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Hyperlinks are, at present, a novel feature in virtual world platforms, aside from hyperlinks in the in-built chat clients between users' avatars. In the latter 2000s, however, a number of architectures were created for various decentralized virtual world platforms in order to facilitate easier travel of avatars between two or more separately-hosted grids or servers.
Open Cobalt uses a method of hyperlinking , known as "space-linking", [ 1 ] which resembles a window frame or portal and, when revolved, shows a 360-degree real-time view of one region to a user in another region; such portals can also be walked through by users. Space-linking is an alternative to teleportation, a more common means of traversing between regions or spaces, and is also a primary means of travelling between whole grids.
Like MediaWiki 's redlinks , such portals are also used to link to uncreated spaces or regions (colored in black) in order to indicate the need to create newer spaces. [ 2 ]
OpenSimulator also uses an architecture known as " Hypergrid ", which allows users to teleport between multiple OpenSim-based virtual worlds by providing a hyperlinked map which indexes public grids. [ 3 ] This allows for public grids to retain teleportation links to each other without having to be on the same grid. | https://en.wikipedia.org/wiki/Hyperlinks_in_virtual_worlds |
Hypermedia , an extension of hypertext , is a nonlinear medium of information that includes graphics, audio, video, plain text and hyperlinks . This designation contrasts with the broader term multimedia , which may include non-interactive linear presentations as well as hypermedia. The term was first used in a 1965 article written by Ted Nelson . [ 1 ] [ 2 ] Hypermedia is a type of multimedia that features interactive elements, such as hypertext, buttons, or interactive images and videos, allowing users to navigate and engage with content in a non-linear manner.
The World Wide Web is a classic example of hypermedia to access web content , whereas a conventional cinema presentation is an example of standard multimedia, due to its inherent linearity and lack of interactivity via hyperlinks.
The first hypermedia work was, arguably, the Aspen Movie Map . Bill Atkinson 's HyperCard popularized hypermedia writing, while a variety of literary hypertext and non-fiction hypertext works, demonstrated the promise of hyperlinks. Most modern hypermedia is delivered via electronic pages from a variety of systems including media players , web browsers , and stand-alone applications (i.e., software that does not require network access). Audio hypermedia is emerging with voice command devices and voice browsing . [ 3 ]
Hypermedia may be developed in a number of ways. Any programming tool can be used to write programs that link data from internal variables and nodes for external data files. Multimedia development software such as Adobe Flash , Adobe Director , Macromedia Authorware , and MatchWare Mediator may be used to create stand-alone hypermedia applications, with emphasis on entertainment content. Some database software, such as Visual FoxPro and FileMaker Developer , may be used to develop stand-alone hypermedia applications, with emphasis on educational and business content management.
Hypermedia applications may be developed on embedded devices for the mobile and the digital signage industries using the Scalable Vector Graphics (SVG) specification from W3C ( World Wide Web Consortium ). Software applications, such as Ikivo Animator and Inkscape , simplify the development of hypermedia content based on SVG. Embedded devices, such as the iPhone , natively support SVG specifications and may be used to create mobile and distributed hypermedia applications.
Hyperlinks may also be added to data files using most business software via the limited scripting and hyperlinking features built in. Documentation software, such as the Microsoft Office Suite and LibreOffice , allow for hypertext links to other content within the same file, other external files, and URL links to files on external file servers . For more emphasis on graphics and page layout , hyperlinks may be added using most modern desktop publishing tools. This includes presentation programs , such as Microsoft PowerPoint and LibreOffice Impress , add-ons to print layout programs such as Quark Immedia , and tools to include hyperlinks in PDF documents such as Adobe InDesign for creating and Adobe Acrobat for editing. Hyper Publish is a tool specifically designed and optimized for hypermedia and hypertext management. Any HTML editor may be used to build HTML files, accessible by any web browser. CD/DVD authoring tools, such as DVD Studio Pro , may be used to hyperlink the content of DVDs for DVD players or web links when the disc is played on a personal computer connected to the internet.
There have been a number of theories concerning hypermedia and learning. One important claim in the literature on hypermedia and learning is that it offers more control over the instructional environment for the reader or student. [ citation needed ] Another claim is that it levels the playing field among students of varying abilities and enhances collaborative learning. [ citation needed ] A claim from psychology includes the notion that hypermedia more closely models the structure of the brain, in comparison with printed text. [ 4 ]
Hypermedia is used as a medium and constraint in certain application programming interfaces . HATEOAS , Hypermedia as the Engine of Application State, is a constraint of the REST application architecture where a client interacts with the server entirely through hypermedia provided dynamically by application servers. This means that in theory no API documentation is needed, because the client needs no prior knowledge about how to interact with any particular application or server beyond a generic understanding of hypermedia. In other service-oriented architectures (SOA), clients and servers interact through a fixed interface shared through documentation or an interface description language (IDL). | https://en.wikipedia.org/wiki/Hypermedia |
Hypermetabolism is defined as an elevated resting energy expenditure (REE) > 110% of predicted REE. [ 1 ] Hypermetabolism is accompanied by a variety of internal and external symptoms, most notably extreme weight loss, and can also be a symptom in itself. This state of increased metabolic activity can signal underlying issues, especially hyperthyroidism . Patients with Fatal familial insomnia can also present with hypermetabolism; however, this universally fatal disorder is exceedingly rare, with only a few known cases worldwide. The drastic impact of the hypermetabolic state on patient nutritional requirements is often understated or overlooked as well.
Symptoms may last for days, weeks, or months until the disorder is healed. The most apparent sign of hypermetabolism is an abnormally high intake of calories followed by continuous weight loss. Internal symptoms of hypermetabolism include: peripheral insulin resistance , elevated catabolism of protein , carbohydrates and triglycerides , and a negative nitrogen balance in the body. [ 2 ] Outward symptoms of hypermetabolism may include:
During the acute phase , the liver redirects protein synthesis , causing up-regulation of certain proteins and down-regulation of others. Measuring the serum level of proteins that are up- and down-regulated during the acute phase can reveal extremely important information about the patient's nutritional state. The most important up-regulated protein is C-reactive protein , which can rapidly increase 20- to 1,000-fold during the acute phase .
Hypermetabolism also causes expedited catabolism of carbohydrates , proteins , and triglycerides in order to meet the increased metabolic demands.
Quantitation by indirect calorimetry, as opposed to the Harris-Benedict equation, is needed to accurately measure REE in cancer patients. [ 1 ]
Many different illnesses can cause an increase in metabolic activity as the body combats illness and disease in order to heal itself.
Hypermetabolism is a common symptom of various pathologies . Some of the most prevalent diseases characterized by hypermetabolism are listed below.
Ibuprofen, polyunsaturated fatty acids, and beta-blockers have been reported in some preliminary studies to decrease REE, which may allow patients to meet their caloric needs and gain weight. [ 1 ] | https://en.wikipedia.org/wiki/Hypermetabolism |
In statistical mechanics the hypernetted-chain equation is a closure relation to solve the Ornstein–Zernike equation which relates the direct correlation function to the total correlation function. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function . It is given by:
where ρ = N V {\displaystyle \rho ={\frac {N}{V}}} is the number density of molecules, h ( r ) = g ( r ) − 1 {\displaystyle h(r)=g(r)-1} , g ( r ) {\displaystyle g(r)} is the radial distribution function , u ( r ) {\displaystyle u(r)} is the direct interaction between pairs. β = 1 k B T {\displaystyle \beta ={\frac {1}{k_{\rm {B}}T}}} with T {\displaystyle T} being the Thermodynamic temperature and k B {\displaystyle k_{\rm {B}}} the Boltzmann constant .
The direct correlation function represents the direct correlation between two particles in a system containing N − 2 other particles. It can be represented by
where g t o t a l ( r ) = g ( r ) = exp [ − β w ( r ) ] {\displaystyle g_{\rm {total}}(r)=g(r)=\exp[-\beta w(r)]} (with w ( r ) {\displaystyle w(r)} the potential of mean force ) and g i n d i r e c t ( r ) {\displaystyle g_{\rm {indirect}}(r)} is the radial distribution function without the direct interaction between pairs u ( r ) {\displaystyle u(r)} included; i.e. we write g i n d i r e c t ( r ) = exp { − β [ w ( r ) − u ( r ) ] } {\displaystyle g_{\rm {indirect}}(r)=\exp\{-\beta [w(r)-u(r)]\}} . Thus we approximate c ( r ) {\displaystyle c(r)} by
By expanding the indirect part of g ( r ) {\displaystyle g(r)} in the above equation and introducing the function y ( r ) = e β u ( r ) g ( r ) ( = g i n d i r e c t ( r ) ) {\displaystyle y(r)=e^{\beta u(r)}g(r)(=g_{\rm {indirect}}(r))} we can approximate c ( r ) {\displaystyle c(r)} by writing:
with f ( r ) = e − β u ( r ) − 1 {\displaystyle f(r)=e^{-\beta u(r)}-1} .
This equation is the essence of the hypernetted chain equation. We can equivalently write
If we substitute this result in the Ornstein–Zernike equation
one obtains the hypernetted-chain equation :
This article about statistical mechanics is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypernetted-chain_equation |
A hypernova is a very energetic supernova which is believed to result from an extreme core collapse scenario. In this case, a massive star (>30 solar masses ) collapses to form a rotating black hole emitting twin astrophysical jets and surrounded by an accretion disk . It is a type of stellar explosion that ejects material with an unusually high kinetic energy , an order of magnitude higher than most supernovae, with a luminosity at least 10 times greater. Hypernovae release such intense gamma rays that they often appear similar to a type Ic supernova , but with unusually broad spectral lines indicating an extremely high expansion velocity. Hypernovae are one of the mechanisms for producing long gamma ray bursts (GRBs) , which range from 2 seconds to over a minute in duration. They have also been referred to as superluminous supernovae , though that classification also includes other types of extremely luminous stellar explosions that have different origins.
In the 1980s, the term hypernova was used to describe a theoretical type of supernova now known as a pair-instability supernova . It referred to the extremely high energy of the explosion compared to typical core collapse supernovae . [ 1 ] [ 2 ] [ 3 ] The term had previously been used to describe hypothetical explosions from diverse events such as hyperstars , extremely massive population III stars in the early universe, [ 4 ] or from events such as black hole mergers. [ 5 ]
In February 1997, Dutch-Italian satellite BeppoSAX was able to trace GRB 970508 to a faint galaxy roughly 6 billion light years away. [ 6 ] From analyzing the spectroscopic data for both the GRB 970508 and its host galaxy, Bloom et al. concluded in 1998 that a hypernova was the likely cause. [ 6 ] That same year, hypernovae were hypothesized in greater detail by Polish astronomer Bohdan Paczyński as supernovae from rapidly spinning stars. [ 7 ]
The usage of the term hypernova from the late 20th century has since been refined to refer to those supernovae with unusually large kinetic energy. [ 8 ] The first hypernova observed was SN 1998bw , with a luminosity 100 times higher than a standard Type Ib. [ 9 ] This supernova was the first to be associated with a gamma-ray burst (GRB) and it produced a shockwave containing an order of magnitude more energy than a normal supernova. Other scientists prefer to call these objects simply broad-lined type Ic supernovae . [ 10 ] Since then the term has been applied to a variety of objects, not all of which meet the standard definition; for example ASASSN-15lh . [ 11 ]
In 2023, the observation of the highly energetic, non-quasar transient event AT2021lwx was published with an extremely strong emission from mid-infrared to X-ray wavelengths and an overall energy of 1.5 10 46 Joule . [ 12 ] This object is not thought to be a hypernova; instead, it is likely to be a huge gas cloud being absorbed by a massive black hole. The event was also assigned the random name "ZTF20abrbeie" by the Zwicky Transient Facility . This name and the seeming ferocity of the event led to nickname "Scary Barbie", drawing the attention of the mainstream press. [1]
Hypernovae are thought to be supernovae with ejecta having a kinetic energy larger than about 10 45 joule , an order of magnitude higher than a typical core collapse supernova. The ejected nickel masses are large and the ejection velocity up to 99% of the speed of light . These are typically of type Ic, and some are associated with long-duration gamma-ray bursts . The electromagnetic energy released by these events varies from comparable to other type Ic supernova, to some of the most luminous supernovae known such as SN 1999as . [ 13 ] [ 14 ]
The archetypal hypernova, SN 1998bw, was associated with GRB 980425 . Its spectrum showed no hydrogen and no clear helium features, but strong silicon lines identified it as a type Ic supernova. The main absorption lines were extremely broadened and the light curve showed a very rapid brightening phase, reaching the brightness of a type Ia supernova at day 16. The total ejected mass was about 10 M ☉ and the mass of nickel ejected about 0.4 M ☉ . [ 13 ] All supernovae associated with GRBs have shown the high-energy ejecta that characterises them as hypernovae. [ 15 ]
Unusually bright radio supernovae have been observed as counterparts to hypernovae, and have been termed "radio hypernovae". [ 16 ]
Models for hypernova focus on the efficient transfer of energy into the ejecta. In normal core collapse supernovae , 99% of neutrinos generated in the collapsing core escape without driving the ejection of material. It is thought that rotation of the supernova progenitor drives a jet that accelerates material away from the explosion at close to the speed of light. Binary systems are increasingly being studied as the best method for both stripping stellar envelopes to leave a bare carbon-oxygen core, and for inducing the necessary spin conditions to drive a hypernova.
The collapsar model describes a type of supernova that produces a gravitationally collapsed object, or black hole . The word "collapsar", short for "collapsed star ", was formerly used to refer to the end product of stellar gravitational collapse , a stellar-mass black hole . The word is now sometimes used to refer to a specific model for the collapse of a fast-rotating star. When core collapse occurs in a star with a core at least around fifteen times the Sun's mass ( M ☉ ) — though chemical composition and rotational rate are also significant — the explosion energy is insufficient to expel the outer layers of the star, and it will collapse into a black hole without producing a visible supernova outburst.
A star with a core mass slightly below this level — in the range of 5–15 M ☉ — will undergo a supernova explosion, but so much of the ejected mass falls back onto the core remnant that it still collapses into a black hole. If such a star is rotating slowly, then it will produce a faint supernova, but if the star is rotating quickly enough, then the fallback to the black hole will produce relativistic jets . Those powerful jets plough through stellar material produce strong shock waves, with the vigorous winds of newly-formed 56 Ni blowing off the accretion disk, detonating the hypernova explosion. The ejected radioactive decay of 56 Ni renders the visible outburst substantially more luminous than a standard supernova. [ 17 ] The jets also beam high energy particles and gamma rays directly outward and thereby produce x-ray or gamma-ray bursts; the jets can last for several seconds or longer and correspond to long-duration gamma-ray bursts, but they do not appear to explain short-duration gamma-ray bursts. [ 18 ] [ 19 ]
The mechanism for producing the stripped progenitor, a carbon-oxygen star lacking any significant hydrogen or helium, of type Ic supernovae was once thought to be an extremely evolved massive star, for example a type WO Wolf-Rayet star whose dense stellar wind expelled all its outer layers. Observations have failed to detect any such progenitors. It is still not conclusively shown that the progenitors are actually a different type of object, but several cases suggest that lower-mass "helium giants" are the progenitors. These stars are not sufficiently massive to expel their envelopes simply by stellar winds, and they would be stripped by mass transfer to a binary companion. Helium giants are increasingly favoured as the progenitors of type Ib supernovae, but the progenitors of type Ic supernovae is still uncertain. [ 20 ]
One proposed mechanism for producing gamma-ray bursts is induced gravitational collapse , where a neutron star is triggered to collapse into a black hole by the core collapse of a close companion consisting of a stripped carbon-oxygen core. The induced neutron star collapse allows for the formation of jets and high-energy ejecta that have been difficult to model from a single star. [ 21 ] | https://en.wikipedia.org/wiki/Hypernova |
A hypernucleus is similar to a conventional atomic nucleus , but contains at least one hyperon in addition to the normal protons and neutrons . Hyperons are a category of baryon particles that carry non-zero strangeness quantum number, which is conserved by the strong and electromagnetic interactions .
A variety of reactions give access to depositing one or more units of strangeness in a nucleus. Hypernuclei containing the lightest hyperon, the lambda (Λ), tend to be more tightly bound than normal nuclei, though they can decay via the weak force with a mean lifetime of around 200 ps . Sigma (Σ) hypernuclei have been sought, as have doubly-strange nuclei containing xi baryons (Ξ) or two Λ's.
Hypernuclei are named in terms of their atomic number and baryon number , as in normal nuclei, plus the hyperon(s) which are listed in a left subscript of the symbol, with the caveat that atomic number is interpreted as the total charge of the hypernucleus, including charged hyperons such as the xi minus (Ξ − ) as well as protons. For example, the hypernucleus 16 Λ O contains 8 protons, 7 neutrons, and one Λ (which carries no charge). [ 1 ]
The first was discovered by Marian Danysz and Jerzy Pniewski in 1952 using a nuclear emulsion plate exposed to cosmic rays , based on their energetic but delayed decay. This event was inferred to be due to a nuclear fragment containing a Λ baryon. [ 2 ] Experiments until the 1970s would continue to study hypernuclei produced in emulsions using cosmic rays, and later using pion (π) and kaon (K) beams from particle accelerators . [ 1 ]
Since the 1980s, more efficient production methods using pion and kaon beams have allowed further investigation at various accelerator facilities, including CERN , Brookhaven National Laboratory , KEK , DAφNE , and JPARC . [ 3 ] [ 4 ] In the 2010s, heavy ion experiments such as ALICE and STAR first allowed the production and measurement of light hypernuclei formed through hadronization from quark–gluon plasma . [ 5 ]
Hypernuclear physics differs from that of normal nuclei because a hyperon is distinguishable from the four nucleon spin and isospin . That is, a single hyperon is not restricted by the Pauli exclusion principle , and can sink to the lowest energy level. [ 6 ] As such, hypernuclei are often smaller and more tightly bound than normal nuclei; [ 7 ] for example, the lithium hypernucleus 7 Λ Li is 19% smaller than the normal nucleus 6 Li. [ 8 ] [ 9 ] However, the hyperons can decay via the weak force ; the mean lifetime of a free Λ is 263 ± 2 ps , and that of a Λ hypernucleus is usually slightly shorter. [ 10 ]
A generalized mass formula developed for both the non-strange normal nuclei and strange hypernuclei can estimate masses of hypernuclei containing Λ, ΛΛ, Σ, and Ξ hyperon(s). [ 11 ] [ 12 ] The neutron and proton driplines for hypernuclei are predicted and existence of some exotic hypernuclei beyond the normal neutron and proton driplines are suggested. [ 7 ] This generalized mass formula was named the "Samanta formula" by Botvina and Pochodzalla and used to predict relative yields of hypernuclei in heavy-ion collisions. [ 13 ]
The simplest, and most well understood, type of hypernucleus includes only the lightest hyperon, the Λ. [ 6 ]
While two nucleons can interact through the nuclear force mediated by a virtual pion, the Λ becomes a Σ baryon upon emitting a pion, [ a ] so the Λ–nucleon interaction is mediated solely by more massive mesons such as the η and ω mesons, or through the simultaneous exchange of two or more mesons. [ 15 ] This means that the Λ–nucleon interaction is weaker and has a shorter range than the standard nuclear force, and the potential well of a Λ in the nucleus is shallower than that of a nucleon; [ 16 ] in hypernuclei, the depth of the Λ potential is approximately 30 MeV . [ 17 ] However, one-pion exchange in the Λ–nucleon interaction does cause quantum-mechanical mixing of the Λ and Σ baryons in hypernuclei (which does not happen in free space), especially in neutron-rich hypernuclei. [ 18 ] [ 19 ] [ 20 ] Additionally, the three-body force between a Λ and two nucleons is expected to be more important than the three-body interaction in nuclei, since the Λ can exchange two pions with a virtual Σ intermediate, while the equivalent process in nucleons requires a relatively heavy delta baryon (Δ) intermediate. [ 15 ]
Like all hyperons, Λ hypernuclei can decay through the weak interaction , which changes it to a lighter baryon and emits a meson or a lepton –antilepton pair. In free space, the Λ usually decays via the weak force to a proton and a π – meson, or a neutron and a π 0 , with a total half-life of 263 ± 2 ps . [ 21 ] A nucleon in the hypernucleus can cause the Λ to decay via the weak force without emitting a pion; this process becomes dominant in heavy hypernuclei, due to suppression of the pion-emitting decay mode. [ 22 ] The half-life of the Λ in a hypernucleus is considerably shorter, plateauing to about 215 ± 14 ps near 56 Λ Fe , [ 23 ] but some empirical measurements substantially disagree with each other or with theoretical predictions. [ 24 ]
The simplest hypernucleus is the hypertriton ( 3 Λ H ), which consists of one proton, one neutron, and one Λ hyperon. The Λ in this system is very loosely bound, having a separation energy of 130 keV and a large radius of 10.6 fm , [ 25 ] compared to about 2.13 fm for the deuteron . [ 26 ]
This loose binding would imply a lifetime similar to a free Λ. However, the measured hypertriton lifetime averaged across all experiments (about 206 +15 −13 ps ) is substantially shorter than predicted by theory, as the non-mesonic decay mode is expected to be relatively minor; some experimental results are substantially shorter or longer than this average. [ 27 ] [ 28 ]
The existence of hypernuclei containing a Σ baryon is less clear. Several experiments in the early 1980s reported bound hypernuclear states above the Λ separation energy and presumed to contain one of the slightly heavier Σ baryons, but experiments later in the decade ruled out the existence of such states. [ 6 ] Results from exotic atoms containing a Σ − bound to a nucleus by the electromagnetic force have found a net repulsive Σ–nucleon interaction in medium-sized and large hypernuclei, which means that no Σ hypernuclei exist in such mass range. [ 6 ] However, an experiment in 1998 definitively observed the light Σ hypernucleus 4 Σ He . [ 6 ]
Hypernuclei containing two Λ baryons have been made. However, such hypernuclei are much harder to produce due to containing two strange quarks and, as of 2016, only seven candidate ΛΛ hypernuclei have been observed. [ 29 ] Like the Λ–nucleon interaction, empirical and theoretical models predict that the Λ–Λ interaction is mildly attractive. [ 30 ] [ 31 ]
Hypernuclei containing a Ξ baryon are known. [ citation needed ] Empirical studies and theoretical models indicate that the Ξ – –proton interaction is attractive, but weaker than the Λ–nucleon interaction. [ 30 ] Like the Σ – and other negatively charged particles, the Ξ – can also form an exotic atom. When a Ξ – is bound in an exotic atom or a hypernucleus, it quickly decays to a ΛΛ hypernucleus or to two Λ hypernuclei by exchanging a strange quark with a proton, which releases about 29 MeV of energy in free space: [ b ]
Hypernuclei containing the omega baryon (Ω) were predicted using lattice QCD in 2018; in particular, the proton–Ω and Ω–Ω dibaryons (bound systems containing two baryons) are expected to be stable. [ 35 ] [ 36 ] As of 2022 [update] , no such hypernuclei have been observed under any conditions, but the lightest such species could be produced in heavy-ion collisions, [ 37 ] and measurements by the STAR experiment are consistent with the existence of the proton–Ω dibaryon. [ 38 ]
Since the Λ is electrically neutral and its nuclear force interactions are attractive, there are predicted to be arbitrarily large hypernuclei with high strangeness and small net charge, including species with no nucleons. Binding energy per baryon in multi-strange hypernuclei can reach up to 21 MeV/ A under certain conditions, [ 7 ] compared to 8.80 MeV/ A for the ordinary nucleus 62 Ni . [ 39 ] Additionally, formation of Ξ baryons should quickly become energetically favorable, unlike when there are no Λ's, because the exchange of strangeness with a nucleon would be impossible due to the Pauli exclusion principle. [ 40 ]
Several modes of production have been devised to make hypernuclei through bombardment of normal nuclei.
One method of producing a K − meson exchanges a strange quark with a nucleon and changes it to a Λ: [ 41 ]
The cross section for the formation of a hypernucleus is maximized when the momentum of the kaon beam is approximately 500 MeV/ c . [ 42 ] Several variants of this setup exist, including ones where the incident kaons are either brought to rest before colliding with a nucleus. [ 41 ]
In rare cases, the incoming K − can instead produce a Ξ hypernucleus via the reaction:
The equivalent strangeness production reaction involves a π + meson reacts with a neutron to change it to a Λ: [ 44 ]
This reaction has a maximum cross section at a beam momentum of 1.05 GeV/ c , and is the most efficient production route for Λ hypernuclei, but requires larger targets than strangeness exchange methods. [ 44 ]
Electron scattering off of a proton can change it to a Λ and produce a K + : [ 45 ]
where the prime symbol denotes a scattered electron. The energy of an electron beam can be more easily tuned than pion or kaon beams, making it easier to measure and calibrate hypernuclear energy levels. [ 45 ] Initially theoretically predicted in the 1980s, this method was first used experimentally in the early 2000s. [ 46 ]
The capture of a Ξ − baryon by a nucleus can make a Ξ − exotic atom or hypernucleus. [ 33 ] Upon capture, it changes to a ΛΛ hypernucleus or two Λ hypernuclei. [ 47 ] The disadvantage is that the Ξ − baryon is harder to make into a beam than singly strange hadrons. [ 48 ] However, an experiment at J-PARC begun in 2020 will compile data on Ξ and ΛΛ hypernuclei using a similar, non-beam setup where scattered Ξ − baryons rain onto an emulsion target. [ 33 ]
The K – meson can orbit a nucleus in an exotic atom, such as in kaonic hydrogen . [ 49 ] Although the K – -proton strong interaction in kaonic hydrogen is repulsive, [ 50 ] the K – –nucleus interaction is attractive for larger systems, so this meson can enter a strongly bound state closely related to a hypernucleus; [ 6 ] in particular, the K – –proton–proton system is experimentally known and more tightly bound than a normal nucleus. [ 51 ]
Nuclei containing a charm quark have been predicted theoretically since 1977, [ 52 ] and are described as charmed hypernuclei despite the possible absence of strange quarks. [ 53 ] In particular, the lightest charmed baryons, the Λ c and Σ c baryons, [ c ] are predicted to exist in bound states in charmed hypernuclei, and could be created in processes analogous to those used to make hypernuclei. [ 53 ] The depth of the Λ c potential in nuclear matter is predicted to be 58 MeV, [ 53 ] but unlike Λ hypernuclei, larger hypernuclei containing the positively charged Λ c would be less stable than the corresponding Λ hypernuclei due to Coulomb repulsion . [ 54 ] The mass difference between the Λ c and the Σ + c is too large for appreciable mixing of these baryons to occur in hypernuclei. [ 55 ] Weak decays of charmed hypernuclei have strong relativistic corrections compared to those in ordinary hypernuclei, as the energy released in the decay process is comparable to the mass of the Λ baryon. [ 56 ]
In August 2024 the STAR Collaboration reported the observation of the heaviest antimatter nucleus known, antihyperhydrogen-4 Λ ¯ 4 H ¯ {\displaystyle {}_{\bar {\boldsymbol {\Lambda }}}{}^{\bf {4}}{\bar {\bf {H}}}} consisting of one antiproton , two antineutrons and an antihyperon . [ 57 ] [ 58 ] [ 59 ]
The anti-lambda hyperon Λ ¯ {\displaystyle {\bar {\Lambda }}} [ 60 ] and the antihypertriton Λ ¯ 3 H ¯ {\displaystyle {}_{\bar {\Lambda }}{}^{3}{\bar {\rm {H}}}} [ 61 ] have also been previously observed. | https://en.wikipedia.org/wiki/Hypernuclear_spectroscopy |
A hypernucleus is similar to a conventional atomic nucleus , but contains at least one hyperon in addition to the normal protons and neutrons . Hyperons are a category of baryon particles that carry non-zero strangeness quantum number, which is conserved by the strong and electromagnetic interactions .
A variety of reactions give access to depositing one or more units of strangeness in a nucleus. Hypernuclei containing the lightest hyperon, the lambda (Λ), tend to be more tightly bound than normal nuclei, though they can decay via the weak force with a mean lifetime of around 200 ps . Sigma (Σ) hypernuclei have been sought, as have doubly-strange nuclei containing xi baryons (Ξ) or two Λ's.
Hypernuclei are named in terms of their atomic number and baryon number , as in normal nuclei, plus the hyperon(s) which are listed in a left subscript of the symbol, with the caveat that atomic number is interpreted as the total charge of the hypernucleus, including charged hyperons such as the xi minus (Ξ − ) as well as protons. For example, the hypernucleus 16 Λ O contains 8 protons, 7 neutrons, and one Λ (which carries no charge). [ 1 ]
The first was discovered by Marian Danysz and Jerzy Pniewski in 1952 using a nuclear emulsion plate exposed to cosmic rays , based on their energetic but delayed decay. This event was inferred to be due to a nuclear fragment containing a Λ baryon. [ 2 ] Experiments until the 1970s would continue to study hypernuclei produced in emulsions using cosmic rays, and later using pion (π) and kaon (K) beams from particle accelerators . [ 1 ]
Since the 1980s, more efficient production methods using pion and kaon beams have allowed further investigation at various accelerator facilities, including CERN , Brookhaven National Laboratory , KEK , DAφNE , and JPARC . [ 3 ] [ 4 ] In the 2010s, heavy ion experiments such as ALICE and STAR first allowed the production and measurement of light hypernuclei formed through hadronization from quark–gluon plasma . [ 5 ]
Hypernuclear physics differs from that of normal nuclei because a hyperon is distinguishable from the four nucleon spin and isospin . That is, a single hyperon is not restricted by the Pauli exclusion principle , and can sink to the lowest energy level. [ 6 ] As such, hypernuclei are often smaller and more tightly bound than normal nuclei; [ 7 ] for example, the lithium hypernucleus 7 Λ Li is 19% smaller than the normal nucleus 6 Li. [ 8 ] [ 9 ] However, the hyperons can decay via the weak force ; the mean lifetime of a free Λ is 263 ± 2 ps , and that of a Λ hypernucleus is usually slightly shorter. [ 10 ]
A generalized mass formula developed for both the non-strange normal nuclei and strange hypernuclei can estimate masses of hypernuclei containing Λ, ΛΛ, Σ, and Ξ hyperon(s). [ 11 ] [ 12 ] The neutron and proton driplines for hypernuclei are predicted and existence of some exotic hypernuclei beyond the normal neutron and proton driplines are suggested. [ 7 ] This generalized mass formula was named the "Samanta formula" by Botvina and Pochodzalla and used to predict relative yields of hypernuclei in heavy-ion collisions. [ 13 ]
The simplest, and most well understood, type of hypernucleus includes only the lightest hyperon, the Λ. [ 6 ]
While two nucleons can interact through the nuclear force mediated by a virtual pion, the Λ becomes a Σ baryon upon emitting a pion, [ a ] so the Λ–nucleon interaction is mediated solely by more massive mesons such as the η and ω mesons, or through the simultaneous exchange of two or more mesons. [ 15 ] This means that the Λ–nucleon interaction is weaker and has a shorter range than the standard nuclear force, and the potential well of a Λ in the nucleus is shallower than that of a nucleon; [ 16 ] in hypernuclei, the depth of the Λ potential is approximately 30 MeV . [ 17 ] However, one-pion exchange in the Λ–nucleon interaction does cause quantum-mechanical mixing of the Λ and Σ baryons in hypernuclei (which does not happen in free space), especially in neutron-rich hypernuclei. [ 18 ] [ 19 ] [ 20 ] Additionally, the three-body force between a Λ and two nucleons is expected to be more important than the three-body interaction in nuclei, since the Λ can exchange two pions with a virtual Σ intermediate, while the equivalent process in nucleons requires a relatively heavy delta baryon (Δ) intermediate. [ 15 ]
Like all hyperons, Λ hypernuclei can decay through the weak interaction , which changes it to a lighter baryon and emits a meson or a lepton –antilepton pair. In free space, the Λ usually decays via the weak force to a proton and a π – meson, or a neutron and a π 0 , with a total half-life of 263 ± 2 ps . [ 21 ] A nucleon in the hypernucleus can cause the Λ to decay via the weak force without emitting a pion; this process becomes dominant in heavy hypernuclei, due to suppression of the pion-emitting decay mode. [ 22 ] The half-life of the Λ in a hypernucleus is considerably shorter, plateauing to about 215 ± 14 ps near 56 Λ Fe , [ 23 ] but some empirical measurements substantially disagree with each other or with theoretical predictions. [ 24 ]
The simplest hypernucleus is the hypertriton ( 3 Λ H ), which consists of one proton, one neutron, and one Λ hyperon. The Λ in this system is very loosely bound, having a separation energy of 130 keV and a large radius of 10.6 fm , [ 25 ] compared to about 2.13 fm for the deuteron . [ 26 ]
This loose binding would imply a lifetime similar to a free Λ. However, the measured hypertriton lifetime averaged across all experiments (about 206 +15 −13 ps ) is substantially shorter than predicted by theory, as the non-mesonic decay mode is expected to be relatively minor; some experimental results are substantially shorter or longer than this average. [ 27 ] [ 28 ]
The existence of hypernuclei containing a Σ baryon is less clear. Several experiments in the early 1980s reported bound hypernuclear states above the Λ separation energy and presumed to contain one of the slightly heavier Σ baryons, but experiments later in the decade ruled out the existence of such states. [ 6 ] Results from exotic atoms containing a Σ − bound to a nucleus by the electromagnetic force have found a net repulsive Σ–nucleon interaction in medium-sized and large hypernuclei, which means that no Σ hypernuclei exist in such mass range. [ 6 ] However, an experiment in 1998 definitively observed the light Σ hypernucleus 4 Σ He . [ 6 ]
Hypernuclei containing two Λ baryons have been made. However, such hypernuclei are much harder to produce due to containing two strange quarks and, as of 2016, only seven candidate ΛΛ hypernuclei have been observed. [ 29 ] Like the Λ–nucleon interaction, empirical and theoretical models predict that the Λ–Λ interaction is mildly attractive. [ 30 ] [ 31 ]
Hypernuclei containing a Ξ baryon are known. [ citation needed ] Empirical studies and theoretical models indicate that the Ξ – –proton interaction is attractive, but weaker than the Λ–nucleon interaction. [ 30 ] Like the Σ – and other negatively charged particles, the Ξ – can also form an exotic atom. When a Ξ – is bound in an exotic atom or a hypernucleus, it quickly decays to a ΛΛ hypernucleus or to two Λ hypernuclei by exchanging a strange quark with a proton, which releases about 29 MeV of energy in free space: [ b ]
Hypernuclei containing the omega baryon (Ω) were predicted using lattice QCD in 2018; in particular, the proton–Ω and Ω–Ω dibaryons (bound systems containing two baryons) are expected to be stable. [ 35 ] [ 36 ] As of 2022 [update] , no such hypernuclei have been observed under any conditions, but the lightest such species could be produced in heavy-ion collisions, [ 37 ] and measurements by the STAR experiment are consistent with the existence of the proton–Ω dibaryon. [ 38 ]
Since the Λ is electrically neutral and its nuclear force interactions are attractive, there are predicted to be arbitrarily large hypernuclei with high strangeness and small net charge, including species with no nucleons. Binding energy per baryon in multi-strange hypernuclei can reach up to 21 MeV/ A under certain conditions, [ 7 ] compared to 8.80 MeV/ A for the ordinary nucleus 62 Ni . [ 39 ] Additionally, formation of Ξ baryons should quickly become energetically favorable, unlike when there are no Λ's, because the exchange of strangeness with a nucleon would be impossible due to the Pauli exclusion principle. [ 40 ]
Several modes of production have been devised to make hypernuclei through bombardment of normal nuclei.
One method of producing a K − meson exchanges a strange quark with a nucleon and changes it to a Λ: [ 41 ]
The cross section for the formation of a hypernucleus is maximized when the momentum of the kaon beam is approximately 500 MeV/ c . [ 42 ] Several variants of this setup exist, including ones where the incident kaons are either brought to rest before colliding with a nucleus. [ 41 ]
In rare cases, the incoming K − can instead produce a Ξ hypernucleus via the reaction:
The equivalent strangeness production reaction involves a π + meson reacts with a neutron to change it to a Λ: [ 44 ]
This reaction has a maximum cross section at a beam momentum of 1.05 GeV/ c , and is the most efficient production route for Λ hypernuclei, but requires larger targets than strangeness exchange methods. [ 44 ]
Electron scattering off of a proton can change it to a Λ and produce a K + : [ 45 ]
where the prime symbol denotes a scattered electron. The energy of an electron beam can be more easily tuned than pion or kaon beams, making it easier to measure and calibrate hypernuclear energy levels. [ 45 ] Initially theoretically predicted in the 1980s, this method was first used experimentally in the early 2000s. [ 46 ]
The capture of a Ξ − baryon by a nucleus can make a Ξ − exotic atom or hypernucleus. [ 33 ] Upon capture, it changes to a ΛΛ hypernucleus or two Λ hypernuclei. [ 47 ] The disadvantage is that the Ξ − baryon is harder to make into a beam than singly strange hadrons. [ 48 ] However, an experiment at J-PARC begun in 2020 will compile data on Ξ and ΛΛ hypernuclei using a similar, non-beam setup where scattered Ξ − baryons rain onto an emulsion target. [ 33 ]
The K – meson can orbit a nucleus in an exotic atom, such as in kaonic hydrogen . [ 49 ] Although the K – -proton strong interaction in kaonic hydrogen is repulsive, [ 50 ] the K – –nucleus interaction is attractive for larger systems, so this meson can enter a strongly bound state closely related to a hypernucleus; [ 6 ] in particular, the K – –proton–proton system is experimentally known and more tightly bound than a normal nucleus. [ 51 ]
Nuclei containing a charm quark have been predicted theoretically since 1977, [ 52 ] and are described as charmed hypernuclei despite the possible absence of strange quarks. [ 53 ] In particular, the lightest charmed baryons, the Λ c and Σ c baryons, [ c ] are predicted to exist in bound states in charmed hypernuclei, and could be created in processes analogous to those used to make hypernuclei. [ 53 ] The depth of the Λ c potential in nuclear matter is predicted to be 58 MeV, [ 53 ] but unlike Λ hypernuclei, larger hypernuclei containing the positively charged Λ c would be less stable than the corresponding Λ hypernuclei due to Coulomb repulsion . [ 54 ] The mass difference between the Λ c and the Σ + c is too large for appreciable mixing of these baryons to occur in hypernuclei. [ 55 ] Weak decays of charmed hypernuclei have strong relativistic corrections compared to those in ordinary hypernuclei, as the energy released in the decay process is comparable to the mass of the Λ baryon. [ 56 ]
In August 2024 the STAR Collaboration reported the observation of the heaviest antimatter nucleus known, antihyperhydrogen-4 Λ ¯ 4 H ¯ {\displaystyle {}_{\bar {\boldsymbol {\Lambda }}}{}^{\bf {4}}{\bar {\bf {H}}}} consisting of one antiproton , two antineutrons and an antihyperon . [ 57 ] [ 58 ] [ 59 ]
The anti-lambda hyperon Λ ¯ {\displaystyle {\bar {\Lambda }}} [ 60 ] and the antihypertriton Λ ¯ 3 H ¯ {\displaystyle {}_{\bar {\Lambda }}{}^{3}{\bar {\rm {H}}}} [ 61 ] have also been previously observed. | https://en.wikipedia.org/wiki/Hypernucleus |
In mathematics , the hyperoperation sequence [ nb 1 ] is an infinite sequence of arithmetic operations (called hyperoperations in this context) [ 1 ] [ 11 ] [ 13 ] that starts with a unary operation (the successor function with n = 0). The sequence continues with the binary operations of addition ( n = 1), multiplication ( n = 2), and exponentiation ( n = 3).
After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity . For the operations beyond exponentiation, the n th member of this sequence is named by Reuben Goodstein after the Greek prefix of n suffixed with -ation (such as tetration ( n = 4), pentation ( n = 5), hexation ( n = 6), etc.) [ 5 ] and can be written as using n − 2 arrows in Knuth's up-arrow notation .
Each hyperoperation may be understood recursively in terms of the previous one by:
It may also be defined according to the recursion rule part of the definition, as in Knuth's up-arrow version of the Ackermann function :
This can be used to easily show numbers much larger than those which scientific notation can, such as Skewes's number and googolplexplex (e.g. 50 [ 50 ] 50 {\displaystyle 50[50]50} is much larger than Skewes's number and googolplexplex), but there are some numbers which even they cannot easily show, such as Graham's number and TREE(3) . [ 14 ]
This recursion rule is common to many variants of hyperoperations.
The hyperoperation sequence H n ( a , b ) : ( N 0 ) 3 → N 0 {\displaystyle H_{n}(a,b)\colon (\mathbb {N} _{0})^{3}\rightarrow \mathbb {N} _{0}} is the sequence of binary operations H n : ( N 0 ) 2 → N 0 {\displaystyle H_{n}\colon (\mathbb {N} _{0})^{2}\rightarrow \mathbb {N} _{0}} , defined recursively as follows:
(Note that for n = 0, the binary operation essentially reduces to a unary operation ( successor function ) by ignoring the first argument.)
For n = 0, 1, 2, 3, this definition reproduces the basic arithmetic operations of successor (which is a unary operation), addition , multiplication , and exponentiation , respectively, as
The H n {\displaystyle H_{n}} operations for n ≥ 3 can be written in Knuth's up-arrow notation .
So what will be the next operation after exponentiation? We defined multiplication so that H 2 ( a , 3 ) = a [ 2 ] 3 = a × 3 = a + a + a , {\displaystyle H_{2}(a,3)=a[2]3=a\times 3=a+a+a,} and defined exponentiation so that H 3 ( a , 3 ) = a [ 3 ] 3 = a ↑ 3 = a 3 = a × a × a , {\displaystyle H_{3}(a,3)=a[3]3=a\uparrow 3=a^{3}=a\times a\times a,} so it seems logical to define the next operation, tetration, so that H 4 ( a , 3 ) = a [ 4 ] 3 = a ↑ ↑ 3 = tetration ( a , 3 ) = a a a , {\displaystyle H_{4}(a,3)=a[4]3=a\uparrow \uparrow 3=\operatorname {tetration} (a,3)=a^{a^{a}},} with a tower of three 'a'. Analogously, the pentation of (a, 3) will be tetration(a, tetration(a, a)), with three "a" in it.
Knuth's notation could be extended to negative indices ≥ −2 in such a way as to agree with the entire hyperoperation sequence, except for the lag in the indexing:
The hyperoperations can thus be seen as an answer to the question "what's next" in the sequence : successor , addition , multiplication , exponentiation , and so on. Noting that
the relationship between basic arithmetic operations is illustrated, allowing the higher operations to be defined naturally as above. The parameters of the hyperoperation hierarchy are sometimes referred to by their analogous exponentiation term; [ 15 ] so a is the base , b is the exponent (or hyperexponent ), [ 12 ] and n is the rank (or grade ), [ 6 ] and moreover, H n ( a , b ) {\displaystyle H_{n}(a,b)} is read as "the b th n -ation of a ", e.g. H 4 ( 7 , 9 ) {\displaystyle H_{4}(7,9)} is read as "the 9th tetration of 7", and H 123 ( 456 , 789 ) {\displaystyle H_{123}(456,789)} is read as "the 789th 123-ation of 456".
In common terms, the hyperoperations are ways of compounding numbers that increase in growth based on the iteration of the previous hyperoperation. The concepts of successor, addition, multiplication and exponentiation are all hyperoperations; the successor operation (producing x + 1 from x ) is the most primitive, the addition operator specifies the number of times 1 is to be added to itself to produce a final value, multiplication specifies the number of times a number is to be added to itself, and exponentiation refers to the number of times a number is to be multiplied by itself.
Define iteration of a function f of two variables as
The hyperoperation sequence can be defined in terms of iteration, as follows. For all integers x , n , a , b ≥ 0 , {\displaystyle x,n,a,b\geq 0,} define
As iteration is associative , the last line can be replaced by
The definitions of the hyperoperation sequence can naturally be transposed to term rewriting systems (TRS) .
The basic definition of the hyperoperation sequence corresponds with the reduction rules
To compute H n ( a , b ) {\displaystyle H_{n}(a,b)} one can use a stack , which initially contains the elements ⟨ n , a , b ⟩ {\displaystyle \langle n,a,b\rangle } .
Then, repeatedly until no longer possible, three elements are popped and replaced according to the rules [ nb 2 ]
Schematically, starting from ⟨ n , a , b ⟩ {\displaystyle \langle n,a,b\rangle } :
Example
Compute H 2 ( 2 , 2 ) → ∗ 4 {\displaystyle H_{2}(2,2)\rightarrow _{*}4} . [ 16 ]
The reduction sequence is [ nb 2 ] [ 17 ]
When implemented using a stack, on input ⟨ 2 , 2 , 2 ⟩ {\displaystyle \langle 2,2,2\rangle }
The definition using iteration leads to a different set of reduction rules
As iteration is associative , instead of rule r11 one can define
Like in the previous section the computation of H n ( a , b ) = H n 1 ( a , b ) {\displaystyle H_{n}(a,b)=H_{n}^{1}(a,b)} can be implemented using a stack.
Initially the stack contains the four elements ⟨ 1 , n , a , b ⟩ {\displaystyle \langle 1,n,a,b\rangle } .
Then, until termination, four elements are popped and replaced according to the rules [ nb 2 ]
Schematically, starting from ⟨ 1 , n , a , b ⟩ {\displaystyle \langle 1,n,a,b\rangle } :
Example
Compute H 3 ( 0 , 3 ) → ∗ 0 {\displaystyle H_{3}(0,3)\rightarrow _{*}0} .
On input ⟨ 1 , 3 , 0 , 3 ⟩ {\displaystyle \langle 1,3,0,3\rangle } the successive stack configurations are
The corresponding equalities are
When reduction rule r11 is replaced by rule r12, the stack is transformed according to
The successive stack configurations will then be
The corresponding equalities are
Remarks
Below is a list of the first seven (0th to 6th) hyperoperations ( 0⁰ is defined as 1).
H n (0, b ) =
H n (1, b ) =
H n ( a , 0) =
H n ( a , 1) =
H n ( a , a ) =
H n ( a , −1) = [ nb 5 ]
H n (2, 2) =
One of the earliest discussions of hyperoperations was that of Albert Bennett in 1914, who developed some of the theory of commutative hyperoperations (see below ). [ 6 ] About 12 years later, Wilhelm Ackermann defined the function ϕ ( a , b , n ) {\displaystyle \phi (a,b,n)} , which somewhat resembles the hyperoperation sequence. [ 20 ]
In his 1947 paper, [ 5 ] Reuben Goodstein introduced the specific sequence of operations that are now called hyperoperations , and also suggested the Greek names tetration , pentation, etc., for the extended operations beyond exponentiation (because they correspond to the indices 4, 5, etc.). As a three-argument function, e.g., G ( n , a , b ) = H n ( a , b ) {\displaystyle G(n,a,b)=H_{n}(a,b)} , the hyperoperation sequence as a whole is seen to be a version of the original Ackermann function ϕ ( a , b , n ) {\displaystyle \phi (a,b,n)} — recursive but not primitive recursive — as modified by Goodstein to incorporate the primitive successor function together with the other three basic operations of arithmetic ( addition , multiplication , exponentiation ), and to make a more seamless extension of these beyond exponentiation.
The original three-argument Ackermann function ϕ {\displaystyle \phi } uses the same recursion rule as does Goodstein's version of it (i.e., the hyperoperation sequence), but differs from it in two ways. First, ϕ ( a , b , n ) {\displaystyle \phi (a,b,n)} defines a sequence of operations starting from addition ( n = 0) rather than the successor function , then multiplication ( n = 1), exponentiation ( n = 2), etc. Secondly, the initial conditions for ϕ {\displaystyle \phi } result in ϕ ( a , b , 3 ) = G ( 4 , a , b + 1 ) = a [ 4 ] ( b + 1 ) {\displaystyle \phi (a,b,3)=G(4,a,b+1)=a[4](b+1)} , thus differing from the hyperoperations beyond exponentiation. [ 7 ] [ 21 ] [ 22 ] The significance of the b + 1 in the previous expression is that ϕ ( a , b , 3 ) {\displaystyle \phi (a,b,3)} = a a ⋅ ⋅ ⋅ a {\displaystyle a^{a^{\cdot ^{\cdot ^{\cdot ^{a}}}}}} , where b counts the number of operators (exponentiations), rather than counting the number of operands ("a"s) as does the b in a [ 4 ] b {\displaystyle a[4]b} , and so on for the higher-level operations. (See the Ackermann function article for details.)
This is a list of notations that have been used for hyperoperations.
In 1928, Wilhelm Ackermann defined a 3-argument function ϕ ( a , b , n ) {\displaystyle \phi (a,b,n)} which gradually evolved into a 2-argument function known as the Ackermann function . The original Ackermann function ϕ {\displaystyle \phi } was less similar to modern hyperoperations, because his initial conditions start with ϕ ( a , 0 , n ) = a {\displaystyle \phi (a,0,n)=a} for all n > 2. Also he assigned addition to n = 0, multiplication to n = 1 and exponentiation to n = 2, so the initial conditions produce very different operations for tetration and beyond.
Another initial condition that has been used is A ( 0 , b ) = 2 b + 1 {\displaystyle A(0,b)=2b+1} (where the base is constant a = 2 {\displaystyle a=2} ), due to Rózsa Péter , which does not form a hyperoperation hierarchy.
In 1984, C. W. Clenshaw and F. W. J. Olver began the discussion of using hyperoperations to prevent computer floating-point overflows. [ 29 ] Since then, many other authors [ 30 ] [ 31 ] [ 32 ] have renewed interest in the application of hyperoperations to floating-point representation. (Since H n ( a , b ) are all defined for b = -1.) While discussing tetration , Clenshaw et al. assumed the initial condition F n ( a , 0 ) = 0 {\displaystyle F_{n}(a,0)=0} , which makes yet another hyperoperation hierarchy. Just like in the previous variant, the fourth operation is very similar to tetration , but offset by one.
An alternative for these hyperoperations is obtained by evaluation from left to right. [ 9 ] Since
define (with ° or subscript)
with
This was extended to ordinal numbers by Doner and Tarski, [ 33 ] by :
It follows from Definition 1(i), Corollary 2(ii), and Theorem 9, that, for a ≥ 2 and b ≥ 1, that [ original research? ]
But this suffers a kind of collapse, failing to form the "power tower" traditionally expected of hyperoperators: [ 34 ] [ nb 6 ]
If α ≥ 2 and γ ≥ 2, [ 28 ] [Corollary 33(i)] [ nb 6 ]
Commutative hyperoperations were considered by Albert Bennett as early as 1914, [ 6 ] which is possibly the earliest remark about any hyperoperation sequence. Commutative hyperoperations are defined by the recursion rule
which is symmetric in a and b , meaning all hyperoperations are commutative. This sequence does not contain exponentiation , and so does not form a hyperoperation hierarchy.
R. L. Goodstein [ 5 ] used the sequence of hyperoperators to create systems of numeration for the nonnegative integers. The so-called complete hereditary representation of integer n , at level k and base b , can be expressed as follows using only the first k hyperoperators and using as digits only 0, 1, ..., b − 1, together with the base b itself:
Unnecessary parentheses can be avoided by giving higher-level operators higher precedence in the order of evaluation; thus,
and so on.
In this type of base- b hereditary representation, the base itself appears in the expressions, as well as "digits" from the set {0, 1, ..., b − 1}. This compares to ordinary base-2 representation when the latter is written out in terms of the base b ; e.g., in ordinary base-2 notation, 6 = (110) 2 = 2 [3] 2 [2] 1 [1] 2 [3] 1 [2] 1 [1] 2 [3] 0 [2] 0, whereas the level-3 base-2 hereditary representation is 6 = 2 [3] (2 [3] 1 [2] 1 [1] 0) [2] 1 [1] (2 [3] 1 [2] 1 [1] 0). The hereditary representations can be abbreviated by omitting any instances of [1] 0, [2] 1, [3] 1, [4] 1, etc.; for example, the above level-3 base-2 representation of 6 abbreviates to 2 [3] 2 [1] 2.
Examples:
The unique base-2 representations of the number 266 , at levels 1, 2, 3, 4, and 5 are as follows: | https://en.wikipedia.org/wiki/Hyperoperation |
Hyperpigmentation , also known as the dark spots or circles on the skin, is the darkening of an area of skin or nails caused by increased melanin .
Hyperpigmentation can be caused by sun damage, inflammation , or other skin injuries, including those related to acne vulgaris . [ 1 ] [ 2 ] [ 3 ] : 854 People with darker skin tones are more prone to hyperpigmentation, especially with excess sun exposure. [ 4 ]
Many forms of hyperpigmentation are caused by an excess production of melanin. [ 4 ] Hyperpigmentation can be diffuse or focal, affecting such areas as the face and the back of the hands. Melanin is produced by melanocytes at the lower layer of the epidermis . Melanin is a class of pigment responsible for producing color in the body in places such as the eyes, skin, and hair. The process of melanin synthesis (melanogenesis) starts with the oxidation of l -tyrosine to l-dopa by the enzyme tyrosine hydroxylase , then to l -dopaquinone and dopachrome , which forms melanin. [ 5 ]
As the body ages, melanocyte distribution becomes less diffuse and its regulation less controlled by the body. UV light stimulates melanocyte activity, and where concentration of the cells is greater, hyperpigmentation occurs. Another form of hyperpigmentation is post-inflammatory hyperpigmentation. These are dark and discoloured spots that appear on the skin following acne that has healed. [ 6 ]
Hyperpigmentation is associated with a number of diseases or conditions, including the following:
Hyperpigmentation can sometimes be induced by dermatological laser procedures.
There are a wide range of depigmenting treatments used for hyperpigmentation conditions, and responses to most are variable. [ 11 ]
Most often treatment of hyperpigmentation caused by melanin overproduction (such as melasma, acne scarring, liver spots) includes the use of topical depigmenting agents, which vary in their efficacy and safety, as well as in prescription rules. [ 12 ]
Many topical treatments disrupt the synthesis of melanin by inhibiting the enzyme tyrosine hydroxylase . [ 5 ]
Several are prescription only in the US, especially in high doses, such as hydroquinone , azelaic acid , [ 13 ] and kojic acid . [ 14 ] Some are available without prescription, such as niacinamide , [ 15 ] [ 16 ] l - ascorbic acid , [ citation needed ] retinoids such as tretinoin , [ 17 ] or cysteamine hydrochloride . [ 18 ] [ 19 ] Hydroquinone was the most commonly prescribed hyperpigmentation treatment before the long-term safety concerns were raised, [ 20 ] and the use of it became more regulated in several countries and discouraged in general by WHO . [ 21 ] For the US, only 2% is at present sold over-the-counter, and 4% needs prescription. In the EU hydroquinone was banned from cosmetic applications. [ 22 ]
Oral medication with procyanidin plus vitamins A, C, and E also shows promise as safe and effective for epidermal melasma. In an 8-week randomized, double-blind, placebo-controlled trial in 56 Filipino women, treatment was associated with significant improvements in the left and right malar regions, and was safe and well tolerated. [ 23 ] Other treatments that do not involve topical agents are also available, including fraction lasers [ 24 ] and dermabrasion. [ 12 ]
Laser toning using YAG lasers [ 25 ] and intense pulsed light have been used to treat hyperpigmentation such as melasma and post-inflammatory hyperpigmentation. [ 26 ] | https://en.wikipedia.org/wiki/Hyperpigmentation |
In geometry , a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension . Like a plane in space , a hyperplane is a flat hypersurface , a subspace whose dimension is one less than that of the ambient space . Two lower-dimensional examples of hyperplanes are one-dimensional lines in a plane and zero-dimensional points on a line.
Most commonly, the ambient space is n -dimensional Euclidean space , in which case the hyperplanes are the ( n − 1) -dimensional "flats" , each of which separates the space into two half spaces . [ 1 ] A reflection across a hyperplane is a kind of motion ( geometric transformation preserving distance between points), and the group of all motions is generated by the reflections. A convex polytope is the intersection of half-spaces.
In non-Euclidean geometry , the ambient space might be the n -dimensional sphere or hyperbolic space , or more generally a pseudo-Riemannian space form , and the hyperplanes are the hypersurfaces consisting of all geodesics through a point which are perpendicular to a specific normal geodesic.
In other kinds of ambient spaces, some properties from Euclidean space are no longer relevant. For example, in affine space , there is no concept of distance, so there are no reflections or motions. In a non-orientable space such as elliptic space or projective space , there is no concept of half-planes. In greatest generality, the notion of hyperplane is meaningful in any mathematical space in which the concept of the dimension of a subspace is defined.
The difference in dimension between a subspace and its ambient space is known as its codimension . A hyperplane has codimension 1 .
In geometry , a hyperplane of an n -dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V . The space V may be a Euclidean space or more generally an affine space , or a vector space or a projective space , and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can be given in coordinates as the solution of a single (due to the "codimension 1" constraint) algebraic equation of degree 1.
If V is a vector space, one distinguishes "vector hyperplanes" (which are linear subspaces , and therefore must pass through the origin) and "affine hyperplanes" (which need not pass through the origin; they can be obtained by translation of a vector hyperplane). A hyperplane in a Euclidean space separates that space into two half spaces , and defines a reflection that fixes the hyperplane and interchanges those two half spaces.
Several specific types of hyperplanes are defined with properties that are well suited for particular purposes. Some of these specializations are described here.
An affine hyperplane is an affine subspace of codimension 1 in an affine space .
In Cartesian coordinates , such a hyperplane can be described with a single linear equation of the following form (where at least one of the a i {\displaystyle a_{i}} s is non-zero and b {\displaystyle b} is an arbitrary constant):
In the case of a real affine space, in other words when the coordinates are real numbers, this affine space separates the space into two half-spaces, which are the connected components of the complement of the hyperplane, and are given by the inequalities
and
As an example, a point is a hyperplane in 1-dimensional space, a line is a hyperplane in 2-dimensional space, and a plane is a hyperplane in 3-dimensional space. A line in 3-dimensional space is not a hyperplane, and does not separate the space into two parts (the complement of such a line is connected).
Any hyperplane of a Euclidean space has exactly two unit normal vectors: ± n ^ {\displaystyle \pm {\hat {n}}} . In particular, if we consider R n + 1 {\displaystyle \mathbb {R} ^{n+1}} equipped with the conventional inner product ( dot product ), then one can define the affine subspace with normal vector n ^ {\displaystyle {\hat {n}}} and origin translation b ~ ∈ R n + 1 {\displaystyle {\tilde {b}}\in \mathbb {R} ^{n+1}} as the set of all x ∈ R n + 1 {\displaystyle x\in \mathbb {R} ^{n+1}} such that n ^ ⋅ ( x − b ~ ) = 0 {\displaystyle {\hat {n}}\cdot (x-{\tilde {b}})=0} .
Affine hyperplanes are used to define decision boundaries in many machine learning algorithms such as linear-combination (oblique) decision trees , and perceptrons .
In a vector space, a vector hyperplane is a subspace of codimension 1, only possibly shifted from the origin by a vector, in which case it is referred to as a flat . Such a hyperplane is the solution of a single linear equation .
Projective hyperplanes , are used in projective geometry . A projective subspace is a set of points with the property that for any two points of the set, all the points on the line determined by the two points are contained in the set. [ 2 ] Projective geometry can be viewed as affine geometry with vanishing points (points at infinity) added. An affine hyperplane together with the associated points at infinity forms a projective hyperplane. One special case of a projective hyperplane is the infinite or ideal hyperplane , which is defined with the set of all points at infinity.
In projective space, a hyperplane does not divide the space into two parts; rather, it takes two hyperplanes to separate points and divide up the space. The reason for this is that the space essentially "wraps around" so that both sides of a lone hyperplane are connected to each other.
In convex geometry , two disjoint convex sets in n-dimensional Euclidean space are separated by a hyperplane, a result called the hyperplane separation theorem .
In machine learning , hyperplanes are a key tool to create support vector machines for such tasks as computer vision and natural language processing .
The datapoint and its predicted value via a linear model is a hyperplane.
In astronomy , hyperplanes can be used to calculate shortest distance between star systems, galaxies and celestial bodies with regard of general relativity and curvature of space-time as optimized geodesic or paths influenced by gravitational fields.
The dihedral angle between two non-parallel hyperplanes of a Euclidean space is the angle between the corresponding normal vectors . The product of the transformations in the two hyperplanes is a rotation whose axis is the subspace of codimension 2 obtained by intersecting the hyperplanes, and whose angle is twice the angle between the hyperplanes.
A hyperplane H is called a "support" hyperplane of the polyhedron P if P is contained in one of the two closed half-spaces bounded by H and H ∩ P ≠ ∅ {\displaystyle H\cap P\neq \varnothing } . [ 3 ] The intersection of P and H is defined to be a "face" of the polyhedron. The theory of polyhedra and the dimension of the faces are analyzed by looking at these intersections involving hyperplanes. | https://en.wikipedia.org/wiki/Hyperplane |
In geometry , any hyperplane H of a projective space P may be taken as a hyperplane at infinity . Then the set complement P ∖ H is called an affine space . For instance, if ( x 1 , ..., x n , x n +1 ) are homogeneous coordinates for n -dimensional projective space, then the equation x n +1 = 0 defines a hyperplane at infinity for the n -dimensional affine space with coordinates ( x 1 , ..., x n ) . H is also called the ideal hyperplane .
Similarly, starting from an affine space A , every class of parallel lines can be associated with a point at infinity . The union over all classes of parallels constitute the points of the hyperplane at infinity. Adjoining the points of this hyperplane (called ideal points ) to A converts it into an n -dimensional projective space, such as the real projective space R P n .
By adding these ideal points, the entire affine space A is completed to a projective space P , which may be called the projective completion of A . Each affine subspace S of A is completed to a projective subspace of P by adding to S all the ideal points corresponding to the directions of the lines contained in S . The resulting projective subspaces are often called affine subspaces of the projective space P , as opposed to the infinite or ideal subspaces, which are the subspaces of the hyperplane at infinity (however, they are projective spaces, not affine spaces).
In the projective space, each projective subspace of dimension k intersects the ideal hyperplane in a projective subspace "at infinity" whose dimension is k − 1 .
A pair of non- parallel affine hyperplanes intersect at an affine subspace of dimension n − 2 , but a parallel pair of affine hyperplanes intersect at a projective subspace of the ideal hyperplane (the intersection lies on the ideal hyperplane). Thus, parallel hyperplanes, which did not meet in the affine space, intersect in the projective completion due to the addition of the hyperplane at infinity. | https://en.wikipedia.org/wiki/Hyperplane_at_infinity |
Hyperpolarization is a change in a cell's membrane potential that makes it more negative. Cells typically have a negative resting potential, with neuronal action potentials depolarizing the membrane. When the resting membrane potential is made more negative, it increases the minimum stimulus needed to surpass the needed threshold. Neurons naturally become hyperpolarized at the end of an action potential , which is often referred to as the relative refractory period. Relative refractory periods typically last 2 milliseconds, during which a stronger stimulus is needed to trigger another action potential. Cells can also become hyperpolarized depending on channels and receptors present on the membrane, which can have an inhibitory effect.
Hyperpolarization is often caused by efflux of K + (a cation ) through K + channels , or influx of Cl – (an anion ) through Cl – channels . On the other hand, influx of cations , e.g. Na + through Na + channels or Ca 2+ through Ca 2+ channels , inhibits hyperpolarization. If a cell has Na + or Ca 2+ currents at rest, then inhibition of those currents will also result in hyperpolarization. This voltage-gated ion channel response is how the hyperpolarization state is achieved. [ 1 ]
Voltage gated ion channels respond to changes in the membrane potential. Voltage gated potassium, chloride and sodium channels are key components in the generation of the action potential as well as hyper-polarization. These channels work by selecting an ion based on electrostatic attraction or repulsion allowing the ion to bind to the channel. [ 2 ] This releases the water molecule attached to the channel and the ion is passed through the pore. Voltage gated sodium channels open in response to a stimulus and close again. This means the channel either is open or not, there is no part way open. Sometimes the channel closes but is able to be reopened right away, known as channel gating, or it can be closed without being able to be reopened right away, known as channel inactivation.
At resting potential , both the voltage gated sodium and potassium channels are closed but as the cell membrane becomes depolarized the voltage gated sodium channels begin to open up and the neuron begins to depolarize, creating a current feedback loop known as the Hodgkin cycle . [ 2 ] However, potassium ions naturally move out of the cell and if the original depolarization event was not significant enough then the neuron does not generate an action potential. If all the sodium channels are open, however, then the neuron becomes ten times more permeable to sodium than potassium, quickly depolarizing the cell to a peak of +40 mV. [ 2 ] At this level the sodium channels begin to inactivate and voltage gated potassium channels begin to open. This combination of closed sodium channels and open potassium channels leads to the neuron re-polarizing and becoming negative again. The neuron continues to re-polarize until the cell reaches ~ –75 mV, [ 2 ] which is the equilibrium potential of potassium ions. This is the point at which the neuron is hyperpolarized, between –70 mV and –75 mV. After hyperpolarization the potassium channels close and the natural permeability of the neuron to sodium and potassium allows the neuron to return to its resting potential of –70 mV. During the refractory period , which is after hyper-polarization but before the neuron has returned to its resting potential the neuron is capable of triggering an action potential due to the sodium channels ability to be opened, however, because the neuron is more negative it becomes more difficult to reach the action potential threshold.
HCN channels are activated by hyperpolarization.
Recent research has shown that neuronal refractory periods can exceed 20 milliseconds where the relation between hyperpolarization and the neuronal refractory was questioned. [ 3 ] [ 4 ]
Hyperpolarization is a change in membrane potential. Neuroscientists measure it using a technique known as patch clamping that allows them to record ion currents passing through individual channels. This is done using a glass micropipette, also called a patch pipette, with a 1 micrometer diameter. There is a small patch that contains a few ion channels and the rest is sealed off, making this the point of entry for the current. Using an amplifier and a voltage clamp , which is an electronic feedback circuit, allows the experimenter to maintain the membrane potential at a fixed point and the voltage clamp then measures tiny changes in current flow. The membrane currents giving rise to hyperpolarization are either an increase in outward current or a decrease in inward current. [ 2 ]
GABA receptors are commonly known to downregulate neuronal activity by various means.
Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels have been identified as channels that mediate hyperpolarization. They were initially discovered in pacemaker cells of the heart. [ 7 ] These channels are controlled by cAMP, and activated by a hyperpolarized membrane. They allow the flow of Na + and K + ions, typically leading to a slight depolarization. | https://en.wikipedia.org/wiki/Hyperpolarization_(biology) |
Hyperpolarization is the spin polarization of the atomic nuclei of a material in a magnetic field far beyond thermal equilibrium conditions determined by the Boltzmann distribution . [ 1 ] It can be applied to gases such as 129 Xe and 3 He , and small molecules where the polarization levels can be enhanced by a factor of 10 4 –10 5 above thermal equilibrium levels. Hyperpolarized noble gases are typically used in magnetic resonance imaging (MRI) of the lungs. [ 2 ] Hyperpolarized small molecules are typically used for in vivo metabolic imaging. For example, a hyperpolarized metabolite can be injected into animals or patients and the metabolic conversion can be tracked in real-time. Other applications include determining the function of the neutron spin-structures by scattering polarized electrons from a very polarized target ( 3 He), surface interaction studies, and neutron polarizing experiments. [ 3 ]
Spin exchange optical pumping (SEOP) [ 3 ] is one of several hyperpolarization techniques discussed on this page. This technique specializes in creating hyperpolarized (HP) noble gases, such as 3 He, 129 Xe, and quadrupolar 131 Xe, 83 Kr, and 21 Ne. [ 4 ] Noble gases are required because SEOP is performed in the gas phase, they are chemically inert, non-reactive, chemically stable with respect to alkali metals, and their T 1 is long enough to build up polarization. Spin 1/2 noble gases meet all these requirements, and spin 3/2 noble gases do to an extent, although some spin 3/2 do not have a sufficient T 1 . Each of these noble gases has their own specific application, such as characterizing lung space and tissue via in vivo molecular imaging and functional imaging of lungs, to study changes in metabolism of healthy versus cancer cells, [ 4 ] or use as targets for nuclear physics experiments. [ 5 ] During this process, circularly polarized infrared laser light, tuned to the appropriate wavelength, is used to excite electrons in an alkali metal , such as caesium or rubidium inside a sealed glass vessel. Infrared light is necessary because it contains the wavelengths necessary to excite the alkali metal electrons, although the wavelength necessary to excite sodium electrons is below this region (Table 1).
The angular momentum is transferred from the alkali metal electrons to the noble gas nuclei through collisions. Nitrogen is used as a quenching gas, which prevents the fluorescence of the polarized alkali metal, which would lead to de-polarization of the noble gas. If fluorescence was not quenched, the light emitted during relaxation would be randomly polarized, working against the circularly polarized laser light. While different sizes of glass vessels (also called cells), and therefore different pressures, are used depending on the application, one amagat of total pressure of noble gas and nitrogen is sufficient for SEOP and 0.1 amagat of nitrogen density is needed to quench fluorescence. [ 3 ] Great improvements in 129 Xe hyperpolarization technology have achieved > 50% level at flow rates of 1–2 L/min, which enables human clinical applications. [ 9 ]
The discovery of SEOP took decades for all the pieces to fall into place to create a complete technique. First, in 1897, Zeeman's studies of sodium vapor led to the first result of optical pumping . [ 4 ] [ 10 ] The next piece was found in 1950 when Kastler determined a method to electronically spin-polarize rubidium alkali metal vapor using an applied magnetic field and illuminating the vapor with resonant circularly polarized light. [ 4 ] Ten years later, Marie-Anne Bouchiat , T. M. Carver, and C. M. Varnum performed spin exchange , in which the electronic spin polarization was transferred to nuclear spins of a noble gas ( 3 He and 129 Xe) through gas-phased collisions. [ 4 ] Since then, this method has been greatly improved and expanded to use with other noble gases and alkali metals.
To explain the processes of excitation, optical pumping, and spin exchange easier, the most common alkali metal used for this process, rubidium, will be used as an example. Rubidium has an odd number of electrons, with only one in the outermost shell that can be excited under the right conditions. There are two transitions that can occur, one referred to as the D 1 line where the transition occurs from the 5 2 S 1/2 state to the 5 2 P 1/2 state and another referred to the D 2 line where the transition occurs from the 5 2 S 1/2 to the 5 2 P 3/2 state. [ 7 ] [ 11 ] The D 1 and D 2 transitions can occur if the rubidium atoms are illuminated with light at a wavelength of 794.7 nm and 780 nm, respectively (Figure 1). [ 7 ] While it is possible to cause either excitation, laser technology is well-developed for causing the D 1 transition to occur. Those lasers are said to be tuned to the D 1 wavelength (794.7 nm) of rubidium.
In order to increase the polarization level above thermal equilibrium, the populations of the spin states must be altered. In the absence of magnetic field, the two spin states of a spin I = 1 / 2 nuclei are in the same energy level, but in the presence of a magnetic field, the energy levels split into m s = ± 1 / 2 energy levels (Figure 2). [ 12 ] Here, m s is the spin angular momentum with possible values of + 1 / 2 (spin up) or − 1 / 2 (spin down), often drawn as vectors pointing up or down, respectively. The difference in population between these two energy levels is what produces an NMR signal. For example, the two electrons in the spin down state cancel two of the electrons in the spin up state, leaving only one spin up nucleus to be detected with NMR. However, the populations of these states can be altered via hyperpolarization, allowing the spin up energy level to be more populated and therefore increase the NMR signal. This is done by first optically pumping alkali metal, then transferring the polarization to a noble gas nucleus to increase the population of the spin up state.
The absorption of laser light by the alkali metal is the first process in SEOP. [ 3 ] Left-circularly polarized light tuned to the D 1 wavelength of the alkali metal excites the electrons from the spin down 2 S 1/2 (m s =−1/2) state into the spin up 2 P 1/2 (m s =+1/2) state, where collisional mixing then occurs as the noble gas atoms collide with the alkali metal atoms and the m s =−1/2 state is partially populated (Figure 3). [ 3 ] Circularly polarized light is necessary at low magnetic fields because it allows only one type of angular momentum to be absorbed, allowing the spins to be polarized. [ 3 ] Relaxation then occurs from the excited states (m s =±1/2) to the ground states (m s =±1/2) as the atoms collide with nitrogen, thus quenching any chance of fluorescence and causing the electrons to return to the two ground states in equal populations. [ 3 ] Once the spins are depolarized (return to the m s =−1/2 state), they are excited again by the continuous wave laser light and the process repeats itself. In this way, a larger population of electron spins in the m s =+1/2 state accumulates. The polarization of the rubidium, P Rb , can be calculated by using the formula below:
Where n ↑ and n ↓ and are the number of atoms in the spin up (m S =+1/2) and spin down (m S =−1/2) 2 S 1/2 states. [ 13 ]
Next, the optically pumped alkali metal collides with the noble gas, allowing for spin exchange to occur where the alkali metal electron polarization is transferred to the noble gas nuclei (Figure 4). There are two mechanisms in which this can occur. The angular momentum can be transferred via binary collisions (Figure 4A, also called two-body collisions) or while the noble gas, N 2 buffer gas , and vapor phase alkali metal are held in close proximity via van der Waals forces (Figure 4B, also called three body collisions). [ 3 ] In cases where van der Waals forces are very small compared to binary collisions (such is the case for 3 He), the noble gas and alkali metal collide and polarization is transferred from the AM to the noble gas. [ 3 ] Binary collisions are also possible for 129 Xe. At high pressures, van der Waals forces dominate, but at low pressures binary collisions dominate. [ 3 ]
This cycle of excitation, polarization, depolarization, and re-polarization, etc. takes time before a net polarization is achieved. The buildup of nuclear polarization, P N (t), is given by:
Where ⟨P A ⟩ is the alkali metal polarization, γ SE is the spin exchange rate, and Γ is the longitudinal relaxation rate of the noble gas. [ 14 ] Relaxation of the nuclear polarization can occur via several mechanisms and is written as a sum of these contributions:
Where Γ t , Γ p , Γ g , and Γ w represent the relaxation from the transient Xe 2 dimer, the persistent Xe 2 dimer, diffusion through gradients in the applied magnetic field, and wall relaxation, respectively. [ 14 ] In most cases, the largest contributors to the total relaxation are persistent dimers and wall relaxations. [ 14 ] A Xe 2 dimer can occur when two Xe atoms collide and are held together via van der Waals forces, and it can be broken when a third atom collides with it. [ 15 ] It is similar to Xe-Rb during spin exchange (spin transfer) where they are held in close proximity to each other via van der Waals forces. [ 15 ] Wall relaxation is when the hyperpolarized Xe collides with the walls of the cell and is de-polarized due to paramagnetic impurities in the glass.
The buildup time constant, Γ B , can be measured by collecting NMR spectra at time intervals falling within the time it takes to reach steady-state polarization (i.e. the maximum polarization that can be achieved, seen by the maximum signal output). The signal integrals are then plotted over time and can be fit to obtain the buildup time constant. Collecting a buildup curve at several different temperatures and plotting the values as a function of alkali metal vapor density (since vapor density increases with an increase in cell temperature) can be used to determine the spin destruction rate and the per-atom spin exchange rate using:
Where γ' is the per-atom spin exchange rate, [AM] is the alkali metal vapor density, and Γ SD is the spin destruction rate. [ 16 ] This plot should be linear, where γ' is the slope and Γ SD is the y-intercept.
Spin exchange optical pumping can continue indefinitely with continuous illumination, but there are several factors that cause relaxation of polarization and thus a return to the thermal equilibrium populations when illumination is stopped. In order to use hyperpolarized noble gases in applications such as lung imaging, the gas must be transferred from the experimental setup to a patient. As soon as the gas is no longer actively being optically pumped, the degree of hyperpolarization begins to decrease until thermal equilibrium is reached. However, the hyperpolarization must last long enough to transfer the gas to the patient and obtain an image. The longitudinal spin relaxation time, denoted as T 1 , can be measured easily by collecting NMR spectra as the polarization decreases over time once illumination is stopped. This relaxation rate is governed by several depolarization mechanisms and is written as:
Where the three contributing terms are for collisional relaxation (CR), magnetic field inhomogeneity (MFI) relaxation, and relaxation caused by the presence of paramagnetic oxygen (O2). [ 17 ] The T 1 duration could be anywhere from minutes to several hours, depending on how much care is put into lessening the effects of CR, MFI, and O 2 . The last term has been quantified to be 0.360 s −1 amagat −1 , [ 18 ] but the first and second terms are hard to quantify since the degree of their contribution to the overall T 1 is dependent on how well the experimental setup and cell are optimized and prepared. [ 18 ]
In order to perform SEOP, it is first necessary to prepare the optical cell. Optical cells (Figure 5) are designed for the particular system in mind and glass blown using a transparent material, typically pyrex glass (borosilicate). This cell must then be cleaned to eliminate all contaminants, particularly paramagnetic materials which decrease polarization and the T 1 . The inner surface of the cell is then coated to (a) serve as a protective layer for the glass in order to lessen the chance of corrosion by the alkali metal, and (b) minimize depolarization caused by the collisions of polarized gas molecules with the walls of the cell. [ 19 ] Decreasing wall relaxation leads to longer and higher polarization of the noble gas. [ 19 ]
While several coatings have been tested over the years, SurfaSil (Figure 6, now referred to as hydrocarbon soluble siliconizing fluid) is the most common coating used in a ratio of 1:10 SurfaSil: hexane because it provides long T 1 values. [ 19 ] The thickness of the SurfaSil layer is about 0.3-0.4 μm. [ 19 ] Once evenly coated and dried, the cell is then placed in an inert environment and a droplet of alkali metal (≈200 mg) is placed in the cell, which is then dispersed to create an even coating on the walls of the cells. One method for transferring the alkali metal into the cell is by distillation. [ 20 ] In the distillation method, the cell is connected to a glass manifold equipped to hold both pressurized gas and vacuum, where an ampoule of alkali metal is connected. [ 21 ] The manifold and cell are vacuumed, then the ampoule seal is broken and the alkali metal is moved into the cell using the flame of a gas torch. [ 21 ] The cell is then filled with the desired gas mixture of nitrogen and noble gas. [ 5 ] Care must be taken not to poison the cell at any stage of cell preparation (expose the cell to atmospheric air).
Several cell sizes and designs have been used over the years. The application desired is what governs the design of the optical pumping cell and is dependent on laser diameter, optimization needs, and clinical use considerations. The specific alkali metal(s) and gases are also chosen based on the desired applications.
Once the cell is complete, a surface coil (or coils, depending on the desired coil type) is taped to the outside of the cell, which a) allows RF pulses to be produced in order to tip the polarized spins into the detection field (x,y plane) and b) detects the signal produced by the polarized nuclear spins. The cell is placed in an oven which allows for the cell and its contents to be heated so the alkali metal enters the vapor phase, and the cell is centered in a coil system which generates an applied magnetic field (along the z-axis). A laser, tuned to the D 1 line (electric-dipole transition [ 14 ] ) of the alkali metal and with a beam diameter matching the diameter of the optical cell, is then aligned with the optical flats of the cell in such a way where the entirety of the cell is illuminated by laser light to provide the largest polarization possible (Figure 7). The laser can be anywhere between tens of watts to hundreds of watts, [ 3 ] where higher the power yields larger polarization but is more costly. In order to further increase polarization, a retro-reflective mirror is placed behind the cell in order to pass the laser light through the cell twice. Additionally, an IR iris is placed behind the mirror, providing information of laser light absorption by the alkali metal atoms. When the laser is illuminating the cell, but the cell is at room temperature, the IR iris is used to measure the percent transmittance of laser light through the cell. As the cell is heated, the rubidium enters the vapor phase and starts to absorb laser light, causing the percent transmittance to decrease. The difference in the IR spectrum between a room temperature spectrum and a spectrum taken while the cell is heated can be used to calculate an estimated rubidium polarization value, P Rb .
As SEOP continues to develop and improve, there are several types of NMR coils, ovens, magnetic field generating coils, and lasers that have been and are being used to generate hyperpolarized gases. Generally, the NMR coils are hand made for the specific purpose, either by turning copper wire by hand in the desired shape, [ 22 ] or by 3D printing the coil. [ 23 ] Commonly, the oven is a forced-air oven, with two faces made of glass for the laser light to pass through the cell, a removable lid, and a hole through which a hot air line is connected, which allows the cell to be heated via conduction. [ 24 ] The magnetic field generating coils can be a pair of Helmholtz coils, used to generate the desired magnetic field strength, [ 24 ] whose desired field is governed by:
Where ω is the Larmour frequency, or desired detection frequency, γ is the gyromagnetic ratio of the nuclei of interest, and B 0 is the magnetic field required to detect the nuclei at the desired frequency. [ 25 ] A set of four electromagnetic coils can also be used (i.e. from Acutran) [ 22 ] and other coil designs are being tested.
In the past, laser technology was a limiting factor for SEOP, where only a couple alkali metals could be used due to the lack of, for example, cesium lasers. However, there have been several new developments, including better cesium lasers, higher power, narrower spectral width, etc. which are allowing the reaches of SEOP to increase. Nevertheless, there are several key features required. Ideally, the laser should be continuous wave to ensure the alkali metal and noble gas remains polarized at all times. In order to induce this polarization, the laser light must be circularly polarized in the direction which allows the electrons to become spin polarized. This is done by passing the laser light through a polarizing beam splitter to separate the s and p components, then through a quarter wave plate, which converts the linearly polarized light into circularly polarized light. [ 17 ]
SEOP has successfully been used and is fairly well developed for 3 He, 129 Xe, and 83 Kr for biomedical applications. [ 4 ] Additionally, several improvements are under way to get enhanced and interpretable imaging of cancer cells in biomedical science. [ 26 ] Studies involving hyperpolarization of 131 Xe are underway, piquing the interest of physicists. There are also improvements being made to allow not only rubidium to be utilized in the spin transfer, but also cesium. In principle, any alkali metal can be used for SEOP, but rubidium is usually preferred due to its high vapor pressure, allowing experiments to be carried out at relatively low temperatures (80 °C-130 °C), decreasing the chance of damaging the glass cell. [ 3 ] Additionally, laser technology for the alkali metal of choice has to exist and be developed enough get substantial polarization. Previously, the lasers available to excite the D 1 cesium transition were not well-developed, but they are now becoming more powerful and less expensive. Preliminary studies even show that cesium may provide better results than rubidium, even though rubidium has been the go-to alkali metal of choice for SEOP.
The hyperpolarization method called spin-exchange optical pumping (SEOP) is being used to hyperpolarize noble gases such as Xenon-129 and Helium-3. When an inhaled hyperpolarized gas like 3He or 129Xe is imaged, there is a higher magnetization density of NMR-active molecules in the lung compared to traditional 1H imaging, which improves the MRI images that can be obtained. Unlike proton MRI which reports on anatomical features of lung tissues, XenonMRI reports lung function including gas ventilation, diffusion, and perfusion. [ 27 ]
Our target is to identify the infection or disease (cancer, for example) anywhere in our body like cerebral, brain, blood, and fluid, and tissues. This infectious cell is called collectively biomarker. [ 28 ] According to the World Health Organization (WHO) and collaborating with United Nations and International Labor organization have convincingly defined the Biomarker as "any substance, structure, or process that can be measured in the body or its products and influence or predict the incidence of outcome or disease". Biomarker has to be quantifiable up-to certain level in biological process in well-being. [ 28 ]
One specific example of biomarker is blood cholesterol that is commonly acquainted with us reliable for coronary heart disease; another biomarker is PSA (Prostate-Specific Antigen) and has been contributing to prostate cancer. [ 28 ] There are a lot of biomarkers are considering as being cancer: Hepatitis C virus ribonucleic acid (HCV-RNA), International Normalized Ratio (INR), Prothrombin Time (PT), Monoclonal Protein (M protein), Cancer Antigen-125 (CA-125), Human Immunodeficiency Virus -Ribonucleic Acid (HIV RNA), B-type Natriuretic Peptide (BNP). 27 and Lymphoma cell (Ramos cell lines and Jurkat cell lines) a form of cancer. [ 29 ]
Other common biomarkers are breast cancer, Ovarian cancer, Colorectal cancer, Lung cancer and brain tumor. [ 30 ]
This disease-causing verdict agent is the biomarker is existing extremely trace amount especially initial state of the disease. Therefore, identifying or getting images of biomarker is tricky and, in few circumstances, uncertain by NMR tech. Hence, we must use the contrasting agent to enhance the images at least to visualize level to Physicians. As molecules of biomarker is less abundant in vivo system. The NMR or MRI experiment provides a very small signal even in some cases, the analyzer can miss the signal peak in data due to the lack in abundance of biomarkers. Therefore, to make sure, to reach the true conclusion about the existence of trouble-causing biomarkers, we need to enhance the probe (contrasting mechanisms) to get the clear peak at the most visible level of peak height as well as the position of the peak in data. If it is possible to gather the acceptable and clearly interpretable data from NMR or MRI experiment by using the contrasting agent, then experts can take a right initial step to recover the patients who already have been suffering from cancer. [ 28 ] Among the various technique to get the enhanced data in MRI experiment, SEOP is one of them.
Researchers in SEOP are interested to use the 129 Xe. [ citation needed ] Because 129 Xe has a number of favorable facts in NMR Tech. for working as a contrasting agent even over the other novel gases:
Solubility of Xenon in water medium 11% means at 25 °C 11 mL Xenon gas could be absorbed by 100 mL of water.
Figure-9 below, In NMR experimental data, there are different chemical shift values for different tissues in in vivo environment. All peaks are positioned through such a big range of chemical shift values for 129 Xe is viable. Because 129 Xe has long range up-to 1700ppm chemical shift value range in NMR data. [ citation needed ] Other important spectral information includes:
Figure 9. NMR data for Xe-129 biosensor in in vivo biological system. [ citation needed ]
(Figure-10) 129 Xe (g) shows satisfactory enhancement in polarization during SEOP compared to the thermal enhancement in polarization. This is demonstrated by the experimental data values when NMR spectra are acquired at different magnetic field strengths. [ 22 ] A couple of important points from experimental data are:
(Figure 11) Longitudinal spin relaxation time (T 1 ) is very sensitive with an increase of magnetic field and hence enhance the NMR signals is noticeable in SEOP in case of 129 Xe. [ 22 ] As T 1 is higher for blue marking conditioning NMR experiment shows more enhanced peak compare to other. [ 22 ] For hyperpolarized 129 Xe in tedlar bags, the T 1 is 38±12 minutes when data collected in presence of 1.5 mT magnetic field. However, satisfactory increment in T 1 delay time (354±24 minutes) when data was collected in presence of 3000 mT magnetic field. [ 22 ]
In general, we can use the either 87 Rb or 133 Cs alkali metal atoms with inert nitrogen gas. However, we are using 133 Cs atoms with nitrogen to make the spin exchange with 129 Xe for number of advantages:
Although 129 Xe has a bunch of preferable characteristic applications in NMR technique, 83 Kr can also be used since it has a lot of advantages in NMR techniques in different ways than 129 Xe.
Steps are also being taken in academia and industry to use this hyperpolarized gas for lung imaging. Once the gas ( 129 Xe) is hyperpolarized through the SEOP process and the alkali metal is removed, a patient (either healthy or suffering from a lung disease), can breathe in the gas and an MRI can be taken. [ 34 ] This results in an image of the spaces in the lungs filled with the gas. While the process to get to the point of imaging the patient may require knowledge from scientists very familiar with this technique and the equipment, steps are being taken to eliminate the need for this knowledge so that a hospital technician would be able to produce the hyperpolarized gas using a polarizer. [ 22 ] [ 23 ]
Hyperpolarization machines are currently being used to develop hyperpolarized xenon gas that is used as a visualization agent for the lungs. Xenon-129 is a safe inert noble gas that can be used to quantify lung function. With a single 10-second breath hold, hyperpolarized Xenon-129 is used with MRI to enable 3-dimensional lung imaging. [ 35 ] Xenon MRI is being used to monitor patients with pulmonary-vascular, obstructive, or fibrotic lung disease. [ 36 ]
Temperature-ramped 129 Xe SEOP in an automated high-output batch model hyperpolarized 129 Xe can utilize three prime temperature range to put certain conditions: First, 129 Xe hyperpolarization rate is superlative high at hot condition. Second, in warm condition the hyperpolarization of 129 Xe is unity. Third, at cold condition, the level of hyperpolarization of 129 Xe gas at least can get the (at human body's temperature) imaging although during the transferring into the Tedlar bag having poor percentage of 87 Rb (less than 5 ng/L dose). [ 37 ]
Multiparameter analysis of 87 Rb/ 129 Xe SEOP at high xenon pressure and photon flux could be used as 3D-printing and stopped flow contrasting agent in clinical scale. [ 38 ] In situ technique, the NMR machine was run for tracking the dynamics of 129 Xe polarization as a function of SEOP-cell conditioning with different operating parameters such as data collecting temperature, photon flux, and 129 Xe partial pressure to enhance the 129 Xe polarization ( P Xe ). [ 38 ]
All of those polarization values of 129 Xe has been approved by pushing the hyperpolarized 129 Xe gas and all MRI experiment also done at lower magnetic field 47.5 mT. [ 38 ] Finally demonstrations indicated that such a high pressure region, polarization of 129 Xe gases could be increment even more that the limit that already has been shown. Better SEOP thermal management and optimizing the polarizing kinetics has been further improved with good efficacy. [ 38 ]
Not only can SEOP be used to hyperpolarize noble gases, but a more recent development is SEOP on solids. It was first performed in 2007 [ 21 ] and was used to polarize nuclei in a solid, allowing for nuclei that cannot be polarized by other methods to become hyperpolarized. [ 21 ] For example, nuclear polarization of 133 Cs in the form of a solid film of CsH can be increased above the Boltzmann limit. [ 21 ] This is done by first optically pumping cesium vapor, then transferring the spin polarization to CsH salt, yielding an enhancement of 4.0. [ 21 ]
The cells are made as previously described using distillation, then filled with hydrogen gas and heated to allow for the Cs metal to react with the gaseous hydrogen to form the CsH salt. [ 21 ] Unreacted hydrogen was removed, and the process was repeated several times to increase the thickness of the CsH film, then pressurized with nitrogen gas. [ 21 ] Usually, SEOP experiments are done with the cell centered in Helmholtz or electromagnetic coils, as previously described, but these experiments were done in a superconducting 9.4 T magnet by shining the laser through the magnet and electrically heating the cell. [ 21 ] In the future, it may be possible to use this technique to transfer polarization to 6 Li or 7 Li, leading to even more applications since the T 1 is expected to be longer. [ 21 ] Since the discovery of this technique that allows solids to be characterized, it has been improved in such a way where polarized light is not necessary to polarize the solid; instead, unpolarized light in a magnetic field can be used. [ 39 ] In this method, glass wool is coated with CsH salt, increasing the surface area of the CsH and therefore increasing the chances of spin transfer, yielding 80-fold enhancements at low field (0.56 T). [ 39 ] Like in hyperpolarizing CsH film, the cesium metal in this glass wool method was allowed to react with hydrogen gas, but in this case the CsH formed on the glass fibers instead of the glass cell. [ 39 ]
3 He can also be hyperpolarized using metastability exchange optical pumping (MEOP). [ citation needed ] This process is able to polarize 3 He nuclei in the ground state with optically pumped 3 He nuclei in the metastable state. MEOP only involves 3 He nuclei at room temperature and at low pressure (≈a few mbars). The process of MEOP is very efficient (high polarization rate), however, compression of the gas up to atmospheric pressure is needed.
Compounds containing NMR -sensitive nuclei, such as 1 H, 13 C or 15 N , can be hyperpolarized using Dynamic nuclear polarization (DNP). DNP is typically performed at low temperature (≈1 K) and high magnetic field (≈3 T). The compound is subsequently thawed and dissolved to yield a room temperature solution containing hyperpolarized nuclei. [ 40 ] This liquid can be used in in vivo metabolic imaging [ 41 ] for oncology [ 42 ] and other applications. The 13 C polarization levels in solid compounds can reach up to ≈64% and the losses during dissolution and transfer of the sample for NMR measurements can be minimized to a few percent. [ 43 ] Compounds containing NMR -active nuclei can also be hyperpolarized using chemical reactions with para-hydrogen , see Para-Hydrogen Induced Polarization (PHIP).
Molecular hydrogen, H 2 , contains two different spin isomers , para-hydrogen and ortho-hydrogen, with a ratio of 25:75 at room temperature. Creating para-hydrogen induced polarization (PHIP) [ 44 ] means that this ratio is increased, in other words that para-hydrogen is enriched. This can be accomplished by cooling hydrogen gas and then inducing ortho-to-para conversion via an iron-oxide or charcoal catalyst. When performing this procedure at ≈70 K (i.e. with liquid nitrogen), para-hydrogen is enriched from 25% to ca. 50%. When cooling to below 20 K and then inducing the ortho-to-para conversion, close to 100% parahydrogen can be obtained. [ citation needed ]
For practical applications, the PHIP is most commonly transferred to organic molecules by reacting the hyperpolarized hydrogen with precursor molecules in the presence of a transition metal catalyst. Proton NMR signals with ca. 10,000-fold increased intensity [ 45 ] can be obtained compared to NMR signals of the same organic molecule without PHIP and thus only "thermal" polarization at room temperature.
Signal amplification by reversible exchange (SABRE) is a technique to hyperpolarize samples without chemically modifying them. Compared to orthohydrogen or organic molecules, a much greater fraction of the hydrogen nuclei in parahydrogen align with an applied magnetic field. In SABRE, a metal center reversibly binds to both the test molecule and a parahydrogen molecule facilitating the target molecule to pick up the polarization of the parahydrogen. [ 46 ] This technique can be improved and utilized for a wide range of organic molecules by using an intermediate "relay" molecule like ammonia. The ammonia efficiently binds to the metal center and picks up the polarization from the parahydrogen. The ammonia then transfers it other molecules that don't bind as well to the metal catalyst. [ 47 ] This enhanced NMR signal allows the rapid analysis of very small amounts of material. | https://en.wikipedia.org/wiki/Hyperpolarization_(physics) |
A hyperpositive nonlinear effect is a very specific case of a nonlinear effect. A nonlinear effect in asymmetric catalysis is a phenomenon in which the enantiopurity of the catalyst (or chiral auxiliary ) is not proportional to the enantiopurity of the product obtained. These phenomena were rationalized in the mid-1980s by Henri B. Kagan , who proposed simple mechanistic models, supported by mathematical models, to model experimental curves. [ 1 ]
In 1994, H. B. Kagan and collaborators proposed more elaborate models that more closely resembled the experimental results observed at the time. Using these models, the authors were able to make theoretical predictions about situations that had not been encountered experimentally. An example is a case “ where the enantiomeric excess could take on much larger values for a partially resolved ligand than for an enantiomerically pure ligand ”. [ 2 ] The authors proposed the term “hyperpositive nonlinear effect” to characterize this situation.
This statement may seem somewhat implausible at first glance, but the possibility was observed experimentally 26 years later: the first experimental example of a hyperpositive nonlinear effect was described in 2020 by S. Bellemin-Laponnaz and colleagues, [ 3 ] but the mechanism of this phenomenon turned out to be different from that originally proposed. [ 4 ] This mechanism, which explains a hyperpositive nonlinear effect, has also been validated to explain cases of enantiodivergence. [ 4 ] | https://en.wikipedia.org/wiki/Hyperpositive_nonlinear_effect |
Hyperpredation , also known as hypopredation , is when a generalist predator increases its predation pressure as a result of the introduction of a substitute prey. [ 1 ] Hyperpredation has been proven, for instance, in lab settings using two hosts and a parasitoid wasp. [ 2 ] Prey that require more handling time than they are worth in terms of nutritional value leads to hyperpredation. In severe circumstances, predators that fed on such prey went extinct. [ 3 ] [ 4 ] Introduced Eastern cottontails cause an apparent competition with the European hare , as a result this along with the red fox being their main predator causes hyperpredation. [ 5 ]
After the invasion of feral pigs , golden eagles (which had inhabited the islands due to DDT wiping out the more territorial Bald eagle population) began preying heavily on the alien species. Another prey on the islands, the Island fox , nearly went locally extinct due to the predation pressure from the golden eagles. These incidents happened in the California Channel Islands . [ 6 ]
Theoretical research indicates that this increased predation may be sufficient to have a demographic impact on prey populations. The empirical data on hyperpredation that are now available are only applicable to situations where the introduction of a feral prey led to an overexploitation of the local prey. The most common cause of hyperpredation is apparent competition between the native and alien prey. [ 7 ] | https://en.wikipedia.org/wiki/Hyperpredation |
In mathematics , hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. [ 1 ] A hyperreal number x {\displaystyle x} is said to be finite if, and only if, | x | < n {\displaystyle |x|<n} for some integer n {\displaystyle n} . [ 1 ] [ 2 ] x {\displaystyle x} is said to be infinitesimal if, and only if, | x | < 1 / n {\displaystyle |x|<1/n} for all positive integers n {\displaystyle n} . [ 1 ] [ 2 ] The term "hyper-real" was introduced by Edwin Hewitt in 1948. [ 3 ]
The hyperreal numbers satisfy the transfer principle , a rigorous version of Leibniz's heuristic law of continuity . The transfer principle states that true first-order statements about R are also valid in * R . [ 4 ] For example, the commutative law of addition, x + y = y + x , holds for the hyperreals just as it does for the reals; since R is a real closed field , so is * R . Since sin ( π n ) = 0 {\displaystyle \sin({\pi n})=0} for all integers n , one also has sin ( π H ) = 0 {\displaystyle \sin({\pi H})=0} for all hyperintegers H {\displaystyle H} . The transfer principle for ultrapowers is a consequence of Łoś's theorem of 1955.
Concerns about the soundness of arguments involving infinitesimals date back to ancient Greek mathematics, with Archimedes replacing such proofs with ones using other techniques such as the method of exhaustion . [ 5 ] In the 1960s, Abraham Robinson proved that the hyperreals were logically consistent if and only if the reals were. This put to rest the fear that any proof involving infinitesimals might be unsound, provided that they were manipulated according to the logical rules that Robinson delineated.
The application of hyperreal numbers and in particular the transfer principle to problems of analysis is called nonstandard analysis . One immediate application is the definition of the basic concepts of analysis such as the derivative and integral in a direct fashion, without passing via logical complications of multiple quantifiers. Thus, the derivative of f ( x ) becomes f ′ ( x ) = st ( f ( x + Δ x ) − f ( x ) Δ x ) {\displaystyle f'(x)=\operatorname {st} \left({\frac {f(x+\Delta x)-f(x)}{\Delta x}}\right)} for an infinitesimal Δ x {\displaystyle \Delta x} , where st(⋅) denotes the standard part function , which "rounds off" each finite hyperreal to the nearest real. Similarly, the integral is defined as the standard part of a suitable infinite sum .
The idea of the hyperreal system is to extend the real numbers R to form a system * R that includes infinitesimal and infinite numbers, but without changing any of the elementary axioms of algebra. Any statement of the form "for any number x ..." that is true for the reals is also true for the hyperreals. For example, the axiom that states "for any number x , x + 0 = x " still applies. The same is true for quantification over several numbers, e.g., "for any numbers x and y , xy = yx ." This ability to carry over statements from the reals to the hyperreals is called the transfer principle . However, statements of the form "for any set of numbers S ..." may not carry over. The only properties that differ between the reals and the hyperreals are those that rely on quantification over sets , or other higher-level structures such as functions and relations, which are typically constructed out of sets. Each real set, function, and relation has its natural hyperreal extension, satisfying the same first-order properties. The kinds of logical sentences that obey this restriction on quantification are referred to as statements in first-order logic .
The transfer principle, however, does not mean that R and * R have identical behavior. For instance, in * R there exists an element ω such that
but there is no such number in R . (In other words, * R is not Archimedean .) This is possible because the nonexistence of ω cannot be expressed as a first-order statement.
Informal notations for non-real quantities have historically appeared in calculus in two contexts: as infinitesimals, like dx , and as the symbol ∞, used, for example, in limits of integration of improper integrals .
As an example of the transfer principle, the statement that for any nonzero number x , 2x ≠ x , is true for the real numbers, and it is in the form required by the transfer principle, so it is also true for the hyperreal numbers. This shows that it is not possible to use a generic symbol such as ∞ for all the infinite quantities in the hyperreal system; infinite quantities differ in magnitude from other infinite quantities, and infinitesimals from other infinitesimals.
Similarly, the casual use of 1/0 = ∞ is invalid, since the transfer principle applies to the statement that zero has no multiplicative inverse. The rigorous counterpart of such a calculation would be that if ε is a non-zero infinitesimal, then 1/ε is infinite.
For any finite hyperreal number x , the standard part , st( x ), is defined as the unique closest real number to x ; it necessarily differs from x only infinitesimally. The standard part function can also be defined for infinite hyperreal numbers as follows: If x is a positive infinite hyperreal number, set st( x ) to be the extended real number + ∞ {\displaystyle +\infty } , and likewise, if x is a negative infinite hyperreal number, set st( x ) to be − ∞ {\displaystyle -\infty } (the idea is that an infinite hyperreal number should be smaller than the "true" absolute infinity but closer to it than any real number is).
One of the key uses of the hyperreal number system is to give a precise meaning to the differential operator d as used by Leibniz to define the derivative and the integral.
For any real-valued function f , {\displaystyle f,} the differential d f {\displaystyle df} is defined as a map which sends every ordered pair ( x , d x ) {\displaystyle (x,dx)} (where x {\displaystyle x} is real and d x {\displaystyle dx} is nonzero infinitesimal) to an infinitesimal
Note that the very notation " d x {\displaystyle dx} " used to denote any infinitesimal is consistent with the above definition of the operator d , {\displaystyle d,} for if one interprets x {\displaystyle x} (as is commonly done) to be the function f ( x ) = x , {\displaystyle f(x)=x,} then for every ( x , d x ) {\displaystyle (x,dx)} the differential d ( x ) {\displaystyle d(x)} will equal the infinitesimal d x {\displaystyle dx} .
A real-valued function f {\displaystyle f} is said to be differentiable at a point x {\displaystyle x} if the quotient
is the same for all nonzero infinitesimals d x . {\displaystyle dx.} If so, this quotient is called the derivative of f {\displaystyle f} at x {\displaystyle x} .
For example, to find the derivative of the function f ( x ) = x 2 {\displaystyle f(x)=x^{2}} , let d x {\displaystyle dx} be a non-zero infinitesimal. Then,
The use of the standard part in the definition of the derivative is a rigorous alternative to the traditional practice of neglecting the square [ citation needed ] of an infinitesimal quantity. Dual numbers are a number system based on this idea. After the third line of the differentiation above, the typical method from Newton through the 19th century would have been simply to discard the dx 2 term. In the hyperreal system, dx 2 ≠ 0, since dx is nonzero, and the transfer principle can be applied to the statement that the square of any nonzero number is nonzero. However, the quantity dx 2 is infinitesimally small compared to dx ; that is, the hyperreal system contains a hierarchy of infinitesimal quantities.
Using hyperreal numbers for differentiation allows for a more algebraically manipulable approach to derivatives. In standard differentiation, partial differentials and higher-order differentials are not independently manipulable through algebraic techniques. However, using the hyperreals, a system can be established for doing so, though resulting in a slightly different notation. [ 6 ]
Another key use of the hyperreal number system is to give a precise meaning to the integral sign ∫ used by Leibniz to define the definite integral.
For any infinitesimal function ε ( x ) , {\displaystyle \ \varepsilon (x),\ } one may define the integral ∫ ( ε ) {\displaystyle \int (\varepsilon )\ } as a map sending any ordered triple ( a , b , d x ) {\displaystyle (a,b,dx)} (where a {\displaystyle \ a\ } and b {\displaystyle \ b\ } are real, and d x {\displaystyle \ dx\ } is infinitesimal of the same sign as b − a {\displaystyle \,b-a} ) to the value
where N {\displaystyle \ N\ } is any hyperinteger number satisfying st ( N d x ) = b − a . {\displaystyle \ \operatorname {st} (N\ dx)=b-a.}
A real-valued function f {\displaystyle f} is then said to be integrable over a closed interval [ a , b ] {\displaystyle \ [a,b]\ } if for any nonzero infinitesimal d x , {\displaystyle \ dx,\ } the integral
is independent of the choice of d x . {\displaystyle \ dx.} If so, this integral is called the definite integral (or antiderivative) of f {\displaystyle f} on [ a , b ] . {\displaystyle \ [a,b].}
This shows that using hyperreal numbers, Leibniz's notation for the definite integral can actually be interpreted as a meaningful algebraic expression (just as the derivative can be interpreted as a meaningful quotient). [ 7 ]
The hyperreals * R form an ordered field containing the reals R as a subfield . Unlike the reals, the hyperreals do not form a standard metric space , but by virtue of their order they carry an order topology .
The use of the definite article the in the phrase the hyperreal numbers is somewhat misleading in that there is not a unique ordered field that is referred to in most treatments. However, a 2003 paper by Vladimir Kanovei and Saharon Shelah [ 8 ] shows that there is a definable, countably saturated (meaning ω-saturated but not countable ) elementary extension of the reals, which therefore has a good claim to the title of the hyperreal numbers. Furthermore, the field obtained by the ultrapower construction from the space of all real sequences, is unique up to isomorphism if one assumes the continuum hypothesis .
The condition of being a hyperreal field is a stronger one than that of being a real closed field strictly containing R . It is also stronger than that of being a superreal field in the sense of Dales and Woodin . [ 9 ]
The hyperreals can be developed either axiomatically or by more constructively oriented methods. The essence of the axiomatic approach is to assert (1) the existence of at least one infinitesimal number, and (2) the validity of the transfer principle. In the following subsection we give a detailed outline of a more constructive approach. This method allows one to construct the hyperreals if given a set-theoretic object called an ultrafilter , but the ultrafilter itself cannot be explicitly constructed.
When Newton and (more explicitly) Leibniz introduced differentials, they used infinitesimals and these were still regarded as useful by later mathematicians such as Euler and Cauchy . Nonetheless these concepts were from the beginning seen as suspect, notably by George Berkeley . Berkeley's criticism centered on a perceived shift in hypothesis in the definition of the derivative in terms of infinitesimals (or fluxions), where dx is assumed to be nonzero at the beginning of the calculation, and to vanish at its conclusion (see Ghosts of departed quantities for details). When in the 1800s calculus was put on a firm footing through the development of the (ε, δ)-definition of limit by Bolzano , Cauchy, Weierstrass , and others, infinitesimals were largely abandoned, though research in non-Archimedean fields continued (Ehrlich 2006).
However, in the 1960s Abraham Robinson showed how infinitely large and infinitesimal numbers can be rigorously defined and used to develop the field of nonstandard analysis . [ 10 ] Robinson developed his theory nonconstructively , using model theory ; however it is possible to proceed using only algebra and topology , and proving the transfer principle as a consequence of the definitions. In other words hyperreal numbers per se , aside from their use in nonstandard analysis, have no necessary relationship to model theory or first order logic, although they were discovered by the application of model theoretic techniques from logic. Hyper-real fields were in fact originally introduced by Hewitt (1948) by purely algebraic techniques, using an ultrapower construction.
We are going to construct a hyperreal field via sequences of reals. [ 11 ] In fact we can add and multiply sequences componentwise; for example:
and analogously for multiplication.
This turns the set of such sequences into a commutative ring , which is in fact a real algebra A . We have a natural embedding of R in A by identifying the real number r with the sequence ( r , r , r , …) and this identification preserves the corresponding algebraic operations of the reals. The intuitive motivation is, for example, to represent an infinitesimal number using a sequence that approaches zero. The inverse of such a sequence would represent an infinite number. As we will see below, the difficulties arise because of the need to define rules for comparing such sequences in a manner that, although inevitably somewhat arbitrary, must be self-consistent and well defined. For example, we may have two sequences that differ in their first n members, but are equal after that; such sequences should clearly be considered as representing the same hyperreal number. Similarly, most sequences oscillate randomly forever, and we must find some way of taking such a sequence and interpreting it as, say, 7 + ϵ {\displaystyle 7+\epsilon } , where ϵ {\displaystyle \epsilon } is a certain infinitesimal number.
Comparing sequences is thus a delicate matter. We could, for example, try to define a relation between sequences in a componentwise fashion:
but here we run into trouble, since some entries of the first sequence may be bigger than the corresponding entries of the second sequence, and some others may be smaller. It follows that the relation defined in this way is only a partial order . To get around this, we have to specify which positions matter. Since there are infinitely many indices, we don't want finite sets of indices to matter. A consistent choice of index sets that matter is given by any free ultrafilter U on the natural numbers ; these can be characterized as ultrafilters that do not contain any finite sets. (The good news is that Zorn's lemma guarantees the existence of many such U ; the bad news is that they cannot be explicitly constructed.) We think of U as singling out those sets of indices that "matter": We write ( a 0 , a 1 , a 2 , ...) ≤ ( b 0 , b 1 , b 2 , ...) if and only if the set of natural numbers { n : a n ≤ b n } is in U .
This is a total preorder and it turns into a total order if we agree not to distinguish between two sequences a and b if a ≤ b and b ≤ a . With this identification, the ordered field *R of hyperreals is constructed. From an algebraic point of view, U allows us to define a corresponding maximal ideal I in the commutative ring A (namely, the set of the sequences that vanish in some element of U ), and then to define *R as A / I ; as the quotient of a commutative ring by a maximal ideal, *R is a field. This is also notated A / U , directly in terms of the free ultrafilter U ; the two are equivalent. The maximality of I follows from the possibility of, given a sequence a , constructing a sequence b inverting the non-null elements of a and not altering its null entries. If the set on which a vanishes is not in U , the product ab is identified with the number 1, and any ideal containing 1 must be A . In the resulting field, these a and b are inverses.
The field A / U is an ultrapower of R .
Since this field contains R it has cardinality at least that of the continuum . Since A has cardinality
it is also no larger than 2 ℵ 0 {\displaystyle 2^{\aleph _{0}}} , and hence has the same cardinality as R .
One question we might ask is whether, if we had chosen a different free ultrafilter V , the quotient field A / U would be isomorphic as an ordered field to A / V . This question turns out to be equivalent to the continuum hypothesis ; in ZFC with the continuum hypothesis we can prove this field is unique up to order isomorphism , and in ZFC with the negation of continuum hypothesis we can prove that there are non-order-isomorphic pairs of fields that are both countably indexed ultrapowers of the reals. [ 12 ]
For more information about this method of construction, see ultraproduct .
The following is an intuitive way of understanding the hyperreal numbers. The approach taken here is very close to the one in the book by Goldblatt . [ 13 ] Recall that the sequences converging to zero are sometimes called infinitely small. These are almost the infinitesimals in a sense; the true infinitesimals include certain classes of sequences that contain a sequence converging to zero.
Let us see where these classes come from. Consider first the sequences of real numbers. They form a ring , that is, one can multiply, add and subtract them, but not necessarily divide by a non-zero element. The real numbers are considered as the constant sequences, the sequence is zero if it is identically zero, that is, a n = 0 for all n .
In our ring of sequences one can get ab = 0 with neither a = 0 nor b = 0. Thus, if for two sequences a , b {\displaystyle a,b} one has ab = 0, at least one of them should be declared zero. Surprisingly enough, there is a consistent way to do it. As a result, the equivalence classes of sequences that differ by some sequence declared zero will form a field, which is called a hyperreal field . It will contain the infinitesimals in addition to the ordinary real numbers, as well as infinitely large numbers (the reciprocals of infinitesimals, including those represented by sequences diverging to infinity). Also every hyperreal that is not infinitely large will be infinitely close to an ordinary real, in other words, it will be the sum of an ordinary real and an infinitesimal.
This construction is parallel to the construction of the reals from the rationals given by Cantor . He started with the ring of the Cauchy sequences of rationals and declared all the sequences that converge to zero to be zero. The result is the reals. To continue the construction of hyperreals, consider the zero sets of our sequences, that is, the z ( a ) = { i : a i = 0 } {\displaystyle z(a)=\{i:a_{i}=0\}} , that is, z ( a ) {\displaystyle z(a)} is the set of indexes i {\displaystyle i} for which a i = 0 {\displaystyle a_{i}=0} . It is clear that if a b = 0 {\displaystyle ab=0} , then the union of z ( a ) {\displaystyle z(a)} and z ( b ) {\displaystyle z(b)} is N (the set of all natural numbers), so:
Now the idea is to single out a bunch U of subsets X of N and to declare that a = 0 {\displaystyle a=0} if and only if z ( a ) {\displaystyle z(a)} belongs to U . From the above conditions one can see that:
Any family of sets that satisfies (2–4) is called a filter (an example: the complements to the finite sets, it is called the Fréchet filter and it is used in the usual limit theory). If (1) also holds, U is called an ultrafilter (because you can add no more sets to it without breaking it). The only explicitly known example of an ultrafilter is the family of sets containing a given element (in our case, say, the number 10). Such ultrafilters are called trivial, and if we use it in our construction, we come back to the ordinary real numbers. Any ultrafilter containing a finite set is trivial. It is known that any filter can be extended to an ultrafilter, but the proof uses the axiom of choice . The existence of a nontrivial ultrafilter (the ultrafilter lemma ) can be added as an extra axiom, as it is weaker than the axiom of choice.
Now if we take a nontrivial ultrafilter (which is an extension of the Fréchet filter) and do our construction, we get the hyperreal numbers as a result.
If f {\displaystyle f} is a real function of a real variable x {\displaystyle x} then f {\displaystyle f} naturally extends to a hyperreal function of a hyperreal variable by composition:
where { … } {\displaystyle \{\dots \}} means "the equivalence class of the sequence … {\displaystyle \dots } relative to our ultrafilter", two sequences being in the same class if and only if the zero set of their difference belongs to our ultrafilter.
All the arithmetical expressions and formulas make sense for hyperreals and hold true if they are true for the ordinary reals. It turns out that any finite (that is, such that | x | < a {\displaystyle |x|<a} for some ordinary real a {\displaystyle a} ) hyperreal x {\displaystyle x} will be of the form y + d {\displaystyle y+d} where y {\displaystyle y} is an ordinary (called standard) real and d {\displaystyle d} is an infinitesimal. It can be proven by bisection method used in proving the Bolzano-Weierstrass theorem, the property (1) of ultrafilters turns out to be crucial.
The finite elements F of *R form a local ring , and in fact a valuation ring , with the unique maximal ideal S being the infinitesimals; the quotient F / S is isomorphic to the reals. Hence we have a homomorphic mapping, st( x ), from F to R whose kernel consists of the infinitesimals and which sends every element x of F to a unique real number whose difference from x is in S ; which is to say, is infinitesimal. Put another way, every finite nonstandard real number is "very close" to a unique real number, in the sense that if x is a finite nonstandard real, then there exists one and only one real number st( x ) such that x – st( x ) is infinitesimal. This number st( x ) is called the standard part of x , conceptually the same as x to the nearest real number . This operation is an order-preserving homomorphism and hence is well-behaved both algebraically and order theoretically. It is order-preserving though not isotonic; i.e. x ≤ y {\displaystyle x\leq y} implies st ( x ) ≤ st ( y ) {\displaystyle \operatorname {st} (x)\leq \operatorname {st} (y)} , but x < y {\displaystyle x<y} does not imply st ( x ) < st ( y ) {\displaystyle \operatorname {st} (x)<\operatorname {st} (y)} .
The map st is continuous with respect to the order topology on the finite hyperreals; in fact it is locally constant .
Suppose X is a Tychonoff space , also called a T 3.5 space, and C( X ) is the algebra of continuous real-valued functions on X . Suppose M is a maximal ideal in C( X ). Then the factor algebra A = C( X )/ M is a totally ordered field F containing the reals. If F strictly contains R then M is called a hyperreal ideal (terminology due to Hewitt (1948)) and F a hyperreal field . Note that no assumption is being made that the cardinality of F is greater than R ; it can in fact have the same cardinality.
An important special case is where the topology on X is the discrete topology ; in this case X can be identified with a cardinal number κ and C( X ) with the real algebra R κ of functions from κ to R . The hyperreal fields we obtain in this case are called ultrapowers of R and are identical to the ultrapowers constructed via free ultrafilters in model theory. | https://en.wikipedia.org/wiki/Hyperreal_number |
A hypersaline lake is a landlocked body of water that contains significant concentrations of sodium chloride , brines , and other salts , with saline levels surpassing those of ocean water (3.5%, i.e. 35 grams per litre or 0.29 pounds per US gallon).
Specific microbial species can thrive in high-salinity environments [ 1 ] that are inhospitable to most lifeforms, [ 2 ] including some that are thought to contribute to the color of pink lakes . [ 3 ] [ 4 ] Some of these species enter a dormant state when desiccated , and some species are thought to survive for over 250 million years. [ 2 ]
The water in hypersaline lakes has great buoyancy due to its high salt content. [ 5 ]
Hypersaline lakes are found on every continent, especially in arid or semi-arid regions . [ 1 ]
In the Arctic , the Canadian Devon Ice Cap contains two subglacial lakes that are hypersaline. [ 6 ] In Antarctica , there are larger hypersaline water bodies, lakes in the McMurdo Dry Valleys such as Lake Vanda with salinity of over 35% (i.e. 10 times as salty as ocean water). [ citation needed ]
The most saline water body in the world is the Gaet'ale Pond , located in the Danakil Depression in Afar , Ethiopia. The water of Gaet'ale Pond has a salinity of 43%, making it the saltiest water body on Earth [ 7 ] (i.e. 12 times as salty as ocean water). Previously, it was considered that the most saline lake outside of Antarctica was Lake Assal , [ 8 ] in Djibouti , which has a salinity of 34.8% (i.e. 10 times as salty as ocean water). The best-known hypersaline lakes are the Dead Sea (34.2% salinity in 2010) and the Great Salt Lake in the state of Utah , US (5–27% variable salinity). The Dead Sea , dividing Israel and the West Bank from Jordan , is the world's deepest hypersaline lake. The Great Salt Lake, while having nearly three times the surface area of the Dead Sea, is shallower and experiences much greater fluctuations in salinity. At its lowest recorded water levels, it approaches 7.7 times the salinity of ocean water, but when its levels are high, its salinity drops to only slightly higher than that of the ocean. [ 9 ] [ 10 ] [ 11 ] | https://en.wikipedia.org/wiki/Hypersaline_lake |
In computing, hyperscale is the ability of an architecture to scale appropriately as increased demand is added to the system.
This typically involves the ability to seamlessly provide and add compute, memory, networking, and storage resources to a given node or set of nodes that make up a larger computing , distributed computing , or grid computing environment. Hyperscale computing is necessary in order to build a robust and scalable cloud , big data , map reduce , or distributed storage system and is often associated with the infrastructure required to run large distributed sites such as Google , Facebook , Twitter , Amazon , Microsoft , IBM Cloud or Oracle Cloud.
Companies like Ericsson , AMD , and Intel provide hyperscale infrastructure kits for IT service providers. [ 1 ]
Companies like Scaleway , Switch , Alibaba , IBM , QTS, Digital Realty Trust, Equinix , Oracle , Meta, Amazon Web Services , SAP , Microsoft and Google build data centers for hyperscale computing. [ 2 ] [ 3 ] [ 4 ] [ 5 ] Such companies are sometimes called " hyperscalers ." They are recognized for their massive scale in cloud computing and data management, operating in environments that require extensive infrastructure to accommodate large-scale data processing and storage. [ 6 ]
This computer science article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hyperscale_computing |
Neutrophil hypersegmentation can be defined as the presence of neutrophils whose nuclei have six or more lobes or the presence of more than 3% of neutrophils with at least five nuclear lobes. [ 1 ] This is a clinical laboratory finding. It is visualized by drawing blood from a patient and viewing the blood smeared on a slide under a microscope . Normal neutrophils are uniform in size, with an apparent diameter of about 13 μm in a film. When stained, neutrophils have a segmented nucleus and pink/orange cytoplasm under light microscope. The majority of neutrophils have three nuclear segments (lobes) connected by tapering chromatin strands. A small percentage have four lobes, and occasionally five lobes may be seen. Up to 8% of circulating neutrophils are unsegmented (‘band’ forms). [ 1 ]
The presence of hypersegmented neutrophils is an important diagnostic feature of megaloblastic anaemias . Hypersegmentation can also be seen in many other conditions but with relatively less diagnostic significance.
Hypersegmentation can sometimes be difficult to assert since interobserver variation is high and segmentation may vary with race. A 1996 study performed in the United States found that blacks have a greater neutrophil segmentation than whites. [ 2 ]
Neutrophil hypersegmentation is one of the earliest, most sensitive and specific signs of megaloblastic anemia (mainly caused by hypovitaminosis of vitamin B12 & folic acid ). Nuclear hypersegmentation of DNA in neutrophils strongly suggests megaloblastosis when associated with macro-ovalocytosis. If megaloblastosis is suspected, a formal lobe count/neutrophil (i.e. lobe index) above 3.5% can be obtained. Hypersegmentation persists for an average of 14 days after institution of specific therapy. [ citation needed ] | https://en.wikipedia.org/wiki/Hypersegmented_neutrophil |
In genetics , a hypersensitive site is a short region of chromatin and is detected by its super sensitivity to cleavage by DNase I and other various nucleases ( DNase II and micrococcal nucleases ). In a hypersensitive site, the nucleosomal structure is less compacted, increasing the availability of the DNA to binding by proteins, such as transcription factors and DNase I. These sites account for many inherited tendencies. [ 2 ]
Hypersensitive sites are found on every active gene, and many of these genes often have more than one hypersensitive site. Most often, hypersensitive sites are found only in chromatin of cells in which the associated gene is being expressed, and do not occur when the gene is inactive.
In DNA being transcribed, 5'hypersensitive sites appear before transcription begins, and the DNA sequences within the hypersensitive sites are required for gene expression . Note: hypersensitive sites precede active promoters .
Hypersensitive sites are generated as a result of the binding of transcription factors that displace histone octamers .
They can also be located by indirect end labelling. A fragment of DNA is cut once at the hypersensitive site with DNase and at another site with a restriction enzyme . The distance from the known restriction site to the DNase cut is then measured to give the location.
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypersensitive_site |
In mathematical logic , the hypersequent framework is an extension of the proof-theoretical framework of sequent calculi used in structural proof theory to provide analytic calculi for logics that are not captured in the sequent framework. A hypersequent is usually taken to be a finite multiset of ordinary sequents , written
The sequents making up a hypersequent are called components. The added expressivity of the hypersequent framework is provided by rules manipulating different components, such as the communication rule for the intermediate logic LC ( Gödel–Dummett logic )
or the modal splitting rule for the modal logic S5 : [ 1 ]
Hypersequent calculi have been used to treat modal logics , intermediate logics , and substructural logics . Hypersequents usually have a formula interpretation, i.e., are interpreted by a formula in the object language, nearly always as some kind of disjunction. The precise formula interpretation depends on the considered logic.
Formally, a hypersequent is usually taken to be a finite multiset of ordinary sequents , written
The sequents making up a hypersequent consist of pairs of multisets of formulae, and are called the components of the hypersequent. Variants defining hypersequents and sequents in terms of sets or lists instead of multisets are also considered, and depending on the considered logic the sequents can be classical or intuitionistic . The rules for the propositional connectives usually are adaptions of the corresponding standard sequent rules with an additional side hypersequent, also called hypersequent context. E.g., a common set of rules for the functionally complete set of connectives { ⊥ , → } {\displaystyle \{\bot ,\to \}} for classical propositional logic is given by the following four rules:
G ∣ Γ , A ⇒ B , Δ G ∣ Γ ⇒ A → B , Δ {\displaystyle {\frac {{\mathcal {G}}\mid \Gamma ,A\Rightarrow B,\Delta }{{\mathcal {G}}\mid \Gamma \Rightarrow A\to B,\Delta }}}
Due to the additional structure in the hypersequent setting, the structural rules are considered in their internal and external variants. The internal weakening and internal contraction rules are the adaptions of the corresponding sequent rules with an added hypersequent context:
G ∣ Γ , A , A ⇒ Δ G ∣ Γ , A ⇒ Δ {\displaystyle {\frac {{\mathcal {G}}\mid \Gamma ,A,A\Rightarrow \Delta }{{\mathcal {G}}\mid \Gamma ,A\Rightarrow \Delta }}}
G ∣ Γ ⇒ A , A , Δ G ∣ Γ ⇒ A , Δ {\displaystyle {\frac {{\mathcal {G}}\mid \Gamma \Rightarrow A,A,\Delta }{{\mathcal {G}}\mid \Gamma \Rightarrow A,\Delta }}}
The external weakening and external contraction rules are the corresponding rules on the level of hypersequent components instead of formulae:
G G ∣ Γ ⇒ Δ {\displaystyle {\frac {\mathcal {G}}{{\mathcal {G}}\mid \Gamma \Rightarrow \Delta }}}
G ∣ Γ ⇒ Δ ∣ Γ ⇒ Δ G ∣ Γ ⇒ Δ {\displaystyle {\frac {{\mathcal {G}}\mid \Gamma \Rightarrow \Delta \mid \Gamma \Rightarrow \Delta }{{\mathcal {G}}\mid \Gamma \Rightarrow \Delta }}}
Soundness of these rules is closely connected to the formula interpretation of the hypersequent structure, nearly always as some form of disjunction . The precise formula interpretation depends on the considered logic, see below for some examples.
Hypersequents have been used to obtain analytic calculi for modal logics , for which analytic sequent calculi proved elusive. In the context of modal logics the standard formula interpretation of a hypersequent
is the formula
Here if Γ {\displaystyle \Gamma } is the multiset A 1 , … , A n {\displaystyle A_{1},\dots ,A_{n}} we write ◻ Γ {\displaystyle \Box \Gamma } for the result of prefixing every formula in Γ {\displaystyle \Gamma } with ◻ {\displaystyle \Box } , i.e., the multiset ◻ A 1 , … , ◻ A n {\displaystyle \Box A_{1},\dots ,\Box A_{n}} . Note that the single components are interpreted using the standard formula interpretation for sequents, and the hypersequent bar ∣ {\displaystyle \mid } is interpreted as a disjunction of boxes. The prime example of a modal logic for which hypersequents provide an analytic calculus is the logic S5 . In a standard hypersequent calculus for this logic [ 1 ] the formula interpretation is as above, and the propositional and structural rules are the ones from the previous section. Additionally, the calculus contains the modal rules
G ∣ Γ , A ⇒ Δ G ∣ Γ , ◻ A ⇒ Δ {\displaystyle {\frac {{\mathcal {G}}\mid \Gamma ,A\Rightarrow \Delta }{{\mathcal {G}}\mid \Gamma ,\Box A\Rightarrow \Delta }}}
G ∣ ◻ Γ , Σ ⇒ ◻ Δ , Π G ∣ ◻ Γ ⇒ ◻ Δ ∣ Σ ⇒ Π {\displaystyle {\frac {{\mathcal {G}}\mid \Box \Gamma ,\Sigma \Rightarrow \Box \Delta ,\Pi }{{\mathcal {G}}\mid \Box \Gamma \Rightarrow \Box \Delta \mid \Sigma \Rightarrow \Pi }}}
Admissibility of a suitably formulated version of the cut rule can be shown by a syntactic argument on the structure of derivations or by showing completeness of the calculus without the cut rule directly using the semantics of S5. In line with the importance of modal logic S5, a number of alternative calculi have been formulated. [ 2 ] [ 3 ] [ 1 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] Hypersequent calculi have also been proposed for many other modal logics. [ 6 ] [ 7 ] [ 8 ] [ 9 ]
Hypersequent calculi based on intuitionistic or single-succedent sequents have been used successfully to capture a large class of intermediate logics , i.e., extensions of intuitionistic propositional logic . Since the hypersequents in this setting are based on single-succedent sequents, they have the following form:
The standard formula interpretation for such an hypersequent is
Most hypersequent calculi for intermediate logics include the single-succedent versions of the propositional rules given above and a selection of the structural rules. The characteristics of a particular intermediate logic are mostly captured using a number of additional structural rules . E.g., the standard calculus for intermediate logic LC , sometimes also called Gödel–Dummett logic, contains additionally the so-called communication rule: [ 1 ]
Hypersequent calculi for many other intermediate logics have been introduced, [ 1 ] [ 10 ] [ 11 ] [ 12 ] and there are very general results about cut elimination in such calculi. [ 13 ]
As for intermediate logics, hypersequents have been used to obtain analytic calculi for many substructural logics and fuzzy logics . [ 1 ] [ 13 ] [ 14 ]
The hypersequent structure seem to have appeared first in [ 2 ] under the name of cortege , to obtain a calculus for the modal logic S5 . It seems to have been developed independently in, [ 3 ] also for treating modal logics, and in the influential, [ 1 ] where calculi for modal, intermediate and substructural logics are considered, and the term hypersequent is introduced. | https://en.wikipedia.org/wiki/Hypersequent |
Hypersonic flight is flight through the atmosphere below altitudes of about 90 km (56 mi) at speeds greater than Mach 5 , a speed where dissociation of air begins to become significant and high heat loads exist. Speeds over Mach 25 have been achieved below the thermosphere as of 2020. [ 1 ]
Hypersonic vehicles are able to maneuver through the atmosphere in a non-parabolic trajectory , but their aerodynamic heat loads need to be managed.
The first manufactured object to achieve hypersonic flight was the two-stage Bumper rocket, consisting of a WAC Corporal second stage set on top of a V-2 first stage. In February 1949, at White Sands , the rocket reached a speed of 8,290 km/h (5,150 mph), or about Mach 6.7. [ 2 ] The vehicle, however, burned on atmospheric re-entry , and only charred remnants were found. In April 1961, Russian Major Yuri Gagarin became the first human to travel at hypersonic speed, during the world's first piloted orbital flight . Soon after, in May 1961, Alan Shepard became the first American and second person to fly hypersonic when his capsule reentered the atmosphere at a speed above Mach 5 at the end of his suborbital flight over the Atlantic Ocean. [ 3 ]
In November 1961, Air Force Major Robert White flew the X-15 research aircraft at speeds over Mach 6. [ 4 ] [ 5 ] On 3 October 1967, in California, an X-15 reached Mach 6.7. [ 6 ]
The reentry problem of a space vehicle was extensively studied. [ 7 ] The NASA X-43A flew on scramjet for 10 seconds, and then glided for 10 minutes on its last flight in 2004. The Boeing X-51 Waverider flew on scramjet for 210 seconds in 2013, finally reaching Mach 5.1 on its fourth flight test. The hypersonic regime has since become the subject of further study during the 21st century, and strategic competition between the United States, India, Russia, and China. [ 8 ]
The stagnation point of air flowing around a body is a point where its local velocity is zero. [ 7 ] At this point the air flows around this location. A shock wave forms, which deflects the air from the stagnation point and insulates the flight body from the atmosphere. [ 7 ] This can affect the lifting ability of a flight surface to counteract its drag and subsequent free fall . [ 9 ] [ a ]
In order to maneuver in the atmosphere at faster speeds than supersonic, the forms of propulsion can still be airbreathing systems, but a ramjet does not suffice for a system to attain Mach 5, as a ramjet slows down the airflow to subsonic. [ 11 ] Some systems ( waveriders ) use a first stage rocket to boost a body into the hypersonic regime. Other systems ( boost-glide vehicles) use scramjets after their initial boost, in which the speed of the air passing through the scramjet remains supersonic. Other systems ( munitions ) use a cannon for their initial boost. [ 12 ]
Hypersonic flow is a high energy flow. [ 13 ] The ratio of kinetic energy to the internal energy of the gas increases as the square of the Mach number. When this flow enters a boundary layer, there are high viscous effects due to the friction between air and the high-speed object. In this case, the high kinetic energy is converted in part to internal energy and gas energy is proportional to the internal energy. Therefore, hypersonic boundary layers are high temperature regions due to the viscous dissipation of the flow's kinetic energy. Another region of high temperature flow is the shock layer behind the strong bow shock wave. In the case of the shock layer, the flow's velocity decreases discontinuously as it passes through the shock wave. This results in a loss of kinetic energy and a gain of internal energy behind the shock wave. Due to high temperatures behind the shock wave, dissociation of molecules in the air becomes thermally active. For example, for air at T > 2,000 K (1,730 °C; 3,140 °F), dissociation of diatomic oxygen into oxygen radicals is active: O 2 → 2O [ 14 ] : 41 [ 15 ] [ 16 ] For T > 4,000 K (3,730 °C; 6,740 °F), dissociation of diatomic nitrogen into N radicals is active: N 2 → 2N [ 14 ] : 39 Consequently, in this temperature range, a plasma forms: [ 17 ] —molecular dissociation followed by recombination of oxygen and nitrogen radicals produces nitric oxide: N 2 + O 2 → 2NO, which then dissociates and recombines to form ions: N + O → NO + + e − [ 14 ] : 39 [ 18 ]
At standard sea-level condition for air, the mean free path of air molecules is about λ = 68 n m {\displaystyle \lambda =68\,\mathrm {nm} } . At an altitude of 104 km (65 mi), where the air is thinner, the mean free path is λ = 1 f t = 0.305 m {\displaystyle \lambda =1\,\mathrm {ft} =0.305\,\mathrm {m} } . Because of this large free mean path aerodynamic concepts, equations, and results based on the assumption of a continuum begin to break down, therefore aerodynamics must be considered from kinetic theory. This regime of aerodynamics is called low-density flow.
For a given aerodynamic condition low-density effects depends on the value of a nondimensional parameter called the Knudsen number K n {\displaystyle \mathrm {Kn} } , defined as K n = λ l {\displaystyle \mathrm {Kn} ={\frac {\lambda }{l}}} where l {\displaystyle l} is the typical length scale of the object considered. The value of the Knudsen number based on nose radius, K n = λ R {\displaystyle \mathrm {Kn} ={\frac {\lambda }{R}}} , can be near one.
Hypersonic vehicles frequently fly at very high altitudes and therefore encounter low-density conditions. Hence, the design and analysis of hypersonic vehicles sometimes require consideration of low-density flow. New generations of hypersonic airplanes may spend a considerable portion of their mission at high altitudes, and for these vehicles, low-density effects will become more significant. [ 13 ]
The flow field between the shock wave and the body surface is called the shock layer. As the Mach number M increases, the angle of the resulting shock wave decreases. This Mach angle is described by the equation μ = sin − 1 ( a / v ) {\displaystyle \mu =\sin ^{-1}(a/v)} where a is the speed of the sound wave and v is the flow velocity. Since M=v/a, the equation becomes μ = sin − 1 ( 1 / M ) {\displaystyle \mu =\sin ^{-1}(1/M)} . Higher Mach numbers position the shock wave closer to the body surface, thus at hypersonic speeds, the shock wave lies extremely close to the body surface, resulting in a thin shock layer. At low Reynolds number, the boundary layer grows quite thick and merges with the shock wave, leading to a fully viscous shock layer. [ 19 ]
The compressible flow boundary layer increases proportionately to the square of the Mach number, and inversely to the square root of the Reynolds number.
At hypersonic speeds, this effect becomes much more pronounced, due to the exponential reliance on the Mach number. Since the boundary layer becomes so large, it interacts more viscously with the surrounding flow. The overall effect of this interaction is to create a much higher skin friction than normal, causing greater surface heat flow. Additionally, the surface pressure spikes, which results in a much larger aerodynamic drag coefficient. This effect is extreme at the leading edge and decreases as a function of length along the surface. [ 13 ]
The entropy layer is a region of large velocity gradients caused by the strong curvature of the shock wave. The entropy layer begins at the nose of the aircraft and extends downstream close to the body surface. Downstream of the nose, the entropy layer interacts with the boundary layer which causes an increase in aerodynamic heating at the body surface. Although the shock wave at the nose at supersonic speeds is also curved, the entropy layer is only observed at hypersonic speeds because the magnitude of the curve is far greater at hypersonic speeds. [ 13 ]
Researchers in China have used shock waves in a detonation chamber to compress ionized argon plasma waves moving at Mach 14. The waves are directed into magnetohydrodynamic (MHD) generators to create a current pulse that could be scaled up to gigawatt scale, given enough argon gas to feed into the MHD generators. [ 20 ]
A rotating detonation engine (RDE) [ 21 ] might propel airframes in hypersonic flight; on 14 December 2023 engineers at GE Aerospace demonstrated their test rig, which is to combine an RDE with a ramjet/ scramjet , in order to evaluate the regimes of rotating detonation combustion. The goal is to achieve sustainable turbine-based combined cycle (TBCC) propulsion systems, at speeds between Mach 1 and Mach 5. [ 22 ] [ 23 ] [ 24 ]
Companies such as Hermeus , Venus Aerospace, and AstroMechanica are developing hybrid engines capable of operating from subsonic to hypersonic speeds.
Transport consumes energy for three purposes: overcoming gravity, overcoming air/water friction, and achieving terminal velocity. The reduced trip times and higher flight altitudes reduce the first two, while increasing the third. Proponents claim that the net energy costs of hypersonic transport can be lower than those of conventional transport while slashing journey times. [ 27 ]
Stratolaunch Roc can be used to launch hypersonic aircraft. [ 28 ]
Hermeus demonstrated transition from turbojet aircraft engine operation to ramjet operation on 17 November 2022, [ 29 ] thus avoiding the need to boost aircraft velocities by rocket or scramjet. [ 30 ]
Two main types of hypersonic weapons are hypersonic cruise missiles and hypersonic glide vehicles . [ b ] [ 36 ] Hypersonic weapons, by definition, travel five or more times the speed of sound. Hypersonic cruise missiles, which are powered by scramjets , are limited to below 30 km (19 mi); [ c ] hypersonic glide vehicles can travel higher.
Hypersonic vehicles are much slower than ballistic (i.e. sub-orbital or fractional orbital) missiles, because they travel in the atmosphere, and ballistic missiles travel in the vacuum above the atmosphere. However, they can use the atmosphere to manoeuvre, making them capable of large-angle deviations from a ballistic trajectory. [ 11 ] A hypersonic glide vehicle is usually launched with a ballistic first stage, then deploys wings and switches to hypersonic flight as it re-enters the atmosphere, allowing the final stage to evade existing missile defense systems which were designed for ballistic-only missiles. [ 39 ]
According to a CNBC July 2019 report (and now in a CNN 2022 report), Russia and China lead in hypersonic weapon development, trailed by the United States, [ 40 ] [ 41 ] [ 42 ] [ 8 ] [ 43 ] and in this case the problem is being addressed in a joint program of the entire Department of Defense. [ 44 ] To meet this development need, the US Army is participating in a joint program with the US Navy and Air Force, to develop a hypersonic glide body. [ 52 ] India is also developing such weapons. [ 53 ] France and Australia may also be pursuing the technology. [ 11 ] Japan is acquiring both scramjet (Hypersonic Cruise Missile), and boost-glide weapons (Hyper Velocity Gliding Projectile). [ 54 ]
China's XingKong-2 (星空二号, Starry-sky-2 ), a waverider , had its first flight 3 August 2018. [ 55 ] [ 56 ] [ 57 ] [ 58 ] In August 2021 China launched a boost-glide vehicle to low-earth orbit, circling Earth before maneuvering toward its target location, missing its target by two dozen miles. [ 59 ] [ 60 ] However China has responded that the vehicle was a spacecraft, and not a missile; [ 61 ] there was a July 2021 test of a spaceplane, according to Chinese Foreign Ministry Spokesperson Zhao Lijian ; [ 62 ] [ 63 ] [ 64 ] Todd Harrison points out that an orbital trajectory would take 90 minutes for a spaceplane to circle Earth (which would defeat the mission of a weapon in hypersonic flight). [ 62 ] The US DoD's headquarters (The Pentagon) reported in October 2021 that two such hypersonic launches have occurred; one launch did not demonstrate the accuracy needed for a precision weapon; [ 59 ] the second launch by China demonstrated its ability to change trajectories, according to Pentagon reports on the 2021 competition in arms capabilities. [ 65 ]
In 2022, China unveiled two more hypersonic models. [ 66 ] [ 67 ] An AI simulation has revealed that a Mach 11 aircraft can simply outrun a Mach 1.3 fighter attempting to engage it, while firing its missile at the "pursuing" fighter. [ 68 ] This strategy entails a fire control system to accomplish an over-the-shoulder missile launch, which does not yet exist (2023). [ 68 ]
In February 2023, the DF-27 covered 1,900 km (1,200 mi) in 12 minutes, according to leaked secret documents . [ 69 ] The capability directly threatens Guam, and US Navy aircraft carriers. [ 69 ]
In 2016, Russia is believed to have conducted two successful tests of Avangard , a hypersonic glide vehicle. The third known test, in 2017, failed. [ 70 ] In 2018, an Avangard was launched at the Dombarovskiy missile base , reaching its target at the Kura shooting range , a distance of 5,955 km (3,700 mi). [ 71 ] Avangard uses new composite materials which are to withstand temperatures of up to 2,000 °C (3,630 °F). [ 72 ] The Avangard's environment at hypersonic speeds reaches such temperatures. [ 72 ] Russia considered its carbon fiber solution to be unreliable, [ 73 ] and replaced it with new composite materials. [ 72 ] Two Avangard hypersonic glide vehicles (HGVs) [ 74 ] will first be mounted on SS-19 ICBMs; on 27 December 2019 the weapon was first fielded to the Yasnensky Missile Division, a unit in the Orenburg Oblast . [ 75 ] In an earlier report, Franz-Stefan Gady named the unit as the 13th Regiment/Dombarovskiy Division (Strategic Missile Force). [ 74 ] In 2021 Russia launched a 3M22 Zircon antiship missile over the White Sea , as part of a series of tests. [ 76 ] " Kinzhal and Zircon (Tsirkon) are standoff strike weapons". [ 77 ] In February 2022, a coordinated series of missile exercises, some of them hypersonic, were launched on 18 February 2022 in an apparent display of power projection . The launch platforms ranged from submarines in the Barents sea in the Arctic, as well as from ships on the Black sea to the south of Russia. The exercise included a RS-24 Yars ICBM, which was launched from the Plesetsk Cosmodrome in Northern Russia until it reached its destination on the Kamchatka Peninsula in Eastern Russia . [ 78 ] Ukraine estimated a 3M22 Zircon was used against it, but apparently did not exceed Mach 3 and was shot down 7 February 2024 in Kyiv. [ 79 ]
These tests have prompted US responses in weapons development. [ 80 ] By 2018, the AGM-183 [ 81 ] and Long-Range Hypersonic Weapon [ 82 ] were in development per John Hyten 's USSTRATCOM statement on 8 August 2018 (UTC). [ 83 ] At least one vendor is developing ceramics to handle the temperatures of hypersonics systems. [ 84 ] There are over a dozen US hypersonics projects as of 2018, notes the commander of USSTRATCOM; [ 83 ] [ 85 ] [ 82 ] [ 86 ] [ 87 ] [ 88 ] from which a future hypersonic cruise missile is sought, perhaps by Q4 FY2021. [ 89 ] [ 90 ] [ 91 ] The Long range precision fires (LRPF) CFT is supporting Space and Missile Defense Command 's pursuit of hypersonics. [ 94 ] Joint programs in hypersonics are informed by Army work; [ 95 ] [ 96 ] however, at the strategic level, the bulk of the hypersonics work remains at the Joint level. [ 101 ] Long Range Precision Fires (LRPF) is an Army priority, and also a DoD joint effort. [ 96 ] The Army and Navy's Common Hypersonic Glide Body (C-HGB) had a successful test of a prototype in March 2020. [ 102 ] [ 100 ] A wind tunnel for testing hypersonic vehicles was completed in Texas (2021). [ 103 ] The Army's Land-based Hypersonic Missile "is intended to have a range of 2,300 km (1,400 mi)". [ 104 ] : p.6 [ 51 ] [ 105 ] [ 106 ] [ 107 ] [ 108 ] By adding rocket propulsion to a shell or glide body, the joint effort shaved five years off the likely fielding time for hypersonic weapon systems. [ 109 ] [ 110 ] Countermeasures against hypersonics will require sensor data fusion: both radar and infrared sensor tracking data will be required to capture the signature of a hypersonic vehicle in the atmosphere. [ 115 ] There are also privately developed hypersonic systems, [ 116 ] as well as critics. [ 117 ] [ 118 ]
DoD tested a Common Hypersonic Glide Body (C-HGB) in 2020. [ 102 ] [ 119 ] The Air Force dropped out of the tri-service hypersonic project in 2020, leaving only the Army and Navy on the C-HGB. [ 120 ] [ 121 ] [ 122 ] According to Air Force chief scientist, Dr. Greg Zacharias , the US anticipates having hypersonic weapons by the 2020s, [ 123 ] hypersonic drones by the 2030s, and recoverable hypersonic drone aircraft by the 2040s. [ 124 ] The focus of DoD development will be on air-breathing boost-glide hypersonics systems. [ 125 ] Countering hypersonic weapons during their cruise phase will require radar with longer range, as well as space-based sensors, and systems for tracking and fire control. [ 125 ] [ 126 ] [ 111 ] [ 127 ] A mid-2021 report from the Congressional Research Service states the United States is "unlikely" to field an operational hypersonic glide vehicle (HGV) until 2023. [ 128 ]
On 21 October 2021, the Pentagon stated that a test of a hypersonic glide body failed to complete because its booster failed; according to Lt. Cmdr. Timothy Gorman the booster was not part of the equipment under test, but the booster's failure mode will be reviewed to improve the test setup. [ 129 ] The test occurred at Pacific Spaceport Complex – Alaska , on Kodiak island. [ 130 ] Three rocketsondes at Wallops Island completed successful tests earlier that week, for the hypersonics effort. [ 130 ] On 29 October 2021 the booster rocket for the Long-Range Hypersonic Weapon was successfully tested in a static test; the first stage thrust vector control system control system was included. [ 131 ] On 26 October 2022 Sandia National Laboratories conducted a successful test of hypersonic technologies at Wallops Island . [ 132 ] [ 133 ] On 28 June 2024 DoD announced a successful recent end-to-end test of the US Army's Long-Range Hypersonic Weapon all-up round (AUR) and the US Navy's Conventional Prompt Strike. The missile was launched from the Pacific Missile Range Facility , Kauai, Hawaii. [ 134 ]
In September 2021, and in March 2022, US vendors Raytheon/Northrop Grumman, [ 135 ] [ 136 ] [ 137 ] and Lockheed [ 138 ] [ 139 ] respectively, first successfully tested their air-launched, scramjet-powered hypersonic cruise missiles, which were funded by DARPA . [ c ] By September 2022 Raytheon was selected for fielding Hypersonic Attack Cruise Missile (HACM), a scramjet-powered hypersonic missile by FY2027. [ 140 ] [ 141 ]
In March 2024 Stratolaunch Roc launched TA-1, a vehicle which is nearing Mach 5 at 10.67 km (6.63 mi) in a powered flight, a risk-reduction exercise for TA-2. [ 142 ] In a similar development Castelion launched its low-cost hypersonic platform in the Mojave desert, in March 2024. [ 143 ]
In 2022, Iran was believed to have constructed their first hypersonic missile. Amir Ali Hajizadeh , the commander of the Air Force of the Islamic Republic of Iran's Revolutionary Guards Corps, announced the construction of the Islamic Republic's first hypersonic missile. He noted: "This new missile was produced to counter air defense shields and passes through all missile defense systems and which represents a big leap in the generation of missiles" [ 144 ] and has a speed above Mach 13. [ 145 ] but Col. Rob Lodwick, the spokesman for the Pentagon on Middle East affairs said that there are doubts in this regard. [ 146 ]
In 2021, DoD was codifying flight test guidelines, knowledge gained from Conventional Prompt Strike (CPS), and the other hypersonics programs, [ 147 ] for some 70 hypersonics R&D programs alone, as of 2021. [ 148 ] [ 149 ] In 2021–2023, Heidi Shyu , the Under Secretary of Defense for Research and Engineering (USD(R&E)) is pursuing a program of annual rapid joint experiments, [ 150 ] including hypersonics capabilities, to bring down their cost of development. [ 151 ] [ 152 ] A hypersonic test bed aims to bring the frequency of tests to one per week. [ 153 ] [ 154 ]
France , [ 128 ] Australia , [ 128 ] India , [ 155 ] Germany , [ 128 ] Japan , [ 128 ] South Korea , [ 156 ] North Korea , [ 157 ] and Iran [ 158 ] also have ongoing hypersonic weapon projects or research programs. [ 128 ]
Australia and the US have begun joint development of air-launched hypersonic missiles, as announced by a Pentagon statement on 30 November 2020. The development will build on the $54 million Hypersonic International Flight Research Experimentation (HIFiRE) under which both nations collaborated on over a 15-year period. [ 159 ] Small and large companies will all contribute to the development of these hypersonic missiles, [ 160 ] named SCIFIRE in 2022. [ 161 ] [ 140 ]
In May 2023 Ukraine shot down a Kinzhal with a Patriot . [ 162 ] IBCS, or the Integrated Air and Missile Defense Battle Command System is an Integrated Air and Missile Defense (IAMD) capability designed to work with Patriots and other missiles.
Rand Corporation (28 September 2017) estimates there is less than a decade to prevent Hypersonic Missile proliferation. [ 163 ] In the same way that anti-ballistic missiles were developed as countermeasures to ballistic missiles , counter-countermeasures to hypersonics systems were not yet in development, as of 2019. [ 11 ] [ 164 ] [ 73 ] [ 165 ] See the National Defense Space Architecture (2021), above . But by 2019, $157.4 million was allocated in the FY2020 Pentagon budget for hypersonic defense, out of $2.6 billion for all hypersonic-related research. [ 104 ] $207 million of the FY2021 budget was allocated to defensive hypersonics, up from the FY2020 budget allocation of $157 million. [ 148 ] [ 166 ] [ 50 ] Both the US and Russia withdrew from the Intermediate-Range Nuclear Forces (INF) Treaty in February 2019. This will spur arms development, including hypersonic weapons, [ 167 ] [ 168 ] in FY2021 and forward. [ 169 ] By 2021 the Missile Defense Agency was funding regional countermeasures against hypersonic weapons in their glide phase . [ 170 ] [ 171 ] [ 172 ] James Acton characterized the proliferation of hypersonic vehicles as never-ending in October 2021; Jeffery Lewis views the proliferation as additional arguments for ending the arms race. [ 173 ] Doug Loverro assesses that both missile defense and competition need rethinking. [ 174 ] CSIS assesses that hypersonic defense should be the US' priority over hypersonic weapons. [ 175 ] [ d ] [ 176 ] [ 177 ]
As part of their Hypersonic vehicle tracking mission, the Space Development Agency (SDA) launched four satellites and the Missile Defense Agency (MDA) launched two satellites on 14 February 2024 (launch USSF-124). [ 178 ] [ 179 ] The satellites will share the same orbit, which allows the SDA's wide field of view (WFOV) satellites and the MDA's medium field of view (MFOV) downward-looking satellites to traverse the same terrain of Earth. The SDA's four satellites are part of its Tranche 0 tracking layer (T0TL). The MDA's two satellites are HBTSS or Hypersonic and ballistic tracking space sensors. [ e ]
Additional capabilities of Tranche 0 of the National defense space architecture (NDSA), also known as the Proliferated warfighting space architecture (PWSA) will be tested over the next two years. [ 179 ] [ 184 ] | https://en.wikipedia.org/wiki/Hypersonic_flight |
In aerodynamics , a hypersonic speed is one that exceeds five times the speed of sound , often stated as starting at speeds of Mach 5 and above. [ 1 ]
The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since individual physical changes in the airflow (like molecular dissociation and ionization ) occur at different speeds; these effects collectively become important around Mach 5–10. The hypersonic regime can also be alternatively defined as speeds where specific heat capacity changes with the temperature of the flow as kinetic energy of the moving object is converted into heat. [ 2 ]
While the definition of hypersonic flow can be quite vague and is generally debatable (especially because of the absence of discontinuity between supersonic and hypersonic flows), a hypersonic flow may be characterized by certain physical phenomena that can no longer be analytically discounted as in supersonic flow. [ citation needed ] The peculiarities in hypersonic flows are as follows: [ citation needed ]
As a body's Mach number increases, the density behind a bow shock generated by the body also increases, which corresponds to a decrease in volume behind the shock due to conservation of mass . Consequently, the distance between the bow shock and the body decreases at higher Mach numbers. [ 3 ]
As Mach numbers increase, the entropy change across the shock also increases, which results in a strong entropy gradient and highly vortical flow that mixes with the boundary layer .
A portion of the large kinetic energy associated with flow at high Mach numbers transforms into internal energy in the fluid due to viscous effects. The increase in internal energy is realized as an increase in temperature. Since the pressure gradient normal to the flow within a boundary layer is approximately zero for low to moderate hypersonic Mach numbers, the increase of temperature through the boundary layer coincides with a decrease in density. This causes the bottom of the boundary layer to expand, so that the boundary layer over the body grows thicker and can often merge with the shock wave near the body leading edge. [ citation needed ]
High temperatures due to a manifestation of viscous dissipation cause non-equilibrium chemical flow properties such as vibrational excitation and dissociation and ionization of molecules resulting in convective and radiative heat-flux . [ citation needed ]
Although "subsonic" and "supersonic" usually refer to speeds below and above the local speed of sound respectively, aerodynamicists often use these terms to refer to particular ranges of Mach values. When an aircraft approaches transonic speeds (around Mach 1), it enters a special regime. The usual approximations based on the Navier–Stokes equations , which work well for subsonic designs, start to break down because, even in the freestream, some parts of the flow locally exceed Mach 1. So, more sophisticated methods are needed to handle this complex behavior. [ 4 ]
The "supersonic regime" usually refers to the set of Mach numbers for which linearised theory may be used; for example, where the ( air ) flow is not chemically reacting and where heat transfer between air and vehicle may be reasonably neglected in calculations. Generally, NASA defines "high" hypersonic as any Mach number from 10 to 25, and re-entry speeds as anything greater than Mach 25. Among the spacecraft operating in these regimes are returning Soyuz and Dragon space capsules ; the previously-operated Space Shuttle ; various reusable spacecraft in development such as SpaceX Starship and Rocket Lab Electron ; and (theoretical) spaceplanes . [ citation needed ]
In the following table, the "regimes" or "ranges of Mach values" are referenced instead of the usual meanings of "subsonic" and "supersonic". [ citation needed ]
The subsonic speed range is that range of speeds within which, all of the airflow over an aircraft is less than Mach 1. The critical Mach number (Mcrit) is lowest free stream Mach number at which airflow over any part of the aircraft first reaches Mach 1. So the subsonic speed range includes all speeds that are less than Mcrit.
The transonic speed range is that range of speeds within which the airflow over different parts of an aircraft is between subsonic and supersonic. So the regime of flight from Mcrit up to Mach 1.3 is called the transonic range. [ citation needed ]
Aircraft designed to fly at supersonic speeds show large differences in their aerodynamic design because of the radical differences in the behavior of flows above Mach 1. Sharp edges, thin aerofoil -sections, and all-moving tailplane / canards are common. Modern combat aircraft must compromise in order to maintain low-speed handling; "true" supersonic designs, generally incorporating delta wings, are rarer.
The categorization of airflow relies on a number of similarity parameters , which allow the simplification of a nearly infinite number of test cases into groups of similarity. For transonic and compressible flow , the Mach and Reynolds numbers alone allow good categorization of many flow cases. [ citation needed ]
Hypersonic flows, however, require other similarity parameters. First, the analytic equations for the oblique shock angle become nearly independent of Mach number at high (~>10) Mach numbers. Second, the formation of strong shocks around aerodynamic bodies means that the freestream Reynolds number is less useful as an estimate of the behavior of the boundary layer over a body (although it is still important). Finally, the increased temperature of hypersonic flow mean that real gas effects become important. Research in hypersonics is therefore often called aerothermodynamics , rather than aerodynamics . [ 10 ]
The introduction of real gas effects means that more variables are required to describe the full state of a gas. Whereas a stationary gas can be described by three variables ( pressure , temperature , adiabatic index ), and a moving gas by four ( flow velocity ), a hot gas in chemical equilibrium also requires state equations for the chemical components of the gas, and a gas in nonequilibrium solves those state equations using time as an extra variable. This means that for nonequilibrium flow, something between 10 and 100 variables may be required to describe the state of the gas at any given time. Additionally, rarefied hypersonic flows (usually defined as those with a Knudsen number above 0.1) do not follow the Navier–Stokes equations . [ citation needed ]
Hypersonic flows are typically categorized by their total energy, expressed as total enthalpy (MJ/kg), total pressure (kPa-MPa), stagnation pressure (kPa-MPa), stagnation temperature (K), or flow velocity (km/s). [ citation needed ]
Wallace D. Hayes developed a similarity parameter, similar to the Whitcomb area rule , which allowed similar configurations to be compared. [ citation needed ] In the study of hypersonic flow over slender bodies, the product of the freestream Mach number M ∞ {\displaystyle M_{\infty }} and the flow deflection angle θ {\displaystyle \theta } , known as the hypersonic similarity parameter: K = M ∞ θ {\displaystyle K=M_{\infty }\theta } is considered to be an important governing parameter. [ 10 ] The slenderness ratio of a vehicle τ = d / l {\displaystyle \tau =d/l} , where d {\displaystyle d} is the diameter and l {\displaystyle l} is the length, is often substituted for θ {\displaystyle \theta } .
Hypersonic flow can be approximately separated into a number of regimes. The selection of these regimes is rough, due to the blurring of the boundaries where a particular effect can be found. [ citation needed ]
In this regime, the gas can be regarded as an ideal gas . Flow in this regime is still Mach number dependent. Simulations start to depend on the use of a constant-temperature wall, rather than the adiabatic wall typically used at lower speeds. The lower border of this region is around Mach 5, where ramjets become inefficient, and the upper border around Mach 10–12. [ citation needed ]
This is a subset of the perfect gas regime, where the gas can be considered chemically perfect, but the rotational and vibrational temperatures of the gas must be considered separately, leading to two temperature models. See particularly the modeling of supersonic nozzles, where vibrational freezing becomes important. [ citation needed ]
In this regime, diatomic or polyatomic gases (the gases found in most atmospheres) begin to dissociate as they come into contact with the bow shock generated by the body. Surface catalysis plays a role in the calculation of surface heating, meaning that the type of surface material also has an effect on the flow. The lower border of this regime is where any component of a gas mixture first begins to dissociate in the stagnation point of a flow (which for nitrogen is around 2000 K). At the upper border of this regime, the effects of ionization start to have an effect on the flow. [ citation needed ]
In this regime the ionized electron population of the stagnated flow becomes significant, and the electrons must be modeled separately. Often the electron temperature is handled separately from the temperature of the remaining gas components. This region occurs for freestream flow velocities around 3–4 km/s. Gases in this region are modeled as non-radiating plasmas . [ citation needed ]
Above around 12 km/s, the heat transfer to a vehicle changes from being conductively dominated to radiatively dominated. The modeling of gases in this regime is split into two classes: [ citation needed ]
The modeling of optically thick gases is extremely difficult, since, due to the calculation of the radiation at each point, the computation load theoretically expands exponentially as the number of points considered increases. | https://en.wikipedia.org/wiki/Hypersonic_speed |
A hypersonic wind tunnel is designed to generate a hypersonic flow field in the working section, thus simulating the typical flow features of this flow regime - including compression shocks and pronounced boundary layer effects, entropy layer and viscous interaction zones and most importantly high total temperatures of the flow. The speed of these tunnels vary from Mach 5 to 15. The power requirement of a wind tunnel increases linearly with its cross section and flow density, but cubically with the test velocity required. Hence installation of a continuous, closed circuit wind tunnel remains a costly affair. The first continuous Mach 7-10 wind tunnel with 1x1 m test section was planned at Kochel am See, Germany during WW II [ 1 ] and finally put into operation as 'Tunnel A' in the late 1950s at AEDC Tullahoma, TN, USA for an installed power of 57 MW. In view of these high facility demands, also intermittently operated experimental facilities like blow-down wind tunnels are designed and installed to simulate the hypersonic flow. A hypersonic wind tunnel comprises in flow direction the main components: heater/cooler arrangements, dryer, convergent/divergent nozzle, test section, second throat and diffuser. A blow-down wind tunnel has a low vacuum reservoir at the back end, while a continuously operated, closed circuit wind tunnel has a high power compressor installation instead. Since the temperature drops with the expanding flow, the air inside the test section has the chance of becoming liquefied . For that reason, preheating is particularly critical (the nozzle may require cooling).
There are several technological problems in designing and constructing a hyper-velocity wind tunnel:
Simulations of a flow at 5.5 km/s, 45 km altitude would require tunnel temperatures of as much as 9000 K , and a pressure of 3 GPa .
One form of HWT is known as a Gun Tunnel or hot shot tunnel (up to M =27), which can be used for analysis of flows past ballistic missiles, space vehicles in atmospheric entry, and plasma physics or heat transfer at high temperatures. It runs intermittently, but has a very low running time (less than a second).
The method of operation is based on a high temperature and pressurized gas (air or nitrogen) produced in an arc-chamber, and a near-vacuum in the remaining part of the tunnel. The arc-chamber can reach several MPa , while pressures in the vacuum chamber can be as low as 0.1 Pa . This means that the pressure ratios of these tunnels are in the order of 10 million. Also, the temperatures of the hot gas are up to 5000 K. The arc chamber is mounted in the gun barrel. The high pressure gas is separated from the vacuum by a diaphragm.
Prior to a test run commencing, a membrane separates the compressed air from the gun barrel breech. A rifle (or similar) is used to rupture the membrane. Compressed air rushes into the breech of the gun barrel, forcing a small projectile to accelerate rapidly down the barrel. Although the projectile is prevented from leaving the barrel, the air in front of the projectile emerges at hypersonic velocity into the working section. Naturally the duration of the test is extremely brief, so high speed instrumentation is required to get any meaningful data.
The Indian Space Research Organization (ISRO) commissioned three major facilities, namely a Hypersonic Wind Tunnel, a Shock Tunnel and a Plasma Tunnel at Vikram Sarabhai Space Center as part of its continuous and concerted efforts to minimize cost of access into space. This integrated facility was named as Satish Dhawan Wind Tunnel Complex as a tribute to Prof. Satish Dhawan , who has made very significant contributions in the field of wind tunnels and aerodynamics. ISRO Chairman A. S. Kiran Kumar said commissioning of such facilities would provide adequate data for design and development of current and future space transportation systems in India. [ 2 ]
Defence Research and Development Organisation (DRDO) commissioned an advanced Hypersonic Wind Tunnel (HWT) test facility at Dr APJ Abdul Kalam Missile Complex on 20 December 2020 as part of facility development programme for Hypersonic Technology Demonstrator Vehicle project. [ 3 ]
The MARHy Hypersonic low density Wind Tunnel , located at the ICARE [ 4 ] Laboratory in Orléans, France, is a research facility used extensively for fundamental and applied research of fluid dynamic phenomena in rarefied compressible flows, applied to space research. Its name is an acronym for M ach A daptable R arefied Hy personic and the wind tunnel is recorded under this name under the European portal MERIL. | https://en.wikipedia.org/wiki/Hypersonic_wind_tunnel |
Hyperspectral imaging collects and processes information from across the electromagnetic spectrum . [ 1 ] The goal of hyperspectral imaging is to obtain the spectrum for each pixel in the image of a scene, with the purpose of finding objects, identifying materials, or detecting processes. [ 2 ] [ 3 ] There are three general types of spectral imagers. There are push broom scanners and the related whisk broom scanners (spatial scanning), which read images over time, band sequential scanners (spectral scanning), which acquire images of an area at different wavelengths, and snapshot hyperspectral imagers , which uses a staring array to generate an image in an instant.
Whereas the human eye sees color of visible light in mostly three bands (long wavelengths, perceived as red; medium wavelengths, perceived as green; and short wavelengths, perceived as blue), spectral imaging divides the spectrum into many more bands. This technique of dividing images into bands can be extended beyond the visible. In hyperspectral imaging, the recorded spectra have fine wavelength resolution and cover a wide range of wavelengths. Hyperspectral imaging measures continuous spectral bands, as opposed to multiband imaging which measures spaced spectral bands. [ 4 ]
Engineers build hyperspectral sensors and processing systems for applications in astronomy, agriculture, molecular biology, biomedical imaging, geosciences, physics, and surveillance. Hyperspectral sensors look at objects using a vast portion of the electromagnetic spectrum. Certain objects leave unique "fingerprints" in the electromagnetic spectrum. Known as spectral signatures, these "fingerprints" enable identification of the materials that make up a scanned object. For example, a spectral signature for oil helps geologists find new oil fields . [ 5 ]
Figuratively speaking, hyperspectral sensors collect information as a set of "images." Each image represents a narrow wavelength range of the electromagnetic spectrum, also known as a spectral band. These "images" are combined to form a three-dimensional ( x , y , λ ) hyperspectral data cube for processing and analysis, where x and y represent two spatial dimensions of the scene, and λ represents the spectral dimension (comprising a range of wavelengths). [ 6 ]
Technically speaking, there are four ways for sensors to sample the hyperspectral cube: spatial scanning, spectral scanning, snapshot imaging, [ 5 ] [ 7 ] and spatio-spectral scanning. [ 8 ]
Hyperspectral cubes are generated from airborne sensors like NASA's Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), or from satellites like NASA's EO-1 with its hyperspectral instrument Hyperion. [ 9 ] [ 10 ] However, for many development and validation studies, handheld sensors are used. [ 11 ]
The precision of these sensors is typically measured in spectral resolution, which is the width of each band of the spectrum that is captured. If the scanner detects a large number of fairly narrow frequency bands, it is possible to identify objects even if they are only captured in a handful of pixels. However, spatial resolution is a factor in addition to spectral resolution. If the pixels are too large, then multiple objects are captured in the same pixel and become difficult to identify. If the pixels are too small, then the intensity captured by each sensor cell is low, and the decreased signal-to-noise ratio reduces the reliability of measured features.
The acquisition and processing of hyperspectral images is also referred to as imaging spectroscopy or, with reference to the hyperspectral cube, as 3D spectroscopy.
There are four basic techniques for acquiring the three-dimensional ( x , y , λ ) dataset of a hyperspectral cube. The choice of technique depends on the specific application, seeing that each technique has context-dependent advantages and disadvantages.
In spatial scanning, each two-dimensional (2D) sensor output represents a full slit spectrum ( x , λ ). Hyperspectral imaging (HSI) devices for spatial scanning obtain slit spectra by projecting a strip of the scene onto a slit and dispersing the slit image with a prism or a grating. These systems have the drawback of having the image analyzed per lines (with a push broom scanner ) and also having some mechanical parts integrated into the optical train. With these line-scan cameras , the spatial dimension is collected through platform movement or scanning. This requires stabilized mounts or accurate pointing information to 'reconstruct' the image. Nonetheless, line-scan systems are particularly common in remote sensing , where it is sensible to use mobile platforms. Line-scan systems are also used to scan materials moving by on a conveyor belt. A special case of line scanning is point scanning (with a whisk broom scanner ), where a point-like aperture is used instead of a slit, and the sensor is essentially one-dimensional instead of 2D. [ 7 ] [ 12 ]
In spectral scanning, each 2D sensor output represents a monochromatic (i.e. single wavelength), spatial ( x , y )-map of the scene. HSI devices for spectral scanning are typically based on optical band-pass filters (either tunable or fixed). The scene is spectrally scanned by exchanging one filter after another while the platform remains stationary. In such "staring", wavelength scanning systems, spectral smearing can occur if there is movement within the scene, invalidating spectral correlation/detection. Nonetheless, there is the advantage of being able to pick and choose spectral bands, and having a direct representation of the two spatial dimensions of the scene. [ 6 ] [ 7 ] [ 12 ] If the imaging system is used on a moving platform, such as an airplane, acquired images at different wavelengths corresponds to different areas of the scene. The spatial features on each of the images may be used to realign the pixels.
In non-scanning, a single 2D sensor output contains all spatial ( x , y ) and spectral ( λ ) data. HSI devices for non-scanning yield the full datacube at once, without any scanning. Figuratively speaking, a single snapshot represents a perspective projection of the datacube, from which its three-dimensional structure can be reconstructed. [ 7 ] [ 13 ] The most prominent benefits of these snapshot hyperspectral imaging systems are the snapshot advantage (higher light throughput) and shorter acquisition time. A number of systems have been designed, including computed tomographic imaging spectrometry (CTIS), fiber-reformatting imaging spectrometry (FRIS), integral field spectroscopy with lenslet arrays (IFS-L), multi-aperture integral field spectrometer (Hyperpixel Array), integral field spectroscopy with image slicing mirrors (IFS-S), image-replicating imaging spectrometry (IRIS), filter stack spectral decomposition (FSSD), coded aperture snapshot spectral imaging (CASSI), image mapping spectrometry (IMS), and multispectral Sagnac interferometry (MSI). [ 14 ] However, computational effort and manufacturing costs are high. In an effort to reduce the computational demands and potentially the high cost of non-scanning hyperspectral instrumentation, prototype devices based on Multivariate Optical Computing have been demonstrated. These devices have been based on the Multivariate Optical Element [ 15 ] [ 16 ] spectral calculation engine or the Spatial Light Modulator [ 17 ] spectral calculation engine. In these platforms, chemical information is calculated in the optical domain prior to imaging such that the chemical image relies on conventional camera systems with no further computing. As a disadvantage of these systems, no spectral information is ever acquired, i.e. only the chemical information, such that post processing or reanalysis is not possible.
In spatiospectral scanning, each 2D sensor output represents a wavelength-coded ("rainbow-colored", λ = λ ( y )), spatial ( x , y )-map of the scene. A prototype for this technique, introduced in 2014, consists of a camera at some non-zero distance behind a basic slit spectroscope (slit + dispersive element). [ 8 ] [ 18 ] Advanced spatiospectral scanning systems can be obtained by placing a dispersive element before a spatial scanning system. Scanning can be achieved by moving the whole system relative to the scene, by moving the camera alone, or by moving the slit alone. Spatiospectral scanning unites some advantages of spatial and spectral scanning, thereby alleviating some of their disadvantages. [ 8 ]
Hyperspectral imaging is part of a class of techniques commonly referred to as spectral imaging or spectral analysis . The term “hyperspectral imaging” derives from the development of NASA's Airborne Imaging Spectrometer (AIS) and AVIRIS in the mid-1980s. Although NASA prefers the earlier term “imaging spectroscopy” over “hyperspectral imaging,” use of the latter term has become more prevalent in scientific and non-scientific language. In a peer reviewed letter, experts recommend using the terms “imaging spectroscopy” or “spectral imaging” and avoiding exaggerated prefixes such as “hyper-,” “super-” and "ultra-,” to prevent misnomers in discussion. [ 19 ]
Hyperspectral imaging is related to multispectral imaging . The distinction between hyper- and multi-band is sometimes based incorrectly on an arbitrary "number of bands" or on the type of measurement. Hyperspectral imaging (HSI) uses continuous and contiguous ranges of wavelengths (e.g. 400 - 1100 nm in steps of 1 nm) whilst multiband imaging (MSI) uses a subset of targeted wavelengths at chosen locations (e.g. 400 - 1100 nm in steps of 20 nm). [ 20 ]
Multiband imaging deals with several images at discrete and somewhat narrow bands. Being "discrete and somewhat narrow" is what distinguishes multispectral imaging in the visible wavelength from color photography . A multispectral sensor may have many bands covering the spectrum from the visible to the longwave infrared. Multispectral images do not produce the "spectrum" of an object. Landsat is a prominent practical example of multispectral imaging.
Hyperspectral deals with imaging narrow spectral bands over a continuous spectral range, producing the spectra of all pixels in the scene. A sensor with only 20 bands can also be hyperspectral when it covers the range from 500 to 700 nm with 20 bands each 10 nm wide, while a sensor with 20 discrete bands covering the visible, near, short wave, medium wave and long wave infrared would be considered multispectral.
Ultraspectral could be reserved for interferometer type imaging sensors with a very fine spectral resolution. These sensors often have (but not necessarily) a low spatial resolution of several pixels only, a restriction imposed by the high data rate.
Hyperspectral remote sensing is used in a wide array of applications. Although originally developed for mining and geology (the ability of hyperspectral imaging to identify various minerals makes it ideal for the mining and oil industries, where it can be used to look for ore and oil), [ 11 ] [ 21 ] it has now spread into fields as widespread as ecology and surveillance, as well as historical manuscript research, such as the imaging of the Archimedes Palimpsest . This technology is continually becoming more available to the public. Organizations such as NASA and the USGS have catalogues of various minerals and their spectral signatures, and have posted them online to make them readily available for researchers. On a smaller scale, NIR hyperspectral imaging can be used to rapidly monitor the application of pesticides to individual seeds for quality control of the optimum dose and homogeneous coverage.
Although the cost of acquiring hyperspectral images is typically high for specific crops and in specific climates, hyperspectral remote sensing use is increasing for monitoring the development and health of crops. In Australia , work is under way to use imaging spectrometers to detect grape variety and develop an early warning system for disease outbreaks. [ 22 ] Furthermore, work is under way to use hyperspectral data to detect the chemical composition of plants, [ 23 ] which can be used to detect the nutrient and water status of wheat in irrigated systems. [ 24 ] On a smaller scale, NIR hyperspectral imaging can be used to rapidly monitor the application of pesticides to individual seeds for quality control of the optimum dose and homogeneous coverage. [ 25 ]
Another application in agriculture is the detection of animal proteins in compound feeds to avoid bovine spongiform encephalopathy (BSE) , also known as mad-cow disease. Different studies have been done to propose alternative tools to the reference method of detection, (classical microscopy ). One of the first alternatives is near infrared microscopy (NIR), which combines the advantages of microscopy and NIR. In 2004, the first study relating this problem with hyperspectral imaging was published. [ 26 ] Hyperspectral libraries that are representative of the diversity of ingredients usually present in the preparation of compound feeds were constructed. These libraries can be used together with chemometric tools to investigate the limit of detection, specificity and reproducibility of the NIR hyperspectral imaging method for the detection and quantification of animal ingredients in feed.
HSI cameras can also be used to detect stress from heavy metals in plants and become an earlier and faster alternative to post-harvest wet chemical methods. [ 27 ] [ 28 ]
Hyperspectral imaging is also used in zoology; it is used to investigate the spatial distribution of coloration and its extension into the near-infrared and SWIR range of the spectrum. [ 29 ] Some animals for example, such as some tropical frogs and certain leaf-sitting insects are highly reflective in the near-infrared. [ 29 ] [ 30 ]
Hyperspectral imaging can provide information about the chemical constituents of materials which makes it useful for waste sorting and recycling . [ 31 ] It has been applied to distinguish between substances with different fabrics and to identify natural, animal and synthetic fibers. [ 32 ] HSI cameras can be integrated with machine vision systems and, via simplifying platforms, allow end-customers to create new waste sorting applications and other sorting/identification applications. [ 33 ] A system of machine learning and hyperspectral camera can distinguish between 12 different types of plastics such as PET and PP for automated separation of waste of, as of 2020, highly unstandardized [ 34 ] [ additional citation(s) needed ] plastics products and packaging . [ 35 ] [ 36 ]
Researchers at the Université de Montréal are working with Photon etc. and Optina Diagnostics [ 37 ] to test the use of hyperspectral photography in the diagnosis of retinopathy and macular edema before damage to the eye occurs. The metabolic hyperspectral camera will detect a drop in oxygen consumption in the retina, which indicates potential disease. An ophthalmologist will then be able to treat the retina with injections to prevent any potential damage. [ 38 ]
In the food processing industry, hyperspectral imaging, combined with intelligent software, enables digital sorters (also called optical sorters ) to identify and remove defects and foreign material (FM) that are invisible to traditional camera and laser sorters. [ 39 ] [ 40 ] By improving the accuracy of defect and FM removal, the food processor’s objective is to enhance product quality and increase yields.
Adopting hyperspectral imaging on digital sorters achieves non-destructive, 100 percent inspection in-line at full production volumes. The sorter’s software compares the hyperspectral images collected to user-defined accept/reject thresholds, and the ejection system automatically removes defects and foreign material.
The recent commercial adoption of hyperspectral sensor-based food sorters is most advanced in the nut industry where installed systems maximize the removal of stones, shells and other foreign material (FM) and extraneous vegetable matter (EVM) from walnuts, pecans, almonds, pistachios, peanuts and other nuts. Here, improved product quality, low false reject rates and the ability to handle high incoming defect loads often justify the cost of the technology.
Commercial adoption of hyperspectral sorters is also advancing at a fast pace in the potato processing industry where the technology promises to solve a number of outstanding product quality problems. Work is under way to use hyperspectral imaging to detect “sugar ends,” [ 41 ] “hollow heart” [ 42 ] and “common scab,” [ 43 ] conditions that plague potato processors.
Geological samples, such as drill cores , can be rapidly mapped for nearly all minerals of commercial interest with hyperspectral imaging. Fusion of SWIR and LWIR spectral imaging is standard for the detection of minerals in the feldspar , silica , calcite , garnet , and olivine groups, as these minerals have their most distinctive and strongest spectral signature in the LWIR regions. [ 44 ]
Hyperspectral remote sensing of minerals is well developed. Many minerals can be identified from airborne images, and their relation to the presence of valuable minerals, such as gold and diamonds, is well understood. Currently, progress is towards understanding the relationship between oil and gas leakages from pipelines and natural wells, and their effects on the vegetation and the spectral signatures. Recent work includes the PhD dissertations of Werff [ 45 ] and Noomen. [ 46 ]
Hyperspectral surveillance is the implementation of hyperspectral scanning technology for surveillance purposes. Hyperspectral imaging is particularly useful in military surveillance because of countermeasures that military entities now take to avoid airborne surveillance. The idea that drives hyperspectral surveillance is that hyperspectral scanning draws information from such a large portion of the light spectrum that any given object should have a unique spectral signature in at least a few of the many bands that are scanned. Hyperspectral imaging has also shown potential to be used in facial recognition purposes. Facial recognition algorithms using hyperspectral imaging have been shown to perform better than algorithms using traditional imaging. [ 47 ]
Traditionally, commercially available thermal infrared hyperspectral imaging systems have needed liquid nitrogen or helium cooling, which has made them impractical for most surveillance applications. In 2010, Specim introduced a thermal infrared hyperspectral camera that can be used for outdoor surveillance and UAV applications without an external light source such as the sun or the moon. [ 48 ] [ 49 ]
In astronomy, hyperspectral imaging is used to determine a spatially-resolved spectral image. Since a spectrum is an important diagnostic, having a spectrum for each pixel allows more science cases to be addressed. In astronomy, this technique is commonly referred to as integral field spectroscopy , and examples of this technique include FLAMES [ 50 ] and SINFONI [ 51 ] on the Very Large Telescope , but also the Advanced CCD Imaging Spectrometer on Chandra X-ray Observatory uses this technique.
Soldiers can be exposed to a wide variety of chemical hazards. These threats are mostly invisible but detectable by hyperspectral imaging technology. The Telops Hyper-Cam, introduced in 2005, has demonstrated this at distances up to 5 km. [ 53 ]
Most countries require continuous monitoring of emissions produced by coal and oil-fired power plants, municipal and hazardous waste incinerators, cement plants, as well as many other types of industrial sources. This monitoring is usually performed using extractive sampling systems coupled with infrared spectroscopy techniques. Some recent standoff measurements performed allowed the evaluation of the air quality but not many remote independent methods allow for low uncertainty measurements.
Recent research indicates that hyperspectral imaging may be useful to detect the development of cracks in pavements [ 55 ] which are hard to detect from images taken with visible spectrum cameras. [ 55 ]
Hyperspectral imaging has also been used to detect cancer, identify nerves and analyze bruises. [ 56 ]
The primary advantage to hyperspectral imaging is that, because an entire spectrum is acquired at each point, the operator needs no prior knowledge of the sample, and postprocessing allows all available information from the dataset to be mined. Hyperspectral imaging can also take advantage of the spatial relationships among the different spectra in a neighbourhood, allowing more elaborate spectral-spatial models for a more accurate segmentation and classification of the image. [ 57 ] [ 58 ]
The primary disadvantages are cost and complexity. Fast computers, sensitive detectors, and large data storage capacities are needed for analyzing hyperspectral data. Significant data storage capacity is necessary since uncompressed hyperspectral cubes are large, multidimensional datasets, potentially exceeding hundreds of megabytes . All of these factors greatly increase the cost of acquiring and processing hyperspectral data. Also, one of the hurdles researchers have had to face is finding ways to program hyperspectral satellites to sort through data on their own and transmit only the most important images, as both transmission and storage of that much data could prove difficult and costly. [ 9 ] As a relatively new analytical technique, the full potential of hyperspectral imaging has not yet been realized. | https://en.wikipedia.org/wiki/Hyperspectral_imaging |
Hyperstructures are algebraic structures equipped with at least one multi-valued operation, called a hyperoperation . The largest classes of the hyperstructures are the ones called H v {\displaystyle Hv} – structures.
A hyperoperation ( ⋆ ) {\displaystyle (\star )} on a nonempty set H {\displaystyle H} is a mapping from H × H {\displaystyle H\times H} to the nonempty power set P ∗ ( H ) {\displaystyle P^{*}\!(H)} , meaning the set of all nonempty subsets of H {\displaystyle H} , i.e.
For A , B ⊆ H {\displaystyle A,B\subseteq H} we define
( H , ⋆ ) {\displaystyle (H,\star )} is a semihypergroup if ( ⋆ ) {\displaystyle (\star )} is an associative hyperoperation, i.e. x ⋆ ( y ⋆ z ) = ( x ⋆ y ) ⋆ z {\displaystyle x\star (y\star z)=(x\star y)\star z} for all x , y , z ∈ H . {\displaystyle x,y,z\in H.}
Furthermore, a hypergroup is a semihypergroup ( H , ⋆ ) {\displaystyle (H,\star )} , where the reproduction axiom is valid, i.e. a ⋆ H = H ⋆ a = H {\displaystyle a\star H=H\star a=H} for all a ∈ H . {\displaystyle a\in H.}
This abstract algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hyperstructure |
Hyperthecosis , or ovarian hyperthecosis , is hyperplasia of the theca interna of the ovary . [ 1 ] Hyperthecosis occurs when an area of luteinization occurs along with stromal hyperplasia. The luteinized cells produce androgens , which may lead to hirsutism and virilization (or masculinization) in affected women. [ 2 ]
The term hyperthecosis refers to the presence of nests of luteinized theca cells in the ovarian stroma due to differentiation of the ovarian interstitial cells into steroidogenically active luteinized stromal cells. These nests or islands of luteinized theca cells are scattered throughout the stroma of the ovary, rather than being confined to areas around cystic follicles as in polycystic ovary syndrome (PCOS) . These luteinized theca cells result in greater production of androgens.
Seen as a severe form of PCOS, the clinical features of hyperthecosis are similar to those of PCOS. [ 3 ] Women with hyperthecosis often have more markedly elevated testosterone, more hirsutism, and are much more likely to be virilized. [ 4 ] While elevated androgens in postmenopausal women is rare, [ 5 ] hyperthecosis can present in both premenopausal or postmenopausal women. Women with hyperthecosis may or may not have always had underlying PCOS. [ 6 ]
The etiology of hyperthecosis is unknown, however evidence suggests a possibility of genetic transmission. Hyperthecosis has been documented in familiar patterns. [ 7 ] Insulin resistance may also play a role in the pathogenesis of hyperthecosis. Women with hyperthecosis have a significant degree of insulin resistance and insulin may stimulate the ovarian stromal androgen synthesis. [ 8 ]
Although no large studies showing the long term outcomes for women with hyperthecosis exist, a diagnosis of hyperthecosis may suggest an increased risk for metabolic complications of hyperlipidemia and type 2 diabetes . [ 9 ] In postmenopausal women, hyperthecosis may also contribute to the pathogenesis of endometrial polyp, endometrial hyperplasia, and endometrioid adenocarcinoma due to the association of hyperestrinism (excess estrins in the body) and hyperthecosis. [ 10 ] Treatment for hyperthecosis is based upon each case, but may range from pharmacological interventions to surgical. [ 11 ] | https://en.wikipedia.org/wiki/Hyperthecosis |
Hyperthermia , also known simply as overheating , is a condition in which an individual's body temperature is elevated beyond normal due to failed thermoregulation . The person's body produces or absorbs more heat than it dissipates. When extreme temperature elevation occurs, it becomes a medical emergency requiring immediate treatment to prevent disability or death. [ citation needed ] Almost half a million deaths are recorded every year from hyperthermia. [ citation needed ]
The most common causes include heat stroke and adverse reactions to drugs. Heat stroke is an acute temperature elevation caused by exposure to excessive heat, or combination of heat and humidity, that overwhelms the heat-regulating mechanisms of the body. The latter is a relatively rare side effect of many drugs, particularly those that affect the central nervous system . Malignant hyperthermia is a rare complication of some types of general anesthesia . Hyperthermia can also be caused by a traumatic brain injury . [ 4 ] [ 5 ] [ 6 ]
Hyperthermia differs from fever in that the body's temperature set point remains unchanged. The opposite is hypothermia , which occurs when the temperature drops below that required to maintain normal metabolism. The term is from Greek ὑπέρ, hyper , meaning "above", and θέρμος, thermos , meaning "heat".
In humans, hyperthermia is defined as a temperature greater than 37.5–38.3 °C (99.5–100.9 °F), depending on the reference used, that occurs without a change in the body's temperature set point . [ 3 ] [ 10 ]
The normal human body temperature can be as high as 37.7 °C (99.9 °F) in the late afternoon. [ 2 ] Hyperthermia requires an elevation from the temperature that would otherwise be expected. Such elevations range from mild to extreme; body temperatures above 40 °C (104 °F) can be life-threatening.
An early stage of hyperthermia can be "heat exhaustion" (or "heat prostration" or "heat stress"), whose symptoms can include heavy sweating, rapid breathing and a fast, weak pulse. If the condition progresses to heat stroke, then hot, dry skin is typical [ 2 ] as blood vessels dilate in an attempt to increase heat loss. An inability to cool the body through perspiration may cause dry skin . Hyperthermia from neurological disease may include little or no sweating , cardiovascular problems, and confusion or delirium .
Other signs and symptoms vary. Accompanying dehydration can produce nausea , vomiting, headaches , and low blood pressure and the latter can lead to fainting or dizziness , especially if the standing position is assumed quickly.
In severe heat stroke, confusion and aggressive behavior may be observed. Heart rate and respiration rate will increase ( tachycardia and tachypnea ) as blood pressure drops and the heart attempts to maintain adequate circulation . The decrease in blood pressure can then cause blood vessels to contract reflexively, resulting in a pale or bluish skin color in advanced cases. Young children, in particular, may have seizures . Eventually, organ failure , unconsciousness and death will result.
Heat stroke occurs when thermoregulation is overwhelmed by a combination of excessive metabolic production of heat (exertion), excessive environmental heat, and insufficient or impaired heat loss, resulting in an abnormally high body temperature. [ 2 ] In severe cases, temperatures can exceed 40 °C (104 °F). [ 13 ] Heat stroke may be non-exertional (classic) or exertional .
Significant physical exertion in hot conditions can generate heat beyond the ability to cool, because, in addition to the heat, humidity of the environment may reduce the efficiency of the body's normal cooling mechanisms. [ 2 ] Human heat-loss mechanisms are limited primarily to sweating (which dissipates heat by evaporation , assuming sufficiently low humidity ) and vasodilation of skin vessels (which dissipates heat by convection proportional to the temperature difference between the body and its surroundings, according to Newton's law of cooling ). Other factors, such as insufficient water intake, consuming alcohol, or lack of air conditioning , can worsen the problem.
The increase in body temperature that results from a breakdown in thermoregulation affects the body biochemically. Enzymes involved in metabolic pathways within the body such as cellular respiration fail to work effectively at higher temperatures, and further increases can lead them to denature , reducing their ability to catalyse essential chemical reactions. This loss of enzymatic control affects the functioning of major organs with high energy demands such as the heart and brain. [ 14 ] Loss of fluid and electrolytes cause heat cramps – slow muscular contraction and severe muscular spasm lasting between one and three minutes. Almost all cases of heat cramps involve vigorous physical exertion. Body temperature may remain normal or a little higher than normal and cramps are concentrated in heavily used muscles.
Situational heat stroke occurs in the absence of exertion. It mostly affects the young and elderly. In the elderly in particular, it can be precipitated by medications that reduce vasodilation and sweating, such as anticholinergic drugs, antihistamines, and diuretics. [ 2 ] In this situation, the body's tolerance for high environmental temperature may be insufficient, even at rest.
Heat waves are often followed by a rise in the death rate, and these 'classical hyperthermia' deaths typically involve the elderly and infirm. This is partly because thermoregulation involves cardiovascular, respiratory and renal systems which may be inadequate for the additional stress because of the existing burden of aging and disease, further compromised by medications. During the July 1995 heatwave in Chicago, there were at least 700 heat-related deaths. The strongest risk factors were being confined to bed, and living alone, while the risk was reduced for those with working air conditioners and those with access to transportation. Even then, reported deaths may be underestimated as diagnosis can be mis-classified as stroke or heart attack. [ 15 ]
Some drugs cause excessive internal heat production. [ 2 ] The rate of drug-induced hyperthermia is higher where use of these drugs is higher. [ 2 ]
Those working in industry, in the military, or as first responders may be required to wear personal protective equipment (PPE) against hazards such as chemical agents, gases, fire, small arms and improvised explosive devices (IEDs). PPE includes a range of hazmat suits , firefighting turnout gear , body armor and bomb suits , among others. Depending on design, the wearer may be encapsulated in a microclimate, [ 20 ] due to an increase in thermal resistance and decrease in vapor permeability. As physical work is performed, the body's natural thermoregulation (i.e. sweating) becomes ineffective. This is compounded by increased work rates, high ambient temperature and humidity levels, and direct exposure to the sun. The net effect is that desired protection from some environmental threats inadvertently increases the threat of heat stress.
The effect of PPE on hyperthermia has been noted in fighting the 2014 Ebola virus epidemic in Western Africa. Doctors and healthcare workers were only able to work for 40 minutes at a time in their protective suits, fearing heat stroke. [ 21 ]
Other rare causes of hyperthermia include thyrotoxicosis and an adrenal gland tumor, called pheochromocytoma , both of which can cause increased heat production. [ 2 ] Damage to the central nervous system from brain hemorrhage, traumatic brain injury, status epilepticus , and other kinds of injury to the hypothalamus can also cause hyperthermia. [ 2 ]
A fever occurs when the core temperature is set higher, through the action of the pre-optic region of the anterior hypothalamus . For example, in response to a bacterial or viral infection, certain white blood cells within the blood will release pyrogens which have a direct effect on the anterior hypothalamus, causing body temperature to rise, much like raising the temperature setting on a thermostat .
In contrast, hyperthermia occurs when the body temperature rises without a change in the heat control centers.
Some of the gastrointestinal symptoms of acute exertional heatstroke, such as vomiting, diarrhea, and gastrointestinal bleeding, may be caused by barrier dysfunction and subsequent endotoxemia . Ultraendurance athletes have been found to have significantly increased plasma endotoxin levels. Endotoxin stimulates many inflammatory cytokines, which in turn may cause multiorgan dysfunction. Experimentally, monkeys treated with oral antibiotics prior to induction of heat stroke do not become endotoxemic. [ 22 ]
There is scientific support for the concept of a temperature set point; that is, maintenance of an optimal temperature for the metabolic processes that life depends on. Nervous activity in the preoptic-anterior hypothalamus of the brain triggers heat losing (sweating, etc.) or heat generating (shivering and muscle contraction, etc.) activities through stimulation of the autonomic nervous system. The pre-optic anterior hypothalamus has been shown to contain warm sensitive, cool sensitive, and temperature insensitive neurons, to determine the body's temperature setpoint. As the temperature that these neurons are exposed to rises above 37 °C (99 °F), the rate of electrical discharge of the warm-sensitive neurons increases progressively. Cold-sensitive neurons increase their rate of electrical discharge progressively below 37 °C (99 °F). [ 23 ]
Hyperthermia is generally diagnosed by the combination of unexpectedly high body temperature and a history that supports hyperthermia instead of a fever. [ 2 ] Most commonly this means that the elevated temperature has occurred in a hot, humid environment (heat stroke) or in someone taking a drug for which hyperthermia is a known side effect (drug-induced hyperthermia). The presence of signs and symptoms related to hyperthermia syndromes, such as extrapyramidal symptoms characteristic of neuroleptic malignant syndrome, and the absence of signs and symptoms more commonly related to infection-related fevers, are also considered in making the diagnosis.
If fever-reducing drugs lower the body temperature, even if the temperature does not return entirely to normal, then hyperthermia is excluded. [ 2 ]
When ambient temperature is excessive, humans and many other animals cool themselves below ambient by evaporative cooling of sweat (or other aqueous liquid; saliva in dogs, for example); this helps prevent potentially fatal hyperthermia. The effectiveness of evaporative cooling depends upon humidity . Wet-bulb temperature , which takes humidity into account, or more complex calculated quantities such as wet-bulb globe temperature (WBGT), which also takes solar radiation into account, give useful indications of the degree of heat stress and are used by several agencies as the basis for heat-stress prevention guidelines. (Wet-bulb temperature is essentially the lowest skin temperature attainable by evaporative cooling at a given ambient temperature and humidity.)
A sustained wet-bulb temperature exceeding 35 °C (95 °F) is likely to be fatal even to fit and healthy people unclothed in the shade next to a fan; at this temperature, environmental heat gain instead of loss occurs. As of 2012 [update] , wet-bulb temperatures only very rarely exceeded 30 °C (86 °F) anywhere, although significant global warming may change this. [ 24 ] [ 25 ]
In cases of heat stress caused by physical exertion, hot environments, or protective equipment, prevention or mitigation by frequent rest breaks, careful hydration, and monitoring body temperature should be attempted. [ 26 ] However, in situations demanding one is exposed to a hot environment for a prolonged period or must wear protective equipment, a personal cooling system is required as a matter of health and safety. There are a variety of active or passive personal cooling systems; [ 20 ] these can be categorized by their power sources and whether they are person- or vehicle-mounted.
Because of the broad variety of operating conditions, these devices must meet specific requirements concerning their rate and duration of cooling, their power source, and their adherence to health and safety regulations. Among other criteria are the user's need for physical mobility and autonomy. For example, active-liquid systems operate by chilling water and circulating it through a garment; the skin surface area is thereby cooled through conduction. This type of system has proven successful in certain military, law enforcement, and industrial applications. Bomb-disposal technicians wearing special suits to protect against improvised explosive devices (IEDs) use a small, ice-based chiller unit that is strapped to one leg; a liquid-circulating garment, usually a vest, is worn over the torso to maintain a safe core body temperature. By contrast, soldiers traveling in combat vehicles can face microclimate temperatures in excess of 65 °C (149 °F) and require a multiple-user, vehicle-powered cooling system with rapid connection capabilities. Requirements for hazmat teams, the medical community, and workers in heavy industry vary further.
The underlying cause must be removed. Mild hyperthemia caused by exertion on a hot day may be adequately treated through self-care measures, such as increased water consumption and resting in a cool place. Hyperthermia that results from drug exposure requires prompt cessation of that drug, and occasionally the use of other drugs as counter measures.
Antipyretics (e.g., acetaminophen , aspirin , other nonsteroidal anti-inflammatory drugs ) have no role in the treatment of heatstroke because antipyretics interrupt the change in the hypothalamic set point caused by pyrogens ; they are not expected to work on a healthy hypothalamus that has been overloaded, as in the case of heatstroke. In this situation, antipyretics actually may be harmful in patients who develop hepatic , hematologic , and renal complications because they may aggravate bleeding tendencies. [ 27 ]
When body temperature is significantly elevated, mechanical cooling methods are used to remove heat and to restore the body's ability to regulate its own temperatures. [ 2 ] Passive cooling techniques, such as resting in a cool, shady area and removing clothing can be applied immediately. Active cooling methods, such as sponging the head, neck, and trunk with cool water, remove heat from the body and thereby speed the body's return to normal temperatures. When methods such as immersion are impractical, misting the body with water and using a fan have also been shown to be effective. [ 28 ]
Sitting in a bathtub of tepid or cool water (immersion method) can remove a significant amount of heat in a relatively short period of time. It was once thought that immersion in very cold water is counterproductive, as it causes vasoconstriction in the skin and thereby prevents heat from escaping the body core. However, a British analysis of various studies stated: "this has never been proven experimentally. Indeed, a recent study using normal volunteers has shown that cooling rates were fastest when the coldest water was used." [ 29 ] The analysis concluded that iced water immersion is the most-effective cooling technique for exertional heat stroke. [ 29 ] No superior cooling method has been found for non-exertional heat stroke . [ 30 ] Thus, aggressive ice-water immersion remains the gold standard for life-threatening heat stroke . [ 31 ] [ 32 ]
When the body temperature reaches about 40 °C (104 °F), or if the affected person is unconscious or showing signs of confusion, hyperthermia is considered a medical emergency that requires treatment in a proper medical facility. A cardiopulmonary resuscitation (CPR) may be necessary if the person goes into cardiac arrest (stop of heart beats). Already in a hospital, more aggressive cooling measures are available, including intravenous hydration , gastric lavage with iced saline , and even hemodialysis to cool the blood. [ 2 ]
Hyperthermia affects those who are unable to regulate their body heat, mainly due to environmental conditions. The main risk factor for hyperthermia is the lack of ability to sweat. People who are dehydrated or who are older may not produce the sweat they need to regulate their body temperature. [ 33 ] High heat conditions can put certain groups at risk for hyperthermia including: physically active individuals, soldiers, construction workers, landscapers and factory workers. Some people that do not have access to cooler living conditions, like people with lower socioeconomic status, may have a difficult time fighting the heat. People are at risk for hyperthermia during high heat and dry conditions, most commonly seen in the summer.
Various cases of different types of hyperthermia have been reported. A research study was published in March 2019 that looked into multiple case reports of drug induced hyperthermia. The study concluded that psychotropic drugs such as anti-psychotics, antidepressants, and anxiolytics were associated with an increased heat-related mortality as opposed to the other drugs researched (anticholinergics, diuretics, cardiovascular agents, etc.). [ 34 ] A different study was published in June 2019 that examined the association between hyperthermia in older adults and the temperatures in the United States. Hospitalization records of elderly patients in the US between 1991 and 2006 were analyzed and concluded that cases of hyperthermia were observed to be highest in regions with arid climates. The study discussed finding a disproportionately high number of cases of hyperthermia in early seasonal heat waves indicating that people were not yet practicing proper techniques to stay cool and prevent overheating in the early presence of warm, dry weather. [ 35 ]
In urban areas people are at an increased susceptibility to hyperthermia. This is due to a phenomenon called the urban heat island effect . [ 36 ] Since the 20th century in the United States, the north-central region (Ohio, Indiana, Illinois, Missouri, Iowa, and Nebraska) was the region with the highest morbidity resulting from hyperthermia. Northeastern states had the next highest. Regions least affected by heat wave-related hyperthermia causing death were Southern and Pacific Coastal states. [ 37 ] Northern cities in the United States are at greater risk of hyperthermia during heat waves due to the fact that people tend to have a lower minimum mortality temperature at higher latitudes. [ 38 ] In contrast, cities residing in lower latitudes within the continental US typically have higher thresholds for ambient temperatures. [ 38 ] In India, hundreds die every year from summer heat waves, [ 39 ] including more than 2,500 in the year 2015 . [ 40 ] Later that same summer, the 2015 Pakistani heat wave killed about 2,000 people. [ 41 ] An extreme 2003 European heat wave caused tens of thousands of deaths. [ 42 ]
Causes of hyperthermia include dehydration, use of certain medications, using cocaine and amphetamines or excessive alcohol use. [ 43 ] Bodily temperatures greater than 37.5–38.3 °C (99.5–100.9 °F) can be diagnosed as a hyperthermic case. [ 43 ] As body temperatures increase or excessive body temperatures persist, individuals are at a heightened risk of developing progressive conditions. Greater risk complications of hyperthermia include heat stroke, organ malfunction, organ failure, and death. There are two forms of heat stroke ; classical heatstroke and exertional heatstroke. Classical heatstroke occurs from extreme environmental conditions, such as heat waves. Those who are most commonly affected by classical heatstroke are very young, elderly or chronically ill. Exertional heatstroke appears in individuals after vigorous physical activity. Exertional heatstroke is displayed most commonly in healthy 15-50 year old people. Sweating is often present in exertional heatstroke. [ 44 ] The associated mortality rate of heatstroke is 40 to 64%. [ 43 ]
Hyperthermia can also be deliberately induced using drugs or medical devices, and is being studied and applied in clinical routine as a treatment of some kinds of cancer . [ 45 ] Research has shown that medically controlled hyperthermia can shrink tumours. [ 46 ] [ 47 ] This occurs when a high body temperature damages cancerous cells by destroying proteins and structures within each cell. [ 48 ] [ 46 ] Hyperthermia has also been researched to investigate whether it causes cancerous tumours to be more prone to radiation as a form of treatment; which as a result has allowed hyperthermia to be used to complement other forms of cancer therapy. [ 49 ] [ 46 ] Various techniques of hyperthermia in the treatment of cancer include local or regional hyperthermia, as well as whole body techniques. [ 46 ] | https://en.wikipedia.org/wiki/Hyperthermia |
In the mathematical branch of topology , a hyperspace (or a space equipped with a hypertopology) is a topological space , which consists of the set CL(X) of all non-empty closed subsets of another topological space X , equipped with a topology so that the canonical map
i : x ↦ { x } ¯ , {\displaystyle i:x\mapsto {\overline {\{x\}}},}
is a homeomorphism onto its image. As a consequence, a copy of the original space X lives inside its hyperspace CL(X) . [ 1 ] [ 2 ]
Early examples of hypertopology include the Hausdorff metric [ 3 ] and Vietoris topology . [ 4 ]
This topology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypertopology |
A hypertranscendental function or transcendentally transcendental function is a transcendental analytic function which is not the solution of an algebraic differential equation with coefficients in Z {\displaystyle \mathbb {Z} } (the integers ) and with algebraic initial conditions .
The term 'transcendentally transcendental' was introduced by E. H. Moore in 1896; the term 'hypertranscendental' was introduced by D. D. Morduhai-Boltovskoi in 1914. [ 1 ] [ 2 ]
One standard definition (there are slight variants) defines solutions of differential equations of the form
where F {\displaystyle F} is a polynomial with constant coefficients, as algebraically transcendental or differentially algebraic . Transcendental functions which are not algebraically transcendental are transcendentally transcendental . Hölder's theorem shows that the gamma function is in this category. [ 3 ] [ 4 ] [ 5 ]
Hypertranscendental functions usually arise as the solutions to functional equations , for example the gamma function . | https://en.wikipedia.org/wiki/Hypertranscendental_function |
A hypertriton is a type of hypernucleus , formed of a proton , a neutron and any hyperon . [ 1 ] The name comes from hyperon , which refers to baryons containing strange quarks , and triton , which refers to the nucleus of tritium . Because low-mass hyperons are longer-lived and easier to create than high-mass hyperons, the most common hypertritons are those containing Lambda baryons – 3 Λ H.
Its antiparticle, the antihypertriton , is formed of an antiproton , an antineutron and any antihyperon. The first one was discovered in March 2010 by the STAR detector of the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory . [ 2 ]
This nuclear physics or atomic physics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypertriton |
In pathology , hypertrophic decidual vasculopathy , abbreviated HDV , is the histomorphologic correlate of gestational hypertension , as may be seen in intrauterine growth restriction (IUGR) [ 1 ] and HELLP syndrome .
The name of the condition describes its appearance under the microscope ; the smooth muscle of the decidual (or maternal ) blood vessels is hypertrophic , i.e. the muscle part of the blood vessels feeding the placenta is larger due to cellular enlargement.
The morphologic features of mild and moderate HDV include: [ 1 ]
Severe HDV is characterized by: | https://en.wikipedia.org/wiki/Hypertrophic_decidual_vasculopathy |
Hyperuniform materials are characterized by an anomalous suppression of density fluctuations at large scales. More precisely, the vanishing of density fluctuations in the long-wave length limit (like for crystals ) distinguishes hyperuniform systems from typical gases , liquids , or amorphous solids . [ 1 ] [ 2 ] Examples of hyperuniformity include all perfect crystals , [ 1 ] perfect quasicrystals , [ 3 ] [ 4 ] and exotic amorphous states of matter. [ 2 ]
Quantitatively, a many-particle system is said to be hyperuniform if the variance of the number of points within a spherical observation window grows more slowly than the volume of the observation window. This definition is equivalent to a vanishing of the structure factor in the long-wavelength limit, [ 1 ] and it has been extended to include heterogeneous materials as well as scalar, vector, and tensor fields. [ 5 ] Disordered hyperuniform systems, were shown to be poised at an "inverted" critical point. [ 1 ] They can be obtained via equilibrium or nonequilibrium routes, and are found in both classical physical and quantum-mechanical systems. [ 1 ] [ 2 ] Hence, the concept of hyperuniformity now connects a broad range of topics in physics, [ 2 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] mathematics, [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] biology, [ 16 ] [ 17 ] [ 18 ] and materials science. [ 19 ] [ 20 ] [ 21 ]
The concept of hyperuniformity generalizes the traditional notion of long-range order and thus defines an exotic state of matter . A disordered hyperuniform many-particle system can be statistically isotropic like a liquid , with no Bragg peaks and no conventional type of long-range order. Nevertheless, at large scales, hyperuniform systems resemble crystals , in their suppression of large-scale density fluctuations. This unique combination is known to endow disordered hyperuniform materials with novel physical properties that are, e.g., both nearly optimal and direction independent (in contrast to those of crystals that are anisotropic). [ 2 ]
The term hyperuniformity (also independently called super-homogeneity in the context of cosmology [ 22 ] ) was coined and studied by Salvatore Torquato and Frank Stillinger in a 2003 paper, [ 1 ] in which they showed that, among other things, hyperuniformity provides a unified framework to classify and structurally characterize crystals , quasicrystals , and exotic disordered varieties. In that sense, hyperuniformity is a long-range property that can be viewed as generalizing the traditional notion of long-range order (e.g., translational / orientational order of crystals or orientational order of quasicrystals) to also encompass exotic disordered systems. [ 2 ]
Hyperuniformity was first introduced for point processes [ 1 ] and later generalized to two-phase materials (or porous media ) [ 3 ] and random scalar or vectors fields . [ 5 ] It has been observed in theoretical models, simulations, and experiments, see list of examples below. [ 2 ]
A many-particle system in d {\displaystyle d} -dimensional Euclidean space R d {\displaystyle R^{d}} is said to be hyperuniform if the number of points in a spherical observation window with radius R {\displaystyle R} has a variance σ N 2 ( R ) {\displaystyle \sigma _{N}^{2}(R)} that scales slower than the volume of the observation window: [ 1 ] lim R → ∞ σ N 2 ( R ) R d = 0. {\displaystyle \lim _{R\to \infty }{\frac {\sigma _{N}^{2}(R)}{R^{d}}}=0.} This definition is (essentially) equivalent to the vanishing of the structure factor at the origin: [ 1 ] lim k → 0 S ( k ) = 0 {\displaystyle \lim _{\mathbf {k} \to 0}S(\mathbf {k} )=0} for wave vectors k ∈ R d {\displaystyle \mathbf {k} \in \mathbb {R} ^{d}} .
Similarly, a two-phase medium consisting of a solid and a void phase is said to be hyperuniform if the volume of the solid phase inside the spherical observation window has a variance that scales slower than the volume of the observation window. This definition is, in turn, equivalent to a vanishing of the spectral density at the origin. [ 3 ]
An essential feature of hyperuniform systems is their scaling of the number variance σ N 2 ( R ) {\displaystyle \sigma _{N}^{2}(R)} for large radii or, equivalently, of the structure factor S ( k ) {\displaystyle S(k)} for small wave numbers . If we consider hyperuniform systems that are characterized by a power-law behavior of the structure factor close to the origin: [ 2 ] S ( k ) ∼ | k | α for k → 0 {\displaystyle S(\mathbf {k} )\sim |\mathbf {k} |^{\alpha }{\text{ for }}\mathbf {k} \to 0} with a constant 0 < α < ∞ {\displaystyle 0<\alpha <\infty } , then there are three distinct scaling behaviors that define three classes of hyperuniformity : σ N 2 ( R ) ∼ { R d − 1 , α > 1 ( CLASS I ) R d − 1 ln R , α = 1 ( CLASS II ) R d − α , 0 < α < 1 ( CLASS III ) {\displaystyle \sigma _{N}^{2}(R)\sim {\begin{cases}R^{d-1},&\alpha >1&({\text{CLASS I}})\\R^{d-1}\ln R,&\alpha =1&({\text{CLASS II}})\\R^{d-\alpha },&0<\alpha <1&({\text{CLASS III}})\\\end{cases}}} Examples are known for all three classes of hyperuniformity. [ 2 ]
Examples of disordered hyperuniform systems in physics are disordered ground states, [ 7 ] jammed disordered sphere packings, [ 6 ] [ 23 ] [ 24 ] [ 25 ] [ 26 ] [ 27 ] [ 28 ] [ 29 ] [ 30 ] amorphous ices, [ 31 ] amorphous speckle patterns, [ 32 ] certain fermionic systems, [ 33 ] random self-organization, [ 8 ] [ 34 ] [ 35 ] [ 36 ] [ 37 ] [ 38 ] [ 9 ] perturbed lattices, [ 39 ] [ 40 ] [ 41 ] [ 42 ] and avian photoreceptor cells. [ 16 ]
In mathematics, disordered hyperuniformity has been studied in the context of probability theory, [ 10 ] [ 43 ] [ 11 ] geometry, [ 13 ] [ 14 ] and number theory, [ 44 ] [ 12 ] [ 45 ] where the prime numbers have been found to be effectively limit periodic and hyperuniform in a certain scaling limit. [ 12 ] Further examples include certain random walks [ 46 ] and stable matchings of point processes. [ 15 ] [ 24 ] [ 25 ] [ 26 ] [ 27 ] [ 47 ]
Examples of ordered, hyperuniform systems include all crystals, [ 1 ] all quasicrystals, [ 3 ] [ 4 ] [ 48 ] and limit-periodic sets. [ 49 ] While weakly correlated noise typically preserves hyperuniformity, correlated excitations at finite temperature tend to destroy hyperuniformity. [ 50 ]
Hyperuniformity was also reported for fermionic quantum matter in correlated electron systems as a result of cramming. [ 51 ]
Torquato (2014) [ 52 ] gives an illustrative example of the hidden order found in a "shaken box of marbles", [ 52 ] which fall into an arrangement, called maximally random jammed packing . [ 6 ] [ 53 ] Such hidden order may eventually be used for self-organizing colloids or optics with the ability to transmit light with an efficiency like a crystal but with a highly flexible design. [ 52 ]
It has been found that disordered hyperuniform systems possess unique optical properties. For example, disordered hyperuniform photonic networks have been found to exhibit complete photonic band gaps that are comparable in size to those of photonic crystals but with the added advantage of isotropy, which enables free-form waveguides not possible with crystal structures. [ 19 ] [ 20 ] [ 54 ] [ 55 ] Moreover, in stealthy hyperuniform systems, [ 7 ] light of any wavelength longer than a value specific to the material is able to propagate forward without loss (due to the correlated disorder) even for high particle density. [ 56 ]
By contrast, in conditions where light is propagated through an uncorrelated, disordered material of the same density, the material would appear opaque due to multiple scattering. “Stealthy” hyperuniform materials can be theoretically designed for light of any wavelength, and the applications of the concept cover a wide variety of fields of wave physics and materials engineering. [ 56 ] [ 57 ]
Disordered hyperuniformity was recently discovered in amorphous 2‑D materials, including amorphous silica [ 58 ] as well as amorphous graphene, [ 59 ] which was shown to enhance electronic transport in the material. [ 58 ] It was shown that the Stone-Wales topological defects, which transform two-pair of neighboring hexagons to a pair of pentagons and a pair of heptagons by flipping a bond, preserves the hyperuniformity of the parent honeycomb lattice. [ 59 ]
Disordered hyperuniformity was found in the photoreceptor cell patterns in the eyes of chickens . [ 16 ] This is thought to be the case because the light-sensitive cells in chicken or other bird eyes cannot easily attain an optimal crystalline arrangement but instead form a disordered configuration that is as uniform as possible. [ 16 ] [ 60 ] [ 61 ] Indeed, it is the remarkable property of "mulithyperuniformity" of the avian cone patterns, that enables birds to achieve acute color sensing. [ 16 ]
It may also emerge in the mysterious biological patterns known as fairy circles - circle and patterns of circles that emerge in arid places. [ 62 ] [ 63 ] It is believed such vegetation patterns can optimize the efficiency of water utility, which is crucial for the survival of the plants.
A universal hyperuniform organization was observed in the looped vein network of tree leaves, including ficus religiosa, ficus caulocarpa, ficus microcarpa, smilax indica, populus rotundifolia, and yulania denudate, etc. [ 64 ] It was shown the hyperuniform network optimizes the diffusive transport of water and nutrients from the vein to the leaf cells. [ 64 ] The hyperuniform vein network organization was believed to result from a regulation of growth factor uptake during vein network development. [ 64 ]
The challenge of creating disordered hyperuniform materials is partly attributed to the inevitable presence of imperfections, such as defects and thermal fluctuations. For example, the fluctuation-compressibility relation dictates that any compressible one-component fluid in thermal equilibrium cannot be strictly hyperuniform at finite temperature. [ 2 ]
Recently Chremos & Douglas (2018) proposed a design rule for the practical creation of hyperuniform materials at the molecular level. [ 65 ] [ 66 ] Specifically, effective hyperuniformity as measured by the hyperuniformity index is achieved by specific parts of the molecules (e.g., the core of the star polymers or the backbone chains in the case of bottlebrush polymers). [ 67 ] [ 2 ] The combination of these features leads to molecular packings that are highly uniform at both small and large length scales. [ 65 ] [ 66 ]
Disordered hyperuniformity implies a long-ranged direct correlation function (the Ornstein–Zernike equation ). [ 1 ] In an equilibrium many-particle system, this requires delicately designed effectively long-ranged interactions, which are not necessary for the dynamic self-assembly of non-equilibrium hyperuniform states. In 2019, Ni and co-workers theoretically predicted a non-equilibrium strongly hyperuniform fluid phase that exists in systems of circularly swimming active hard spheres, [ 34 ] which was confirmed experimentally in 2022. [ 68 ]
This new hyperuniform fluid features a special length scale, i.e., the diameter of the circular trajectory of active particles, below which large density fluctuations are observed. Moreover, based on a generalized random organising model, Lei and Ni (2019) [ 35 ] formulated a hydrodynamic theory for non-equilibrium hyperuniform fluids, and the length scale above which the system is hyperuniform is controlled by the inertia of the particles. The theory generalizes the mechanism of fluidic hyperuniformity as the damping of the stochastic harmonic oscillator, which indicates that the suppressed long-wavelength density fluctuation can exhibit as either acoustic (resonance) mode or diffusive (overdamped) mode. [ 35 ] In the Lei-Ni reactive hard-sphere model, [ 35 ] it was found that the discontinuous absorbing transition of metastable hyperuniform fluid into an immobile absorbing state does not have the kinetic pathway of nucleation and growth, and the transition rate decreases with increasing the system size. This challenges the common understanding of metastability in discontinuous phase transitions and suggests that non-equilibrium hyperuniform fluid is fundamentally different from conventional equilibrium fluids. [ 69 ] | https://en.wikipedia.org/wiki/Hyperuniformity |
In chemistry , a hypervalent molecule (the phenomenon is sometimes colloquially known as expanded octet ) is a molecule that contains one or more main group elements apparently bearing more than eight electrons in their valence shells . Phosphorus pentachloride ( PCl 5 ), sulfur hexafluoride ( SF 6 ), chlorine trifluoride ( ClF 3 ), the chlorite ( ClO − 2 ) ion in chlorous acid and the triiodide ( I − 3 ) ion are examples of hypervalent molecules.
Hypervalent molecules were first formally defined by Jeremy I. Musher in 1969 as molecules having central atoms of group 15–18 in any valence other than the lowest (i.e. 3, 2, 1, 0 for Groups 15, 16, 17, 18 respectively, based on the octet rule ). [ 1 ]
Several specific classes of hypervalent molecules exist:
N-X-L nomenclature, introduced collaboratively by the research groups of Martin , Arduengo , and Kochi in 1980, [ 2 ] is often used to classify hypervalent compounds of main group elements, where:
Examples of N-X-L nomenclature include:
The debate over the nature and classification of hypervalent molecules goes back to Gilbert N. Lewis and Irving Langmuir and the debate over the nature of the chemical bond in the 1920s. [ 3 ] Lewis maintained the importance of the two-center two-electron (2c–2e) bond in describing hypervalence, thus using expanded octets to account for such molecules. Using the language of orbital hybridization, the bonds of molecules like PF 5 and SF 6 were said to be constructed from sp 3 d n orbitals on the central atom. Langmuir, on the other hand, upheld the dominance of the octet rule and preferred the use of ionic bonds to account for hypervalence without violating the rule (e.g. " SF 2+ 4 2F − " for SF 6 ).
In the late 1920s and 1930s, Sugden argued for the existence of a two-center one-electron (2c–1e) bond and thus rationalized bonding in hypervalent molecules without the need for expanded octets or ionic bond character; this was poorly accepted at the time. [ 3 ] In the 1940s and 1950s, Rundle and Pimentel popularized the idea of the three-center four-electron bond , which is essentially the same concept which Sugden attempted to advance decades earlier; the three-center four-electron bond can be alternatively viewed as consisting of two collinear two-center one-electron bonds, with the remaining two nonbonding electrons localized to the ligands. [ 3 ]
The attempt to actually prepare hypervalent organic molecules began with Hermann Staudinger and Georg Wittig in the first half of the twentieth century, who sought to challenge the extant valence theory and successfully prepare nitrogen and phosphorus-centered hypervalent molecules. [ 4 ] The theoretical basis for hypervalency was not delineated until J.I. Musher's work in 1969. [ 1 ]
In 1990, Magnusson published a seminal work definitively excluding the significance of d-orbital hybridization in the bonding of hypervalent compounds of second-row elements. This had long been a point of contention and confusion in describing these molecules using molecular orbital theory . Part of the confusion here originates from the fact that one must include d-functions in the basis sets used to describe these compounds (or else unreasonably high energies and distorted geometries result), and the contribution of the d-function to the molecular wavefunction is large. These facts were historically interpreted to mean that d-orbitals must be involved in bonding. However, Magnusson concludes in his work that d-orbital involvement is not implicated in hypervalency. [ 5 ]
Nevertheless, a 2013 study showed that although the Pimentel ionic model best accounts for the bonding of hypervalent species, the energetic contribution of an expanded octet structure is also not null. In this modern valence bond theory study of the bonding of xenon difluoride , it was found that ionic structures account for about 81% of the overall wavefunction, of which 70% arises from ionic structures employing only the p orbital on xenon while 11% arises from ionic structures employing an s d z 2 {\displaystyle \mathrm {sd} _{z^{2}}} hybrid on xenon. The contribution of a formally hypervalent structure employing an orbital of sp 3 d hybridization on xenon accounts for 11% of the wavefunction, with a diradical contribution making up the remaining 8%. The 11% sp 3 d contribution results in a net stabilization of the molecule by 7.2 kcal (30 kJ) mol −1 , [ 6 ] a minor but significant fraction of the total energy of the total bond energy (64 kcal (270 kJ) mol −1 ). [ 7 ] Other studies have similarly found minor but non-negligible energetic contributions from expanded octet structures in SF 6 (17%) and XeF 6 (14%). [ 8 ]
Despite the lack of chemical realism, the IUPAC recommends the drawing of expanded octet structures for functional groups like sulfones and phosphoranes , in order to avoid the drawing of a large number of formal charges or partial single bonds. [ 9 ]
A special type of hypervalent molecules is hypervalent hydrides. Most known hypervalent molecules contain substituents more electronegative than their central atoms. [ 10 ] [ 11 ] Hypervalent hydrides are of special interest because hydrogen is usually less electronegative than the central atom. A number of computational studies have been performed on chalcogen hydrides [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] [ 16 ] and pnictogen hydrides . [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] Recently, a new computational study has shown that most hypervalent halogen hydrides XH n can exist. It is suggested that IH 3 and IH 5 are stable enough to be observable or, possibly, even isolable. [ 22 ]
Both the term and concept of hypervalency still fall under criticism. In 1984, in response to this general controversy, Paul von Ragué Schleyer proposed the replacement of 'hypervalency' with use of the term hypercoordination because this term does not imply any mode of chemical bonding and the question could thus be avoided altogether. [ 3 ]
The concept itself has been criticized by Ronald Gillespie who, based on an analysis of electron localization functions, wrote in 2002 that "as there is no fundamental difference between the bonds in hypervalent and non-hypervalent (Lewis octet) molecules there is no reason to continue to use the term hypervalent." [ 23 ]
For hypercoordinated molecules with electronegative ligands such as PF 5 , it has been demonstrated that the ligands can pull away enough electron density from the central atom so that its net content is again 8 electrons or fewer. Consistent with this alternative view is the finding that hypercoordinated molecules based on fluorine ligands, for example PF 5 do not have hydride counterparts, e.g. phosphorane (PH 5 ) which is unknown.
The ionic model holds up well in thermochemical calculations. It predicts favorable exothermic formation of PF + 4 F − from phosphorus trifluoride PF 3 and fluorine F 2 whereas a similar reaction forming PH + 4 H − is not favorable. [ 24 ]
Durrant has proposed an alternative definition of hypervalency, based on the analysis of atomic charge maps obtained from atoms in molecules theory. [ 25 ] This approach defines a parameter called the valence electron equivalent, γ, as “the formal shared electron count at a given atom, obtained by any combination of valid ionic and covalent resonance forms that reproduces the observed charge distribution”. For any particular atom X, if the value of γ(X) is greater than 8, that atom is hypervalent. Using this alternative definition, many species such as PCl 5 , SO 2− 4 , and XeF 4 , that are hypervalent by Musher's definition, are reclassified as hypercoordinate but not hypervalent, due to strongly ionic bonding that draws electrons away from the central atom. On the other hand, some compounds that are normally written with ionic bonds in order to conform to the octet rule, such as ozone O 3 , nitrous oxide NNO, and trimethylamine N-oxide (CH 3 ) 3 NO , are found to be genuinely hypervalent. Examples of γ calculations for phosphate PO 3− 4 (γ(P) = 2.6, non-hypervalent) and orthonitrate NO 3− 4 (γ(N) = 8.5, hypervalent) are shown below.
Early considerations of the geometry of hypervalent molecules returned familiar arrangements that were well explained by the VSEPR model for atomic bonding. Accordingly, AB 5 and AB 6 type molecules would possess a trigonal bi-pyramidal and octahedral geometry, respectively. However, in order to account for the observed bond angles, bond lengths and apparent violation of the Lewis octet rule , several alternative models have been proposed.
In the 1950s an expanded valence shell treatment of hypervalent bonding was adduced to explain the molecular architecture, where the central atom of penta- and hexacoordinated molecules would utilize d AOs in addition to s and p AOs. However, advances in the study of ab initio calculations have revealed that the contribution of d-orbitals to hypervalent bonding is too small to describe the bonding properties, and this description is now regarded as much less important. [ 5 ] It was shown that in the case of hexacoordinated SF 6 , d-orbitals are not involved in S-F bond formation, but charge transfer between the sulfur and fluorine atoms and the apposite resonance structures were able to account for the hypervalency (See below).
Additional modifications to the octet rule have been attempted to involve ionic characteristics in hypervalent bonding. As one of these modifications, in 1951, the concept of the 3-center 4-electron (3c-4e) bond , which described hypervalent bonding with a qualitative molecular orbital , was proposed. The 3c-4e bond is described as three molecular orbitals given by the combination of a p atomic orbital on the central atom and an atomic orbital from each of the two ligands on opposite sides of the central atom. Only one of the two pairs of electrons is occupying a molecular orbital that involves bonding to the central atom, the second pair being non-bonding and occupying a molecular orbital composed of only atomic orbitals from the two ligands. This model in which the octet rule is preserved was also advocated by Musher. [ 3 ]
A complete description of hypervalent molecules arises from consideration of molecular orbital theory through quantum mechanical methods. An LCAO in, for example, sulfur hexafluoride, taking a basis set of the one sulfur 3s-orbital, the three sulfur 3p-orbitals, and six octahedral geometry symmetry-adapted linear combinations (SALCs) of fluorine orbitals, a total of ten molecular orbitals are obtained (four fully occupied bonding MOs of the lowest energy, two fully occupied intermediate energy non-bonding MOs and four vacant antibonding MOs with the highest energy) providing room for all 12 valence electrons. This is a stable configuration only for S X 6 molecules containing electronegative ligand atoms like fluorine, which explains why SH 6 is not a stable molecule. In the bonding model, the two non-bonding MOs (1e g ) are localized equally on all six fluorine atoms.
For hypervalent compounds in which the ligands are more electronegative than the central, hypervalent atom, resonance structures can be drawn with no more than four covalent electron pair bonds and completed with ionic bonds to obey the octet rule. For example, in phosphorus pentafluoride (PF 5 ), 5 resonance structures can be generated each with four covalent bonds and one ionic bond with greater weight in the structures placing ionic character in the axial bonds, thus satisfying the octet rule and explaining both the observed trigonal bipyramidal molecular geometry and the fact that the axial bond length (158 pm) is longer than the equatorial (154 pm). [ 26 ]
For a hexacoordinate molecule such as sulfur hexafluoride , each of the six bonds is the same length. The rationalization described above can be applied to generate 15 resonance structures each with four covalent bonds and two ionic bonds, such that the ionic character is distributed equally across each of the sulfur-fluorine bonds.
Spin-coupled valence bond theory has been applied to diazomethane and the resulting orbital analysis was interpreted in terms of a chemical structure in which the central nitrogen has five covalent bonds;
This led the authors to the interesting conclusion that "Contrary to what we were all taught as undergraduates, the nitrogen atom does indeed form five covalent linkages and the availability or otherwise of d-orbitals has nothing to do with this state of affairs." [ 27 ]
Hexacoordinate phosphorus molecules involving nitrogen, oxygen, or sulfur ligands provide examples of Lewis acid-Lewis base hexacoordination. [ 28 ] For the two similar complexes shown below, the length of the C–P bond increases with decreasing length of the N–P bond; the strength of the C–P bond decreases with increasing strength of the N–P Lewis acid–Lewis base interaction.
This trend is also generally true of pentacoordinated main-group elements with one or more lone-pair-containing ligand, including the oxygen-pentacoordinated silicon examples shown below.
The Si-halogen bonds range from close to the expected van der Waals value in A (a weak bond) almost to the expected covalent single bond value in C (a strong bond). [ 28 ]
Corriu and coworkers performed early work characterizing reactions thought to proceed through a hypervalent transition state. [ 29 ] Measurements of the reaction rates of hydrolysis of tetravalent chlorosilanes incubated with catalytic amounts of water returned a rate that is first order in chlorosilane and second order in water. This indicated that two water molecules interacted with the silane during hydrolysis and from this a binucleophilic reaction mechanism was proposed. Corriu and coworkers then measured the rates of hydrolysis in the presence of nucleophilic catalyst HMPT, DMSO or DMF. It was shown that the rate of hydrolysis was again first order in chlorosilane, first order in catalyst and now first order in water. Appropriately, the rates of hydrolysis also exhibited a dependence on the magnitude of charge on the oxygen of the nucleophile.
Taken together this led the group to propose a reaction mechanism in which there is a pre-rate determining nucleophilic attack of the tetracoordinated silane by the nucleophile (or water) in which a hypervalent pentacoordinated silane is formed. This is followed by a nucleophilic attack of the intermediate by water in a rate determining step leading to hexacoordinated species that quickly decomposes giving the hydroxysilane.
Silane hydrolysis was further investigated by Holmes and coworkers [ 30 ] in which tetracoordinated Mes 2 SiF 2 (Mes = mesityl ) and pentacoordinated Mes 2 SiF − 3 were reacted with two equivalents of water. Following twenty-four hours, almost no hydrolysis of the tetracoordinated silane was observed, while the pentacoordinated silane was completely hydrolyzed after fifteen minutes. Additionally, X-ray diffraction data collected for the tetraethylammonium salts of the fluorosilanes showed the formation of hydrogen bisilonate lattice supporting a hexacoordinated intermediate from which HF − 2 is quickly displaced leading to the hydroxylated product. This reaction and crystallographic data support the mechanism proposed by Corriu et al. .
The apparent increased reactivity of hypervalent molecules, contrasted with tetravalent analogues, has also been observed for Grignard reactions. The Corriu group measured [ 31 ] Grignard reaction half-times by NMR for related 18-crown-6 potassium salts of a variety of tetra- and pentacoordinated fluorosilanes in the presence of catalytic amounts of nucleophile.
Though the half reaction method is imprecise, the magnitudinal differences in reactions rates allowed for a proposed reaction scheme wherein, a pre-rate determining attack of the tetravalent silane by the nucleophile results in an equilibrium between the neutral tetracoordinated species and the anionic pentavalent compound. This is followed by nucleophilic coordination by two Grignard reagents as normally seen, forming a hexacoordinated transition state and yielding the expected product.
The mechanistic implications of this are extended to a hexacoordinated silicon species that is thought to be active as a transition state in some reactions. The reaction of allyl - or crotyl -trifluorosilanes with aldehydes and ketones only precedes with fluoride activation to give a pentacoordinated silicon. This intermediate then acts as a Lewis acid to coordinate with the carbonyl oxygen atom. The further weakening of the silicon–carbon bond as the silicon becomes hexacoordinate helps drive this reaction. [ 32 ]
Similar reactivity has also been observed for other hypervalent structures such as the miscellany of phosphorus compounds, for which hexacoordinated transition states have been proposed.
Hydrolysis of phosphoranes and oxyphosphoranes have been studied [ 33 ] and shown to be second order in water. Bel'skii et al. . have proposed a prerate determining nucleophilic attack by water resulting in an equilibrium between the penta- and hexacoordinated phosphorus species, which is followed by a proton transfer involving the second water molecule in a rate determining ring-opening step, leading to the hydroxylated product.
Alcoholysis of pentacoordinated phosphorus compounds, such as trimethoxyphospholene with benzyl alcohol, have also been postulated to occur through a similar octahedral transition state, as in hydrolysis, however without ring opening. [ 34 ]
It can be understood from these experiments that the increased reactivity observed for hypervalent molecules, contrasted with analogous nonhypervalent compounds, can be attributed to the congruence of these species to the hypercoordinated activated states normally formed during the course of the reaction.
The enhanced reactivity at pentacoordinated silicon is not fully understood. Corriu and coworkers suggested that greater electropositive character at the pentavalent silicon atom may be responsible for its increased reactivity. [ 35 ] Preliminary ab initio calculations supported this hypothesis to some degree, but used a small basis set. [ 36 ]
A software program for ab initio calculations, Gaussian 86 , was used by Dieters and coworkers to compare tetracoordinated silicon and phosphorus to their pentacoordinate analogues. This ab initio approach is used as a supplement to determine why reactivity improves in nucleophilic reactions with pentacoordinated compounds. For silicon, the 6-31+G* basis set was used because of its pentacoordinated anionic character and for phosphorus, the 6-31G* basis set was used. [ 36 ]
Pentacoordinated compounds should theoretically be less electrophilic than tetracoordinated analogues due to steric hindrance and greater electron density from the ligands, yet experimentally show greater reactivity with nucleophiles than their tetracoordinated analogues. Advanced ab initio calculations were performed on series of tetracoordinated and pentacoordinated species to further understand this reactivity phenomenon. Each series varied by degree of fluorination. Bond lengths and charge densities are shown as functions of how many hydride ligands are on the central atoms. For every new hydride, there is one less fluoride. [ 36 ]
For silicon and phosphorus bond lengths, charge densities, and Mulliken bond overlap, populations were calculated for tetra and pentacoordinated species by this ab initio approach. [ 36 ] Addition of a fluoride ion to tetracoordinated silicon shows an overall average increase of 0.1 electron charge, which is considered insignificant. In general, bond lengths in trigonal bipyramidal pentacoordinate species are longer than those in tetracoordinate analogues. Si-F bonds and Si-H bonds both increase in length upon pentacoordination and related effects are seen in phosphorus species, but to a lesser degree. The reason for the greater magnitude in bond length change for silicon species over phosphorus species is the increased effective nuclear charge at phosphorus. Therefore, silicon is concluded to be more loosely bound to its ligands.
In addition Dieters and coworkers [ 36 ] show an inverse correlation between bond length and bond overlap for all series. Pentacoordinated species are concluded to be more reactive because of their looser bonds as trigonal-bipyramidal structures.
By calculating the energies for the addition and removal of a fluoride ion in various silicon and phosphorus species, several trends were found. In particular, the tetracoordinated species have much higher energy requirements for ligand removal than do pentacoordinated species. Further, silicon species have lower energy requirements for ligand removal than do phosphorus species, which is an indication of weaker bonds in silicon. | https://en.wikipedia.org/wiki/Hypervalent_molecule |
Unlike its lighter congeners , the halogen iodine forms a number of stable organic compounds , in which iodine exhibits higher formal oxidation states than −1 or coordination number exceeding 1. These are the hypervalent organoiodines , often called iodanes after the IUPAC rule used to name them.
These iodine compounds are hypervalent because the iodine atom formally contains in its valence shell more than the 8 electrons required for the octet rule . Hypervalent iodine oxyanions are known for oxidation states +1, +3, +5, and +7; organic analogues of these moieties are known for each oxidation state except +7.
In terms of chemical behavior, λ 3 ‑ and λ 5 ‑iodanes are generally oxidizing and/or electrophilic species. They have been widely applied towards those ends in organic synthesis . [ 1 ]
Several different naming conventions are in use for the hypervalent organoiodines.
All begin with nonstandard formal charge assignments. In iodane chemistry, carbon is considered more electronegative than iodine, despite the Pauling electronegativities of those respective atoms. [ 2 ] Thus iodobenzene ( C 6 H 5 I ) is an iodine(I) compound, (dichloroiodo)benzene ( C 6 H 5 ICl 2 ) and iodosobenzene ( C 6 H 5 IO ) iodine(III) compounds, and iodoxybenzene ( C 6 H 5 IO 2 ) an iodine(V) compound.
With that convention in place, IUPAC names assume complete electron transfer. Thus when iodine is ligated to an organic residue and two Lewis acids , it is in the +3 oxidation state and the corresponding compound is a λ 3 ‑iodane . A compound with iodine(V) would be a λ 5 ‑iodane , and a hypothetical iodine(VII)‑containing compound would be a λ 7 ‑iodane . Organyl-iodine ethers , a kind of λ 3 ‑iodane , are sometimes called organic hypoiodites .
Alternatively, the hypervalent iodines can be classified using neutral electron counting . Iodine itself contains 7 valence electrons, and, in a monovalent iodane such as iodobenzene ( C 6 H 5 I ), the phenyl ligand donates one additional electron to give a completed octet. In a λ 3 ‑iodane , each X-type ligand donates an additional electron, for 10 in total; the result is a decet structure. Similarly, many λ 5 ‑iodanes are dodecet molecules, and hypothetical λ 7 ‑iodanes are tetradecet molecules. As with other hypervalent compounds, N‑X‑L notation can be used to describe the formal electron count of iodanes, in which N stands for the number of electrons around the central atom X (in this case iodine), and L is the total number of ligand bonds with X. Thus, λ 3 ‑iodanes can be described as 10‑I‑3 compounds, λ 5 ‑iodanes as 12‑I‑5 compounds, and hypothetical λ 7 ‑iodanes as 14‑I‑7 compounds.
As with other hypervalent compounds, iodanes bonding was formerly described using d -orbital participation. 3-center-4-electron bonding is now believed to be the primary bonding mode. This paradigm was developed by J.J. Musher in 1969.
One such bond exists in iodine(III) compounds, two such bonds reside in iodine(V) compounds and three such bonds would reside in the hypothetical iodine(VII) compounds.
Hypervalent organoiodine compounds are prepared by the oxidation of an organyl iodide .
In 1886, German chemist Conrad Willgerodt prepared the first hypervalent iodine compound, iodobenzene dichloride ( Ph I Cl 2 ), by passing chlorine gas through iodobenzene in a cooled solution of chloroform : [ 3 ]
Ph I + Cl 2 → PhICl 2
This preparation can be varied to produce iodobenzene pseudohalides . Cleaner preparations [ 4 ] begin with solutions of peracetic acid in glacial acetic acid , also due to Willgerodt: [ 5 ]
C 6 H 5 I + CH 3 C(O)OOH + CH 3 COOH → C 6 H 5 I(OC(O)CH 3 ) 2 + H 2 O
The iodobenzene diacetate product hydrolyzes to the polymeric iodosobenzene (PhIO), which is stable in cool alkaline solution . [ 6 ] In hot water (or, in Willgerodt's original preparation, steam distillation ), iodosobenzene instead disproportionates to iodoxybenzene and iodobenzene : [ 7 ]
2-Iodobenzoic acid reacts with oxone [ 8 ] or a combination of potassium bromate and sulfuric acid to produce the insoluble λ 5 ‑iodane 2-iodoxybenzoic (IBX) acid . [ 9 ] IBX acid is unstable and explosive, but acetylation tempers it to the stabler Dess-Martin periodinane . [ 10 ]
Aliphatic hypoiodites can be synthesized through a variant on the Williamson ether synthesis : an alkoxide reacts with iodine monochloride , releasing the alkyl hypoiodite and chloride . [ 11 ] Alternatively, the Meyer-Hartmann reaction applies: a silver alkoxide reacts with elemental iodine to give the hypoiodite and silver iodide . They are unstable to visible light , cleaving into alkoxyl and iodine radicals. [ 12 ]
The synthesis of organyl periodyl derivatives (λ 7 -iodanes) has been attempted since the early 20th century. [ 13 ] Efforts so far have met with failure, although aryl λ 7 ‑chloranes are known. Organic diesters of iodine(VII) are presumed intermediates in the periodate cleavage of diols ( Malaprade reaction ), although no carbon-iodine(VII) bond is present in this process.
Diaryliodonium salts are compounds of the type [Ar−I + −Ar]X − . [ 14 ] They are formally composed of a diaryliodonium cation [ 15 ] paired with a counteranion , but crystal structures show a long, weak, partially- covalent bond between the iodine and the counterion. Some authors have described this interaction as an example of halogen bonding , [ 16 ] but the interaction exists even with traditionally noncoordinating ions , such as perchlorate , triflate , or tetrafluoroborate . [ 17 ] As a result, other authors regard the diaryliodonia as λ 3 -iodanes. [ 18 ]
The salts are generally T-shaped, with the counteranion occupying an apical position. [ 18 ] The overall geometry at the iodine atom is pseudotrigonal bipyramidal . The placement of ligands exhibits apicophilicity : the phenyl group and chlorine group attain apical positions, while the other phenyl group and a lone pair of electrons hold equatorial ones.
Salts with a halide counterion are poorly soluble in many organic solvents, possibly because the halides bridge dimers . Solubility improves with triflate and tetrafluoroborate counterions. [ 17 ]
In general, the salts can be prepared from preformed hypervalent iodines such as iodic acid , iodosyl sulfate or iodosyl triflate . The first such compound was synthesised in 1894, via the silver hydroxide -catalyzed coupling of two aryl iodides (the Meyer–Hartmann reaction ): [ 19 ] [ 20 ] [ 21 ]
Alternatively, the iodane may be formed in situ : an aryl iodide is oxidized to an aryliodine(III) compound (such as ArIO), followed by a ligand exchange . The latter can occur with organometallized arenes such as an arylstannane or -silane (a nucleophilic aromatic substitution reaction) or unfunctionalized arenes in the presence of a Brønsted or Lewis acid (an electrophilic aromatic substitution reaction).
Diaryliodonium salts react with nucleophiles at iodine, replacing one ligand to form the substituted arene ArNu and iodobenzene ArI. Diaryliodonium salts also react with metals M through ArMX intermediates in cross-coupling reactions .
Hypervalent iodine compounds are predominantly used as oxidizing reagents , although they are specialized and expensive. In some cases they replace more toxic oxidants. [ 23 ]
Iodobenzene diacetate (PhIAc 2 ) and iodobenzene di(trifluoroacetate) are both strong oxidizing agents used in organic oxidations , as well as precursors for further organoiodine compounds. A hypervalent iodine (III) reagent was used as oxidant, together with ammonium acetate as nitrogen source, to provide 2-Furonitrile , a pharmaceutical intermediate and potential artificial sweetener. [ 24 ]
Current research focuses on the use of iodanes in carbon-carbon and carbon-heteroatom bond-forming reactions . In one study, an intramolecular C-N coupling of an alkoxyhydroxylamine to its anisole group is accomplished with a catalytic amount of aryliodide in trifluoroethanol . [ 25 ] | https://en.wikipedia.org/wiki/Hypervalent_organoiodine_compounds |
Hypervariable may refer to: | https://en.wikipedia.org/wiki/Hypervariable |
A hypervariable region ( HVR ) is a location within a sequence where polymorphisms frequently occur. It is used in two contexts:
Because there already is a separate article for the antibody region, this article will focus on the nucleic acid case.
There are two mitochondrial hypervariable regions used in human mitochondrial genealogical DNA testing . HVR1 is considered a "low resolution" region and HVR2 is considered a "high resolution" region. Getting HVR1 and HVR2 DNA tests can help determine one's haplogroup . In the revised Cambridge Reference Sequence of the human mitogenome, the most variable sites of HVR1 are numbered 16024-16383 (this subsequence is called HVR-I), and the most variable sites of HVR2 are numbered 57-372 ( i.e., HVR-II) and 438-574 ( i.e., HVR-III). [ 2 ] [ 3 ]
In some bony fishes , for example certain Protacanthopterygii and Gadidae , the mitochondrial control region evolves remarkably slowly. Even functional mitochondrial genes accumulate mutations faster and more freely. It is not known whether such hypovariable control regions are more widespread. In the Ayu ( Plecoglossus altivelis ), an East Asian protacanthopterygian, control region mutation rate is not markedly lowered, but sequence differences between subspecies are far lower in the control region than elsewhere. This phenomenon completely defies explanation at present. [ 4 ]
The 16S ribosomal RNA in prokaryotes have nine hypervariable regions where mutation rates are higher than neighboring parts, numbered V1 to V9. V4 one of the most conservative, while V3 is one of the fastest-evolving. These regions offer a way to quickly determine the identity of a prokaryote: because the surrounding regions are relatively conserved, a "universal primer" can be used to selectively amplify one or a stretch of several HV regions using PCR. The resultant amplicon is sequenced, and each unique sequence is termed an amplicon sequence variant (ASV). [ 5 ] A database such as Greengenes2 can then be used to look up an ASV (often an exact match) in the taxonomic and phylogenetic trees. [ 6 ]
Simple sequence repeats, specifically variable number tandem repeats and microsatellites , commonly occur in the human genome. Their repeated nature allows a unique form of mutation: the number of copies can increase or decrease when strand slippage occurs during DNA replication. (Regular point mutation still happens and could be more frequent than slippage.) [ 7 ] Their copy number not only have use in forensics and ancestry testing, [ 8 ] but are also linked to diseases. [ 9 ] | https://en.wikipedia.org/wiki/Hypervariable_region |
Hypervelocity is very high velocity , approximately over 3,000 meters per second (11,000 km/h, 6,700 mph, 10,000 ft/s, or Mach 8.8). In particular, hypervelocity is velocity so high that the strength of materials upon impact is very small compared to inertial stresses. [ 1 ] Thus, metals and fluids behave alike under hypervelocity impact. An impact under extreme hypervelocity results in vaporization of the impactor and target. For structural metals, hypervelocity is generally considered to be over 2,500 m/s (5,600 mph, 9,000 km/h, 8,200 ft/s, or Mach 7.3). Meteorite craters are also examples of hypervelocity impacts.
The term "hypervelocity" refers to velocities in the range from a few kilometers per second to some tens of kilometers per second. This is especially relevant in the field of space exploration and military use of space, where hypervelocity impacts (e.g. by space debris or an attacking projectile ) can result in anything from minor component degradation to the complete destruction of a spacecraft or missile. The impactor, as well as the surface it hits, can undergo temporary liquefaction . The impact process can generate plasma discharges, which can interfere with spacecraft electronics.
Hypervelocity usually occurs during meteor showers and deep space reentries, as carried out during the Zond , Apollo and Luna programs. Given the intrinsic unpredictability of the timing and trajectories of meteors, space capsules are prime data gathering opportunities for the study of thermal protection materials at hypervelocity (in this context, hypervelocity is defined as greater than escape velocity ). Given the rarity of such observation opportunities since the 1970s, the Genesis and Stardust Sample Return Capsule (SRC) reentries as well as the recent Hayabusa SRC reentry have spawned observation campaigns, most notably at NASA's Ames Research Center .
Hypervelocity collisions can be studied by examining the results of naturally occurring collisions (between micrometeorites and spacecraft , or between meteorites and planetary bodies), or they may be performed in laboratories. Currently, the primary tool for laboratory experiments is a light-gas gun , but some experiments have used linear motors to accelerate projectiles to hypervelocity. The properties of metals under hypervelocity have been integrated with weapons, such as explosively formed penetrator . The vaporization upon impact and liquification of surfaces allow metal projectiles formed under hypervelocity forces to penetrate vehicle armor better than conventional bullets.
NASA studies the effects of simulated orbital debris at the White Sands Test Facility Remote Hypervelocity Test Laboratory (RHTL). [ 2 ] Objects smaller than a softball cannot be detected on radar. [ citation needed ] This has prompted spacecraft designers to develop shields to protect spacecraft from unavoidable collisions. At RHTL, micrometeoroid and orbital debris (MMOD) impacts are simulated on spacecraft components and shields allowing designers to test threats posed by the growing orbital debris environment and evolve shield technology to stay one step ahead. At RHTL, four two-stage light-gas guns propel 0.05 to 22.2 mm (0.0020 to 0.8740 in) diameter projectiles to velocities as fast as 8.5 km/s (5.3 mi/s).
According to the United States Army , hypervelocity can also refer to the muzzle velocity of a weapon system, [ 4 ] with the exact definition dependent upon the weapon in question. When discussing small arms a muzzle velocity of 5,000 ft/s (1524 m/s) or greater is considered hypervelocity, while for tank cannons the muzzle velocity must meet or exceed 3,350 ft/s (1021.08 m/s) to be considered hypervelocity, and the threshold for artillery cannons is 3,500 ft/s (1066.8 m/s). [ 5 ] | https://en.wikipedia.org/wiki/Hypervelocity |
A hyperview in computing is a hypertextual view of the content of a database or set of data on a group of activities. As with a hyperdiagram multiple views are linked to form a hyperview. [ 1 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hyperview_(computing) |
Hyper–Rayleigh scattering optical activity ( / ˈ r eɪ l i / RAY -lee ), a form of chiroptical harmonic scattering , is a nonlinear optical physical effect whereby chiral scatterers (such as nanoparticles or molecules) convert light (or other electromagnetic radiation ) to higher frequencies via harmonic generation processes, in a way that the intensity of generated light depends on the chirality of the scatterers. "Hyper–Rayleigh scattering" is a nonlinear optical counterpart to Rayleigh scattering . " Optical activity " refers to any changes in light properties (such as intensity or polarization) that are due to chirality .
The effect was theoretically predicted in 1979, [ 1 ] in a mathematical description of hyper Raman scattering optical activity. Within this theoretical model, upon setting the initial and final frequencies of light to the same value, the mathematics describe the hyper Rayleigh scattering optical activity. The theory was well in advance of its time, and the effect remained elusive for 40 years. Its author David L. Andrews referred to it as the "impossible theory". However, in January 2019, an experimental demonstration was reported by Ventsislav K. Valev and his team. [ 2 ] [ 3 ] The team investigated the hyper Rayleigh scattering (at the second harmonic generation frequency) from chiral nanohelices made of silver. Valev and his team observed that the intensity of the hyper Rayleigh scattering light depended on the direction of circularly polarized light and that this dependence reversed with the chirality of the nanohelices. Valev's work unambiguously established that the effect is physically possible, opening the way for nonlinear chiroptical investigations of a variety of chiral light-scattering materials; including molecules, [ 4 ] plasmonic metal nanoparticles [ 5 ] and semiconductor nanoparticles. [ 6 ]
Hyper Rayleigh scattering optical activity (HRS OA) is arguably the most fundamental nonlinear chiral optical (chiroptical) effect; since other nonlinear chiroptical effects have additional requirements, which make them conceptually more involved, i.e. less fundamental. HRS OA is a scattering effect and therefore it does not require the frequency conversion process to be coherent, contrary to other nonlinear chiroptical effects, such as second harmonic generation circular dichroism [ 7 ] or second harmonic generation optical rotation. [ 8 ] Moreover, HRS OA is a parametric process : the initial and final quantum mechanical states of the excited electron are the same. Because the excitation proceeds via virtual states , there is no restriction on the frequency of incident light. By contrast, other nonlinear scattering effects, such as two-photon circular dichroism and hyper-Raman are non-parametric: they require real energy states that restrict the frequencies at which these effects can be observed.
Soon after the first demonstration of hyper Rayleigh scattering optical activity in metal nanoparticles, [ 3 ] the effect was replicated in organic molecules, specifically aromatic oligoamide foldamers. [ 4 ]
Whereas the initial experimental demonstration of hyper-Rayleigh scattering optical activity was observed at the second harmonic of the illumination frequency of light, the effect is general and can be observed at higher harmonics. The first demonstration of hyper-Rayleigh scattering optical activity at the third harmonic was reported by Valev's team in 2021, from silver nanohelices. [ 9 ] [ 10 ] | https://en.wikipedia.org/wiki/Hyper–Rayleigh_scattering |
See text
The Hyphomicrobiales (synonom Rhizobiales ) are an order of Gram-negative Alphaproteobacteria .
The rhizobia , which fix nitrogen and are symbiotic with plant roots, appear in several different families. The four families Nitrobacteraceae , Hyphomicrobiaceae , Phyllobacteriaceae , and Rhizobiaceae contain at least several genera of nitrogen-fixing, legume-nodulating , microsymbiotic bacteria . Examples are the genera Bradyrhizobium and Rhizobium . Species of the Methylocystaceae are methanotrophs ; they use methanol (CH 3 OH) or methane (CH 4 ) as their sole energy and carbon sources. Other important genera are the human pathogens Bartonella and Brucella , as well as Agrobacterium , an important tool in genetic engineering .
The following genus has not been assigned to a family:
These taxa have been published, but have not been validated according to the Bacteriological Code :
The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature [ 7 ] and the phylogeny is based on whole-genome sequences. [ 2 ] [ a ]
Parvibaculaceae
Hyphomicrobiaceae
Amorphaceae
Rhodobiaceae
Afifellaceae
Cohaesibacteraceae
Breoghaniaceae
Stappiaceae
Devosiaceae
Aurantimonadaceae
Ahrensiaceae
Notoacmeibacteraceae
Phyllobacteriaceae
Rhizobiaceae
Bartonellaceae
Phyllobacterium [ b ]
Brucellaceae
Tepidamorphaceae
Kaistiaceae
Pseudoxanthobacteraceae
Prosthecomicrobium [ c ]
Pleomorphomonadaceae
Blastochloridaceae
Xanthobacteraceae
Phreatobacteraceae
Nitrobacteraceae
Beijerinckiaceae
Roseiarcaceae
Methylocystaceae
Chelatococcaceae
Boseaceae
Salinarimonadaceae
Methylobacteriaceae
Rhodobacterales
Parvularculales
Caulobacterales
Natural genetic transformation has been reported in at least four Hyphomicrobiales species: Agrobacterium tumefaciens , [ 8 ] Methylobacterium organophilum , [ 9 ] Ensifer adhaerens , [ 10 ] and Bradyrhizobium japonicum . [ 11 ] Natural genetic transformation is a sexual process involving DNA transfer from one bacterial cell to another through the intervening medium, and the integration of the donor sequence into the recipient genome by homologous recombination . | https://en.wikipedia.org/wiki/Hyphomicrobiales |
A hypnozygote is a resting cyst resulting from sexual fusion; it is commonly thick-walled. A synonym of zygotic cyst. [ 1 ] Hypnozygotes have the ability to remain dormant in mud and other sediments until conditions become more favorable for growth. [ 2 ]
This microbiology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypnozygote |
Hypobromous acid is an inorganic compound with chemical formula of H O Br . It is a weak, unstable acid . It is mainly produced and handled in an aqueous solution. It is generated both biologically and commercially as a disinfectant . Salts of hypobromite are rarely isolated as solids.
Addition of bromine to water gives hypobromous acid and hydrobromic acid (HBr(aq)) via a disproportionation reaction.
In nature, hypobromous acid is produced by bromoperoxidases , which are enzymes that catalyze the oxidation of bromide with hydrogen peroxide: [ 2 ] [ 3 ]
Hypobromous acid has a p K a of 8.65 and is therefore only partially dissociated in water at pH 7. Like the acid, hypobromite salts are unstable and undergo a slow disproportionation reaction to yield the respective bromate and bromide salts.
Its chemical and physical properties are similar to those of other hypohalites .
HOBr is used as a bleach , an oxidizer , a deodorant , and a disinfectant , due to its ability to kill the cells of many pathogens . The compound is generated in warm-blooded vertebrate organisms especially by eosinophils , which produce it by the action of eosinophil peroxidase , an enzyme which preferentially uses bromide. [ 4 ] Bromide is also used in hot tubs and spas as a germicidal agent, using the action of an oxidizing agent to generate hypobromite in a similar fashion to the peroxidase in eosinophils.
It is especially effective when used in combination with its congener, hypochlorous acid . | https://en.wikipedia.org/wiki/Hypobromous_acid |
Hypochlorous acid is an inorganic compound with the chemical formula Cl O H , also written as HClO, HOCl, or ClHO. [ 2 ] [ 3 ] Its structure is H−O−Cl . It is an acid that forms when chlorine dissolves in water , and itself partially dissociates , forming a hypochlorite anion , ClO − . HClO and ClO − are oxidizers , and the primary disinfection agents of chlorine solutions. [ 4 ] HClO cannot be isolated from these solutions due to rapid equilibration with its precursor , chlorine .
Because of its strong antimicrobial properties, the related compounds sodium hypochlorite (NaOCl) and calcium hypochlorite ( Ca(OCl) 2 ) are ingredients in many commercial bleaches , deodorants , and disinfectants . [ 5 ] The white blood cells of mammals , such as humans , also contain hypochlorous acid as a tool against foreign bodies . [ 6 ] In living organisms , HOCl is generated by the reaction of hydrogen peroxide with chloride ions under the catalysis of the heme enzyme myeloperoxidase (MPO). [ 7 ]
Like many other disinfectants, hypochlorous acid solutions will destroy pathogens , such as COVID-19 , absorbed on surfaces. [ 8 ] In low concentrations, such solutions can serve to disinfect open wounds . [ 9 ]
Hypochlorous acid was discovered in 1834 by the French chemist Antoine Jérôme Balard (1802–1876) by adding, to a flask of chlorine gas, a dilute suspension of mercury(II) oxide in water. [ 10 ] He also named the acid and its compounds. [ 11 ]
Despite being relatively easy to make, it is difficult to maintain a stable hypochlorous acid solution. It is not until recent years that scientists have been able to cost-effectively produce and maintain hypochlorous acid water for stable commercial use.
Addition of chlorine to water gives both hydrochloric acid (HCl) and hypochlorous acid (HClO): [ 24 ]
When acids are added to aqueous salts of hypochlorous acid (such as sodium hypochlorite in commercial bleach solution), the resultant reaction is driven to the left, and chlorine gas is formed. Thus, the formation of stable hypochlorite bleaches is facilitated by dissolving chlorine gas into basic water solutions, such as sodium hydroxide .
The acid can also be prepared by dissolving dichlorine monoxide in water; under standard aqueous conditions, anhydrous hypochlorous acid is currently impossible to prepare due to the readily reversible equilibrium between it and its anhydride: [ 25 ]
The presence of light or transition metal oxides of copper , nickel , or cobalt accelerates the exothermic [ dubious – discuss ] decomposition into hydrochloric acid and oxygen : [ 25 ]
In aqueous solution, hypochlorous acid partially dissociates into the anion hypochlorite ClO − :
Salts of hypochlorous acid are called hypochlorites . One of the best-known hypochlorites is NaClO , the active ingredient in bleach.
HClO is a stronger oxidant than chlorine under standard conditions.
HClO reacts with HCl to form chlorine:
HClO reacts with ammonia to form monochloramine :
HClO can also react with organic amines , forming N -chloroamines.
Hypochlorous acid exists in equilibrium with its anhydride , dichlorine monoxide . [ 25 ]
Hypochlorous acid reacts with a wide variety of biomolecules, including DNA , RNA , [ 15 ] [ 26 ] [ 27 ] [ 28 ] fatty acid groups, cholesterol [ 29 ] [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 36 ] and proteins. [ 32 ] [ 37 ] [ 38 ] [ 39 ] [ 40 ] [ 41 ] [ 42 ]
Knox et al. [ 40 ] first noted that HClO is a sulfhydryl inhibitor that, in sufficient quantity, could completely inactivate proteins containing sulfhydryl groups . This is because HClO oxidises sulfhydryl groups, leading to the formation of disulfide bonds [ 43 ] that can result in crosslinking of proteins . The HClO mechanism of sulfhydryl oxidation is similar to that of monochloramine , and may only be bacteriostatic, because once the residual chlorine is dissipated, some sulfhydryl function can be restored. [ 39 ] One sulfhydryl-containing amino acid can scavenge up to four molecules of HClO. [ 42 ] Consistent with this, it has been proposed that sulfhydryl groups of sulfur-containing amino acids can be oxidized a total of three times by three HClO molecules, with the fourth reacting with the α-amino group. The first reaction yields sulfenic acid ( R−S−OH ) then sulfinic acid ( R−S(=O)−OH ) and finally R−S(=O) 2 −OH . Sulfenic acids form disulfides with another protein sulfhydryl group, causing cross-linking and aggregation of proteins. Sulfinic acid and R−S(=O) 2 −OH derivatives are produced only at high molar excesses of HClO, and disulfides are formed primarily at bacteriocidal levels. [ 28 ] Disulfide bonds can also be oxidized by HClO to sulfinic acid. [ 43 ] Because the oxidation of sulfhydryls and disulfides evolves hydrochloric acid , [ 28 ] this process results in the depletion HClO.
Hypochlorous acid reacts readily with amino acids that have amino group side-chains, with the chlorine from HClO displacing a hydrogen, resulting in an organic chloramine. [ 44 ] Chlorinated amino acids rapidly decompose, but protein chloramines are longer-lived and retain some oxidative capacity. [ 14 ] [ 42 ] Thomas et al. [ 14 ] concluded from their results that most organic chloramines decayed by internal rearrangement and that fewer available NH 2 groups promoted attack on the peptide bond , resulting in cleavage of the protein . McKenna and Davies [ 45 ] found that 10 mM or greater HClO is necessary to fragment proteins in vivo. Consistent with these results, it was later proposed that the chloramine undergoes a molecular rearrangement, releasing HCl and ammonia to form an aldehyde . [ 46 ] The aldehyde group can further react with another amino group to form a Schiff base , causing cross-linking and aggregation of proteins. [ 32 ]
Hypochlorous acid reacts slowly with DNA and RNA as well as all nucleotides in vitro. [ 26 ] [ 47 ] GMP is the most reactive because HClO reacts with both the heterocyclic NH group and the amino group. In similar manner, TMP with only a heterocyclic NH group that is reactive with HClO is the second-most reactive. AMP and CMP , which have only a slowly reactive amino group, are less reactive with HClO. [ 47 ] UMP has been reported to be reactive only at a very slow rate. [ 15 ] [ 26 ] The heterocyclic NH groups are more reactive than amino groups, and their secondary chloramines are able to donate the chlorine. [ 28 ] These reactions likely interfere with DNA base pairing, and, consistent with this, Prütz [ 47 ] has reported a decrease in viscosity of DNA exposed to HClO similar to that seen with heat denaturation. The sugar moieties are nonreactive and the DNA backbone is not broken. [ 47 ] NADH can react with chlorinated TMP and UMP as well as HClO. This reaction can regenerate UMP and TMP and results in the 5-hydroxy derivative of NADH. The reaction with TMP or UMP is slowly reversible to regenerate HClO. A second slower reaction that results in cleavage of the pyridine ring occurs when excess HClO is present. NAD + is inert to HClO. [ 28 ] [ 47 ]
Hypochlorous acid reacts with unsaturated bonds in lipids , but not saturated bonds , and the ClO − ion does not participate in this reaction. This reaction occurs by hydrolysis with addition of chlorine to one of the carbons and a hydroxyl to the other. The resulting compound is a chlorohydrin. [ 29 ] The polar chlorine disrupts lipid bilayers and could increase permeability. [ 30 ] When chlorohydrin formation occurs in lipid bilayers of red blood cells, increased permeability occurs. Disruption could occur if enough chlorohydrin is formed. [ 29 ] [ 35 ] The addition of preformed chlorohydrin to red blood cells can affect permeability as well. [ 31 ] Cholesterol chlorohydrin have also been observed, [ 30 ] [ 33 ] but do not greatly affect permeability, and it is believed that Cl 2 is responsible for this reaction. [ 33 ] Hypochlorous acid also reacts with a subclass of glycerophospholipids called plasmalogens , yielding chlorinated fatty aldehydes which are capable of protein modification and may play a role in inflammatory processes such as platelet aggregation and the formation of neutrophil extracellular traps . [ 48 ] [ 49 ] [ 50 ]
E. coli exposed to hypochlorous acid lose viability in less than 0.1 seconds due to inactivation of many vital systems. [ 24 ] [ 51 ] [ 52 ] [ 53 ] [ 54 ] Hypochlorous acid has a reported LD 50 of 0.0104–0.156 ppm [ 55 ] and 2.6 ppm caused 100% growth inhibition in 5 minutes. [ 45 ] However, the concentration required for bactericidal activity is also highly dependent on bacterial concentration. [ 40 ]
In 1948, Knox et al. [ 40 ] proposed the idea that inhibition of glucose oxidation is a major factor in the bacteriocidal nature of chlorine solutions. They proposed that the active agent or agents diffuse across the cytoplasmic membrane to inactivate key sulfhydryl -containing enzymes in the glycolytic pathway . This group was also the first to note that chlorine solutions (HClO) inhibit sulfhydryl enzymes . Later studies have shown that, at bacteriocidal levels, the cytosol components do not react with HClO. [ 56 ] In agreement with this, McFeters and Camper [ 57 ] found that aldolase , an enzyme that Knox et al. [ 40 ] proposes would be inactivated, was unaffected by HClO in vivo . It has been further shown that loss of sulfhydryls does not correlate with inactivation. [ 39 ] That leaves the question concerning what causes inhibition of glucose oxidation. The discovery that HClO blocks induction of β-galactosidase by added lactose [ 58 ] led to a possible answer to this question. The uptake of radiolabeled substrates by both ATP hydrolysis and proton co-transport may be blocked by exposure to HClO preceding loss of viability. [ 56 ] From this observation, it proposed that HClO blocks uptake of nutrients by inactivating transport proteins. [ 38 ] [ 56 ] [ 57 ] [ 59 ] The question of loss of glucose oxidation has been further explored in terms of loss of respiration. Venkobachar et al. [ 60 ] found that succinic dehydrogenase was inhibited in vitro by HClO, which led to the investigation of the possibility that disruption of electron transport could be the cause of bacterial inactivation. Albrich et al. [ 15 ] subsequently found that HClO destroys cytochromes and iron-sulfur clusters and observed that oxygen uptake is abolished by HClO and adenine nucleotides are lost. It was also observed that irreversible oxidation of cytochromes paralleled the loss of respiratory activity. One way of addressing the loss of oxygen uptake was by studying the effects of HClO on succinate-dependent electron transport . [ 61 ] Rosen et al. [ 54 ] found that levels of reductable cytochromes in HClO-treated cells were normal, and these cells were unable to reduce them. Succinate dehydrogenase was also inhibited by HClO, stopping the flow of electrons to oxygen. Later studies [ 52 ] revealed that Ubiquinol oxidase activity ceases first, and the still-active cytochromes reduce the remaining quinone. The cytochromes then pass the electrons to oxygen , which explains why the cytochromes cannot be reoxidized, as observed by Rosen et al. [ 54 ] However, this line of inquiry was ended when Albrich et al. [ 37 ] found that cellular inactivation precedes loss of respiration by using a flow mixing system that allowed evaluation of viability on much smaller time scales. This group found that cells capable of respiring could not divide after exposure to HClO.
Having eliminated loss of respiration, Albrich et al. [ 37 ] proposes that the cause of death may be due to metabolic dysfunction caused by depletion of adenine nucleotides. Barrette et al. [ 58 ] studied the loss of adenine nucleotides by studying the energy charge of HClO-exposed cells and found that cells exposed to HClO were unable to step up their energy charge after addition of nutrients. The conclusion was that exposed cells have lost the ability to regulate their adenylate pool, based on the fact that metabolite uptake was only 45% deficient after exposure to HClO and the observation that HClO causes intracellular ATP hydrolysis. It was also confirmed that, at bacteriocidal levels of HClO, cytosolic components are unaffected. So it was proposed that modification of some membrane-bound protein results in extensive ATP hydrolysis, and this, coupled with the cells inability to remove AMP from the cytosol, depresses metabolic function. One protein involved in loss of ability to regenerate ATP has been found to be ATP synthetase . [ 38 ] Much of this research on respiration reconfirms the observation that relevant bacteriocidal reactions take place at the cell membrane. [ 38 ] [ 58 ] [ 62 ]
Recently it has been proposed that bacterial inactivation by HClO is the result of inhibition of DNA replication. When bacteria are exposed to HClO, there is a precipitous decline in DNA synthesis that precedes inhibition of protein synthesis, and closely parallels loss of viability. [ 45 ] [ 63 ] During bacterial genome replication, the origin of replication (oriC in E. coli ) binds to proteins that are associated with the cell membrane, and it was observed that HClO treatment decreases the affinity of extracted membranes for oriC, and this decreased affinity also parallels loss of viability. A study by Rosen et al. [ 64 ] compared the rate of HClO inhibition of DNA replication of plasmids with different replication origins and found that certain plasmids exhibited a delay in the inhibition of replication when compared to plasmids containing oriC. Rosen's group proposed that inactivation of membrane proteins involved in DNA replication are the mechanism of action of HClO.
HClO is known to cause post-translational modifications to proteins , the notable ones being cysteine and methionine oxidation. A recent examination of HClO's bactericidal role revealed it to be a potent inducer of protein aggregation. [ 65 ] Hsp33, a chaperone known to be activated by oxidative heat stress, protects bacteria from the effects of HClO by acting as a holdase , effectively preventing protein aggregation. Strains of Escherichia coli and Vibrio cholerae lacking Hsp33 were rendered especially sensitive to HClO. Hsp33 protected many essential proteins from aggregation and inactivation due to HClO, which is a probable mediator of HClO's bactericidal effects.
Hypochlorites are the salts of hypochlorous acid; commercially important hypochlorites are calcium hypochlorite and sodium hypochlorite .
Solutions of hypochlorites can be produced in-situ by electrolysis of an aqueous sodium chloride solution in both batch and flow processes. [ 66 ] The composition of the resulting solution depends on the pH at the anode. In acid conditions the solution produced will have a high hypochlorous acid concentration, but will also contain dissolved gaseous chlorine, which can be corrosive, at a neutral pH the solution will be around 75% hypochlorous acid and 25% hypochlorite. Some of the chlorine gas produced will dissolve forming hypochlorite ions. Hypochlorites are also produced by the disproportionation of chlorine gas in alkaline solutions.
HClO is classified as non-hazardous by the Environmental Protection Agency in the US. As an oxidising agent, it can be corrosive or irritant depending on its concentration and pH.
In a clinical test, hypochlorous acid water was tested for eye irritation, skin irritation, and toxicity. The test concluded that it was non-toxic and non-irritating to the eye and skin. [ 67 ]
In a 2017 study, a saline hygiene solution preserved with pure hypochlorous acid was shown to reduce the bacterial load significantly without altering the diversity of bacterial species on the eyelids. After 20 minutes of treatment, there was more than 99% reduction of the Staphylococci bacteria. [ 68 ]
Commercial disinfection applications remained elusive for a long time after the discovery of hypochlorous acid because the stability of its solution in water is difficult to maintain. The active compounds quickly deteriorate back into salt water, losing the solution its disinfecting capability, which makes it difficult to transport for wide use. It is less commonly used as a disinfectant compared to bleach and alcohol due to cost, despite its stronger disinfecting capabilities.
Technological developments have reduced manufacturing costs and allow for manufacturing and bottling of hypochlorous acid water for home and commercial use. However, most hypochlorous acid water has a short shelf life. Storing away from heat and direct sunlight can help slow the deterioration. The further development of continuous flow electrochemical cells has been implemented in new products, allowing the commercialisation of domestic and industrial continuous flow devices for the in-situ generation of hypochlorous acid for disinfection purposes. [ 69 ] | https://en.wikipedia.org/wiki/Hypochlorous_acid |
Hypofluorous acid , chemical formula H O F , is the only known oxyacid of fluorine and the only known oxoacid in which the main atom gains electrons from oxygen to create a negative oxidation state. The oxidation state of the oxygen in this acid (and in the hypofluorite ion OF − and in its salts called hypofluorites) is 0, while its valence is 2. It is also the only hypohalous acid that can be isolated as a solid . HOF is an intermediate in the oxidation of water by fluorine , which produces hydrogen fluoride , oxygen difluoride , hydrogen peroxide , ozone and oxygen . HOF is explosive at room temperature, forming HF and O 2 : [ 1 ]
This reaction is catalyzed by water. [ 2 ]
It was isolated in the pure form by passing F 2 gas over ice at −40 °C, rapidly collecting the HOF gas away from the ice, and condensing it: [ 2 ]
The compound has been characterized in the solid phase by X-ray crystallography [ 1 ] as a bent molecule with an angle of 101°. The O–F and O–H bond lengths are 144.2 and 96.4 picometres , respectively. The solid framework consists of chains with O–H···O linkages. The structure has also been analyzed in the gas phase, a state in which the H–O–F bond angle is slightly narrower (97.2°).
Chemists commonly call a solution of hypofluorous acid in acetonitrile (generated in situ by passing gaseous fluorine through water in acetonitrile) Rozen's reagent. [ 3 ]
The formal oxidation state of oxygen in hypofluorous acid and hypofluorite is 0; the same oxidation state found in molecular oxygen . In most oxygen compounds, including the other hypohalous acids, oxygen takes on a state of −2. The oxygen (0) atom is the root of hypofluorous acid's strength as an oxidizer, in contrast to the halogen (+1) atom in other hypohalic acids.
This alters the acid's chemistry. Where reduction of a general hypohalous acid reduces the halogen atom and yields the corresponding elemental halogen gas,
reduction of hypofluorous acid instead reduces the oxygen atom and yields fluoride directly.
Unlike other hypohalous acids, HOF is a weaker oxidant than elemental fluorine.
Hypofluorites are formally derivatives of OF − , which is the conjugate base of hypofluorous acid. One example is trifluoromethyl hypofluorite ( CF 3 OF ), which is a trifluoromethyl ester of hypofluorous acid. The conjugate base is known in salts such as lithium hypofluorite . | https://en.wikipedia.org/wiki/Hypofluorous_acid |
In mathematics , the hypograph or subgraph of a function f : R n → R {\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbb {R} } is the set of points lying on or below its graph .
A related definition is that of such a function's epigraph , which is the set of points on or above the function's graph.
The domain (rather than the codomain ) of the function is not particularly important for this definition; it can be an arbitrary set [ 1 ] instead of R n {\displaystyle \mathbb {R} ^{n}} .
The definition of the hypograph was inspired by that of the graph of a function , where the graph of f : X → Y {\displaystyle f:X\to Y} is defined to be the set
The hypograph or subgraph of a function f : X → [ − ∞ , ∞ ] {\displaystyle f:X\to [-\infty ,\infty ]} valued in the extended real numbers [ − ∞ , ∞ ] = R ∪ { ± ∞ } {\displaystyle [-\infty ,\infty ]=\mathbb {R} \cup \{\pm \infty \}} is the set [ 2 ]
Similarly, the set of points on or above the function is its epigraph . The strict hypograph is the hypograph with the graph removed:
Despite the fact that f {\displaystyle f} might take one (or both) of ± ∞ {\displaystyle \pm \infty } as a value (in which case its graph would not be a subset of X × R {\displaystyle X\times \mathbb {R} } ), the hypograph of f {\displaystyle f} is nevertheless defined to be a subset of X × R {\displaystyle X\times \mathbb {R} } rather than of X × [ − ∞ , ∞ ] . {\displaystyle X\times [-\infty ,\infty ].}
The hypograph of a function f {\displaystyle f} is empty if and only if f {\displaystyle f} is identically equal to negative infinity.
A function is concave if and only if its hypograph is a convex set . The hypograph of a real affine function g : R n → R {\displaystyle g:\mathbb {R} ^{n}\to \mathbb {R} } is a halfspace in R n + 1 . {\displaystyle \mathbb {R} ^{n+1}.}
A function is upper semicontinuous if and only if its hypograph is closed .
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypograph_(mathematics) |
Hypohidrosis is a medical condition in which a person exhibits diminished sweating in response to appropriate stimuli. In contrast with hyperhidrosis , which is a socially troubling yet often benign condition, the consequences of untreated hypohidrosis include hyperthermia , heat stroke and death. [ 2 ] An extreme case of hypohidrosis in which there is a complete absence of sweating and the skin is dry is termed anhidrosis . [ 3 ] The condition is also known as adiaphoresis , [ 4 ] ischidrosis , [ 5 ] oligidria , [ 6 ] oligohidrosis [ 7 ] and sweating deficiency .
The causes are the following: [ citation needed ]
Physical agents
Dermatological
Neuropathic
Sweat is readily visualized by a topical indicator such as iodinated starch ( Minor test ) or sodium alizarin sulphonate, both of which undergo a dramatic colour change when moistened by sweat. A thermoregulatory sweat test can evaluate the body’s response to a thermal stimulus by inducing sweating through a hot box (also called a hot room ), a thermal blanket, or physical exercise. Failure of the topical indicator to undergo a colour change during thermoregulatory sweat testing indicates hypohidrosis, and further tests may be required to localize the lesion . [ citation needed ]
Magnetic resonance imaging of the brain and/or spinal cord is the best modality for evaluation when the lesion is suspected to be localized to the central nervous system . [ citation needed ]
Skin biopsies are useful when anhidrosis occurs as part of a dermatological disorder. Biopsy results may reveal the sweat gland destruction, necrosis or fibrosis , in addition to the findings of the primary dermatological disorder. [ citation needed ]
The treatment options for hypohidrosis and anhidrosis are largely limited to preventing overheating and attempting to resolve or prevent further deterioration of any known underlying causes.
Those with hypohidrosis should avoid drugs that can aggravate the condition (see "Medications", under § Causes ). They should limit activities that raise the core body temperature and if exercises are to be performed, they should be supervised and be performed in a cool, sheltered, and well-ventilated environment.
When the cause is known, treatment should be directed at the primary pathology. In autoimmune diseases, such as Sjögren syndrome and systemic sclerosis , treatment of the underlying disease using immunosuppressive drugs may lead to improvement in hypohidrosis. In neurological diseases, the primary pathology is often irreversible. In these instances, prevention of further neurological damage, such as good glycaemic control in diabetes , is the cornerstone of management. In acquired generalized anhidrosis , spontaneous remission may be observed in some cases. Corticosteroid pulse therapy has increased sweating in some people. [ 8 ]
Horses can also have hypohidrosis. [ 9 ] Management includes avoiding exercise in warm weather and using water or other cooling devices. [ 9 ] Horses may have inflammation of the airway, which may reduce the horse's ability to use panting as a form of thermoregulation. [ 9 ] | https://en.wikipedia.org/wiki/Hypohidrosis |
Hypoiodous acid is an inorganic compound with the chemical formula H I O . It forms when an aqueous solution of iodine is treated with mercuric or silver salts . It rapidly decomposes by disproportionation : [ 2 ]
Hypoiodous acid is a weak acid with a p K a of about 11. The conjugate base is hypoiodite ( IO − ). Salts of this anion can be prepared by treating iodine with alkali hydroxides . They rapidly disproportionate to form iodides and iodates , [ 2 ] but an iodine–hydroxide mixture can be used an in situ preparation of hypoiodite for other reactions. [ 3 ]
Ammonium hypoiodites can be formed by oxidation of the analogous iodide salts. These and also sodium hypoiodite are useful as oxidizing agents for a various types of organic compounds and also for a reaction analogous to the haloform reaction . [ 3 ]
Hypoiodite is one of the active oxidizing agents generated by lactoperoxidase as part of the mammalian innate immune system . [ 4 ] [ 5 ]
Hypoiodous acid is part of a series of oxyacids in which iodine can assume oxidation states of −1, +1, +3, +5, or +7. A number of neutral iodine oxides are also known.
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypoiodous_acid |
In plant biology , the hyponastic response is a nastic movement characterized by an upward bending of leaves or other plant parts, resulting from accelerated growth of the lower side of the petiole in comparison to its upper part. This can be observed in many terrestrial plants and is linked to the plant hormone ethylene .
The plant’s root senses the water excess and produces 1-Aminocyclopropane-1-carboxylic acid which then is converted into ethylene, regulating this process. [ 1 ]
Submerged plants often show a hyponastic response, where the upward bending of the leaves and the elongation of the petioles might help the plant to restore normal gas exchange with the atmosphere.
Plants that are exposed to elevated ethylene levels in experimental set-ups also show a hyponastic response.
This plant physiology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hyponastic_response |
Hydroxy- λ 5 -phosphanone Oxo- λ 5 -phosphanol Oxo- λ 5 -phosphinous acid
1.22 g/cm 3 (50 wt% aq. solution)
Hypophosphorous acid ( HPA ), or phosphinic acid , is a phosphorus oxyacid and a powerful reducing agent with molecular formula H 3 PO 2 . It is a colorless low-melting compound, which is soluble in water, dioxane and alcohols. The formula for this acid is generally written H 3 PO 2 , but a more descriptive presentation is HOP(O)H 2 , which highlights its monoprotic character. Salts derived from this acid are called hypophosphites . [ 3 ]
HOP(O)H 2 exists in equilibrium with the minor tautomer HP(OH) 2 . Sometimes the minor tautomer is called hypophosphorous acid and the major tautomer is called phosphinic acid.
Hypophosphorous acid was first prepared in 1816 by the French chemist Pierre Louis Dulong (1785–1838). [ 4 ]
The acid is prepared industrially via a two step process: Firstly, elemental white phosphorus reacts with alkali and alkaline earth hydroxides to give an aqueous solution of hypophosphites:
Any phosphites produced in this step can be selectively precipitated out by treatment with calcium salts. The purified material is then treated with a strong, non-oxidizing acid (often sulfuric acid ) to give the free hypophosphorous acid:
HPA is usually supplied as a 50% aqueous solution. Anhydrous acid cannot be obtained by simple evaporation of the water, as the acid readily oxidises to phosphorous acid and phosphoric acid and also disproportionates to phosphorous acid and phosphine . Pure anhydrous hypophosphorous acid can be formed by the continuous extraction of aqueous solutions with diethyl ether . [ 5 ]
The molecule displays P(═O)H to P–OH tautomerism similar to that of phosphorous acid ; the P(═O) form is strongly favoured. [ 6 ]
HPA is usually supplied as a 50% aqueous solution and heating at low temperatures (up to about 90 °C) prompts it to react with water to form phosphorous acid and hydrogen gas.
Heating above 110 °C causes hypophosphorous acid to undergo disproportionation to give phosphorous acid and phosphine . [ 7 ]
Hypophosphorous acid can reduce chromium(III) oxide to chromium(II) oxide :
Most metal-hypophosphite complexes are unstable, owing to the tendency of hypophosphites to reduce metal cations back into the bulk metal. Some examples have been characterised, [ 8 ] [ 9 ] including the important nickel salt [Ni(H 2 O) 6 ](H 2 PO 2 ) 2 . [ 10 ]
Because hypophosphorous acid can reduce elemental iodine to form hydroiodic acid , which is a reagent effective for reducing ephedrine or pseudoephedrine to methamphetamine , [ 11 ] the United States Drug Enforcement Administration designated hypophosphorous acid (and its salts) as a List I precursor chemical effective November 16, 2001. [ 12 ] Accordingly, handlers of hypophosphorous acid or its salts in the United States are subject to stringent regulatory controls including registration, recordkeeping, reporting, and import/export requirements pursuant to the Controlled Substances Act and 21 CFR §§ 1309 and 1310. [ 12 ] [ 13 ] [ 14 ]
In organic chemistry, H 3 PO 2 can be used for the reduction of arenediazonium salts , converting Ar− + N≡N to Ar−H . [ 15 ] [ 16 ] [ 17 ] When diazotized in a concentrated solution of hypophosphorous acid, an amine substituent can be removed from arenes.
Owing to its ability to function as a mild reducing agent and oxygen scavenger it is sometimes used as an additive in Fischer esterification reactions, where it prevents the formation of colored impurities.
It is used to prepare phosphinic acid derivatives. [ 18 ]
Hypophosphorous acid (and its salts) are used to reduce metal salts back into bulk metals. It is effective for various transition metals ions (i.e. those of: Co, Cu, Ag, Mn, Pt) but is most commonly used to reduce nickel . [ 19 ] This forms the basis of electroless nickel plating (Ni–P), which is the single largest industrial application of hypophosphites. For this application it is principally used as a salt ( sodium hypophosphite ). [ 20 ]
[ 1 ] | https://en.wikipedia.org/wiki/Hypophosphorous_acid |
The hyporheic zone is the region of sediment and porous space beneath and alongside a stream bed , where there is mixing of shallow groundwater and surface water . The flow dynamics and behavior in this zone (termed hyporheic flow or underflow ) is recognized to be important for surface water/groundwater interactions, as well as fish spawning , among other processes. [ 1 ] As an innovative urban water management practice, the hyporheic zone can be designed by engineers and actively managed for improvements in both water quality and riparian habitat. [ 2 ]
The assemblages of organisms that inhabits this zone are called hyporheos .
The term hyporheic was originally coined by Traian Orghidan [ 3 ] in 1959 by combining two Greek words: hypo (below) and rheos (flow).
The hyporheic zone is the area of rapid exchange, where water is moved into and out of the stream bed and carries dissolved gas and solutes, contaminants, microorganisms and particles with it. [ 4 ] Depending on the underlying geology and topography, the hyporheic zone can be only several centimeters deep, or extend up to tens of meters laterally or deep.
The conceptual framework of the hyporheic zone as both a mixing and storage zone are integral to the study of hydrology . The first key concept related to the hyporheic zone is that of residence time ; water in the channel moves at a much faster rate compared to the hyporheic zone, so this flow of slower water effectively increases the water residence time within the stream channel. Water residence times influence nutrient and carbon processing rates. Longer residence times promote dissolved solute retention, which can be later released back into the channel, delaying or attenuating the signals produced by the stream channel. [ 5 ]
The other key concept is that of hyporheic exchange, [ 6 ] [ 7 ] or the speed at which water enters or leaves the subsurface zone. Stream water enters the hyporheic zone temporarily, but eventually the stream water reenters the surface channel or contributes to groundwater storage. The rate of hyporheic exchange is influenced by streambed structure, with shorter water flow paths created by streambed roughness. [ 8 ] [ 9 ] Longer flowpaths are induced by geomorphic features, such as stream meander patterns, pool-riffle sequences, large woody debris dams, and other features.
The hyporheic zone and its interactions influence the volume of stream water that is moved downstream. Gaining reaches indicate that groundwater is discharged into the stream as water moves downstream, so that the volume of water in the main channel increases from upstream to downstream. Conversely, when surface water infiltrates into the groundwater zone (thereby resulting in a net loss of surface water), then that stream reach is considered to be "losing" water.
The hyporheic zone provides a variety of ecological benefits. Examples include: [ 10 ]
A stream or river ecosystem is more than just the flowing water that can be seen on the surface: rivers are connected to the adjacent riparian areas. [ 11 ] Therefore, streams and rivers include the dynamic hyporheic zone that lies below and lateral to the main channel. Because the hyporheic zone lies underneath the surface water, it can be difficult to identify, quantify, and observe. However, the hyporheic zone is a zone of biological and physical activity, and therefore has functional significance for stream and river ecosystems. [ 12 ] Researchers use tools such as wells and piezometers , conservative and reactive tracers, [ 13 ] and transport models that account for advection and dispersion of water in both the stream channel and the subsurface. [ 14 ] These tools can be used independently to study water movement through the hyporheic zone and to the stream channel, but are often complementary for a more accurate picture of water dynamics in the channel as a whole.
The hyporheic zone is an ecotone between the stream and subsurface: it is a dynamic area of mixing between surface water and groundwater at the sediment-water interface. From a biogeochemical perspective, groundwater is often low in dissolved oxygen but carries dissolved nutrients. Conversely, stream water from the main channel contains higher dissolved oxygen and lower nutrients. This creates a biogeochemical gradient, which can exist at varying depths depending on the extent of the hyporheic zone. Often, the hyporheic zone is dominated by heterotrophic microorganisms that process the dissolved nutrients exchanged at this interface.
The main differences between the surface water and groundwater concern the oxygen concentration, the temperature and the pH. [ 15 ] As interface region between the main stream and the groundwater the hyporheic zone is subjected to physic-chemical gradients generating biochemical reactions able to regulate the behavior of the chemical compounds and the aquatic organisms within the exchange area. [ 16 ] The hyporheic zone provides an important contribution to the attenuation of contaminants dissolved in the channel water [ 17 ] and to the cycle of energy, nutrients and organic compounds. [ 18 ] Moreover, it exhibits a significant control on the transport of pollutants across the river basin. [ 19 ]
The main factors affecting the hyporheic exchange are: [ 20 ] | https://en.wikipedia.org/wiki/Hyporheic_zone |
Hypostatic abstraction in philosophy and mathematical logic , also known as hypostasis or subjectal abstraction , is a formal operation that transforms a predicate into a relation ; for example "Honey is sweet" is transformed into "Honey has sweetness". The relation is created between the original subject and a new term that represents the property expressed by the original predicate.
Hypostasis changes a propositional formula of the form X is Y to another one of the form X has the property of being Y or X has Y-ness . The logical functioning of the second object Y-ness consists solely in the truth-values of those propositions that have the corresponding abstract property Y as the predicate. The object of thought introduced in this way may be called a hypostatic object and in some senses an abstract object and a formal object .
The above definition is adapted from the one given by Charles Sanders Peirce . [ 1 ] As Peirce describes it, the main point about the formal operation of hypostatic abstraction, insofar as it operates on formal linguistic expressions, is that it converts a predicative adjective or predicate into an extra subject, thus increasing by one the number of "subject" slots—called the arity or adicity —of the main predicate.
The distinction between particular objects and a formal object is noted by Anthony Kenny : [ 2 ] we might identify any object as having a certain property to which we respond, but the formal object of that response is the property which we implicitly ascribe to the particular object by virtue of us having that response: thus if a certain red rose is "lovely", the rose has the property of loveliness, and this loveliness is the formal object of our aesthetic appreciation of the rose. [ 3 ]
The grammatical trace of this hypostatic transformation is a process that extracts the adjective "sweet" from the predicate "is sweet", replacing it by a new, increased-arity predicate "possesses", and as a by-product of the reaction, as it were, precipitating out the substantive "sweetness" as a second subject of the new predicate.
The abstraction of hypostasis takes the concrete physical sense of "taste" found in "honey is sweet" and ascribes to it the formal metaphysical characteristics in "honey has sweetness". | https://en.wikipedia.org/wiki/Hypostatic_abstraction |
In geometry , a hypotenuse is the side of a right triangle opposite the right angle . [ 1 ] It is the longest side of any such triangle; the two other shorter sides of such a triangle are called catheti or legs . The length of the hypotenuse can be found using the Pythagorean theorem , which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two legs. Mathematically, this can be written as a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} , where a is the length of one leg, b is the length of another leg, and c is the length of the hypotenuse. [ 2 ]
For example, if one of the legs of a right angle has a length of 3 and the other has a length of 4, then their squares add up to 25 = 9 + 16 = 3 × 3 + 4 × 4. Since 25 is the square of the hypotenuse, the length of the hypotenuse is the square root of 25, that is, 5. In other words, if a = 3 {\displaystyle a=3} and b = 4 {\displaystyle b=4} , then c = a 2 + b 2 = 5 {\displaystyle c={\sqrt {a^{2}+b^{2}}}=5} .
The word hypotenuse is derived from Greek ἡ τὴν ὀρθὴν γωνίαν ὑποτείνουσα (sc. γραμμή or πλευρά ), meaning "[side] subtending the right angle" ( Apollodorus ), [ 3 ] ὑποτείνουσα hupoteinousa being the feminine present active participle of the verb ὑποτείνω hupo-teinō "to stretch below, to subtend", from τείνω teinō "to stretch, extend". The nominalised participle, ἡ ὑποτείνουσα , was used for the hypotenuse of a triangle in the 4th century BCE (attested in Plato , Timaeus 54d). The Greek term was loaned into Late Latin , as hypotēnūsa . [ 4 ] [ 5 ] The spelling in -e , as hypotenuse , is French in origin ( Estienne de La Roche 1520). [ 6 ]
In a right triangle , the hypotenuse is the side that is opposite the right angle , while the other two sides are called the catheti or legs . [ 7 ] The length of the hypotenuse can be calculated using the square root function implied by the Pythagorean theorem . It states that the sum of the two legs squared equals the hypotenuse squared. In mathematical notation, with the respective legs labelled a {\displaystyle a} and b {\displaystyle b} , and the hypotenuse labelled c {\displaystyle c} , it is written as a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} . Using the square root function on both sides of the equation, it follows that
This calculation of c {\displaystyle c} from a {\displaystyle a} and b {\displaystyle b} is called Pythagorean addition , [ 8 ] and is available in many software libraries as the hypot function. [ 9 ] [ 10 ]
As a consequence of the Pythagorean theorem, the hypotenuse is the longest side of any right triangle; that is, the hypotenuse is longer than either of the triangle's legs. For example, given the length of the legs a = 5 and b = 12, then the sum of the legs squared is (5 × 5) + (12 × 12) = 169, the square of the hypotenuse. The length of the hypotenuse is thus the square root of 169, denoted 169 {\displaystyle {\sqrt {169}}} , which equals 13.
The Pythagorean theorem, and hence this length, can also be derived from the law of cosines in trigonometry . In a right triangle, the cosine of an angle is the ratio of the leg adjacent of the angle and the hypotenuse. For a right angle γ (gamma), where the adjacent leg equals 0, the cosine of γ also equals 0. The law of cosines formulates that c 2 = a 2 + b 2 − 2 a b cos θ {\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos \theta } holds for some angle θ (theta). By observing that the angle opposite the hypotenuse is right and noting that its cosine is 0, so in this case θ = γ = 90°:
Many computer languages support the ISO C standard function hypot( x , y ), which returns the value above. [ 11 ] The function is designed not to fail where the straightforward calculation might overflow or underflow and can be slightly more accurate and sometimes significantly slower.
Some languages have extended the definition to higher dimensions. For example, C++17 supports std::hypot ( x , y , z ) = x 2 + y 2 + z 2 {\displaystyle {\mbox{std::hypot}}(x,y,z)={\sqrt {x^{2}+y^{2}+z^{2}}}} ; [ 12 ] this gives the length of the diagonal of a rectangular cuboid with edges x , y , and z . Python 3.8 extended math.hypot {\displaystyle {\mbox{math.hypot}}} to handle an arbitrary number of arguments. [ 13 ]
Some scientific calculators [ which? ] provide a function to convert from rectangular coordinates to polar coordinates . This gives both the length of the hypotenuse and the angle the hypotenuse makes with the base line ( c 1 above) at the same time when given x and y . The angle returned is normally given by atan2 ( y , x ).
By means of trigonometric ratios , one can obtain the value of two acute angles, α {\displaystyle \alpha \,} and β {\displaystyle \beta \,} , of the right triangle.
Given the length of the hypotenuse c {\displaystyle c\,} and of a cathetus b {\displaystyle b\,} , the ratio is:
The trigonometric inverse function is:
in which β {\displaystyle \beta \,} is the angle opposite the cathetus b {\displaystyle b\,} .
The adjacent angle of the catheti b {\displaystyle b\,} is α {\displaystyle \alpha \,} = 90° – β {\displaystyle \beta \,}
One may also obtain the value of the angle β {\displaystyle \beta \,} by the equation:
in which a {\displaystyle a\,} is the other cathetus. | https://en.wikipedia.org/wiki/Hypotenuse |
In true slime molds ( myxogastria ), lichens , and in species of the family Clavicipitaceae , the hypothallus is the layer on which the fruit body sits, lying in contact with the substrate. The word is derived from the Ancient Greek root hypó ("under") and thallós ("shoot" or " thallus "). [ 1 ]
The hypothallus is produced by the plasmodium at the beginning of fructification . Depending on the species, it can be membranous to thick or tender to solid and nearly transparent to brightly coloured. It may surround an individual fruit body, or may form a contiguous connection between multiple fruit bodies. In some rare cases it is missing entirely. [ 2 ]
In crustose lichens , the hypothallus is the blackish lower layer of the thallus that produces rhizines , which are holdfasts that attach the lichen to its substrate . [ 1 ]
In some taxa the hypothallus may be involved in the formation of the fruit body. In the "epihypothallic" Stemonitida , the hypothallus forms hollow, tubular stems and a columella , [ 3 ] up which the remaining plasmodium then rises, producing the spores . [ 4 ] In all other myxogastria "subhypothallic" development takes place. Here, the hypothallus produces a layer on the plasmodium, which creates the rooms of the single fruit bodies during fructification. As the surrounding plasmodium flows in the fruit body, the hypothallus will lie directly on the substrate, shrinking and creating the edge of the mature fruit body. Here, the hypothallus is part of a morphological unit with peridium and stem, which serves as a membranous surface of the whole structure with the spores. [ 5 ] Epihypothaly is an autapomorphy of the stemonitida and is, in comparison to subhypothaly, a primitive feature. [ 6 ] | https://en.wikipedia.org/wiki/Hypothallus |
In the history of physics , hypotheses non fingo ( Latin for "I frame no hypotheses ", or "I contrive no hypotheses") is a phrase used by Isaac Newton in the essay General Scholium , which was appended to the second edition of Philosophiae Naturalis Principia Mathematica in 1713.
A 1999 translation of the Principia presents Newton's remark as follows:
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. [ 1 ]
The 19th-century philosopher of science William Whewell qualified this statement, saying that, "it was by such a use of hypotheses, that both Newton himself and Kepler , on whose discoveries those of Newton were based, made their discoveries". Whewell stated:
What is requisite is, that the hypothesis should be close to the facts, and not connected with them by other arbitrary and untried facts; and that the philosopher should be ready to resign it as soon as the facts refuse to confirm it. [ 2 ]
Later, Imre Lakatos asserted that such a resignation should not be too rushed. [ citation needed ]
This philosophy of science -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypotheses_non_fingo |
A hypothetical chemical compound is a chemical compound that has been conceived of, but is not known to have been synthesized , observed, or isolated (identified or shown to exist). [ citation needed ]
Some hypothetical compounds cannot form at all, due to steric effects (e.g. tetra- tert -butylmethane , C(C(CH 3 ) 3 ) 4 , chlorine heptafluoride, ClF 7 , or bromine heptafluoride, BrF 7 ) or bond stress (e.g. tetrahedrane C 4 H 4 ). Others might turn out to be highly unstable , decomposing , isomerizing , polymerizing , rearranging , or disproportionating . Some are thought to exist only briefly as reactive intermediates or in vacuum. Some have no known pathway for synthesis (e.g. hypercubane ).
Some compounds of radioactive elements have never been synthesized due to their radioactive decay and short half-lives (e.g. francium hydroxide FrOH, radon hexafluoride RnF 6 , astatine heptafluoride AtF 7 , polonium(II) fluoride PoF 2 ).
Some "parent compounds" have not been or cannot be isolated, even though stable structural analogs with substituents have been discovered or synthesized (e.g. borole C 4 H 4 BH ). Hypothetical compounds are often predicted or expected from known compounds, such as a families of salts for which the "parent acid" is not a stable molecule, or in which salts form with some cations but not others. Examples of such "phantom acids" are disulfurous acid HO−S(=O)−S(=O) 2 −OH and sulfurous acid O=S(−OH) 2 , whose salts are stable.
Hypothetical compounds are used in some thought experiments .
Some compounds long regarded as hypothetical have later been isolated. Ethylene dione was suggested in 1913 and observed spectroscopically in 2015. [ 1 ] Another stable compound, potassium trichromate, has been produced in a small scale and is known to be a very powerful oxidizing agent . Sodium trichromate and sodium and potassium tetrachromate have been hypothesized but are yet to be synthesized. [ when? ]
Other compounds were once thought to have already been produced, but are now regarded as hypothetical chemical compounds unlikely to ever be produced, such as polywater , oxygen tetrafluoride OF 4 , chromium hexafluoride CrF 6 and osmium octafluoride OsF 8 .
Other examples of hypothetical compounds are xenon octafluoride XeF 8 , pentazole N 5 H (all nitrogen analog of azole ), hexazine N 6 (all nitrogen analog of benzene ), octaazacubane N 8 (all nitrogen analog of cubane ), cyclotrioxidane O 3 , nitrogen pentafluoride NF 5 , tetrafluoroammonium fluoride [NF 4 ] + F − .
Despite the fact that rhenium heptahydride ReH 7 has not been isolated, its salt potassium nonahydridorhenate(VII) (K + ) 2 [ReH 9 ] 2− is stable.
Stability and other properties can be predicted using energy calculations and computational chemistry .
"[Using] the Born–Haber cycle to estimate ... the heat of formation ... can be used to determine whether a hypothetical compound is stable." However, "a negative formation enthalpy does not automatically imply the existence of a hypothetical compound." The method predicts that NaCl is stable but NeCl is not. It predicted XePtF 6 based on the stability of O 2 PtF 6 . [ 2 ] | https://en.wikipedia.org/wiki/Hypothetical_chemical_compound |
In biochemistry , a hypothetical protein is a protein whose existence has been predicted , but for which there is a lack of experimental evidence that it is expressed in vivo . Sequencing of several genomes has resulted in numerous predicted open reading frames to which functions cannot be readily assigned. These proteins, either orphan or conserved hypothetical proteins, make up an estimated 20% to 40% of proteins encoded in each newly sequenced genome. The real evidences for the hypothetical protein functioning in the metabolism of the organism can be predicted by comparing its sequence or structure homology by considering the conserved domain analysis. [ 1 ] Even when there is enough evidence that the product of the gene is expressed, by techniques such as microarray and mass spectrometry , it is difficult to assign a function to it given its lack of identity to protein sequences with annotated biochemical function. Nowadays, most protein sequences are inferred from computational analysis of genomic DNA sequence . Hypothetical proteins are created by gene prediction software during genome analysis. When the bioinformatic tool used for the gene identification finds a large open reading frame without a characterised homologue in the protein database , it returns "hypothetical protein" as an annotation remark.
The function of a hypothetical protein can be predicted by domain homology searches with various confidence levels. [ 2 ] Conserved domains are available in the hypothetical proteins which need to be compared with the known family domains by which hypothetical protein could be classified into particular protein families even though they have not been in vivo investigated. The function of hypothetical protein could also be predicted by homology modelling, in which hypothetical protein has to align with known protein sequence whose three dimensional structure is known and by modelling method if structure predicted then the capability of hypothetical protein to function could be ascertained computationally. [ 2 ] [ 3 ] [ 4 ] Further, approaches to annotate function to hypothetical proteins include determination of 3-dimensional structure of these proteins by structural genomics initiatives, understanding the nature and mode of prosthetic group/metal ion binding, fold similarity with other proteins of known functions and annotating possible catalytic site and regulatory site. [ 5 ] Structure prediction with biochemical function assessment by screening for various substrate is another promising approach to annotate function. [ 2 ]
This protein -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypothetical_protein |
In classical logic , a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises . Ancient references point to the works of Theophrastus and Eudemus for the first investigation of this kind of syllogisms. [ 1 ] [ 2 ]
Hypothetical syllogisms come in two types: mixed and pure. A mixed hypothetical syllogism has two premises: one conditional statement and one statement that either affirms or denies the antecedent or consequent of that conditional statement. For example,
In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent. The second premise "affirms" the antecedent. The conclusion, that the consequent must be true, is deductively valid .
A mixed hypothetical syllogism has four possible forms, two of which are valid, while the other two are invalid. A valid mixed hypothetical syllogism either affirms the antecedent ( modus ponens ) or denies the consequent ( modus tollens ). An invalid hypothetical syllogism either affirms the consequent (fallacy of the converse ) or denies the antecedent (fallacy of the inverse ).
A pure hypothetical syllogism is a syllogism in which both premises and the conclusion are all conditional statements . The antecedent of one premise must match the consequent of the other for the conditional to be valid. Consequently, one of the conditionals contains the remained term as antecedent and the other conditional contains the removed term as consequent.
An example in English:
In propositional logic , hypothetical syllogism is the name of a valid rule of inference (often abbreviated HS and sometimes also called the chain argument , chain rule , or the principle of transitivity of implication ). The rule may be stated:
In other words, whenever instances of " P → Q {\displaystyle P\to Q} ", and " Q → R {\displaystyle Q\to R} " appear on lines of a proof , " P → R {\displaystyle P\to R} " can be placed on a subsequent line.
The rule of hypothetical syllogism holds in classical logic , intuitionistic logic , most systems of relevance logic , and many other systems of logic. However, it does not hold in all logics, including, for example, non-monotonic logic , probabilistic logic and default logic . The reason for this is that these logics describe defeasible reasoning , and conditionals that appear in real-world contexts typically allow for exceptions, default assumptions, ceteris paribus conditions, or just simple uncertainty.
An example, derived from Ernest W. Adams, [ 3 ]
Clearly, (3) does not follow from (1) and (2). (1) is true by default, but fails to hold in the exceptional circumstances of Smith dying. In practice, real-world conditionals always tend to involve default assumptions or contexts, and it may be infeasible or even impossible to specify all the exceptional circumstances in which they might fail to be true. For similar reasons, the rule of hypothetical syllogism does not hold for counterfactual conditionals .
The hypothetical syllogism inference rule may be written in sequent notation, which amounts to a specialization of the cut rule:
where ⊢ {\displaystyle \vdash } is a metalogical symbol and A ⊢ B {\displaystyle A\vdash B} meaning that B {\displaystyle B} is a syntactic consequence of A {\displaystyle A} in some logical system ;
and expressed as a truth-functional tautology or theorem of propositional logic :
where P {\displaystyle P} , Q {\displaystyle Q} , and R {\displaystyle R} are propositions expressed in some formal system .
An alternative form of hypothetical syllogism, more useful for classical propositional calculus systems with implication and negation (i.e. without the conjunction symbol), is the following:
Yet another form is:
An example of the proofs of these theorems in such systems is given below. We use two of the three axioms used in one of the popular systems described by Jan Łukasiewicz .
The proofs relies on two out of the three axioms of this system:
The proof of the (HS1) is as follows:
The proof of the (HS2) is given here .
Whenever we have two theorems of the form T 1 = ( Q → R ) {\displaystyle T_{1}=(Q\to R)} and T 2 = ( P → Q ) {\displaystyle T_{2}=(P\to Q)} , we can prove ( P → R ) {\displaystyle (P\to R)} by the following steps: | https://en.wikipedia.org/wiki/Hypothetical_syllogism |
Several forms of biochemistry are agreed to be scientifically viable but are not proven to exist at this time. [ 2 ] The kinds of living organisms currently known on Earth all use carbon compounds for basic structural and metabolic functions, water as a solvent , and DNA or RNA to define and control their form. If life exists on other planets or moons it may be chemically similar, though it is also possible that there are organisms with quite different chemistries [ 3 ] – for instance, involving other classes of carbon compounds, compounds of another element, or another solvent in place of water.
The possibility of life-forms being based on "alternative" biochemistries is the topic of an ongoing scientific discussion, informed by what is known about extraterrestrial environments and about the chemical behaviour of various elements and compounds. It is of interest in synthetic biology and is also a common subject in science fiction .
The element silicon has been much discussed as a hypothetical alternative to carbon. Silicon is in the same group as carbon on the periodic table and, like carbon, it is tetravalent . Hypothetical alternatives to water include ammonia , which, like water, is a polar molecule, and cosmically abundant; and non-polar hydrocarbon solvents such as methane and ethane , which are known to exist in liquid form on the surface of Titan .
In comparison, Hachimoji DNA changes the base pairs instead of the backbone. These new base pairs are P ( 2-Aminoimidazo[1,2a][1,3,5]triazin-4(1 H )-one ), Z ( 6-Amino-5-nitropyridin-2-one ), B ( Isoguanine ), and S (rS = Isocytosine for RNA, dS = 1-Methylcytosine for DNA). [ 6 ] [ 7 ]
A shadow biosphere is a hypothetical microbial biosphere of Earth that uses radically different biochemical and molecular processes than currently known life. [ 11 ] [ 12 ] Although life on Earth is relatively well-studied, the shadow biosphere may still remain unnoticed because the exploration of the microbial world targets primarily the biochemistry of the macro-organisms.
Perhaps the least unusual alternative biochemistry would be one with differing chirality of its biomolecules. In known Earth-based life, amino acids are almost universally of the L form and sugars are of the D form. Molecules using D amino acids or L sugars may be possible; molecules of such a chirality, however, would be incompatible with organisms using the opposing chirality molecules. Amino acids whose chirality is opposite to the norm are found on Earth, and these substances are generally thought to result from decay of organisms of normal chirality. However, physicist Paul Davies speculates that some of them might be products of "anti-chiral" life. [ 13 ]
It is questionable, however, whether such a biochemistry would be truly alien. Although it would certainly be an alternative stereochemistry , molecules that are overwhelmingly found in one enantiomer throughout the vast majority of organisms can nonetheless often be found in another enantiomer in different (often basal ) organisms such as in comparisons between members of Archaea and other domains , [ citation needed ] making it an open topic whether an alternative stereochemistry is truly novel.
On Earth, all known living things have a carbon-based structure and system. Scientists have speculated about the advantages and disadvantages of using elements other than carbon to form the molecular structures necessary for life, but no one has proposed a theory employing such atoms to form all the necessary structures. However, as Carl Sagan argued, it is very difficult to be certain whether a statement that applies to all life on Earth will turn out to apply to all life throughout the universe. [ 14 ] Sagan used the term " carbon chauvinism " for such an assumption. [ 15 ] He regarded silicon and germanium as conceivable alternatives to carbon [ 15 ] (other plausible elements include but are not limited to palladium and titanium ); but, on the other hand, he noted that carbon does seem more chemically versatile and is more abundant in the cosmos. [ 16 ] Norman Horowitz devised the experiments to determine whether life might exist on Mars that were carried out by the Viking Lander of 1976 , the first U.S. mission to successfully land a probe on the surface of Mars. Horowitz argued that the great versatility of the carbon atom makes it the element most likely to provide solutions, even exotic solutions, to the problems of survival on other planets. [ 17 ] He considered that there was only a remote possibility that non-carbon life forms could exist with genetic information systems capable of self-replication and the ability to evolve and adapt.
The silicon atom has been much discussed as the basis for an alternative biochemical system, because silicon has many chemical similarities to carbon and is in the same group of the periodic table . Like carbon, silicon can create molecules that are sufficiently large to carry biological information. [ 18 ]
However, silicon has several drawbacks as a carbon alternative. Carbon is ten times more cosmically abundant than silicon, and its chemistry appears naturally more complex. [ 19 ] By 1998, astronomers had identified 84 carbon-containing molecules in the interstellar medium , but only 8 containing silicon, of which half also included carbon. [ 20 ] Even though Earth and other terrestrial planets are exceptionally silicon-rich and carbon-poor (silicon is roughly 925 times more abundant in Earth's crust than carbon), terrestrial life bases itself on carbon. It may avoid silicon because silicon compounds are less varied, unstable in the presence of water , or block the flow of heat. [ 19 ]
Relative to carbon, silicon has a much larger atomic radius , and forms much weaker covalent bonds to atoms — except oxygen and fluorine , with which it forms very strong bonds. [ 18 ] Almost no multiple bonds to silicon are stable, although silicon does exhibit varied coordination number . [ 21 ] Silanes , silicon analogues to the alkanes , react rapidly with water, and long-chain silanes spontaneously decompose. [ 22 ] Consequently, most terrestrial silicon is "locked up" in silica , and not a wide variety of biogenic precursors. [ 21 ]
Silicones , which alternate between silicon and oxygen atoms, are much more stable than silanes, and may even be more stable than the equivalent hydrocarbons in sulfuric acid-rich extraterrestrial environments. [ 22 ] Alternatively, the weak bonds in silicon compounds may help maintain a rapid pace of life at cryogenic temperatures. Polysilanols, the silicon homologues to sugars , are among the few compounds soluble in liquid nitrogen . [ 23 ] [ unreliable source? ] [ 21 ]
All known silicon macromolecules are artificial polymers, and so "monotonous compared with the combinatorial universe of organic macromolecules". [ 18 ] [ 21 ] Even so, some Earth life uses biogenic silica : diatoms ' silicate skeletons . A. G. Cairns-Smith hypothesized that silicate minerals in water played a crucial role in abiogenesis , in that biogenic carbon compounds formed around their crystal structures . [ 24 ] [ 25 ] Although not observed in nature, carbon–silicon bonds have been added to biochemistry under directed evolution (artificial selection): a cytochrome c protein from Rhodothermus marinus has been engineered to catalyze new carbon–silicon bonds between hydrosilanes and diazo compounds. [ 26 ]
While arsenic , which is chemically similar to phosphorus , is poisonous for most life forms on Earth, it is incorporated into the biochemistry of some organisms. [ 29 ] Some marine algae incorporate arsenic into complex organic molecules such as arsenosugars and arsenobetaines . Fungi and bacteria can produce volatile methylated arsenic compounds. Arsenate reduction and arsenite oxidation have been observed in microbes ( Chrysiogenes arsenatis ). [ 30 ] Additionally, some prokaryotes can use arsenate as a terminal electron acceptor during anaerobic growth and some can utilize arsenite as an electron donor to generate energy.
It has been speculated that the earliest life forms on Earth may have used arsenic biochemistry in place of phosphorus in the structure of their DNA. [ 31 ] A common objection to this scenario is that arsenate esters are so much less stable to hydrolysis than corresponding phosphate esters that arsenic is poorly suited for this function. [ 32 ]
The authors of a 2010 geomicrobiology study, supported in part by NASA, have postulated that a bacterium, named GFAJ-1 , collected in the sediments of Mono Lake in eastern California , can employ such 'arsenic DNA' when cultured without phosphorus. [ 33 ] [ 34 ] They proposed that the bacterium may employ high levels of poly-β-hydroxybutyrate or other means to reduce the effective concentration of water and stabilize its arsenate esters. [ 34 ] This claim was heavily criticized almost immediately after publication for the perceived lack of appropriate controls. [ 35 ] [ 36 ] Science writer Carl Zimmer contacted several scientists for an assessment: "I reached out to a dozen experts ... Almost unanimously, they think the NASA scientists have failed to make their case". [ 37 ] Other authors were unable to reproduce their results and showed that the study had issues with phosphate contamination, suggesting that the low amounts present could sustain extremophile lifeforms. [ 38 ] Alternatively, it was suggested that GFAJ-1 cells grow by recycling phosphate from degraded ribosomes, rather than by replacing it with arsenate. [ 39 ]
In addition to carbon compounds, all currently known terrestrial life also requires water as a solvent. This has led to discussions about whether water is the only liquid capable of filling that role. The idea that an extraterrestrial life-form might be based on a solvent other than water has been taken seriously in recent scientific literature by the biochemist Steven Benner , [ 40 ] and by the astrobiological committee chaired by John A. Baross. [ 41 ] Solvents discussed by the Baross committee include ammonia , [ 42 ] sulfuric acid , [ 43 ] formamide , [ 44 ] hydrocarbons, [ 44 ] and (at temperatures much lower than Earth's) liquid nitrogen , or hydrogen in the form of a supercritical fluid . [ 45 ]
Water as a solvent limits the forms biochemistry can take. For example, Steven Benner, proposes the polyelectrolyte theory of the gene that claims that for a genetic biopolymer such as DNA to function in water, it requires repeated ionic charges. [ 46 ] If water is not required for life, these limits on genetic biopolymers are removed.
Carl Sagan once described himself as both a carbon chauvinist and a water chauvinist; [ 47 ] however, on another occasion he said that he was a carbon chauvinist but "not that much of a water chauvinist". [ 48 ] He speculated on hydrocarbons, [ 48 ] : 11 hydrofluoric acid , [ 49 ] and ammonia [ 48 ] [ 49 ] as possible alternatives to water.
Some of the properties of water that are important for life processes include:
Water as a compound is cosmically abundant, although much of it is in the form of vapor or ice. Subsurface liquid water is considered likely or possible on several of the outer moons: Enceladus (where geysers have been observed), Europa , Titan , and Ganymede . Earth and Titan are the only worlds currently known to have stable bodies of liquid on their surfaces.
Not all properties of water are necessarily advantageous for life, however. [ 50 ] For instance, water ice has a high albedo , [ 50 ] meaning that it reflects a significant quantity of light and heat from the Sun. During ice ages , as reflective ice builds up over the surface of the water, the effects of global cooling are increased. [ 50 ]
There are some properties that make certain compounds and elements much more favorable than others as solvents in a successful biosphere. The solvent must be able to exist in liquid equilibrium over a range of temperatures the planetary object would normally encounter. Because boiling points vary with the pressure, the question tends not to be does the prospective solvent remain liquid, but at what pressure . For example, hydrogen cyanide has a narrow liquid-phase temperature range at 1 atmosphere, but in an atmosphere with the pressure of Venus , with 92 bars (91 atm) of pressure, it can indeed exist in liquid form over a wide temperature range.
The ammonia molecule (NH 3 ), like the water molecule, is abundant in the universe, being a compound of hydrogen (the simplest and most common element) with another very common element, nitrogen. [ 51 ] The possible role of liquid ammonia as an alternative solvent for life is an idea that goes back at least to 1954, when J. B. S. Haldane raised the topic at a symposium about life's origin. [ 52 ]
Numerous chemical reactions are possible in an ammonia solution, and liquid ammonia has chemical similarities with water. [ 51 ] [ 53 ] Ammonia can dissolve most organic molecules at least as well as water does and, in addition, it is capable of dissolving many elemental metals. Haldane made the point that various common water-related organic compounds have ammonia-related analogs; for instance the ammonia-related amine group (−NH 2 ) is analogous to the water-related hydroxyl group (−OH). [ 53 ]
Ammonia, like water, can either accept or donate an H + ion. When ammonia accepts an H + , it forms the ammonium cation (NH 4 + ), analogous to hydronium (H 3 O + ). When it donates an H + ion, it forms the amide anion (NH 2 − ), analogous to the hydroxide anion (OH − ). [ 42 ] Compared to water, however, ammonia is more inclined to accept an H + ion, and less inclined to donate one; it is a stronger nucleophile . [ 42 ] Ammonia added to water functions as an Arrhenius base : it increases the concentration of the anion hydroxide. Conversely, using a solvent system definition of acidity and basicity, water added to liquid ammonia functions as an acid, because it increases the concentration of the cation ammonium. [ 53 ] The carbonyl group (C=O), which is much used in terrestrial biochemistry, would not be stable in ammonia solution, but the analogous imine group (C=NH) could be used instead. [ 42 ]
However, ammonia has some problems as a basis for life. The hydrogen bonds between ammonia molecules are weaker than those in water, causing ammonia's heat of vaporization to be half that of water, its surface tension to be a third, and reducing its ability to concentrate non-polar molecules through a hydrophobic effect. Gerald Feinberg and Robert Shapiro have questioned whether ammonia could hold prebiotic molecules together well enough to allow the emergence of a self-reproducing system. [ 54 ] Ammonia is also flammable in oxygen and could not exist sustainably in an environment suitable for aerobic metabolism . [ 55 ]
A biosphere based on ammonia would likely exist at temperatures or air pressures that are extremely unusual in relation to life on Earth. Life on Earth usually exists between the melting point and boiling point of water, at a pressure designated as normal pressure , between 0 and 100 °C (273 and 373 K ). When also held to normal pressure, ammonia's melting and boiling points are −78 °C (195 K) and −33 °C (240 K) respectively. Because chemical reactions generally proceed more slowly at lower temperatures, ammonia-based life existing in this set of conditions might metabolize more slowly and evolve more slowly than life on Earth. [ 55 ] On the other hand, lower temperatures could also enable living systems to use chemical species that would be too unstable at Earth temperatures to be useful. [ 51 ]
A set of conditions where ammonia is liquid at Earth-like temperatures would involve it being at a much higher pressure. For example, at 60 atm ammonia melts at −77 °C (196 K) and boils at 98 °C (371 K). [ 42 ]
Ammonia and ammonia–water mixtures remain liquid at temperatures far below the freezing point of pure water, so such biochemistries might be well suited to planets and moons orbiting outside the water-based habitability zone . Such conditions could exist, for example, under the surface of Saturn 's largest moon Titan . [ 56 ]
Methane (CH 4 ) is a simple hydrocarbon: that is, a compound of two of the most common elements in the cosmos: hydrogen and carbon. It has a cosmic abundance comparable with ammonia. [ 51 ] Hydrocarbons could act as a solvent over a wide range of temperatures, but would lack polarity . Isaac Asimov, the biochemist and science fiction writer, suggested in 1981 that poly- lipids could form a substitute for proteins in a non-polar solvent such as methane. [ 51 ] Lakes composed of a mixture of hydrocarbons, including methane and ethane , have been detected on the surface of Titan by the Cassini spacecraft .
There is debate about the effectiveness of methane and other hydrocarbons as a solvent for life compared to water or ammonia. [ 57 ] [ 58 ] [ 59 ] Water is a stronger solvent than the hydrocarbons, enabling easier transport of substances in a cell. [ 60 ] However, water is also more chemically reactive and can break down large organic molecules through hydrolysis. [ 57 ] A life-form whose solvent was a hydrocarbon would not face the threat of its biomolecules being destroyed in this way. [ 57 ] Also, the water molecule's tendency to form strong hydrogen bonds can interfere with internal hydrogen bonding in complex organic molecules. [ 50 ] Life with a hydrocarbon solvent could make more use of hydrogen bonds within its biomolecules. [ 57 ] Moreover, the strength of hydrogen bonds within biomolecules would be appropriate to a low-temperature biochemistry. [ 57 ]
Astrobiologist Chris McKay has argued, on thermodynamic grounds, that if life does exist on Titan's surface, using hydrocarbons as a solvent, it is likely also to use the more complex hydrocarbons as an energy source by reacting them with hydrogen, reducing ethane and acetylene to methane. [ 61 ] Possible evidence for this form of life on Titan was identified in 2010 by Darrell Strobel of Johns Hopkins University ; a greater abundance of molecular hydrogen in the upper atmospheric layers of Titan compared to the lower layers, arguing for a downward diffusion at a rate of roughly 10 25 molecules per second and disappearance of hydrogen near Titan's surface. As Strobel noted, his findings were in line with the effects Chris McKay had predicted if methanogenic life-forms were present. [ 60 ] [ 61 ] [ 62 ] The same year, another study showed low levels of acetylene on Titan's surface, which were interpreted by Chris McKay as consistent with the hypothesis of organisms reducing acetylene to methane. [ 60 ] While restating the biological hypothesis, McKay cautioned that other explanations for the hydrogen and acetylene findings are to be considered more likely: the possibilities of yet unidentified physical or chemical processes (e.g. a non-living surface catalyst enabling acetylene to react with hydrogen), or flaws in the current models of material flow. [ 63 ] He noted that even a non-biological catalyst effective at 95 K would in itself be a startling discovery. [ 63 ]
A hypothetical cell membrane termed an azotosome, capable of functioning in liquid methane in Titan conditions was computer-modeled in an article published in February 2015. Composed of acrylonitrile , a small molecule containing carbon, hydrogen, and nitrogen, it is predicted to have stability and flexibility in liquid methane comparable to that of a phospholipid bilayer (the type of cell membrane possessed by all life on Earth) in liquid water. [ 64 ] [ 65 ] An analysis of data obtained using the Atacama Large Millimeter / submillimeter Array (ALMA), completed in 2017, confirmed substantial amounts of acrylonitrile in Titan's atmosphere. [ 66 ] [ 67 ] Later studies questioned whether acrylonitrile would be able to self-assemble into azotosomes. [ 68 ]
Hydrogen fluoride (HF), like water, is a polar molecule, and due to its polarity it can dissolve many ionic compounds. At atmospheric pressure , its melting point is 189.15 K (−84.00 °C), and its boiling point is 292.69 K (19.54 °C); the difference between the two is a little more than 100 K. HF also makes hydrogen bonds with its neighbor molecules, as do water and ammonia. It has been considered as a possible solvent for life by scientists such as Peter Sneath [ 69 ] and Carl Sagan. [ 49 ]
HF is dangerous to the systems of molecules that Earth-life is made of, but certain other organic compounds, such as paraffin waxes , are stable with it. [ 49 ] Like water and ammonia, liquid hydrogen fluoride supports an acid–base chemistry. Using a solvent system definition of acidity and basicity, nitric acid functions as a base when it is added to liquid HF. [ 70 ]
However, hydrogen fluoride is cosmically rare, unlike water, ammonia, and methane. [ 71 ]
Hydrogen sulfide is the closest chemical analog to water , [ 72 ] but is less polar and is a weaker inorganic solvent. [ 73 ] Hydrogen sulfide is quite plentiful on Jupiter's moon Io and may be in liquid form a short distance below the surface; astrobiologist Dirk Schulze-Makuch has suggested it as a possible solvent for life there. [ 74 ] On a planet with hydrogen sulfide oceans, the source of the hydrogen sulfide could come from volcanoes, in which case it could be mixed in with a bit of hydrogen fluoride , which could help dissolve minerals. Hydrogen sulfide life might use a mixture of carbon monoxide and carbon dioxide as their carbon source. They might produce and live on sulfur monoxide , which is analogous to oxygen (O 2 ). Hydrogen sulfide, like hydrogen cyanide and ammonia, suffers from the small temperature range where it is liquid, though that, like that of hydrogen cyanide and ammonia, increases with increasing pressure.
Silicon dioxide , also known as silica and quartz, is very abundant in the universe and has a large temperature range where it is liquid. However, its melting point is 1,600 to 1,725 °C (2,912 to 3,137 °F), so it would be impossible to make organic compounds in that temperature, because all of them would decompose. Silicates are similar to silicon dioxide and some have lower melting points than silica. Feinberg and Shapiro have suggested that molten silicate rock could serve as a liquid medium for organisms with a chemistry based on silicon, oxygen, and other elements such as aluminium . [ 75 ]
Other solvents sometimes proposed:
Sulfuric acid in liquid form is strongly polar. It remains liquid at higher temperatures than water, its liquid range being 10 °C to 337 °C at a pressure of 1 atm, although above 300 °C it slowly decomposes. Sulfuric acid is known to be abundant in the clouds of Venus , in the form of aerosol droplets. In a biochemistry that used sulfuric acid as a solvent, the alkene group (C=C), with two carbon atoms joined by a double bond, could function analogously to the carbonyl group (C=O) in water-based biochemistry. [ 43 ]
A proposal has been made that life on Mars may exist and be using a mixture of water and hydrogen peroxide as its solvent. [ 79 ] A 61.2% (by mass) mix of water and hydrogen peroxide has a freezing point of −56.5 °C and tends to super-cool rather than crystallize. It is also hygroscopic , an advantage in a water-scarce environment. [ 80 ] [ 81 ]
Supercritical carbon dioxide has been proposed as a candidate for alternative biochemistry due to its ability to selectively dissolve organic compounds and assist the functioning of enzymes and because "super-Earth"- or "super-Venus"-type planets with dense high-pressure atmospheres may be common. [ 76 ]
Physicists have noted that, although photosynthesis on Earth generally involves green plants, a variety of other-colored plants could also support photosynthesis, essential for most life on Earth, and that other colors might be preferred in places that receive a different mix of stellar radiation than Earth. [ 82 ] [ 83 ] These studies indicate that blue plants would be unlikely; however yellow or red plants may be relatively common. [ 83 ]
Many Earth plants and animals undergo major biochemical changes during their life cycles as a response to changing environmental conditions, for example, by having a spore or hibernation state that can be sustained for years or even millennia between more active life stages. [ 84 ] Thus, it would be biochemically possible to sustain life in environments that are only periodically consistent with life as we know it.
For example, frogs in cold climates can survive for extended periods of time with most of their body water in a frozen state, [ 84 ] whereas desert frogs in Australia can become inactive and dehydrate in dry periods, losing up to 75% of their fluids, yet return to life by rapidly rehydrating in wet periods. [ 85 ] Either type of frog would appear biochemically inactive (i.e. not living) during dormant periods to anyone lacking a sensitive means of detecting low levels of metabolism.
The genetic code may have evolved during the transition from the RNA world to a protein world. [ 86 ] The Alanine World Hypothesis postulates that the evolution of the genetic code (the so-called GC phase [ 87 ] ) started with only four basic amino acids : alanine , glycine , proline and ornithine (now arginine ). [ 88 ] The evolution of the genetic code ended with 20 proteinogenic amino acids . From a chemical point of view, most of them are Alanine-derivatives particularly suitable for the construction of α-helices and β-sheets – basic secondary structural elements of modern proteins. Direct evidence of this is an experimental procedure in molecular biology known as alanine scanning .
A hypothetical "Proline World" would create a possible alternative life with the genetic code based on the proline chemical scaffold as the protein backbone . Similarly, a "Glycine World" and "Ornithine World" are also conceivable, but nature has chosen none of them. [ 89 ] Evolution of life with Proline, Glycine, or Ornithine as the basic structure for protein-like polymers ( foldamers ) would lead to parallel biological worlds. They would have morphologically radically different body plans and genetics from the living organisms of the known biosphere . [ 90 ]
In 2007, Vadim N. Tsytovich and colleagues proposed that lifelike behaviors could be exhibited by dust particles suspended in a plasma , under conditions that might exist in space. [ 91 ] [ 92 ] Computer models showed that, when the dust became charged, the particles could self-organize into microscopic helical structures, and the authors offer "a rough sketch of a possible model of...helical grain structure reproduction".
In 2020, Luis A. Anchordoqu and Eugene M. Chudnovsky of the City University of New York hypothesized that cosmic necklace-based life composed of magnetic monopoles connected by cosmic strings could evolve inside stars. [ 8 ] This would be achieved by a stretching of cosmic strings due to the star's intense gravity, thus allowing it to take on more complex forms and potentially form structures similar to the RNA and DNA structures found within carbon-based life. As such, it is theoretically possible that such beings could eventually become intelligent and construct a civilization using the power generated by the star's nuclear fusion. Because such use would use up part of the star's energy output, the luminosity would also fall. For this reason, it is thought that such life might exist inside stars observed to be cooling faster or dimmer than current cosmological models predict.
Frank Drake suggested in 1973 that intelligent life could inhabit neutron stars . [ 93 ] Physical models in 1973 implied that Drake's creatures would be microscopic. [ citation needed ]
Scientists who have considered possible alternatives to carbon-water biochemistry include: | https://en.wikipedia.org/wiki/Hypothetical_types_of_biochemistry |
Hypothiocyanite is the anion [OSCN] − and the conjugate base of hypothiocyanous acid ( HOSCN ). It is an organic compound part of the thiocyanates as it contains the functional group SCN. It is formed when an oxygen is singly bonded to the thiocyanate group. Hypothiocyanous acid is a fairly weak acid; its acid dissociation constant (p K a ) is 5.3.
Hypothiocyanite is formed by peroxidase [ 1 ] catalysis of hydrogen peroxide and thiocyanate:
Hypothiocyanite occurs naturally in the antimicrobial immune system of the human respiratory tract [ 2 ] in a redox reaction catalyzed by the enzyme lactoperoxidase . [ 3 ] It has been researched extensively for its capabilities as an alternative antibiotic as it is harmless to human body cells while being cytotoxic to bacteria. [ 4 ] The exact processes for making hypothiocyanite have been patented as such an effective antimicrobial has many commercial applications. [ 5 ]
Lactoperoxidase-catalysed reactions yield short-lived intermediary oxidation products of SCN − , providing antibacterial activity. [ 6 ]
The major intermediary oxidation product is hypothiocyanite OSCN − , which is produced in an amount of about 1 mole per mole of hydrogen peroxide. At the pH optimum of 5.3, the OSCN − is in equilibrium with HOSCN. The uncharged HOSCN is considered to be the greater bactericidal of the two forms. [ 7 ] At pH 7, it was evaluated that HOSCN represents 2% compare to OSCN − 98%. [ 8 ]
The action of OSCN − against bacteria is reported to be caused by sulfhydryl (SH) oxidation. [ 9 ]
The oxidation of -SH groups in the bacterial cytoplasmic membrane results in loss of the ability to transport glucose and also in leaking of potassium ions, amino acids and peptide.
OSCN − has also been identified as an antimicrobial agent in milk, saliva, [ 10 ] tears, and mucus.
OSCN − is considered as a safe product as it is not mutagenic. [ 11 ]
Initially, this particular lactoperoxidase-catalyzed compound was originally discovered while viewing the specific environment of cystic fibrosis patients' weakened respiratory immune system against bacterial infection. [ 12 ]
Symptoms of cystic fibrosis include an inability to secrete sufficient quantities of SCN − which results in a shortage of necessary hypothiocyanite, resulting in increasing mucous viscosity, inflammation and bacterial infection in the respiratory tract.
Lactoferrin with hypothiocyanite has been granted orphan drug status by the EMEA [ 13 ] and the FDA . [ 14 ]
Naturally, the discovery correlated with studies exploring different methods seeking to further gain alternative antibiotics, understanding that most older antibiotics are decreasing in effectiveness against bacteria with antibiotic resistance. [ medical citation needed ]
OSCN − , which is not an antibiotic, has proved efficacy on superbugs including MRSA reference strains, BCC, Mucoid PA [ medical citation needed ]
Schema of LPO/SCN − /H 2 O 2 in human lung :
Non exhaustive list of microorganisms.
Bacteria (Gram-positive and -negative)
Viruses [ 15 ]
Yeasts and moulds | https://en.wikipedia.org/wiki/Hypothiocyanite |
A hypotonic-hyporesponsive episode (HHE) is defined as sudden onset of poor muscle tone , reduced consciousness , and pale or bluish skin occurring within 48 hours after vaccination , most commonly pertussis vaccination . [ 2 ] An HHE is estimated to occur after 1 in 4,762 to 1 in 1,408 doses of whole cell pertussis vaccine, and after 1 in 14,286 to 1 in 2,778 doses of acellular pertussis vaccine. [ 3 ]
This medical symptom article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypotonic-hyporesponsive_episode |
Hypoxemia (also spelled hypoxaemia ) is an abnormally low level of oxygen in the blood . [ 1 ] [ 2 ] More specifically, it is oxygen deficiency in arterial blood. [ 3 ] Hypoxemia is usually caused by pulmonary disease. Sometimes the concentration of oxygen in the air is decreased leading to hypoxemia.
Hypoxemia refers to the low level of oxygen in arterial blood. Tissue hypoxia refers to low levels of oxygen in the tissues of the body and the term hypoxia is a general term for low levels of oxygen. [ 2 ] Hypoxemia is usually caused by pulmonary disease whereas tissue oxygenation requires additionally adequate circulation of blood and perfusion of tissue to meet metabolic demands. [ 4 ]
Hypoxemia is usually defined in terms of reduced partial pressure of oxygen (mm Hg) in arterial blood, but also in terms of reduced content of oxygen (ml oxygen per dl blood) or percentage saturation of hemoglobin (the oxygen-binding protein within red blood cells ) with oxygen, which is either found singly or in combination. [ 2 ] [ 5 ]
While there is general agreement that an arterial blood gas measurement which shows that the partial pressure of oxygen is lower than normal constitutes hypoxemia, [ 5 ] [ 6 ] [ 7 ] there is less agreement concerning whether the oxygen content of blood is relevant in determining hypoxemia. This definition would include oxygen carried by hemoglobin . The oxygen content of blood is thus sometimes viewed as a measure of tissue delivery rather than hypoxemia. [ 7 ]
Just as extreme hypoxia can be called anoxia, extreme hypoxemia can be called anoxemia.
In an acute context, hypoxemia can cause symptoms such as those in respiratory distress . These include breathlessness , an increased rate of breathing, use of the chest and abdominal muscles to breathe, and lip pursing . [ 8 ] : 642
Chronic hypoxemia may be compensated or uncompensated. The compensation may cause symptoms to be overlooked initially, however, further disease or a stress such as any increase in oxygen demand may finally unmask the existing hypoxemia. In a compensated state, blood vessels supplying less-ventilated areas of the lung may selectively contract , to redirect the blood to areas of the lungs which are better ventilated. However, in a chronic context, and if the lungs are not well ventilated generally, this mechanism can result in pulmonary hypertension , overloading the right ventricle of the heart and causing cor pulmonale and right sided heart failure . Polycythemia can also occur. [ 8 ] In children, chronic hypoxemia may manifest as delayed growth, neurological development and motor development and decreased sleep quality with frequent sleep arousals. [ 9 ]
Other symptoms of hypoxemia may include cyanosis , digital clubbing , and symptoms that may relate to the cause of the hypoxemia, including cough and hemoptysis . [ 8 ] : 642
Serious hypoxemia typically occurs when the partial pressure of oxygen in blood is less than 60 mmHg (8.0 kPa), the beginning of the steep portion of the oxygen–hemoglobin dissociation curve , where a small decrease in the partial pressure of oxygen results in a large decrease in the oxygen content of the blood. [ 6 ] [ 10 ] Severe hypoxia can lead to respiratory failure . [ 8 ]
Hypoxemia refers to insufficient oxygen in the blood. Thus any cause that influences the rate or volume of air entering the lungs ( ventilation ) or any cause that influences the transfer of air from the lungs to the blood may cause hypoxemia. As well as these respiratory causes, cardiovascular causes such as shunts may also result in hypoxemia.
Hypoxemia is caused by five categories of etiologies: hypoventilation , ventilation/perfusion mismatch , right-to-left shunt , diffusion impairment, and low PO 2 . Low PO 2 and hypoventilation are associated with a normal alveolar–arterial gradient (A-a gradient) whereas the other categories are associated with an increased A-a gradient. [ 11 ] : 229
If the alveolar ventilation is low, there will not be enough oxygen delivered to the alveoli for the body's use. This can cause hypoxemia even if the lungs are normal, as the cause is in the brainstem's control of ventilation or in the body's inability to breathe effectively.
Respiration is controlled by centers in the medulla , which influence the rate of breathing and the depth of each breath. This is influenced by the blood level of carbon dioxide, as determined by central and peripheral chemoreceptors located in the central nervous system and carotid and aortic bodies, respectively. Hypoxia occurs when the breathing center doesn't function correctly or when the signal is not appropriate:
A variety of conditions that physically limit airflow can lead to hypoxemia.
In conditions where the proportion of oxygen in the air is low, or when the partial pressure of oxygen has decreased, less oxygen is present in the alveoli of the lungs. The alveolar oxygen is transferred to hemoglobin , a carrier protein inside red blood cells , with an efficiency that decreases with the partial pressure of oxygen in the air.
This refers to a disruption in the ventilation/perfusion equilibrium. Oxygen entering the lungs typically diffuses across the alveolar-capillary membrane into blood. However this equilibration does not occur when the alveolus is insufficiently ventilated, and as a consequence the blood exiting that alveolus is relatively hypoxemic. When such blood is added to blood from well ventilated alveoli, the mix has a lower oxygen partial pressure than the alveolar air, and so the A-a difference develops. Examples of states that can cause a ventilation-perfusion mismatch include:
Shunting refers to blood that bypasses the pulmonary circulation, meaning that the blood does not receive oxygen from the alveoli. In general, a shunt may be within the heart or lungs, and cannot be corrected by administering oxygen alone. Shunting may occur in normal states:
Shunting may also occur in disease states:
Exercise-induced arterial hypoxemia occurs during exercise when a trained individual exhibits an arterial oxygen saturation below 93%. It occurs in fit, healthy individuals of varying ages and genders. [ 26 ] Adaptations due to training include an increased cardiac output from cardiac hypertrophy, improved venous return, and metabolic vasodilation of muscles, and an increased VO 2 max . There must be a corresponding increase in VCO 2 thus a necessity to clear the carbon dioxide to prevent a metabolic acidosis . Hypoxemia occurs in these individuals due to increased pulmonary blood flow causing:
Key to understanding whether the lung is involved in a particular case of hypoxemia is the difference between the alveolar and the arterial oxygen levels ; this A-a difference is often called the A-a gradient and is normally small. The arterial oxygen partial pressure is obtained directly from an arterial blood gas determination . The oxygen contained in the alveolar air can be calculated because it will be directly proportional to its fractional composition in air. Since the airways humidify (and so dilute) the inhaled air, the barometric pressure of the atmosphere is reduced by the vapor pressure of water.
The term hypoxemia was originally used to describe low blood oxygen occurring at high altitudes and was defined generally as defective oxygenation of the blood. [ 27 ]
In modern times there are a lot of tools to detects hypoxemia including smartwatches . In 2022 a research has shown smartwatches can detect short-time hypoxemia as well as standard medical devices. [ 28 ] [ 29 ] | https://en.wikipedia.org/wiki/Hypoxemia |
Hypoxia ( hypo : 'below', oxia : 'oxygenated') refers to low oxygen conditions. Hypoxia is problematic for air-breathing organisms, yet it is essential for many anaerobic organisms. Hypoxia applies to many situations, but usually refers to the atmosphere and natural waters. [ 3 ]
Atmospheric hypoxia occurs naturally at high altitudes. Total atmospheric pressure decreases as altitude increases, causing a lower partial pressure of oxygen, which is defined as hypobaric hypoxia. Oxygen remains at 20.9% of the total gas mixture, differing from hypoxic hypoxia , where the percentage of oxygen in the air (or blood) is decreased. This is common in the sealed burrows of some subterranean animals, such as blesmols . [ 4 ] Atmospheric hypoxia is also the basis of altitude training , which is a standard part of training for elite athletes. Several companies mimic hypoxia using normobaric artificial atmosphere .
An aquatic system lacking dissolved oxygen (0% saturation) is termed anaerobic, reducing , or anoxic .
In water, oxygen levels are approximately 7 ppm or 0.0007% in good quality water, but fluctuate. [ 5 ] Many organisms require hypoxic conditions. Oxygen is poisonous to anaerobic bacteria for example. [ 3 ]
Oxygen depletion is typically expressed as a percentage of the oxygen that would dissolve in the water at the prevailing temperature and salinity. A system with low concentration—in the range between 1 and 30% saturation—is called hypoxic or dysoxic . Most fish cannot live below 30% saturation since they rely on oxygen to derive energy from their nutrients. Hypoxia leads to impaired reproduction of remaining fish via endocrine disruption . [ 6 ] A "healthy" aquatic environment should seldom experience less than 80% saturation. The exaerobic zone is found at the boundary of anoxic and hypoxic zones.
Hypoxia can occur throughout the water column and also at high altitudes as well as near sediments on the bottom. It usually extends throughout 20–50% of the water column, but depends on the water depth and location of pycnoclines (rapid changes in water density with depth). It can occur in 10–80% of the water column. For example, in a 10-meter water column, it can reach up to 2 meters below the surface. In a 20-meter water column, it can extend up to 8 meters below the surface. [ 7 ]
Hypolimnetic oxygen depletion can lead to both summer and winter "kills". During summer stratification , inputs or organic matter and sedimentation of primary producers can increase rates of respiration in the hypolimnion . If oxygen depletion becomes extreme, aerobic organisms, like fish, may die, resulting in what is known as a "summer kill". [ 8 ] The same phenomena can occur in the winter, but for different reasons. During winter, ice and snow cover can attenuate light, and therefore reduce rates of photosynthesis. The freezing over of a lake also prevents air-water interactions that allow the exchange of oxygen. This creates a lack of oxygen while respiration continues. When the oxygen becomes badly depleted, anaerobic organisms can die, resulting in a "winter kill". [ 8 ]
Oxygen depletion can result from a number of natural factors, but is most often a concern as a consequence of pollution and eutrophication in which plant nutrients enter a river, lake, or ocean, and phytoplankton blooms are encouraged. While phytoplankton, through photosynthesis , will raise DO saturation during daylight hours, the dense population of a bloom reduces DO saturation during the night by respiration . When phytoplankton cells die, they sink towards the bottom and are decomposed by bacteria , a process that further reduces DO in the water column. If oxygen depletion progresses to hypoxia, fish kills can occur and invertebrates like worms and clams on the bottom may be killed as well.
Hypoxia may also occur in the absence of pollutants. In estuaries, for example, because freshwater flowing from a river into the sea is less dense than salt water, stratification in the water column can result. Vertical mixing between the water bodies is therefore reduced, restricting the supply of oxygen from the surface waters to the more saline bottom waters. The oxygen concentration in the bottom layer may then become low enough for hypoxia to occur. Areas particularly prone to this include shallow waters of semi-enclosed water bodies such as the Waddenzee or the Gulf of Mexico , where land run-off is substantial. In these areas a so-called " dead zone " can be created. Low dissolved oxygen conditions are often seasonal, as is the case in Hood Canal and areas of Puget Sound , in Washington State. [ 9 ] The World Resources Institute has identified 375 hypoxic coastal zones around the world, concentrated in coastal areas in Western Europe, the Eastern and Southern coasts of the US, and East Asia, particularly in Japan. [ 10 ]
Hypoxia may also be the explanation for periodic phenomena such as the Mobile Bay jubilee , where aquatic life suddenly rushes to the shallows, perhaps trying to escape oxygen-depleted water. Recent widespread shellfish kills near the coasts of Oregon and Washington are also blamed on cyclic dead zone ecology. [ 11 ]
Phytoplankton are mostly made up of lignin and cellulose, which are broken down by oxidative mechanism, which consume oxygen. [ 12 ]
The breakdown of phytoplankton in the environment depends on the presence of oxygen, and once oxygen is no longer in the bodies of water, ligninperoxidases cannot continue to break down the lignin. When oxygen is not present in the water, the time required for breakdown of phytoplankton changes from 10.7 days to a total of 160 days.
The rate of phytoplankton breakdown can be represented using this equation:
G ( t ) = G ( 0 ) e − k t {\displaystyle G(t)=G(0)e^{-kt}}
In this equation, G(t) is the amount of particulate organic carbon (POC) overall at a given time, t. G(0) is the concentration of POC before breakdown takes place. k is a rate constant in year-1, and t is time in years. For most POC of phytoplankton, the k is around 12.8 years-1, or about 28 days for nearly 96% of carbon to be broken down in these systems. Whereas for anoxic systems, POC breakdown takes 125 days, over four times longer. [ 15 ] It takes approximately 1 mg of oxygen to break down 1 mg of POC in the environment, and therefore, hypoxia takes place quickly as oxygen is used up quickly to digest POC. About 9% of POC in phytoplankton can be broken down in a single day at 18 °C. Therefore, it takes about eleven days to completely break down phytoplankton. [ 16 ]
After POC is broken down, this particulate matter can be turned into other dissolved carbon, such as carbon dioxide, bicarbonate ions, and carbonate. As much as 30% of phytoplankton can be broken down into dissolved carbon. When this particulate organic carbon interacts with 350 nm ultraviolet light, dissolved inorganic carbon is formed, removing even more oxygen from the environment in the forms of carbon dioxide, bicarbonate ions, and carbonate. Dissolved inorganic carbon is made at a rate of 2.3–6.5 mg/(m 3 ⋅day). [ 17 ]
As phytoplankton breakdown, free phosphorus and nitrogen become available in the environment, which also fosters hypoxic conditions. As the breakdown of this phytoplankton takes place, the more phosphorus turns into phosphates, and nitrogens turn into nitrates. This depletes the oxygen even more so in the environment, further creating hypoxic zones in higher quantities. As more minerals such as phosphorus and nitrogen are displaced into these aquatic systems, the growth of phytoplankton greatly increases, and after their death, hypoxic zones are formed. [ 18 ] | https://en.wikipedia.org/wiki/Hypoxia_(environmental) |
Fish are exposed to large oxygen fluctuations in their aquatic environment since the inherent properties of water can result in marked spatial and temporal differences in the concentration of oxygen (see oxygenation and underwater ). Fish respond to hypoxia with varied behavioral, physiological, and cellular responses to maintain homeostasis and organism function in an oxygen-depleted environment. The biggest challenge fish face when exposed to low oxygen conditions is maintaining metabolic energy balance, as 95% of the oxygen consumed by fish is used for ATP production releasing the chemical energy of nutrients through the mitochondrial electron transport chain . [ 1 ] Therefore, hypoxia survival requires a coordinated response to secure more oxygen from the depleted environment and counteract the metabolic consequences of decreased ATP production at the mitochondria.
A fish's hypoxia tolerance can be represented in different ways. A commonly used representation is the critical O 2 tension (P crit ), which is the lowest water O 2 tension (P O 2 ) at which a fish can maintain a stable O 2 consumption rate (M O 2 ). [ 2 ] A fish with a lower P crit is therefore thought to be more hypoxia-tolerant than a fish with a higher P crit . But while P crit is often used to represent hypoxia tolerance, it more accurately represents the ability to take up environmental O 2 at hypoxic P O 2 s and does not incorporate the significant contributions of anaerobic glycolysis and metabolic suppression to hypoxia tolerance (see below). P crit is nevertheless closely tied to a fish's hypoxia tolerance, [ 3 ] in part because some fish prioritize their use of aerobic metabolism over anaerobic metabolism and metabolic suppression. [ 4 ] It therefore remains a widely used hypoxia tolerance metric. [ 5 ]
A fish's hypoxia tolerance can also be represented as the amount of time it can spend at a particular hypoxic P O 2 before it loses dorsal-ventral equilibrium (called time-to-LOE), or the P O 2 at which it loses equilibrium when P O 2 is decreased from normoxia to anoxia at some set rate (called P O 2 -of-LOE). A higher time-to-LOE value or a lower P O 2 -of-LOE value therefore imply enhanced hypoxia tolerances. In either case, LOE is a more holistic representation of overall hypoxia tolerance because it incorporates all contributors to hypoxia tolerance, including aerobic metabolism, anaerobic metabolism and metabolic suppression.
In mammals there are several structures that have been implicated as oxygen sensing structures; however, all of these structures are situated to detect aortic or internal hypoxia since mammals rarely run into environmental hypoxia. These structures include the type I cells of the carotid body , [ 6 ] the neuroepithelial bodies of the lungs [ 7 ] as well as some central and peripheral neurons and vascular smooth muscle cells.
In fish, the neuroepithelial cells (NEC) have been implicated as the major oxygen sensing cells. [ 8 ] NEC have been found in all teleost fish studied to date, and are likely a highly conserved structure within many taxa of fish. NEC are also found in all four gill arches within several different structures, such as along the filaments, at the ends of the gill rakers and throughout the lamellae. Two separate neural pathways have been identified within the zebrafish gill arches both the motor and sensory nerve fibre pathways. [ 9 ] Since neuroepithelial cells are distributed throughout the gills, they are often ideally situated to detect both arterial as well as environmental oxygen. [ 10 ]
Neuroepithelial cells (NEC) are thought to be neuron -like chemoreceptor cells because they rely on membrane potential changes for the release of neurotransmitters and signal transmission onto nearby cells. Once NEC of the zebrafish gills come in contact with either environmental or aortic hypoxia , an outward K + "leak" channel is inhibited. It remains unclear how these K + channels are inhibited by a shortage of oxygen because there are yet to be any known direct binding sites for "a lack of oxygen", only whole cell and ion channel responses to hypoxia. K + "leak" channels are two-pore-domain ion channels that are open at the resting membrane potential of the cell and play a major role in setting the equilibrium resting membrane potential of the cell. [ 11 ] Once this "leak" channel is closed, the K + is no longer able to freely flow out of the cell, and the membrane potential of the NEC increases; the cell becomes depolarized. This depolarization causes voltage-gated Ca 2+ channels to open, and for extracellular Ca 2+ to flow down its concentration gradient into the cell causing the intracellular Ca 2+ concentration to greatly increase. Once the Ca 2+ is inside the cell, it binds to the vesicle release machinery and facilitates binding of the t-snare complex on the vesicle to the s-snare complex on the NEC cell membrane which initiates the release of neurotransmitters into the synaptic cleft .
If the post-synaptic cell is a sensory neuron, then an increased firing rate in that neuron will transmit the signal to the central nervous system for integration. Whereas, if the post-synaptic cell is a connective pillar cell or a vascular smooth muscle cell, then the serotonin will cause vasoconstriction and previously unused lamellae will be recruited through recruitment of more capillary beds, and the total surface area for gas exchange per lamella will be increased. [ 12 ]
In fish, the hypoxic signal is carried up to the brain for processing by the glossopharyngeal (cranial nerve IX) and vagus (cranial nerve X) nerves. The first branchial arch is innervated by the glossopharyngeal nerve (cranial nerve IX); however all four arches are innervated by the vagus nerve (cranial nerve X). Both the glossopharyngeal and vagus nerves carry sensory nerve fibres into the brain and central nervous system.
Through studies using mammalian model organisms, there are two main hypotheses for the location of oxygen sensing in chemoreceptor cells: the membrane hypothesis and the mitochondrial hypothesis. The membrane hypothesis was proposed for the carotid body in mice, [ 13 ] and it predicts that oxygen sensing is an ion balance initiated process. The mitochondrial hypothesis was also proposed for the carotid body of mice, but it relies on the levels of oxidative phosphorylation and/or reactive oxygen species (ROS) production as a cue for hypoxia. Specifically, the oxygen sensitive K + currents are inhibited by H 2 O 2 and NADPH oxidase activation. [ 14 ] There is evidence for both of these hypotheses depending on the species used for the study. For the neuroepithelial cells in the zebrafish gills, there is strong evidence supporting the "membrane hypothesis" due to their capacity to respond to hypoxia after removal of the contents of the cell. However, there is no evidence against multiple sites for oxygen sensing in organisms.
Many hypoxic environments never reach the level of anoxia and most fish are able to cope with this stress using different physiological and behavioural strategies. Fish that use air breathing organs (ABO) tend to live in environments with highly variable oxygen content and rely on aerial respiration during times when there is not enough oxygen to support water-breathing. [ 15 ] Though all teleosts have some form of swim bladder , many of them are not capable of breathing air, and they rely on aquatic surface respiration as a supply of more oxygenated water at the surface of the water. However, many species of teleost fish are obligate water breathers and do not display either of these surface respiratory behaviours.
Typically, acute hypoxia causes hyperventilation , bradycardia and an elevation in gill vascular resistance in teleosts. [ 16 ] However, the benefit of these changes in blood pressure to oxygen uptake has not been supported in a recent study of the rainbow trout . [ 17 ] It is possible that the acute hypoxia response is simply a stress response, and the advantages found in early studies may only result after acclimatization to the environment.
Hypoxia can modify normal behavior. [ 18 ] Parental behaviour meant to provide oxygen to the eggs is often affected by hypoxia. For example, fanning behavior (swimming on the spot near the eggs to create a flow of water over them, and thus a constant supply of oxygen) is often increased when oxygen is less available. This has been documented in sticklebacks, [ 19 ] [ 20 ] gobies, [ 21 ] [ 22 ] and clownfishes, [ 23 ] among others. Gobies may also increase the size of the openings in the nest they build, even though this may increase the risk of predation on the eggs. [ 24 ] [ 25 ] Rainbow cichlids often move their young fry closer to the water surface, where oxygen is more available, during hypoxic episodes. [ 26 ]
Behavioural adaptations meant to survive when oxygen is scarce include reduced activity levels, aquatic surface respiration, and air breathing.
As oxygen levels decrease, fish may at first increase movements in an attempt to escape the hypoxic zone, but eventually they greatly reduce their activity levels, thus reducing their energetic (and therefore oxygen) demands. Atlantic herring show this exact pattern. [ 27 ] Other examples of fishes that reduce their activity levels under hypoxia include the common sole , [ 28 ] the guppy , [ 29 ] the small-spotted catshark , [ 30 ] and the viviparous eelpout . [ 31 ] Some sharks that ram-ventilate their gills may understandably increase their swimming speeds under hypoxia, to bring more water to the gills. [ 32 ]
In response to decreasing dissolved oxygen level in the environment, fish swim up to the surface of the water column and ventilate at the top layer of the water where it contains relatively higher level of dissolved oxygen, a behavior called aquatic surface respiration (ASR). [ 33 ] Oxygen diffuses into water from air and therefore the top layer of water in contact with air contains more oxygen. This is true only in stagnant water; in running water all layers are mixed together and oxygen levels are the same throughout the water column. One environment where ASR often takes place is tidepools, particularly at night. [ 34 ] Separation from the sea at low tide means that water is not renewed, fish crowding within the pool means that oxygen is quickly depleted, and absence of light at night means that there is no photosynthesis to replenish the oxygen. Examples of tidepool species that perform ASR include the tidepool sculpin , [ 35 ] [ 36 ] the three-spined stickleback , [ 37 ] and the mummichog . [ 38 ] [ 39 ]
But ASR is not limited to the intertidal environment. Most tropical and temperate fish species living in stagnant waters engage in ASR during hypoxia. [ 40 ] One study looked at 26 species representing eight families of non-air breathing fishes from the North American great plains, and found that all but four of them performed ASR during hypoxia. [ 41 ] Another study looked at 24 species of tropical fish common to the pet trade, from tetras to barbs to cichlids, and found that all of them performed ASR. [ 42 ] An unusual situation in which ASR is performed is during winter, in lakes covered by ice, at the interface between water and ice or near air bubbles trapped underneath the ice. [ 43 ] [ 44 ] [ 45 ]
Some species may show morphological adaptations, such as a flat head and an upturned mouth, that allow them to perform ASR without breaking the water surface (which would make them more visible to aerial predators). [ 46 ] One example is the mummichog , whose upturned mouth suggests surface feeding, but whose feeding habits are not particularly restricted to the surface. In the tambaqui , a South American species, exposure to hypoxia induces within hours the development of additional blood vessels inside the lower lip, enhancing its ability to take up oxygen during ASR. [ 47 ] Swimming upside down may also help fishes perform ASR, as in some upside-down catfish . [ 48 ]
Some species may hold an air bubble within the mouth during ASR. This may assist buoyancy as well as increase the oxygen content of the water passing over the bubble on its way to the gills. [ 49 ] Another way to reduce buoyancy costs is to perform ASR on rocks or plants that provide support near the water surface.
ASR significantly affects survival of fish during severe hypoxia. [ 50 ] In the shortfin molly for example, survival was approximately four times higher in individuals able to perform ASR as compared to fish not allowed to perform ASR during their exposure to extreme hypoxia. [ 51 ]
ASR may be performed more often when the need for oxygen is higher. In the sailfin molly , gestating females (this species is a livebearer) spend about 50% of their time in ASR as compared to only 15% in non-gestating females under the same low levels of oxygen. [ 52 ]
Aerial respiration is the 'gulping' of air at the surface of water to directly extract oxygen from the atmosphere. Aerial respiration evolved in fish that were exposed to more frequent hypoxia; also, species that engage in aerial respiration tend to be more hypoxia tolerant than those which do not air-breath during the hypoxia. [ 53 ]
There are two main types of air breathing fish—facultative and non-facultative. Under normoxic conditions facultative fish can survive without having to breathe air from the surface of the water. However, non-facultative fish must respire at the surface even in normal dissolved oxygen levels because their gills cannot extract enough oxygen from the water.
Many air breathing freshwater teleosts use ABOs to effectively extract oxygen from air while maintaining functions of the gills. ABOs are modified gastrointestinal tracts , gas bladders , and labyrinth organs ; [ 54 ] they are highly vascularized and provide additional method of extracting oxygen from the air. [ 55 ] Fish also use ABO for storing the retained oxygen.
Both ASR and aerial respiration require fish to travel to the top of water column and this behaviour increases the predation risks by aerial predators or other piscivores inhabiting near the surface of the water. [ 55 ] To cope with the increased predation risk upon surfacing, some fish perform ASR or aerial respiration in schools [ 54 ] [ 56 ] to 'dilute' the predation risk. When fish can visually detect the presence of their aerial predators, they simply refrain from surfacing, or prefer to surface in areas where they can be detected less easily (i.e. turbid, shaded areas). [ 57 ]
Gill remodelling happens in only a few species of fish, and it involves the buildup or removal of an inter-lamellar cell mass (ILCM). As a response to hypoxia, some fish are able to remodel their gills to increase respiratory surface area, with some species such as goldfish doubling their lamellar surface areas in as little as 8 hours. [ 58 ] The increased respiratory surface area comes as a trade-off with increased metabolic costs because the gills are a very important site for many important processes including respiratory gas exchange , acid-base regulation , nitrogen excretion , osmoregulation , hormone regulation , metabolism , and environmental sensing. [ 59 ]
The crucian carp is one species able to remodel its gill filaments in response to hypoxia. Their inter-lamellar cells have high rates of mitotic activity which are influenced by both hypoxia and temperature. [ 60 ] In cold (15 °C) water the crucian carp has more ILCM, but when the temperature is increased to 25 °C the ILCM is removed, just as it would be in hypoxic conditions. This same transition in gill morphology occurs in the goldfish when the temperature was raised from 7.5 °C to 15 °C. [ 61 ] This difference may be due to the temperature regimes that these fish are typically found in, or there could be an underlying protective mechanism to prevent a loss of ion balance in stressful temperatures. Temperature also affects the speed at which the gills can be remodelled: for example, at 20 °C in hypoxia, the crucian carp can completely remove its ILCM in 6 hours, whereas at 8 °C, the same process takes 3–7 days. [ 60 ] The ILCM is likely removed by apoptosis , but it is possible that when the fish is faced with the double stress of hypoxia at high temperature, the lamellae may be lost by physical degradation. Covering the gill lamellae may protect species like the crucian carp from parasites and environmental toxins during normoxia by limiting their surface area for inward diffusion while still maintaining oxygen transport due to an extremely high hemoglobin oxygen binding affinity . [ 60 ]
The naked carp , a closely related species native to the high-altitude Lake Qinghai , is also able to remodel their gills in response to hypoxic conditions. In response to oxygen levels 95% lower than normoxic conditions, apoptosis of ILCM increases lamellar surface area by up to 60% after just 24 hours. [ 62 ] However, this comes at a significant osmoregulatory cost, reducing sodium and chloride levels in the cytoplasm by over 10%. [ 62 ] The morphological response to hypoxia by scaleless carp is the fastest respiratory surface remodelling reported in vertebrates thus far. [ 63 ]
Fish exhibit a wide range of tactics to counteract aquatic hypoxia, but when escape from the hypoxic stress is not possible, maintaining oxygen extraction and delivery becomes an essential component to survival. [ 64 ] Except for the Antarctic ice fish that does not, most fish use hemoglobin (Hb) within their red blood cells to bind chemically and deliver 95% of the oxygen extracted from the environment to the working tissues. Maintaining oxygen extraction and delivery to the tissues allows continued activity under hypoxic stress and is in part determined by modifications in two different blood parameters: hematocrit and the binding properties of hemoglobin.
In general, hematocrit is the number of red blood cells (RBC) in circulation and is highly variable among fish species. Active fish, like the blue marlin , tend to have higher hematocrits, [ 65 ] whereas less active fish, such as the starry flounder exhibit lower hematocrits. [ 66 ] Hematocrit may be increased in response to both short-term (acute) or long-term (chronic) hypoxia exposure and results in an increase in the total amount of oxygen the blood can carry, also known as the oxygen carrying capacity of the blood. [ 67 ] Acute changes in hematocrit are the result of circulating stress hormones (see - catecholamines ) activating receptors on the spleen that cause the release of RBCs into circulation. [ 68 ] During chronic hypoxia exposure, the mechanism used to increase hematocrit is independent of the spleen and results from hormonal stimulation of the kidney by erythropoetin (EPO) . Increasing hematocrit in response to erythropoietin is observed after approximately one week and is therefore likely under genetic control of hypoxia inducible factor hypoxia inducible factor (HIF) . [ 69 ] While increasing hematocrit means that the blood can carry a larger total amount of oxygen, a possible advantage during hypoxia, increasing the number of RBCs in the blood can also lead to certain disadvantages. First, A higher hematocrit results in more viscous blood (especially in cold water) increasing the amount of energy the cardiac system requires to pump the blood through the system and secondly depending on the transit time of the blood across the branchial arch and the diffusion rate of oxygen, an increased hematocrit may result in less efficient transfer of oxygen from the environment to the blood. [ 65 ]
An alternative mechanism to preserve O 2 delivery in the face of low ambient oxygen is to increase the affinity of the blood. The oxygen content of the blood is related to PaO 2 and is illustrated using an oxygen equilibrium curve (OEC). Fish hemoglobins, with the exception of the agnathans , are tetramers that exhibit cooperativity of O 2 binding and have sigmoidal OECs.
The binding affinity of hemoglobin to oxygen is estimated using a measurement called P50 (the partial pressure of oxygen at which hemoglobin is 50% bound with oxygen) and can be extremely variable. [ 70 ] If the hemoglobin has a weak affinity for oxygen, it is said to have a high P50 and therefore constrains the environment in which a fish can inhabit to those with relatively high environmental PO 2 . Conversely, fish hemoglobins with a low P50 bind strongly to oxygen and are then of obvious advantage when attempting to extract oxygen from hypoxic or variable PO 2 environments. The use of high affinity (low P50) hemoglobins results in reduced ventillatory and therefore energetic requirements when facing hypoxic insult. [ 65 ] The oxygen binding affinity of hemoglobin (Hb-O 2 ) is regulated through a suite of allosteric modulators ; the principal modulators used for controlling Hb-O 2 affinity under hypoxic insult are:
In rainbow trout as well as a variety of other teleosts, increased RBC pH stems from the activation of B-andrenergic Na + /H + exchange protein (BNHE) on the RBC membrane via circulating catelcholamines. [ 71 ] This process causes the internal pH of the RBC to increase through the outwards movement of H + and inwards movement of Na + . [ 72 ] The net consequence of alkalizing the RBC is an increase in Hb-O 2 affinity via the Bohr effect . The net influx of Na + ions and the compensatory activation of Na + /K + -ATPase to maintain ionic equilibrium within the RBC results in a steady decline in cellular ATP, also serving to increase Hb-O 2 affinity. [ 73 ] As a further result of inward Na + movement, the osmolarity of the RBC increases causing osmotic influx of water and cell swelling. The dilution of the cell contents causes further spatial separation of hemoglobin from the inorganic phosphates and again serves to increase Hb-O 2 affinity. [ 65 ] Intertidal hypoxia-tolerant triplefin fish (Family Tripterygiidae ) species seem to take advantage of intracellular acidosis and appears to "bypasse" the traditional oxidative phosphorylation and directly drives mitochondrial ATP synthesis using the cytosolic pool of protons that likely accumulates in hypoxia (via lactic acidosis and ATP hydrolysis). [ 74 ]
Nearly all animals have more than one kind of Hb present in the RBC. Multiple Hb isoforms (see isoforms ) are particularly common in ectotherms , but especially in fish that are required to cope with both fluctuating temperature and oxygen availability. Hbs isolated from the European eel can be separated into anodic and cathodic isoforms. The anodic isoforms have low oxygen affinities (high P50) and marked Bohr effects, while the cathodic lack significant pH effects and are therefore thought to confer hypoxia tolerance. [ 75 ] Several species of African cichlids raised from early stage development under either hypoxic or normoxic conditions were contrasted in an attempt to compare Hb isoforms. They demonstrated there were Hb isoforms specific to the hypoxia-raised individuals. [ 76 ]
To deal with decreased ATP production through the electron transport chain, fish must activate anaerobic means of energy production (see anaerobic metabolism ) while suppressing metabolic demands. The ability to decrease energy demand by metabolic suppression is essential to ensure hypoxic survival due to the limited efficiency of anaerobic ATP production.
Aerobic respiration, in which oxygen is used as the terminal electron acceptor, is crucial to all water-breathing fish. When fish are deprived of oxygen, they require other ways to produce ATP. Thus, a switch from aerobic metabolism to anaerobic metabolism occurs at the onset of hypoxia. Glycolysis and substrate-level phosphorylation are used as alternative pathways for ATP production. [ 77 ] However, these pathways are much less efficient than aerobic metabolism. For example, when using the same substrate, the total yield of ATP in anaerobic metabolism is 15 times lower than in aerobic metabolism. This level of ATP production is not sufficient to maintain a high metabolic rate, therefore, the only survival strategy for fish is to alter their metabolic demands.
Metabolic suppression is the regulated and reversible reduction of metabolic rate below basal metabolic rate (called standard metabolic rate in ectothermic animals). [ 1 ] This reduces the fish's rate of ATP use, which prolongs its survival time at severely hypoxic sub-P crit P O 2 s by reducing the rate at which the fish's finite anaerobic fuel stores ( glycogen ) are used. Metabolic suppression also reduces the accumulation rate of deleterious anaerobic end-products ( lactate and protons), which delays their negative impact on the fish.
The mechanisms that fish use to suppress metabolic rate occur at behavioral, physiological and biochemical levels. Behaviorally, metabolic rate can be lowered through reduced locomotion, feeding, courtship, and mating. [ 78 ] [ 79 ] [ 80 ] Physiologically, metabolic rate can be lowered through reduced growth, digestion, gonad development, and ventilation efforts. [ 81 ] [ 82 ] And biochemically, metabolic rate can be further lowered below standard metabolic rate through reduced gluconeogenesis, protein synthesis and degradation rates, and ion pumping across cellular membranes. [ 83 ] [ 84 ] [ 85 ] Reductions in these processes lower ATP use rates, but it remains unclear whether metabolic suppression is induced through an initial reduction in ATP use or ATP supply.
The prevalence of metabolic suppression use among fish species has not been thoroughly explored. This is partly because the metabolic rates of hypoxia-exposed fish, including suppressed metabolic rates, can only be accurately measured using direct calorimetry , and this technique is seldom used for fish. [ 86 ] [ 87 ] The few studies that have used calorimetry reveal that some fish species employ metabolic suppression in hypoxia/anoxia (e.g., goldfish, tilapia, European eel) while others do not (e.g. rainbow trout, zebrafish). [ 88 ] [ 89 ] [ 90 ] [ 91 ] [ 1 ] The species that employ metabolic suppression are more hypoxia-tolerant than the species that do not, which suggests that metabolic suppression enhances hypoxia tolerance. Consistent with this, differences in hypoxia tolerance among isolated threespine stickleback populations appear to result from differences in the use of metabolic suppression, with the more tolerant stickleback using metabolic suppression. [ 92 ]
Fish that are capable of hypoxia-induced metabolic suppression reduce their metabolic rates by 30% to 80% relative to standard metabolic rates. [ 93 ] [ 94 ] [ 95 ] [ 90 ] Because this is not a complete cessation of metabolic rate, metabolic suppression can only prolong hypoxic survival, not sustain it indefinitely. If the hypoxic exposure lasts sufficiently long, the fish will succumb to a depletion of its glycogen stores and/or the over-accumulation of deleterious anaerobic end-products. Furthermore, the severely limited energetic scope that comes with a metabolically suppressed state means that the fish is unable to complete critical tasks such a predator avoidance and reproduction. Perhaps for these reasons, goldfish prioritize their use of aerobic metabolism in most hypoxic environments, reserving metabolic suppression for the extreme case of anoxia. [ 90 ]
In addition to a reduction in the rate of protein synthesis, it appears that some species of hypoxia-tolerant fish conserve energy by employing Hochachka's ion channel arrest hypothesis. This hypothesis makes two predictions:
The first prediction holds true. When membrane permeability to Na+ and K+ ions was compared between reptiles and mammals, reptile membranes were discovered to be five times less leaky. [ 98 ] The second prediction has been more difficult to prove experimentally; however, indirect measures have shown a decrease in Na+/K+-ATPase activity in eel and trout hepatocytes during hypoxic conditions. [ 99 ] [ 100 ] Results seem to be tissue-specific, as crucian carp exposed to hypoxia do not undergo a reduction in Na+/K+ ATPase activity in their brain. [ 101 ] Although evidence is limited, ion channel arrest enables organisms to maintain ion channel concentration gradients and membrane potentials without consuming large amounts of ATP.
The limiting factor for fish undergoing hypoxia is the availability of fermentable substrate for anaerobic metabolism; once substrate runs out, ATP production ceases. Endogenous glycogen is present in tissue as a long term energy storage molecule. It can be converted into glucose and subsequently used as the starting material in glycolysis.
A key adaptation to long-term survival during hypoxia is the ability of an organism to store large amounts of glycogen. Many hypoxia-tolerant species, such as carp, goldfish, killifish , and oscar contain the largest glycogen content (300-2000 μmol glocosyl units/g) in their tissue compared to hypoxia-sensitive fish, such as rainbow trout, which contain only 100 μmol glocosyl units/g. [ 102 ] The more glycogen stored in a tissue indicates the capacity for that tissue to undergo glycolysis and produce ATP.
When anaerobic pathways are turned on, glycogen stores are depleted and accumulation of acidic waste products occurs. This is known as a Pasteur effect . A challenge hypoxia-tolerant fish face is how to produce ATP anaerobically without creating a significant Pasteur effect. Along with a reduction in metabolism, some fish have adapted traits to avoid accumulation of lactate . For example, the crucian carp, a highly hypoxia-tolerant fish, has evolved to survive months of anoxic waters. A key adaptation is the ability to convert lactate to ethanol in the muscle and excrete it out of their gills. [ 103 ] Although this process is energetically costly it is crucial to their survival in hypoxic waters.
DNA microarray studies done on different fish species exposed to low-oxygen conditions have shown that at the genetic level fish respond to hypoxia by changing the expression of genes involved in oxygen transport, ATP production, and protein synthesis . In the liver of mudsuckers exposed to hypoxia there were changes in the expression of genes involved in heme metabolism such as hemopexin , heme oxygenase 1 , and ferritin . [ 104 ] Changes in the sequestration and metabolism of iron may suggest hypoxia induced erythropoiesis and increased demand for hemoglobin synthesis, leading to increased oxygen uptake and transport. Increased expression of myoglobin , which is normally only found in muscle tissue, has also been observed after hypoxia exposure in the gills of zebrafish [ 105 ] and in non-muscle tissue of the common carp [ 106 ] suggesting increased oxygen transport throughout fish tissues.
Microarray studies done on fish species exposed to hypoxia typically show a metabolic switch, that is, a decrease in the expression of genes involved in aerobic metabolism and an increase in expression of genes involved in anaerobic metabolism. Zebrafish embryos exposed to hypoxia decreased expression of genes involved in the citric acid cycle including, succinate dehydrogenase , malate dehydrogenase , and citrate synthase , and increased expression of genes involved in glycolysis such as phosphoglycerate mutase , enolase , aldolase , and lactate dehydrogenase . [ 107 ] A decrease in protein synthesis is an important response to hypoxia to decrease ATP demand for whole organism metabolic suppression. Decreases in the expression of genes involved in protein synthesis, such as elongation factor-2 and several ribosomal proteins , have been shown in the muscle of the mudsucker [ 104 ] and gills of adult zebrafish [ 105 ] after hypoxia exposure .
Research in mammals has implicated hypoxia inducible factor (HIF) as a key regulator of gene expression changes in response to hypoxia [ 108 ] However, a direct link between fish HIFs and gene expression changes in response to hypoxia has yet to be found. Phylogenetic analysis of available fish, tetrapod , and bird HIF-α and -β sequences shows that the isoforms of both subunits present in mammals are also represented in fish Within fish, HIF sequences group close together and are distinct from tetrapod and bird sequences. [ 1 ] As well, amino acid analysis of available fish HIF-α and -β sequences reveals that they contain all functional domains shown to be important for mammalian HIF function, [ 1 ] including the basic helix-loop-helix (bHLH) domain, Per-ARNT-Sim (PAS) domain, and the oxygen-dependent degradation domain (ODD), which render the HIF-α subunit sensitive to oxygen levels. [ 108 ] The evolutionary similarity between HIF sequences in fish, tetrapods and birds, as well as the conservation of important functional domains suggests that HIF function and regulation is similar between fish and mammalian species. There is also evidence of novel HIF mechanisms present in fish not found in mammals. In mammals, HIF-α protein is continuously synthesized and regulated post-translationally by changing oxygen conditions, [ 109 ] but it has been shown in different fish species that HIF-α mRNA levels are also responsive to hypoxia. In the hypoxia tolerant grass carp , substantial increases in HIF-1α and HIF-3α mRNA were observed in all tissues after hypoxia exposure. [ 110 ] Likewise, mRNA levels of HIF-1α and HIF-2α were hypoxia-responsive in the ovaries of the Atlantic croaker during both short and long term hypoxia. [ 111 ] | https://en.wikipedia.org/wiki/Hypoxia_in_fish |
Hypoxic air technology for fire prevention , also known as oxygen reduction system ( ORS ), is an active fire protection technique based on a permanent reduction of the oxygen concentration in the protected rooms. Unlike traditional fire suppression systems that usually extinguish fire after it is detected , hypoxic air is able to prevent fire.
In a volume protected by hypoxic air, a normobaric hypoxic atmosphere is continuously retained: hypoxic means that the partial pressure of the oxygen is lower than at the sea level, normobaric means that the barometric pressure is equal to the barometric pressure at the sea level. Usually 1/4 to 1/2 of the oxygen contained in the air (that is, 5 to 10% of the air) is replaced by the same amount of nitrogen : as a consequence a hypoxic atmosphere containing around 15 Vol% of oxygen and 85 Vol% of nitrogen is created. In a normobaric hypoxic environment, common materials cannot ignite or burn when exposed to a localized small scale ignition source. [ 1 ] A reduction of the oxygen level to 15% does not achieve conditions where a fire cannot occur or is extinguished. However, it reduces the probability of a fire occurring by increasing the ignition energy needed, and there are also indications of increased ignition times. [ 2 ]
Air with a reduced oxygen content is injected to the protected volumes to lower the oxygen concentration until the desired oxygen concentration is reached. Then, because of air infiltration , the oxygen concentration inside the protected volumes rises: when it exceeds a certain threshold, low-oxygen air is again injected to the protected volumes until the desired oxygen concentration is reached. Oxygen sensors are installed in the protected volumes to continuously monitor the oxygen concentration.
The exact oxygen level to retain in the protected volumes is determined after a careful assessment of materials, configurations, and hazards. [ 3 ] Tables list ignition-limiting oxygen thresholds for some materials. Alternatively, the ignition-limiting threshold is determined by performing a proper ignition test described in BSI PAS 95:2011 Hypoxic air fire prevention systems specification. [ 4 ]
Smoke detectors are installed in protected volumes because, similar to gas suppression systems , hypoxic air does not prevent smoldering and pyrolyzing processes.
Air with low oxygen concentration is produced by hypoxic air generators, also known as air splitting units. There are three different types of hypoxic air generators: membrane-based , PSA-based , and VSA-based . VSA-based hypoxic air generators usually have a lower energy consumption compared to PSA-based and membrane-based generators. Hypoxic air generators can be located inside or outside the protected rooms. Hypoxic air systems can be integrated with the building management system and can include systems to recover the heat generated by the hypoxic air generator that, would otherwise be wasted. [ 5 ]
Air with low oxygen concentration is transported to the protected volumes through dedicated pipes or, more simply, via an existing ventilation system . In the latter case, dedicated pipes or ducts are not required.
The benefits of preventing a fire instead of suppressing it makes hypoxic air suitable for applications where a fire would cause unacceptable damage. Unlike traditional fire-suppression systems, dedicated pipes or nozzles are not required.
Hypoxic air for fire prevention are used in [ citation needed ] :
The reduction of artifact degradation and food deterioration is a plus for applications like food warehouses, storage and archives.
Hypoxic air fire prevention systems can also be used for purposes other than fire prevention, for example:
Combining fire prevention, indoor climate and reduction of artefacts/food degradation is a completely new approach for a fire safety system.
Fire-prevention systems which result in the oxygen content being less than 19.5% are not permitted for occupied spaces without providing employees supplemental respirators by federal regulation (OSHA) in the United States. [ 6 ]
However, hypoxic air is considered by some to be safe to breathe for most people. [ 7 ] Medical studies have been undertaken on this topic.
Angerer and Novak's conclusion is that "working environments with low oxygen concentrations to a minimum of 13% and normal barometric pressure do not impose a health hazard, provided that precautions are observed, comprising medical examinations and limitation of exposure time." [ 8 ] Küpper et al. say that oxygen concentration between 17.0 and 14.8% does not cause any risk for healthy people by hypoxia. It also does not cause risks for people with chronic diseases of moderate severity. The ability for strenuous work is reduced as the concentration decreases with the time that exertion can be sustained becoming very low below these levels, below around 17% it may be necessary to take breaks outside the environment if more than 6 hours is to be spent inside, especially if any physical exertion is performed [ 9 ]
Pressurized aircraft cabins are typically maintained at 75 kPa, the pressure found at 2,500 m (8,200 ft) altitude, resulting in an oxygen partial pressure of about 16 kPa, which is the same as a 15% oxygen concentration in a hypoxic-air application at sea-level pressure. However, passengers are sedentary and crew members have immediate access to supplemental oxygen.
Hypoxic air is to be considered clean air and not contaminated air when assessing oxygen depletion hazards.
Information relating access to the protected areas i.e. oxygen-reduced atmosphere are illustrated:
Inspection body accreditation criteria are established according to ISO/IEC 17010 for third party verification of hypoxic air fire prevention system conformance to BSI PAS 95:2011 and VdS 3527en:2007 [ 12 ] | https://en.wikipedia.org/wiki/Hypoxic_air_technology_for_fire_prevention |
In spectroscopy , hypsochromic shift (from Ancient Greek ὕψος (upsos) ' height ' and χρῶμα (chrōma) ' color ' ) is a change of spectral band position in the absorption , reflectance , transmittance , or emission spectrum of a molecule to a shorter wavelength (higher frequency ). Because the blue color in the visible spectrum has a shorter wavelength than most other colors, this effect is also commonly called a blue shift . [ 1 ] It should not be confused with a bathochromic shift , which is the opposite process – the molecule's spectra are changed to a longer wavelength (lower frequency).
Hypsochromic shifts can occur because of a change in environmental conditions. For example, a change in solvent polarity will result in solvatochromism . A series of structurally related molecules in a substitution series can also show a hypsochromic shift. Hypsochromic shift is a phenomenon seen in molecular spectra, not atomic spectra - it is thus more common to speak of the movement of the peaks in the spectrum rather than lines.
where λ {\displaystyle \lambda } is the wavelength of the spectral peak of interest and λ state 1 observed > λ state 2 observed . {\displaystyle \lambda \!_{{\text{state 1}} \atop {\text{observed}}}>\,\lambda \!_{{\text{state 2}} \atop {\text{observed}}}\!.}
For example, β-acylpyrrole will show a hypsochromic shift of 30-40 nm in comparison with α-acylpyrroles.
This spectroscopy -related article is a stub . You can help Wikipedia by expanding it .
This article about materials science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hypsochromic_shift |
A hypsometer is an instrument for measuring height or elevation . Two different principles may be used: trigonometry and atmospheric pressure .
The English word hypsometer originates from the Ancient Greek words ὕψος (húpsos, "height") and μέτρον (métron, "measure").
A simple scale hypsometer allows the height of a building or tree to be measured by sighting across a ruler to the base and top of the object being measured, when the distance from the object to the observer is known. Modern hypsometers use a combination of laser rangefinder and clinometer to measure distances to the top and bottom of objects, and the angle between the lines from the observer to each to calculate height.
An example of such a scale hypsometer is illustrated here, and can be seen to consist of a sighting tube, a fixed horizontal scale, and an adjustable vertical scale with attached plumb line. The principle of operation of such a scale hypsometer is based on the idea of similar triangles in geometry. First the adjustable vertical scale is set at a suitable height. Then as in step 1 in the illustration, a sighting is taken on the top of the object whose height is to be determined, and the reading on the horizontal scale, h', recorded. Calculation from this value will eventually give the height h, from the eye-line of the observer to the top of the object whose height is to be determined. Similarly as in step 2 of the illustration, a sighting is taken on the base of the object whose height is to be determined, and the reading on the horizontal scale, d', recorded. Calculation from this value will eventually give the distance from the base of the object to the eye-line of the observer. Finally the distance x from the observer to the object needs to be measured.
Looking at the geometry involved in step 1 results in sketch a: two right angled triangles, shown here with the identical small angles in yellow. Next in sketch b we see that the two triangles have identical angles - each has a right angle, the same small angle shown in yellow, and the same larger angle shown in orange. Therefore in sketch c we see that using the principle of similar triangles, given that each triangle has identical angles, the sides will be in proportion: x the distance to the object in proportion to x', the height set on the vertical scale of the hypsometer, and h the height of the object above the observers eye-line in proportion to h', the reading from the horizontal scale of the hypsometer.
Given that Tan (small yellow angle) = Opposite Side / Adjacent Side, therefore Tan (small yellow angle) = h / x = h' / x'. Therefore h = h'x / x'.
Likewise the geometry involved in step 2 results in sketch d: two right angled triangles. Next in sketch e we see that the two triangles again have identical angles - each has a right angle, the same small angle shown in yellow, and the same larger angle shown in orange. Therefore in sketch f we see that using the principle of similar triangles, given that each triangle has identical angles, the sides will be in proportion: x the distance to the object in proportion to x', the height set on the vertical scale of the hypsometer, and d the depth of the object below the observers eye-line in proportion to d', the reading from the horizontal scale of the hypsometer.
Given that Tan (small angle) = Opposite Side / Adjacent Side, therefore Tan (small angle) = d / x = d' / x'. Therefore d = d'x / x'.
Thus the overall height of the object is x (d' + h') / x'
A pressure hypsometer as shown in the drawing (right) employs the principle that the boiling point of a liquid is lowered by diminishing the barometric pressure , and that the barometric pressure varies with the height of the point of observation. [ 1 ]
The instrument consists of a cylindrical vessel in which the liquid, usually water, is boiled, surmounted by a jacketed column, in the outer partitions of which the vapour circulates, while in the central one a thermometer is placed. To deduce the height of the station from the observed boiling point, it is necessary to know the relation existing between the boiling point and pressure, and also between the pressure and height of the atmosphere. [ 1 ] | https://en.wikipedia.org/wiki/Hypsometer |
The hypsometric equation , also known as the thickness equation , relates an atmospheric pressure ratio to the equivalent thickness of an atmospheric layer considering the layer mean of virtual temperature , gravity , and occasionally wind . It is derived from the hydrostatic equation and the ideal gas law .
The hypsometric equation is expressed as: [ 1 ] h = z 2 − z 1 = R ⋅ T v ¯ g ln ( p 1 p 2 ) , {\displaystyle h=z_{2}-z_{1}={\frac {R\cdot {\overline {T_{v}}}}{g}}\,\ln \left({\frac {p_{1}}{p_{2}}}\right),} where:
In meteorology , p 1 {\displaystyle p_{1}} and p 2 {\displaystyle p_{2}} are isobaric surfaces. In radiosonde observation, the hypsometric equation can be used to compute the height of a pressure level given the height of a reference pressure level and the mean virtual temperature in between. Then, the newly computed height can be used as a new reference level to compute the height of the next level given the mean virtual temperature in between, and so on.
The hydrostatic equation:
where ρ {\displaystyle \rho } is the density [kg/m 3 ], is used to generate the equation for hydrostatic equilibrium , written in differential form:
This is combined with the ideal gas law :
to eliminate ρ {\displaystyle \rho } :
This is integrated from z 1 {\displaystyle z_{1}} to z 2 {\displaystyle z_{2}} :
R and g are constant with z , so they can be brought outside the integral.
If temperature varies linearly with z (e.g., given a small change in z ),
it can also be brought outside the integral when replaced with T v ¯ {\displaystyle {\overline {T_{v}}}} , the average virtual temperature between z 1 {\displaystyle z_{1}} and z 2 {\displaystyle z_{2}} .
Integration gives
simplifying to
Rearranging:
or, eliminating the natural log:
The Eötvös effect can be taken into account as a correction to the hypsometric equation. Physically, using a frame of reference that rotates with Earth, an air mass moving eastward effectively weighs less, which corresponds to an increase in thickness between pressure levels, and vice versa. The corrected hypsometric equation follows: [ 2 ] h = z 2 − z 1 = R ⋅ T v ¯ g ( 1 + A ) ⋅ ln ( p 1 p 2 ) , {\displaystyle h=z_{2}-z_{1}={\frac {R\cdot {\overline {T_{v}}}}{g(1+A)}}\cdot \ln \left({\frac {p_{1}}{p_{2}}}\right),} where the correction due to the Eötvös effect , A, can be expressed as follows: A = − 1 g ( 2 Ω u ¯ cos ϕ + u ¯ 2 + v ¯ 2 r ) , {\displaystyle A=-{\frac {1}{g}}\left(2\Omega {\overline {u}}\cos \phi +{\frac {{\overline {u}}^{2}+{\overline {v}}^{2}}{r}}\right),} where
This correction is considerable in tropical large-scale atmospheric motion. | https://en.wikipedia.org/wiki/Hypsometric_equation |
Hyraceum ( / h aɪ ˈ r eɪ s i ə m / ) is the petrified and rock-like excrement composed of both urine and feces of the rock hyrax ( Procavia capensis ) and closely related species.
The rock hyrax defecates in the same location over generations, which may be sheltered in caves. These locations form middens that are composed of hyraceum and hyrax pellets, which can be petrified and preserved for over 50,000 years. These middens form a record of past climate and vegetation. [ 1 ]
It is also a sought-after material that has been used in both traditional South African medicine and perfumery.
The material hardens and ages until it becomes a fairly sterile, rock-like material (also referred to as "Africa Stone") that contains compounds giving it an animalic, deeply complex fermented scent that combines the elements of musk , castoreum , civet , tobacco and agarwood . The material is harvested without disturbing the animals by digging strata of the brittle, resinous, irregular, blackish-brown stone; because animals are not harmed in its harvesting, it is often an ethical substitute for deer musk and civet, which require killing or inflicting pain on the animal.
Hyraceum accumulates extremely slowly, [ 1 ] making it essentially a non-renewable resource. Considering that hyraceum – accumulating in the form of rock hyrax middens – is in many cases the only available source for information regarding climate and environmental change in arid regions of Africa and Arabia, its collection for commercial sale has been criticized in scientific circles as the destruction of a critical resource that could help to understand the impact of climate change in sensitive regions. [ 1 ]
After it has been fossilized hyraceum has been used as a traditional folk medicine in South Africa for treating epilepsy. [ 2 ]
One clinical study of 14 samples of the material collected at various geographical locations in South Africa tested the material for its affinity for the GABA- benzodiazepine receptor , a neurologic receptor site that is effective in the treatment of seizures with benzodiazapines such as diazepam and lorazepam . Four of the hyraceum samples assayed positive for having an affinity for the receptor sites; however, extracts in water were inactive. [ citation needed ] | https://en.wikipedia.org/wiki/Hyraceum |
Hysteresivity derives from “ hysteresis ”, meaning “lag”. It is the tendency to react slowly to an outside force, or to not return completely to its original state. Whereas the area within a hysteresis loop represents energy dissipated to heat and is an extensive quantity with units of energy, the hysteresivity represents the fraction of the elastic energy that is lost to heat, and is an intensive property that is dimensionless.
When a force deforms a material it generates elastic stresses and internal frictional stresses . Most often, frictional stress is described as being analogous to the stress that results from the flow of a viscous fluid , but in many engineering materials, in soft biological tissues , and in living cells , the concept that friction arises only from a viscous stress is now known to be erroneous. [ 1 ] [ 2 ] For example, Bayliss and Robertson [ 3 ] and Hildebrandt [ 4 ] demonstrated that frictional stress in lung tissue is dependent upon the amount of lung expansion but not the rate of expansion , findings that are fundamentally incompatible with the notion of friction being caused by a viscous stress. If not by a viscous stress, how then does friction arise, and how is it properly described?
In many inert and living materials, the relationship between elastic and frictional stresses turns out to be very nearly invariant (something unaltered by a transformation). In lung tissues, for example, the frictional stress is almost invariably between 0.1 and 0.2 of the elastic stress, where this fraction is called the hysteresivity, h, or, equivalently, the structural damping coefficient. [ 2 ] It is a simple phenomenological fact, therefore, that for each unit of peak elastic strain energy that is stored during a cyclic deformation, 10 to 20% of that elastic energy is taxed as friction and lost irreversibly to heat. This fixed relationship holds at the level of the whole lung [ 5 ] , [ 6 ] [ 7 ] isolated lung parenchymal tissue strips, [ 8 ] isolated smooth muscle strips, [ 2 ] [ 9 ] and even isolated living cells. [ 10 ] [ 11 ] [ 12 ] [ 13 ]
This close relationship between frictional and elastic stresses is called the structural damping law [ 1 ] [ 2 ] [ 4 ] [ 14 ] or, sometimes, the constant phase model . [ 5 ] The structural damping law implies that frictional losses are coupled tightly to elastic stresses rather than to viscous stresses, but the precise molecular mechanical origin of this phenomenon remains unknown. [ 10 ] [ 15 ] '
In material science , the complex elastic modulus of a material, G *( f ), at frequency of oscillatory deformation f , is given by,
where:
This relationship can be rewritten as,
where:
In systems conforming to the structural damping law, the hysteresivity h is constant with or insensitive to changes in oscillatory frequency , and the loss modulus G ′′ (= hG ′) becomes a constant fraction of the elastic modulus. | https://en.wikipedia.org/wiki/Hysteresivity |
The Hytort process is an above-ground shale oil extraction process developed by the Institute of Gas Technology . It is classified as a reactive fluid process, [ 1 ] which produces shale oil by hydrogenation .
The Hytort process has advantages when processing oil shales containing less hydrogen, such as the eastern United States Devonian oil shales . In this process, oil shale is processed at controlled heating rates in a high-pressure hydrogen environment, which allows a carbon conversion rate of around 80%. [ 2 ] [ 3 ] Hydrogen reacts with coke precursors (a chemical structure in the oil shale that is prone to form char during retorting but has not yet done so). In the case of Eastern US Devonian shales, the reaction roughly doubles the yield of oil, depending on the characteristics of the oil shale and process. [ 4 ] [ 5 ]
In 1980, the HYCRUDE Corporation was established to commercialize the Hytort technology. The feasibility study was conducted by HYCRUDE Corporation, Phillips Petroleum Company , Bechtel Group and the Institute of Gas Technology. [ 6 ] | https://en.wikipedia.org/wiki/Hytort_process |
In statistics , the Hájek–Le Cam convolution theorem states that any regular estimator in a parametric model is asymptotically equivalent to a sum of two independent random variables, one of which is normal with asymptotic variance equal to the inverse of Fisher information , and the other having arbitrary distribution.
The obvious corollary from this theorem is that the "best" among regular estimators are those with the second component identically equal to zero. Such estimators are called efficient and are known to always exist for regular parametric models .
The theorem is named after Jaroslav Hájek and Lucien Le Cam .
Let ℘ = { P θ | θ ∈ Θ ⊂ ℝ k } be a regular parametric model , and q ( θ ): Θ → ℝ m be a parameter in this model (typically a parameter is just one of the components of vector θ ). Assume that function q is differentiable on Θ, with the m × k matrix of derivatives denoted as q̇ θ . Define
where I ( θ ) is the Fisher information matrix for model ℘, ℓ ˙ ( θ ) {\displaystyle \scriptstyle {\dot {\ell }}(\theta )} is the score function , and ′ denotes matrix transpose .
Theorem ( Bickel 1998 , Th.2.3.1). Suppose T n is a uniformly (locally) regular estimator of the parameter q . Then | https://en.wikipedia.org/wiki/Hájek–Le_Cam_convolution_theorem |
Håvard J. Haugen (born January 23, 1975) is a Norwegian professor. He is Head of the Department of Biomaterials [ 1 ] in Faculty of Dentistry at University of Oslo , Norway. [ 2 ]
In 2021, Haugen completed his Master in Chemical Engineering at the Imperial College of Science, Technology and Medicine in London, United Kingdom . [ 3 ] [ 4 ] Haugen earned a doctoral engineering from the Technische Universitat Munchen in 2004. [ 3 ] His PhD thesis title was "Development of an implant to heal gastro-oesophageal reflux diseases." [ 5 ]
Haugen worked as a researcher in the biological group: "bioloeart gical hvalves" at Helmholtz Institute for Biomedical Engineering, RWTH Aachen in Germany . [ 6 ] He worked as a researcher at the Centre for Tissue Engineering and Regenerative Medicine, Imperial College London in UK . Between 2001 and 2004, he worked at the Central Institute for Medical Engineering at the Technical University of Munich . [ 6 ] [ 7 ]
He was a Postdoctoral researcher at the Department of Biomaterials, Institute of Clinical Dentistry , University of Oslo from 2005 to 2009. Since 2014, he has been a professor and Head of Department of Biomaterials at University of Oslo. [ 7 ] [ 8 ] [ 9 ]
Haugen`s research interest focuses on biomaterials and bone regeneration. [ 2 ] His research areas include biomaterials science , medical devices , bone graft , dental materials and orthopaedics . [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ]
In 2000, Haugen received The British Petroleum Prize in Chemical Engineering, London, UK. Three years later, he received The City and Guild Associateship Award in Chemical Engineering, London, UK. [ 3 ] He won the German Innovation Award in Germany, in 2009. [ 3 ] [ 7 ]
Between 2012 and 2016, Haugen was the President of the Scandinavian Society for Biomaterials . [ 16 ] [ 17 ] He is the project manager and recipient of the Research Council of Norway funded research grant between 2022 and 2027, with project title: "Multispecies biofilm for investigate non-antibiotic therpies in dentistry (MISFAITH)". [ 18 ] [ 19 ]
This biographical article about a Norwegian academic is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Håvard_Jostein_Haugen |
In mathematical analysis , Hölder's inequality , named after Otto Hölder , is a fundamental inequality between integrals and an indispensable tool for the study of L p spaces .
Hölder's inequality — Let ( S , Σ, μ ) be a measure space and let p , q ∈ [1, ∞] with 1/ p + 1/ q = 1 . Then for all measurable real - or complex -valued functions f and g on S ,
‖ f g ‖ 1 ≤ ‖ f ‖ p ‖ g ‖ q . {\displaystyle \|fg\|_{1}\leq \|f\|_{p}\|g\|_{q}.}
If, in addition, p , q ∈ (1, ∞) and f ∈ L p ( μ ) and g ∈ L q ( μ ) , then Hölder's inequality becomes an equality if and only if | f | p and | g | q are linearly dependent in L 1 ( μ ) , meaning that there exist real numbers α , β ≥ 0 , not both of them zero, such that α | f | p = β | g | q μ - almost everywhere .
The numbers p and q above are said to be Hölder conjugates of each other. The special case p = q = 2 gives a form of the Cauchy–Schwarz inequality . [ 1 ] Hölder's inequality holds even if ‖ fg ‖ 1 is infinite , the right-hand side also being infinite in that case. Conversely, if f is in L p ( μ ) and g is in L q ( μ ) , then the pointwise product fg is in L 1 ( μ ) .
Hölder's inequality is used to prove the Minkowski inequality , which is the triangle inequality in the space L p ( μ ) , and also to establish that L q ( μ ) is the dual space of L p ( μ ) for p ∈ [1, ∞) .
Hölder's inequality (in a slightly different form) was first found by Leonard James Rogers ( 1888 ). Inspired by Rogers' work, Hölder (1889) gave another proof as part of a work developing the concept of convex and concave functions and introducing Jensen's inequality , [ 2 ] which was in turn named for work of Johan Jensen building on Hölder's work. [ 3 ]
The brief statement of Hölder's inequality uses some conventions.
As above, let f and g denote measurable real- or complex-valued functions defined on S . If ‖ fg ‖ 1 is finite, then the pointwise products of f with g and its complex conjugate function are μ -integrable, the estimate
and the similar one for fg hold, and Hölder's inequality can be applied to the right-hand side. In particular, if f and g are in the Hilbert space L 2 ( μ ) , then Hölder's inequality for p = q = 2 implies
where the angle brackets refer to the inner product of L 2 ( μ ) . This is also called Cauchy–Schwarz inequality , but requires for its statement that ‖ f ‖ 2 and ‖ g ‖ 2 are finite to make sure that the inner product of f and g is well defined. We may recover the original inequality (for the case p = 2 ) by using the functions | f | and | g | in place of f and g .
If ( S , Σ, μ ) is a probability space , then p , q ∈ [1, ∞] just need to satisfy 1/ p + 1/ q ≤ 1 , rather than being Hölder conjugates. A combination of Hölder's inequality and Jensen's inequality implies that
for all measurable real- or complex-valued functions f and g on S .
For the following cases assume that p and q are in the open interval (1,∞) with 1/ p + 1/ q = 1 .
For the n {\displaystyle n} -dimensional Euclidean space , when the set S {\displaystyle S} is { 1 , … , n } {\displaystyle \{1,\dots ,n\}} with the counting measure , we have
Often the following practical form of this is used, for any ( r , s ) ∈ R + {\displaystyle (r,s)\in \mathbb {R} _{+}} :
For more than two sums, the following generalisation ( Lohwater (1982) , Chen (2014) ) holds, with real positive exponents λ i {\displaystyle \lambda _{i}} and λ a + λ b + ⋯ + λ z = 1 {\displaystyle \lambda _{a}+\lambda _{b}+\cdots +\lambda _{z}=1} :
Equality holds iff | a 1 | : | a 2 | : ⋯ : | a n | = | b 1 | : | b 2 | : ⋯ : | b n | = ⋯ = | z 1 | : | z 2 | : ⋯ : | z n | {\displaystyle |a_{1}|:|a_{2}|:\cdots :|a_{n}|=|b_{1}|:|b_{2}|:\cdots :|b_{n}|=\cdots =|z_{1}|:|z_{2}|:\cdots :|z_{n}|} .
If S = N {\displaystyle S=\mathbb {N} } with the counting measure, then we get Hölder's inequality for sequence spaces :
If S {\displaystyle S} is a measurable subset of R n {\displaystyle \mathbb {R} ^{n}} with the Lebesgue measure , and f {\displaystyle f} and g {\displaystyle g} are measurable real- or complex-valued functions on S {\displaystyle S} , then Hölder's inequality is
For the probability space ( Ω , F , P ) , {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} ),} let E {\displaystyle \mathbb {E} } denote the expectation operator . For real- or complex-valued random variables X {\displaystyle X} and Y {\displaystyle Y} on Ω , {\displaystyle \Omega ,} Hölder's inequality reads
Let 1 < r < s < ∞ {\displaystyle 1<r<s<\infty } and define p = s r . {\displaystyle p={\tfrac {s}{r}}.} Then q = p p − 1 {\displaystyle q={\tfrac {p}{p-1}}} is the Hölder conjugate of p . {\displaystyle p.} Applying Hölder's inequality to the random variables | X | r {\displaystyle |X|^{r}} and 1 Ω {\displaystyle 1_{\Omega }} we obtain
In particular, if the s th absolute moment is finite, then the r th absolute moment is finite, too. (This also follows from Jensen's inequality .)
For two σ-finite measure spaces ( S 1 , Σ 1 , μ 1 ) and ( S 2 , Σ 2 , μ 2 ) define the product measure space by
where S is the Cartesian product of S 1 and S 2 , the σ-algebra Σ arises as product σ-algebra of Σ 1 and Σ 2 , and μ denotes the product measure of μ 1 and μ 2 . Then Tonelli's theorem allows us to rewrite Hölder's inequality using iterated integrals : If f and g are Σ -measurable real- or complex-valued functions on the Cartesian product S , then
This can be generalized to more than two σ-finite measure spaces.
Let ( S , Σ, μ ) denote a σ-finite measure space and suppose that f = ( f 1 , ..., f n ) and g = ( g 1 , ..., g n ) are Σ -measurable functions on S , taking values in the n -dimensional real- or complex Euclidean space. By taking the product with the counting measure on {1, ..., n } , we can rewrite the above product measure version of Hölder's inequality in the form
If the two integrals on the right-hand side are finite, then equality holds if and only if there exist real numbers α , β ≥ 0 , not both of them zero, such that
for μ -almost all x in S .
This finite-dimensional version generalizes to functions f and g taking values in a normed space which could be for example a sequence space or an inner product space .
There are several proofs of Hölder's inequality; the main idea in the following is Young's inequality for products .
If ‖ f ‖ p = 0 , then f is zero μ -almost everywhere, and the product fg is zero μ -almost everywhere, hence the left-hand side of Hölder's inequality is zero.
The same is true if ‖ g ‖ q = 0 .
Therefore, we may assume ‖ f ‖ p > 0 and ‖ g ‖ q > 0 in the following.
If ‖ f ‖ p = ∞ or ‖ g ‖ q = ∞ , then the right-hand side of Hölder's inequality is infinite.
Therefore, we may assume that ‖ f ‖ p and ‖ g ‖ q are in (0, ∞) .
If p = ∞ and q = 1 , then | fg | ≤ ‖ f ‖ ∞ | g | almost everywhere and Hölder's inequality follows from the monotonicity of the Lebesgue integral. Similarly for p = 1 and q = ∞ .
Therefore, we may assume p , q ∈ (1,∞) .
We now use Young's inequality for products , which states that whenever p , q {\displaystyle p,q} are in (1,∞) with 1 p + 1 q = 1 {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}=1}
for all nonnegative a and b , where equality is achieved if and only if a p = b q . Hence
Integrating both sides gives
which proves the claim.
Under the assumptions p ∈ (1, ∞) and ‖ f ‖ p = ‖ g ‖ q , equality holds if and only if | f | p = | g | q almost everywhere.
More generally, if ‖ f ‖ p and ‖ g ‖ q are in (0, ∞) , then Hölder's inequality becomes an equality if and only if there exist real numbers α , β > 0 , namely
such that
The case ‖ f ‖ p = 0 corresponds to β = 0 in (*). The case ‖ g ‖ q = 0 corresponds to α = 0 in (*).
Alternative proof using Jensen's inequality:
The function x ↦ x p {\displaystyle x\mapsto x^{p}} on (0,∞) is convex because p ≥ 1 {\displaystyle p\geq 1} , so by Jensen's inequality,
where ν is any probability distribution and h any ν -measurable function. Let μ be any measure, and ν the distribution whose density w.r.t. μ is proportional to g q {\displaystyle g^{q}} , i.e.
Hence we have, using 1 p + 1 q = 1 {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}=1} , hence p ( 1 − q ) + q = 0 {\displaystyle p(1-q)+q=0} , and letting h = f g 1 − q {\displaystyle h=fg^{1-q}} ,
Finally, we get
This assumes that f , g are real and non-negative, but the extension to complex functions is straightforward (use the modulus of f , g ).
It also assumes that ‖ f ‖ p , ‖ g ‖ q {\displaystyle \|f\|_{p},\|g\|_{q}} are neither null nor infinity, and that p , q > 1 {\displaystyle p,q>1} : all these assumptions can also be lifted as in the proof above.
We could also bypass use of both Young's and Jensen's inequalities. The proof below also explains why and where the Hölder exponent comes in naturally.
As in the previous proof, it suffices to prove
where ν ( X ) = 1 {\displaystyle \nu (X)=1} and h {\displaystyle h} is ν {\displaystyle \nu } -measurable (real or complex) function on X {\displaystyle X} . To prove this, we must bound | h | {\displaystyle |h|} by | h | p {\displaystyle |h|^{p}} . There is no constant C {\displaystyle C} that will make | h ( x ) | ≤ C | h ( x ) | p {\displaystyle |h(x)|~\leq ~C|h(x)|^{p}} for all x > 0 {\displaystyle x>0} . Hence, we seek an inequality of the form
for suitable choices of a ′ {\displaystyle a'} and b ′ {\displaystyle b'} .
We wish to obtain A := ‖ f ‖ p {\displaystyle A:=\|f\|_{p}} on the right-hand side after integrating this inequality. By trial and error, we see that the inequality we wish should have the form
where a , b {\displaystyle a,b} are non-negative and a + b = 1 {\displaystyle a+b=1} . Indeed, the integral of the right-hand side is precisely A {\displaystyle A} . So, it remains to prove that such an inequality does hold with the right choice of a , b . {\displaystyle a,b.}
The inequality we seek would follow from:
which, in turn, is equivalent to
It turns out there is one and only one choice of a , b {\displaystyle a,b} , subject to a + b = 1 {\displaystyle a+b=1} , that makes this true: a = 1 p {\displaystyle a={\tfrac {1}{p}}} and, necessarily, b = 1 − 1 p {\displaystyle b=1-{\tfrac {1}{p}}} . (This is where Hölder conjugate exponent is born!) This completes the proof of the inequality at the first paragraph of this proof. Proof of Hölder's inequality follows from this as in the previous proof. Alternatively, we can deduce Young's inequality and then resort to the first proof given above. Young's inequality follows from the inequality (*) above by choosing z = a b q − 1 {\displaystyle z={\tfrac {a}{b^{q-1}}}} and multiplying both sides by b q {\displaystyle b^{q}} .
Assume that 1 ≤ p < ∞ and let q denote the Hölder conjugate. Then for every f ∈ L p ( μ ) ,
where max indicates that there actually is a g maximizing the right-hand side. When p = ∞ and if each set A in the σ-field Σ with μ ( A ) = ∞ contains a subset B ∈ Σ with 0 < μ ( B ) < ∞ (which is true in particular when μ is σ-finite ), then
Proof of the extremal equality:
By Hölder's inequality, the integrals are well defined and, for 1 ≤ p ≤ ∞ ,
hence the left-hand side is always bounded above by the right-hand side.
Conversely, for 1 ≤ p ≤ ∞ , observe first that the statement is obvious when ‖ f ‖ p = 0 . Therefore, we assume ‖ f ‖ p > 0 in the following.
If 1 ≤ p < ∞ , define g on S by
By checking the cases p = 1 and 1 < p < ∞ separately, we see that ‖ g ‖ q = 1 and
It remains to consider the case p = ∞ . For ε ∈ (0, 1) define
Since f is measurable, A ∈ Σ . By the definition of ‖ f ‖ ∞ as the essential supremum of f and the assumption ‖ f ‖ ∞ > 0 , we have μ ( A ) > 0 . Using the additional assumption on the σ-field Σ if necessary, there exists a subset B ∈ Σ of A with 0 < μ ( B ) < ∞ . Define g on S by
Then g is well-defined, measurable and | g ( x ) | ≤ 1/ μ ( B ) for x ∈ B , hence ‖ g ‖ 1 ≤ 1 . Furthermore,
Assume that r ∈ (0, ∞] and p 1 , ..., p n ∈ (0, ∞] such that
where 1/∞ is interpreted as 0 in this equation, and r=∞ implies p 1 , ..., p n ∈ (0, ∞] are all equal to ∞. Then, for all measurable real or complex-valued functions f 1 , ..., f n defined on S ,
where we interpret any product with a factor of ∞ as ∞ if all factors are positive, but the product is 0 if any factor is 0.
In particular, if f k ∈ L p k ( μ ) {\displaystyle f_{k}\in L^{p_{k}}(\mu )} for all k ∈ { 1 , … , n } {\displaystyle k\in \{1,\ldots ,n\}} then ∏ k = 1 n f k ∈ L r ( μ ) . {\displaystyle \prod _{k=1}^{n}f_{k}\in L^{r}(\mu ).}
Note: For r ∈ ( 0 , 1 ) , {\displaystyle r\in (0,1),} contrary to the notation, ‖ . ‖ r is in general not a norm because it doesn't satisfy the triangle inequality .
Proof of the generalization:
We use Hölder's inequality and mathematical induction . If n = 1 {\displaystyle n=1} then the result is immediate. Let us now pass from n − 1 {\displaystyle n-1} to n . {\displaystyle n.} Without loss of generality assume that p 1 ≤ ⋯ ≤ p n . {\displaystyle p_{1}\leq \cdots \leq p_{n}.}
Case 1: If p n = ∞ {\displaystyle p_{n}=\infty } then
Pulling out the essential supremum of | f n | and using the induction hypothesis, we get
Case 2: If p n < ∞ {\displaystyle p_{n}<\infty } then necessarily r < ∞ {\displaystyle r<\infty } as well, and then
are Hölder conjugates in (1, ∞) . Application of Hölder's inequality gives
Raising to the power 1 / r {\displaystyle 1/r} and rewriting,
Since q r = p n {\displaystyle qr=p_{n}} and
the claimed inequality now follows by using the induction hypothesis.
Let p 1 , ..., p n ∈ (0, ∞] and let θ 1 , ..., θ n ∈ (0, 1) denote weights with θ 1 + ... + θ n = 1 . Define p {\displaystyle p} as the weighted harmonic mean , that is,
Given measurable real- or complex-valued functions f k {\displaystyle f_{k}} on S , then the above generalization of Hölder's inequality gives
In particular, taking f 1 = ⋯ = f n =: f {\displaystyle f_{1}=\cdots =f_{n}=:f} gives
Specifying further θ 1 = θ and θ 2 = 1- θ , in the case n = 2 , {\displaystyle n=2,} we obtain the interpolation result
Littlewood's inequality — For θ ∈ ( 0 , 1 ) {\displaystyle \theta \in (0,1)} and 1 p θ = θ p 1 + 1 − θ p 0 {\displaystyle {\frac {1}{p_{\theta }}}={\frac {\theta }{p_{1}}}+{\frac {1-\theta }{p_{0}}}} ,
‖ f ‖ p θ ⩽ ‖ f ‖ p 1 θ ⋅ ‖ f ‖ p 0 1 − θ , {\displaystyle \|f\|_{p_{\theta }}\leqslant \|f\|_{p_{1}}^{\theta }\cdot \|f\|_{p_{0}}^{1-\theta },}
An application of Hölder gives
Lyapunov's inequality — If p = ( 1 − θ ) p 0 + θ p 1 , θ ∈ ( 0 , 1 ) , {\displaystyle p=(1-\theta )p_{0}+\theta p_{1},\qquad \theta \in (0,1),} then
‖ | f 0 | p 0 ( 1 − θ ) p ⋅ | f 1 | p 1 θ p ‖ p p ≤ ‖ f 0 ‖ p 0 p 0 ( 1 − θ ) ‖ f 1 ‖ p 1 p 1 θ {\displaystyle \left\||f_{0}|^{\frac {p_{0}(1-\theta )}{p}}\cdot |f_{1}|^{\frac {p_{1}\theta }{p}}\right\|_{p}^{p}\leq \|f_{0}\|_{p_{0}}^{p_{0}(1-\theta )}\|f_{1}\|_{p_{1}}^{p_{1}\theta }}
and in particular
‖ f ‖ p p ⩽ ‖ f ‖ p 0 p 0 ( 1 − θ ) ⋅ ‖ f ‖ p 1 p 1 θ . {\displaystyle \|f\|_{p}^{p}\leqslant \|f\|_{p_{0}}^{p_{0}(1-\theta )}\cdot \|f\|_{p_{1}}^{p_{1}\theta }.}
Both Littlewood and Lyapunov imply that if f ∈ L p 0 ∩ L p 1 {\displaystyle f\in L^{p_{0}}\cap L^{p_{1}}} then f ∈ L p {\displaystyle f\in L^{p}} for all p 0 < p < p 1 . {\displaystyle p_{0}<p<p_{1}.} [ 4 ]
Assume that p ∈ (1, ∞) and that the measure space ( S , Σ, μ ) satisfies μ ( S ) > 0 . Then for all measurable real- or complex-valued functions f and g on S such that g ( s ) ≠ 0 for μ -almost all s ∈ S ,
If
then the reverse Hölder inequality is an equality if and only if
Note: The expressions:
‖ f ‖ 1 p {\displaystyle \|f\|_{\frac {1}{p}}} and ‖ g ‖ − 1 p − 1 , {\displaystyle \|g\|_{\frac {-1}{p-1}},}
are not norms, they are just compact notations for
Note that p and
are Hölder conjugates.
Application of Hölder's inequality gives
Raising to the power p gives us:
Therefore:
Now we just need to recall our notation.
The Reverse Hölder inequality (above) can be generalized to the case of multiple functions if all but one conjugate is negative.
That is,
This follows from the symmetric form of the Hölder inequality (see below).
It was observed by Aczél and Beckenbach [ 5 ] that Hölder's inequality can be put in a more symmetric form, at the price of introducing an extra vector (or function):
Let f = ( f ( 1 ) , … , f ( m ) ) , g = ( g ( 1 ) , … , g ( m ) ) , h = ( h ( 1 ) , … , h ( m ) ) {\displaystyle f=(f(1),\dots ,f(m)),g=(g(1),\dots ,g(m)),h=(h(1),\dots ,h(m))} be vectors with positive entries and such that f ( i ) g ( i ) h ( i ) = 1 {\displaystyle f(i)g(i)h(i)=1} for all i {\displaystyle i} . If p , q , r {\displaystyle p,q,r} are nonzero real numbers such that 1 p + 1 q + 1 r = 0 {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}+{\frac {1}{r}}=0} , then:
The standard Hölder inequality follows immediately from this symmetric form (and in fact is easily seen to be equivalent to it). The symmetric statement also implies the reverse Hölder inequality (see above).
The result can be extended to multiple vectors:
Let f 1 , … , f n {\displaystyle f_{1},\dots ,f_{n}} be n {\displaystyle n} vectors in R m {\displaystyle \mathbb {R} ^{m}} with positive entries and such that f 1 ( i ) … f n ( i ) = 1 {\displaystyle f_{1}(i)\dots f_{n}(i)=1} for all i {\displaystyle i} . If p 1 , … , p n {\displaystyle p_{1},\dots ,p_{n}} are nonzero real numbers such that 1 p 1 + ⋯ + 1 p n = 0 {\displaystyle {\frac {1}{p_{1}}}+\dots +{\frac {1}{p_{n}}}=0} , then:
As in the standard Hölder inequalities, there are corresponding statements for infinite sums and integrals.
Let (Ω, F , P {\displaystyle \mathbb {P} } ) be a probability space, G ⊂ F a sub- σ-algebra , and p , q ∈ (1, ∞) Hölder conjugates, meaning that 1/ p + 1/ q = 1 . Then for all real- or complex-valued random variables X and Y on Ω ,
Remarks:
Proof of the conditional Hölder inequality:
Define the random variables
and note that they are measurable with respect to the sub-σ-algebra . Since
it follows that | X | = 0 a.s. on the set { U = 0} . Similarly, | Y | = 0 a.s. on the set { V = 0} , hence
and the conditional Hölder inequality holds on this set. On the set
the right-hand side is infinite and the conditional Hölder inequality holds, too. Dividing by the right-hand side, it therefore remains to show that
This is done by verifying that the inequality holds after integration over an arbitrary
Using the measurability of U, V, 1 G with respect to the sub-σ-algebra , the rules for conditional expectations, Hölder's inequality and 1/ p + 1/ q = 1 , we see that
Let S be a set and let F ( S , C ) {\displaystyle F(S,\mathbb {C} )} be the space of all complex-valued functions on S . Let N be an increasing seminorm on F ( S , C ) , {\displaystyle F(S,\mathbb {C} ),} meaning that, for all real-valued functions f , g ∈ F ( S , C ) {\displaystyle f,g\in F(S,\mathbb {C} )} we have the following implication (the seminorm is also allowed to attain the value ∞):
Then:
where the numbers p {\displaystyle p} and q {\displaystyle q} are Hölder conjugates. [ 6 ]
Remark: If ( S , Σ, μ ) is a measure space and N ( f ) {\displaystyle N(f)} is the upper Lebesgue integral of | f | {\displaystyle |f|} then the restriction of N to all Σ -measurable functions gives the usual version of Hölder's inequality.
Hölder inequality can be used to define statistical dissimilarity measures [ 7 ] between probability distributions. Those Hölder divergences are projective: They do not depend on the normalization factor of densities. | https://en.wikipedia.org/wiki/Hölder's_inequality |
In mathematics , Hölder's theorem states that the gamma function does not satisfy any algebraic differential equation whose coefficients are rational functions . This result was first proved by Otto Hölder in 1887; several alternative proofs have subsequently been found. [ 1 ]
The theorem also generalizes to the q {\displaystyle q} -gamma function .
For every n ∈ N 0 , {\displaystyle n\in \mathbb {N} _{0},} there is no non-zero polynomial P ∈ C [ X ; Y 0 , Y 1 , … , Y n ] {\displaystyle P\in \mathbb {C} [X;Y_{0},Y_{1},\ldots ,Y_{n}]} such that ∀ z ∈ C ∖ Z ≤ 0 : P ( z ; Γ ( z ) , Γ ′ ( z ) , … , Γ ( n ) ( z ) ) = 0 , {\displaystyle \forall z\in \mathbb {C} \setminus \mathbb {Z} _{\leq 0}:\qquad P\left(z;\Gamma (z),\Gamma '(z),\ldots ,{\Gamma ^{(n)}}(z)\right)=0,} where Γ {\displaystyle \Gamma } is the gamma function .
For example, define P ∈ C [ X ; Y 0 , Y 1 , Y 2 ] {\displaystyle P\in \mathbb {C} [X;Y_{0},Y_{1},Y_{2}]} by P = df X 2 Y 2 + X Y 1 + ( X 2 − ν 2 ) Y 0 . {\displaystyle P~{\stackrel {\text{df}}{=}}~X^{2}Y_{2}+XY_{1}+(X^{2}-\nu ^{2})Y_{0}.}
Then the equation P ( z ; f ( z ) , f ′ ( z ) , f ″ ( z ) ) = z 2 f ″ ( z ) + z f ′ ( z ) + ( z 2 − ν 2 ) f ( z ) ≡ 0 {\displaystyle P\left(z;f(z),f'(z),f''(z)\right)=z^{2}f''(z)+zf'(z)+\left(z^{2}-\nu ^{2}\right)f(z)\equiv 0} is called an algebraic differential equation , which, in this case, has the solutions f = J ν {\displaystyle f=J_{\nu }} and f = Y ν {\displaystyle f=Y_{\nu }} — the Bessel functions of the first and second kind respectively. Hence, we say that J ν {\displaystyle J_{\nu }} and Y ν {\displaystyle Y_{\nu }} are differentially algebraic (also algebraically transcendental ). Most of the familiar special functions of mathematical physics are differentially algebraic. All algebraic combinations of differentially algebraic functions are differentially algebraic. Furthermore, all compositions of differentially algebraic functions are differentially algebraic. Hölder’s Theorem simply states that the gamma function, Γ {\displaystyle \Gamma } , is not differentially algebraic and is therefore transcendentally transcendental . [ 2 ]
Let n ∈ N 0 , {\displaystyle n\in \mathbb {N} _{0},} and assume that a non-zero polynomial P ∈ C [ X ; Y 0 , Y 1 , … , Y n ] {\displaystyle P\in \mathbb {C} [X;Y_{0},Y_{1},\ldots ,Y_{n}]} exists such that ∀ z ∈ C ∖ Z ≤ 0 : P ( z ; Γ ( z ) , Γ ′ ( z ) , … , Γ ( n ) ( z ) ) = 0. {\displaystyle \forall z\in \mathbb {C} \setminus \mathbb {Z} _{\leq 0}:\qquad P\left(z;\Gamma (z),\Gamma '(z),\ldots ,{\Gamma ^{(n)}}(z)\right)=0.}
As a non-zero polynomial in C [ X ] {\displaystyle \mathbb {C} [X]} can never give rise to the zero function on any non-empty open domain of C {\displaystyle \mathbb {C} } (by the fundamental theorem of algebra ), we may suppose, without loss of generality, that P {\displaystyle P} contains a monomial term having a non-zero power of one of the indeterminates Y 0 , Y 1 , … , Y n {\displaystyle Y_{0},Y_{1},\ldots ,Y_{n}} .
Assume also that P {\displaystyle P} has the lowest possible overall degree with respect to the lexicographic ordering Y 0 < Y 1 < ⋯ < Y n < X . {\displaystyle Y_{0}<Y_{1}<\cdots <Y_{n}<X.} For example, deg ( − 3 X 10 Y 0 2 Y 1 4 + i X 2 Y 2 ) < deg ( 2 X Y 0 3 − Y 1 4 ) {\displaystyle \deg \left(-3X^{10}Y_{0}^{2}Y_{1}^{4}+iX^{2}Y_{2}\right)<\deg \left(2XY_{0}^{3}-Y_{1}^{4}\right)} because the highest power of Y 0 {\displaystyle Y_{0}} in any monomial term of the first polynomial is smaller than that of the second polynomial.
Next, observe that for all z ∈ C ∖ Z ≤ 0 {\displaystyle z\in \mathbb {C} \smallsetminus \mathbb {Z} _{\leq 0}} we have: P ( z + 1 ; Γ ( z + 1 ) , Γ ′ ( z + 1 ) , Γ ″ ( z + 1 ) , … , Γ ( n ) ( z + 1 ) ) = P ( z + 1 ; z Γ ( z ) , [ z Γ ( z ) ] ′ , [ z Γ ( z ) ] ″ , … , [ z Γ ( z ) ] ( n ) ) = P ( z + 1 ; z Γ ( z ) , z Γ ′ ( z ) + Γ ( z ) , z Γ ″ ( z ) + 2 Γ ′ ( z ) , … , z Γ ( n ) ( z ) + n Γ ( n − 1 ) ( z ) ) . {\displaystyle {\begin{aligned}&P\left(z+1;\Gamma (z+1),\Gamma '(z+1),\Gamma ''(z+1),\ldots ,\Gamma ^{(n)}(z+1)\right)\\[1ex]&=P\left(z+1;z\Gamma (z),[z\Gamma (z)]',[z\Gamma (z)]'',\ldots ,[z\Gamma (z)]^{(n)}\right)\\[1ex]&=P\left(z+1;z\Gamma (z),z\Gamma '(z)+\Gamma (z),z\Gamma ''(z)+2\Gamma '(z),\ldots ,z{\Gamma ^{(n)}}(z)+n{\Gamma ^{(n-1)}}(z)\right).\end{aligned}}}
If we define a second polynomial Q ∈ C [ X ; Y 0 , Y 1 , … , Y n ] {\displaystyle Q\in \mathbb {C} [X;Y_{0},Y_{1},\ldots ,Y_{n}]} by the transformation Q = df P ( X + 1 ; X Y 0 , X Y 1 + Y 0 , X Y 2 + 2 Y 1 , … , X Y n + n Y n − 1 ) , {\displaystyle Q~{\stackrel {\text{df}}{=}}~P(X+1;XY_{0},XY_{1}+Y_{0},XY_{2}+2Y_{1},\ldots ,XY_{n}+nY_{n-1}),} then we obtain the following algebraic differential equation for Γ {\displaystyle \Gamma } : ∀ z ∈ C ∖ Z ≤ 0 : Q ( z ; Γ ( z ) , Γ ′ ( z ) , … , Γ ( n ) ( z ) ) ≡ 0. {\displaystyle \forall z\in \mathbb {C} \setminus \mathbb {Z} _{\leq 0}:\qquad Q\left(z;\Gamma (z),\Gamma '(z),\ldots ,{\Gamma ^{(n)}}(z)\right)\equiv 0.}
Furthermore, if X h Y 0 h 0 Y 1 h 1 ⋯ Y n h n {\displaystyle X^{h}Y_{0}^{h_{0}}Y_{1}^{h_{1}}\cdots Y_{n}^{h_{n}}} is the highest-degree monomial term in P {\displaystyle P} , then the highest-degree monomial term in Q {\displaystyle Q} is X h + h 0 + h 1 + ⋯ + h n Y 0 h 0 Y 1 h 1 ⋯ Y n h n . {\displaystyle X^{h+h_{0}+h_{1}+\cdots +h_{n}}Y_{0}^{h_{0}}Y_{1}^{h_{1}}\cdots Y_{n}^{h_{n}}.}
Consequently, the polynomial Q − X h 0 + h 1 + ⋯ + h n P {\displaystyle Q-X^{h_{0}+h_{1}+\cdots +h_{n}}P} has a smaller overall degree than P {\displaystyle P} , and as it clearly gives rise to an algebraic differential equation for Γ {\displaystyle \Gamma } , it must be the zero polynomial by the minimality assumption on P {\displaystyle P} . Hence, defining R ∈ C [ X ] {\displaystyle R\in \mathbb {C} [X]} by R = df X h 0 + h 1 + ⋯ + h n , {\displaystyle R~{\stackrel {\text{df}}{=}}~X^{h_{0}+h_{1}+\cdots +h_{n}},} we get Q = P ( X + 1 ; X Y 0 , X Y 1 + Y 0 , X Y 2 + 2 Y 1 , … , X Y n + n Y n − 1 ) = R ( X ) ⋅ P ( X ; Y 0 , Y 1 , … , Y n ) . {\displaystyle Q=P(X+1;XY_{0},XY_{1}+Y_{0},XY_{2}+2Y_{1},\ldots ,XY_{n}+nY_{n-1})=R(X)\cdot P(X;Y_{0},Y_{1},\ldots ,Y_{n}).}
Now, let X = 0 {\displaystyle X=0} in Q {\displaystyle Q} to obtain Q ( 0 ; Y 0 , Y 1 , … , Y n ) = P ( 1 ; 0 , Y 0 , 2 Y 1 , … , n Y n − 1 ) = R ( 0 ) ⋅ P ( 0 ; Y 0 , Y 1 , … , Y n ) = 0 C [ Y 0 , Y 1 , … , Y n ] . {\displaystyle Q(0;Y_{0},Y_{1},\ldots ,Y_{n})=P(1;0,Y_{0},2Y_{1},\ldots ,nY_{n-1})=R(0)\cdot P(0;Y_{0},Y_{1},\ldots ,Y_{n})=0_{\mathbb {C} [Y_{0},Y_{1},\ldots ,Y_{n}]}.}
A change of variables then yields P ( 1 ; 0 , Y 1 , Y 2 , … , Y n ) = 0 C [ Y 0 , Y 1 , … , Y n ] , {\displaystyle P(1;0,Y_{1},Y_{2},\ldots ,Y_{n})=0_{\mathbb {C} [Y_{0},Y_{1},\ldots ,Y_{n}]},} and an application of mathematical induction (along with a change of variables at each induction step) to the earlier expression P ( X + 1 ; X Y 0 , X Y 1 + Y 0 , X Y 2 + 2 Y 1 , … , X Y n + n Y n − 1 ) = R ( X ) ⋅ P ( X ; Y 0 , Y 1 , … , Y n ) {\displaystyle P(X+1;XY_{0},XY_{1}+Y_{0},XY_{2}+2Y_{1},\ldots ,XY_{n}+nY_{n-1})=R(X)\cdot P(X;Y_{0},Y_{1},\ldots ,Y_{n})} reveals that ∀ m ∈ N : P ( m ; 0 , Y 1 , Y 2 , … , Y n ) = 0 C [ Y 0 , Y 1 , … , Y n ] . {\displaystyle \forall m\in \mathbb {N} :\qquad P(m;0,Y_{1},Y_{2},\ldots ,Y_{n})=0_{\mathbb {C} [Y_{0},Y_{1},\ldots ,Y_{n}]}.}
This is possible only if P {\displaystyle P} is divisible by Y 0 {\displaystyle Y_{0}} , which contradicts the minimality assumption on P {\displaystyle P} . Therefore, no such P {\displaystyle P} exists, and so Γ {\displaystyle \Gamma } is not differentially algebraic. [ 2 ] [ 3 ] Q.E.D. | https://en.wikipedia.org/wiki/Hölder's_theorem |
In organic chemistry , Hückel's rule predicts that a planar ring molecule will have aromatic properties if it has 4 n + 2 π-electrons , where n is a non-negative integer . The quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931. [ 1 ] [ 2 ] The succinct expression as the 4 n + 2 rule has been attributed to W. v. E. Doering (1951), [ 3 ] [ 4 ] although several authors were using this form at around the same time. [ 5 ]
In agreement with the Möbius–Hückel concept , a cyclic ring molecule follows Hückel's rule when the number of its π-electrons equals 4 n + 2, although clearcut examples are really only established for values of n = 0 up to about n = 6. [ 6 ] Hückel's rule was originally based on calculations using the Hückel method , although it can also be justified by considering a particle in a ring system, by the LCAO method [ 5 ] and by the Pariser–Parr–Pople method .
Aromatic compounds are more stable than theoretically predicted using hydrogenation data of simple alkenes ; the additional stability is due to the delocalized cloud of electrons, called resonance energy . Criteria for simple aromatics are:
The rule can be used to understand the stability of completely conjugated monocyclic hydrocarbons (known as annulenes ) as well as their cations and anions.
The best-known example is benzene (C 6 H 6 ) with a conjugated system of six π electrons, which equals 4 n + 2 for n = 1. The molecule undergoes substitution reactions which preserve the six π electron system rather than addition reactions which would destroy it. The stability of this π electron system is referred to as aromaticity . Still, in most cases, catalysts are necessary for substitution reactions to occur.
The cyclopentadienyl anion ( C 5 H – 5 ) with six π electrons is planar and readily generated from the unusually acidic cyclopentadiene ( p K a 16), while the corresponding cation with four π electrons is destabilized, being harder to generate than a typical acyclic pentadienyl cations and is thought to be antiaromatic. [ 8 ] Similarly, the tropylium cation ( C 7 H + 7 ), also with six π electrons, is so stable compared to a typical carbocation that its salts can be crystallized from ethanol. [ 8 ] On the other hand, in contrast to cyclopentadiene , cycloheptatriene is not particularly acidic (p K a 37) and the anion is considered nonaromatic. The cyclopropenyl cation ( C 3 H + 3 ) [ 9 ] [ 10 ] and the triboracyclopropenyl dianion ( B 3 H 2– 3 ) are considered examples of a two π electron system, which are stabilized relative to the open system, despite the angle strain imposed by the 60° bond angles. [ 11 ] [ 12 ]
Planar ring molecules with 4 n π electrons do not obey Hückel's rule, and theory predicts that they are less stable and have triplet ground states with two unpaired electrons. In practice, such molecules distort from planar regular polygons. Cyclobutadiene (C 4 H 4 ) with four π electrons is stable only at temperatures below 35 K and is rectangular rather than square. [ 8 ] Cyclooctatetraene (C 8 H 8 ) with eight π electrons has a nonplanar "tub" structure. However, the dianion C 8 H 2– 8 ( cyclooctatetraenide anion ), with ten π electrons obeys the 4 n + 2 rule for n = 2 and is planar, while the 1,4-dimethyl derivative of the dication, with six π electrons, is also believed to be planar and aromatic. [ 8 ] The Cyclononatetraenide anion ( C 9 H – 9 ) is the largest all- cis monocyclic annulene/annulenyl system that is planar and aromatic. These bond angles (140°) differ significantly from the ideal angles of 120°. Larger rings possess trans bonds to avoid the increased angle strain. However, 10 to 14-membered systems all experience considerable transannular strain . Thus, these systems are either nonaromatic or experience modest aromaticity. This changes when we get to [18]annulene , with (4×4) + 2 = 18 π electrons, which is large enough to accommodate six interior hydrogen atoms in a planar configuration (3 cis double bonds and 6 trans double bonds). Thermodynamic stabilization, NMR chemical shifts, and nearly equal bond lengths all point to considerable aromaticity for [18]annulene.
The (4n+2) rule is a consequence of the degeneracy of the π orbitals in cyclic conjugated hydrocarbon molecules. As predicted by Hückel molecular orbital theory , the lowest π orbital in such molecules is non-degenerate and the higher orbitals form degenerate pairs. Benzene's lowest π orbital is non-degenerate and can hold 2 electrons, and its next 2 π orbitals form a degenerate pair which can hold 4 electrons. Its 6 π electrons therefore form a stable closed shell in a regular hexagonal molecule. [ 13 ] [ 8 ]
However for cyclobutadiene or cyclooctatrene with regular geometries, the highest molecular orbital pair is occupied by only 2 π electrons forming a less stable open shell. The molecules therefore stabilize by geometrical distortions which separate the degenerate orbital energies so that the last two electrons occupy the same orbital, but the molecule as a whole is less stable in the presence of such a distortion. [ 8 ]
Hückel's rule can also be applied to molecules containing other atoms such as nitrogen or oxygen. For example, pyridine (C 5 H 5 N) has a ring structure similar to benzene, except that one -CH- group is replaced by a nitrogen atom with no hydrogen. There are still six π electrons and the pyridine molecule is also aromatic and known for its stability. [ 14 ]
Hückel's rule is not valid for many compounds containing more than one ring. For example, pyrene and trans-bicalicene contain 16 conjugated electrons (8 bonds), and coronene contains 24 conjugated electrons (12 bonds). Both of these polycyclic molecules are aromatic, even though they fail the 4 n + 2 rule. Indeed, Hückel's rule can only be theoretically justified for monocyclic systems. [ 5 ]
In 2000, Andreas Hirsch and coworkers in Erlangen , Germany , formulated a rule to determine when a spherical compound will be aromatic. They found that closed-shell compounds were aromatic when they had 2( n + 1) 2 π- electrons , for instance the buckminsterfullerene species C 60 10+ . [ 15 ] [ 16 ]
In 2011, Jordi Poater and Miquel Solà expanded the rule to open-shell spherical compounds, finding they were aromatic when they had 2 n 2 + 2 n + 1 π- electrons , with spin S = (n + 1/2) - corresponding to a half-filled last occupied energy level with the same spin. For instance C 60 1– is also observed to be aromatic with a spin of 11/2. [ 16 ] | https://en.wikipedia.org/wiki/Hückel's_rule |
The Hückel method or Hückel molecular orbital theory , proposed by Erich Hückel in 1930, is a simple method for calculating molecular orbitals as linear combinations of atomic orbitals . The theory predicts the molecular orbitals for π-electrons in π-delocalized molecules , such as ethylene , benzene , butadiene , and pyridine . [ 1 ] [ 2 ] [ 3 ] It provides the theoretical basis for Hückel's rule that cyclic, planar molecules or ions with 4 n + 2 {\displaystyle 4n+2} π-electrons are aromatic . It was later extended to conjugated molecules such as pyridine , pyrrole and furan that contain atoms other than carbon and hydrogen ( heteroatoms ). [ 4 ] A more dramatic extension of the method to include σ-electrons, known as the extended Hückel method (EHM), was developed by Roald Hoffmann . The extended Hückel method gives some degree of quantitative accuracy for organic molecules in general (not just planar systems) and was used to provide computational justification for the Woodward–Hoffmann rules . [ 5 ] To distinguish the original approach from Hoffmann's extension, the Hückel method is also known as the simple Hückel method (SHM).
Although undeniably a cornerstone of organic chemistry, Hückel's concepts were undeservedly unrecognized for two decades. Pauling and Wheland characterized his approach as "cumbersome" at the time, and their competing resonance theory was relatively easier to understand for chemists without fundamental physics background, even if they couldn't grasp the concept of quantum superposition and confused it with tautomerism . His lack of communication skills contributed: when Robert Robinson sent him a friendly request, he responded arrogantly that he is not interested in organic chemistry. [ 6 ]
In spite of its simplicity, the Hückel method in its original form makes qualitatively accurate and chemically useful predictions for many common molecules and is therefore a powerful and widely taught educational tool. It is described in many introductory quantum chemistry and physical organic chemistry textbooks, and organic chemists in particular still routinely apply Hückel theory to obtain a very approximate, back-of-the-envelope understanding of π-bonding.
The method has several characteristics:
The results for a few simple molecules are tabulated below:
HOMO/LUMO/SOMO = Highest occupied/lowest unoccupied/singly-occupied molecular orbitals.
The theory predicts two energy levels for ethylene with its two π electrons filling the low-energy HOMO and the high energy LUMO remaining empty. In butadiene the 4 π-electrons occupy 2 low energy molecular orbitals, out of a total of 4, and for benzene 6 energy levels are predicted, two of them degenerate .
For linear and cyclic systems (with N atoms), general solutions exist: [ 9 ]
The energy levels for cyclic systems can be predicted using the Frost circle [ de ] mnemonic (named after the American chemist Arthur Atwater Frost [ de ] ). A circle centered at α with radius 2β is inscribed with a regular N- gon with one vertex pointing down; the y -coordinate of the vertices of the polygon then represent the orbital energies of the [ N ]annulene/annulenyl system. [ 11 ] Related mnemonics exists for linear and Möbius systems. [ 12 ]
The value of α is the energy of an electron in a 2p orbital, relative to an unbound electron at infinity. This quantity is negative, since the electron is stabilized by being electrostatically bound to the positively charged nucleus. For carbon this value is known to be approximately –11.4 eV. Since Hückel theory is generally only interested in energies relative to a reference localized system, the value of α is often immaterial and can be set to zero without affecting any conclusions.
Roughly speaking, β physically represents the energy of stabilization experienced by an electron allowed to delocalize in a π molecular orbital formed from the 2p orbitals of adjacent atoms, compared to being localized in an isolated 2p atomic orbital. As such, it is also a negative number, although it is often spoken of in terms of its absolute value. The value for |β| in Hückel theory is roughly constant for structurally similar compounds, but not surprisingly, structurally dissimilar compounds will give very different values for |β|. For example, using the π bond energy of ethylene (65 kcal/mole) and comparing the energy of a doubly-occupied π orbital (2α + 2β) with the energy of electrons in two isolated p orbitals (2α), a value of |β| = 32.5 kcal/mole can be inferred. On the other hand, using the resonance energy of benzene (36 kcal/mole, derived from heats of hydrogenation) and comparing benzene (6α + 8β) with a hypothetical "non-aromatic 1,3,5-cyclohexatriene" (6α + 6β), a much smaller value of |β| = 18 kcal/mole emerges. These differences are not surprising, given the substantially shorter bond length of ethylene (1.33 Å) compared to benzene (1.40 Å). The shorter distance between the interacting p orbitals accounts for the greater energy of interaction, which is reflected by a higher value of |β|. Nevertheless, heat of hydrogenation measurements of various polycyclic aromatic hydrocarbons like naphthalene and anthracene all imply values of |β| between 17 and 20 kcal/mol.
However, even for the same compound, the correct assignment of |β| can be controversial. For instance, it is argued that the resonance energy measured experimentally via heats of hydrogenation is diminished by the distortions in bond lengths that must take place going from the single and double bonds of "non-aromatic 1,3,5-cyclohexatriene" to the delocalized bonds of benzene. Taking this distortion energy into account, the value of |β| for delocalization without geometric change (called the "vertical resonance energy") for benzene is found to be around 37 kcal/mole. On the other hand, experimental measurements of electronic spectra have given a value of |β| (called the "spectroscopic resonance energy") as high as 3 eV (~70 kcal/mole) for benzene. [ 13 ] Given these subtleties, qualifications, and ambiguities, Hückel theory should not be called upon to provide accurate quantitative predictions – only semi-quantitative or qualitative trends and comparisons are reliable and robust.
With this caveat in mind, many predictions of the theory have been experimentally verified:
The analysis of the optical activity of a molecule depends to a certain extent on the study of its chiral characteristics. However, for achiral molecules applying pesudoscalars to simplify the calculations of optical activity cannot be achieved due to the lack of spatial average. [ 16 ]
Instead of traditional chiroptical solution measurements, Hückel theory helps focus on oriented π systems by separating from σ electrons especially in the planar, C 2 v {\displaystyle C_{\mathrm {2v} }} -symmetric cases. Transition dipole moments derived by multiplying each wavefunction of individual planar molecule one by one, contribute to the directions of the most optical activity, where sit at the bisectors of two orthogonal ones. Despite the zero value for the trace of the tensor, cis-butadiene shows considerable off diagonal component which was computed as the first optical activity evaluation of achiral molecule. [ 17 ]
Consider 3,5-dimethylene-1-cyclopentene as an example. Transition electric dipole, magnetic dipole and electric quadrupole moments interactions result in optical rotation(OR), which can be described by both tensor components and chemical geometries. The in phase overlap of two molecular orbitals yield negative charge while depleting charge out of phase. The movement can be interpreted quantitatively by corresponding π and π* orbitals coefficients.
The delocalization energy, π-bond orders, and π-electron population are chemically significant parameters that can be gleaned from the orbital energies and coefficients that are the direct outputs of Hückel theory. [ 18 ] These are quantities strictly derived from theory, as opposed to measurable physical properties, though they correlate with measurable qualitative and quantitative properties of the chemical species. Delocalization energy is defined as the difference in energy between that of the most stable localized Lewis structure and the energy of the molecule computed from Hückel theory orbital energies and occupancies. Since all energies are relative, we set α = 0 {\displaystyle \alpha =0} without loss of generality to simplify discussion. The energy of the localized structure is then set to be 2β for every two-electron localized π-bond. The Hückel energy of the molecule is ∑ i n i E i {\displaystyle \sum _{i}n_{i}E_{i}} , where the sum is over all Hückel orbitals, n i {\displaystyle n_{i}} is the occupancy of orbital i , set to be 2 for doubly-occupied orbitals, 1 for singly-occupied orbitals, and 0 for unoccupied orbitals, and E i {\displaystyle E_{i}} is the energy of orbital i . Thus, the delocalization energy, conventionally a positive number, is defined as
In the case of benzene, the occupied orbitals have energies (again setting α = 0 {\displaystyle \alpha =0} ) 2β, β, and β. This gives the Hückel energy of benzene as 2 × 2 β + 2 × β + 2 × β = 8 β {\displaystyle 2\times 2\beta +2\times \beta +2\times \beta =8\beta } . Each Kekulé structure of benzene has three double bonds, so the localized structure is assigned an energy of 2 β × 3 = 6 β {\displaystyle 2\beta \times 3=6\beta } . The delocalization energy, measured in units of | β | {\displaystyle |\beta |} , is then | 8 β − 6 β | = 2 | β | {\displaystyle |8\beta -6\beta |=2|\beta |} .
The π-bond orders derived from Hückel theory are defined using the orbital coefficients of the Hückel MOs. The π-bond order between atoms j and k is defined as
where n i {\displaystyle n_{i}} is again the orbital occupancy of orbital i and c j ( i ) {\displaystyle c_{j}^{(i)}} and c k ( i ) {\displaystyle c_{k}^{(i)}} are the coefficients on atoms j and k , respectively, for orbital i . For benzene, the three occupied MOs, expressed as linear combinations of AOs ϕ i {\displaystyle \phi _{i}} , are: [ 19 ]
Perhaps surprisingly, the π-bond order formula gives a bond order of
for the bond between carbons 1 and 2. [ 20 ] The resulting total (σ + π) bond order of 1 2 3 {\displaystyle 1{\frac {2}{3}}} is the same between any other pair of adjacent carbon atoms. This is more than the naive π-bond order of 1 2 {\displaystyle {\frac {1}{2}}} (for a total bond order of 1 1 2 {\displaystyle 1{\frac {1}{2}}} ) that one might guess when simply considering the Kekulé structures and the usual definition of bond order in valence bond theory. The Hückel definition of bond order attempts to quantify any additional stabilization that the system enjoys resulting from delocalization. In a sense, the Hückel bond order suggests that there are four π-bonds in benzene instead of the three that are implied by the Kekulé-type Lewis structures. The "extra" bond is attributed to the additional stabilization that results from the aromaticity of the benzene molecule. (This is only one of several definitions for non-integral bond orders, and other definitions will lead to different values that fall between 1 and 2.)
The π-electron population is calculated in a very similar way to the bond order using the orbital coefficients of the Hückel MOs. The π-electron population on atom j is defined as
The associated Hückel Coulomb charge is defined as q j = N π ( j ) − n π ( j ) {\displaystyle q_{j}=N_{\pi }(j)-n_{\pi }(j)} , where N π ( j ) {\displaystyle N_{\pi }(j)} is the number of π-electrons contributed by a neutral, sp 2 -hybridized atom j (we always have N π = 1 {\displaystyle N_{\pi }=1} for carbon).
For carbon 1 on benzene, this yields a π-electron population of
Since each carbon atom contributes one π-electron to the molecule, this gives a Coulomb charge of 0 for carbon 1 (and all other carbon atoms), as expected.
In the cases of benzyl cation and benzyl anion shown above,
The mathematics of the Hückel method is based on the Ritz method . In short, given a basis set of n normalized atomic orbitals { ϕ i } i = 1 n {\displaystyle \{\phi _{i}\}_{i=1}^{n}} , an ansatz molecular orbital ψ g = N ( c 1 ϕ 1 + ⋯ + c n ϕ n ) {\displaystyle \psi _{g}=N(c_{1}\phi _{1}+\cdots +c_{n}\phi _{n})} is written down, with normalization constant N and coefficients c i {\displaystyle c_{i}} which are to be determined. In other words, we are assuming that the molecular orbital (MO) can be written as a linear combination of atomic orbitals, a conceptually intuitive and convenient approximation (the linear combination of atomic orbitals or LCAO approximation). The variational theorem states that given an eigenvalue problem H ^ | ψ ( i ) ⟩ = E ( i ) | ψ ( i ) ⟩ {\displaystyle {\hat {H}}|\psi ^{(i)}\rangle =E^{(i)}|\psi ^{(i)}\rangle } with smallest eigenvalue E ( 0 ) {\displaystyle E^{(0)}} and corresponding wavefunction ψ ( 0 ) {\displaystyle \psi ^{(0)}} , any normalized trial wavefunction ψ g {\displaystyle \psi _{g}} (i.e., ⟨ ψ g | ψ g ⟩ = ∫ R 3 ψ g ∗ ψ g d V = 1 {\textstyle \langle \psi _{g}|\psi _{g}\rangle =\int _{\mathbb {R} ^{3}}\psi _{g}^{*}\,\psi _{g}\,dV=1} holds) will satisfy
with equality holding if and only if ψ g = ψ ( 0 ) {\displaystyle \psi _{g}=\psi ^{(0)}} . Thus, by minimizing E ( c 1 , … , c n ) = E [ ψ g ] {\displaystyle E(c_{1},\ldots ,c_{n})={\mathcal {E}}[\psi _{g}]} with respect to coefficients c i {\displaystyle c_{i}} for normalized trial wavefunctions ψ g ( c 1 , … , c n ) {\displaystyle \psi _{g}(c_{1},\ldots ,c_{n})} , we obtain a closer approximation of the true ground-state wavefunction and its energy.
To start, we apply the normalization condition to the ansatz and expand to get an expression for N in terms of the c i {\displaystyle c_{i}} . Then, we substitute the ansatz into the expression for E and expand, yielding
In the remainder of the derivation, we will assume that the atomic orbitals are real. (For the simple case of the Hückel theory, they will be the 2p z orbitals on carbon.) Thus, S i j = S j i ∗ = S j i {\displaystyle S_{ij}=S_{ji}^{*}=S_{ji}} , and because the Hamiltonian operator is hermitian , H i j = H j i ∗ = H j i {\displaystyle H_{ij}=H_{ji}^{*}=H_{ji}} . Setting ∂ E / ∂ c i = 0 {\displaystyle \partial {E}/\partial {c_{i}}=0} for i = 1 , … , n {\displaystyle i=1,\ldots ,n} to minimize E and collecting terms, we obtain a system of n simultaneous equations
When i ≠ j {\displaystyle i\neq j} , S i j {\displaystyle S_{ij}} and H i j {\displaystyle H_{ij}} are called the overlap and resonance (or exchange ) integrals , respectively, while H i i {\displaystyle H_{ii}} is called the Coulomb integral , and S i i = 1 {\displaystyle S_{ii}=1} simply expresses the fact that the ϕ i {\displaystyle \phi _{i}} are normalized. The n × n matrices [ S i j ] {\displaystyle [S_{ij}]} and [ H i j ] {\displaystyle [H_{ij}]} are known as the overlap and Hamiltonian matrices , respectively.
By a well-known result from linear algebra , nontrivial solutions ( c 1 , c 2 , … , c n ) {\displaystyle (c_{1},c_{2},\ldots ,c_{n})} to the above system of linear equations can only exist if the coefficient matrix [ H i j − E S i j ] {\displaystyle [H_{ij}-ES_{ij}]} is singular . Hence, E {\displaystyle E} must have a value such that the determinant of the coefficient matrix vanishes:
This determinant expression is known as the secular determinant and gives rise to a generalized eigenvalue problem . The variational theorem guarantees that the lowest value of E {\displaystyle E} that gives rise to a nontrivial (that is, not all zero) solution vector ( c 1 , c 2 , … , c n ) {\displaystyle (c_{1},c_{2},\ldots ,c_{n})} represents the best LCAO approximation of the energy of the most stable π orbital; higher values of E {\displaystyle E} with nontrivial solution vectors represent reasonable estimates of the energies of the remaining π orbitals.
The Hückel method makes a few further simplifying assumptions concerning the values of the S i j {\displaystyle S_{ij}} and H i j {\displaystyle H_{ij}} . In particular, it is first assumed that distinct ϕ i {\displaystyle \phi _{i}} have zero overlap. Together with the assumption that ϕ i {\displaystyle \phi _{i}} are normalized, this means that the overlap matrix is the n × n identity matrix: [ S i j ] = I n {\displaystyle [S_{ij}]=\mathbf {I} _{n}} . Solving for E in (*) then reduces to finding the eigenvalues of the Hamiltonian matrix.
Second, in the simplest case of a planar, unsaturated hydrocarbon, the Hamiltonian matrix H = [ H i j ] {\displaystyle \mathbf {H} =[H_{ij}]} is parameterized in the following way:
To summarize, we are assuming that: (1) the energy of an electron in an isolated C(2p z ) orbital is H i i = α {\displaystyle H_{ii}=\alpha } ; (2) the energy of interaction between C(2p z ) orbitals on adjacent carbons i and j (i.e., i and j are connected by a σ-bond) is H i j = β {\displaystyle H_{ij}=\beta } ; (3) orbitals on carbons not joined in this way are assumed not to interact, so H i j = 0 {\displaystyle H_{ij}=0} for nonadjacent i and j ; and, as mentioned above, (4) the spatial overlap of electron density between different orbitals, represented by non-diagonal elements of the overlap matrix, is ignored by setting S i j = 0 ( i ≠ j ) {\displaystyle S_{ij}=0\ \ (i\neq j)} , even when the orbitals are adjacent .
This neglect of orbital overlap is an especially severe approximation. In actuality, orbital overlap is a prerequisite for orbital interaction, and it is impossible to have H i j = β {\displaystyle H_{ij}=\beta } while S i j = 0 {\displaystyle S_{ij}=0} . For typical bond distances (1.40 Å) as might be found in benzene , for example, the true value of the overlap for C(2p z ) orbitals on adjacent atoms i and j is about S i j = 0.21 {\displaystyle S_{ij}=0.21} ; even larger values are found when the bond distance is shorter (e.g., S i j = 0.27 {\displaystyle S_{ij}=0.27} ethylene). [ 21 ] A major consequence of having nonzero overlap integrals is the fact that, compared to non-interacting isolated orbitals, bonding orbitals are not energetically stabilized by nearly as much as antibonding orbitals are destabilized. The orbital energies derived from the Hückel treatment do not account for this asymmetry ( see Hückel solution for ethylene (below) for details ).
The eigenvalues of H {\displaystyle \mathbf {H} } are the Hückel molecular orbital energies E 1 , … , E n {\displaystyle E_{1},\ldots ,E_{n}} , expressed in terms of α {\displaystyle \alpha } and β {\displaystyle \beta } , while the eigenvectors are the Hückel MOs Ψ 1 , … , Ψ n {\displaystyle \Psi _{1},\ldots ,\Psi _{n}} , expressed as linear combinations of the atomic orbitals ϕ i {\displaystyle \phi _{i}} . Using the expression for the normalization constant N and the fact that [ S i j ] = I n {\displaystyle [S_{ij}]=\mathbf {I} _{n}} , we can find the normalized MOs by incorporating the additional condition
The Hückel MOs are thus uniquely determined when eigenvalues are all distinct. When an eigenvalue is degenerate (two or more of the E i {\displaystyle E_{i}} are equal), the eigenspace corresponding to the degenerate energy level has dimension greater than 1, and the normalized MOs at that energy level are then not uniquely determined. When that happens, further assumptions pertaining to the coefficients of the degenerate orbitals (usually ones that make the MOs orthogonal and mathematically convenient [ 22 ] ) have to be made in order to generate a concrete set of molecular orbital functions.
If the substance is a planar, unsaturated hydrocarbon, the coefficients of the MOs can be found without appeal to empirical parameters, while orbital energies are given in terms of only α {\displaystyle \alpha } and β {\displaystyle \beta } . On the other hand, for systems containing heteroatoms, such as pyridine or formaldehyde , values of correction constants h X {\displaystyle h_{\mathrm {X} }} and k X − Y {\displaystyle k_{\mathrm {X-Y} }} have to be specified for the atoms and bonds in question, and α {\displaystyle \alpha } and β {\displaystyle \beta } in (**) are replaced by α + h X β {\displaystyle \alpha +h_{\mathrm {X} }\beta } and k X − Y β {\displaystyle k_{\mathrm {X-Y} }\beta } , respectively.
In the Hückel treatment for ethylene , we write the Hückel MOs Ψ {\displaystyle \Psi \,} as a linear combination of the atomic orbitals (2p orbitals) on each of the carbon atoms:
Applying the result obtained by the Ritz method, we have the system of equations
where:
(Since 2p z atomic orbital can be expressed as a pure real function, the * representing complex conjugation can be dropped.) The Hückel method assumes that all overlap integrals (including the normalization integrals) equal the Kronecker delta , S i j = δ i j {\displaystyle S_{ij}=\delta _{ij}\,} , all Coulomb integrals H i i {\displaystyle H_{ii}\,} are equal, and the resonance integral H i j {\displaystyle H_{ij}\,} is nonzero when the atoms i and j are bonded. Using the standard Hückel variable names, we set
The Hamiltonian matrix is
The matrix equation that needs to be solved is then
or, dividing by β {\displaystyle \beta } ,
Setting x := α − E β {\displaystyle x:={\frac {\alpha -E}{\beta }}} , we obtain
This homogeneous system of equations has nontrivial solutions for c 1 , c 2 {\displaystyle c_{1},c_{2}} (solutions besides the physically meaningless c 1 = c 2 = 0 {\displaystyle c_{1}=c_{2}=0} ) iff the matrix is singular and the determinant is zero:
Solving for x {\displaystyle x} ,
Since E = α − x β {\displaystyle E=\alpha -x\beta } , the energy levels are
The coefficients can then be found by expanding (***):
Since the matrix is singular, the two equations are linearly dependent, and the solution set is not uniquely determined until we apply the normalization condition. We can only solve for c 2 {\displaystyle c_{2}} in terms of c 1 {\displaystyle c_{1}} :
After normalization with c 1 2 + c 2 2 = 1 {\displaystyle c_{1}^{2}+c_{2}^{2}=1} , the numerical values of c 1 {\displaystyle c_{1}} and c 2 {\displaystyle c_{2}} can be found:
Finally, the Hückel molecular orbitals are
The constant β in the energy term is negative; therefore, E + = α + β {\displaystyle E_{+}=\alpha +\beta } with Ψ + = 1 2 ( ϕ 1 + ϕ 2 ) {\textstyle \Psi _{+}={\frac {1}{\sqrt {2}}}(\phi _{1}+\phi _{2})\,} is the lower energy corresponding to the HOMO energy and E − = α − β {\displaystyle E_{-}=\alpha -\beta } with Ψ − = 1 2 ( ϕ 1 − ϕ 2 ) {\textstyle \Psi _{-}={\frac {1}{\sqrt {2}}}(\phi _{1}-\phi _{2})\,} is the LUMO energy.
If, contrary to the Hückel treatment, a positive value for S := S 12 = S 21 {\displaystyle S:=S_{12}=S_{21}} were included, the energies would instead be
while the corresponding orbitals would take the form
An important consequence of setting S > 0 {\displaystyle S>0} is that the bonding (in-phase) combination is always stabilized to a lesser extent than the antibonding (out-of-phase) combination is destabilized, relative to the energy of the free 2p orbital. Thus, in general, 2-center 4-electron interactions, where both the bonding and antibonding orbitals are occupied, are destabilizing overall. This asymmetry is ignored by Hückel theory. In general, for the orbital energies derived from Hückel theory, the sum of stabilization energies for the bonding orbitals is equal to the sum of destabilization energies for the antibonding orbitals, as in the simplest case of ethylene shown here and the case of butadiene shown below.
The Hückel MO theory treatment of 1,3-butadiene is largely analogous to the treatment of ethylene, shown in detail above, though we must now find the eigenvalues and eigenvectors of a 4 × 4 Hamiltonian matrix. We first write the molecular orbital Ψ {\displaystyle \Psi \,} as a linear combination of the four atomic orbitals ϕ i {\displaystyle \phi _{i}} (carbon 2p orbitals) with coefficients c i {\displaystyle c_{i}} :
The Hamiltonian matrix is
In the same way, we write the secular equations in matrix form as
which leads to
and
The orbitals are given by | https://en.wikipedia.org/wiki/Hückel_method |
Hügelkultur ( German pronunciation: [ˈhyːɡl̩kʊlˌtuːɐ̯] , alternative spelling without umlaut : Huegelkultur), literally mound bed or mound culture , is a horticultural technique where a mound constructed from decaying wood debris and other compostable biomass plant materials is later (or immediately) planted as a raised bed . Considered a permaculture practice, advocates claim that the technique helps to improve soil fertility , water retention, and soil warming, thus benefitting plants grown on or near such mounds. [ 1 ] [ 2 ]
Hügelkultur is a German word meaning mound culture or hill culture. [ 3 ] Though the technique is alleged to have been practiced in German and Eastern European societies for hundreds of years, [ 1 ] [ 4 ] the term was first published in a 1962 German gardening booklet by Herrman Andrä. [ 5 ] Inspired by the diversity of plants growing in a pile of woody debris in his grandmother's garden, Andrä promoted "mound culture" as opposed to "flatland culture". [ 5 ] This was also posited as an easy way to utilise woody debris without burning, which was illegal. [ 5 ] Andrä appears to have been influenced by Rudolf Steiner 's biodynamic agriculture . Steiner explained his biodynamic philosophy as developed through meditation and clairvoyance , on the grounds that his methods were “true and correct unto themselves.” [ 6 ] Andrä quotes a 1924 lecture on biodynamics by Steiner, which describes mixing of soil with composting or decaying material in earthen hillocks. [ 5 ] Joined by author Hans Beba, another German gardener, "Hill Culture - the horticultural method of the future" was revised and republished several times in the 1970s and 1980s. [ 5 ] [ 7 ]
The technique was later adopted and developed by Sepp Holzer , an Austrian permaculture advocate. [ 8 ] More recent permaculture advocates such as Paul Wheaton strongly promote Hügelkultur beds as a perfect permaculture design. [ 9 ]
In its basic form, mounds are constructed by piling logs, branches, plant waste, compost and additional soil directly on the ground. The pile has the form of a pyramid. (Note—Wheaton suggests piling the wood higgledy-piggledy rather than in a neat stack as shown, for structural engineering of the steep slope, or perpendicular to the spine of the mound.) The sides of the two slopes both have a grade of between 65 and 80 degrees. [ 10 ] The beds are usually about 3 by 6 feet (0.91 by 1.83 m) in area and about 3 feet (0.91 m) high. [ 1 ] However, this height reduces as decomposition progresses. [ 5 ]
When positioned on sloped terrain, the beds need to be placed on contour or put at an angle to the hillside (rather than parallel to it). This makes sure the beds do not receive unequal amounts of water. In most cases, it is useful to have the beds positioned against the prevailing wind direction.
The raised bed can form light-duty swales , circles and mazes. [ 11 ] [ 12 ] Mounds may also be made from alternating layers of wood, sod, [ 13 ] compost, straw, and soil. Although their construction is straightforward, planning is necessary to prevent steep slopes that would result in erosion. [ 8 ] [ 4 ]
In his book Desert or Paradise: Restoring Endangered Landscapes Using Water Management, Including Lake and Pond Construction , Holzer describes a method of constructing Hügelkultur which incorporates rubbish such as cardboard, clothes and kitchen waste. He recommends building mounds that are 1 meter (3.3 ft) wide and any length. Mounds are built in a 0.7 meters (2.3 ft) trench in sandy soil, and without a trench if the ground is wet. [ 10 ]
The mound is left to rest for several months before planting, [ 5 ] although some advise immediate planting. [ citation needed ]
Anything can be grown on the raised beds, but if the bed will decompose/release its nutrients quickly (so long as it is not made of bulky materials like tree trunks), more demanding crops such as pumpkins, zucchini, cucumbers, cabbages, tomatoes, sweet corn, celery, or potatoes are grown in the first year, after which the bed is used for less demanding crops like beans, peas, and strawberries. [ citation needed ]
The original German publications described the mounds as having a lifespan of 5–6 years, after which they had to be rebuilt from scratch. [ 5 ]
There are few peer-reviewed scientific studies available regarding the efficacy of the technique. [ 5 ] A few university student projects have investigated Hügelkultur, but those results have not made it into the peer-reviewed literature. [ 5 ]
One small scale and short term student project investigated the Hügelkultur method as a potential use for yard trimmings waste, and also if lima beans, kale and okra planted on a Hügelkultur mound showed any signs of nutrient deficiency compared to a non-raised control bed. It was found that over 11 tons of yard trimmings were used in the mound, and no evidence of macronutrient deficiency could be detected in the crops in the short term. [ 14 ] Indeed, despite concerns that incorporation of large quantities of high carbon woody matter would lead to nitrogen immobilization and hence nitrogen deficiency in the crop, a higher level of nitrogen was found in the raised bed. However, the micronutrient iron was lower relative to the control bed. [ 14 ] The author speculated that no nitrogen deficiency occurred since the roots of the plants did not penetrate past the superficial layers of the mound into the deeper wood-containing region. [ 14 ]
A student thesis investigated the water holding capacity of Hügelkultur beds and whether the technique could be useful to prevent karst rocky desertification in China. [ 15 ] Over 3 months of measurements, water concentration in hügel mounds remained high. Samples from hügel sites contained almost twice as much water as those from flat control plots. It was suggested that 1 ha ( 2 + 1 ⁄ 2 acres) of hügels has 3-10 times more water than a flat plot affected by karst rocky desertification. [ 15 ]
A 2024 study comparing different permaculture approaches found increased carbon content in soils treated with Hügelkultur, and reduce waterlogging. [ 16 ] Combined with prior results regarding the improvement of water holding capacity in China, these results suggest that Hügelkultur could be a valuable natural soil conditioner .
Many publications and websites advocate the technique based on personal experience of the authors. [ 5 ] Some have criticised the technique as lacking genuine scientific principles, and running counter to the ecological principles of soil building with litterfall . [ 5 ]
Hügelkultur is said to replicate the natural process of decomposition that occurs on forest floors , however in natural ecosystems wood would be present at the soil surface. [ 5 ] Trees that fall in a forest often become nurse logs [ 8 ] decaying and providing ecological facilitation to seedlings. As the wood decays, its porosity increases, allowing it to store water like a sponge. The water is slowly released back into the environment, benefiting nearby plants. [ 1 ]
These beds are also considered beneficial because of the air pockets created by the settling caused by the wood's decomposition. This gives the benefits of tilling, without the destruction of soil microorganisms that come with tilling ("every time you till the soil, you lose 30% of the organic material (microbial soil life is killed, and plants feast on their bodies)" [ 17 ] ). And, the organic material of the rotting wood also houses beneficial soil microorganisms. [ 17 ]
Hügelkultur beds are said to be ideal for areas where the underlying soil is of poor quality or compacted. They tend to be easier to maintain due to their relative height above the ground. [ 8 ]
The decomposition speed of organic material depends on the carbon to nitrogen ratio of the material, among other factors. Wood breaks down relatively slowly because it has one of the highest carbon to nitrogen ratios of all organic matter that is used in composting. If the wood is not processed into smaller pieces with larger surface area to speed up chemical reactions, breakdown is even slower. The decomposition process may, in the short term, take more nitrogen from the soil through microbial activity ( nitrogen immobilization ), if not enough nitrogen is available. [ 18 ] Thus, in the short term, the fertility of the soil may be decreased before, eventually, perhaps after one to two years, the nitrogen level is increased past the original level. [ 18 ] Traditionally, therefore, it is said to be advantageous to balance "browns" (e.g. woodchippings) with "greens" (e.g. grass clippings) for efficient composting, and to allow compost to become well-rotted before applying it to a bed, to prevent competition between soil bacteria and plants for nitrogen, which reduces yield.
Although Hügelkultur beds can safely retain water in light-duty applications (for example, conserving the moisture of rain that falls on the bed), creating heavy-duty rainwater retention areas behind Hügelkultur beds on contour, to catch surface runoff from surrounding areas, can be dangerous. Some designers conflate the Hügelkultur bed's appearance with that of solid earthworks , but Hügelkultur beds cannot predictably control large amounts of stormwater in the way that solid earthworks can. Whereas embankment dams or the hillsides of swales can be relied on to hold back many thousands of gallons of water for weeks to allow it to seep into the ground, and berms can slow runoff, Hügelkultur beds are different in two ways: earthworks have no buoyant core (whereas Hügelkultur mounds contain logs), and the soil that they are made of is compacted. If fresh or dried timber is used in the bed, it may become buoyant in the water-saturated substrate, bursting from the soil covering and releasing all the sitting water through a breach. This can be an issue for years, until the wood is sufficiently rotten and infused with water. Another consideration is that Hügelkultur beds will degrade, shrinking over time into much lower mounds of soft, rich soil. This means that the retention area will have less depth as time goes on, but it also means that the uncompacted soil will remain a threat to breaching even if the logs become saturated.
Some permaculturists have taken mild positions against the "hügel swales" still being promoted by other permaculturists, citing the danger and cross-purposes of Hügelkultur beds and swales. Swales are for long-term installations where perennials - like fruit trees - are grown. Hügelkultur is used for shorter term, more annual crops, as the soil settling that occurs with hugel decomposition is bad for the root system of fruit trees. [ 19 ] A common practice is to plant fruit trees beside a hugelkultur mound where some nutrient runoff can feed the tree without the tree’s support collapsing under it, while also allowing the tree to extend its roots laterally under or upward into the hugelkultur mound as far as it “needs.”
There is a recorded instance of a breach occurring in a new project. Upon the first rainstorm, the retention areas behind the Hügelkultur beds filled with water and broke through. The released water carried the freshly-buried logs and dirt downhill, smashing a hole in a building being used as a church and filling the space with mud. No injuries were reported. [ 20 ]
Over-fertilized plants are said to have less flavor, [ 21 ] and too much nitrogen can be consumed by eating certain plants which have been over-fertilised (e.g., spinach). [ 21 ] Advocates state that overfertilization is a risk in the first year if woodchips are used, which will break down too fast. [ 21 ] Instead raised beds made with whole logs release nutrients slowly over a period of years. [ 21 ] It has been suggested that excessive use of decomposing organic matter in Hügelkultur could leach out and contaminate and disrupt soil and water habitats. [ 5 ] | https://en.wikipedia.org/wiki/Hügelkultur |
The Hütte - Das Ingenieurwissen (originally Des Ingenieurs Taschenbuch , stylized as "HÜTTE" and pronounced IPA: [ˈhʏtə] ) is a reference work for engineers of various disciplines. It was compiled for the first time in 1857 [ 2 ] by the Akademischer Verein Hütte [ de ] (short Die Hütte , translating as "the hut") of the Königliches Gewerbe-Institut [ de ] in Berlin, from which the association of German engineers Verein Deutscher Ingenieure (VDI) emerged. The authors were members of the association. The technical illustrations were created in woodcut technique by Otto Ebel [ de ] . It is published in constantly revised editions to this day and is therefore the oldest German reference work still available today. [ 3 ]
The book was initially divided into three sections: Mathematik und Mechanik (Mathematics and Mechanics), Maschinenbau und Technologie (Mechanical Engineering and Technology) and Bauwissenschaft (Building Science) and was originally published by the publishing house Ernst & Korn (Gropius'sche Buch- und Kunsthandlung), Berlin , [ 2 ] [ nb 1 ] the later Ernst & Sohn [ de ] , [ nb 1 ] who published it until 1971. [ 4 ]
For the 150th anniversary in 2007, the first edition was reissued as a bibliophile reprint. [ 5 ] [ 6 ]
Starting with the first edition in 1857, [ 1 ] further book series have been developed over the decades. The reference work quickly developed into a standard work for engineers and was frequently reprinted and translated into other languages due to the great demand. The first translation ever was into Russian in 1863. [ 2 ] In 1890, the work was divided into two, in 1908 into three, and finally in 1922 into four volumes. With the 27th edition in 1949, volume four was no longer available.
An English version was published by McGraw-Hill Book Co. , New York, in 1916 as "Mechanical engineers' handbook, based on the Hütte and prepared by a staff of specialists" edited by Lionel Simeon Marks . This led to Marks' Standard Handbook for Mechanical Engineers , a work, which spawned several translations on its own and is continued up to the present with its 100th anniversary 12th edition published in 2017.
Another work initially influenced by the 1936 Russian translation of the 1931 edition of Hütte is the so called Bronshtein and Semendyayev (BS) handbook of mathematics. [ 7 ] [ 8 ] [ 2 ] Written in 1939/1940 in Russia, it was first published in 1945. [ 2 ] Translated into German in 1958, [ 2 ] the latter is maintained and, in turn, translated into many other languages up to the present (2020).
In the first years after the Second World War the work was temporarily relocated both to the Federal Republic of Germany (FRG) and German Democratic Republic (GDR).
The scientific Springer-Verlag has been publishing the book since 16 June 1971 and has been the publisher of all Hütte handbooks so far. For some time, the series was called " Hütte – Taschenbücher der Technik " (Technical Pocket Books). From the completely revised 29th edition in 1989 (volume editor Horst Czichos [ de ] ), the work once again appeared in one volume under the title " Hütte - Die Grundlagen der Ingenieurwissenschaften " (The Basics of Engineering). With the 32nd edition, it was renamed to the current title " Hütte - Das Ingenieurwissen " (Engineering Knowledge).
For the 150th anniversary in 2007, the 33rd edition of the book was published. [ 9 ] It was updated to reflect the current state of science and technology and meet the curricula of technical universities and technical colleges. It comprises the following sections:
The 34th edition was published in 2012, [ 10 ] and the 35th edition was planned for 2020 [ 11 ] and is now scheduled to be released in 2023. | https://en.wikipedia.org/wiki/Hütte |
Uranyl hydroxide is a hydroxide of uranium with the chemical formula UO 2 (OH) 2 in the monomeric form and [(UO 2 ) 2 (OH) 4 ] 2- in the dimeric; both forms may exist in normal aqueous media. In aerobic conditions, up to 5 hydroxides can bind to uranyl ([(UO 2 ) 2 (OH) 5 ] 3- ). Uranyl hydroxide hydrate is precipitated as a colloidal yellowcake from oxidized uranium liquors near neutral pH.
Uranyl hydroxide was once used in glassmaking and ceramics in the colouring of the vitreous phases and the preparation of pigments for high temperature firing. The introduction of alkaline di uranates (like sodium diuranate ) into glasses leads to yellow by transmission, green by reflection; moreover these glasses become dichroic and fluorescent under ultraviolet rays.
Uranyl hydroxide is teratogenic and radioactive .
The formation of uranyl hydroxide hydrate can occur via hydrated uranyl fluoride [(UO 2 F 2 )(H 2 O)] 7 ·4H 2 O which is not stable at an elevated water vapor pressure. A complete loss of fluorine is undergone and the formation of uranyl hydroxide hydrate ([(UO 2 ) 4 O(OH) 6 ]·5H 2 O) occurs. This uranyl hydroxide species is structurally similar to the uranyl hydroxide hydrate minerals schoepite and metaschoepite. X-ray diffraction data was gathered and found that this species has expanded interlayer spacing suggesting there may be additional water molecules in between uranyl layers. Unlike metaschoepite, however, this species does not form UO 2 (OH) 2 upon dehydration. [ 1 ]
UO 2 (OH) 2 reacts with water in a hydration reaction to form [(UO 2 (OH) 2 )(H 2 O)] + and the monohydrate form also reacted with water to form dihydrates [(UO 2 OH)(H 2 O) 2 ] + and trihydrates [(UO 2 OH)(H 2 O) 3 ] + . The hydration reaction to form the monohydrate was significantly slower than if the hydroxide were replaced with acetate or nitrate. This could be due to the strongly basic (OH) − reducing the Lewis acidity of U or because the more complex acetate and nitrate anions provide more degrees of freedom. However, it was found that the formation of the dihydrate uranyl hydroxide hydrate (2) was nearly three times faster than the monohydrate (1). [ 2 ]
A mechanism for oxygen exchange between the UO 2 2+ cations in a highly alkaline solution was proposed and investigated by Shamov et al. in the Journal of the American Chemical Society . [ 3 ] An equilibrium between [UO 2 (OH) 4 ] 2- and [UO 2 (OH) 5 ] 3- was observed followed by the formation of the stable [UO 3 (OH) 3 ·H 2 O] 3- intermediate that formed from [UO 2 (OH) 5 ] 3- via intramolecular water elimination. | https://en.wikipedia.org/wiki/H₂O₄U |
Hydrogen sulfide is a chemical compound with the formula H 2 S . It is a colorless chalcogen-hydride gas , and is toxic, corrosive, and flammable. Trace amounts in ambient atmosphere have a characteristic foul odor of rotten eggs. [ 11 ] Swedish chemist Carl Wilhelm Scheele is credited with having discovered the chemical composition of purified hydrogen sulfide in 1777. [ 12 ]
Hydrogen sulfide is toxic to humans and most other animals by inhibiting cellular respiration in a manner similar to hydrogen cyanide . When it is inhaled or its salts are ingested in high amounts, damage to organs occurs rapidly with symptoms ranging from breathing difficulties to convulsions and death. [ 13 ] [ 14 ] Despite this, the human body produces small amounts of this sulfide and its mineral salts, and uses it as a signalling molecule . [ 15 ]
Hydrogen sulfide is often produced from the microbial breakdown of organic matter in the absence of oxygen, such as in swamps and sewers; this process is commonly known as anaerobic digestion , which is done by sulfate-reducing microorganisms . It also occurs in volcanic gases , natural gas deposits, and sometimes in well-drawn water.
Hydrogen sulfide is slightly denser than air. A mixture of H 2 S and air can be explosive.
In general, hydrogen sulfide acts as a reducing agent , as indicated by its ability to reduce sulfur dioxide in the Claus process . Hydrogen sulfide burns in oxygen with a blue flame to form sulfur dioxide ( SO 2 ) and water :
If an excess of oxygen is present, sulfur trioxide ( SO 3 ) is formed, which quickly hydrates to sulfuric acid :
It is slightly soluble in water and acts as a weak acid ( p K a = 6.9 in 0.01–0.1 mol/litre solutions at 18 °C), giving the hydrosulfide ion HS − . Hydrogen sulfide and its solutions are colorless. When exposed to air, it slowly oxidizes to form elemental sulfur, which is not soluble in water. The sulfide anion S 2− is not formed in aqueous solution. [ 16 ]
H 2 S and H 2 O exchange protons rapidly. This behavior is the basis of technologies for the purification of deuterium oxide ("heavy water" or D 2 O ), which exploits the easy distillation of these compounds. [ 17 ]
At pressures above 90 GPa ( gigapascal ), hydrogen sulfide becomes a metallic conductor of electricity. When cooled below a critical temperature this high-pressure phase exhibits superconductivity . The critical temperature increases with pressure, ranging from 23 K at 100 GPa to 150 K at 200 GPa. [ 18 ] If hydrogen sulfide is pressurized at higher temperatures, then cooled, the critical temperature reaches 203 K (−70 °C), which was the highest accepted superconducting critical temperature until the discovery of Lanthanum decahydride in 2019. By substituting a small part of sulfur with phosphorus and using even higher pressures, it has been predicted that it may be possible to raise the critical temperature to above 0 °C (273 K) and achieve room-temperature superconductivity . [ 19 ]
Hydrogen sulfide decomposes without a presence of a catalyst under atmospheric pressure around 1200 °C into hydrogen and sulfur. [ 20 ]
Hydrogen sulfide reacts with metal ions to form metal sulfides, which are insoluble, often dark colored solids. This behavior is the basis of the use of hydrogen sulfide as a reagent in the qualitative inorganic analysis of metal ions. In these analyses, heavy metal (and nonmetal ) ions (e.g., Pb(II), Cu(II), Hg(II), As(III)) are precipitated from solution upon exposure to H 2 S . The components of the resulting solid are then identified by their reactivity. Lead(II) acetate paper is used to detect hydrogen sulfide because it readily converts to lead(II) sulfide , which is black. [ 21 ] [ 22 ]
Hydrogen sulfide is also responsible for tarnishing on various metals including copper and silver ; the chemical responsible for black toning found on silver coins is silver sulfide ( Ag 2 S ), which is produced when the silver on the surface of the coin reacts with atmospheric hydrogen sulfide. [ 23 ] Coins that have been subject to toning by hydrogen sulfide and other sulfur-containing compounds may have the toning add to the numismatic value of a coin based on aesthetics, as the toning may produce thin-film interference , resulting in the coin taking on an attractive coloration. [ 24 ] Coins can also be intentionally treated with hydrogen sulfide to induce toning, though artificial toning can be distinguished from natural toning, and is generally criticised among collectors. [ 25 ]
Hydrogen sulfide is most commonly obtained by its separation from sour gas , which is natural gas with a high content of H 2 S . It can also be produced by treating hydrogen with molten elemental sulfur at about 450 °C. Hydrocarbons can serve as a source of hydrogen in this process. [ 26 ]
The very favorable thermodynamics for the hydrogenation of sulfur implies that the dehydrogenation (or cracking ) of hydrogen sulfide would require very high temperatures. [ 27 ]
A standard lab preparation is to treat ferrous sulfide with a strong acid in a Kipp generator :
For use in qualitative inorganic analysis , thioacetamide is used to generate H 2 S :
Many metal and nonmetal sulfides, e.g. aluminium sulfide , phosphorus pentasulfide , silicon disulfide liberate hydrogen sulfide upon exposure to water: [ 28 ]
This gas is also produced by heating sulfur with solid organic compounds and by reducing sulfurated organic compounds with hydrogen.
It can also be produced by mixing ammonium thiocyanate to concentrated sulphuric acid and adding water to it.
Hydrogen sulfide can be generated in cells via enzymatic or non-enzymatic pathways. Three enzymes catalyze formation of H 2 S : cystathionine γ-lyase (CSE), cystathionine β-synthetase (CBS), and 3-mercaptopyruvate sulfurtransferase (3-MST). [ 29 ] CBS and CSE are the main proponents of H 2 S biogenesis, which follows the trans-sulfuration pathway. [ 30 ] These enzymes have been identified in a breadth of biological cells and tissues, and their activity is induced by a number of disease states. [ 31 ] These enzymes are characterized by the transfer of a sulfur atom from methionine to serine to form a cysteine molecule. [ 30 ] 3-MST also contributes to hydrogen sulfide production by way of the cysteine catabolic pathway. [ 31 ] [ 30 ] Dietary amino acids, such as methionine and cysteine serve as the primary substrates for the transulfuration pathways and in the production of hydrogen sulfide. Hydrogen sulfide can also be derived from proteins such as ferredoxins and Rieske proteins . [ 31 ]
Sulfate-reducing (resp. sulfur-reducing ) bacteria generate usable energy under low-oxygen conditions by using sulfates (resp. elemental sulfur) to oxidize organic compounds or hydrogen; this produces hydrogen sulfide as a waste product. [ 32 ]
H 2 S in the body acts as a gaseous signaling molecule with implications for health and in diseases. [ 29 ] [ 33 ] [ 34 ] [ 35 ]
Hydrogen sulfide is involved in vasodilation in animals, as well as in increasing seed germination and stress responses in plants. [ 36 ] Hydrogen sulfide signaling is moderated by reactive oxygen species (ROS) and reactive nitrogen species (RNS). [ 36 ] H 2 S has been shown to interact with the NO pathway resulting in several different cellular effects, including the inhibition of cGMP phosphodiesterases, [ 37 ] as well as the formation of another signal called nitrosothiol. [ 36 ] Hydrogen sulfide is also known to increase the levels of glutathione, which acts to reduce or disrupt ROS levels in cells. [ 36 ]
The field of H 2 S biology has advanced from environmental toxicology to investigate the roles of endogenously produced H 2 S in physiological conditions and in various pathophysiological states. [ 38 ] H 2 S has been implicated in cancer, in Down syndrome and in vascular disease. [ 39 ] [ 40 ] [ 41 ] [ 42 ]
At lower concentrations, it stimulates mitochondrial function via multiple mechanisms including direct electron donation. [ 43 ] [ 44 ] However, at higher concentrations, it inhibits Complex IV of the mitochondrial electron transport chain, which effectively reduces ATP generation and biochemical activity within cells. [ 36 ]
Hydrogen sulfide is mainly consumed as a precursor to elemental sulfur. This conversion, called the Claus process , involves partial oxidation to sulfur dioxide. The latter reacts with hydrogen sulfide to give elemental sulfur. The conversion is catalyzed by alumina. [ 45 ]
Many fundamental organosulfur compounds are produced using hydrogen sulfide. These include methanethiol , ethanethiol , and thioglycolic acid . [ 26 ] Hydrosulfides can be used in the production of thiophenol . [ 46 ]
Upon combining with alkali metal bases, hydrogen sulfide converts to alkali hydrosulfides such as sodium hydrosulfide and sodium sulfide :
Sodium sulfides are used in the paper making industry. Specifically, salts of SH − break bonds between lignin and cellulose components of pulp in the Kraft process . [ 26 ]
As indicated above, many metal ions react with hydrogen sulfide to give the corresponding metal sulfides. Oxidic ores are sometimes treated with hydrogen sulfide to give the corresponding metal sulfides which are more readily purified by flotation .Metal parts are sometimes passivated with hydrogen sulfide. Catalysts used in hydrodesulfurization are routinely activated with hydrogen sulfide. [ 26 ]
Volcanoes and some hot springs (as well as cold springs ) emit some H 2 S . Hydrogen sulfide can be present naturally in well water, often as a result of the action of sulfate-reducing bacteria . [ 47 ] [ better source needed ] Hydrogen sulfide is produced by the human body in small quantities through bacterial breakdown of proteins containing sulfur in the intestinal tract; it therefore contributes to the characteristic odor of flatulence. It is also produced in the mouth ( halitosis ). [ 48 ]
A portion of global H 2 S emissions are due to human activity. By far the largest industrial source of H 2 S is petroleum refineries : The hydrodesulfurization process liberates sulfur from petroleum by the action of hydrogen. The resulting H 2 S is converted to elemental sulfur by partial combustion via the Claus process , which is a major source of elemental sulfur. Other anthropogenic sources of hydrogen sulfide include coke ovens, paper mills (using the Kraft process), tanneries and sewerage . H 2 S arises from virtually anywhere where elemental sulfur comes in contact with organic material, especially at high temperatures. Depending on environmental conditions, it is responsible for deterioration of material through the action of some sulfur oxidizing microorganisms. It is called biogenic sulfide corrosion . [ citation needed ]
In 2011 it was reported that increased concentrations of H 2 S were observed in the Bakken formation crude, possibly due to oil field practices, and presented challenges such as "health and environmental risks, corrosion of wellbore, added expense with regard to materials handling and pipeline equipment, and additional refinement requirements". [ 49 ]
Besides living near gas and oil drilling operations, ordinary citizens can be exposed to hydrogen sulfide by being near waste water treatment facilities, landfills and farms with manure storage. Exposure occurs through breathing contaminated air or drinking contaminated water. [ 50 ]
In municipal waste landfill sites , the burial of organic material rapidly leads to the production of anaerobic digestion within the waste mass and, with the humid atmosphere and relatively high temperature that accompanies biodegradation , biogas is produced as soon as the air within the waste mass has been reduced. If there is a source of sulfate bearing material, such as plasterboard or natural gypsum (calcium sulfate dihydrate), under anaerobic conditions sulfate reducing bacteria converts this to hydrogen sulfide. These bacteria cannot survive in air but the moist, warm, anaerobic conditions of buried waste that contains a high source of carbon – in inert landfills, paper and glue used in the fabrication of products such as plasterboard can provide a rich source of carbon [ 51 ] – is an excellent environment for the formation of hydrogen sulfide.
In industrial anaerobic digestion processes, such as waste water treatment or the digestion of organic waste from agriculture , hydrogen sulfide can be formed from the reduction of sulfate and the degradation of amino acids and proteins within organic compounds. [ 52 ] Sulfates are relatively non-inhibitory to methane forming bacteria but can be reduced to H 2 S by sulfate reducing bacteria , of which there are several genera. [ 53 ]
A number of processes have been designed to remove hydrogen sulfide from drinking water . [ 54 ]
Hydrogen sulfide is commonly found in raw natural gas and biogas. It is typically removed by amine gas treating technologies. In such processes, the hydrogen sulfide is first converted to an ammonium salt, whereas the natural gas is unaffected. [ 57 ] [ 58 ]
The bisulfide anion is subsequently regenerated by heating of the amine sulfide solution. Hydrogen sulfide generated in this process is typically converted to elemental sulfur using the Claus Process .
The underground mine gas term for foul-smelling hydrogen sulfide-rich gas mixtures is stinkdamp . Hydrogen sulfide is a highly toxic and flammable gas ( flammable range : 4.3–46%). It can poison several systems in the body, although the nervous system is most affected. [ citation needed ] The toxicity of H 2 S is comparable with that of carbon monoxide . [ 59 ] It binds with iron in the mitochondrial cytochrome enzymes , thus preventing cellular respiration . Its toxic properties were described in detail in 1843 by Justus von Liebig . [ 60 ]
Even before hydrogen sulfide was discovered, Italian physician Bernardino Ramazzini hypothesized in his 1713 book De Morbis Artificum Diatriba that occupational diseases of sewer-workers and blackening of coins in their clothes may be caused by an unknown invisible volatile acid (moreover, in late 18th century toxic gas emanation from Paris sewers became a problem for the citizens and authorities). [ 61 ]
Although very pungent at first (it smells like rotten eggs [ 62 ] ), it quickly deadens the sense of smell, creating temporary anosmia , [ 63 ] so victims may be unaware of its presence until it is too late. Safe handling procedures are provided by its safety data sheet (SDS) . [ 64 ]
Since hydrogen sulfide occurs naturally in the body, the environment, and the gut, enzymes exist to metabolize it. At some threshold level, believed to average around 300–350 ppm, the oxidative enzymes become overwhelmed. Many personal safety gas detectors, such as those used by utility, sewage and petrochemical workers, are set to alarm at as low as 5 to 10 ppm and to go into high alarm at 15 ppm. Metabolism causes oxidation to sulfate, which is harmless. [ 65 ] Hence, low levels of hydrogen sulfide may be tolerated indefinitely. [ citation needed ]
Exposure to lower concentrations can result in eye irritation, a sore throat and cough , nausea, shortness of breath, and fluid in the lungs . [ 59 ] These effects are believed to be due to hydrogen sulfide combining with alkali present in moist surface tissues to form sodium sulfide , a caustic . [ 66 ] These symptoms usually subside in a few weeks.
Long-term, low-level exposure may result in fatigue , loss of appetite, headaches , irritability, poor memory, and dizziness . Chronic exposure to low level H 2 S (around 2 ppm ) has been implicated in increased miscarriage and reproductive health issues among Russian and Finnish wood pulp workers, [ 67 ] but the reports have not (as of 1995) been replicated.
Short-term, high-level exposure can induce immediate collapse, with loss of breathing and a high probability of death. If death does not occur, high exposure to hydrogen sulfide can lead to cortical pseudolaminar necrosis , degeneration of the basal ganglia and cerebral edema . [ 59 ] Although respiratory paralysis may be immediate, it can also be delayed up to 72 hours. [ 68 ]
Inhalation of H 2 S resulted in about 7 workplace deaths per year in the U.S. (2011–2017 data), second only to carbon monoxide (17 deaths per year) for workplace chemical inhalation deaths. [ 69 ]
Treatment involves immediate inhalation of amyl nitrite , injections of sodium nitrite , or administration of 4-dimethylaminophenol in combination with inhalation of pure oxygen, administration of bronchodilators to overcome eventual bronchospasm , and in some cases hyperbaric oxygen therapy (HBOT). [ 59 ] HBOT has clinical and anecdotal support. [ 74 ] [ 75 ] [ 76 ]
Hydrogen sulfide was used by the British Army as a chemical weapon during World War I . It was not considered to be an ideal war gas, partially due to its flammability and because the distinctive smell could be detected from even a small leak, alerting the enemy to the presence of the gas. It was nevertheless used on two occasions in 1916 when other gases were in short supply. [ 77 ]
On September 2, 2005, a leak in the propeller room of a Royal Caribbean Cruise Liner docked in Los Angeles resulted in the deaths of 3 crewmen due to a sewage line leak. As a result, all such compartments are now required to have a ventilation system. [ 78 ] [ 79 ]
A dump of toxic waste containing hydrogen sulfide is believed to have caused 17 deaths and thousands of illnesses in Abidjan , on the West African coast, in the 2006 Côte d'Ivoire toxic waste dump . [ 80 ]
In September 2008, three workers were killed and two suffered serious injury, including long term brain damage, at a mushroom growing company in Langley , British Columbia . A valve to a pipe that carried chicken manure , straw and gypsum to the compost fuel for the mushroom growing operation became clogged, and as workers unclogged the valve in a confined space without proper ventilation the hydrogen sulfide that had built up due to anaerobic decomposition of the material was released, poisoning the workers in the surrounding area. [ 81 ] An investigator said there could have been more fatalities if the pipe had been fully cleared and/or if the wind had changed directions. [ 82 ]
In 2014, levels of hydrogen sulfide as high as 83 ppm were detected at a recently built mall in Thailand called Siam Square One at the Siam Square area. Shop tenants at the mall reported health complications such as sinus inflammation, breathing difficulties and eye irritation. After investigation it was determined that the large amount of gas originated from imperfect treatment and disposal of waste water in the building. [ 83 ]
In 2014, hydrogen sulfide gas killed workers at the Promenade shopping center in North Scottsdale, Arizona , USA [ 84 ] after climbing into 15 ft deep chamber without wearing personal protective gear . "Arriving crews recorded high levels of hydrogen cyanide and hydrogen sulfide coming out of the sewer."
In November 2014, a substantial amount of hydrogen sulfide gas shrouded the central, eastern and southeastern parts of Moscow . Residents living in the area were urged to stay indoors by the emergencies ministry. Although the exact source of the gas was not known, blame had been placed on a Moscow oil refinery. [ 85 ]
In June 2016, a mother and her daughter were found dead in their still-running 2006 Porsche Cayenne SUV against a guardrail on Florida's Turnpike , initially thought to be victims of carbon monoxide poisoning . [ 86 ] [ 87 ] Their deaths remained unexplained as the medical examiner waited for results of toxicology tests on the victims, [ 88 ] until urine tests revealed that hydrogen sulfide was the cause of death. A report from the Orange-Osceola Medical Examiner's Office indicated that toxic fumes came from the Porsche's starter battery , located under the front passenger seat. [ 89 ] [ 90 ]
In January 2017, three utility workers in Key Largo, Florida , died one by one within seconds of descending into a narrow space beneath a manhole cover to check a section of paved street. [ 91 ] In an attempt to save the men, a firefighter who entered the hole without his air tank (because he could not fit through the hole with it) collapsed within seconds and had to be rescued by a colleague. [ 92 ] The firefighter was airlifted to Jackson Memorial Hospital and later recovered. [ 93 ] [ 94 ] A Monroe County Sheriff officer initially determined that the space contained hydrogen sulfide and methane gas produced by decomposing vegetation. [ 95 ]
On May 24, 2018, two workers were killed, another seriously injured, and 14 others hospitalized by hydrogen sulfide inhalation at a Norske Skog paper mill in Albury, New South Wales . [ 96 ] [ 97 ] An investigation by SafeWork NSW found that the gas was released from a tank used to hold process water . The workers were exposed at the end of a 3-day maintenance period. Hydrogen sulfide had built up in an upstream tank, which had been left stagnant and untreated with biocide during the maintenance period. These conditions allowed sulfate-reducing bacteria to grow in the upstream tank, as the water contained small quantities of wood pulp and fiber . The high rate of pumping from this tank into the tank involved in the incident caused hydrogen sulfide gas to escape from various openings around its top when pumping was resumed at the end of the maintenance period. The area above it was sufficiently enclosed for the gas to pool there, despite not being identified as a confined space by Norske Skog. One of the workers who was killed was exposed while investigating an apparent fluid leak in the tank, while the other who was killed and the worker who was badly injured were attempting to rescue the first after he collapsed on top of it. In a resulting criminal case , Norske Skog was accused of failing to ensure the health and safety of its workforce at the plant to a reasonably practicable extent. It pleaded guilty, and was fined AU$1,012,500 and ordered to fund the production of an anonymized educational video about the incident. [ 98 ] [ 99 ] [ 96 ] [ 100 ]
In October 2019, an Odessa, Texas employee of Aghorn Operating Inc. and his wife were killed due to a water pump failure. Produced water with a high concentration of hydrogen sulfide was released by the pump. The worker died while responding to an automated phone call he had received alerting him to a mechanical failure in the pump, while his wife died after driving to the facility to check on him. [ 101 ] A CSB investigation cited lax safety practices at the facility, such as an informal lockout-tagout procedure and a nonfunctioning hydrogen sulfide alert system. [ 102 ]
The gas, produced by mixing certain household ingredients, was used in a suicide wave in 2008 in Japan. [ 103 ] The wave prompted staff at Tokyo's suicide prevention center to set up a special hotline during " Golden Week ", as they received an increase in calls from people wanting to kill themselves during the annual May holiday. [ 104 ]
As of 2010, this phenomenon has occurred in a number of US cities, prompting warnings to those arriving at the site of the suicide. [ 105 ] [ 106 ] [ 107 ] [ 108 ] [ 109 ]
In 2020, H 2 S ingestion was used as a suicide method by Japanese pro wrestler Hana Kimura . [ 110 ]
In 2024, Lucy-Bleu Knight, stepdaughter of famed musician Slash , also used H 2 S ingestion to commit suicide. [ 111 ]
Hydrogen sulfide is a central participant in the sulfur cycle , the biogeochemical cycle of sulfur on Earth. [ 112 ]
In the absence of oxygen , sulfur-reducing and sulfate-reducing bacteria derive energy from oxidizing hydrogen or organic molecules by reducing elemental sulfur or sulfate to hydrogen sulfide. Other bacteria liberate hydrogen sulfide from sulfur-containing amino acids ; this gives rise to the odor of rotten eggs and contributes to the odor of flatulence .
As organic matter decays under low-oxygen (or hypoxic ) conditions (such as in swamps, eutrophic lakes or dead zones of oceans), sulfate-reducing bacteria will use the sulfates present in the water to oxidize the organic matter, producing hydrogen sulfide as waste. Some of the hydrogen sulfide will react with metal ions in the water to produce metal sulfides, which are not water-soluble. These metal sulfides, such as ferrous sulfide FeS, are often black or brown, leading to the dark color of sludge .
Several groups of bacteria can use hydrogen sulfide as fuel, oxidizing it to elemental sulfur or to sulfate by using dissolved oxygen, metal oxides (e.g., iron oxyhydroxides and manganese oxides ), or nitrate as electron acceptors. [ 113 ]
The purple sulfur bacteria and the green sulfur bacteria use hydrogen sulfide as an electron donor in photosynthesis , thereby producing elemental sulfur. This mode of photosynthesis is older than the mode of cyanobacteria , algae , and plants , which uses water as electron donor and liberates oxygen.
The biochemistry of hydrogen sulfide is a key part of the chemistry of the iron-sulfur world . In this model of the origin of life on Earth, geologically produced hydrogen sulfide is postulated as an electron donor driving the reduction of carbon dioxide. [ 114 ]
Hydrogen sulfide is lethal to most animals, but a few highly specialized species ( extremophiles ) do thrive in habitats that are rich in this compound. [ 115 ]
In the deep sea, hydrothermal vents and cold seeps with high levels of hydrogen sulfide are home to a number of extremely specialized lifeforms, ranging from bacteria to fish. [ which? ] [ 116 ] Because of the absence of sunlight at these depths, these ecosystems rely on chemosynthesis rather than photosynthesis . [ 117 ]
Freshwater springs rich in hydrogen sulfide are mainly home to invertebrates, but also include a small number of fish: Cyprinodon bobmilleri (a pupfish from Mexico), Limia sulphurophila (a poeciliid from the Dominican Republic ), Gambusia eurystoma (a poeciliid from Mexico), and a few Poecilia (poeciliids from Mexico). [ 115 ] [ 118 ] Invertebrates and microorganisms in some cave systems, such as Movile Cave , are adapted to high levels of hydrogen sulfide. [ 119 ]
Hydrogen sulfide has often been detected in the interstellar medium. [ 120 ] It also occurs in the clouds of planets in our solar system. [ 121 ] [ 122 ]
Hydrogen sulfide has been implicated in several mass extinctions that have occurred in the Earth's past. In particular, a buildup of hydrogen sulfide in the atmosphere may have caused, or at least contributed to, the Permian-Triassic extinction event 252 million years ago. [ 123 ] [ 124 ] [ 125 ]
Organic residues from these extinction boundaries indicate that the oceans were anoxic (oxygen-depleted) and had species of shallow plankton that metabolized H 2 S . The formation of H 2 S may have been initiated by massive volcanic eruptions, which emitted carbon dioxide and methane into the atmosphere, which warmed the oceans, lowering their capacity to absorb oxygen that would otherwise oxidize H 2 S . The increased levels of hydrogen sulfide could have killed oxygen-generating plants as well as depleted the ozone layer, causing further stress. Small H 2 S blooms have been detected in modern times in the Dead Sea and in the Atlantic Ocean off the coast of Namibia . [ 123 ] | https://en.wikipedia.org/wiki/H₂S |
The i'm Watch is a smartwatch developed by Italian company i'm S.p.A. It was conceptualized by Manuel Zanella and Massimiliano Bertolini in early 2011, with funding provided by H-Invest and then released in the middle of 2012. The i'm Watch can receive calls, texts and notifications from social media accounts, provide news and weather reports, control music, view and save photos, and create appointments. The watch can also be paired to iOS 4 or higher, Android 4 or higher and BlackBerry 10 devices. On September 19, 2014, i'm S.p.A. announced the discontinuation of sales and its exit from the smartwatch market. [ 1 ]
Utilizing a touchscreen , the i'm Watch features a 1.54-inch, color LCD screen. Sensors for the watch include an accelerometer and a magnetometer . In terms of operating system, it has its own customized version of Android 1.6 called i'm Droid 2 . It also has a built-in microphone and speaker, as well as 4GB of memory space. It uses Bluetooth 2 for connectivity. For charging, a USB proprietary cable is attached to the headphone jack. The i'm Watch is available in four watch case materials: aluminum, gold, silver and titanium. It has six wristband color options: black, pink, red, blue, white and yellow.
Critics have considered the i'm Watch as a flop. CNET praises the device for its smooth interface and how it displays notifications and messages in an easily viewable format. The downside to this though, is that the watch is very difficult to set up. Battery life is very low, as it falls way short of other devices on the market. [ 2 ] Laptop Magazine liked the internal memory capacity, but feels that the Bluetooth tethering causes too much hassle when connecting. They added that the watch looks like "a timepiece from the future, but its performance does not match the Dick Tracy-style feature set." [ 3 ] Tech Radar commends the i'm Watch for its ability to pair with Android, iOS and BlackBerry devices, but is concerned about the poor hands-free control quality and lack of text message alerts. [ 4 ] | https://en.wikipedia.org/wiki/I'm_Watch |
I, Too, Am Harvard is a campaign primarily expressed as a collection of photos, which were posted on Tumblr to illustrate the personal experiences of black students at Harvard University , a private Ivy League university in Cambridge, Massachusetts . The multimedia project was the product of interviews with 61 undergraduate Harvard College students who held signs with various messages about the experiences of black students at Harvard. [ 1 ]
Between 2010 and 2014, Harvard's admissions of minorities, including blacks, Latinos, and Asian-Americans, ranged between 43% and 45.6%. [ 2 ] As of 2014, African Americans make up 9.4% of the approximately 7,500 undergraduates at Harvard. [ 2 ] [ 3 ]
The project was started in fall 2013 by Kimiko Matsuda-Lawrence, a Harvard undergraduate, and others, and was conducted under the direction of Harvard professor Glenda Carpio. As part of it, minority students at Harvard were interviewed about their experiences at the college. They reported feelings of alienation about the Harvard campus, being the lone black student in some classes, or feeling uncomfortable about comments and social interactions with other students on campus. [ 3 ]
Matsuda-Lawrence reported that students made comments such as "I've never told anyone this before" or "I've never been able to talk about this." [ 3 ] The students comments were kept anonymous and she used them to write a play. To promote the play, she assembled a group of students to help create the multimedia project that appears on Tumblr. The Tumblr project consists of photos taken of students holding signs with racially insensitive and offensive remarks by peers and response they would like to make. [ 2 ] Examples of signs included "No, I will not teach you how to 'twerk'" and "Don't you wish you were white like the rest of us?" [ 3 ] [ 4 ] [ 5 ] [ 6 ]
The project and campaign aim to the personal experiences of minority students at Harvard, especially those that have left them feeling alienated at the university. [ 3 ] By March 6, 2014, a link on BuzzFeed had produced over a million views. [ 2 ] In an email to undergraduate students, Donald Pfister, interim dean of Harvard College, expressed support for the project and said: "Harvard is also about inclusion. This photo campaign, based on a play which will premiere Friday night, is a great example of students speaking about how we can become a stronger community. 'I, Too, Am Harvard' makes clear that our conversation about community does not and should not stop." [ 2 ]
Student organizers at Harvard reported messages of support from other universities, including Yale University , Duke University , the University of Pennsylvania , McGill University , and the University of Oxford , [ 3 ]
Inspired by the campaign, minority students at McGill University, [ 7 ] the University of Oxford, [ 8 ] [ 9 ] and the University of Cambridge [ 10 ] developed similar multimedia campaigns. [ 11 ] [ 12 ] | https://en.wikipedia.org/wiki/I,_Too,_Am_Harvard |
I-CreI is a homing endonuclease whose gene was first discovered in the chloroplast genome of Chlamydomonas reinhardtii , a species of unicellular green algae . [ 1 ] It is named for the facts that: it resides in an I ntron; it was isolated from C lamydomonas re inhardtii ; it was the first ( I ) such gene isolated from C. reinhardtii . Its gene resides in a group I intron in the 23S ribosomal RNA gene of the C. reinhardtii chloroplast, and I-CreI is only expressed when its mRNA is spliced from the primary transcript of the 23S gene. I-CreI enzyme , which functions as a homodimer , recognizes a 22-nucleotide sequence of duplex DNA and cleaves one phosphodiester bond on each strand at specific positions. I-CreI is a member of the LAGLIDADG family of homing endonucleases, all of which have a conserved LAGLIDADG amino acid motif that contributes to their associative domains and active sites. When the I-CreI-containing intron encounters a 23S allele lacking the intron, I-CreI enzyme "homes" in on the "intron-minus" allele of 23S and effects its parent intron's insertion into the intron-minus allele. Introns with this behavior are called mobile introns . Because I-CreI provides for its own propagation while conferring no benefit on its host, it is an example of selfish DNA .
I-CreI was first observed as an intervening sequence in the 23S rRNA gene of the C. reinhardtii chloroplast genome. [ 1 ] The 23S gene is an RNA gene , meaning that its transcript is not translated into protein. As RNA, it forms part of the large subunit of the ribosome . An open reading frame coding for a 163-amino acid protein was found in this 23S intron, suggesting that a protein might facilitate the homing behavior of the mobile intron. Furthermore, the predicted protein had a LAGLIDADG motif, a conserved amino acid sequence that is present in other proteins coded for in group I mobile introns. A 1991 study established that the ORF codes for a DNA endonuclease, I-CreI, which selectively cuts a site corresponding to where the intron is spliced out of the 23S primary transcript. [ 2 ] The study also showed that the intron was able to invade 23S alleles that did not already have it. [ 2 ]
I-CreI has evolved to cut a 22-nucleotide sequence of DNA that occurs in alleles of the 23S ribosomal RNA gene that lack the I-CreI-containing intron. When such an "intron-minus" allele is cut, pathways of double-strand break repair are activated in the cell. The cell uses as a template for repair the 23S allele that yielded the responsible I-CreI enzyme, thus replicating the I-CreI-containing intron. [ 3 ] The resulting "intron-plus" allele no longer contains an intact homing site for the I-CreI enzyme, and is therefore not cleaved. Since this intron provides for its own replication without conferring any benefit on its host, I-CreI is a form of selfish DNA .
Because I-CreI has evolved to cut such a long sequence of DNA, unlike restriction endonucleases that typically cut four- or six-nucleotide sequences, it is capable of cutting a single site within a very large genome . A four- or six-nucleotide sequence is expected to occur many, many times in a genome of millions or billions of nucleotides simply by chance, whereas a 22-nucleotide sequence might occur only once (10 9 /4 6 vs. 10 9 /4 22 ). This specificity of I-CreI cleavage makes I-CreI a promising tool for gene targeting . If a person were to have a disease due to a defective allele of some gene , it would be helpful to be able to replace that allele with a functional one. If one could cause I-CreI to cut the DNA only in the defective allele while simultaneously providing a normal allele for the cell to use as a repair template, the patient's own homologous recombination machinery could insert the desired allele in place of the dysfunctional one. The specificity of I-CreI also allows for the reduction of deleterious effects due to double-strand breaks outside of the gene of interest.
In order to use I-CreI as a tool in this fashion, it is necessary to make it recognize and cleave sequences of DNA different from its native homing site. An Escherichia coli genetic system for studying the relationship between I-CreI structure and its homing site specificity was created in 1997. [ 5 ] In 1997, the structure of the I-CreI protein was determined, [ 6 ] and in 1998, its crystal structure bound to its native DNA homing site was solved, greatly aiding research in altering the homing site recognition of the protein. [ 4 ] Mutant forms of the protein have since been created that exhibit altered homing site specificity. [ 7 ] [ 8 ] [ 9 ] A genetic system in Saccharomyces cerevisiae has also been created, yielding additional I-CreI mutants with modified homing site specificities. [ 10 ] [ 11 ]
I-CreI has already been used successfully to induce homologous recombination in Drosophila melanogaster , an extremely popular eukaryotic model organism . [ 12 ] It seems very likely that advances in molecular biological techniques and generation of a library of I-CreI-derived novel endonucleases will eventually allow for the targeting of many genes of etiological significance. | https://en.wikipedia.org/wiki/I-CreI |
I-III-VI 2 semiconductors are solid semiconducting materials that contain three or more chemical elements belonging to groups I, III and VI (IUPAC groups 1/11, 13 and 16) of the periodic table . They usually involve two metals and one chalcogen . Some of these materials have a direct bandgap , E g , of approximately 1.5 eV, which makes them efficient absorbers of sunlight and thus potential solar cell materials. A fourth element is often added to a I-III-VI 2 material to tune the bandgap for maximum solar cell efficiency . A representative example is copper indium gallium selenide (CuIn x Ga (1– x ) Se 2 , E g = 1.7–1.0 eV for x = 0–1 [ 1 ] ), which is used in copper indium gallium selenide solar cells .
CuGaO 2 exists in two main polymorphs , α and β. The α form has the delafossite crystal structure and can be prepared by reacting Cu 2 O with Ga 2 O 3 at high temperatures. The β form has a wurtzite -like crystal structure ( space group Pna2 1 ); it is metastable, but exhibits a long-term stability at temperatures below 300 °C. [ 3 ] It can be obtained by an ion exchange of Na + ions in a β-NaGaO 2 precursor with Cu + ions in CuCl under vacuum, to avoid the oxidation of Cu + to Cu 2+ . [ 2 ]
Unlike most I-III-VI 2 oxides , which are transparent, electrically insulating solids with a bandgap above 2 eV, β-CuGaO 2 has a direct bandgap of 1.47 eV, which is favorable for solar cell applications. In contrast, β-AgGaO 2 and β-AgAlO 2 have an indirect bandgap. Undoped β-CuGaO 2 is a p-type semiconductor . [ 2 ]
Similarly to CuGaO 2 , α-AgGaO 2 and α-AgAlO 2 have the delafossite crystal structure while the structure of the corresponding β phases is similar to wurtzite ( space group Pna2a). β-AgGaO 2 is metastable and can be synthesized by ion exchange with a β-NaGaO 2 precursor. The bandgaps of β-AgGaO 2 and β-AgAlO 2 (2.2 and 2.8 eV respectively) are indirect; they fall into the visible range and can be tuned by alloying with ZnO . For this reason, both materials are hardly suitable for solar cells, but have potential applications in photocatalysis . [ 2 ]
Contrary to LiGaO 2 , AgGaO 2 can not be alloyed with ZnO by heating their mixture because of the Ag + reduction to metallic silver; therefore, magnetron sputtering of AgGaO 2 and ZnO targets is used instead. [ 2 ]
Pure single crystals of β-LiGaO 2 with a length of several inches can be grown by the Czochralski method . Their cleaved surfaces have lattice constants that match those of ZnO and GaN and are therefore suitable for epitaxial growth of thin films of those materials. β-LiGaO 2 is a potential nonlinear optics material, but its direct bandgap of 5.6 eV is too wide for visible light applications. It can be reduced down to 3.2 eV by alloying β-LiGaO 2 with ZnO. The bandgap tuning is discontinuous because ZnO and β-LiGaO 2 do not mix but form a Zn 2 LiGaO 4 phase when their ratio is between ca. 0.2 and 1. [ 2 ]
LiGaTe 2 crystals with a size up to 5 mm can be grown in three steps. First, Li, Ga, and Te elements are fused in an evacuated quartz ampoule at 1250 K for 24 hours. At this stage Li reacts with the ampoule walls, releasing heat, and is partly consumed. In the second stage, the melt is homogenized in a sealed quartz ampoule, which is coated inside with pyrolytic carbon to reduce Li reactivity. The homogenization temperature is selected ca. 50 K above the melting point of LiGaTe 2 . The crystals are then grown from the homogenized melt by the Bridgman–Stockbarger technique in a two-zone furnace. The temperature at the start of crystallization is a few degrees below the LiGaTe 2 melting point. The ampoule is moved the cold zone at a rate of 2.5 mm/day for 20 days. [ 4 ] | https://en.wikipedia.org/wiki/I-III-VI_semiconductors |
i-Tree is a collection of urban and rural forestry analysis and benefits assessment tools. It was designed and developed by the United States Forest Service to quantify and value ecosystem services provided by trees including pollution removal, carbon sequestration , avoided carbon emissions , avoided stormwater runoff , and more. i-Tree provides baseline data so that the growth of trees can be followed over time, and is used for planning purposes. Different tools within the i-Tree Suite use different types of inputs and provide different kinds of reports; some tools use a 'bottom up' approach based on tree inventories on the ground, while other tools use a 'top down' approach based on remote sensing data. i-Tree is peer-reviewed and has a process of ongoing collaboration to improve it.
There are seven different i-Tree applications which can enhance an individual's or organization's understanding of the benefits which trees provide in modern society. [ 1 ] Over the course of many years the U.S. Forest Service has developed and refined these different applications: i-Tree Eco, i-Tree Landscape, i-Tree Hydro, i-Tree Design, i-Tree Canopy, i-Tree Species, and i-Tree MyTree. [ 2 ]
i-Tree began in 2002 as survey of a sample of urban forest to simulate taking a tree inventory of an entire urban forest. It then added hand held devices for efficient inventory of street trees. The current version of i-Tree includes different tools which allow for several sources of data to be used, such as National Land Cover Data, Google Maps, and tree inventories. Some tools use continuous data on air pollution and meteorology for more accurate results.
Researchers using i-Tree have examined: [ 3 ] | https://en.wikipedia.org/wiki/I-Tree |
In commutative algebra , the mathematical study of commutative rings , adic topologies are a family of topologies on the underlying set of a module , generalizing the p -adic topologies on the integers .
Let R be a commutative ring and M an R -module. Then each ideal 𝔞 of R determines a topology on M called the 𝔞 -adic topology, characterized by the pseudometric d ( x , y ) = 2 − sup { n ∣ x − y ∈ a n M } . {\displaystyle d(x,y)=2^{-\sup {\{n\mid x-y\in {\mathfrak {a}}^{n}M\}}}.} The family { x + a n M : x ∈ M , n ∈ Z + } {\displaystyle \{x+{\mathfrak {a}}^{n}M:x\in M,n\in \mathbb {Z} ^{+}\}} is a basis for this topology. [ 1 ]
An 𝔞 -adic topology is a linear topology (a topology generated by some submodules).
With respect to the topology, the module operations of addition and scalar multiplication are continuous , so that M becomes a topological module . However, M need not be Hausdorff ; it is Hausdorff if and only if ⋂ n > 0 a n M = 0 , {\displaystyle \bigcap _{n>0}{{\mathfrak {a}}^{n}M}=0{\text{,}}} so that d becomes a genuine metric . Related to the usual terminology in topology, where a Hausdorff space is also called separated, in that case, the 𝔞 -adic topology is called separated . [ 1 ]
By Krull's intersection theorem , if R is a Noetherian ring which is an integral domain or a local ring , it holds that ⋂ n > 0 a n = 0 {\displaystyle \bigcap _{n>0}{{\mathfrak {a}}^{n}}=0} for any proper ideal 𝔞 of R . Thus under these conditions, for any proper ideal 𝔞 of R and any R -module M , the 𝔞 -adic topology on M is separated.
For a submodule N of M , the canonical homomorphism to M / N induces a quotient topology which coincides with the 𝔞 -adic topology. The analogous result is not necessarily true for the submodule N itself: the subspace topology need not be the 𝔞 -adic topology. However, the two topologies coincide when R is Noetherian and M finitely generated . This follows from the Artin–Rees lemma . [ 2 ]
When M is Hausdorff, M can be completed as a metric space; the resulting space is denoted by M ^ {\displaystyle {\widehat {M}}} and has the module structure obtained by extending the module operations by continuity. It is also the same as (or canonically isomorphic to): M ^ = lim ← M / a n M {\displaystyle {\widehat {M}}=\varprojlim M/{\mathfrak {a}}^{n}M} where the right-hand side is an inverse limit of quotient modules under natural projection. [ 3 ]
For example, let R = k [ x 1 , … , x n ] {\displaystyle R=k[x_{1},\ldots ,x_{n}]} be a polynomial ring over a field k and 𝔞 = ( x 1 , ..., x n ) the (unique) homogeneous maximal ideal . Then R ^ = k [ [ x 1 , … , x n ] ] {\displaystyle {\hat {R}}=k[[x_{1},\ldots ,x_{n}]]} , the formal power series ring over k in n variables. [ 4 ]
The 𝔞 -adic closure of a submodule N ⊆ M {\displaystyle N\subseteq M} is N ¯ = ⋂ n > 0 ( N + a n M ) . {\textstyle {\overline {N}}=\bigcap _{n>0}{(N+{\mathfrak {a}}^{n}M)}{\text{.}}} [ 5 ] This closure coincides with N whenever R is 𝔞 -adically complete and M is finitely generated. [ 6 ]
R is called Zariski with respect to 𝔞 if every ideal in R is 𝔞 -adically closed. There is a characterization:
In particular a Noetherian local ring is Zariski with respect to the maximal ideal. [ 7 ] | https://en.wikipedia.org/wiki/I-adic_topology |
An I-beam is any of various structural members with an Ɪ- (serif capital letter 'I') or H-shaped cross-section . Technical terms for similar items include H-beam , I-profile , universal column ( UC ), w-beam (for "wide flange"), universal beam ( UB ), rolled steel joist ( RSJ ), or double-T (especially in Polish , Bulgarian , Spanish , Italian , and German ). I-beams are typically made of structural steel and serve a wide variety of construction uses.
The horizontal elements of the Ɪ are called flanges , and the vertical element is known as the "web". The web resists shear forces , while the flanges resist most of the bending moment experienced by the beam. The Euler–Bernoulli beam equation shows that the Ɪ-shaped section is a very efficient form for carrying both bending and shear loads in the plane of the web. On the other hand, the cross-section has a reduced capacity in the transverse direction, and is also inefficient in carrying torsion , for which hollow structural sections are often preferred.
In 1849, the method of producing an I-beam, as rolled from a single piece of wrought iron, [ 1 ] was patented by Alphonse Halbou of Forges de la Providence in Marchienne-au-Pont , Belgium. [ 2 ]
Bethlehem Steel , headquartered in Bethlehem, Pennsylvania , was a leading supplier of rolled structural steel of various cross-sections in American bridge and skyscraper work of the mid-20th century. [ 3 ] Rolled cross-sections now have been partially displaced in such work by fabricated cross-sections.
There are two standard I-beam forms:
I-beams are commonly made of structural steel but may also be formed from aluminium or other materials. A common type of I-beam is the rolled steel joist (RSJ), sometimes incorrectly rendered as reinforced steel joist. British and European standards also specify Universal Beams (UBs) and Universal Columns (UCs). These sections have parallel flanges, shown as "W-Section" in the accompanying illustration, as opposed to the varying thickness of RSJ flanges, illustrated as "S-Section", which are seldom now rolled in the United Kingdom . Parallel flanges are easier to connect to and do away with the need for tapering washers. UCs have equal or near-equal width and depth and are more suited to being oriented vertically to carry axial load such as columns in multi-storey construction, while UBs are significantly deeper than they are wide are more suited to carrying bending load such as beam elements in floors.
I-joists , I-beams engineered from wood with fiberboard or laminated veneer lumber , or both, are also becoming increasingly popular in construction, especially residential, as they are both lighter and less prone to warping than solid wooden joists . However, there has been some concern as to their rapid loss of strength in a fire if unprotected.
I-beams are widely used in the construction industry and are available in a variety of standard sizes. Tables are available to allow easy selection of a suitable steel I-beam size for a given applied load. I-beams may be used both as beams and as columns .
I-beams may be used both on their own, or acting compositely with another material, typically concrete . Design may be governed by any of the following criteria:
A beam under bending sees high stresses along the axial fibers that are farthest from the neutral axis . To prevent failure, most of the material in the beam must be located in these regions. Comparatively little material is needed in the area close to the neutral axis. This observation is the basis of the I-beam cross-section; the neutral axis runs along the center of the web which can be relatively thin and most of the material can be concentrated in the flanges.
The ideal beam is the one with the least cross-sectional area (and hence requiring the least material) needed to achieve a given section modulus . Since the section modulus depends on the value of the moment of inertia , an efficient beam must have most of its material located as far from the neutral axis as possible. The farther a given amount of material is from the neutral axis, the larger is the section modulus and hence a larger bending moment can be resisted.
When designing a symmetric I-beam to resist stresses due to bending the usual starting point is the required section modulus. If the allowable stress is σ max and the maximum expected bending moment is M max , then the required section modulus is given by: [ 4 ]
where I is the moment of inertia of the beam cross-section and c is the distance of the top of the beam from the neutral axis (see beam theory for more details).
For a beam of cross-sectional area a and height h , the ideal cross-section would have half the area at a distance h / 2 above the cross-section and the other half at a distance h / 2 below the cross-section. [ 4 ] For this cross-section,
However, these ideal conditions can never be achieved because material is needed in the web for physical reasons, including to resist buckling. For wide-flange beams, the section modulus is approximately
which is superior to that achieved by rectangular beams and circular beams.
Though I-beams are excellent for unidirectional bending in a plane parallel to the web, they do not perform as well in bidirectional bending. These beams also show little resistance to twisting and undergo sectional warping under torsional loading. For torsion dominated problems, box beams and other types of stiff sections are used in preference to the I-beam.
It is possible to increase the shear capacity in a beam web by adding out of plane stiffness using transverse web stiffeners. These can be added to both sides of the web, or just one. They are usually steel plates welded into place, but bolting can be used. [ 5 ] [ 6 ]
In the United States , the most commonly mentioned I-beam is the wide-flange (W) shape. These beams have flanges whose inside surfaces are parallel over most of their area. Other I-beams include American Standard (designated S) shapes, in which inner flange surfaces are not parallel, and H-piles (designated HP), which are typically used as pile foundations. Wide-flange shapes are available in grade ASTM A992, [ 7 ] which has generally replaced the older ASTM grades A572 and A36. Ranges of yield strength:
Like most steel products, I-beams often contain some recycled content.
The following standards define the shape and tolerances of I-beam steel sections:
The American Institute of Steel Construction (AISC) publishes the Steel Construction Manual for designing structures of various shapes. It documents the common approaches, Allowable Strength Design (ASD) and Load and Resistance Factor Design (LRFD), (starting with 13th ed.) to create such designs.
In the United States , steel I-beams are commonly specified using the depth and weight of the beam. For example, a "W10x22" beam is approximately 10 in (254 mm) in depth with a nominal height of the I-beam from the outer face of one flange to the outer face of the other flange, and weighs 22 lb/ft (33 kg/m). Wide flange section beams often vary from their nominal depth. In the case of the W14 series, they may be as deep as 22.84 in (580 mm). [ 9 ] '
In Canada , steel I-beams are now commonly specified using the depth and weight of the beam in metric terms. For example, a "W250x33" beam is approximately 250 millimetres (9.8 in) in depth (height of the I-beam from the outer face of one flange to the outer face of the other flange) and weighs approximately 33 kg/m (22 lb/ft; 67 lb/yd). [ 10 ] I-beams are still available in US sizes from many Canadian manufacturers.
In Mexico , steel I-beams are called IR and commonly specified using the depth and weight of the beam in metric terms. For example, a "IR250x33" beam is approximately 250 mm (9.8 in) in depth (height of the I-beam from the outer face of one flange to the outer face of the other flange) and weighs approximately 33 kg/m (22 lb/ft). [ 11 ]
In India , I-beams are designated as ISMB, ISJB, ISLB, ISWB. ISMB: Indian Standard Medium Weight Beam, ISJB: Indian Standard Junior Beams, ISLB: Indian Standard Light Weight Beams, and ISWB: Indian Standard Wide Flange Beams. Beams are designated as per respective abbreviated reference followed by the depth of section, such as for example ISMB 450 , where 450 is the depth of section in millimetres (mm). The dimensions of these beams are classified as per IS:808 (as per BIS ). [ citation needed ]
In the United Kingdom , these steel sections are commonly specified with a code consisting of the major dimension, usually the depth, -x-the minor dimension-x-the mass per metre-ending with the section type, all measurements being metric. Therefore, a 152x152x23UC would be a column section (UC = universal column) of approximately 152 mm (6.0 in) depth, 152 mm width and weighing 23 kg/m (46 lb/yd) of length. [ 12 ]
In Australia , these steel sections are commonly referred to as Universal Beams (UB) or Columns (UC). The designation for each is given as the approximate height of the beam, the type (beam or column) and then the unit metre rate (e.g., a 460UB67.1 is an approximately 460 mm (18.1 in) deep universal beam that weighs 67.1 kg/m (135 lb/yd)). [ 8 ]
Cellular beams are the modern version of the traditional castellated beam , which results in a beam approximately 40–60% deeper than its parent section. The exact finished depth, cell diameter and cell spacing are flexible. A cellular beam is up to 1.5 times stronger than its parent section and is therefore utilized to create efficient large span constructions. [ 13 ] | https://en.wikipedia.org/wiki/I-beam |
I-cells , also called inclusion cells , are abnormal fibroblasts having a large number of dark inclusions in the cytoplasm of the cell (mainly in the central area). Inclusion bodies are nuclear or cytoplasmic aggregates of stainable substances, usually proteins. [ 1 ] These metabolically inactive aggregates are not enclosed by a membrane, and are composed of fats, proteins, carbohydrates, pigments, and excretory products. When cells have an abundance of these inclusions, they are called I-Cells and are associated with neurodegenerative diseases. They are seen in Mucolipidosis II , and Mucolipidosis III , also called inclusion-cell or I-cell disease where lysosomal enzyme transport and storage is affected.
Inclusion bodies were first described in the late 19th and 20th centuries. One of the earliest figures associated with the discovery of inclusion bodies is Fritz Heinrich Jakob Lewy. He discovered peculiar inclusions in neurons of certain brain nuclei in patients with Paralysis agitans, which would later be coined a “ Lewy Body ” by Gonzalo Rodriguez Lafora. [ 2 ] This discovery is one of the most famous early observations of inclusion bodies.
In I-cell disease, the inclusions form due to a defect in the sorting of enzymes to the lysosomes, where waste materials are broken down. This defect is caused by a mutation in the GNPTAB gene in the enzyme N-acetylglucosamine-1-phosphotransferase . [ 3 ] This leads to a failure to tag the lysosomal enzymes with mannose-6-phosphate . Without this tag, the enzymes cannot be delivered correctly to the lysosomes, and waste materials are stored as inclusions rather than degraded. These inclusions disrupt cellular functions and cause symptoms like developmental delays, abnormal growth, coarse facial features, and enlarged organs. This mutation is inherited in an autosomal recessive manner, so both parents must be carriers of one copy of the mutated gene in order for kin to develop this condition. [ 4 ]
I-cell disease is associated with various clinical features that affect physical appearance, organ function, and growth development. The severity of these symptoms varies between individuals, though the prognosis is poor due to the disease’s systemic nature. I-Cell Disease patients may also experience impaired cognitive and motor development. Individuals may also possess coarse facial features like a prominent forehead, flat nasal bridge, or thickened skin. [ 3 ]
Skeletal abnormalities such as dysostosis multiplex or short stature are also common. Organ functioning may be affected by hepatosplenomegaly , the enlargement of the liver and spleen, or cardiac issues like valvular abnormalities. The disease may manifest neurologically in cognitive impairments or seizures, or in joint and limb issues such as arthropathy , a progressive joint pain and stiffness.
Other possible symptoms of the disease include gastrointestinal problems, vision or hearing issues, immunological concerns (increased infection risk), and a shortened life expectancy. Mucolipidosis II is more severe than Mucolipidosis III, and generally results in death of the patient in the first 10 years of life. [ 5 ]
To diagnose I-Cell Disease, specialists conduct a combination of clinical evaluations, biochemical tests, and genetic analyses. First, physicians consider the patient’s medical history for any symptoms like growth delays, coarse facial features, organ enlargement, or skeletal abnormalities. These initial examinations commonly reveal features like hepatosplenomegaly, joint stiffness, or dysostosis multiplex. [ 6 ]
The next method to diagnose the disease is to consider biochemical tests such as measuring the activity of the lysosomal enzymes in blood or urine. In individuals with the disease, specific enzymes (like β-glucuronidase and N-acetylgalactosamine-4-sulfatase ) appear in higher concentrations with decreased activity (due to mislocalization). Urine tests may also reveal elevated levels of glycosaminoglycans (GAGs), complex carbohydrates that accumulate in lysosomal storage disorders. Additionally, specific enzyme assays can be used to assess lysosomal enzyme activity. [ 6 ]
If the biochemical tests reveal lysosomal enzyme activity that suggest I-Cell Disease, specialists perform genetic testing to identify any GNPTAB gene mutations. To identify specific mutations, physicians may use Sanger sequencing or next-generation sequencing methods. Family members may also undergo genetic testing to determine carrier status. X-rays and ultrasounds may also be utilized to evaluate skeletal or organ abnormalities, and MRI or CT scans may be utilized to examine brain structure in individuals experiencing neurological symptoms. Occasionally, a biopsy of affected tissues may reveal inclusion bodies in the cells.
A proper diagnosis aims to differentiate I-Cell Disease from other lysosomal storage disorders, which proves to be difficult due to their similar clinical features. Identification of specific enzyme deficiencies and genetic testing help establish the correct diagnosis. These diagnoses are essential to manage symptoms of the disease, though there is no known cure.
Because there is no cure for I-Cell Disease, the treatment focus remains on supportive care and management strategies to alleviate symptoms to improve quality of life. A multidisciplinary approach is necessary for management of the disease due to its multisystem nature. A team of healthcare professionals are generally involved, including geneticists, neurologists, orthopedic specialists, and physical therapists. [ 7 ]
Physical and occupational therapy are used to address mobility issues. These therapies help to manage joint stiffness, promote motor functioning, and increase muscle strength. Sometimes, surgical interventions may be necessary to repair skeletal deformities or relieve joint pain. Nutritional support is also used to combat feeding difficulties or growth delays in affected individuals. This nutritional support allows for specific dietary plans or the use of feeding tubes. [ 8 ]
Regular management of complications such as cardiac or respiratory issues is crucial. Along with physical therapies, counseling is utilized for affected individuals and families to provide emotional support. More targeted therapies such as enzyme replacement and gene therapy are being researched in hopes of discovering more effective treatments. One study examining the outcomes of hematopoietic stem cell transplantation in mucolipidosis II patients found that after hematopoietic stem cell transplantation , the patient's skin roughness was significantly improved, limb muscle tension was significantly reduced, and gross and fine motor skills were improved. [ 3 ]
Research on I-Cell Disease focuses on understanding underlying mechanisms of the disorder in hopes of developing additional treatments. Enzyme replacement therapy (ERT) aims to supplement the deficient lysosomal enzymes which are not correctly trafficked to the lysosomes in individuals with the disease. ERT could reduce the accumulation of undegraded materials within the cells, helping to alleviate associated symptoms. [ 6 ]
Along with ERT, researchers are exploring gene therapy, which aims to correct GNPTAB gene mutations. Gene editing technologies like CRISPR/Cas9 are being improved, offering hope in potentially restoring normal enzyme functioning. [ 9 ] Small molecule drugs can also enhance activity of enzyme function and improve trafficking of lysosomal enzymes, and are being investigated as potential treatments for the disease.
Researchers are also studying the pathophysiological mechanisms of I-Cell Disease to understand how substrate accumulation leads to cellular dysfunction. This understanding could aid in the development of therapies and treatments that address specific affected pathways. Research institutions, patient advocacy groups, and biopharmaceutical companies must cooperate in order to more fully understand and treat the disease. Ongoing research shows promise in improving treatment options for I-Cell Disease and patient outcomes. | https://en.wikipedia.org/wiki/I-cell |
The I. I. Rabi Award , founded in 1983, is awarded annually by IEEE .
The award is named after Isidor Isaac Rabi , Nobel Prize winner in 1944. He was the first recipient of the award, for his experimental and theoretical work on atomic beam resonance spectroscopy . [ 1 ] | https://en.wikipedia.org/wiki/I._I._Rabi_Award |
The I. I. Rabi Prize in Atomic, Molecular, and Optical Physics is given by the American Physical Society to recognize outstanding work by mid-career researchers in the field of atomic, molecular, and optical physics . The award was endowed in 1989 in honor of the physicist I. I. Rabi and has been awarded biannually since 1991.
The prize citation reads:
"To recognize and encourage outstanding research in Atomic, Molecular and Optical Physics by investigators who have held a Ph.D. for no more than 10 years prior to the nomination deadline. The prize consists of $10,000 and a certificate citing the contributions made by the recipient. An allowance will be provided for travel expenses of the recipient to the Society meeting at which the prize is presented. It is awarded in odd-numbered years." [ 1 ]
Source: [ 2 ] | https://en.wikipedia.org/wiki/I._I._Rabi_Prize |
I/O Acceleration Technology ( I/OAT ) is a DMA engine (an embedded DMA controller ) by Intel bundled with high-end server motherboards , that offloads memory copies from the main processor by performing direct memory accesses (DMA). It is typically used for accelerating network traffic, but supports any kind of copy.
Using I/OAT for network acceleration is supported by Microsoft Windows since the release of Scalable Networking Pack for Windows Server 2003 SP1. [ 1 ] However, it is no longer included in Windows from version 8 on-wards. [ 2 ] It was used by the Linux kernel starting in 2006 [ 3 ] but this feature was subsequently disabled due to an alleged lack of performance benefits while creating a possibility of data corruption. [ 4 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/I/O_Acceleration_Technology |
Iodine sulfate is an inorganic compound with the formula I 2 (SO 4 ) 3 . [ 1 ] It appears as light yellow crystals and reacts with water.
Reaction of diiodosyl sulfate and sulfur trioxide : [ 2 ] [ 3 ] [ 4 ]
Iodine sulfate is also produced when elemental I 2 , I 2 O 5 and SO 3 react. [ 5 ]
Iodine sulfate forms light yellow hygroscopic crystals. [ 2 ] [ 3 ] [ 6 ]
Iodine sulfate is soluble in organic liquids [ 3 ] and stable in anhydrous and strongly acidic solvents. [ 6 ] In a humid environment, it darkens due to decomposition that releases molecular iodine . [ 2 ] | https://en.wikipedia.org/wiki/I2(SO4)3 |
Iodine trichloride is an interhalogen compound of iodine and chlorine . It is bright yellow but upon time and exposure to light it turns red due to the presence of elemental iodine. In the solid state is present as a planar dimer I 2 Cl 6 , with two bridging Cl atoms. [ 1 ]
It can be prepared by reacting iodine with an excess of liquid chlorine at −70 °C, [ 2 ] or heating a mixture of liquid iodine and chlorine gas to 105 °C. [ citation needed ] In the molten state it is conductive, which may indicate dissociation: [ 2 ]
It is an oxidizing agent , capable of causing fire on contact with organic materials. [ citation needed ] That oxidizing power also makes it a useful catalyst for organic chlorination reactions . [ 3 ]
Iodine trichloride reacts with concentrated hydrochloric acid , forming tetrachloroiodic acid : [ 4 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/I2Cl6 |
Diiodine tetraoxide , I 2 O 4 , is a chemical compound of oxygen and iodine . It belongs to the class of iodine oxides , and is a mixed oxide , consisting of iodine(III) and iodine(V) oxidation states .
The oxide is formed by the reaction of hot concentrated sulfuric acid on iodic acid for several days. [ 2 ]
It is formed from diiodine pentoxide and iodine in concentrated sulfuric acid or iodosyl sulfate (IO) 2 SO 4 added to water: [ 3 ]
Alternatively, excess of concentrated nitric acid oxidizes dry iodine to this salt. [ 4 ]
Diiodine tetraoxide is a yellow, granular powder. At temperatures above 85 °C it decomposes to diiodine pentoxide and iodine: [ 2 ]
This process is even faster at 135 °C. It dissolves in hot water to form iodate and iodide . [ 2 ] Structurally, the compound is an iodyl iodite O 2 I-OIO (iodine(V,III) oxide) [ 2 ] with bent I V O 2 units (I–O distances 1.80 and 1.85 Å; ∠OIO angle 97°) and bent I III O 2 units (IO distances 1.93 Å, OIO angle 95.8°). Both units are linked via I—O—I bridges to form polymeric zigzag chains (I 2 O 4 ) x . [ 2 ]
Diiodine tetraoxide has a monoclinic crystal structure with the space group P 2 1 / c (space group number 14). Unit cell dimensions are a = 8.483 b = 6.696 c = 8.333 Å and β = 124.69°. Unit cell volume = 389.15 Å 3 . Z = 4. Density is 2.57 Mg/m 3 [ 3 ] [ 5 ]
Diiodine tetroxide oxidises hydrochloric acid: [ 6 ]
It decomposes [ vague ] in water . [ 4 ] [ 7 ] | https://en.wikipedia.org/wiki/I2O4 |
Iodine pentoxide is the chemical compound with the formula I 2 O 5 . This iodine oxide is the anhydride of iodic acid , and one of the few iodine oxides that is stable. It is produced by dehydrating iodic acid at 200 °C in a stream of dry air: [ 1 ]
I 2 O 5 is bent with an I–O–I angle of 139.2°, but the molecule has no mirror plane so its symmetry is C 2 rather than C 2v . The terminal I–O distances are around 1.80 Å and the bridging I–O distances are around 1.95 Å. [ 3 ]
Iodine pentoxide easily oxidises carbon monoxide to carbon dioxide at room temperature:
This reaction can be used to analyze the concentration of CO in a gaseous sample.
I 2 O 5 forms iodyl salts, [IO 2 + ], with SO 3 and S 2 O 6 F 2 , but iodosyl salts, [IO + ], with concentrated sulfuric acid .
Iodine pentoxide decomposes to iodine (vapor) and oxygen when heated to about 350 °C. [ 4 ] | https://en.wikipedia.org/wiki/I2O5 |
Diiodine hexaoxide , is a chemical compound of oxygen and iodine with the chemical formula I 2 O 6 . It belongs to the class of iodine oxides , and is a mixed oxide , consisting of iodine(V) and iodine(VII) oxidation states .
Reaction of periodic acid with iodic acid in sulfuric acid : [ 2 ]
The thermal decomposition of meta -periodic acid in vacuum also leads to the formation of diiodine hexoxide. [ 2 ]
Below 100 °C, diiodine hexaoxide can be stored stably in the absence of moisture. When dissolved in water, an exothermic reaction to form iodine and periodic acid takes place. When heated above 150 °C, decomposition into diiodine pentoxide can be observed:
The compound is diamagnetic, which is attributed to the different oxidation numbers of the iodine atoms. [ 2 ] Structurally, the compound is iodyl periodate , an iodine(V,VII) oxide approximating IO 2 + IO 4 − . [ 2 ] As a solid, the compound crystallizes in the space group P 1 (space group no. 2) with the lattice constants a = 500.6 pm, b = 674.1 pm, c = 679.5 pm, α = 97.1°, β = 96.43°, γ = 105.36° with one formula unit per unit cell. [ 1 ] | https://en.wikipedia.org/wiki/I2O6 |
Lead(II) iodide (or lead iodide ) is a chemical compound with the formula PbI 2 . At room temperature , it is a bright yellow odorless crystalline solid, that becomes orange and red when heated. [ 11 ] It was formerly called plumbous iodide .
The compound currently has a few specialized applications, such as the manufacture of solar cells , [ 12 ] X-rays and gamma-ray detectors. [ 13 ] Its preparation is an entertaining and popular demonstration in chemistry education, to teach topics such as precipitation reactions and stoichiometry . [ 14 ] It is decomposed by light at temperatures above 125 °C (257 °F), and this effect has been used in a patented photographic process. [ 4 ] [ 15 ]
Lead iodide was formerly employed as a yellow pigment in some paints, with the name iodide yellow . However, that use has been largely discontinued due to its toxicity and poor stability. [ 16 ]
PbI 2 is commonly synthesized via a precipitation reaction between potassium iodide KI and lead(II) nitrate Pb ( NO 3 ) 2 in water solution:
While the potassium nitrate KNO 3 is soluble, the lead iodide PbI 2 is nearly insoluble at room temperature , and thus precipitates out. [ 17 ]
Other soluble compounds containing lead(II) and iodide can be used instead, for example lead(II) acetate [ 12 ] and sodium iodide .
The compound can also be synthesized by reacting iodine vapor with molten lead between 500 and 700 °C. [ 18 ]
A thin film of PbI 2 can also be prepared by depositing a film of lead sulfide PbS and exposing it to iodine vapor, by the reaction
The sulfur is then washed with dimethyl sulfoxide . [ 19 ]
Lead iodide prepared from cold solutions usually consists of many small hexagonal platelets, giving the yellow precipitate a silky appearance. Larger crystals can be obtained by exploiting the fact that solubility of lead iodide in water (like those of lead chloride and lead bromide ) increases dramatically with temperature. The compound is colorless when dissolved in hot water, but crystallizes on cooling as thin but visibly larger bright yellow flakes, that settle slowly through the liquid — a visual effect often described as "golden rain". [ 20 ] Larger crystals can be obtained by autoclaving the PbI 2 with water under pressure at 200 °C. [ 21 ]
Even larger crystals can be obtained by slowing down the common reaction. A simple setup is to submerge two beakers containing the concentrated reactants in a larger container of water, taking care to avoid currents. As the two substances diffuse through the water and meet, they slowly react and deposit the iodide in the space between the beakers. [ 22 ]
Another similar method is to react the two substances in a gel medium, that slows down the diffusion and supports the growing crystal away from the container's walls. Patel and Rao have used this method to grow crystals up to 30 mm in diameter and 2 mm thick. [ 23 ]
The reaction can be slowed also by separating the two reagents with a permeable membrane. This approach, with a cellulose membrane, was used in September 1988 to study the growth of PbI 2 crystals in zero gravity, in an experiment flown on the Space Shuttle Discovery . [ 24 ]
PbI 2 can also be crystallized from powder by sublimation at 390 °C, in near vacuum [ 25 ] or in a current of argon with some hydrogen . [ 26 ]
Large high-purity crystals can be obtained by zone melting or by the Bridgman–Stockbarger technique . [ 18 ] [ 25 ] These processes can remove various impurities from commercial PbI 2 . [ 27 ]
Lead iodide is a precursor material in the fabrication of highly efficient Perovskite solar cell . Typically, a solution of PbI 2 in an organic solvent, such as dimethylformamide or dimethylsulfoxide, is applied over a titanium dioxide layer by spin coating . The layer is then treated with a solution of methylammonium iodide CH 3 NH 3 I and annealed , turning it into the double salt methylammonium lead iodide CH 3 NH 3 PbI 3 , with a perovskite structure. The reaction changes the film's color from yellow to light brown. [ 12 ]
PbI 2 is also used as a high-energy photon detector for gamma-rays and X-rays, due to its wide band gap which ensures low noise operation. [ 4 ] [ 13 ] [ 25 ]
Lead iodide was formerly used as a paint pigment under the name "iodine yellow". It was described by Prosper Mérimée (1830) as "not yet much known in commerce, is as bright as orpiment or chromate of lead . It is thought to be more permanent; but time only can prove its pretension to so essential a quality. It is prepared by precipitating a solution of acetate or nitrate of lead, with potassium iodide: the nitrate produces a more brilliant yellow color." [ 16 ] However, due to the toxicity and instability of the compound it is no longer used as such. [ 16 ] It may still be used in art for bronzing and in gold-like mosaic tiles. [ 4 ]
Common material characterization techniques such as electron microscopy can damage samples of lead(II) iodide. [ 28 ] Thin films of lead(II) iodide are unstable in ambient air. [ 29 ] Ambient air oxygen oxidizes iodide into elemental iodine :
Lead iodide is very toxic to human health. Ingestion will cause many acute and chronic consequences characteristic of lead poisoning . [ 30 ] Lead iodide has been found to be a carcinogen in animals suggesting the same may hold true in humans. [ 31 ] Lead iodide is an inhalation hazard, and appropriate respirators should be used when handling powders of lead iodide.
The structure of PbI 2 , as determined by X-ray powder diffraction , is primarily hexagonal close-packed system with alternating between layers of lead atoms and iodide atoms, with largely ionic bonding. Weak van der Waals interactions have been observed between lead–iodide layers. [ 13 ] The most common stacking forms are 2H and 4H. The 4H polymorph is most common in samples grown from the melt, by precipitation, or by sublimation, whereas the 2H polymorph is usually formed by sol-gel synthesis. [ 9 ] The solid can also take an R6 rhombohedral structure. [ 32 ] | https://en.wikipedia.org/wiki/I2Pb |
Samarium(II) iodide is an inorganic compound with the formula SmI 2 . When employed as a solution for organic synthesis , it is known as Kagan 's reagent . SmI 2 is a green solid and forms a dark blue solution in THF . [ 1 ] It is a strong one-electron reducing agent that is used in organic synthesis .
In solid samarium(II) iodide, the metal centers are seven-coordinate with a face-capped octahedral geometry . [ 2 ]
In its ether adducts , samarium remains heptacoordinate with five ether and two terminal iodide ligands. [ 3 ]
Samarium iodide is easily prepared in nearly quantitative yields from samarium metal and either diiodomethane or 1,2-diiodoethane . [ 4 ] When prepared in this way, its solutions is most often used without purification of the inorganic reagent.
Solid, solvent-free SmI 2 forms by high temperature decomposition of samarium(III) iodide (SmI 3 ). [ 5 ] [ 6 ] [ 7 ]
Samarium(II) iodide is a powerful reducing agent – for example it rapidly reduces water to hydrogen . [ 2 ] It is available commercially as a dark blue 0.1 M solution in THF. Although used typically in superstoichiometric amounts, catalytic applications have been described. [ 8 ]
Samarium(II) iodide is a reagent for carbon-carbon bond formation, for example in a Barbier reaction (similar to the Grignard reaction ) between a ketone and an alkyl iodide to form a tertiary alcohol : [ 9 ]
Typical reaction conditions use SmI 2 in THF in the presence of catalytic NiI 2 .
Esters react similarly (adding two R groups), but aldehydes give by-products. The reaction is convenient in that it is often very rapid (5 minutes or less in the cold). Although samarium(II) iodide is considered a powerful single-electron reducing agent, it does display remarkable chemoselectivity among functional groups. For example, sulfones and sulfoxides can be reduced to the corresponding sulfide in the presence of a variety of carbonyl -containing functionalities (such as esters , ketones , amides , aldehydes , etc.). This is presumably due to the considerably slower reaction with carbonyls as compared to sulfones and sulfoxides . Furthermore, hydrodehalogenation of halogenated hydrocarbons to the corresponding hydrocarbon compound can be achieved using samarium(II) iodide. Also, it can be monitored by the color change that occurs as the dark blue color of SmI 2 in THF discharges to a light yellow once the reaction has occurred. The picture shows the dark colour disappearing immediately upon contact with the Barbier reaction mixture.
Work-up is with dilute hydrochloric acid , and the samarium is removed as aqueous Sm 3+ .
Carbonyl compounds can also be coupled with simple alkenes to form five, six or eight membered rings. [ 10 ]
Tosyl groups can be removed from N -tosylamides almost instantaneously, using SmI 2 in conjunction with distilled water and an amine base. The reaction is even effective for deprotection of sensitive substrates such as aziridines : [ 11 ]
In the Markó-Lam deoxygenation , an alcohol could be almost instantaneously deoxygenated by reducing their toluate ester in presence of SmI 2 .
SmI 2 can also be used in the transannulation of bicyclic molecules . An example is the SmI 2 induced ketone - alkene cyclization of 5-methylenecyclooctanone which proceeds through a ketyl intermediate:
The applications of SmI 2 have been reviewed. [ 12 ] [ 13 ] [ 14 ] The book Organic Synthesis Using Samarium Diiodide , published in 2009, gives a detailed overview of reactions mediated by SmI 2 . [ 15 ] | https://en.wikipedia.org/wiki/I2Sm |
Zinc iodide is the inorganic compound with the formula ZnI 2 . It exists both in anhydrous form and as a dihydrate. Both are white and readily absorb water from the atmosphere. It has no major application.
It can be prepared by the direct reaction of zinc and iodine in water [ 1 ] [ 2 ] or refluxing ether : [ 3 ]
Absent a solvent, the elements do not combine directly at room temperature. [ 4 ]
The structure of solid ZnI 2 is unusual relative to the dichloride. While zinc centers are tetrahedrally coordinated, as in ZnCl 2 , groups of four of these tetrahedra share three vertices to form “super-tetrahedra” of composition {Zn 4 I 10 }, which are linked by their vertices to form a three-dimensional structure. [ 5 ] These "super-tetrahedra" are similar to the P 4 O 10 structure. [ 5 ] [ 6 ]
Molecular ZnI 2 is linear as predicted by VSEPR theory with a Zn-I bond length of 238 pm. [ 5 ]
In aqueous solution the following have been detected: Zn(H 2 O) 6 2+ , [ZnI(H 2 O) 5 ] + , tetrahedral ZnI 2 (H 2 O) 2 , ZnI 3 (H 2 O) − , and ZnI 4 2− . [ 7 ] | https://en.wikipedia.org/wiki/I2Zn |
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