both envy-free and Pareto efficient . This result is known as Weller's theorem .
Brouwer's fixed-point theorem is a special case of Kakutani fixed-point theorem. Conversely, Kakutani fixed-point theorem is an immediate generalization via the approximate selection theorem : [ 8 ]
By the approximate selection theorem, there exists a sequence of continuous Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle f_n: S \to S} such that graph ( f n ) ⊂ [ graph ( φ ) ] 1 / n {\displaystyle \operatorname {graph} (f_{n})\subset [\operatorname {graph} (\varphi )]_{1/n}} . By Brouwer fixed-point theorem, there exists a sequence x n {\displaystyle x_{n}} such that f n ( x n ) = x n {\displaystyle f_{n}(x_{n})=x_{n}} , so ( x n , x n ) ∈ [ graph ( φ ) ] 1 / n {\displaystyle (x_{n},x_{n})\in [\operatorname {graph} (\varphi )]_{1/n}} .
Since S {\displaystyle S} is compact, we can take a convergent subsequence x n → x {\displaystyle x_{n}\to x} . Then ( x , x ) ∈ graph ( φ ) {\displaystyle (x,x)\in \operatorname {graph} (\varphi )} since it is a closed set.
The proof of Kakutani's theorem is simplest for set-valued functions defined over closed intervals of the real line. Moreover, the proof of this case is instructive since its general strategy can be carried over to the higher-dimensional case as well.
Let φ: [0,1]→2 [0,1] be a set-valued function on the closed interval [0,1] which satisfies the conditions of Kakutani's fixed-point theorem.
Let ( a i , b i , p i , q i ) for i = 0, 1, … be a sequence with the following properties:
Thus, the closed intervals [ a i , b i ] form a sequence of subintervals of [0,1]. Condition (2) tells us that these subintervals continue to become smaller while condition (3)–(6) tell us that the function φ shifts the left end of each subinterval to its right and shifts the right end of each subinterval to its left.
Such a sequence can be constructed as follows. Let a 0 = 0 and b 0 = 1. Let p 0 be any point in φ(0) and q 0 be any point in φ(1). Then, conditions (1)–(4) are immediately fulfilled. Moreover, since p 0 ∈ φ(0) ⊂ [0,1], it must be the case that p 0 ≥ 0 and hence condition (5) is fulfilled. Similarly condition (6) is fulfilled by q 0 .
Now suppose we have chosen a k , b k , p k and q k satisfying (1)–(6). Let,
Then m ∈ [0,1] because [0,1] is convex .
If there is a r ∈ φ( m ) such that r ≥ m , then we take,
Otherwise, since φ( m ) is non-empty, there must be a s ∈ φ( m ) such that s ≤ m . In this case let,
It can be verified that a k +1 , b k +1 , p k +1 and q k +1 satisfy conditions (1)–(6).
We have a pair of sequences of intervals, and we would like to show them to converge to a limiting point with the Bolzano-Weierstrass theorem . To do so, we construe these two interval sequences as a single sequence of points, ( a n , p n , b n , q n ). This lies in the cartesian product [0,1]×[0,1]×[0,1]×[0,1], which is a compact set by Tychonoff's theorem . Since our sequence ( a n , p n , b n , q n ) lies in a compact set, it must have a convergent subsequence by Bolzano-Weierstrass . Let's fix attention on such a subsequence and let its limit be ( a *, p *, b *, q *). Since the graph of φ is closed it must be the case that p * ∈ φ( a *) and q * ∈ φ( b *). Moreover, by condition (5), p * ≥ a * and by condition (6), q * ≤ b *.
But since ( b i − a i ) ≤ 2 − i by condition (2),
So, b * equals a *. Let x = b * = a *.
Then we have the situation that
If p * = q * then p * = x = q *. Since p * ∈ φ( x ), x is a fixed point of φ.
Otherwise, we can write the following. Recall that we can parameterize a line between two points a and b by (1-t)a + tb. Using our finding above that q<x<p, we can create such a line between p and q as a function of x (notice the fractions below are on the unit interval). By a convenient writing of x, and since φ( x ) is convex and
it once again follows that x must belong to φ( x ) since p * and q * do and hence x is a fixed point of φ.
In dimensions greater one, n -simplices are the simplest objects on which Kakutani's theorem can be proved. Informally, a n -simplex is the higher-dimensional version of a triangle. Proving Kakutani's theorem for set-valued function defined on a simplex is not essentially different from proving it for intervals. The additional complexity in the higher-dimensional case exists in the first step of chopping up the domain into finer subpieces:
Once these changes have been made to the first step, the second and third steps of finding a limiting point and proving that it is a fixed point are almost unchanged from the one-dimensional case.
Kakutani's theorem for n-simplices can be used to prove the theorem for an arbitrary compact, convex S . Once again we employ the same technique of creating increasingly finer subdivisions. But instead of triangles with straight edges as in the case of n-simplices, we now use triangles with curved edges. In formal terms, we find a simplex which covers S and then move the problem from S to the simplex by using a deformation retract . Then we can apply the already established result for n-simplices.
Kakutani's fixed-point theorem was extended to infinite-dimensional locally convex topological vector spaces by Irving Glicksberg [ 9 ] and Ky Fan . [ 10 ] To state the theorem in this case, we need a few more definitions:
Then the Kakutani–Glicksberg–Fan theorem can be stated as: [ 11 ]
The corresponding result for single-valued functions is the Tychonoff fixed-point theorem .
There is another version that the statement of the theorem becomes the same as that in the Euclidean case: [ 5 ]
In his game theory textbook, [ 12 ] Ken Binmore recalls that Kakutani once asked him at a conference why so many economists had attended his talk. When Binmore told him that it was probably because of the Kakutani fixed point theorem, Kakutani was puzzled and replied, "What is the Kakutani fixed point theorem?" | https://en.wikipedia.org/wiki/Kakutani_fixed-point_theorem |
The art of kalai (kalhai or qalai) is the process of coating an alloy surface such as copper or brass by deposition of metal tin on it. [ 1 ] The word "kalai" is derived from Sanskrit word kalya lepa , which means "white wash or tin". [ 2 ] A cultural Sanskrit work by Keladi Basava called "Sivatattva Ratnakara" (1699) mentions "kalaya-lepa" in the chapter of cookery or " supashashtra " which means applying kalai on utensils. [ 2 ] People practicing the art of kalai are called Kalaiwala or Kalaigar. [ 3 ] Basically, Kalaigars or Kalaiwalas are community craftsmen. [ 4 ]
Vessels with kalai, both on its interior and exterior have been found in the excavations of Bramhapuri at Kolhapur , Maharashtra which adds to the archeological evidence of kalai art. [ 2 ] From this evidence, P K. Gode , who studied tin coating on metallic vessels in India , stated that the history of tin coating dates back to 1300 C.E. [ 2 ] The history of kalai is also recorded in “Parsibhashanushasana” of Vikaramasimha (before Samvat 1600 i.e. C.E. 1544) and also in the famous Ain- I -Akbari (C.E. 1590) by Abul Fazal. [ 2 ]
The copper vessels with kalai were used to store water and cook food earlier because of a spiritual belief that copper attracts and transmits a divine consciousness also called “Chaitanya”. [ 5 ] The spiritual approach to the use of copper vessels to store water is that copper and tin have Sattva-Raja (the basic component of creation/universe) component that is transferred to water. [ 5 ]
Earlier, copper and brass vessels were used because of their high conductivity . [ 6 ] High conductivity of copper vessels reduces the fuel cost. However, a chemical reaction between copper and oxygen called oxidization turns the copper vessels black. [ 7 ] Copper also reacts with the moisture in air and creates copper carbonate , which can be noticed as light green rust on the surface. Copper carbonate is poisonous and can make a person severely ill if it gets mixed with food. [ 7 ] The copper can get dissolved in water in trace amounts when the water is stored in copper vessels for a long period of time. The process is known as the “ oligodynamic effect ”. [ 6 ] Kalai protects from food poisoning and blackening of copper vessels by preventing direct contact of air with the copper or brass surface. Tin is also a good conductor of heat like copper, hence applying kalai does not result in loss of heat conductivity for the utensil.
The kalai is required to be done on the vessels approximately every two months. [ 6 ] Tin will melt if the temperature is above 425 degrees Fahrenheit (218.333 degrees Celsius). [ 7 ] Also, the tin coating wears away with time. In order to protect the coating, one should use wooden or silicone spatulas and avoid cooking acidic foods.
Kalai can be done in various ways. Virgin grade tin (called ‘ranga’ in Hindi ), caustic soda , sal ammoniac ( ammonium chloride , called ‘nausadar’ powder in Hindi), and water are used in the process. [ 6 ]
The first step of kalai is to clean the utensil with water. There are two ways of cleaning the utensil further to remove any impurities such as dust. The first is to clean it with caustic soda. The other is to wash it with dilute acid solution which contains a gold purifying compound known as ‘sufa’. If the latter is used, the utensil should be cleaned immediately after applying the dilute acidic solution as it may bear a mark if not done immediately.
After the cleaning, the vessel is heated on burning coal for about 2 to 3 minutes. The Kalaiwala, Kalaigar or Kalaikar then digs a small pit in the ground to burn the coal. He/she prepares a temporary blast furnace to do kalai and blows air through bellows. After the vessel turns pinkish hot, virgin grade tin (in the form of strips) is applied on the hot vessel. This step is called ‘casting’ by the Kalaigars. The ‘nausadar’ powder is sprinkled on the vessel. The tin melts rapidly which is then rubbed evenly on the utensil with the help of a cotton cloth or a swab of cotton. The rubbing process is known as ‘majaay’ in Hindi. A whitish smoke with the peculiar smell of ammonia is released when the ‘nausadar’ powder is rubbed on the utensil. A silvery lining appears on the vessel with a shine. The final step of kalai is to dip the utensil in cold water. [ 3 ] [ 8 ] [ 9 ]
Kalai was earlier done with silver instead of tin but now it would be too expensive. [ 10 ] As stainless steel and aluminum ware came into being, the usage of copper and brass utensils decreased, which led the Kalaigars to suffer losses. [ 3 ] Nowadays only some hotels and a very few people use vessels with kalai. [ 11 ] As a result, there are a very few Kalaigars left and the art of kalai is vanishing. [ citation needed ] | https://en.wikipedia.org/wiki/Kalai_(process) |
The Kalai–Smorodinsky (KS) bargaining solution is a solution to the Bargaining problem . It was suggested by Ehud Kalai and Meir Smorodinsky, [ 1 ] as an alternative to Nash's bargaining solution suggested 25 years earlier. The main difference between the two solutions is that the Nash solution satisfies independence of irrelevant alternatives , while the KS solution instead satisfies resource monotonicity .
A two-person bargain problem consists of a pair ( F , d ) {\displaystyle (F,d)} :
It is assumed that the problem is nontrivial, i.e., the agreements in F {\displaystyle F} are better for both parties than the disagreement.
A bargaining solution is a function f {\displaystyle f} that takes a bargaining problem ( F , d ) {\displaystyle (F,d)} and returns a point in its feasible agreements set, f ( F , d ) ∈ F {\displaystyle f(F,d)\in F} .
The Nash and KS solutions both agree on the following three requirements:
Pareto optimality is a necessary condition. For every bargaining problem, the returned agreement f ( F , d ) {\displaystyle f(F,d)} must be Pareto-efficient.
Symmetry is also necessary. The names of the players should not matter: if player 1 and player 2 switch their utilities, then the agreement should be switched accordingly.
Invariant to positive affine transformations also seems like a necessary condition: if the utility function of one or more players is transformed by a linear function, then the agreement should also be transformed by the same linear function. This makes sense if we assume that the utility functions are only representations of a preference relation, and do not have a real numeric meaning.
In addition to these requirements, Nash requires Independence of irrelevant alternatives (IIA). This means that, if the set of possible agreements grows (more agreements become possible), but the bargaining solution picks an agreement that was contained in the smaller set, then this agreement must be the same as the agreement reached when only the smaller set was available, since the new agreements are irrelevant. For example, suppose that in Sunday we can agree on option A or option B, and we pick option A. Then, in Monday we can agree on option A or B or C, but we do not pick option C. Then, Nash says that we must pick option A. The new option C is irrelevant since we do not select it anyway.
Kalai and Smorodinsky differ from Nash on this issue. They claim that the entire set of alternatives must affect the agreement reached. In the above example, suppose the preference relation of player 2 is: C>>B>A (C is much better than B, which is somewhat better than A) while the preference relation of 1 is reversed: A>>B>>C. The fact that option C becomes available allows player 2 to say: "if I give up my best option - C, I have a right to demand that at least my second-best option will be chosen".
Therefore, KS remove the IIA requirement. Instead, they add a monotonicity requirement. This requirement says that, for each player, if the utility attainable by this player for each utility of the other player is weakly larger, then the utility this player gets in the selected agreement should also be weakly larger. In other words, a player with better options should get a weakly-better agreement.
The formal definition of monotonicity is based on the following definitions.
The monotonicity requirement says that, if ( F , d ) {\displaystyle (F,d)} and ( F ′ , d ) {\displaystyle (F',d)} are two bargaining problems such that:
Then, the solution f must satisfy:
In the words of KS:
By symmetry, the same requirement holds if we switch the roles of players 1 and 2.
The KS solution can be calculated geometrically in the following way.
Let b ( F ) {\displaystyle b(F)} be the point of best utilities ( B e s t 1 ( F ) , B e s t 2 ( F ) ) {\displaystyle (Best_{1}(F),Best_{2}(F))} . Draw a line L {\displaystyle L} from d {\displaystyle d} (the point of disagreement) to b {\displaystyle b} (the point of best utilities).
By the non-triviality assumption, the line L {\displaystyle L} has a positive slope. By the convexity of F {\displaystyle F} , the intersection of L {\displaystyle L} with the set F {\displaystyle F} is an interval. The KS solution is the top-right point of this interval.
Mathematically, the KS solution is the maximal point which maintains the ratios of gains. I.e, it is a point μ {\displaystyle \mu } on the Pareto frontier of F {\displaystyle F} , such that:
Alice and George have to choose between three options, that give them the following amounts of money:. [ 2 ] : 88–92 Assume for the purposes of the example that utility is linear in money, and that money cannot be transferred from one party to the other.
They can also mix these options in arbitrary fractions. E.g., they can choose option a for a fraction x of the time, option b for fraction y, and option c for fraction z, such that: x + y + z = 1 {\displaystyle x+y+z=1} . Hence, the set F {\displaystyle F} of feasible agreements is the convex hull of a(60,80) and b(50,110) and c(30,150).
The disagreement point is defined as the point of minimal utility: this is 30 for Alice and 80 for George, so d=(30,80).
For both Nash and KS solutions, we have to normalize the agents' utilities by subtracting the disagreement values, since we are only interested in the gains that the players can receive above this disagreement point. Hence, the normalized values are:
The Nash bargaining solution maximizes the product of normalized utilities:
The maximum is attained when x = 0 {\displaystyle x=0} and y = 7 / 8 {\displaystyle y=7/8} and z = 1 / 8 {\displaystyle z=1/8} (i.e., option b is used 87.5% of the time and option c is used in the remaining time). The utility-gain of Alice is $17.5 and of George $35.
The KS bargaining solution equalizes the relative gains - the gain of each player relative to its maximum possible gain - and maximizes this equal value:
Here, the maximum is attained when x = 0 {\displaystyle x=0} and y = 21 / 26 {\displaystyle y=21/26} and z = 5 / 26 {\displaystyle z=5/26} . The utility-gain of Alice is $16.1 and of George $37.7.
Note that both solutions are Pareto-superior to the "random-dictatorial" solution - the solution that selects a dictator at random and lets him/her selects his/her best option. This solution is equivalent to letting x = 1 / 2 {\displaystyle x=1/2} and y = 0 {\displaystyle y=0} and z = 1 / 2 {\displaystyle z=1/2} , which gives a utility-gain of only $15 to Alice and $35 to George. | https://en.wikipedia.org/wiki/Kalai–Smorodinsky_bargaining_solution |
Bryophyllum
Kalanchoe ( / ˌ k æ l ə ŋ ˈ k oʊ . iː / KAL -əng- KOH -ee ), [ 2 ] [ 3 ] (also called "kalanchöe" or "kalanchoë"), is a genus of about 125 species of tropical, succulent plants in the stonecrop family Crassulaceae , mainly native to Madagascar and tropical Africa . A Kalanchoe species was one of the first plants to be sent into space , sent on a resupply to the Soviet Salyut 1 space station in 1979. [ 4 ] The majority of kalanchoes require around 6–8 hours of sunlight a day; a few cannot tolerate this, and survive with bright, indirect sunlight to bright shade. [ citation needed ]
Most are shrubs or perennial herbaceous plants, but a few are annual or biennial . The largest, Kalanchoe beharensis from Madagascar, can reach 6 m (20 ft) tall, but most species are less than 1 m (3 ft) tall.
Kalanchoes open their flowers by growing new cells on the inner surface of the petals to force them outwards, and on the outside of the petals to close them. Kalanchoe flowers are divided into 4 sections with 8 stamens. The petals are fused into a tube, in a similar way to some related genera such as Cotyledon . [ 5 ]
The genus Kalanchoe was first described by the French botanist Michel Adanson in 1763. [ 6 ]
The genus Bryophyllum was described by Salisbury in 1806 and the genus Kitchingia was created by Baker in 1881. Kitchingia is now regarded as a synonym for Kalanchoe , while Bryophyllum has also been treated as a separate genus, [ 6 ] since species of Bryophyllum appear to be nested within Kalanchoe on molecular phylogenetic analysis, Bryophyllum is considered as a section of the former, dividing the genus into three sections, Kitchingia , Bryophyllum , and Eukalanchoe . [ 7 ] [ 8 ] [ 9 ] these were formalised as subgenera by Smith and Figueiredo (2018). [ 1 ]
Adanson cited Georg Joseph Kamel (Camellus) as his source for the name. [ 10 ] [ 11 ] The name came from the Cantonese name 伽藍菜 ( Jyutping : gaa 1 laam 4 coi 3 ). [ 12 ]
Kalanchoe ceratophylla and Kalanchoe laciniata are both called 伽蓝菜 [ 13 ] (apparently "Buddhist monastery [samghārāma] herb") in China. In Mandarin Chinese, it does not seem very close in pronunciation ( qiélán cài , but possibly jiālán cài or gālán cài as the character 伽 has multiple pronunciations), but the Cantonese gālàahm choi is closer. [ citation needed ]
Several hybrids within Kalanchoe are known:
The genus is predominantly native to the Old World . Only one species originates from the Americas. Fifty-six are from southern and eastern Africa and 60 species on the island of Madagascar . It is also found in south-eastern Asia and China . [ 15 ]
These plants are food plants for caterpillars of the Red Pierrot butterfly. The butterfly lays its eggs on leaves, and after hatching, caterpillars burrow into the leaves and eat their inside cells.
These plants are cultivated as ornamental houseplants and rock or succulent garden plants. They are popular because of their ease of propagation, low water requirements, and wide variety of flower colors typically borne in clusters well above the leaves. The section Bryophyllum —formerly an independent genus—contains species such as the "air-plant" Kalanchoe pinnata . In these plants, new individuals develop vegetatively as plantlets, also known as bulbils or gemmae, at indentations in leaf margins. These young plants eventually drop off and take root. No males have been found of one species of this genus which does flower and produce seeds, and it is commonly called the mother of thousands: Kalanchoe daigremontiana is thus an example of asexual reproduction . [ 16 ]
The cultivars 'Tessa' [ 17 ] and 'Wendy' have gained the Royal Horticultural Society 's Award of Garden Merit . [ 18 ] [ 19 ]
In traditional medicine, Kalanchoe species have been used to treat ailments such as infections, rheumatism and inflammation. Kalanchoe extracts also have immunosuppressive effects. Kalanchoe pinnata has been recorded in Trinidad and Tobago as being used as a traditional treatment for hypertension. [ 20 ]
A variety of bufadienolide compounds have been isolated from various Kalanchoe species. Five different bufadienolides have been isolated from Kalanchoe daigremontiana . [ 21 ] [ 22 ] Two of these, daigremontianin and bersaldegenin 1,3,5-orthoacetate , have been shown to have a pronounced sedative effect. They also have the strong positive inotropic effect associated with cardiac glycosides, and with greater doses an increasing effect on the central nervous system .
Bufadienolide compounds isolated from Kalanchoe pinnata include bryophillin A which showed strong anti-tumor promoting activity, and bersaldegenin-3-acetate and bryophillin C which were less active. [ 23 ] Bryophillin C also showed insecticidal properties. [ 24 ] | https://en.wikipedia.org/wiki/Kalanchoe |
The Kaleshwaram Lift Irrigation Project ( KLIP ) is a multi-purpose irrigation project on the Godavari River in Kaleshwaram , Bhupalpally , Telangana , India . [ 2 ] Currently the world's largest multi-stage lift irrigation project, [ 3 ] its farthest upstream influence is at the confluence of the Pranahita and Godavari rivers. The Pranahita River is itself a confluence of various smaller tributaries including the Wardha , Painganga , and Wainganga rivers which combine to form the seventh-largest drainage basin on the subcontinent, with an estimated annual discharge of more than 6,427,900 acre-feet (7,930 cubic hectometres ) or 280 TMC . It remains untapped as its course is principally through dense forests and other ecologically sensitive zones such as wildlife sanctuaries .
The Kaleshwaram Lift Irrigation Project [ 4 ] [ 5 ] is divided into 7 links and 28 packages spanning a distance of approximately 500 km (310 mi ) through 13 districts and utilizing a canal network of more than 1,800 km (1,100 mi). [ 6 ] The project aims to produce a total of 240 TMC (195 from Medigadda Barrage , 20 from Sripada Yellampalli project and 25 from groundwater ), of which 169 has been allocated for irrigation, 30 for Hyderabad municipal water , 16 for miscellaneous industrial uses and 10 for drinking water in nearby villages, with the remainder being estimated evaporation loss. The project aims at increasing total culturable command area (the sustainable area which can be irrigated after accounting for both upstream and downstream factors) by 1,825,000 acre⋅ft (2,251 hm 3 ) across all 13 districts in addition to stabilizing the existing CCA.
On 21 June 2019, the project was opened by Telangana Governor E. S. L. Narasimhan and Chief minister K. Chandrashekar Rao . National Green Tribunal declared the Scheme is constructed without following the statuary provisions with regard to environmental aspects. [ 7 ]
Four major pumping facilities manage the project's outflow, the largest at Ramadugu ( Medaram , Annaram and Sundilla being the others) is also likely to be the largest in Asia once consistent measurements are available, [ 8 ] requiring seven 140 MWh (500 GJ ) pumps designed and manufactured specifically for the project by the BHEL . [ 9 ] The Engineering giant Megha Engineering and Infrastructures Limited built 15 of 22 Pump houses and undertook major part of the project.
In addition to constructing new reservoirs, Kaleshwaram also rejuvenates existing ones. [ 10 ] Mallanna Sagar reservoir was inaugurated in February 2022. It is one of the biggest artificial reservoirs in India , and was constructed with a capacity of 50 tmcft. [ 11 ]
(in Tmcft )
(in Tmcft )
Total: 1,65,700 acres (New ayacut) Apart from: 1,875,00+ acres (Stabilisation of existing ayacut) [ clarification needed ]
1. Gravity Canal - 1,531 km
2. Gravity Tunnel - 203 km
3. Pressure Mains / Delivery Mains - 98 km
Link-I: From Medigadda Barrage on Godavari River to Sripada Yellampalli Project
Water will be reverse pumped from the confluence point of Godavari and Pranahita Rivers to Sripada Yellampalli Project with the help of 3 barrages (Medigadda, Annaram and Sundilla) and 3 lifts.
As of June 2019, lifts are being commissioned with provision to lift 2 TMC ( 56,63,36,93,184 liters ) [ clarification needed ] of water per day from Medigadda. The water is lifted to backwaters of Annaram barrage. Again from Annaram barrage to Sundilla barrage. Finally from Sundilla to Sripada Yellampalli Project. Civil works are being executed to lift 3 TMC per day but pumps are being installed to lift only 2 TMC. If need be, only pumps would need to be installed to increase capacity by one more TMC.
Link-II: From Sripada Yellampalli Project to Mid Manair Dam
A new balancing reservoir is also being proposed in the outskirts of Hyderabad of 20–30 TMC to store water. The water will be supplied to this balancing reservoir in the same link.
Link-V: From Anicut to Chityala
From Anicut, a series of gravity canals and a small tunnel of 1.2 km are planned to transfer water to Gandamalla Reservoir and Baswapuram Reservoir. Thereafter, gravity canals are planned towards Chityal Mandal and its villages.
Link-VI: From Sri Komaravelli Mallanna Sagar to Singur Dam
From Sri Komaravelli Mallanna Sagar, another sequence of gravity canals, tunnels and lifts are used to transfer water to Singur Dam. Apart from that, if need be, water can be transferred to Nizam Sagar Project and from there, to SRSP.
Link-VII: From SRSP Foreshore to Nizam Sagar Canals and to Dilwarpur and Hangarga village for Nirmal and Mudhole Constituency
From the foreshore waters of SRSP, water will be transferred to reservoirs at Hangarga and Dilwapur villages. Apart from this, existing reservoirs like Masani Tank and kondem Cheruvu will also be linked. Canals under Nizam Sagar will also be irrigated.
The chief minister has said that every year about 400 TMC of water will be lifted.
The project requires about 5,900 MW of electricity to run its several large water pumps. Assuming, on average, the pumps require constant running for two months during the monsoon period, 24 hours a day, the total electricity consumption would be 849 crore units. Taking a unit electricity charge of Rs. 8.0 per kWh, the annual electricity cost is going to be Rs. 7000 crores per year. Assuming the project irrigates about 15 lakh acres, the electricity cost for irrigation is about Rs. 46,666 per acre per year. The chief minister has said that the project requires about Rs. 5000 crore annually for electricity charges. [ 12 ] On the other hand, the state irrigation department had allocated Rs.7000 crores for electricity charges in its 2020 budget. [ 13 ]
The project was mainly funded with the money obtained through loans. Assuming an existing loan of Rs. 80,000 crore, at an interest rate of 6% that needs to paid up over a period of 30 years, the annual loan repayment charge is about Rs. 5760 crores per year. This implies an additional charge of Rs. 38,400 per acre per year towards the loan repayment. Therefore, the total cost of irrigation per acre is approximately Rs. 85,000 per acre per year. On the other hand, the net profit from the cultivation of the main crop i.e., paddy, could be expected to be around Rs.40,000 per acre per year, [ 13 ] assuming two crops in a year. These numbers raise questions about the financial viability of the project.
A recent report by the comptroller and auditor general of India (CAG) has pointed out that the cost to benefit ratio of the project is 1:0.75 in contrast to the state govt.'s claim of 1:1.5. [ 14 ] In addition, by taking in to account the escalated costs for lifting the third TMC, the ratio comes down to 1:0.52. According to the report, the annual operational costs for irrigating an acre of land is Rs. 46,364 cr. The annual electricity costs are estimated to be Rs. 10,374 cr. Despite the negative report by CAG on the financial viability, the state govt. has made no effort refute the report.
Indian Public sector Enterprise BHEL is executing this project and has already commissioned 16 pumping units. [ 15 ] [ 16 ]
In October 2020, the National Green Tribunal , India's court for environmental issues, directed the Telangana government to halt work on the KLIP except the drinking water supply component. A petition had been filed by a farmer from Siddipet district, whose land was affected by the KLIP. The National Green Tribunal found, on hearing his petition, that the environmental clearances for the KLIP had not been obtained before the project, as is required by law, but had been granted by the Union Government of India after work on the project had already begun by the Telangana government. The National Green Tribunal has directed the Indian government's Ministry of Environment, Forests and Climate Change to constitute a committee to investigate the illegally granted clearances, and to file a report with them within six months. [ 17 ] [ 18 ] [ 19 ]
Kaleshwaram Lift Irrigation Project Details PDF .
(Telangana India) | https://en.wikipedia.org/wiki/Kaleshwaram_Lift_Irrigation_Project |
A kaliapparat is a laboratory device invented in 1831 by Justus von Liebig (1803–1873) for the analysis of carbon in organic compounds . [ 1 ] The device, made of glass , consists of a series of five bulbs connected and arranged in a triangular shape.
To determine the carbon in an organic compound with a kaliapparat, the substance is first burned, converting any carbon present into carbon dioxide (CO 2 ). The gaseous products along with the water vapor produced by combustion are passed through the kaliapparat, which is filled with a potassium hydroxide (KOH) solution. The potassium hydroxide reacts with the CO 2 to trap it as potassium carbonate . The global reaction, ignoring intermediate steps and the corresponding ionic dissociation , can be written as follows:
Subtracting the mass of the kaliapparat before the combustion from that measured after the combustion gives the amount of CO 2 absorbed. From the mass of CO 2 thus determined, standard stoichiometric calculations then give the mass of carbon in the original sample.
A stylized symbol of a kaliapparat is used in the American Chemical Society logo since 1909, [ 2 ] originally designed in the early 20th century by Tiffany's Jewelers . [ 3 ] | https://en.wikipedia.org/wiki/Kaliapparat |
The Kalium Database is a manually curated biomedical database on K + channel ligands found in the venom of scorpions, spiders, sea anemones, cone snails, snakes, centipedes, bees, and more. [ 1 ] The first release of the Kalium Database was dedicated to scorpion toxins only, [ 2 ] while its second release (Kalium 2.0) included toxins from other living organisms. [ 3 ] The most recent update (Kalium 3.0) added information on their artificial derivatives. The Kalium Database is meant to assist structural biologists, toxinologists, pharmacologists, medicinal chemists, and other researchers in their pursuit to develop new drugs for cardiovascular and neurological diseases.
This database -related article is a stub . You can help Wikipedia by expanding it .
This toxicology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kalium_Database |
Kallidin belongs to the family kinins , which are the peptide hormones . [ 1 ] Kallidin is a decapeptide whose sequence is H-Lys-Arg-Pro-Pro-Gly-Phe-Ser-Pro-Phe-Arg-OH. It can be converted to bradykinin by the aminopeptidase enzyme. [ citation needed ]
Kallidin is a bioactive kinin peptide formed in response to injury from kininogen precursors through the action of kallikreins . [ 2 ] Like all kinins, kallidin, the deca-peptide, plays an important role in several body pathologies. Kinins can regulate the blood pressure by increasing the level of vasopressor substances . [ 1 ] [ 3 ] They can also bind to the B 1 and B 2 cell surface receptors, which are G-protein coupled receptors . [ 4 ] The mediation of the B 1 receptors by des-Arg kinins as agonists can be expressed in several medical issues, such as cancer and trauma. [ 3 ] By binding to the B 2 receptors, kinins, endogenous agonists, can regulate the vasodilatation and bronchioconstriction . [ 1 ]
Since kinins are peptides, they can be cleaved by the peptidases . Peptidases such as the serine peptidases, carboxypeptidase N and carboxypeptidase M cleave kinins into des-Arg-bradykinin and Lys-des-Arg-bradykinin. [ 5 ] [ 6 ]
Kallidin is identical to bradykinin with an additional lysine residue added at the N-terminal end and signals through the bradykinin receptor . [ citation needed ]
Despite exhibiting similar functions and reactivities, kinins can be differentiated by combining an amino-terminal-directed radioimmunoassay with a carboxy-terminal-directed radioimmunoassay in combination with HPLC . [ 1 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kallidin |
In mathematics, the Kallman–Rota inequality , introduced by Kallman & Rota (1970) , is a generalization of the Landau–Kolmogorov inequality to Banach spaces . It states that
if A is the infinitesimal generator of a one-parameter contraction semigroup then | https://en.wikipedia.org/wiki/Kallman–Rota_inequality |
In mathematics , the Kalmanson combinatorial conditions are a set of conditions on the distance matrix used in determining the solvability of the traveling salesman problem . These conditions apply to a special kind of cost matrix , the Kalmanson matrix , and are named after Kenneth Kalmanson.
This combinatorics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kalmanson_combinatorial_conditions |
The Kalman–Yakubovich–Popov lemma is a result in system analysis and control theory which states: Given a number γ > 0 {\displaystyle \gamma >0} , two n-vectors B, C and an n x n Hurwitz matrix A, if the pair ( A , B ) {\displaystyle (A,B)} is completely controllable , then a symmetric matrix P and a vector Q satisfying
exist if and only if
Moreover, the set { x : x T P x = 0 } {\displaystyle \{x:x^{T}Px=0\}} is the unobservable subspace for the pair ( C , A ) {\displaystyle (C,A)} .
The lemma can be seen as a generalization of the Lyapunov equation in stability theory. It establishes a relation between a linear matrix inequality involving the state space constructs A, B, C and a condition in the frequency domain .
The Kalman–Popov–Yakubovich lemma which was first formulated and proved in 1962 by Vladimir Andreevich Yakubovich [ 1 ] where it was stated that for the strict frequency inequality. The case of nonstrict frequency inequality was published in 1963 by Rudolf E. Kálmán . [ 2 ] In that paper the relation to solvability of the Lur’e equations was also established. Both papers considered scalar-input systems. The constraint on the control dimensionality was removed in 1964 by Gantmakher and Yakubovich [ 3 ] and independently by Vasile Mihai Popov . [ 4 ] Extensive reviews of the topic can be found in [ 5 ] and in Chapter 3 of. [ 6 ]
Given A ∈ R n × n , B ∈ R n × m , M = M T ∈ R ( n + m ) × ( n + m ) {\displaystyle A\in \mathbb {R} ^{n\times n},B\in \mathbb {R} ^{n\times m},M=M^{T}\in \mathbb {R} ^{(n+m)\times (n+m)}} with det ( j ω I − A ) ≠ 0 {\displaystyle \det(j\omega I-A)\neq 0} for all ω ∈ R {\displaystyle \omega \in \mathbb {R} } and ( A , B ) {\displaystyle (A,B)} controllable, the following are equivalent:
The corresponding equivalence for strict inequalities holds even if ( A , B ) {\displaystyle (A,B)} is not controllable. [ 7 ] | https://en.wikipedia.org/wiki/Kalman–Yakubovich–Popov_lemma |
In Kaluza–Klein theory , a unification of general relativity and electromagnetism , the five-dimensional Kaluza–Klein metric is the generalization of the four-dimensional metric tensor. It additionally includes a scalar field called graviscalar (or radion) and a vector field called graviphoton (or gravivector), which correspond to hypothetical particles .
The Kaluza–Klein metric is named after Theodor Kaluza and Oskar Klein .
The Kaluza–Klein metric is given by: [ 1 ] [ 2 ] [ 3 ] [ 4 ]
Its inverse matrix is given by:
Defining an extended gravivector A a = ( A μ , 1 ) {\displaystyle A_{a}=(A_{\mu },1)} shortens the definition to:
which also shows that the radion ϕ {\displaystyle \phi } cannot vanish as this would make the metric singular . | https://en.wikipedia.org/wiki/Kaluza–Klein_metric |
In physics , Kaluza–Klein theory ( KK theory ) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the common 4D of space and time and considered an important precursor to string theory . In their setup, the vacuum has the usual 3 dimensions of space and one dimension of time but with another microscopic extra spatial dimension in the shape of a tiny circle. Gunnar Nordström had an earlier, similar idea. But in that case, a fifth component was added to the electromagnetic vector potential, representing the Newtonian gravitational potential, and writing the Maxwell equations in five dimensions. [ 1 ]
The five-dimensional (5D) theory developed in three steps. The original hypothesis came from Theodor Kaluza , who sent his results to Albert Einstein in 1919 [ 2 ] and published them in 1921. [ 3 ] Kaluza presented a purely classical extension of general relativity to 5D, with a metric tensor of 15 components. Ten components are identified with the 4D spacetime metric, four components with the electromagnetic vector potential, and one component with an unidentified scalar field sometimes called the " radion " or the "dilaton". Correspondingly, the 5D Einstein equations yield the 4D Einstein field equations , the Maxwell equations for the electromagnetic field , and an equation for the scalar field. Kaluza also introduced the "cylinder condition" hypothesis, that no component of the five-dimensional metric depends on the fifth dimension. Without this restriction, terms are introduced that involve derivatives of the fields with respect to the fifth coordinate, and this extra degree of freedom makes the mathematics of the fully variable 5D relativity enormously complex. Standard 4D physics seems to manifest this "cylinder condition" and, along with it, simpler mathematics.
In 1926, Oskar Klein gave Kaluza's classical five-dimensional theory a quantum interpretation, [ 4 ] [ 5 ] to accord with the then-recent discoveries of Werner Heisenberg and Erwin Schrödinger . Klein introduced the hypothesis that the fifth dimension was curled up and microscopic, to explain the cylinder condition. Klein suggested that the geometry of the extra fifth dimension could take the form of a circle, with the radius of 10 −30 cm . More precisely, the radius of the circular dimension is 23 times the Planck length , which in turn is of the order of 10 −33 cm . [ 5 ] Klein also made a contribution to the classical theory by providing a properly normalized 5D metric. [ 4 ] Work continued on the Kaluza field theory during the 1930s by Einstein and colleagues at Princeton University .
In the 1940s, the classical theory was completed, and the full field equations including the scalar field were obtained by three independent research groups: [ 6 ] Yves Thiry, [ 7 ] [ 8 ] [ 9 ] working in France on his dissertation under André Lichnerowicz ; Pascual Jordan , Günther Ludwig, and Claus Müller in Germany, [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] with critical input from Wolfgang Pauli and Markus Fierz ; and Paul Scherrer [ 15 ] [ 16 ] [ 17 ] working alone in Switzerland. Jordan's work led to the scalar–tensor theory of Brans–Dicke ; [ 18 ] Carl H. Brans and Robert H. Dicke were apparently unaware of Thiry or Scherrer. The full Kaluza equations under the cylinder condition are quite complex, and most English-language reviews, as well as the English translations of Thiry, contain some errors. The curvature tensors for the complete Kaluza equations were evaluated using tensor-algebra software in 2015, [ 19 ] verifying results of J. A. Ferrari [ 20 ] and R. Coquereaux & G. Esposito-Farese. [ 21 ] The 5D covariant form of the energy–momentum source terms is treated by L. L. Williams. [ 22 ]
In his 1921 article, [ 3 ] Kaluza established all the elements of the classical five-dimensional theory: the Kaluza–Klein metric , the Kaluza–Klein–Einstein field equations , the equations of motion, the stress–energy tensor, and the cylinder condition. With no free parameters , it merely extends general relativity to five dimensions. One starts by hypothesizing a form of the five-dimensional Kaluza–Klein metric g ~ a b {\displaystyle {\widetilde {g}}_{ab}} , where Latin indices span five dimensions. Let one also introduce the four-dimensional spacetime metric g μ ν {\displaystyle {g}_{\mu \nu }} , where Greek indices span the usual four dimensions of space and time; a 4-vector A μ {\displaystyle A^{\mu }} identified with the electromagnetic vector potential; and a scalar field ϕ {\displaystyle \phi } . Then decompose the 5D metric so that the 4D metric is framed by the electromagnetic vector potential, with the scalar field at the fifth diagonal. This can be visualized as
One can write more precisely
where the index 5 {\displaystyle 5} indicates the fifth coordinate by convention, even though the first four coordinates are indexed with 0, 1, 2, and 3. The associated inverse metric is
This decomposition is quite general, and all terms are dimensionless. Kaluza then applies the machinery of standard general relativity to this metric. The field equations are obtained from five-dimensional Einstein equations , and the equations of motion from the five-dimensional geodesic hypothesis. The resulting field equations provide both the equations of general relativity and of electrodynamics; the equations of motion provide the four-dimensional geodesic equation and the Lorentz force law , and one finds that electric charge is identified with motion in the fifth dimension.
The hypothesis for the metric implies an invariant five-dimensional length element d s {\displaystyle ds} :
The Kaluza–Klein–Einstein field equations of the five-dimensional theory were never adequately provided by Kaluza or Klein because they ignored the scalar field . The full Kaluza field equations are generally attributed to Thiry, [ 8 ] who obtained vacuum field equations, although Kaluza [ 3 ] originally provided a stress–energy tensor for his theory, and Thiry included a stress–energy tensor in his thesis. But as described by Gonner, [ 6 ] several independent groups worked on the field equations in the 1940s and earlier. Thiry is perhaps best known only because an English translation was provided by Applequist, Chodos, & Freund in their review book. [ 23 ] Applequist et al. also provided an English translation of Kaluza's article. Translations of the three (1946, 1947, 1948) Jordan articles can be found on the ResearchGate and Academia.edu archives. [ 10 ] [ 11 ] [ 13 ] The first correct English-language Kaluza field equations, including the scalar field, were provided by Williams. [ 19 ]
To obtain the 5D Kaluza–Klein–Einstein field equations, the 5D Kaluza–Klein–Christoffel symbols Γ ~ b c a {\displaystyle {\widetilde {\Gamma }}_{bc}^{a}} are calculated from the 5D Kaluza–Klein metric g ~ a b {\displaystyle {\widetilde {g}}_{ab}} , and the 5D Kaluza–Klein–Ricci tensor R ~ a b {\displaystyle {\widetilde {R}}_{ab}} is calculated from the 5D connections .
The classic results of Thiry and other authors presume the cylinder condition:
Without this assumption, the field equations become much more complex, providing many more degrees of freedom that can be identified with various new fields. Paul Wesson and colleagues have pursued relaxation of the cylinder condition to gain extra terms that can be identified with the matter fields, [ 24 ] for which Kaluza [ 3 ] otherwise inserted a stress–energy tensor by hand.
It has been an objection to the original Kaluza hypothesis to invoke the fifth dimension only to negate its dynamics. But Thiry argued [ 6 ] that the interpretation of the Lorentz force law in terms of a five-dimensional geodesic militates strongly for a fifth dimension irrespective of the cylinder condition. Most authors have therefore employed the cylinder condition in deriving the field equations. Furthermore, vacuum equations are typically assumed for which
where
and
The vacuum field equations obtained in this way by Thiry [ 8 ] and Jordan's group [ 10 ] [ 11 ] [ 13 ] are as follows.
The field equation for ϕ {\displaystyle \phi } is obtained from
where F α β ≡ ∂ α A β − ∂ β A α , {\displaystyle F_{\alpha \beta }\equiv \partial _{\alpha }A_{\beta }-\partial _{\beta }A_{\alpha },} ◻ ≡ g μ ν ∇ μ ∇ ν , {\displaystyle \Box \equiv g^{\mu \nu }\nabla _{\mu }\nabla _{\nu },} and ∇ μ {\displaystyle \nabla _{\mu }} is a standard, 4D covariant derivative . It shows that the electromagnetic field is a source for the scalar field . Note that the scalar field cannot be set to a constant without constraining the electromagnetic field. The earlier treatments by Kaluza and Klein did not have an adequate description of the scalar field and did not realize the implied constraint on the electromagnetic field by assuming the scalar field to be constant.
The field equation for A ν {\displaystyle A^{\nu }} is obtained from
It has the form of the vacuum Maxwell equations if the scalar field is constant.
The field equation for the 4D Ricci tensor R μ ν {\displaystyle R_{\mu \nu }} is obtained from
where R {\displaystyle R} is the standard 4D Ricci scalar.
This equation shows the remarkable result, called the "Kaluza miracle", that the precise form for the electromagnetic stress–energy tensor emerges from the 5D vacuum equations as a source in the 4D equations: field from the vacuum. This relation allows the definitive identification of A μ {\displaystyle A^{\mu }} with the electromagnetic vector potential. Therefore, the field needs to be rescaled with a conversion constant k {\displaystyle k} such that A μ → k A μ {\displaystyle A^{\mu }\to kA^{\mu }} .
The relation above shows that we must have
where G {\displaystyle G} is the gravitational constant , and μ 0 {\displaystyle \mu _{0}} is the permeability of free space . In the Kaluza theory, the gravitational constant can be understood as an electromagnetic coupling constant in the metric. There is also a stress–energy tensor for the scalar field. The scalar field behaves like a variable gravitational constant, in terms of modulating the coupling of electromagnetic stress–energy to spacetime curvature. The sign of ϕ 2 {\displaystyle \phi ^{2}} in the metric is fixed by correspondence with 4D theory so that electromagnetic energy densities are positive. It is often assumed that the fifth coordinate is spacelike in its signature in the metric.
In the presence of matter, the 5D vacuum condition cannot be assumed. Indeed, Kaluza did not assume it. The full field equations require evaluation of the 5D Kaluza–Klein–Einstein tensor
as seen in the recovery of the electromagnetic stress–energy tensor above. The 5D curvature tensors are complex, and most English-language reviews contain errors in either G ~ a b {\displaystyle {\widetilde {G}}_{ab}} or R ~ a b {\displaystyle {\widetilde {R}}_{ab}} , as does the English translation of Thiry. [ 8 ] In 2015, a complete set of 5D curvature tensors under the cylinder condition, evaluated using tensor-algebra software, was produced. [ 19 ]
The equations of motion are obtained from the five-dimensional geodesic hypothesis [ 3 ] in terms of a 5-velocity U ~ a ≡ d x a / d s {\displaystyle {\widetilde {U}}^{a}\equiv dx^{a}/ds} :
This equation can be recast in several ways, and it has been studied in various forms by authors including Kaluza, [ 3 ] Pauli, [ 25 ] Gross & Perry, [ 26 ] Gegenberg & Kunstatter, [ 27 ] and Wesson & Ponce de Leon, [ 28 ] but it is instructive to convert it back to the usual 4-dimensional length element c 2 d τ 2 ≡ g μ ν d x μ d x ν {\displaystyle c^{2}\,d\tau ^{2}\equiv g_{\mu \nu }\,dx^{\mu }\,dx^{\nu }} , which is related to the 5-dimensional length element d s {\displaystyle ds} as given above:
Then the 5D geodesic equation can be written [ 29 ] for the spacetime components of the 4-velocity:
The term quadratic in U ν {\displaystyle U^{\nu }} provides the 4D geodesic equation plus some electromagnetic terms:
The term linear in U ν {\displaystyle U^{\nu }} provides the Lorentz force law :
This is another expression of the "Kaluza miracle". The same hypothesis for the 5D metric that provides electromagnetic stress–energy in the Einstein equations, also provides the Lorentz force law in the equation of motions along with the 4D geodesic equation. Yet correspondence with the Lorentz force law requires that we identify the component of 5-velocity along the fifth dimension with electric charge:
where m {\displaystyle m} is particle mass, and q {\displaystyle q} is particle electric charge. Thus electric charge is understood as motion along the fifth dimension. The fact that the Lorentz force law could be understood as a geodesic in five dimensions was to Kaluza a primary motivation for considering the five-dimensional hypothesis, even in the presence of the aesthetically unpleasing cylinder condition.
Yet there is a problem: the term quadratic in U 5 {\displaystyle U^{5}} ,
If there is no gradient in the scalar field, the term quadratic in U 5 {\displaystyle U^{5}} vanishes. But otherwise the expression above implies
For elementary particles, U 5 > 10 20 c {\displaystyle U^{5}>10^{20}c} . The term quadratic in U 5 {\displaystyle U^{5}} should dominate the equation, perhaps in contradiction to experience. This was the main shortfall of the five-dimensional theory as Kaluza saw it, [ 3 ] and he gives it some discussion in his original article. [ clarification needed ]
The equation of motion for U 5 {\displaystyle U^{5}} is particularly simple under the cylinder condition. Start with the alternate form of the geodesic equation, written for the covariant 5-velocity:
This means that under the cylinder condition, U ~ 5 {\displaystyle {\widetilde {U}}_{5}} is a constant of the five-dimensional motion:
Kaluza proposed [ 3 ] a five-dimensional matter stress tensor T ~ M a b {\displaystyle {\widetilde {T}}_{M}^{ab}} of the form
where ρ {\displaystyle \rho } is a density, and the length element d s {\displaystyle ds} is as defined above.
Then the spacetime component gives a typical "dust" stress–energy tensor:
The mixed component provides a 4-current source for the Maxwell equations:
Just as the five-dimensional metric comprises the four-dimensional metric framed by the electromagnetic vector potential, the five-dimensional stress–energy tensor comprises the four-dimensional stress–energy tensor framed by the vector 4-current.
Kaluza's original hypothesis was purely classical and extended discoveries of general relativity. By the time of Klein's contribution, the discoveries of Heisenberg, Schrödinger, and Louis de Broglie were receiving a lot of attention. Klein's Nature article [ 5 ] suggested that the fifth dimension is closed and periodic, and that the identification of electric charge with motion in the fifth dimension can be interpreted as standing waves of wavelength λ 5 {\displaystyle \lambda ^{5}} , much like the electrons around a nucleus in the Bohr model of the atom. The quantization of electric charge could then be nicely understood in terms of integer multiples of fifth-dimensional momentum. Combining the previous Kaluza result for U 5 {\displaystyle U^{5}} in terms of electric charge, and a de Broglie relation for momentum p 5 = h / λ 5 {\displaystyle p^{5}=h/\lambda ^{5}} , Klein obtained [ 5 ] an expression for the 0th mode of such waves:
where h {\displaystyle h} is the Planck constant . Klein found that λ 5 ∼ 10 − 30 {\displaystyle \lambda ^{5}\sim 10^{-30}} cm, and thereby an explanation for the cylinder condition in this small value.
Klein's Zeitschrift für Physik article of the same year, [ 4 ] gave a more detailed treatment that explicitly invoked the techniques of Schrödinger and de Broglie. It recapitulated much of the classical theory of Kaluza described above, and then departed into Klein's quantum interpretation. Klein solved a Schrödinger-like wave equation using an expansion in terms of fifth-dimensional waves resonating in the closed, compact fifth dimension.
In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of a very small radius , so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This extra dimension is a compact set , and construction of this compact dimension is referred to as compactification .
In modern geometry, the extra fifth dimension can be understood to be the circle group U(1) , as electromagnetism can essentially be formulated as a gauge theory on a fiber bundle , the circle bundle , with gauge group U(1). In Kaluza–Klein theory this group suggests that gauge symmetry is the symmetry of circular compact dimensions. Once this geometrical interpretation is understood, it is relatively straightforward to replace U(1) by a general Lie group . Such generalizations are often called Yang–Mills theories . If a distinction is drawn, then it is that Yang–Mills theories occur on a flat spacetime, whereas Kaluza–Klein treats the more general case of curved spacetime. The base space of Kaluza–Klein theory need not be four-dimensional spacetime; it can be any ( pseudo- ) Riemannian manifold , or even a supersymmetric manifold or orbifold or even a noncommutative space .
The construction can be outlined, roughly, as follows. [ 30 ] One starts by considering a principal fiber bundle P with gauge group G over a manifold M. Given a connection on the bundle, and a metric on the base manifold, and a gauge invariant metric on the tangent of each fiber, one can construct a bundle metric defined on the entire bundle. Computing the scalar curvature of this bundle metric, one finds that it is constant on each fiber: this is the "Kaluza miracle". One did not have to explicitly impose a cylinder condition, or to compactify: by assumption, the gauge group is already compact. Next, one takes this scalar curvature as the Lagrangian density , and, from this, constructs the Einstein–Hilbert action for the bundle, as a whole. The equations of motion, the Euler–Lagrange equations , can be then obtained by considering where the action is stationary with respect to variations of either the metric on the base manifold, or of the gauge connection. Variations with respect to the base metric gives the Einstein field equations on the base manifold, with the energy–momentum tensor given by the curvature ( field strength ) of the gauge connection. On the flip side, the action is stationary against variations of the gauge connection precisely when the gauge connection solves the Yang–Mills equations . Thus, by applying a single idea: the principle of least action , to a single quantity: the scalar curvature on the bundle (as a whole), one obtains simultaneously all of the needed field equations, for both the spacetime and the gauge field.
As an approach to the unification of the forces, it is straightforward to apply the Kaluza–Klein theory in an attempt to unify gravity with the strong and electroweak forces by using the symmetry group of the Standard Model , SU(3) × SU(2) × U(1) . However, an attempt to convert this interesting geometrical construction into a bona-fide model of reality flounders on a number of issues, including the fact that the fermions must be introduced in an artificial way (in nonsupersymmetric models). Nonetheless, KK remains an important touchstone in theoretical physics and is often embedded in more sophisticated theories. It is studied in its own right as an object of geometric interest in K-theory .
Even in the absence of a completely satisfying theoretical physics framework, the idea of exploring extra, compactified, dimensions is of considerable interest in the experimental physics and astrophysics communities. A variety of predictions, with real experimental consequences, can be made (in the case of large extra dimensions and warped models ). For example, on the simplest of principles, one might expect to have standing waves in the extra compactified dimension(s). If a spatial extra dimension is of radius R , the invariant mass of such standing waves would be M n = nh / Rc with n an integer , h being the Planck constant and c the speed of light . This set of possible mass values is often called the Kaluza–Klein tower . Similarly, in Thermal quantum field theory a compactification of the euclidean time dimension leads to the Matsubara frequencies and thus to a discretized thermal energy spectrum.
However, Klein's approach to a quantum theory is flawed [ citation needed ] and, for example, leads to a calculated electron mass in the order of magnitude of the Planck mass . [ 31 ]
Examples of experimental pursuits include work by the CDF collaboration, which has re-analyzed particle collider data for the signature of effects associated with large extra dimensions/ warped models . [ citation needed ]
Robert Brandenberger and Cumrun Vafa have speculated that in the early universe, cosmic inflation causes three of the space dimensions to expand to cosmological size while the remaining dimensions of space remained microscopic. [ citation needed ]
One particular variant of Kaluza–Klein theory is space–time–matter theory or induced matter theory , chiefly promulgated by Paul Wesson and other members of the Space–Time–Matter Consortium. [ 32 ] In this version of the theory, it is noted that solutions to the equation
may be re-expressed so that in four dimensions, these solutions satisfy Einstein's equations
with the precise form of the T μν following from the Ricci-flat condition on the five-dimensional space. In other words, the cylinder condition of the previous development is dropped, and the stress–energy now comes from the derivatives of the 5D metric with respect to the fifth coordinate. Because the energy–momentum tensor is normally understood to be due to concentrations of matter in four-dimensional space, the above result is interpreted as saying that four-dimensional matter is induced from geometry in five-dimensional space.
In particular, the soliton solutions of R ~ a b = 0 {\displaystyle {\widetilde {R}}_{ab}=0} can be shown to contain the Friedmann–Lemaître–Robertson–Walker metric in both radiation-dominated (early universe) and matter-dominated (later universe) forms. The general equations can be shown to be sufficiently consistent with classical tests of general relativity to be acceptable on physical principles, while still leaving considerable freedom to also provide interesting cosmological models .
The Kaluza–Klein theory has a particularly elegant presentation in terms of geometry. In a certain sense, it looks just like ordinary gravity in free space , except that it is phrased in five dimensions instead of four.
The equations governing ordinary gravity in free space can be obtained from an action , by applying the variational principle to a certain action . Let M be a ( pseudo- ) Riemannian manifold , which may be taken as the spacetime of general relativity . If g is the metric on this manifold, one defines the action S ( g ) as
where R ( g ) is the scalar curvature , and vol( g ) is the volume element . By applying the variational principle to the action
one obtains precisely the Einstein equations for free space:
where R ij is the Ricci tensor .
By contrast, the Maxwell equations describing electromagnetism can be understood to be the Hodge equations of a principal U(1)-bundle or circle bundle π : P → M {\displaystyle \pi :P\to M} with fiber U(1) . That is, the electromagnetic field F {\displaystyle F} is a harmonic 2-form in the space Ω 2 ( M ) {\displaystyle \Omega ^{2}(M)} of differentiable 2-forms on the manifold M {\displaystyle M} . In the absence of charges and currents, the free-field Maxwell equations are
where ⋆ {\displaystyle \star } is the Hodge star operator .
To build the Kaluza–Klein theory, one picks an invariant metric on the circle S 1 {\displaystyle S^{1}} that is the fiber of the U(1)-bundle of electromagnetism. In this discussion, an invariant metric is simply one that is invariant under rotations of the circle. Suppose that this metric gives the circle a total length Λ {\displaystyle \Lambda } . One then considers metrics g ^ {\displaystyle {\widehat {g}}} on the bundle P {\displaystyle P} that are consistent with both the fiber metric, and the metric on the underlying manifold M {\displaystyle M} . The consistency conditions are:
The Kaluza–Klein action for such a metric is given by
The scalar curvature, written in components, then expands to
where π ∗ {\displaystyle \pi ^{*}} is the pullback of the fiber bundle projection π : P → M {\displaystyle \pi :P\to M} . The connection A {\displaystyle A} on the fiber bundle is related to the electromagnetic field strength as
That there always exists such a connection, even for fiber bundles of arbitrarily complex topology, is a result from homology and specifically, K-theory . Applying Fubini's theorem and integrating on the fiber, one gets
Varying the action with respect to the component A {\displaystyle A} , one regains the Maxwell equations. Applying the variational principle to the base metric g {\displaystyle g} , one gets the Einstein equations
with the electromagnetic stress–energy tensor being given by
The original theory identifies Λ {\displaystyle \Lambda } with the fiber metric g 55 {\displaystyle g_{55}} and allows Λ {\displaystyle \Lambda } to vary from fiber to fiber. In this case, the coupling between gravity and the electromagnetic field is not constant, but has its own dynamical field, the radion .
In the above, the size of the loop Λ {\displaystyle \Lambda } acts as a coupling constant between the gravitational field and the electromagnetic field. If the base manifold is four-dimensional, the Kaluza–Klein manifold P is five-dimensional. The fifth dimension is a compact space and is called the compact dimension . The technique of introducing compact dimensions to obtain a higher-dimensional manifold is referred to as compactification . Compactification does not produce group actions on chiral fermions except in very specific cases: the dimension of the total space must be 2 mod 8, and the G-index of the Dirac operator of the compact space must be nonzero. [ 33 ]
The above development generalizes in a more-or-less straightforward fashion to general principal G -bundles for some arbitrary Lie group G taking the place of U(1) . In such a case, the theory is often referred to as a Yang–Mills theory and is sometimes taken to be synonymous. If the underlying manifold is supersymmetric , the resulting theory is a super-symmetric Yang–Mills theory.
No experimental or observational signs of extra dimensions have been officially reported. Many theoretical search techniques for detecting Kaluza–Klein resonances have been proposed using the mass couplings of such resonances with the top quark . An analysis of results from the LHC in December 2010 severely constrains theories with large extra dimensions . [ 34 ]
The observation of a Higgs -like boson at the LHC establishes a new empirical test which can be applied to the search for Kaluza–Klein resonances and supersymmetric particles.
The loop Feynman diagrams that exist in the Higgs interactions allow any particle with electric charge and mass to run in such a loop. Standard Model particles besides the top quark and W boson do not make big contributions to the cross-section observed in the H → γγ decay, but if there are new particles beyond the Standard Model, they could potentially change the ratio of the predicted Standard Model H → γγ cross-section to the experimentally observed cross-section. Hence a measurement of any dramatic change to the H → γγ cross-section predicted by the Standard Model is crucial in probing the physics beyond it.
An article from July 2018 [ 35 ] gives some hope for this theory; in the article they dispute that gravity is leaking into higher dimensions as in brane theory . However, the article does demonstrate that electromagnetism and gravity share the same number of dimensions, and this fact lends support to Kaluza–Klein theory; whether the number of dimensions is really 3 + 1 or in fact 4 + 1 is the subject of further debate. | https://en.wikipedia.org/wiki/Kaluza–Klein_theory |
In Kaluza–Klein theory , a unification of general relativity and electromagnetism , the five-fimensional Kaluza–Klein–Christoffel symbol is the generalization of the four-dimensional Christoffel symbol. They directly appear in the geodesic equations of Kaluza–Klein theory and indirectly through the Kaluza–Klein–Riemann curvature tensor also appear in the Kaluza–Klein–Einstein field equations .
The Kaluza–Klein–Christoffel symbols are named after Theodor Kaluza , Oskar Klein and Elwin Bruno Christoffel .
Let g ~ a b {\displaystyle {\widetilde {g}}_{ab}} be the Kaluza–Klein metric . The Kaluza–Klein–Christoffel symbols are given by: [ 1 ] | https://en.wikipedia.org/wiki/Kaluza–Klein–Christoffel_symbol |
In Kaluza–Klein theory , a speculative unification of general relativity and electromagnetism , the five-dimensional Kaluza–Klein–Einstein field equations are created by adding a hypothetical dimension to the four-dimensional Einstein field equations . They use the Kaluza–Klein–Einstein tensor , a generalization of the Einstein tensor , and can be obtained from the Kaluza–Klein–Einstein–Hilbert action , a generalization of the Einstein–Hilbert action . They also feature a phenomenon known as Kaluza miracle , which is that the description of the five-dimensional vacuum perfectly falls apart in a four-dimensional electrovacuum , Maxwell's equations and an additional radion field equation for the size of the compactified dimension :
The Kaluza–Klein–Einstein field equations are named after Theodor Kaluza , Oskar Klein and Albert Einstein .
Let g ~ a b {\displaystyle {\widetilde {g}}_{ab}} be the Kaluza–Klein metric , R ~ a b {\displaystyle {\widetilde {R}}_{ab}} be the Kaluza–Klein–Ricci tensor and R ~ := g ~ a b R ~ a b {\displaystyle {\widetilde {R}}:={\widetilde {g}}^{ab}{\widetilde {R}}_{ab}} be the Kaluza–Klein–Ricci scalar . The Kaluza–Klein–Einstein tensor is given by: [ 1 ]
This definition is analogous to that of the Einstein tensor and it shares the essential property of being divergence free :
A contraction yields the identity:
Since the five dimensions of spacetime enter, the identity is different from G = − R {\displaystyle G=-R} holding in general relativity.
The Kaluza–Klein–Einstein field equations are given by:
Since G ~ = 0 {\displaystyle {\widetilde {G}}=0} implies R ~ = 0 {\displaystyle {\widetilde {R}}=0} due to the above relation, the vacuum equations G ~ a b = 0 {\displaystyle {\widetilde {G}}_{ab}=0} reduce to R ~ a b = 0 {\displaystyle {\widetilde {R}}_{ab}=0} .
The Kaluza–Klein–Einstein field equations separate into: [ 2 ] [ 3 ]
Especially the first equation has the same structure as the Brans–Dicke–Einstein field equations with vanishing Dicke coupling constant. [ 4 ] A contraction yields:
Important special cases of the Kaluza–Klein–Einstein field equations include a constant radion field ϕ {\displaystyle \phi } and a vanishing graviphoton field A μ {\displaystyle A^{\mu }} . But the radion field ϕ {\displaystyle \phi } cannot vanish as well due to its division in the field equations and more basically, because this would cause the Kaluza–Klein metric to become singular . The exact value of the constant is irrelevant for the second and third equation, but is for the prefactor in the right side of the first equation. But since it can be aborded into the graviphoton field A μ {\displaystyle A^{\mu }} also appearing in the electromagnetic energy–stress tensor T μ ν e m {\displaystyle T_{\mu \nu }^{\mathrm {em} }} in second order, Einstein's gravitational constant can be taken without loss of generality .
For a constant radion field ϕ {\displaystyle \phi } , the field equations become: [ 5 ]
For a vanishing graviphoton field A μ {\displaystyle A^{\mu }} , the field equations become:
Through the process of Kaluza–Klein compactification , the additional extra dimension is rolled up in a circle . Hence spacetime has the structure Σ × S 1 {\displaystyle \Sigma \times S^{1}} with a four-dimensional manifold (or 4-manifold ) Σ {\displaystyle \Sigma } and the circle S 1 {\displaystyle S^{1}} . Taking the canonical generalization of the Einstein–Hilbert action on this manifold with the metric and the Ricci scalar being replaced by the Kaluza–Klein metric and Kaluza–Klein–Ricci scalar results results in the Kaluza–Klein–Einstein–Hilbert action : [ 6 ] : 23 [ 7 ] [ 8 ]
It is a special case of the Brans–Dicke–Einstein–Hilbert action with vanishing Dicke coupling constant as already reflected in the equations above. [ 4 ] The integration ∫ d x 4 {\displaystyle \int \mathrm {d} x^{4}} along the additional dimension is often taking into the gravitational constant . | https://en.wikipedia.org/wiki/Kaluza–Klein–Einstein_field_equations |
In Kaluza–Klein theory , a unification of general relativity and electromagnetism , the five-fimensional Kaluza–Klein–Riemann curvature tensor (or Kaluza–Klein–Riemann–Christoffel curvature tensor ) is the generalization of the four-dimensional Riemann curvature tensor (or Riemann–Christoffel curvature tensor). Its contraction with itself is the Kaluza–Klein–Ricci tensor , a generalization of the Ricci tensor . Its contraction with the Kaluza–Klein metric is the Kaluza–Klein–Ricci scalar , a generalization of the Ricci scalar .
The Kaluza–Klein–Riemann curvature tensor, Kaluza–Klein–Ricci tensor and scalar are namend after Theodor Kaluza , Oskar Klein , Bernhard Riemann and Gregorio Ricci-Curbastro .
Let g ~ a b {\displaystyle {\widetilde {g}}_{ab}} be the Kaluza–Klein metric and Γ ~ a b c {\displaystyle {\widetilde {\Gamma }}_{ab}^{c}} be the Kaluza–Klein–Christoffel symbols . The Kaluza–Klein–Riemann curvature tensor is given by:
The Kaluza–Klein–Ricci tensor and scalar are given by: [ 1 ] | https://en.wikipedia.org/wiki/Kaluza–Klein–Riemann_curvature_tensor |
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In 2012, the company was ranked 456 among the 500 fastest growing companies in Europe (and 15th in Israel) according to the Deloitte Index, based on their income in 2007–2011. [ 4 ]
In May 2014, the company announced that it had not met the target set for the trial for a hereditary emphysema in inhalation. [ 5 ] Following the failure of the experiment, the company's market value fell within a year from $500 million to $150 million. [ 6 ]
Glassia is approved by the FDA to treat lung disease caused by alpha 1-antitrypsin deficiency . The active ingredient in the drug is the protein alpha-1 Antitrypsin (AAT). Glassia is indicated for patients suffering from lung disease called emphysema, due to a genetic deficiency in the AAT protein. Takeda holds the license to manufacture and distribute Glassia in the United States , Canada , Australia , and New Zealand , following a completed technology transfer from Kamada. Under the terms of the agreement between the companies, Kamada is entitled to royalties from Glassia sales in Takeda’s markets. [ 7 ] In other countries where Glassia is available, Kamada partners with local distributors to sell the medicine.
The company has developed a technological platform for the production of specific immunoglobulins ( IgG 's). It produces a specific antibody against the rabies virus, and a product for the treatment of HDN - disease of the newborn hemolytic ( Hemolytic Disease of the Newborn ) - a disease caused from Rh negative in the fetus.
The company cooperates with the Israeli Ministry of Health , in the framework of which it established a GMP standard for the production of serum against snake venom . The product is manufactured from the serum of hyper-immune horses . [ 8 ]
The company has a strategic agreement with Kedrion Pharmaceuticals for the development and marketing of the KamRab rabies immunoglobulin in the United States. [ 9 ] | https://en.wikipedia.org/wiki/Kamada_Ltd. |
A kamal , often called simply khashaba (wood in Arabic), [ 1 ] is a celestial navigation device that determines latitude . The invention of the kamal allowed for the earliest known latitude sailing, [ 2 ] and was thus the earliest step towards the use of quantitative methods in navigation . [ 3 ] It originated with Arab navigators of the late 9th century, [ 4 ] and was employed in the Indian Ocean from the 10th century. [ 2 ] It was adopted by Indian navigators soon after, [ 5 ] and then adopted by Chinese navigators some time before the 16th century. [ 3 ]
Because Polaris is currently close to the celestial pole, its elevation is a good approximation of the latitude of the observer. The kamal consists of a rectangular wooden card about 2 by 1 inch (5.1 by 2.5 cm), to which a string with several equally spaced knots is attached through a hole in the middle of the card. The kamal is used by placing one end of the string in the teeth while the other end is held away from the body roughly parallel to the ground. The card is then moved along the string, positioned so the lower edge is even with the horizon, and the upper edge is occluding a target star, typically Polaris because its angle to the horizon does not change with longitude or time. The angle can then be measured by counting the number of knots from the teeth to the card, or a particular knot can be tied into the string if travelling to a known latitude.
it is not necessary to follow a certain standard or calculation to make your own kamal; all you need is piece of wood, string and help of a sextant or any angle measuring device for the first calibration of your personal kamal. Choose any object, preferably Polaris. Take the angle reading with the sextant, for example 24. Then take a reading with the kamal, for example 15cm as the length of the string to the board, therefore 15cm is equal to 24 degrees. You can keep making different readings the same way for different objects until you have your own standard of measurements. Helpful tip - make a calibration card and print it on the kamal board itself, for example 30cm=45 degrees, and 20cm=30 degrees.
The knots were typically tied to measure angles of one finger-width. When held at arm's length, the width of a finger measures an angle that remains fairly similar from person to person. This was widely used (and still is today) for rough angle measurements, an angle known as issabah إصبع in Arabic or a zhi 指 in Chinese (both meaning 'finger'). By modern measure, this is about 1 degree, 36 minutes, and 25 seconds, or just over 1.5 degrees. It is equal to the arcsine of the ratio of the width of the finger to the length of the arm. In Chinese navigation, the unit of jiao 角 is also used to represent a quarter 指 (an angle of 24 minutes 6 seconds).
Due to the limited width of the card, the kamal was only really useful for measuring Polaris in equatorial latitudes, where Polaris remains close to the horizon. This fact may explain why it was not common in Europe. For these higher-latitude needs somewhat more complex devices based on the same principle were used, notably the cross-staff and backstaff .
The kamal is still a tool recommended for use in sea kayaking . [ 6 ] In such an application, it can be used for estimating distances to land. The distance can be calculated from the formula
where D {\displaystyle D} is the distance to the object, S {\displaystyle S} is the size of the object observed, d {\displaystyle d} is the distance from the kamal to the observer's eye, and s {\displaystyle s} is the size of the kamal. | https://en.wikipedia.org/wiki/Kamal_(navigation) |
Kamal Quadir (born 1971) is a Bangladeshi American entrepreneur and artist best known for introducing e-commerce in Bangladesh by founding CellBazaar, [ 3 ] an electronic marketplace which, after reaching 4 million users, was acquired by Norwegian telecommunications operator Telenor in 2010. CellBazaar later was rebranded as ekhanei.com. [ 4 ] [ 5 ] He is the brother of Iqbal Quadir , who is an entrepreneur and promoter of the role of entrepreneurship and innovation in creating prosperity in low-income countries.
Quadir founded bKash in 2010, [ 6 ] which provides financial services through a network of community-based agents and existing technology, including mobile phones . [ 2 ] bKash serves 78 million verified customers in Bangladesh which is a country of 170 million people. [ 7 ]
Quadir is a founding member of Open World Initiatives , a Lausanne , Switzerland-based organization of young thinkers. He is involved with Anwarul Quadir Foundation which recognises innovations in developing countries. He is a First Mover Fellow of The Aspen Institute . In 2009, TED selected Quadir a TED Fellow [ 8 ] and the World Economic Forum recognised him as a Young Global Leader. [ 9 ]
Quadir was an intern at Insight Venture Partners in New York, led the Business Development Division of Occidental Petroleum 's initiative in Bangladesh and worked for New York City's Chamber of Commerce . He was also the co-founder and creative director of GlobeKids Inc. , an animation company.
Quadir has completed his BA from Oberlin College and MBA from the MIT Sloan School of Management . [ 10 ]
He is also an artist whose art works are in the permanent collection of the Bangladesh National Museum and the Liberation War Museum . [ citation needed ] | https://en.wikipedia.org/wiki/Kamal_Quadir |
The Kamerlingh Onnes Award is in recognition of special merits of scientists active in the field of refrigeration technology, cryogenics and more generally low-temperature science and technology. It was founded in 1948 by the Royal Dutch Association of Refrigeration (Koninklijke Nederlandse Vereniging voor Koude, KNVvK) [ 1 ] The name of the award is intended to keep the memory of Heike Kamerlingh Onnes alive. The award is assigned typically every four years and the winners get a golden medal and a certificate. | https://en.wikipedia.org/wiki/Kamerlingh_Onnes_Award |
A Kaminsky catalyst is a catalytic system for alkene polymerization . [ 1 ] Kaminsky catalysts are based on metallocenes of group 4 transition metals (Ti, Zr, Hf) activated with methylaluminoxane (MAO). These and other innovations have inspired development of new classes of catalysts that in turn led to commercialization of novel engineering polyolefins. [ 2 ]
The catalyst is named after German chemist Walter Kaminsky , who first described it in 1980 along with Hansjörg Sinn and others. [ 3 ] [ 4 ] Prior to Kaminsky's work, titanium chlorides supported on various materials were widely used (and still are) as heterogeneous catalysts for alkene polymerization. These halides are typically activated by treatment with trimethylaluminium . Kaminsky discovered that titanocene and related complexes emulated some aspects of these Ziegler–Natta catalysts but with low activity. He subsequently found that high activity could be achieved upon activation of these metallocenes with methylaluminoxane (MAO). The MAO serves two roles: (i) alkylation of the metallocene halide and (ii) abstraction of an anionic ligand (chloride or methyl) to give an electrophilic catalyst with a labile coordination site. [ 1 ] [ 5 ]
Kaminsky's discovery of well-defined, high activity homogeneous catalysts led to many innovations in the design of novel cyclopentadienyl ligands. These innovations include ansa-metallocenes , C s -symmetric fluorenyl-Cp ligands, [ 6 ] constrained geometry catalysts , [ 7 ] Some Kaminsky-inspired catalysts use of chiral metallocenes that have bridged cyclopentadienyl rings. These innovations made possible highly stereoselective (or stereoregular) polymerization of α-olefins , some of which have been commercialized. [ 2 ] | https://en.wikipedia.org/wiki/Kaminsky_catalyst |
In mathematical logic , the Kanamori–McAloon theorem , due to Kanamori & McAloon (1987) , gives an example of an incompleteness in Peano arithmetic , similar to that of the Paris–Harrington theorem . They showed that a certain finitistic theorem in Ramsey theory is not provable in Peano arithmetic (PA).
Given a set s ⊆ N {\displaystyle s\subseteq \mathbb {N} } of non-negative integers, let min ( s ) {\displaystyle \min(s)} denote the minimum element of s {\displaystyle s} . Let [ X ] n {\displaystyle [X]^{n}} denote the set of all n -element subsets of X {\displaystyle X} .
A function f : [ X ] n → N {\displaystyle f:[X]^{n}\rightarrow \mathbb {N} } where X ⊆ N {\displaystyle X\subseteq \mathbb {N} } is said to be regressive if f ( s ) < min ( s ) {\displaystyle f(s)<\min(s)} for all s {\displaystyle s} not containing 0.
The Kanamori–McAloon theorem states that the following proposition, denoted by ( ∗ ) {\displaystyle (*)} in the original reference, is not provable in PA:
This mathematical logic -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kanamori–McAloon_theorem |
A kanban board is one of the tools that can be used to implement kanban to manage work at a personal or organizational level.
Kanban boards visually depict work at various stages of a process using cards to represent work items and columns to represent each stage of the process. Cards are moved from left to right to show progress and to help coordinate teams performing the work. A kanban board may be divided into horizontal "swimlanes" representing different kinds of work or different teams performing the work.
Kanban boards can be used for knowledge work or manufacturing processes. [ 1 ]
Simple boards have columns for "waiting", "in progress", and "completed" or "to-do", "doing", and "done". Complex kanban boards can be created that subdivide "in progress" work into multiple columns to visualise the flow of work across a whole value stream map .
According to the Project Management Institute , a kanban board is a "visualization tool that shows work in progress to help identify bottlenecks and overcommitments, thereby allowing the team to optimize the workflow." [ 2 ]
Kanban can be used to organize many areas of an organization and can be designed accordingly. The simplest kanban board consists of three columns: "to-do", "doing" and "done", [ 3 ] though some additional detail such as WiP limits is needed to fully support the Kanban Method. [ 4 ] Business functions that use kanban boards include:
A growing number of personal and project management applications incorporate kanban boards into their software, including: | https://en.wikipedia.org/wiki/Kanban_board |
The Kane quantum computer is a proposal for a scalable quantum computer proposed by Bruce Kane in 1998, [ 1 ] who was then at the University of New South Wales . Often thought of as a hybrid between quantum dot and nuclear magnetic resonance (NMR) quantum computers, the Kane computer is based on an array of individual phosphorus donor atoms embedded in a pure silicon lattice. Both the nuclear spins of the donors and the spins of the donor electrons participate in the computation.
Unlike many quantum computation schemes, the Kane quantum computer is in principle scalable to an arbitrary number of qubits. This is possible because qubits may be individually addressed by electrical means.
The original proposal calls for phosphorus donors to be placed in an array with a spacing of 20 nm , approximately 20 nm below the surface. An insulating oxide layer is grown on top of the silicon. Metal A gates are deposited on the oxide above each donor, and J gates between adjacent donors.
The phosphorus donors are isotopically pure 31 P, which have a nuclear spin of 1/2. The silicon substrate is isotopically pure 28 Si which has nuclear spin 0. Using the nuclear spin of the P donors as a method to encode qubits has two major advantages. Firstly, the state has an extremely long decoherence time, perhaps on the order of 10 18 seconds at millikelvin temperatures. Secondly, the qubits may be manipulated by applying an oscillating magnetic field , as in typical NMR proposals. By altering the voltage on the A gates, it should be possible to alter the Larmor frequency of individual donors. This allows them to be addressed individually, by bringing specific donors into resonance with the applied oscillating magnetic field.
Nuclear spins alone will not interact significantly with other nuclear spins 20 nm away. Nuclear spin is useful to perform single-qubit operations, but to make a quantum computer, two-qubit operations are also required. This is the role of electron spin in this design. Under A-gate control, the spin is transferred from the nucleus to the donor electron. Then, a potential is applied to the J gate, drawing adjacent donor electrons into a common region, greatly enhancing the interaction between the neighbouring spins. By controlling the J gate voltage, two-qubit operations are possible.
Kane's proposal for readout was to apply an electric field to encourage spin-dependent tunneling of an electron to transform two neutral donors to a D + –D – state, that is, one where two electrons associate with the same donor. The charge excess is then detected using a single-electron transistor . This method has two major difficulties. Firstly, the D – state has strong coupling with the environment and hence a short decoherence time. Secondly and perhaps more importantly, it's not clear that the D – state has a sufficiently long lifetime to allow for readout—the electron tunnels into the conduction band .
Since Kane's proposal, under the guidance of Robert Clark and now Michelle Simmons , pursuing realisation of the Kane quantum computer has become the primary quantum computing effort in Australia . [ 2 ] Theorists have put forward a number of proposals for improved readout. Experimentally, atomic-precision deposition of phosphorus atoms has been achieved using a scanning tunneling microscope (STM) technique in 2003. [ 3 ] Detection of the movement of single electrons between small, dense clusters of phosphorus donors has also been achieved. The group remains optimistic that a practical large-scale quantum computer can be built. Other groups believe that the idea needs to be modified. [ 4 ]
In 2020, Andrea Morello and others demonstrated that an antimony nucleus (with eight spin states) embedded in silicon could be controlled using an electric field, rather than a magnetic field. [ 5 ] | https://en.wikipedia.org/wiki/Kane_quantum_computer |
In statistics , a Kaniadakis distribution (also known as κ-distribution ) is a statistical distribution that emerges from the Kaniadakis statistics . [ 1 ] There are several families of Kaniadakis distributions related to different constraints used in the maximization of the Kaniadakis entropy, such as the κ-Exponential distribution , κ-Gaussian distribution , Kaniadakis κ-Gamma distribution and κ-Weibull distribution . The κ-distributions have been applied for modeling a vast phenomenology of experimental statistical distributions in natural or artificial complex systems , such as, in epidemiology , [ 2 ] quantum statistics , [ 3 ] [ 4 ] [ 5 ] in astrophysics and cosmology , [ 6 ] [ 7 ] [ 8 ] in geophysics , [ 9 ] [ 10 ] [ 11 ] in economy , [ 12 ] [ 13 ] [ 14 ] in machine learning . [ 15 ]
The κ-distributions are written as function of the κ-deformed exponential, taking the form
enables the power-law description of complex systems following the consistent κ-generalized statistical theory ., [ 16 ] [ 17 ] where exp κ ( x ) = ( 1 + κ 2 x 2 + κ x ) 1 / κ {\displaystyle \exp _{\kappa }(x)=({\sqrt {1+\kappa ^{2}x^{2}}}+\kappa x)^{1/\kappa }} is the Kaniadakis κ-exponential function.
The κ-distribution becomes the common Boltzmann distribution at low energies, while it has a power-law tail at high energies, the feature of high interest of many researchers.
The Kaniadakis distribution of Type IV (or κ-Distribution Type IV ) is a three-parameter family of continuous statistical distributions . [ 1 ]
The κ-Distribution Type IV distribution has the following probability density function :
valid for x ≥ 0 {\displaystyle x\geq 0} , where 0 ≤ | κ | < 1 {\displaystyle 0\leq |\kappa |<1} is the entropic index associated with the Kaniadakis entropy , β > 0 {\displaystyle \beta >0} is the scale parameter, and α > 0 {\displaystyle \alpha >0} is the shape parameter.
The cumulative distribution function of κ-Distribution Type IV assumes the form:
The κ-Distribution Type IV does not admit a classical version, since the probability function and its cumulative reduces to zero in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} .
Its moment of order m {\displaystyle m} given by
The moment of order m {\displaystyle m} of the κ-Distribution Type IV is finite for m < 2 α {\displaystyle m<2\alpha } . | https://en.wikipedia.org/wiki/Kaniadakis_distribution |
Kaniadakis statistics (also known as κ-statistics ) is a generalization of Boltzmann–Gibbs statistical mechanics , [ 1 ] based on a relativistic [ 2 ] [ 3 ] [ 4 ] generalization of the classical Boltzmann–Gibbs–Shannon entropy (commonly referred to as Kaniadakis entropy or κ-entropy). Introduced by the Greek Italian physicist Giorgio Kaniadakis in 2001, [ 5 ] κ-statistical mechanics preserve the main features of ordinary statistical mechanics and have attracted the interest of many researchers in recent years. The κ-distribution is currently considered one of the most viable candidates for explaining complex physical , [ 6 ] [ 7 ] natural or artificial systems involving power-law tailed statistical distributions . Kaniadakis statistics have been adopted successfully in the description of a variety of systems in the fields of cosmology , astrophysics , [ 8 ] [ 9 ] condensed matter , quantum physics , [ 10 ] [ 11 ] seismology , [ 12 ] [ 13 ] genomics , [ 14 ] [ 15 ] economics , [ 16 ] [ 17 ] epidemiology , [ 18 ] and many others.
The mathematical formalism of κ-statistics is generated by κ-deformed functions, especially the κ-exponential function.
The Kaniadakis exponential (or κ-exponential) function is a one-parameter generalization of an exponential function, given by:
with exp − κ ( x ) = exp κ ( x ) {\displaystyle \exp _{-\kappa }(x)=\exp _{\kappa }(x)} .
The κ-exponential for 0 < κ < 1 {\displaystyle 0<\kappa <1} can also be written in the form:
The first five terms of the Taylor expansion of exp κ ( x ) {\displaystyle \exp _{\kappa }(x)} are given by:
exp κ ( x ) = 1 + x + x 2 2 + ( 1 − κ 2 ) x 3 3 ! + ( 1 − 4 κ 2 ) x 4 4 ! + ⋯ {\displaystyle \exp _{\kappa }(x)=1+x+{\frac {x^{2}}{2}}+(1-\kappa ^{2}){\frac {x^{3}}{3!}}+(1-4\kappa ^{2}){\frac {x^{4}}{4!}}+\cdots }
where the first three are the same as a typical exponential function .
Basic properties
The κ-exponential function has the following properties of an exponential function:
For a real number r {\displaystyle r} , the κ-exponential has the property:
The Kaniadakis logarithm (or κ-logarithm) is a relativistic one-parameter generalization of the ordinary logarithm function,
with ln − κ ( x ) = ln κ ( x ) {\displaystyle \ln _{-\kappa }(x)=\ln _{\kappa }(x)} , which is the inverse function of the κ-exponential:
The κ-logarithm for 0 < κ < 1 {\displaystyle 0<\kappa <1} can also be written in the form:
ln κ ( x ) = 1 κ sinh ( κ ln ( x ) ) {\displaystyle \ln _{\kappa }(x)={\frac {1}{\kappa }}\sinh {\Big (}\kappa \ln(x){\Big )}}
The first three terms of the Taylor expansion of ln κ ( x ) {\displaystyle \ln _{\kappa }(x)} are given by:
following the rule
with b 1 ( κ ) = 1 {\displaystyle b_{1}(\kappa )=1} , and
where b n ( 0 ) = 1 {\displaystyle b_{n}(0)=1} and b n ( − κ ) = b n ( κ ) {\displaystyle b_{n}(-\kappa )=b_{n}(\kappa )} . The two first terms of the Taylor expansion of ln κ ( x ) {\displaystyle \ln _{\kappa }(x)} are the same as an ordinary logarithmic function .
Basic properties
The κ-logarithm function has the following properties of a logarithmic function:
For a real number r {\displaystyle r} , the κ-logarithm has the property:
For any x , y ∈ R {\displaystyle x,y\in \mathbb {R} } and | κ | < 1 {\displaystyle |\kappa |<1} , the Kaniadakis sum (or κ-sum) is defined by the following composition law:
that can also be written in form:
where the ordinary sum is a particular case in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} : x ⊕ 0 y = x + y {\displaystyle x{\stackrel {0}{\oplus }}y=x+y} .
The κ-sum, like the ordinary sum, has the following properties:
The κ-difference ⊖ κ {\displaystyle {\stackrel {\kappa }{\ominus }}} is given by x ⊖ κ y = x ⊕ κ ( − y ) {\displaystyle x{\stackrel {\kappa }{\ominus }}y=x{\stackrel {\kappa }{\oplus }}(-y)} .
The fundamental property exp κ ( − x ) exp κ ( x ) = 1 {\displaystyle \exp _{\kappa }(-x)\exp _{\kappa }(x)=1} arises as a special case of the more general expression below: exp κ ( x ) exp κ ( y ) = e x p κ ( x ⊕ κ y ) {\displaystyle \exp _{\kappa }(x)\exp _{\kappa }(y)=exp_{\kappa }(x{\stackrel {\kappa }{\oplus }}y)}
Furthermore, the κ-functions and the κ-sum present the following relationships:
For any x , y ∈ R {\displaystyle x,y\in \mathbb {R} } and | κ | < 1 {\displaystyle |\kappa |<1} , the Kaniadakis product (or κ-product) is defined by the following composition law:
where the ordinary product is a particular case in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} : x ⊗ 0 y = x × y = x y {\displaystyle x{\stackrel {0}{\otimes }}y=x\times y=xy} .
The κ-product, like the ordinary product, has the following properties:
The κ-division ⊘ κ {\displaystyle {\stackrel {\kappa }{\oslash }}} is given by x ⊘ κ y = x ⊗ κ y ¯ {\displaystyle x{\stackrel {\kappa }{\oslash }}y=x{\stackrel {\kappa }{\otimes }}{\overline {y}}} .
The κ-sum ⊕ κ {\displaystyle {\stackrel {\kappa }{\oplus }}} and the κ-product ⊗ κ {\displaystyle {\stackrel {\kappa }{\otimes }}} obey the distributive law: z ⊗ κ ( x ⊕ κ y ) = ( z ⊗ κ x ) ⊕ κ ( z ⊗ κ y ) {\displaystyle z{\stackrel {\kappa }{\otimes }}(x{\stackrel {\kappa }{\oplus }}y)=(z{\stackrel {\kappa }{\otimes }}x){\stackrel {\kappa }{\oplus }}(z{\stackrel {\kappa }{\otimes }}y)} .
The fundamental property ln κ ( 1 / x ) = − ln κ ( x ) {\displaystyle \ln _{\kappa }(1/x)=-\ln _{\kappa }(x)} arises as a special case of the more general expression below:
The Kaniadakis differential (or κ-differential) of x {\displaystyle x} is defined by:
So, the κ-derivative of a function f ( x ) {\displaystyle f(x)} is related to the Leibniz derivative through:
where γ κ ( x ) = 1 + κ 2 x 2 {\displaystyle \gamma _{\kappa }(x)={\sqrt {1+\kappa ^{2}x^{2}}}} is the Lorentz factor. The ordinary derivative d f ( x ) d x {\displaystyle {\frac {\mathrm {d} f(x)}{\mathrm {d} x}}} is a particular case of κ-derivative d f ( x ) d κ x {\displaystyle {\frac {\mathrm {d} f(x)}{\mathrm {d} _{\kappa }x}}} in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} .
The Kaniadakis integral (or κ-integral) is the inverse operator of the κ-derivative defined through
which recovers the ordinary integral in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} .
The Kaniadakis cyclic trigonometry (or κ-cyclic trigonometry) is based on the κ-cyclic sine (or κ-sine) and κ-cyclic cosine (or κ-cosine) functions defined by:
where the κ-generalized Euler formula is
The κ-cyclic trigonometry preserves fundamental expressions of the ordinary cyclic trigonometry, which is a special case in the limit κ → 0, such as:
The κ-cyclic tangent and κ-cyclic cotangent functions are given by:
The κ-cyclic trigonometric functions become the ordinary trigonometric function in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} .
κ-Inverse cyclic function
The Kaniadakis inverse cyclic functions (or κ-inverse cyclic functions) are associated to the κ-logarithm:
The Kaniadakis hyperbolic trigonometry (or κ-hyperbolic trigonometry) is based on the κ-hyperbolic sine and κ-hyperbolic cosine given by:
where the κ-Euler formula is
The κ-hyperbolic tangent and κ-hyperbolic cotangent functions are given by:
The κ-hyperbolic trigonometric functions become the ordinary hyperbolic trigonometric functions in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} .
From the κ-Euler formula and the property exp κ ( − x ) exp κ ( x ) = 1 {\displaystyle \exp _{\kappa }(-x)\exp _{\kappa }(x)=1} the fundamental expression of κ-hyperbolic trigonometry is given as follows:
κ-Inverse hyperbolic function
The Kaniadakis inverse hyperbolic functions (or κ-inverse hyperbolic functions) are associated to the κ-logarithm:
in which are valid the following relations:
The κ-cyclic and κ-hyperbolic trigonometric functions are connected by the following relationships:
The Kaniadakis statistics is based on the Kaniadakis κ-entropy, which is defined through:
where p = { p i = p ( x i ) ; x ∈ R ; i = 1 , 2 , . . . , N ; ∑ i p i = 1 } {\displaystyle p=\{p_{i}=p(x_{i});x\in \mathbb {R} ;i=1,2,...,N;\sum _{i}p_{i}=1\}} is a probability distribution function defined for a random variable X {\displaystyle X} , and 0 ≤ | κ | < 1 {\displaystyle 0\leq |\kappa |<1} is the entropic index.
The Kaniadakis κ-entropy is thermodynamically and Lesche stable [ 19 ] [ 20 ] and obeys the Shannon-Khinchin axioms of continuity, maximality, generalized additivity and expandability.
A Kaniadakis distribution (or κ -distribution ) is a probability distribution derived from the maximization of Kaniadakis entropy under appropriate constraints. In this regard, several probability distributions emerge for analyzing a wide variety of phenomenology associated with experimental power-law tailed statistical distributions.
The Kaniadakis Laplace transform (or κ-Laplace transform) is a κ-deformed integral transform of the ordinary Laplace transform . The κ-Laplace transform converts a function f {\displaystyle f} of a real variable t {\displaystyle t} to a new function F κ ( s ) {\displaystyle F_{\kappa }(s)} in the complex frequency domain, represented by the complex variable s {\displaystyle s} . This κ-integral transform is defined as: [ 21 ]
The inverse κ-Laplace transform is given by:
The ordinary Laplace transform and its inverse transform are recovered as κ → 0 {\displaystyle \kappa \rightarrow 0} .
Properties
Let two functions f ( t ) = L κ − 1 { F κ ( s ) } ( t ) {\displaystyle f(t)={\cal {L}}_{\kappa }^{-1}\{F_{\kappa }(s)\}(t)} and g ( t ) = L κ − 1 { G κ ( s ) } ( t ) {\displaystyle g(t)={\cal {L}}_{\kappa }^{-1}\{G_{\kappa }(s)\}(t)} , and their respective κ-Laplace transforms F κ ( s ) {\displaystyle F_{\kappa }(s)} and G κ ( s ) {\displaystyle G_{\kappa }(s)} , the following table presents the main properties of κ-Laplace transform: [ 21 ]
The κ-Laplace transforms presented in the latter table reduce to the corresponding ordinary Laplace transforms in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} .
The Kaniadakis Fourier transform (or κ-Fourier transform) is a κ-deformed integral transform of the ordinary Fourier transform , which is consistent with the κ-algebra and the κ-calculus. The κ-Fourier transform is defined as: [ 22 ]
which can be rewritten as
where x { κ } = 1 κ a r c s i n h ( κ x ) {\displaystyle x_{\{\kappa \}}={\frac {1}{\kappa }}\,{\rm {arcsinh}}\,(\kappa \,x)} and ω { κ } = 1 κ a r c s i n h ( κ ω ) {\displaystyle \omega _{\{\kappa \}}={\frac {1}{\kappa }}\,{\rm {arcsinh}}\,(\kappa \,\omega )} . The κ-Fourier transform imposes an asymptotically log-periodic behavior by deforming the parameters x {\displaystyle x} and ω {\displaystyle \omega } in addition to a damping factor, namely 1 + κ 2 x 2 {\displaystyle {\sqrt {1+\kappa ^{2}\,x^{2}}}} .
The kernel of the κ-Fourier transform is given by:
h κ ( x , ω ) = exp ( − i x { κ } ω { κ } ) 1 + κ 2 x 2 {\displaystyle h_{\kappa }(x,\omega )={\frac {\exp(-i\,x_{\{\kappa \}}\,\omega _{\{\kappa \}})}{\sqrt {1+\kappa ^{2}\,x^{2}}}}}
The inverse κ-Fourier transform is defined as: [ 22 ]
Let u κ ( x ) = 1 κ cosh ( κ ln ( x ) ) {\displaystyle u_{\kappa }(x)={\frac {1}{\kappa }}\cosh {\Big (}\kappa \ln(x){\Big )}} , the following table shows the κ-Fourier transforms of several notable functions: [ 22 ]
The κ-deformed version of the Fourier transform preserves the main properties of the ordinary Fourier transform, as summarized in the following table.
The properties of the κ-Fourier transform presented in the latter table reduce to the corresponding ordinary Fourier transforms in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} . | https://en.wikipedia.org/wiki/Kaniadakis_statistics |
Kanishka Biswas is an Associate Professor in the New Chemistry Unit at Jawaharlal Nehru Centre for Advanced Scientific Research , Bangalore with research interests focused on renewable energy and clean environment. The areas in which he has worked include solid state inorganic chemistry of metal chalcogenides, thermoelectric materials, 2D layered materials, topological insulators. [ 1 ] [ 2 ]
Kanishk Biswas was born on 25 October 1982. [ 3 ] Biswas obtained his MS degree in chemical science from Indian Institute of Science , Bangalore in 2006 and PhD degree from the same institute in 2009 both under the supervision of C. N. R. Rao . He had spent three years (June 2006 - May 2009) as Postdoctoral Fellow under the supervision of Mercouri Kanatzidis at Northwestern University, Evanston, IL, USA
The honours and awards conferred on Kanishka Biswas include: [ 4 ] | https://en.wikipedia.org/wiki/Kanishka_Biswas |
Kano River Project is a modern integrated agricultural land use development in Northern Nigeria . River Kano also locally called Kogin Kano. The project is a large scale irrigation project developed under the authority of Hadejia-Juma’are River Basin Development Authority. [ 1 ]
The project was started in 1971, and the initial research was conducted in 1976–77 and restricted to 3000 acres. [ 2 ] [ 3 ]
The Kano River project irrigation was commission by the former vice president, Prof. Yemi Osinbajo . It was commission in 2023. [ 4 ] [ 5 ]
The idea of the project might have started in the 1960s following extensive land use surveys and technical assistance by the British Overseas Development Authority (ODA) and USAID . The principal engineering partners of KRP is Netherlands Engineering and Construction Company (NEDECCO). [ 6 ] The project started in earnest after the Nigerian civil war in the late 1960s. Kano River Project (KRP) covers an extensive floodplain coveringRiver Kano, River Challawa, and their convergence through the Hadejia and Jama'are Rivers. The floodplains of these were only locally tapped unless the development of the KRP. The construction of the Tiga and Challawa Gorge dams upstream was the backbone of KRP a development that stalled flooding. The maximum extent of flooding has declined from 300,000 ha in the 1960s to around 70,000 to 100,000 ha. [ 7 ] The Federal Government of Nigeria took over the custody of KRP through the Hadejia Jama'are River Basin Development Authority . [ 8 ]
Other officials who participated at the commissioning were the Fair Chief for Jigawa State Service of Water Assets, Hon. Ibrahim Muhammed Garba, Birnin Kudu Nearby Government Executive, Magagi Yusuf, State Government authorities as well as certain Chiefs and Agent Heads of the Bureaucratic Service of Water Assets and Sterilization, with local area leaders, women, youths, and children in the community. [ 2 ] [ 9 ]
KRP is meant to be a large scale agricultural project with focus on irrigation. This major irrigation scheme is planned to cover 66,000 ha. KRP is sub divided into categories, for now only 22,000 ha or KRP 1 is being developed. The project is dependent on Tiga Dam , Bagauda Dam , and Challawa Dam and the floodplains around them. It is suggested that the net economic benefits of the floodplain (agriculture, fishing, fuelwood) were at least US$32 per 1000 m 3 of water (at 1989 prices). [ 7 ] UNEP finds that, the returns per crops grown in the Kano River Project were at most only US$1.73 per 1000 m 3 and when the operational costs are included, the net benefits of the Project are reduced to US$0.04 per 1000 m 3 . The development of KRP has changed the economic conditions of many local people who are actively engaged in irrigation activities. Various cash crops are produced under the KRP irrigation projects. These include tomato, pepper, rice, wheat, corn, okro and many others grown for local consumption. The produce are mainly sent to local markets in Kano and to many places in southern Nigeria.
[ 10 ]
KRP is challenged for causing landscape desiccation in the Lake Chad basin through impounding of water in dams. Release of water from dams also causes flooding downstream. KRP cannot be a success considering the fact that since its commencement in 1960s/1970s even the KRP 1 is yet to be fully developed. Another challenge is land tenure, the way and manner land is managed is not transparent. Management of water is also one of the challenges plaguing efficiency and sustainability of the KRP. Pollution is also a critical ecological challenge. The major source of pollution are agrochemical overdose and industrial effluents. [ citation needed ] | https://en.wikipedia.org/wiki/Kano_River_Project |
The Kansas City standard ( KCS ), or Byte standard , is a data storage protocol for standard cassette tapes or other audio recording media at 300 bits per second . It originated in a symposium sponsored by Byte magazine in November 1975 in Kansas City, Missouri to develop a standard for the storage of digital microcomputer data on inexpensive consumer quality cassettes. The first systems based on the standard appeared in 1976.
One variation on the basic standard is CUTS, which is identical at 300 bit/s , but with an optional 1200 bit/s mode. CUTS is the default encoding used by several later machine families, including those from Acorn and the MSX . MSX added a higher 2400 bit/s mode that is otherwise similar. The 1200 bit/s mode of CUTS was used as the standard for cross-platform BASICODE distribution.
KCS originated from the earliest days of the microcomputer revolution, among other prolific protocols. Most home computers of the era have unique formats that are incompatible with anything.
Early microcomputers generally use punched tape for program storage, an expensive option. Computer consultant Jerry Ogdin conceived the use of audio tones on a cassette to replace the paper tapes. He took the idea to Les Solomon, editor of Popular Electronics magazine, who was similarly frustrated by punched tapes. In September 1975, the two co-authored an article on the HITS (Hobbyists' Interchange Tape System), using two tones to represent 1s and 0s. Soon after, several manufacturers started using similar approaches, all incompatible. [ 1 ]
Wayne Green , who had just started Byte magazine, wanted all the manufacturers to collaborate on a single cassette standard. He organized a two-day meeting on 7–8 November 1975 in Kansas City, Missouri . [ 2 ] The participants settled on a system based on Don Lancaster 's design. After the meeting, Lee Felsenstein (of Processor Technology ) and Harold Mauch (of Percom ) wrote the standard, which was published in Byte magazine's first issue. [ 3 ]
A KCS cassette interface is similar to a modem connected to a serial port . The 1s and 0s from the serial port are converted to audio tones using audio frequency-shift keying (AFSK). A "0" bit is represented as four cycles of a 1200 Hz sine wave , and a "1" bit as eight cycles of 2400 Hz. This gives a data rate of 300 baud . Each frame starts with one "0" start bit, followed by eight data bits (least significant bit first) followed by two "1" stop bits, so each frame is 11 bits, for a data rate of 27 + 3 ⁄ 11 bytes per second.
The February 1976 issue of Byte has a report [ 4 ] on the symposium, and the March issue features two hardware examples by Don Lancaster [ 5 ] and Harold Mauch. [ 6 ] The 300 baud rate is reliable, but slow; a typical 8-kilobyte BASIC program takes five minutes to load. Most audio cassette circuits support higher speeds.
According to Solomon, the efforts were unsuccessful: "Unfortunately, it didn't last long; before the month ended, everyone went back to his own tape standard and the recording confusion got worse." [ 1 ]
The participants of the Kansas City symposium include these: [ 4 ]
The original standard records data as "marks" (one) and "spaces" (zero). A mark bit consists of eight cycles at a frequency of 2400 Hz , and a space bit consists of four cycles at a frequency of 1200 Hz. A word , usually one byte (8 bits) long, is recorded in little endian order, which is least significant bit first. 7-bit words are followed by a parity bit . As each 8-bit byte is encoded into 11-bits for transmission, the total throughput is 27 bytes per second . [ 7 ]
The Tarbell Cassette Interface , which, according to early PC retailer Stan Veit, "became a de facto standard for S-100 computers", supported the Kansas City Standard in addition to the Tarbell "native" mode ("Tarbell standard"). [ 8 ] The Tarbell format is very different than the KC standard and normally operated at 187 bytes per second, and able to read as high as 540 bytes per second.
Processor Technology developed the popular CUTS (Computer Users' Tape Standard), which works at either 300 or 1200 baud. The 1200 baud version simply reduced the number of cycles per bit, with a mark being two cycles of 2400 and a space being one cycle at 1200. It was otherwise the same as the original KC standard, with a single "0" for the start bit and two trailing "1"s as stop bits, giving an effective data rate of 873 bits per second. The company provided the S-100 bus CUTS Tape I/O interface board, which offers both CUTS and Kansas City standard support to any S-100 system.
The Quick CUTS standard proposed by Bob Cottis and Mike Blandford and published in the Amateur Computer Club newsletter operated at 2400 baud, encoding "0" as a half-cycle of 1200 Hz and "1" as a whole cycle of 2400 Hz. The receiver was self-clocking using a phase-locked loop . [ 9 ] Published in 1978, it predates the 1982 patent for the similar coded mark inversion proposal.
Acorn Computers Ltd used a variation of 1200 baud CUTS for the BBC Micro , [ 10 ] which removed one of the two stop bits to improve the throughput to 960 bits per second . Additionally, the machines used a format for data that broke files into 256-byte blocks which included sequence numbers; if there was an error during a read, the user could rewind the tape just enough to get past the bad block and try again, the system would ignore those block that had been successfully loaded previously.
MSX supports both the 1200 baud variation of the CUTS standard, as well as a new 2400 baud variant which encodes a "0" bit as one cycle of a 2400 Hz wave and a "1" bit as two cycles of a 4800 Hz wave. [ 11 ] This gives an effective rate of approximately 1,745 bits per second. The machine's BIOS can read data at up to 3600 baud from an ideal audio source.
Several use the S-100 bus.
In August 1976 at the Personal Computing show in Atlantic City, New Jersey , Bob Marsh of Processor Technology approached Bob Jones, the publisher of Interface Age magazine, about pressing software onto vinyl records . Processor Technology provided an Intel 8080 program to be recorded. This test record did not work and Processor Technology was unable to devote more time to the effort. [ 14 ] Daniel Meyer and Gary Kay of Southwest Technical Products (SWTPC) arranged for Robert Uiterwyk to provide his 4K BASIC interpreter program for the Motorola 6800 microprocessor. The idea was to record the program on audio tape in the Kansas City format and then make a master record from the tape. Eva-Tone made Soundsheets on thin vinyl that would hold one song, these were inexpensive and could be bound in a magazine. [ 15 ] Bill Turner [ 16 ] and Bill Blomgren [ 17 ] of MicroComputerSystems Inc. along with Bob Jones [8] of Interface Age and Bud Schamburger of Holiday Inn worked with Eva-Tone and developed a successful process. The intermediate stage of recording to tape produced dropouts , so a SWTPC AC-30 [ 18 ] cassette interface was connected directly to the record cutting equipment. The May 1977 issue of Interface Age contains the first "Floppy ROM", a 33 1 ⁄ 3 RPM record containing about six minutes of Kansas City standard audio. The September 1978 Floppy ROM Number 5 has two sides: Apple BASIC , "the automated dress pattern", and IAPS format, "A program for writing letters". | https://en.wikipedia.org/wiki/Kansas_City_standard |
Kansei engineering ( Japanese : 感性工学 kansei kougaku , emotional or affective engineering) aims at the development or improvement of products and services by translating the customer's psychological feelings and needs into the domain of product design (i.e. parameters). It was founded by Mitsuo Nagamachi , professor emeritus of Hiroshima University (also former Dean of Hiroshima International University and CEO of International Kansei Design Institute ). Kansei engineering parametrically links the customer's emotional responses (i.e. physical and psychological) to the properties and characteristics of a product or service. In consequence, products can be designed to bring forward the intended feeling.
It has been adopted as one of the topics for professional development by the Royal Statistical Society .
Product design has become increasingly complex as products contain more functions and have to meet increasing demands such as user-friendliness, manufacturability and ecological considerations. With a shortened product lifecycle , development costs are likely to increase. Since errors in the estimations of market trends can be very expensive, companies therefore perform benchmarking studies that compare with competitors on strategic, process, marketing, and product levels. However, success in a certain market segment not only requires knowledge about the competitors and the performance of competing products, but also about the impressions which a product leaves to the customer. The latter requirement becomes much more important as products and companies are becoming mature. Customers purchase products based on subjective terms such as brand image , reputation, design, impression etc.. A large number of manufacturers have started to consider such subjective properties and develop their products in a way that conveys the company image. A reliable instrument is therefore needed: an instrument which can predict the reception of a product on the market before the development costs become too large.
This demand has triggered the research dealing with the translation of the customer's subjective, hidden needs into concrete products. Research is done foremost in Asia, including Japan and Korea. In Europe, a network has been forged under the 6th EU framework. This network refers to the new research field as " emotional design " or "affective engineering". [ 1 ]
People want to use products that are functional at the physical level, usable at the psychological level and attractive at the emotional level [ citation needed ] . Affective engineering is the study of the interactions between the customer and the product at that third level. It focuses on the relationships between the physical traits of a product and its affective influence on the user. Thanks to this field of research, it is possible to gain knowledge on how to design more attractive products and make the customers satisfied.
Methods in affective engineering (or Kansei engineering) is one of the major areas of ergonomics (human factor engineering) [ citation needed ] . The study of integrating affective values in artifacts is not new at all. Already in the 18th century philosophers such as Baumgarten and Kant established the area of aesthetics. In addition to pure practical values, artifacts always also had an affective component. One example is jewellery found in excavations from the Stone Ages. The period of Renaissance is also a good example.
In the middle of the 20th century, the idea of aesthetics was deployed in scientific contexts. Charles E. Osgood developed his semantic differential method in which he quantified the peoples' perceptions of artifacts. Some years later, in 1960, Professors Shigeru Mizuno and Yoji Akao developed an engineering approach in order to connect peoples' needs to product properties. This method was called quality function deployment (QFD). Another method, the Kano model , was developed in the field of quality in the early 1980s by Professor Noriaki Kano , of Tokyo University. Kano's model is used to establish the importance of individual product features for the customer's satisfaction and hence it creates the optimal requirement for process oriented product development activities. A pure marketing technique is conjoint analysis . Conjoint analysis estimates the relative importance of a product's attributes by analysing the consumer's overall judgment of a product or service. A more artistic method is called Semantic description of environments. It is mainly a tool for examining how a single person or a group of persons experience a certain (architectural) environment.
Although all of these methods are concerned with subjective impact, none of them can translate this impact to design parameters sufficiently. This can, however, be accomplished by Kansei engineering. Kansei engineering (KE) has been used as a tool for affective engineering. It was developed in the early 70s in Japan and is now [ when? ] widely spread among Japanese companies. In the middle of the 90s, the method spread to the United States, but cultural differences may have prevented the method to enfold its whole potential.
As mentioned above, Kansei engineering can be considered as a methodology within the research field of 'affective engineering'. Some researchers have identified the content of the methodology. Shimizu et al. state that 'Kansei Engineering is used as a tool for product development and the basic principles behind it are the following: identification of product properties and correlation between those properties and the design characteristics'.
According to Nagasawa, one of the forerunners of Kansei engineering, there are three focal points in the method:
Source: [ 2 ]
Different types of Kansei engineering are identified and applied in various contexts. Schütte examined different types of Kansei engineering and developed a general model covering the contents of Kansei engineering.
Domain in this context describes the overall idea behind an assembly of products, i.e. the product type in general. Choosing the domain includes the definition of the intended target group and user type, market-niche and type, and the product group in question. Choosing and defining the domain are carried out on existing products, concepts and on design solutions yet unknown. From this, a domain description is formulated, serving as the basis for further evaluation. The process is necessary and has been described by Schütte in detail in a couple of publications.
The expression Semantic space was addressed for the first time by Osgood et al.. He posed that every artifact can be described in a certain vector space defined by semantic expressions (words). This is done by collecting a large number of words that describe the domain. Suitable sources are pertinent literature, commercials, manuals, specification list, experts etc. The number of the words gathered varies according to the product, typically between 100 and 1000 words. In a second step the words are grouped using manual (e.g. Affinity diagram) [ 3 ] or mathematical methods (e.g. factor and/or cluster analysis). [ 4 ] Finally a few representing words are selected from this spanning the Semantic Space. These words are called "Kansei words" or "Kansei Engineering words".
The next step is to span the Space of Product Properties, which is similar to the Semantic Space. The Space of Product Properties collects products representing the domain, identifies key features and selects product properties for further evaluation.
The collection of products representing the domain is done from different sources such as existing products, customer suggestions, possible technical solutions and design concepts etc. The key features are found using specification lists for the products in question. To select properties for further evaluation, a Pareto-diagram [ 3 ] can assist the decision between important and less important features.
Synthesis
In the synthesis step, the Semantic Space and the Space of Properties are linked together, as displayed in Figure 3. Compared to other methods in Affective Engineering, Kansei engineering is the only method that can establish and quantify connections between abstract feelings and technical specifications. For every Kansei word a number of product properties are found, affecting the Kansei word.
The research into constructing these links has been a core part of Nagamachi's work with Kansei engineering in the last few years. Nowadays, a number of different tools is available. Some of the most common tools are :
After doing the necessary stages, the final step of validation remains. This is done in order to check if the prediction model is reliable and realistic. However, in case of prediction model failure, it is necessary to update the Space of Properties and the Semantic Space, and consequently refine the model.
The process of refinement is difficult due to the shortage of methods. This shows the need of new tools to be integrated. The existing tools can partially be found in the previously mentioned methods for the synthesis.
Kansei engineering has always been a statistically and mathematically advanced methodology. Most types require good expert knowledge and a reasonable amount of experience to carry out the studies sufficiently. This has also been the major obstacle for a widespread application of Kansei engineering.
In order to facilitate application some software packages have been developed in the recent years, most of them in Japan. There are two different types of software packages available: User consoles and data collection and analysis tools. User consoles are software programs that calculate and propose a product design based on the users' subjective preferences (Kanseis). However, such software requires a database that quantifies the connections between Kanseis and the combination of product attributes. For building such databases, data collection and analysis tools can be used. This part of the paper demonstrates some of the tools. There are many more tools used in companies and universities, which might not be available to the public.
User consoles
As described above, Kansei data collection and analysis is often complex and connected with statistical analysis. Depending on which synthesis method is used, different computer software is used. Kansei Engineering Software (KESo) uses QT1 for linear analysis. The concept of Kansei Engineering Software (KESo) Linköping University in Sweden. [ 2 ] The software generates online questionnaires for collection of Kansei raw-data
Another software package (Kn6) was developed at the Polytechnic University of Valencia in Spain.
Both software packages improve the collection and evaluation of Kansei data. In this way even users with no specialist competence in advanced statistics can use Kansei engineering. | https://en.wikipedia.org/wiki/Kansei_engineering |
In mathematics , the Kantorovich inequality is a particular case of the Cauchy–Schwarz inequality , which is itself a generalization of the triangle inequality .
The triangle inequality states that the length of two sides of any triangle, added together, will be equal to or greater than the length of the third side. In simplest terms, the Kantorovich inequality translates the basic idea of the triangle inequality into the terms and notational conventions of linear programming . (See vector space , inner product , and normed vector space for other examples of how the basic ideas inherent in the triangle inequality—line segment and distance—can be generalized into a broader context.)
More formally, the Kantorovich inequality can be expressed this way:
The Kantorovich inequality is used in convergence analysis ; it bounds the convergence rate of Cauchy's steepest descent .
Equivalents of the Kantorovich inequality have arisen in a number of different fields. For instance, the Cauchy–Schwarz–Bunyakovsky inequality and the Wielandt inequality are equivalent to the Kantorovich inequality and all of these are, in turn, special cases of the Hölder inequality .
The Kantorovich inequality is named after Soviet economist, mathematician, and Nobel Prize winner Leonid Kantorovich , a pioneer in the field of linear programming .
There is also Matrix version of the Kantorovich inequality due to Marshall and Olkin (1990). Its extensions and their applications to statistics are available; see e.g. Liu and Neudecker (1999) and Liu et al. (2022). | https://en.wikipedia.org/wiki/Kantorovich_inequality |
The Kantorovich theorem , or Newton–Kantorovich theorem, is a mathematical statement on the semi-local convergence of Newton's method . It was first stated by Leonid Kantorovich in 1948. [ 1 ] [ 2 ] It is similar to the form of the Banach fixed-point theorem , although it states existence and uniqueness of a zero rather than a fixed point . [ 3 ]
Newton's method constructs a sequence of points that under certain conditions will converge to a solution x {\displaystyle x} of an equation f ( x ) = 0 {\displaystyle f(x)=0} or a vector solution of a system of equation F ( x ) = 0 {\displaystyle F(x)=0} . The Kantorovich theorem gives conditions on the initial point of this sequence. If those conditions are satisfied then a solution exists close to the initial point and the sequence converges to that point. [ 1 ] [ 2 ]
Let X ⊂ R n {\displaystyle X\subset \mathbb {R} ^{n}} be an open subset and F : X ⊂ R n → R n {\displaystyle F:X\subset \mathbb {R} ^{n}\to \mathbb {R} ^{n}} a differentiable function with a Jacobian F ′ ( x ) {\displaystyle F^{\prime }(\mathbf {x} )} that is locally Lipschitz continuous (for instance if F {\displaystyle F} is twice differentiable). That is, it is assumed that for any x ∈ X {\displaystyle x\in X} there is an open subset U ⊂ X {\displaystyle U\subset X} such that x ∈ U {\displaystyle x\in U} and there exists a constant L > 0 {\displaystyle L>0} such that for any x , y ∈ U {\displaystyle \mathbf {x} ,\mathbf {y} \in U}
holds. The norm on the left is the operator norm. In other words, for any vector v ∈ R n {\displaystyle \mathbf {v} \in \mathbb {R} ^{n}} the inequality
must hold.
Now choose any initial point x 0 ∈ X {\displaystyle \mathbf {x} _{0}\in X} . Assume that F ′ ( x 0 ) {\displaystyle F'(\mathbf {x} _{0})} is invertible and construct the Newton step h 0 = − F ′ ( x 0 ) − 1 F ( x 0 ) . {\displaystyle \mathbf {h} _{0}=-F'(\mathbf {x} _{0})^{-1}F(\mathbf {x} _{0}).}
The next assumption is that not only the next point x 1 = x 0 + h 0 {\displaystyle \mathbf {x} _{1}=\mathbf {x} _{0}+\mathbf {h} _{0}} but the entire ball B ( x 1 , ‖ h 0 ‖ ) {\displaystyle B(\mathbf {x} _{1},\|\mathbf {h} _{0}\|)} is contained inside the set X {\displaystyle X} . Let M {\displaystyle M} be the Lipschitz constant for the Jacobian over this ball (assuming it exists).
As a last preparation, construct recursively, as long as it is possible, the sequences ( x k ) k {\displaystyle (\mathbf {x} _{k})_{k}} , ( h k ) k {\displaystyle (\mathbf {h} _{k})_{k}} , ( α k ) k {\displaystyle (\alpha _{k})_{k}} according to
Now if α 0 ≤ 1 2 {\displaystyle \alpha _{0}\leq {\tfrac {1}{2}}} then
A statement that is more precise but slightly more difficult to prove uses the roots t ∗ ≤ t ∗ ∗ {\displaystyle t^{\ast }\leq t^{**}} of the quadratic polynomial
and their ratio
Then
In 1986, Yamamoto proved that the error evaluations of the Newton method such as Doring (1969), Ostrowski (1971, 1973), [ 6 ] [ 7 ] Gragg-Tapia (1974), Potra-Ptak (1980), [ 8 ] Miel (1981), [ 9 ] Potra (1984), [ 10 ] can be derived from the Kantorovich theorem. [ 11 ]
There is a q -analog for the Kantorovich theorem. [ 12 ] [ 13 ] For other generalizations/variations, see Ortega & Rheinboldt (1970). [ 14 ]
Oishi and Tanabe claimed that the Kantorovich theorem can be applied to obtain reliable solutions of linear programming . [ 15 ] | https://en.wikipedia.org/wiki/Kantorovich_theorem |
In gas dynamics , the Kantrowitz limit refers to a theoretical concept describing choked flow at supersonic or near-supersonic velocities. [ 1 ] When an initially subsonic fluid flow experiences a reduction in cross-section area, the flow speeds up in order to maintain the same mass-flow rate, per the continuity equation . If a near supersonic flow experiences an area contraction, the velocity of the flow will decrease until it reaches the local speed of sound, and the flow will be choked . This is the principle behind the Kantrowitz limit: it is the maximum amount of contraction a flow can experience before the flow chokes, and the flow speed can no longer be increased above this limit, independent of changes in upstream or downstream pressure.
Assume a fluid enters an internally contracting nozzle at cross-section 0, and passes through a throat of smaller area at cross-section 4. A normal shock is assumed to start at the beginning of the nozzle contraction, and this point in the nozzle is referred to as cross-section 2. Due to conservation of mass within the nozzle, the mass flow rate at each cross section must be equal:
For an ideal compressible gas, the mass flow rate at each cross-section can be written as, [ 2 ]
where A {\textstyle A} is the cross-section area at the specified point, γ {\textstyle \gamma } is the Isentropic expansion factor of the gas, M {\textstyle M} is the Mach number of the flow at the specified cross-section, R {\textstyle R} is the ideal gas constant , p t {\textstyle p_{t}} is the stagnation pressure , and T t {\textstyle T_{t}} is the stagnation temperature .
Setting the mass flow rates equal at the inlet and throat, and recognizing that the total temperature, ratio of specific heats, and gas constant are constant, the conservation of mass simplifies to,
Solving for A 4 /A 0 ,
Three assumptions will be made: the flow from behind the normal shock in the inlet is isentropic, or p t4 = p t2 , the flow at the throat (point 4) is sonic such that M 4 = 1, and the pressures between the various point are related through normal shock relations, resulting in the following relation between inlet and throat pressures, [ 1 ]
And since M 4 = 1, shock relations at the throat simplify to, [ 2 ]
Substituting for M 4 {\textstyle M_{4}} and p t 0 p t 4 {\textstyle {\frac {p_{t0}}{p_{t4}}}} in the area ratio expression gives,
This can also be written as, [ 3 ]
The Kantrowitz limit has many applications in gas dynamics of inlet flow, including jet engines and rockets operating at high-subsonic and supersonic velocities, and high-speed transportation systems such as the Hyperloop.
The Kantrowitz limit demonstrates the amount of contraction, or change in two-dimensional cross-section area, that a hypersonic inlet can employ while successfully starting an engine inlet (or avoiding the expelling of the hypersonic inlet shock wave). [ 4 ]
The Kantrowitz limit is a fundamental concept in the Hyperloop , a proposed high-speed transportation system. The Hyperloop moves passengers in sealed pods through a partial-vacuum tube at high-subsonic speeds. As the air in the tube moves into and around the smaller cross-sectional area between the pod and tube, the air flow must speed up due to the continuity principle . If the pod is travelling through the tube fast enough, the air flow around the pod will reach the speed of sound, and the flow will become choked , resulting in large air resistance on the pod. The condition that determines if the flow around the pod chokes is the Kantrowitz limit. The Kantrowitz limit therefore acts a "speed limit" - for a given ratio of tube area and pod area, there is a maximum speed that the pod can travel before flow around the pod chokes and air resistance sharply increases. [ 5 ]
In order to break through the speed limit set by the Kantrowitz limit, there are two possible approaches. The first would increase the diameter of the tube in order to provide more bypass area for the air around the pod, preventing the flow from choking. This solution is not very practical in practice however, as the tube would have to be built very large, and logistical costs of such a large tube are impractical.
As an alternative, it has been found during the main study of the Swissmetro project (1993 -1998) that a turbine can be installed on board of the vehicle to push the displaced air across the vehicle body (TurboSwissMetro) [ 6 ] [ 7 ] and hence to reduce far field impacts. This would avoid the continuous increase of the vehicle drag due to the choking of the flow at the cost of the power required to drive the turbine and hence enable larger speeds. The computer program NUMSTA has been developed in this context; it allows to simulate the dynamical interaction of several high speed vehicles in complex tunnel networks including the choking effect.
This idea has also been proposed by Elon Musk in his 2013 Hyperloop Alpha paper where a compressor is placed at the front of the pod. [ 5 ] The compressor actively draws in air from the front of the pod and transfers it to the rear, bypassing the gap between pod and tube while diverting a fraction of the flow to power a low-friction air-bearing suspension system . [ 5 ] The inclusion of a compressor in the Hyperloop pod circumvents the Kantrowitz limit, allowing the pod to travel at speeds over 700 mph (about 1126 km/h) in a relatively narrow tube.
For a pod travelling through a tube, the Kantrowitz limit is given as the ratio of tube area to bypass area both around the outside of the pod and through any air-bypass compressor: [ 8 ] | https://en.wikipedia.org/wiki/Kantrowitz_limit |
The Kanzelhoehe Solar Observatory or KSO is an astronomical observatory affiliated with the Institute of Geophysics, Astrophysics and Meteorology out of the University of Graz . [ 1 ] It is located near Villach on the southern border of Austria .
Its Web page usually posts current images of the sun, especially in the hydrogen-alpha line that is the strongest visible-light line of hydrogen and that reveals the solar chromosphere.
Founded in 1941 by the German Luftwaffe to research the effects of the Sun on the Earth's ionosphere , the KSO focuses on multispectral synoptic observations of the sun using several telescope on the same mount.
This article about a specific observatory, telescope or astronomical instrument is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kanzelhoehe_Solar_Observatory |
Kaonic hydrogen is an exotic atom consisting of a negatively charged kaon orbiting a proton .
Such particles were first identified, through their X-ray spectrum , at the KEK proton synchrotron in Tsukuba , Japan in 1997. [ 1 ] More detailed studies have been performed at DAFNE in Frascati , Italy . [ 2 ] [ 3 ] Kaonic hydrogen has been created in very low energy collisions of kaons with the protons in a gaseous hydrogen target. At DAFNE, kaons are produced by the decay of φ mesons which are in turn created in collisions between electrons and positrons . The experiments analyzed X-rays from several electronic transitions in kaonic hydrogen.
Unlike in the hydrogen atom , where the binding between electron and proton is dominated by the electromagnetic interaction , kaons and protons interact also to a large extent by the strong interaction .
In kaonic hydrogen this strong contribution was found to be repulsive, shifting the ground state energy by 283 ± 36 (statistical) ± 6 (systematic) eV , thus making the system unstable with a resonance width of 541 ± 89 (stat) ± 22 (syst) eV [ 3 ] (decay into Λ π and Σ π [ 4 ] ).
Kaonic hydrogen is studied mainly because of its importance for the understanding of kaon- nucleon interactions and for testing quantum chromodynamics .
This particle physics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kaonic_hydrogen |
Kaonium is an exotic atom consisting of a bound state of a positively charged and a negatively charged kaon . Kaonium has not been observed experimentally and is expected to have a short lifetime on the order of 10 −18 seconds . [ 1 ] [ 2 ]
This nuclear physics or atomic physics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kaonium |
Kapil Dev Sharma (1920-2006) born in Gujaranwala (now in Pakistan) was an Indian scientist and technologist who specialized as a glass technologist.
Sharma successfully completed his BSc degree at Panjab University , a BSc (Glass Tech.) at Banaras Hindu University ; and an MSc (Technology) from Sheffield. [ 2 ]
He worked in the glass industry for about a year and in 1945 proceeded to UK for higher studies as a Government of India scholar. He carried out research work at Sheffield University under Prof. W.E.S. Turner , F.R.S., and Prof H. Moore. He worked in the glass plants of Rockware Glass Ltd., Greenford , UK and Karhula lasitehdas [ fi ] , Finland. Sharma joined the institute as a scientific officer in September, 1948 and was associated with the planning and development of the institute from almost the beginning. During 1953–54, he worked at the Glass Section of the National Bureau of Standards , US, as a guest worker. He was assistant director in 1954, deputy director in 1960 and director from 1967 to 1980 of the Central Glass and Ceramic Research Institute . [ 2 ]
He has also served with the United Nations Development Program as a glass expert for several short term assignments in Cuba and Jamaica among other places.
Society of Glass Technology , U.K.; Institute of Ceramics, UK; President, Indian Institute of Ceramics; President, Indian Ceramic Society. [ 2 ]
He visited the USSR in 1959 as a member of the Government of India Expert Team for the optical and ophthalmic glass project. He also went to US and UK in 1962 as alternate leader of the NPC [ clarification needed ] Study Team on Glass Industry; Member International Commission on Glass ; and Chairman of ISI [ clarification needed ] Sectional Committee for Glassware. [ 2 ]
He was awarded the R G Nail Gold Medal from M S [ clarification needed ] University, Baroda. [ 2 ]
The "K.D. Sharma Memorial Lecture" has also been instituted. [ 2 ]
A multipurpose hall has also been made at the Central Glass and Ceramic Research Institute complex in Kolkata. [ 3 ]
His name also appears in the book, " Who's who in the world ". | https://en.wikipedia.org/wiki/Kapil_Dev_Sharma |
The Kapitza–Dirac effect is a quantum mechanical effect consisting of the diffraction of matter by a standing wave of light, [ 1 ] [ 2 ] [ 3 ] in complete analogy to the diffraction of light by a periodic grating, but with the role of matter and light reversed.
The effect was first predicted as the diffraction of electrons from a standing wave of light by Paul Dirac and Pyotr Kapitsa (or Peter Kapitza) in 1933. [ 1 ] The effect relies on the wave–particle duality of matter as stated by the de Broglie hypothesis in 1924. The matter-wave diffraction by a standing wave of light was first observed using a beam of neutral atoms. Later, the Kapitza-Dirac effect as originally proposed was observed in 2001. [ 2 ]
In 1924, French physicist Louis de Broglie postulated that matter exhibits a wave-like nature given by:
where h is the Planck constant , and p is the particle's momentum, and λ is the wavelength of the matter wave.
From this, it follows that interference effects between particles of matter will occur. This forms the basis of the Kapitza–Dirac effec: the diffraction of matter wave due to a standing wave of light.
A coherent beam of light will diffract into several peaks once it passes through a periodic diffraction grating . Due to matter-wave duality, the matter can be diffracted by a periodic diffraction grating as well. Such a diffraction grating can be made out of physical matter, [ 4 ] but can also be created by a standing wave of light formed by a pair of counterpropagating light beams, due light-matter interaction. Here, the standing wave of light forms the spatially periodic grating that will diffract the matter wave, as we will now explain.
The original idea [ 1 ] proposes that a beam of electron can be diffracted by a standing wave formed by a superposition of two counterpropagating beams of light. The diffraction is caused by light-matter interaction. In this case, each electron absorbs a photon from one of the beams, and re-emits a photon into the other beam traveling to the opposite direction. This describes a stimulated Compton scattering of photons by the electrons, since the re-emission here is stimulated by the presence of a second beam of light. Due to the nature of the stimulated Compton scattering, the re-emitted photon must carry the same frequency and opposite direction of the absorbed one. Consequently, the momentum transferred to the electron must have a magnitude of 2 ℏ k {\displaystyle 2\hbar k} where k {\displaystyle k} is the wavevector of the light forming the standing wave pattern.
Although the original proposal focused on electrons, the above analysis can be generalized to other types of matter waves that interacts with the light. Cold neutral atoms, for example, can also experience the Kapitza-Dirac effect. Indeed, one of the first observations of Kapitza-Dirac effect was using a beams of cold sodium atoms. Today, the Kapitza-Dirac effect is a standard tool to calibrate the depth of optical lattices which are formed by standing waves of light.
Diffraction from a periodic grating, regardless of electromagnetic or matter wave, can be roughly divided into two regimes: the Bragg regime and Raman-Nath regime. In the Bragg regime, essentially only one diffraction peak is produced. In the Raman-Nath regime, multiple diffraction peaks can be observed. [ 4 ]
It is helpful to go back to the familiar example of light diffraction from a matter grating. In this case, The Bragg regime is reached with a thick grating, whereas the Raman-Nath regime is obtained with a thin grating. The same language can be applied to Kapitza-Dirac effect. Here, the concept of "thickness" of the grating can be transferred to the amount of time the matter wave spent in the light field.
Here we give an example in the Raman-Nath regime, where the matter spends an amount of time in the standing wave that is short compared to the so-called recoil frequency of the particle. This approximation holds if the interaction time is less than the inverse of the recoil frequency of the particle, τ ≪ 1 / ω rec {\displaystyle \tau \ll 1/\omega _{\text{rec}}} where ω rec = ℏ k 2 2 m {\displaystyle \omega _{\text{rec}}={\frac {\hbar k^{2}}{2m}}} .
A coherent beam of particles incident on a standing wave of electromagnetic radiation (typically light) will be diffracted according to the equation:
where n is an integer, λ is the de Broglie wavelength of the incident particles, d is the spacing of the grating and θ is the angle of incidence.
Here we present an analysis of the diffraction pattern of the Kapitza-Dirac effect in the Raman-Nath regime [ 5 ] For a matter wave interacting in a standing wave of light, the effect of the light-matter interaction can be parametrized by the potential energy
U ( z , t ) = U 0 f ( t ) sin 2 ( k z ) , {\displaystyle U(z,t)=U_{0}f(t)\sin ^{2}(kz),}
where U 0 {\displaystyle U_{0}} is the strength of the potential energy, and f ( t ) {\displaystyle f(t)} describes the pulse shape of applied standing wave. For example, for ultracold atoms trapped in an optical lattice, U 0 = ℏ ω R 2 δ {\displaystyle U_{0}={\frac {\hbar \omega _{\text{R}}^{2}}{\delta }}} due to the AC Stark shift.
As described previously, the Raman-Nath regime is reached when the duration is short. In this case, the kinetic energy can be ignored and the resulting Schrodinger equation is greatly simplified. For a given initial state | ψ 0 ⟩ {\displaystyle \left|\psi _{0}\right\rangle } , the time-evolution within the Raman-Nath regime is then given by
| ψ ⟩ = | ψ 0 ⟩ e − i ℏ ∫ d t ′ U ( z , t ′ ) = | ψ 0 ⟩ e − i 2 δ ω R 2 τ e i 2 δ ω R 2 τ cos ( 2 k z ) , {\displaystyle \left|\psi \right\rangle =\left|\psi _{0}\right\rangle e^{-{\frac {i}{\hbar }}\int dt'U(z,t')}=\left|\psi _{0}\right\rangle e^{-{\frac {i}{2\delta }}\omega _{\text{R}}^{2}\tau }e^{{\frac {i}{2\delta }}\omega _{\text{R}}^{2}\tau \cos(2kz)},} where τ = ∫ d t ′ f 2 ( t ′ ) {\textstyle \tau =\int dt'f^{2}(t')} and the integral is over the duration of the interaction. Using the Jacobi–Anger expansion for Bessel functions of the first kind, e i α cos ( β ) = ∑ n = − ∞ ∞ i n J n ( α ) e i n β {\textstyle e^{i\alpha \cos(\beta )}=\sum _{n=-\infty }^{\infty }i^{n}J_{n}(\alpha )e^{in\beta }} , the above wavefunction becomes
where in the second line | ψ 0 ⟩ {\displaystyle |\psi _{0}\rangle } has been taken to be | g , 0 ⟩ {\displaystyle |g,0\rangle } . It can now be seen that 2 n ℏ k {\displaystyle 2n\hbar k} momentum states are populated with a probability of P n = J n 2 ( θ ) {\displaystyle P_{n}=J_{n}^{2}(\theta )} where n = 0 , ± 1 , ± 2 , … {\displaystyle n=0,\pm 1,\pm 2,\ldots } and the pulse area (duration and amplitude of the interaction) θ = ω R 2 2 δ τ = ω R ( 2 ) τ {\textstyle \theta ={\frac {\omega _{\text{R}}^{2}}{2\delta }}\tau =\omega _{\text{R}}^{(2)}\tau } .
The transverse RMS momentum of the diffracted particles is therefore linearly proportional to the pulse area: p rms = ∑ n = − ∞ ∞ ( n ℏ k ) 2 P n = 2 θ ℏ k . {\displaystyle p_{\text{rms}}=\sum _{n=-\infty }^{\infty }(n\hbar k)^{2}P_{n}={\sqrt {2}}\theta \hbar k.}
The invention of the laser in 1960 allowed the production of coherent light and therefore the ability to construct the standing waves of light that are required to observe the effect experimentally.
Kapitsa–Dirac scattering of sodium atoms by a near resonant standing wave laser field was experimentally demonstrated in 1985 by the group of D. E. Pritchard at the Massachusetts Institute of Technology. [ 6 ] A supersonic atomic beam with sub-recoil transverse momentum was passed through a near resonant standing wave and diffraction up to 10ħk was observed.
The scattering of electrons by an intense optical standing wave was experimentally realised by the group of M. Bashkansky at AT&T Bell Laboratories, New Jersey, in 1988. [ 7 ]
The Kapitza-Dirac effect is routinely used in calibration of the depth of the optical lattices .
This quantum mechanics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kapitsa–Dirac_effect |
The Kapitza number ( Ka ) is a dimensionless number named after the prominent Russian physicist Pyotr Kapitsa (Peter Kapitza). He provided the first extensive study of the ways in which a thin film of liquid flows down inclined surfaces. [ 1 ] Expressed as the ratio of surface tension forces to inertial forces, the Kapitza number acts as an indicator of the hydrodynamic wave regime in falling liquid films. [ 2 ] Liquid film behavior represents a subset of the more general class of free boundary problems . and is important in a wide range of engineering and technological applications such as evaporators , heat exchangers , absorbers, microreactors , small-scale electronics/microprocessor cooling schemes, air conditioning and gas turbine blade cooling.
After World War II Kapitza was removed from all his positions, including director of his Institute for Physical Problems , for refusing to work on nuclear weapons . He was at his country house and devised experiments to work on there, including his experiments on falling films of liquid. [ 3 ]
Unlike most dimensionless numbers used in the study of fluid mechanics, the Kapitza number represents a material property, as it is formed by combining powers of the surface tension , density , gravitational acceleration and kinematic viscosity . [ 4 ]
where σ is the surface tension ( SI units: N / m ), g is gravitational acceleration (m/ s 2 ), ρ is density ( kg /m 3 ), β is inclination angle ( rad ), and ν is kinematic viscosity (m 2 /s). | https://en.wikipedia.org/wiki/Kapitza_number |
In mathematics , Kaplansky's theorem on quadratic forms is a result on simultaneous representation of primes by quadratic forms . It was proved in 2003 by Irving Kaplansky . [ 1 ]
Kaplansky's theorem states that a prime p congruent to 1 modulo 16 is representable by both or none of x 2 + 32 y 2 and x 2 + 64 y 2 , whereas a prime p congruent to 9 modulo 16 is representable by exactly one of these quadratic forms.
This is remarkable since the primes represented by each of these forms individually are not describable by congruence conditions. [ 2 ]
Kaplansky's proof uses the facts that 2 is a 4th power modulo p if and only if p is representable by x 2 + 64 y 2 , and that −4 is an 8th power modulo p if and only if p is representable by x 2 + 32 y 2 .
Five results similar to Kaplansky's theorem are known: [ 3 ]
It is conjectured that there are no other similar results involving definite forms. | https://en.wikipedia.org/wiki/Kaplansky's_theorem_on_quadratic_forms |
The Kaplan–Meier estimator , [ 1 ] [ 2 ] also known as the product limit estimator , is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure the fraction of patients living for a certain amount of time after treatment. In other fields, Kaplan–Meier estimators may be used to measure the length of time people remain unemployed after a job loss, [ 3 ] the time-to-failure of machine parts, or how long fleshy fruits remain on plants before they are removed by frugivores . The estimator is named after Edward L. Kaplan and Paul Meier , who each submitted similar manuscripts to the Journal of the American Statistical Association . [ 4 ] The journal editor, John Tukey , convinced them to combine their work into one paper, which has been cited more than 34,000 times since its publication in 1958. [ 5 ] [ 6 ]
The estimator of the survival function S ( t ) {\displaystyle S(t)} (the probability that life is longer than t {\displaystyle t} ) is given by:
with t i {\displaystyle t_{i}} a time when at least one event happened, d i the number of events (e.g., deaths) that happened at time t i {\displaystyle t_{i}} , and n i {\displaystyle n_{i}} the individuals known to have survived (have not yet had an event or been censored) up to time t i {\displaystyle t_{i}} .
A plot of the Kaplan–Meier estimator is a series of declining horizontal steps which, with a large enough sample size, approaches the true survival function for that population. The value of the survival function between successive distinct sampled observations ("clicks") is assumed to be constant.
An important advantage of the Kaplan–Meier curve is that the method can take into account some types of censored data , particularly right-censoring , which occurs if a patient withdraws from a study, is lost to follow-up , or is alive without event occurrence at last follow-up. On the plot, small vertical tick-marks state individual patients whose survival times have been right-censored. When no truncation or censoring occurs, the Kaplan–Meier curve is the complement of the empirical distribution function .
In medical statistics , a typical application might involve grouping patients into categories, for instance, those with Gene A profile and those with Gene B profile. In the graph, patients with Gene B die much quicker than those with Gene A. After two years, about 80% of the Gene A patients survive, but less than half of patients with Gene B.
To generate a Kaplan–Meier estimator, at least two pieces of data are required for each patient (or each subject): the status at last observation (event occurrence or right-censored), and the time to event (or time to censoring). If the survival functions between two or more groups are to be compared, then a third piece of data is required: the group assignment of each subject. [ 7 ]
Let τ ≥ 0 {\displaystyle \tau \geq 0} be a random variable as the time that passes between the start of the possible exposure period, t 0 {\displaystyle t_{0}} , and the time that the event of interest takes place, t 1 {\displaystyle t_{1}} . As indicated above, the goal is to estimate the survival function S {\displaystyle S} underlying τ {\displaystyle \tau } . Recall that this function is defined as
Let τ 1 , … , τ n ≥ 0 {\displaystyle \tau _{1},\dots ,\tau _{n}\geq 0} be independent, identically distributed random variables, whose common distribution is that of τ {\displaystyle \tau } : τ j {\displaystyle \tau _{j}} is the random time when some event j {\displaystyle j} happened. The data available for estimating S {\displaystyle S} is not ( τ j ) j = 1 , … , n {\displaystyle (\tau _{j})_{j=1,\dots ,n}} , but the list of pairs ( ( τ ~ j , c j ) ) j = 1 , … , n {\displaystyle (\,({\tilde {\tau }}_{j},c_{j})\,)_{j=1,\dots ,n}} where for j ∈ [ n ] := { 1 , 2 , … , n } {\displaystyle j\in [n]:=\{1,2,\dots ,n\}} , c j ≥ 0 {\displaystyle c_{j}\geq 0} is a fixed, deterministic integer, the censoring time of event j {\displaystyle j} and τ ~ j = min ( τ j , c j ) {\displaystyle {\tilde {\tau }}_{j}=\min(\tau _{j},c_{j})} . In particular, the information available about the timing of event j {\displaystyle j} is whether the event happened before the fixed time c j {\displaystyle c_{j}} and if so, then the actual time of the event is also available. The challenge is to estimate S ( t ) {\displaystyle S(t)} given this data.
Two derivations of the Kaplan–Meier estimator are shown. Both are based on rewriting the survival function in terms of what is sometimes called hazard , or mortality rates . However, before doing this it is worthwhile to consider a naive estimator.
To understand the power of the Kaplan–Meier estimator, it is worthwhile to first describe a naive estimator of the survival function.
Fix k ∈ [ n ] := { 1 , … , n } {\displaystyle k\in [n]:=\{1,\dots ,n\}} and let t > 0 {\displaystyle t>0} . A basic argument shows that the following proposition holds:
Let k {\displaystyle k} be such that c k ≥ t {\displaystyle c_{k}\geq t} . It follows from the above proposition that
Let X k = I ( τ ~ k ≥ t ) {\displaystyle X_{k}=\mathbb {I} ({\tilde {\tau }}_{k}\geq t)} and consider only those k ∈ C ( t ) := { k : c k ≥ t } {\displaystyle k\in C(t):=\{k\,:\,c_{k}\geq t\}} , i.e. the events for which the outcome was not censored before time t {\displaystyle t} . Let m ( t ) = | C ( t ) | {\displaystyle m(t)=|C(t)|} be the number of elements in C ( t ) {\displaystyle C(t)} . Note that the set C ( t ) {\displaystyle C(t)} is not random and so neither is m ( t ) {\displaystyle m(t)} . Furthermore, ( X k ) k ∈ C ( t ) {\displaystyle (X_{k})_{k\in C(t)}} is a sequence of independent, identically distributed Bernoulli random variables with common parameter S ( t ) = Prob ( τ ≥ t ) {\displaystyle S(t)=\operatorname {Prob} (\tau \geq t)} . Assuming that m ( t ) > 0 {\displaystyle m(t)>0} , this suggests to estimate S ( t ) {\displaystyle S(t)} using
where the second equality follows because τ ~ k ≥ t {\displaystyle {\tilde {\tau }}_{k}\geq t} implies c k ≥ t {\displaystyle c_{k}\geq t} , while the last equality is simply a change of notation.
The quality of this estimate is governed by the size of m ( t ) {\displaystyle m(t)} . This can be problematic when m ( t ) {\displaystyle m(t)} is small, which happens, by definition, when a lot of the events are censored. A particularly unpleasant property of this estimator, that suggests that perhaps it is not the "best" estimator, is that it ignores all the observations whose censoring time precedes t {\displaystyle t} . Intuitively, these observations still contain information about S ( t ) {\displaystyle S(t)} : For example, when for many events with c k < t {\displaystyle c_{k}<t} , τ k < c k {\displaystyle \tau _{k}<c_{k}} also holds, we can infer that events often happen early, which implies that Prob ( τ ≤ t ) {\displaystyle \operatorname {Prob} (\tau \leq t)} is large, which, through S ( t ) = 1 − Prob ( τ ≤ t ) {\displaystyle S(t)=1-\operatorname {Prob} (\tau \leq t)} means that S ( t ) {\displaystyle S(t)} must be small. However, this information is ignored by this naive estimator. The question is then whether there exists an estimator that makes a better use of all the data. This is what the Kaplan–Meier estimator accomplishes. Note that the naive estimator cannot be improved when censoring does not take place; so whether an improvement is possible critically hinges upon whether censoring is in place.
By elementary calculations,
where the second to last equality used that τ {\displaystyle \tau } is integer valued and for the last line we introduced
By a recursive expansion of the equality S ( t ) = q ( t ) S ( t − 1 ) {\displaystyle S(t)=q(t)S(t-1)} , we get
Note that here q ( 0 ) = 1 − Prob ( τ = 0 ∣ τ > − 1 ) = 1 − Prob ( τ = 0 ) {\displaystyle q(0)=1-\operatorname {Prob} (\tau =0\mid \tau >-1)=1-\operatorname {Prob} (\tau =0)} .
The Kaplan–Meier estimator can be seen as a "plug-in estimator" where each q ( s ) {\displaystyle q(s)} is estimated based on the data and the estimator of S ( t ) {\displaystyle S(t)} is obtained as a product of these estimates.
It remains to specify how q ( s ) = 1 − Prob ( τ = s ∣ τ ≥ s ) {\displaystyle q(s)=1-\operatorname {Prob} (\tau =s\mid \tau \geq s)} is to be estimated. By Proposition 1, for any k ∈ [ n ] {\displaystyle k\in [n]} such that c k ≥ s {\displaystyle c_{k}\geq s} , Prob ( τ = s ) = Prob ( τ ~ k = s ) {\displaystyle \operatorname {Prob} (\tau =s)=\operatorname {Prob} ({\tilde {\tau }}_{k}=s)} and Prob ( τ ≥ s ) = Prob ( τ ~ k ≥ s ) {\displaystyle \operatorname {Prob} (\tau \geq s)=\operatorname {Prob} ({\tilde {\tau }}_{k}\geq s)} both hold. Hence, for any k ∈ [ n ] {\displaystyle k\in [n]} such that c k ≥ s {\displaystyle c_{k}\geq s} ,
By a similar reasoning that lead to the construction of the naive estimator above, we arrive at the estimator
(think of estimating the numerator and denominator separately in the definition of the "hazard rate" Prob ( τ = s | τ ≥ s ) {\displaystyle \operatorname {Prob} (\tau =s|\tau \geq s)} ). The Kaplan–Meier estimator is then given by
The form of the estimator stated at the beginning of the article can be obtained by some further algebra. For this, write q ^ ( s ) = 1 − d ( s ) / n ( s ) {\displaystyle {\hat {q}}(s)=1-d(s)/n(s)} where, using the actuarial science terminology, d ( s ) = | { 1 ≤ k ≤ n : τ k = s } | {\displaystyle d(s)=|\{1\leq k\leq n\,:\,\tau _{k}=s\}|} is the number of known deaths at time s {\displaystyle s} , while n ( s ) = | { 1 ≤ k ≤ n : τ ~ k ≥ s } | {\displaystyle n(s)=|\{1\leq k\leq n\,:\,{\tilde {\tau }}_{k}\geq s\}|} is the number of those persons who are alive (and not being censored) at time s − 1 {\displaystyle s-1} .
Note that if d ( s ) = 0 {\displaystyle d(s)=0} , q ^ ( s ) = 1 {\displaystyle {\hat {q}}(s)=1} . This implies that we can leave out from the product defining S ^ ( t ) {\displaystyle {\hat {S}}(t)} all those terms where d ( s ) = 0 {\displaystyle d(s)=0} . Then, letting 0 ≤ t 1 < t 2 < ⋯ < t m {\displaystyle 0\leq t_{1}<t_{2}<\dots <t_{m}} be the times s {\displaystyle s} when d ( s ) > 0 {\displaystyle d(s)>0} , d i = d ( t i ) {\displaystyle d_{i}=d(t_{i})} and n i = n ( t i ) {\displaystyle n_{i}=n(t_{i})} , we arrive at the form of the Kaplan–Meier estimator given at the beginning of the article:
As opposed to the naive estimator, this estimator can be seen to use the available information more effectively: In the special case mentioned beforehand, when there are many early events recorded, the estimator will multiply many terms with a value below one and will thus take into account that the survival probability cannot be large.
Kaplan–Meier estimator can be derived from maximum likelihood estimation of the discrete hazard function . [ 8 ] More specifically given d i {\displaystyle d_{i}} as the number of events and n i {\displaystyle n_{i}} the total individuals at risk at time t i {\displaystyle t_{i}} , discrete hazard rate h i {\displaystyle h_{i}} can be defined as the probability of an individual with an event at time t i {\displaystyle t_{i}} . Then survival rate can be defined as:
and the likelihood function for the hazard function up to time t i {\displaystyle t_{i}} is:
therefore the log likelihood will be:
finding the maximum of log likelihood with respect to h i {\displaystyle h_{i}} yields:
where hat is used to denote maximum likelihood estimation. Given this result, we can write:
More generally (for continuous as well as discrete survival distributions), the Kaplan-Meier estimator may be interpreted as a nonparametric maximum likelihood estimator. [ 9 ]
The Kaplan–Meier estimator is one of the most frequently used methods of survival analysis. The estimate may be useful to examine recovery rates, the probability of death, and the effectiveness of treatment. It is limited in its ability to estimate survival adjusted for covariates ; parametric survival models and the Cox proportional hazards model may be useful to estimate covariate-adjusted survival.
The Kaplan-Meier estimator is directly related to the Nelson-Aalen estimator and both maximize the empirical likelihood . [ 10 ]
The Kaplan–Meier estimator is a statistic , and several estimators are used to approximate its variance . One of the most common estimators is Greenwood's formula: [ 11 ]
where d i {\displaystyle d_{i}} is the number of cases and n i {\displaystyle n_{i}} is the total number of observations, for t i < t {\displaystyle t_{i}<t} .
Greenwood's formula is derived [ 12 ] [ self-published source? ] by noting that probability of getting d i {\displaystyle d_{i}} failures out of n i {\displaystyle n_{i}} cases follows a binomial distribution with failure probability h i {\displaystyle h_{i}} . As a result for maximum likelihood hazard rate h ^ i = d i / n i {\displaystyle {\widehat {h}}_{i}=d_{i}/n_{i}} we have E ( h ^ i ) = h i {\displaystyle E\left({\widehat {h}}_{i}\right)=h_{i}} and Var ( h ^ i ) = h i ( 1 − h i ) / n i {\displaystyle \operatorname {Var} \left({\widehat {h}}_{i}\right)=h_{i}(1-h_{i})/n_{i}} . To avoid dealing with multiplicative probabilities we compute variance of logarithm of S ^ ( t ) {\displaystyle {\widehat {S}}(t)} and will use the delta method to convert it back to the original variance:
using martingale central limit theorem , it can be shown that the variance of the sum in the following equation is equal to the sum of variances: [ 12 ]
as a result we can write:
using the delta method once more:
as desired.
In some cases, one may wish to compare different Kaplan–Meier curves. This can be done by the log rank test , and the Cox proportional hazards test .
Other statistics that may be of use with this estimator are pointwise confidence intervals, [ 13 ] the Hall-Wellner band [ 14 ] and the equal-precision band. [ 15 ] | https://en.wikipedia.org/wiki/Kaplan–Meier_estimator |
In applied mathematics, the Kaplan–Yorke conjecture concerns the dimension of an attractor , using Lyapunov exponents . [ 1 ] [ 2 ] By arranging the Lyapunov exponents in order from largest to smallest λ 1 ≥ λ 2 ≥ ⋯ ≥ λ n {\displaystyle \lambda _{1}\geq \lambda _{2}\geq \dots \geq \lambda _{n}} , let j be the largest index for which
and
Then the conjecture is that the dimension of the attractor is
This idea is used for the definition of the Lyapunov dimension . [ 3 ]
Especially for chaotic systems, the Kaplan–Yorke conjecture is a useful tool in order to estimate the fractal dimension and the Hausdorff dimension of the corresponding attractor. [ 4 ] [ 3 ] | https://en.wikipedia.org/wiki/Kaplan–Yorke_conjecture |
The kappa effect or perceptual time dilation [ 1 ] is a temporal perceptual illusion that can arise when observers judge the elapsed time between sensory stimuli applied sequentially at different locations. In perceiving a sequence of consecutive stimuli, subjects tend to overestimate the elapsed time between two successive stimuli when the distance between the stimuli is sufficiently large, and to underestimate the elapsed time when the distance is sufficiently small.
The kappa effect can occur with visual (e.g., flashes of light), auditory (e.g., tones), or tactile (e.g. taps to the skin) stimuli. Many studies of the kappa effect have been conducted using visual stimuli. For example, suppose three light sources, X, Y, and Z, are flashed successively in the dark with equal time intervals between each of the flashes. If the light sources are placed at different positions, with X and Y closer together than Y and Z, the temporal interval between the X and Y flashes is perceived to be shorter than that between the Y and Z flashes. [ 2 ] The kappa effect has also been demonstrated with auditory stimuli that move in frequency. [ 3 ] However, in some experimental paradigms the auditory kappa effect has not been observed. For example, Roy et al. (2011) found that, opposite to the prediction of the kappa effect, "Increasing the distance between sound sources marking time intervals leads to a decrease of the perceived duration". [ 4 ] In touch, the kappa effect was first described as the "S-effect" by Suto (1952). [ 5 ] Goldreich (2007) [ 6 ] refers to the kappa effect as "perceptual time dilation" in analogy with the physical time dilation of the theory of relativity .
Physically, traversed space and elapsed time are linked by velocity. Accordingly, several theories regarding the brain's expectations about stimulus velocity have been put forward to account for the kappa effect.
According to the constant velocity hypothesis proposed by Jones and Huang (1982), the brain incorporates a prior expectation of speed when judging spatiotemporal intervals. Specifically, the brain expects temporal intervals that would produce constant velocity (i.e., uniform motion ) movement. [ 7 ] [ 8 ] Thus, the kappa effect occurs when we apply our knowledge of motion to stimulus sequences, which sometimes leads us to make mistakes. [ 9 ] Evidence for the role of a uniform motion expectation in temporal perception comes from a study [ 10 ] in which participants observed eight white dots that successively appeared in one direction in a horizontal alignment along a straight line. When the temporal separation was constant and the spatial separation between the dots varied, they observed the kappa effect, which follows the constant velocity hypothesis. However, when both the temporal and spatial separation between the dots varied, they failed to observe the response pattern that the constant velocity hypothesis predicts. A possible explanation is that it is difficult to perceive a uniform motion from such varying, complicated patterns; thus, the context of observed events may affect our temporal perception.
A Bayesian perceptual model [ 6 ] replicates the tactile kappa effect and other tactile spatiotemporal illusions, including the tau effect and the cutaneous rabbit illusion . According to this model, brain circuitry encodes the expectation that tactile stimuli tend to move slowly. The Bayesian model reaches an optimal probabilistic inference by combining uncertain spatial and temporal sensory information with a prior expectation for low-speed movement. The expectation that stimuli tend to move slowly results in the perceptual overestimation of the time elapsed between rapidly successive taps applied to separate skin locations. Simultaneously, the model perceptually underestimates the spatial separation between stimuli, thereby reproducing the cutaneous rabbit illusion and the tau effect. Goldreich (2007) [ 6 ] speculated that a Bayesian slow-speed prior might explain the visual kappa effect as well the tactile one. Recent empirical studies support this suggestion. [ 11 ] [ 12 ]
The kappa effect appears to depend strongly on phenomenal rather than physical extent. [ 7 ] The kappa effect gets bigger as stimuli move faster. [ 8 ] Observers tend to apply their previous knowledge of motion to a sequence of stimuli. When subjects observed vertically arranged stimuli, the kappa effect was stronger for sequences moving downward. This can be attributed to the expectation of downward acceleration and upward deceleration, in that the perceived accelerated downward motion causes us to underestimate temporal separation judgments.
If observers interpret rapid stimulus sequences in light of an expectation regarding velocity, then it would be expected that not only temporal, but also spatial illusions would result. This indeed occurs in the tau effect , when the spatial separation between stimuli is constant and the temporal separation is varied. In this case, the observer decreases the judgment of spatial separation as temporal separation decreases, and vice versa. For example, when equally spaced light sources X, Y, and Z are flashed successively in the dark with a shorter time between X and Y than between Y and Z, X and Y are perceived to be closer together in space than are Y and Z. [ 2 ] Goldreich (2007) [ 6 ] linked the tau and kappa effects to the same underlying expectation regarding movement speed. He noted that, when stimuli move rapidly across space, "perception strikingly shrinks the intervening distance, and expands the elapsed time, between consecutive events". [ 6 ] Goldreich (2007) [ 6 ] termed these two fundamental perceptual distortions "perceptual length contraction" (tau effect) and "perceptual time dilation" (kappa effect) in analogy with the physical length contraction and time dilation of the theory of relativity . Perceptual length contraction and perceptual time dilation result from the same Bayesian observer model, one that expects stimuli to move slowly. [ 6 ] Analogously, in the theory of relativity, length contraction and time dilation both occur when a physical speed ( the speed of light ) cannot be exceeded. | https://en.wikipedia.org/wiki/Kappa_effect |
In biology, Kappa organism or Kappa particle refers to inheritable cytoplasmic symbionts , occurring in some strains of the ciliate Paramecium . Paramecium strains possessing the particles are known as "killer paramecia". They liberate a substance also known as paramecin [ 1 ] [ 2 ] into the culture medium that is lethal to Paramecium that do not contain kappa particles. Kappa particles are found in genotypes of Paramecium aurelia syngen 2 that carry the dominant gene K. [ 3 ] [ 4 ]
Kappa particles are Feulgen -positive and stain with Giemsa after acid hydrolysis. The length of the particles is 0.2–0.5μ. [ 5 ]
While there was initial confusion over the status of kappa particles as viruses , bacteria , organelles , [ 6 ] or mere nucleoprotein , [ 7 ] the particles are intracellular bacterial symbionts called Caedibacter taeniospiralis . [ 8 ] Caedibacter taeniospiralis contains cytoplasmic protein inclusions called R bodies which act as a toxin delivery system.
This microbiology -related article is a stub . You can help Wikipedia by expanding it .
This ciliate -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kappa_organism |
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