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HITRAN (an acronym for Hi gh Resolution Tran smission) molecular spectroscopic database is a compilation of spectroscopic parameters used to simulate and analyze the transmission and emission of light in gaseous media, with an emphasis on planetary atmospheres. The knowledge of spectroscopic parameters for transitions between energy levels in molecules (and atoms) is essential for interpreting and modeling the interaction of radiation (light) within different media.
For half a century, HITRAN has been considered to be an international standard which provides the user a recommended value of parameters for millions of transitions for different molecules. HITRAN includes both experimental and theoretical data which are gathered from a worldwide network of contributors as well as from articles, books, proceedings, databases, theses, reports, presentations, unpublished data, papers in-preparation and private communications. A major effort is then dedicated to evaluating and processing the spectroscopic data. A single transition in HITRAN has many parameters, including a default 160-byte fixed-width format used since HITRAN2004. [ 1 ] Wherever possible, the retrieved data are validated against accurate laboratory data. [ 2 ]
The original version of HITRAN was compiled by the US Air Force Cambridge Research Laboratories (1960s) in order to enable surveillance of military aircraft detected through the terrestrial atmosphere. [ 2 ] One of the early applications of HITRAN was a program called Atmospheric Radiation Measurement (ARM) for the US Department of Energy. [ 2 ] In this program spectral atmospheric measurements were made around the globe in order to better understand the balance between the radiant energy that reaches Earth from the sun and the energy that flows from Earth back out to space. [ 2 ] The US Department of Transportation also utilized HITRAN in its early days for monitoring the gas emissions (NO, SO 2 , NO 2 ) of super-sonic transports flying at high altitude. [ 2 ] HITRAN was first made publicly available in 1973 [ 3 ] and today there are a multitude of ongoing and future NASA satellite missions which incorporate HITRAN. [ 2 ] One of the NASA missions currently utilizing HITRAN is the Orbiting Carbon Observatory (OCO) which measures the sources and sinks of CO 2 in the global atmosphere. [ 2 ] HITRAN is a free resource and is currently maintained and developed at the Center for Astrophysics | Harvard & Smithsonian , Cambridge MA, USA ( CFA/HITRAN ).
HITRAN is the worldwide standard for calculating or simulating atmospheric molecular transmission and radiance from the microwave through ultraviolet region of the spectrum. [ 4 ] The HITRAN database is officially released on a quadrennial basis, with updates posted in the intervening years on HITRAN online . There is a new journal article published in conjunction with the most recent release of the HITRAN database, and users are strongly encouraged to use the most recent edition. [ 5 ] Throughout HITRAN's history, there have been around 50,000 unique users of the database and in recent years there are over 24,000 users registered on HITRAN online . There are YouTube tutorials on the HITRAN online webpage to answer frequently asked questions by users. [ 2 ]
The current version, HITRAN2020, contains 55 molecules in the line-by-line portion of HITRAN along with some of their most significant isotopologues (144 isotopologues in total). [ 5 ] These data are archived as a multitude of high-resolution line transitions, each containing many spectral parameters required for high-resolution simulations.
In addition to the traditional line-by-line spectroscopic absorption parameters, the HITRAN database contains information on absorption cross-sections where the line-by-line parameters are absent or incomplete. Typically HITRAN includes absorption cross-sections for heavy polyatomic molecules (with low-lying vibrational modes) which are difficult for detailed analysis due to the high density of the spectral bands/lines, broadening effects, isomerization, and overall modeling complexity. [ 6 ] There are 327 molecular species in the current edition of the database provided as cross-section files. The cross-section files are provided in the HITRAN format described on the official HITRAN website ( http://hitran.org/docs/cross-sections-definitions/ ).
The HITRAN compilation also provides collision-induced absorption (CIA) [ 7 ] that was first introduced into HITRAN in the 2012 edition. [ 8 ] CIA refers to absorption by transient electric dipoles induced by the interaction between colliding molecules. Instructions for accessing the CIA data files can be found on HITRAN/CIA .
HITRAN2020 also has an aerosols refractive indices section, with data in the visible, infrared, and millimeter spectral ranges of many types of cloud and aerosol particles. Knowledge of the refractive indices of the aerosols and cloud particles and their size distributions is necessary in order to specify their optical properties. [ 9 ]
HITEMP is the molecular spectroscopic database analogous to HITRAN for high-temperature modeling of the spectra of molecules in the gas phase. [ 10 ] HITEMP encompasses many more bands and transitions than HITRAN for eight absorbers: H 2 O, CO 2 , N 2 O, CO, CH 4 , NO, NO 2 and OH. [ 10 ] [ 11 ] [ 12 ] Due to the extremely large number of transitions required for high-temperature simulations, it was necessary to provide the HITEMP data as separate files to that of HITRAN. The HITEMP line lists retain the same 160-character format that was used for earlier editions of HITRAN. [ 10 ] [ 1 ] There are numerous applications for HITEMP data, some examples include the thermometry of high-temperature environments, [ 13 ] analysis of combustion processes, [ 14 ] and modeling spectra of atmospheres in the Solar System, [ 15 ] exoplanets, [ 16 ] brown dwarfs, [ 17 ] and stars. [ 18 ]
A Python library HAPI ( H ITRAN A pplication P rogramming I nterface) has been developed which serves as a tool for absorption and transmission calculations as well as comparisons of spectroscopic data sets. HAPI extends the functionality of the main site, in particular, for the calculation of spectra using several types of line shape calculations, including the flexible HT (Hartmann-Tran) profile. This HT line shape can also be reduced to a number of conventional line profiles such as Gaussian (Doppler), Lorentzian, Voigt, Rautian, Speed-Dependent Voigt and Speed-Dependent Rautian. In addition to accounting for pressure, temperature and optical path length, the user can include a number of instrumental functions to simulate experimental spectra. HAPI is able to account for broadening of lines due to mixtures of gases as well as make use of all broadening parameters supplied by HITRAN. This includes the traditional broadeners (air, self) as well as additional parameters for CO 2 , H 2 O, H 2 and He broadening. [ 19 ] The following spectral functions can be calculated in the current version #1 of HAPI: [ 20 ]
HAPIEST (an acronym for H ITRAN A pplication P rogramming I nterface and E fficient S pectroscopic T ools) is a graphical user interface allowing users to access some of the functionality provided by HAPI without any knowledge of Python programming, including downloading data from HITRAN, and plotting of spectra and cross-sections. The source code for HAPIEST is available on GitHub (HAPIEST) , along with binary distributions for Mac and PC. | https://en.wikipedia.org/wiki/HITRAN |
High-throughput sequencing of RNA isolated by crosslinking immunoprecipitation ( HITS-CLIP ) is a variant of CLIP [ 1 ] for genome -wide mapping protein – RNA binding sites or RNA modification sites in vivo . [ 2 ] [ 3 ] [ 4 ] HITS-CLIP was originally used to generate genome-wide protein-RNA interaction maps for the neuron-specific RNA-binding protein and splicing factor NOVA1 and NOVA2; [ 3 ] since then a number of other splicing factor maps have been generated, including those for PTB, [ 5 ] RbFox2, [ 6 ] SFRS1, [ 7 ] hnRNP C, [ 8 ] and even N6-Methyladenosine (m6A) mRNA modifications. [ 4 ] [ 9 ]
HITS-CLIP of the RNA-binding protein Argonaute has been performed for the identification of microRNA targets [ 10 ] by decoding microRNA -mRNA and protein-RNA interaction maps in mouse brain, [ 11 ] [ 12 ] and subsequently in Caenorhabditis elegans , [ 13 ] embryonic stem cells [ 14 ] and tissue culture cells. [ 15 ]
As a novel modification of HITS-CLIP, m6A-CLIP was developed to precisely map N6-Methyladenosine(m6A) locations in mRNA by UV-crosslinking m6A antibody to the target RNA. [ 4 ] [ 9 ] Recently, improved bioinformatics applied to Argonaute HITS-CLIP enables identification of binding sites with single nucleotide resolution. [ 16 ] | https://en.wikipedia.org/wiki/HITS-CLIP |
Human Immunodeficiency Virus (HIV) has the capability to enter a latent stage of infection where it exists as a dormant provirus in CD4+ T-cells . Most latently infected cells are resting memory T cells, [ 1 ] however a small fraction of latently infected cells isolated from HIV patients are naive CD4 T cells. [ 2 ]
HIV transcription is controlled by the 5' Long Terminal Repeat (LTR) region of the provirus, which serves as the key promoter. [ 3 ]
The LTR promoter has multiple upstream DNA regulatory elements: there are three SP1-binding sites, a TATA element, and an initiator sequence. [ 4 ] The LTR has two NF-кB binding motifs that are capable of binding both NF-кB transcription factors as well as NFATs . [ 4 ] The LTR promoter is very noisy [ 5 ] and prone to large bursts of transcription. [ 6 ] While signaling through the NF-кB enhancers has been shown to be necessary for re-activation of latent proviruses, mutations in these sites do not completely inhibit viral growth in cell line experiments. [ 7 ]
The LTR of HIV is positively auto regulated by the Tat (transcription activator) protein, which is found towards the 3' end of the HIV genome. Without Tat activity, HIV transcription is restricted and often results in abortive transcripts . [ 8 ] Tat activates the LTR through interactions with the elongation factor P-TEFb ; [ 9 ] Tat binds to cyclin T1 , which is a unit of P-TEFb. [ 9 ] [ 10 ] Tat:P-TEFb directs RNA polymerases to the provirus genome by binding the HIV transactivation response (TAR) element, an RNA stem-loop structure. [ 4 ] [ 11 ]
The mechanisms underpinning HIV latency and proviral induction are not thoroughly understood, and two competing models attempt to explain how latency is controlled.
In the cell-dependent model of latency regulation, host cell processes control provirus latency and induction. Generally, this model proposes that the relaxation of active CD4+ T-cells to a resting or quiescent state as memory T cells restricts proviral transcription and leads to latency. [ 12 ]
Multiple host-cell processes have been experimentally linked to HIV latency regulation. Observations both in patient samples and in vitro experiments with T cell lines have correlated latency with the relaxation of activated T cells to a resting-memory state. [ 1 ] [ 13 ] Latency was initially thought to be due to HIV proviral genome integration into heterochromatin , but later it was found that latent proviral transcripts were still preferentially integrated into active genes. [ 14 ] The main changes in cell state observed are epigenetic silencing of the HIV LTR as well as cytosolic sequestration of NF-кB and NFAST, which can activate HIV transcription if present in the nucleus. [ 1 ] The LTRs of latent proviruses acquire heterochromatic structures instead of integrating into previously heterochromatic areas, [ 4 ] and show high levels of deacetylated and methylated histones , [ 15 ] [ 16 ] which reinforces the role of chromatin restriction in latency regulation. [ 17 ] Histone deacetylases ( HDACs ) are recruited to the proviral genome during latency establishment and methylate key Histone H3 Lysines, indicating a role of HDACs in latency regulation. [ 1 ]
In addition to cytosolic sequestration of transcription factors, the P-TEFb complex is restricted in quiescent T cells through incorporation into an RNP complex. [ 18 ] In latently infected cells, NF-кB induction and TNF-α have been shown to be necessary but not sufficient for viral induction. [ 1 ] [ 19 ] T-cell Receptor (TCR) activation has been shown to activate proviral transcription in latently-infected memory T cells, indicating some correlation between proviral induction and T cell state. [ 1 ]
In contrast to the cell-dependent model, the cell-autonomous model proposes that HIV latency decisions are largely driven by the Tat-positive feedback loop and latency is therefore a probabilistic response due to intrinsically generated phenotypic heterogeneity rather than host-cell-determined. [ 12 ]
Multiple studies have found that proviral induction is dependent on the Tat autoregulation response. [ 12 ] [ 11 ] In a study focused on understanding the diversity of roles of Sp1 and NF-кB binding elements in the LTR, authors noted that the Tat autoregulatory circuit resulted in a phenotypic bifurcation of genetically identical cells where viral gene expression was either off or highly induced. [ 11 ] Additionally, primate studies of HIV latency have shown that latent cells emerge before the adaptive immune response is established, indicating that latency cannot entirely be dependent on T-cell relaxation after peak adaptive immune response. [ 20 ] Latency is also established in cell-culture models with up to a 50% probability of establishment. [ 12 ] [ 21 ] [ 22 ]
Some research has shown that the Tat positive-feedback loop in isolation has the ability to establish latency via stochastic noise, [ 23 ] and that T-cell relaxation is not sufficient to drive latency. [ 12 ] This model proposes to explain why many latent proviruses are not reactivated along with T-cell reactivation: instead of a deterministic mechanism, cellular activation or relaxation would probabilistically affect HIV latency decisions, [ 12 ] which is consistent with other work showing that LTR regulatory sites have some influence on the frequency of phenotypic bifurcation of HIV transcription. [ 11 ]
One key hypothesis put forward is that latency allows HIV infection to persist past the initial mucosal stage; latently infected cells could allow HIV to disseminate from mucosal tissue to lymph nodes with much higher populations of the target CD4+ T cells. [ 24 ] This hypothesis is supported by observations that HIV infections appear to expand from single founder sequences, [ 25 ] [ 26 ] indicating that the mucosal infection provides a bottleneck. [ 24 ] A two-compartment model of HIV dissemination and transmission predicts that the probability of latency for an HIV provirus should be close to 50% to balance dissemination from the mucosal tissue and transmission inoculum. [ 24 ]
Latently infected cells are the key barrier to viral elimination by current antiretroviral therapies . A study focused on determining the frequency of latently infected cells in patients on combination antiretroviral therapy found that latently infected cells created a stable reservoir of virus with a half-life of 43 months. [ 27 ] This latent reservoir forces patients to continuously take antiretroviral therapy to avoid viral re-emergence. An additional study found that actively infected cells and viremia re-emerge within weeks of antiretroviral therapy being discontinued. [ 28 ]
Some work has been put into a "shock and kill" strategy to circumvent the challenge posed by latently infected reservoirs: before antiretrovirals, there is a "shock" phase that attempts to reactivate most latent proviruses. So far, these "shock" phases focus on drugs that stimulate P-TEFb nuclear mobilization and direct transcriptional activation of HIV. [ 4 ] Further work is being done to understand LTR noise and more effectively activate or kill latently infected cells. [ 29 ] | https://en.wikipedia.org/wiki/HIV_latency |
The HKA Test , named after Richard R. Hudson , Martin Kreitman , and Montserrat Aguadé , is a statistical test used in genetics to evaluate the predictions of the Neutral Theory of molecular evolution . By comparing the polymorphism within each species and the divergence observed between two species at two or more loci, the test can determine whether the observed difference is likely due to neutral evolution or rather due to adaptive evolution. [ 1 ] Developed in 1987, the HKA test is a precursor to the McDonald–Kreitman test , which was derived in 1991. The HKA test is best used to look for balancing selection , recent selective sweeps or other variation-reducing forces. [ 2 ]
Neutral Evolution Theory, first proposed by Kimura in a 1968 paper, and later fully defined and published in 1983, is the basis for many statistical tests that detect selection at the molecular level. Kimura noted that there was much too high of a rate of mutation within the genome (i.e. high polymorphism) to be strictly under directional evolution. Furthermore, functionally less important regions of the genome evolve at a faster rate. [ 3 ] Kimura then postulated that most of the modifications to the genome are neutral or nearly neutral, and evolve by random genetic drift. Therefore, under the neutral model, polymorphism within a species and divergence between related species at homologous sites will be highly correlated. The Neutral Evolution theory has become the null model against which tests for selection are based, and divergence from this model can be explained by directional or selective evolution.
The rate of mutation within a population can be estimated using the Watterson estimator formula: θ=4Ν e μ, where Ν e is the effective population size and μ is the mutation rate (substitutions per site per unit of time). [ 4 ] Hudson et al. proposed applying these variables to a chi-squared, goodness-of-fit test.
The test statistic proposed by Hudson et al., Χ 2 , is:
This states that, for each locus ( L ) (for which there must be at least two) the sum of the difference in number of observed polymorphic sites in sample A minus the estimate of expected polymorphism squared, all of which is divided by the variance. Similarly, this formula is then applied to Sample B (from another species) and then can be applied to the divergence between two sample species. The sum of these three variables is the test statistic (X 2 ). If the polymorphism within species A, and B, and the divergence between them are all independent, then the test statistic should fall approximately onto a chi-squared distribution. [ 1 ]
For a simple explanation, let D 1 = divergence between species, or the number of fixed differences in locus one. Similarly D 2 = divergence in locus two. Let P 1 and P 2 = the number of polymorphic sites in loci one and two, respectively (a measure of polymorphism within species). If there is no directional evolution, then D 1 /D 2 = P 1 /P 2 .
For these examples, the distance between two species’ loci is determined by measuring the number of substitutions per site when comparing the two species. We can then calculate the rate of mutation (changes to the DNA sequence pre unit of time) if we know the time since the two species diverged from the common ancestor.
A test that suggests neutral evolution: Suppose that you have data from two loci (1 and 2) in two species (A and B). Locus 1 shows high divergence and high polymorphism in both species. Locus 2 shows low divergence and low polymorphism. This can be explained by a neutral difference in the rate of mutations in each loci.
A test that suggests selection: Again suppose you have data as in the last example, only this time locus 2 has equal divergence to locus 1 and yet lower polymorphism in species B. In this case the rate of mutation in each locus is equal, so this can only be explained by a reduction in the effective population size Ne of species B, which is inferred as an act of selection. | https://en.wikipedia.org/wiki/HKA_test |
β-Hydroxy β-methylglutaryl-CoA ( HMG-CoA ), also known as 3-hydroxy-3-methylglutaryl coenzyme A , is an intermediate in the mevalonate and ketogenesis pathways. It is formed from acetyl CoA and acetoacetyl CoA by HMG-CoA synthase . The research of Minor J. Coon and Bimal Kumar Bachhawat in the 1950s at University of Illinois led to its discovery. [ 1 ] [ 2 ]
HMG-CoA is a metabolic intermediate in the metabolism of the branched-chain amino acids , which include leucine , isoleucine , and valine . [ 3 ] Its immediate precursors are β-methylglutaconyl-CoA (MG-CoA) and β-hydroxy β-methylbutyryl-CoA (HMB-CoA). [ 4 ] [ 5 ] [ 6 ]
HMG-CoA reductase catalyzes the conversion of HMG-CoA to mevalonic acid , a necessary step in the biosynthesis of cholesterol.
Mevalonate synthesis begins with the beta-ketothiolase -catalyzed Claisen condensation of two molecules of acetyl-CoA to produce acetoacetyl CoA . The following reaction involves the joining of acetyl-CoA and acetoacetyl-CoA to form HMG-CoA, a process catalyzed by HMG-CoA synthase . [ 8 ]
In the final step of mevalonate biosynthesis, HMG-CoA reductase , an NADPH -dependent oxidoreductase , catalyzes the conversion of HMG-CoA into mevalonate , which is the primary regulatory point in this pathway. Mevalonate serves as the precursor to isoprenoid groups that are incorporated into a wide variety of end-products, including cholesterol in humans. [ 9 ]
HMG-CoA lyase breaks it into acetyl CoA and acetoacetate .
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HMG-CoA |
HMX , also called octogen , is a powerful and relatively insensitive nitroamine high explosive chemically related to RDX . The compound's name is the subject of much speculation, having been variously listed as High Melting Explosive , High-velocity Military Explosive , or High-Molecular-weight RDX . [ 1 ]
The molecular structure of HMX consists of an eight-membered ring of alternating carbon and nitrogen atoms, with a nitro group attached to each nitrogen atom. Because of its high mass-specific enthalpy of formation , it is one of the most potent chemical explosives manufactured, although a number of newer ones, including HNIW and ONC , are more powerful.
HMX is more complicated to manufacture than most explosives, and this confines it to specialist applications. It and RDX are both produced by the Bachmann process —nitration of hexamine using a mixture of ammonium nitrate and nitric acid in a mixture of acetic acid and acetic anhydride as solvent—with the major product determined by the specific reaction conditions. [ 2 ]
Also known as cyclotetramethylene-tetranitramine, tetrahexamine tetranitramine, or octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, HMX was first made in 1930. In 1949 it was discovered that HMX can be prepared by nitrolysis of RDX. Nitrolysis of RDX is performed by dissolving RDX in a 55% HNO 3 solution, followed by placing the solution on a steambath for about six hours. [ 3 ] HMX is used almost exclusively in military applications, including as the detonator in nuclear weapons , in the form of polymer-bonded explosive , and as a solid- rocket propellant .
HMX is used in melt-castable explosives when mixed with TNT , which as a class are referred to as " octols ". Additionally, polymer-bonded explosive compositions containing HMX are used in the manufacture of missile warheads and armor-piercing shaped charges .
HMX is also used in the process of perforating the steel casing in oil and gas wells . The HMX is built into a shaped charge that is detonated within the wellbore to punch a hole through the steel casing and surrounding cement out into the hydrocarbon-bearing formations. The pathway that is created allows formation fluids to flow into the wellbore and onward to the surface. [ 4 ] [ 5 ]
The Hayabusa2 space probe used HMX to excavate a hole in an asteroid in order to access material that had not been exposed to the solar wind . [ 6 ]
Ongoing research aims to reduce its sensitivity and improve some manufacturing properties. [ 7 ] [ 8 ]
HMX enters the environment through air, water, and soil because it is widely used in military and civil applications. At present, reverse-phase HPLC and more sensitive LC-MS methods have been developed to accurately quantify the concentration of HMX in a variety of matrices in environmental assessments. [ 9 ] [ 10 ]
At present, the information needed to determine if HMX causes cancer is insufficient. Due to the lack of information, EPA has determined that HMX is not classifiable as to its human carcinogenicity. [ 11 ]
The available data on the effects on human health of exposure to HMX are limited. HMX causes CNS effects similar to those of RDX, but at considerably higher doses. In one study, volunteers submitted to patch testing , which produced skin irritation. Another study of a cohort of 93 workers at an ammunition plant found no hematological, hepatic, autoimmune, or renal diseases. However, the study did not quantify the levels of exposure to HMX.
HMX exposure has been investigated in several studies on animals. Overall, the toxicity appears to be quite low. HMX is poorly absorbed by ingestion. When applied to the dermis, it induces mild skin irritation but not delayed contact sensitization. Various acute and subchronic neurobehavioral effects have been reported in rabbits and rodents, including ataxia, sedation, hyperkinesia, and convulsions. The chronic effects of HMX that have been documented through animal studies include decreased hemoglobin, increased serum alkaline phosphatase, and decreased albumin. Pathological changes were also observed in the animals' livers and kidneys.
Gas exchange rate was used as an indicator of chemical stress in Northern bobwhite quail ( Colinus virginianus ) eggs, and no evidence of alterations in metabolic rates associated with HMX exposure was observed. [ 12 ] No data are available concerning the possible reproductive, developmental, or carcinogenic effects of HMX. [ 2 ] [ 13 ] HMX is considered less toxic than TNT or RDX . [ 14 ] Remediating HMX-contaminated water supplies has proven to be successful. [ 15 ]
Both wild and transgenic plants can phytoremediate explosives from soil and water. [ 16 ] | https://en.wikipedia.org/wiki/HMX |
Diethanolamine , often abbreviated as DEA or DEOA , is an organic compound with the formula HN(CH 2 CH 2 OH) 2 . Pure diethanolamine is a white solid at room temperature , but its tendencies to absorb water and to supercool [ 2 ] often results in it being found in a colorless, viscous liquid state. Diethanolamine is polyfunctional, being a secondary amine and a diol . Like other organic amines, diethanolamine acts as a weak base . Reflecting the hydrophilic character of the secondary amine and hydroxyl groups, DEA is soluble in water. Amides prepared from DEA are often also hydrophilic. In 2013, the chemical was classified by the International Agency for Research on Cancer as "possibly carcinogenic to humans" ( Group 2B ).
The reaction of ethylene oxide with aqueous ammonia first produces ethanolamine :
which reacts with a second and third equivalent of ethylene oxide to give DEA and triethanolamine :
About 300M kg are produced annually in this way. [ 3 ] The ratio of the products can be controlled by changing the stoichiometry of the reactants. [ 4 ]
DEA is used as a surfactant and a corrosion inhibitor . It is used to remove hydrogen sulfide and carbon dioxide from natural gas.
Diethanolamine is widely used in the preparation of diethanolamides and diethanolamine salts of long-chain fatty acids that are formulated into soaps and surfactants used in liquid laundry and dishwashing detergents, cosmetics, shampoos and hair conditioners. [ 5 ] In oil refineries, a DEA in water solution is commonly used to remove hydrogen sulfide from sour gas . It has an advantage over a similar amine, ethanolamine , in that a higher concentration may be used for the same corrosion potential. This allows refiners to scrub hydrogen sulfide at a lower circulating amine rate with less overall energy usage.
DEA is a chemical feedstock used in the production of morpholine . [ 3 ] [ 4 ]
Amides derived from DEA and fatty acids , known as diethanolamides , are amphiphilic .
The reaction of 2-chloro-4,5-diphenyloxazole with DEA gave rise to ditazole . The reaction of DEA and isobutyraldehyde with water removed produces an oxazolidine . [ 6 ] [ 7 ]
DEA is used in the production of diethanolamides , which are common ingredients in cosmetics and shampoos added to confer a creamy texture and foaming action. Consequently, some cosmetics that include diethanolamides as ingredients contain DEA. [ 8 ] Some of the most commonly used diethanolamides include:
DEA is a potential skin irritant in workers sensitized by exposure to water-based metalworking fluids. [ 9 ]
DEA has potential toxicity properties for aquatic species. [ 10 ]
DEA is a key component of unusual phospholipids that are produced by Morganella morganii , a bacteria in the human microbiome, with elevated levels being linked to increased incidence of major depression. [ 11 ] | https://en.wikipedia.org/wiki/HN(CH2CH2OH)2 |
HNBAP is a control protocol found in Home Node B networks on the Iu-h interface.
The Home Node B Application Part ( HNBAP ) protocol provides the following functions:
The following 3GPP documents are available:
Between the HNB and the HNB-GW is a new interface known as Iu-h .
Iu-h Interface - Residing between an HNB and HNB-GW, the Iu-h interface defines the security architecture used to provide a secure, scalable communications over the Internet. The Iu-h interface also defines an efficient, reliable method for transporting Iu-based traffic as well as a new protocol HNBAP for enabling highly scalable ad hoc HNB deployment.
Within an HNB Access Network there are three new network elements: the Home Node B (or femtocell), the Security Gateway (SeGW) and the Home Node B Gateway , or HNB-GW .
Home Node B (HNB) – Connected to an existing residential broadband service, an HNB provides 3G radio coverage for 3G handsets within a home. HNBs incorporate the capabilities of a standard Node B as well as the radio resource management functions of a standard Radio Network Controller RNC .
Security Gateway (SeGW) - Installed in an operator's network, the Security Gateway establishes IPsec tunnels with HNBs using IKEv2 signaling for IPsec tunnel management. IPsec tunnels are responsible for delivering all voice, messaging and packet data services between HNB and the core network. The SeGW forwards traffic to HNB-GW.
HNB Gateway (HNB-GW) - Installed within an operator's network, the HNB Gateway aggregates traffic from a large number of HNBs back into an existing core service network through the standard Iu-cs and Iu-ps interfaces. | https://en.wikipedia.org/wiki/HNBAP |
HNCA is a 3D triple-resonance NMR experiment commonly used in the field of protein NMR . The name derives from the experiment's magnetization transfer pathway: The magnetization of the amide proton of an amino acid residue is transferred to the amide nitrogen, and then to the alpha carbons of both the starting residue and the previous residue in the protein's amino acid sequence. In contrast, the complementary HNCOCA experiment
transfers magnetization only to the alpha carbon of the previous residue [1] . The HNCA experiment is used, often in tandem with HNCOCA, to assign alpha carbon resonance signals to specific residues in the protein. This experiment requires a purified sample of protein prepared with 13 C and 15 N isotopic labelling , at a concentration greater than 0.1 mM , and is thus generally only applied to recombinant proteins .
The spectrum produced by this experiment has 3 dimensions: A proton axis, a 15 N axis and a 13 C axis. For residue i peaks will appear at {H N (i), N(i), C alpha (i)} and {H N (i), N(i), C alpha (i-1)}, while for the complementary HNCOCA experiment peaks appear only at {H N (i), N(i), C alpha (i-1)}. Together, these two experiments reveal the alpha carbon chemical shift for each amino acid residue in a protein, and provide information linking adjacent residues in the protein's sequence.
Protein NMR Spectroscopy : Principles and Practice (1995) John Cavanagh, Wayne J. Fairbrother, Arthur G. Palmer III, Nicholas J. Skelton, Academic Press
This biophysics -related article is a stub . You can help Wikipedia by expanding it .
This protein -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HNCA_experiment |
HNCOCA is a 3D triple-resonance NMR experiment commonly used in the field of protein NMR . The name derives from the experiment's magnetization transfer pathway: The magnetization of the amide proton of an amino acid residue is transferred to the amide nitrogen, and then to the alpha carbon of the previous residue in the protein's amino acid sequence. In contrast, the complementary HNCA experiment transfers magnetization to the alpha carbons of both the starting residue and the previous residue in the sequence. The HNCOCA experiment is used, often in tandem with HNCA, to assign alpha carbon resonance signals to specific residues in the protein. This experiment requires a purified sample of protein prepared with 13 C and 15 N isotopic labelling , at a concentration greater than 0.1 mM , and is thus generally only applied to recombinant proteins .
The spectrum produced by this experiment has 3 dimensions: A proton axis, a 15 N axis and a 13 C axis. For residue i peaks will appear at {H N (i), N(i), C α (i-1)} only, while for the complementary HNCA experiment peaks appear at {H N (i), N(i), C α (i-1)} and {H N (i), N(i), C α (i)}. Together, these two experiments reveal the alpha carbon chemical shift for each amino acid residue in a protein, and provide information linking adjacent residues in the protein's sequence.
Bax A, Ikura M (May 1991). "An efficient 3D NMR technique for correlating the proton and 15N backbone amide resonances with the alpha-carbon of the preceding residue in uniformly 15N/13C enriched proteins". J. Biomol. NMR . 1 (1): 99– 104. doi : 10.1007/BF01874573 . PMID 1668719 .
John Cavanagh; Wayne J. Fairbrother; Arthur G. Palmer III; Nicholas J. Skelton (1995). Protein NMR Spectroscopy : Principles and Practice . Academic Press .
This biophysics -related article is a stub . You can help Wikipedia by expanding it .
This protein -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HNCOCA_experiment |
Diimide , also called diazene or diimine , is a compound having the formula HN=NH. It exists as two geometric isomers , E ( trans ) and Z ( cis ). The term diazene is more common for organic derivatives of diimide. Thus, azobenzene is an example of an organic diazene.
A traditional route to diimide involves oxidation of hydrazine with hydrogen peroxide or air. [ 1 ]
Alternatively the hydrolysis of diethyl azodicarboxylate or azodicarbonamide affords diimide: [ 2 ]
Nowadays, diimide is generated by thermal decomposition of 2,4,6‐triisopropylbenzenesulfonylhydrazide. [ 3 ]
Because of its instability, diimide is generated and used in-situ . A mixture of both the cis ( Z- ) and trans ( E- ) isomers is produced. Both isomers are unstable, and they undergo a slow interconversion. The trans isomer is more stable, but the cis isomer is the one that reacts with unsaturated substrates, therefore the equilibrium between them shifts towards the cis isomer due to Le Chatelier's principle . Some procedures call for the addition of carboxylic acids, which catalyse the cis–trans isomerization. [ 4 ] Diimide decomposes readily. Even at low temperatures, the more stable trans isomer rapidly undergoes various disproportionation reactions, primarily forming hydrazine and nitrogen gas : [ 5 ]
Because of this competing decomposition reaction, reductions with diimide typically require a large excess of the precursor reagent.
Diimide is occasionally useful as a reagent in organic synthesis . [ 4 ] It hydrogenates alkenes and alkynes with selective delivery of hydrogen from one face of the substrate resulting in the same stereoselectivity as metal-catalysed syn addition of H 2 . The only coproduct released is nitrogen gas. Although the method is cumbersome, the use of diimide avoids the need for high pressures or hydrogen gas and metal catalysts, which can be expensive. [ 6 ] The hydrogenation mechanism involves a six-membered C 2 H 2 N 2 transition state:
Diimide is advantageous because it selectively reduces alkenes and alkynes and is unreactive toward many functional groups that would interfere with normal catalytic hydrogenation . Thus, peroxides , alkyl halides , and thiols are tolerated by diimide, but these same groups would typically be degraded by metal catalysts. The reagent preferentially reduces alkynes and unhindered or strained alkenes [ 1 ] to the corresponding alkenes and alkanes. [ 4 ]
The dicationic form, H−N + ≡N + −H (diazynediium, diprotonated dinitrogen), is calculated to have the strongest known chemical bond. This ion can be thought of as a doubly protonated nitrogen molecule. The relative bond strength order (RBSO) is 3.38. [ 7 ] F−N + ≡N + −H (fluorodiazynediium ion) and F−N + ≡N + −F (difluorodiazynediium ion) have slightly lower strength bonds. [ 7 ]
In the presence of strong bases, diimide deprotonates to form the pernitride anion, N − =N − . | https://en.wikipedia.org/wiki/HNNH |
Nitrous acid (molecular formula H N O 2 ) is a weak and monoprotic acid known only in solution , in the gas phase, and in the form of nitrite ( NO − 2 ) salts. [ 3 ] It was discovered by Carl Wilhelm Scheele , who called it " phlogisticated acid of niter". Nitrous acid is used to make diazonium salts from amines. The resulting diazonium salts are reagents in azo coupling reactions to give azo dyes .
In the gas phase, the planar nitrous acid molecule can adopt both a syn and an anti form. The anti form predominates at room temperature, and IR measurements indicate it is more stable by around 2.3 kJ/mol. [ 3 ]
Free, gaseous nitrous acid is unstable, rapidly disproportionating to nitric oxides :
In aqueous solution, the nitrogen dioxide also disproportionates, for a net reaction producing nitric oxide and nitric acid : [ 4 ] : 1 [ 5 ]
Consequently applications of nitrous acid usually begin with mineral acid acidification of sodium nitrite . The acidification is usually conducted at ice temperatures, and the HNO 2 consumed in situ . [ 6 ] [ 7 ]
Nitrous acid equilibrates with dinitrogen trioxide in water, so that concentrated solutions are visibly blue: [ 4 ] : 2
Addition of dinitrogen trioxide to water is thus another preparatory technique.
Nitrous acid is the main chemophore in the Liebermann reagent , used to spot-test for alkaloids.
At high acidities ( p H ≪ 2 ), nitrous acid is protonated to give water and nitrosonium cations. [ 4 ] : 2
With I − and Fe 2+ ions, NO is formed: [ 8 ]
With Sn 2+ ions, N 2 O is formed:
With SO 2 gas, NH 2 OH is formed:
With Zn in alkali solution, NH 3 is formed:
With N 2 H + 5 , both HN 3 and (subsequently) N 2 gas are formed:
Oxidation by nitrous acid has a kinetic control over thermodynamic control , this is best illustrated that dilute nitrous acid is able to oxidize I − to I 2 , but dilute nitric acid cannot.
It can be seen that the values of E o cell for these reactions are similar, but nitric acid is a more powerful oxidizing agent. Based on the fact that dilute nitrous acid can oxidize iodide into iodine , it can be deduced that nitrous is a faster, rather than a more powerful, oxidizing agent than dilute nitric acid. [ 8 ]
Nitrous acid is used to prepare diazonium salts :
where Ar is an aryl group.
Such salts are widely used in organic synthesis , e.g., for the Sandmeyer reaction and in the preparation azo dyes , brightly colored compounds that are the basis of a qualitative test for anilines . [ 9 ] Nitrous acid is used to destroy toxic and potentially explosive sodium azide . For most purposes, nitrous acid is usually formed in situ by the action of mineral acid on sodium nitrite : [ 10 ] It is mainly blue in colour
Reaction with two α-hydrogen atoms in ketones creates oximes , which may be further oxidized to a carboxylic acid, or reduced to form amines. This process is used in the commercial production of adipic acid .
Nitrous acid reacts rapidly with aliphatic alcohols to produce alkyl nitrites , which are potent vasodilators :
The carcinogens called nitrosamines are produced, usually not intentionally, by the reaction of nitrous acid with secondary amines :
Nitrous acid is involved in the ozone budget of the lower atmosphere , the troposphere . The heterogeneous reaction of nitric oxide (NO) and water produces nitrous acid. When this reaction takes place on the surface of atmospheric aerosols , the product readily photolyses to hydroxyl radicals . [ 11 ] [ 12 ]
Treatment of Escherichia coli cells with nitrous acid causes damage to the cell's DNA including deamination of cytosine to uracil , and these damages are subject to repair by specific enzymes. [ 13 ] Also, nitrous acid causes base substitution mutations in organisms with double-stranded DNA. [ 14 ] | https://en.wikipedia.org/wiki/HNO2 |
Peroxynitric acid or peroxonitric acid is a chemical compound with the formula HNO 4 . It is an oxyacid of nitrogen, after peroxynitrous acid .
Peroxynitrate , the conjugate base of peroxynitric acid, is formed rapidly during decomposition of peroxynitrite in neutral conditions. [ 4 ]
Peroxynitric acid is formed in the atmosphere, although it is unstable, it is important as a reservoir for NO 2 through the reversible radical reaction: [ 5 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HNO4 |
Nitrosylsulfuric acid is the chemical compound with the formula HSO 4 NO . It is a colourless solid that is used industrially in the production of caprolactam , [ 3 ] and was formerly part of the lead chamber process for producing sulfuric acid . The compound is the mixed anhydride of sulfuric acid and nitrous acid .
In organic chemistry, it is used as a reagent for nitrosating , as a diazotizing agent , and as an oxidizing agent . [ 1 ]
A typical procedure entails dissolving sodium nitrite in cold sulfuric acid: [ 4 ] [ 5 ]
It can also be prepared by the reaction of nitric acid and sulfur dioxide . [ 6 ]
HSO 4 NO is used in organic chemistry to prepare diazonium salts from amines , for example in the Sandmeyer reaction . Related NO-delivery reagents include nitrosonium tetrafluoroborate [NO] + [BF 4 ] − and nitrosyl chloride .
In industry, the nitrosodecarboxylation reaction between nitrosylsulfuric acid and cyclohexanecarboxylic acid is used to generate caprolactam: [ 3 ] This is known as the Snia Viscosa process
Nitrosylsulfuric acid is a hazardous material and precautions are indicated. [ 1 ] | https://en.wikipedia.org/wiki/HNO5S |
In chemistry , amines ( / ə ˈ m iː n , ˈ æ m iː n / , [ 1 ] [ 2 ] UK also / ˈ eɪ m iː n / [ 3 ] ) are compounds and functional groups that contain a basic nitrogen atom with a lone pair . Formally, amines are derivatives of ammonia ( NH 3 in which the bond angle between the nitrogen and hydrogen is 107°), wherein one or more hydrogen atoms have been replaced by a substituent such as an alkyl or aryl group [ 4 ] (these may respectively be called alkylamines and arylamines; amines in which both types of substituent are attached to one nitrogen atom may be called alkylarylamines). Important amines include amino acids , biogenic amines , trimethylamine , and aniline . Inorganic derivatives of ammonia are also called amines, such as monochloramine ( NClH 2 ). [ 5 ]
The substituent −NH 2 is called an amino group. [ 6 ]
The chemical notation for amines contains the letter "R", where "R" is not an element, but an "R-group", which in amines could be a single hydrogen or carbon atom, or could be a hydrocarbon chain.
Compounds with a nitrogen atom attached to a carbonyl group , thus having the structure R−C(=O)−NR′R″ , are called amides and have different chemical properties from amines.
Amines can be classified according to the nature and number of substituents on nitrogen . Aliphatic amines contain only H and alkyl substituents. Aromatic amines have the nitrogen atom connected to an aromatic ring.
Amines, alkyl and aryl alike, are organized into three subcategories (see table) based on the number of carbon atoms adjacent to the nitrogen (how many hydrogen atoms of the ammonia molecule are replaced by hydrocarbon groups): [ 6 ] [ 7 ]
A fourth subcategory is determined by the connectivity of the substituents attached to the nitrogen:
It is also possible to have four organic substituents on the nitrogen. These species are not amines but are quaternary ammonium cations and have a charged nitrogen center. Quaternary ammonium salts exist with many kinds of anions .
Amines are named in several ways. Typically, the compound is given the prefix "amino-" or the suffix "-amine". The prefix " N -" shows substitution on the nitrogen atom. An organic compound with multiple amino groups is called a diamine , triamine , tetraamine and so forth.
Lower amines are named with the suffix -amine .
Higher amines have the prefix amino as a functional group. IUPAC however does not recommend this convention, [ 8 ] but prefers the alkanamine form, e.g. butan-2-amine.
Hydrogen bonding significantly influences the properties of primary and secondary amines. For example, methyl and ethyl amines are gases under standard conditions, whereas the corresponding methyl and ethyl alcohols are liquids. Amines possess a characteristic ammonia smell, liquid amines have a distinctive "fishy" and foul smell.
The nitrogen atom features a lone electron pair that can bind H + to form an ammonium ion R 3 NH + . The lone electron pair is represented in this article by two dots above or next to the N. The water solubility of simple amines is enhanced by hydrogen bonding involving these lone electron pairs. Typically salts of ammonium compounds exhibit the following order of solubility in water: primary ammonium ( RNH + 3 ) > secondary ammonium ( R 2 NH + 2 ) > tertiary ammonium (R 3 NH + ). Small aliphatic amines display significant solubility in many solvents , whereas those with large substituents are lipophilic. Aromatic amines, such as aniline , have their lone pair electrons conjugated into the benzene ring, thus their tendency to engage in hydrogen bonding is diminished. Their boiling points are high and their solubility in water is low.
Typically the presence of an amine functional group is deduced by a combination of techniques, including mass spectrometry as well as NMR and IR spectroscopies. 1 H NMR signals for amines disappear upon treatment of the sample with D 2 O. In their infrared spectrum primary amines exhibit two N-H bands, whereas secondary amines exhibit only one. [ 6 ] In their IR spectra, primary and secondary amines exhibit distinctive N-H stretching bands near 3300 cm −1 . Somewhat less distinctive are the bands appearing below 1600 cm −1 , which are weaker and overlap with C-C and C-H modes. For the case of propyl amine , the H-N-H scissor mode appears near 1600 cm −1 , the C-N stretch near 1000 cm −1 , and the R 2 N-H bend near 810 cm −1 . [ 9 ]
Alkyl amines characteristically feature tetrahedral nitrogen centers. C-N-C and C-N-H angles approach the idealized angle of 109°. C-N distances are slightly shorter than C-C distances. The energy barrier for the nitrogen inversion of the stereocenter is about 7 kcal/mol for a trialkylamine. The interconversion has been compared to the inversion of an open umbrella into a strong wind.
Amines of the type NHRR' and NRR′R″ are chiral : the nitrogen center bears four substituents counting the lone pair. Because of the low barrier to inversion, amines of the type NHRR' cannot be obtained in optical purity. For chiral tertiary amines, NRR′R″ can only be resolved when the R, R', and R″ groups are constrained in cyclic structures such as N -substituted aziridines ( quaternary ammonium salts are resolvable).
In aromatic amines ("anilines"), nitrogen is often nearly planar owing to conjugation of the lone pair with the aryl substituent. The C-N distance is correspondingly shorter. In aniline, the C-N distance is the same as the C-C distances. [ 10 ]
Like ammonia, amines are bases . [ 11 ] Compared to alkali metal hydroxides, amines are weaker.
The basicity of amines depends on:
Owing to inductive effects, the basicity of an amine might be expected to increase with the number of alkyl groups on the amine. Correlations are complicated owing to the effects of solvation which are opposite the trends for inductive effects. Solvation effects also dominate the basicity of aromatic amines (anilines). For anilines, the lone pair of electrons on nitrogen delocalizes into the ring, resulting in decreased basicity. Substituents on the aromatic ring, and their positions relative to the amino group, also affect basicity as seen in the table.
Solvation significantly affects the basicity of amines. N-H groups strongly interact with water, especially in ammonium ions. Consequently, the basicity of ammonia is enhanced by 10 11 by solvation. The intrinsic basicity of amines, i.e. the situation where solvation is unimportant, has been evaluated in the gas phase. In the gas phase, amines exhibit the basicities predicted from the electron-releasing effects of the organic substituents. Thus tertiary amines are more basic than secondary amines, which are more basic than primary amines, and finally ammonia is least basic. The order of pK b 's (basicities in water) does not follow this order. Similarly aniline is more basic than ammonia in the gas phase, but ten thousand times less so in aqueous solution. [ 14 ]
In aprotic polar solvents such as DMSO , DMF , and acetonitrile the energy of solvation is not as high as in protic polar solvents like water and methanol. For this reason, the basicity of amines in these aprotic solvents is almost solely governed by the electronic effects.
Industrially significant alkyl amines are prepared from ammonia by alkylation with alcohols: [ 5 ]
Unlike the reaction of amines with alcohols the reaction of amines and ammonia with alkyl halides is used for synthesis in the laboratory:
In such reactions, which are more useful for alkyl iodides and bromides, the degree of alkylation is difficult to control such that one obtains mixtures of primary, secondary, and tertiary amines, as well as quaternary ammonium salts. [ 5 ]
Selectivity can be improved via the Delépine reaction , although this is rarely employed on an industrial scale. Selectivity is also assured in the Gabriel synthesis , which involves organohalide reacting with potassium phthalimide .
Aryl halides are much less reactive toward amines and for that reason are more controllable. A popular way to prepare aryl amines is the Buchwald-Hartwig reaction .
Disubstituted alkenes react with HCN in the presence of strong acids to give formamides, which can be decarbonylated. This method, the Ritter reaction , is used industrially to produce tertiary amines such as tert -octylamine . [ 5 ]
Hydroamination of alkenes is also widely practiced. The reaction is catalyzed by zeolite-based solid acids . [ 5 ]
Via the process of hydrogenation , unsaturated N-containing functional groups are reduced to amines using hydrogen in the presence of a nickel catalyst. Suitable groups include nitriles , azides , imines including oximes , amides, and nitro . In the case of nitriles, reactions are sensitive to acidic or alkaline conditions, which can cause hydrolysis of the −CN group. LiAlH 4 is more commonly employed for the reduction of these same groups on the laboratory scale.
Many amines are produced from aldehydes and ketones via reductive amination , which can either proceed catalytically or stoichiometrically.
Aniline ( C 6 H 5 NH 2 ) and its derivatives are prepared by reduction of the nitroaromatics. In industry, hydrogen is the preferred reductant, whereas, in the laboratory, tin and iron are often employed.
Many methods exist for the preparation of amines, many of these methods being rather specialized.
Aside from their basicity, the dominant reactivity of amines is their nucleophilicity . [ 16 ] Most primary amines are good ligands for metal ions to give coordination complexes . Amines are alkylated by alkyl halides. Acyl chlorides and acid anhydrides react with primary and secondary amines to form amides (the " Schotten–Baumann reaction ").
Similarly, with sulfonyl chlorides, one obtains sulfonamides . This transformation, known as the Hinsberg reaction , is a chemical test for the presence of amines.
Because amines are basic, they neutralize acids to form the corresponding ammonium salts R 3 NH + . When formed from carboxylic acids and primary and secondary amines, these salts thermally dehydrate to form the corresponding amides .
Amines undergo sulfamation upon treatment with sulfur trioxide or sources thereof:
Amines reacts with nitrous acid to give diazonium salts. The alkyl diazonium salts are of little importance because they are too unstable. The most important members are derivatives of aromatic amines such as aniline ("phenylamine") (A = aryl or naphthyl):
Anilines and naphthylamines form more stable diazonium salts, which can be isolated in the crystalline form. [ 17 ] Diazonium salts undergo a variety of useful transformations involving replacement of the N 2 group with anions. For example, cuprous cyanide gives the corresponding nitriles:
Aryldiazoniums couple with electron-rich aromatic compounds such as a phenol to form azo compounds . Such reactions are widely applied to the production of dyes. [ 18 ]
Imine formation is an important reaction. Primary amines react with ketones and aldehydes to form imines . In the case of formaldehyde (R' = H), these products typically exist as cyclic trimers : RNH 2 + R 2 ′ C = O ⟶ R 2 ′ C = NR + H 2 O {\displaystyle {\ce {RNH2 + R'_2C=O -> R'_2C=NR + H2O}}} Reduction of these imines gives secondary amines: R 2 ′ C = NR + H 2 ⟶ R 2 ′ CH − NHR {\displaystyle {\ce {R'_2C=NR + H2 -> R'_2CH-NHR}}}
Similarly, secondary amines react with ketones and aldehydes to form enamines : R 2 NH + R ′ ( R ″ CH 2 ) C = O ⟶ R ″ CH = C ( NR 2 ) R ′ + H 2 O {\displaystyle {\ce {R2NH + R'(R''CH2)C=O -> R''CH=C(NR2)R' + H2O}}}
Mercuric ions reversibly oxidize tertiary amines with an α hydrogen to iminium ions: [ 19 ] Hg 2 + + R 2 NCH 2 R ′ ↽ − − ⇀ Hg + [ R 2 N = CHR ′ ] + + H + {\displaystyle {\ce {Hg^2+ + R2NCH2R' <=> Hg + [R2N=CHR']+ + H+}}}
An overview of the reactions of amines is given below:
Amines are ubiquitous in biology. The breakdown of amino acids releases amines, famously in the case of decaying fish which smell of trimethylamine . Many neurotransmitters are amines, including epinephrine , norepinephrine , dopamine , serotonin , and histamine . Protonated amino groups ( –NH + 3 ) are the most common positively charged moieties in proteins , specifically in the amino acid lysine . [ 20 ] The anionic polymer DNA is typically bound to various amine-rich proteins. [ 21 ] Additionally, the terminal charged primary ammonium on lysine forms salt bridges with carboxylate groups of other amino acids in polypeptides , which is one of the primary influences on the three-dimensional structures of proteins. [ 22 ]
Hormones derived from the modification of amino acids are referred to as amine hormones. Typically, the original structure of the amino acid is modified such that a –COOH, or carboxyl, group is removed, whereas the –NH + 3 , or amine, group remains. Amine hormones are synthesized from the amino acids tryptophan or tyrosine . [ 23 ]
Primary aromatic amines are used as a starting material for the manufacture of azo dyes . It reacts with nitrous acid to form diazonium salt, which can undergo coupling reaction to form an azo compound. As azo-compounds are highly coloured, they are widely used in dyeing industries, such as:
Most drugs and drug candidates contain amine functional groups: [ 24 ]
Aqueous monoethanolamine (MEA), diglycolamine (DGA), diethanolamine (DEA), diisopropanolamine (DIPA) and methyldiethanolamine (MDEA) are widely used industrially for removing carbon dioxide (CO 2 ) and hydrogen sulfide (H 2 S) from natural gas and refinery process streams. They may also be used to remove CO 2 from combustion gases and flue gases and may have potential for abatement of greenhouse gases . Related processes are known as sweetening . [ 26 ]
Amines are often used as epoxy resin curing agents. [ 27 ] [ 28 ] These include dimethylethylamine , cyclohexylamine , and a variety of diamines such as 4,4-diaminodicyclohexylmethane. [ 5 ] Multifunctional amines such as tetraethylenepentamine and triethylenetetramine are also widely used in this capacity. [ 29 ] The reaction proceeds by the lone pair of electrons on the amine nitrogen attacking the outermost carbon on the oxirane ring of the epoxy resin. This relieves ring strain on the epoxide and is the driving force of the reaction. [ 30 ] Molecules with tertiary amine functionality are often used to accelerate the epoxy-amine curing reaction and include substances such as 2,4,6-Tris(dimethylaminomethyl)phenol . It has been stated that this is the most widely used room temperature accelerator for two-component epoxy resin systems. [ 31 ] [ 32 ]
Low molecular weight simple amines, such as ethylamine , are toxic with LD 50 between 100 and 1000 mg/kg. They are skin irritants, especially as some are easily absorbed through the skin. [ 5 ] Amines are a broad class of compounds, and more complex members of the class can be extremely bioactive, for example strychnine . | https://en.wikipedia.org/wiki/HNR2 |
Disodium hydrogen arsenate is the inorganic compound with the formula Na 2 HAsO 4 . 7H 2 O. The compound consists of a salt and seven molecules of water of crystallization although for simplicity the formula usually omits the water component. The other sodium arsenates are NaH 2 AsO 4 and Na 3 AsO 4 , the latter being called sodium arsenate . Disodium hydrogen arsenate is highly toxic. The salt is the conjugate base of arsenic acid . It is a white, water-soluble solid. [ 1 ]
Being a diprotic acid, its acid-base properties is described by two equilibria:
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HNa2AsO4 |
Sodium metatungstate is the inorganic compound with the formula Na 6 [H 2 W 12 O 40 ], sometimes written 3Na 2 WO 4 ·9WO 3 ·H 2 O. It is also referred to as sodium polytungstate (SPT). This salt has been used in the manufacture of dense aqueous solutions . Sodium metatungstate exists as white solid. The anion is the polyoxotungstate [H 2 W 12 O 40 ] 6- , which features six-coordinated tungsten(VI) centers interconnected with doubly- and triply bridging oxo ligands.
Due to its very high solubility in water (max. density 3.1 g/cm 3 ), SPT is widely used as to produce "heavy liquid" for gravity separation (sink /float analysis) and density gradient centrifugation . It has significant advantages when compared to zinc chloride solution or the toxic halogenated carbons for sink-swim analysis. Aqueous SPT is non-toxic (unlike the denser Clerici solution ), non-flammable, odorless, reusable and additionally it has a low viscosity. [ 2 ] | https://en.wikipedia.org/wiki/HNa6O40W12 |
Formic acid (from Latin formica ' ant ' ), systematically named methanoic acid , is the simplest carboxylic acid . It has the chemical formula HCOOH and structure H−C(=O)−O−H . This acid is an important intermediate in chemical synthesis and occurs naturally, most notably in some ants. Esters , salts , and the anion derived from formic acid are called formates . Industrially, formic acid is produced from methanol . [ 5 ]
Formic acid, which has a pungent, penetrating odor, is found naturally in insects, weeds, fruits and vegetables, and forest emissions. It appears in most ants and in stingless bees of the genus Oxytrigona . [ 6 ] [ 7 ] Wood ants from the genus Formica can spray formic acid on their prey or to defend the nest. The puss moth caterpillar ( Cerura vinula ) will spray it as well when threatened by predators. It is also found in the trichomes of stinging nettle ( Urtica dioica ). Apart from that, this acid is incorporated in many fruits such as pineapple (0.21 mg per 100 g), apple (2 mg per 100 g) and kiwi (1 mg per 100 g), as well as in many vegetables, namely onion (45 mg per 100 g), eggplant (1.34 mg per 100 g) and, in extremely low concentrations, cucumber (0.11 mg per 100 g). [ 8 ] Formic acid is a naturally occurring component of the atmosphere primarily due to forest emissions. [ 9 ]
As early as the 15th century, some alchemists and naturalists were aware that ant hills give off an acidic vapor. The first person to describe the isolation of this substance (by the distillation of large numbers of ants) was the English naturalist John Ray , in 1671. [ 10 ] [ 11 ] Ants secrete the formic acid for attack and defense purposes. Formic acid was first synthesized from hydrocyanic acid by the French chemist Joseph Gay-Lussac . In 1855, another French chemist, Marcellin Berthelot , developed a synthesis from carbon monoxide similar to the process used today. [ 12 ]
Formic acid was long considered a chemical compound of only minor interest in the chemical industry. In the late 1960s, significant quantities became available as a byproduct of acetic acid production. It now finds increasing use as a preservative and antibacterial in livestock feed. [ 12 ]
Formic acid is a colorless liquid having a pungent, penetrating odor [ 13 ] at room temperature, comparable to the related acetic acid . Formic acid is about ten times stronger than acetic acid having a (logarithmic) dissociation constant of 3.745 compared to 4.756 for acetic acid. [ 3 ]
It is miscible with water and most polar organic solvents , and is somewhat soluble in hydrocarbons . In hydrocarbons and in the vapor phase, it consists of hydrogen-bonded dimers rather than individual molecules. [ 14 ] [ 15 ] Owing to its tendency to hydrogen-bond, gaseous formic acid does not obey the ideal gas law . [ 15 ] Solid formic acid, which can exist in either of two polymorphs , consists of an effectively endless network of hydrogen-bonded formic acid molecules. Formic acid forms a high-boiling azeotrope with water (107.3 °C; 77.5% formic acid). Liquid formic acid tends to supercool .
Formic acid readily decomposes by dehydration in the presence of concentrated sulfuric acid to form carbon monoxide and water:
Treatment of formic acid with sulfuric acid is a convenient laboratory source of CO. [ 16 ] [ 17 ]
In the presence of platinum , it decomposes with a release of hydrogen and carbon dioxide .
Soluble ruthenium catalysts are also effective for producing carbon monoxide-free hydrogen. [ 18 ]
Formic acid shares most of the chemical properties of other carboxylic acids . Because of its high acidity, solutions in alcohols form esters spontaneously; in Fischer esterifications of formic acid, it self-catalyzes the reaction and no additional acid catalyst is needed. [ 19 ] Formic acid shares some of the reducing properties of aldehydes , reducing solutions of metal oxides to their respective metal. [ 20 ]
Formic acid is a source for a formyl group for example in the formylation of N -methylaniline to N -methylformanilide in toluene . [ 21 ]
In synthetic organic chemistry , formic acid is often used as a source of hydride ion, as in the Eschweiler–Clarke reaction :
It is used as a source of hydrogen in transfer hydrogenation , as in the Leuckart reaction to make amines , and (in aqueous solution or in its azeotrope with triethylamine ) for hydrogenation of ketones . [ 22 ]
Formic acid is unique among the carboxylic acids in its ability to participate in addition reactions with alkenes . Formic acids and alkenes readily react to form formate esters . In the presence of certain acids, including sulfuric and hydrofluoric acids , however, a variant of the Koch reaction occurs instead, and formic acid adds to the alkene to produce a larger carboxylic acid. [ 23 ]
An unstable formic anhydride , H(C=O)−O−(C=O)H, can be obtained by dehydration of formic acid with N , N ′ -dicyclohexylcarbodiimide in ether at low temperature. [ 24 ]
In 2009, the worldwide capacity for producing formic acid was 720 thousand tonnes (1.6 billion pounds) per year, roughly equally divided between Europe (350 thousand tonnes or 770 million pounds, mainly in Germany) and Asia (370 thousand tonnes or 820 million pounds, mainly in China) while production was below 1 thousand tonnes or 2.2 million pounds per year in all other continents. [ 25 ] It is commercially available in solutions of various concentrations between 85 and 99 w/w %. [ 14 ] As of 2009 [update] , the largest producers are BASF , Eastman Chemical Company , LC Industrial , and Feicheng Acid Chemicals , with the largest production facilities in Ludwigshafen (200 thousand tonnes or 440 million pounds per year, BASF, Germany), Oulu (105 thousand tonnes or 230 million pounds, Eastman, Finland), Nakhon Pathom (n/a, LC Industrial), and Feicheng (100 thousand tonnes or 220 million pounds, Feicheng, China). 2010 prices ranged from around €650/tonne (equivalent to around $800/tonne) in Western Europe to $1250/tonne in the United States. [ 25 ]
Regenerating CO 2 to make useful products, that displace incumbent fossil fuel based pathways is a more impactful process than CO 2 sequestration.
Both formic acid and CO (carbon monoxide) are C1 (one carbon molecules). Formic is a hydrogen-rich liquid which can be transported and easily donates its hydrogen to enable a variety of condensation and esterification reactions to make a wide variety of derivative molecules. CO, while more difficult to transport as a gas, is also one of the primary constituents of syngas useful in synthesizing a wide variety of molecules.
CO 2 electrolysis is distinct from photosynthesis and offers a promising alternative to accelerate decarbonization. By converting CO 2 into products using clean electricity, we reduce CO 2 emissions in two ways: first and most simply by the amount of CO 2 that is regenerated, but the second way is less obvious but even more consequential by avoiding the CO 2 emissions otherwise generated by making these same products from fossil fuels. This is known as carbon displacement or abatement.
CO 2 electrolysis holds promise for reducing atmospheric CO 2 levels and providing a sustainable method for producing chemicals, materials, and fuels. Its efficiency and scalability are active areas of research, but now also commercialization, aiming to make it a viable commercial technology for both carbon management and molecule production. [ 26 ]
When methanol and carbon monoxide are combined in the presence of a strong base , the result is methyl formate , according to the chemical equation : [ 14 ]
In industry, this reaction is performed in the liquid phase at elevated pressure. Typical reaction conditions are 80 °C and 40 atm. The most widely used base is sodium methoxide . Hydrolysis of the methyl formate produces formic acid:
Efficient hydrolysis of methyl formate requires a large excess of water. Some routes proceed indirectly by first treating the methyl formate with ammonia to give formamide , which is then hydrolyzed with sulfuric acid :
A disadvantage of this approach is the need to dispose of the ammonium sulfate byproduct. This problem has led some manufacturers to develop energy-efficient methods of separating formic acid from the excess water used in direct hydrolysis. In one of these processes, used by BASF , the formic acid is removed from the water by liquid-liquid extraction with an organic base. [ citation needed ]
A significant amount of formic acid is produced as a byproduct in the manufacture of other chemicals. At one time, acetic acid was produced on a large scale by oxidation of alkanes , by a process that cogenerates significant formic acid. [ 14 ] This oxidative route to acetic acid has declined in importance so that the aforementioned dedicated routes to formic acid have become more important. [ citation needed ]
The catalytic hydrogenation of CO 2 to formic acid has long been studied. This reaction can be conducted homogeneously. [ 27 ] [ 28 ] [ 29 ]
Formic acid can also be obtained by aqueous catalytic partial oxidation of wet biomass by the OxFA process . [ 30 ] [ 31 ] A Keggin-type polyoxometalate (H 5 PV 2 Mo 10 O 40 ) is used as the homogeneous catalyst to convert sugars, wood, waste paper, or cyanobacteria to formic acid and CO 2 as the sole byproduct. Yields of up to 53% formic acid can be achieved. [ citation needed ]
In the laboratory, formic acid can be obtained by heating oxalic acid in glycerol followed by steam distillation. [ 32 ] Glycerol acts as a catalyst, as the reaction proceeds through a glyceryl oxalate intermediate. If the reaction mixture is heated to higher temperatures, allyl alcohol results. The net reaction is thus:
Another illustrative method involves the reaction between lead formate and hydrogen sulfide , driven by the formation of lead sulfide . [ 33 ]
Formate is formed by the electrochemical reduction of CO 2 (in the form of bicarbonate ) at a lead cathode at pH 8.6: [ 34 ]
or
If the feed is CO 2 and oxygen is evolved at the anode, the total reaction is:
Formic acid is named after ants which have high concentrations of the compound in their venom, derived from serine through a 5,10-methenyltetrahydrofolate intermediate. [ 35 ] The conjugate base of formic acid, formate, also occurs widely in nature. An assay for formic acid in body fluids, designed for determination of formate after methanol poisoning, is based on the reaction of formate with bacterial formate dehydrogenase . [ 36 ]
A major use of formic acid is as a preservative and antibacterial agent in livestock feed. It arrests certain decay processes and causes the feed to retain its nutritive value longer,
In Europe, it is applied on silage , including fresh hay, to promote the fermentation of lactic acid and to suppress the formation of butyric acid ; it also allows fermentation to occur quickly, and at a lower temperature, reducing the loss of nutritional value. [ 14 ] It is widely used to preserve winter feed for cattle , [ 37 ] and is sometimes added to poultry feed to kill E. coli bacteria. [ 38 ] [ 39 ] Use as a preservative for silage and other animal feed constituted 30% of the global consumption in 2009. [ 25 ]
Beekeepers use formic acid as a miticide against the tracheal mite ( Acarapis woodi ) and the Varroa destructor mite and Varroa jacobsoni mite . [ 40 ]
Formic acid can be used directly in formic acid fuel cells or indirectly in hydrogen fuel cells . [ 41 ] [ 42 ]
Electrolytic conversion of electrical energy to chemical fuel has been proposed as a large-scale source of formate by various groups. [ 43 ] The formate could be used as feed to modified E. coli bacteria for producing biomass . [ 44 ] [ 45 ] Natural methylotroph microbes can feed on formic acid or formate.
Formic acid has been considered as a means of hydrogen storage . [ 46 ] The co-product of this decomposition, carbon dioxide, can be rehydrogenated back to formic acid in a second step. Formic acid contains 53 g/L hydrogen at room temperature and atmospheric pressure, which is three and a half times as much as compressed hydrogen gas can attain at 350 bar pressure (14.7 g/L). Pure formic acid is a liquid with a flash point of 69 °C, much higher than that of gasoline (−40 °C) or ethanol (13 °C). [ citation needed ]
It is possible to use formic acid as an intermediary to produce isobutanol from CO 2 using microbes. [ 47 ] [ 48 ]
Formic acid has a potential application in soldering . Due to its capacity to reduce oxide layers, formic acid gas can be blasted at an oxide surface to increase solder wettability . [ citation needed ]
Formic acid is used as a volatile pH modifier in HPLC and capillary electrophoresis . Formic acid is often used as a component of mobile phase in reversed-phase high-performance liquid chromatography (RP-HPLC) analysis and separation techniques for the separation of hydrophobic macromolecules, such as peptides, proteins and more complex structures including intact viruses. Especially when paired with mass spectrometry detection, formic acid offers several advantages over the more traditionally used phosphoric acid . [ 49 ] [ 50 ]
Formic acid is also significantly used in the production of leather, including tanning (23% of the global consumption in 2009 [ 25 ] ), and in dyeing and finishing textiles (9% of the global consumption in 2009 [ 25 ] ) because of its acidic nature. Use as a coagulant in the production of rubber [ 14 ] consumed 6% of the global production in 2009. [ 25 ]
Formic acid is also used in place of mineral acids for various cleaning products, [ 14 ] such as limescale remover and toilet bowl cleaner . Some formate esters are artificial flavorings and perfumes.
Formic acid application has been reported to be an effective treatment for warts . [ 51 ]
Formic acid has low toxicity (hence its use as a food additive), with an LD 50 of 1.8 g/kg (tested orally on mice). The concentrated acid is corrosive to the skin. [ 14 ]
Formic acid is readily metabolized and eliminated by the body. Nonetheless, it has specific toxic effects; the formic acid and formaldehyde produced as metabolites of methanol are responsible for the optic nerve damage, causing blindness, seen in methanol poisoning . [ 52 ] Some chronic effects of formic acid exposure have been documented. Some experiments on bacterial species have demonstrated it to be a mutagen . [ 53 ] Chronic exposure in humans may cause kidney damage. [ 53 ] Another possible effect of chronic exposure is development of a skin allergy that manifests upon re-exposure to the chemical.
Concentrated formic acid slowly decomposes to carbon monoxide and water, leading to pressure buildup in the containing vessel. For this reason, 98% formic acid is shipped in plastic bottles with self-venting caps. [ citation needed ]
The hazards of solutions of formic acid depend on the concentration. The following table lists the Globally Harmonized System of Classification and Labelling of Chemicals for formic acid solutions: [ citation needed ]
Formic acid in 85% concentration is flammable, and diluted formic acid is on the U.S. Food and Drug Administration list of food additives. [ 54 ] The principal danger from formic acid is from skin or eye contact with the concentrated liquid or vapors. The U.S. OSHA Permissible Exposure Level ( PEL ) of formic acid vapor in the work environment is 5 parts per million (ppm) of air. [ 55 ] | https://en.wikipedia.org/wiki/HO-CHO |
Carbonic acid is a chemical compound with the chemical formula H 2 C O 3 . The molecule rapidly converts to water and carbon dioxide in the presence of water. However, in the absence of water, it is quite stable at room temperature . [ 5 ] [ 6 ] The interconversion of carbon dioxide and carbonic acid is related to the breathing cycle of animals and the acidification of natural waters . [ 4 ]
In biochemistry and physiology, the name "carbonic acid" is sometimes applied to aqueous solutions of carbon dioxide . These chemical species play an important role in the bicarbonate buffer system , used to maintain acid–base homeostasis . [ 7 ]
In chemistry , the term "carbonic acid" strictly refers to the chemical compound with the formula H 2 CO 3 . Some biochemistry literature effaces the distinction between carbonic acid and carbon dioxide dissolved in extracellular fluid.
In physiology , carbon dioxide excreted by the lungs may be called volatile acid or respiratory acid .
At ambient temperatures, pure carbonic acid is a stable gas. [ 6 ] There are two main methods to produce anhydrous carbonic acid: reaction of hydrogen chloride and potassium bicarbonate at 100 K in methanol and proton irradiation of pure solid carbon dioxide . [ 3 ] Chemically, it behaves as a diprotic Brønsted acid . [ 8 ] [ 9 ]
Carbonic acid monomers exhibit three conformational isomers : cis–cis, cis–trans, and trans–trans. [ 10 ]
At low temperatures and atmospheric pressure , solid carbonic acid is amorphous and lacks Bragg peaks in X-ray diffraction . [ 11 ] But at high pressure, carbonic acid crystallizes, and modern analytical spectroscopy can measure its geometry.
According to neutron diffraction of dideuterated carbonic acid ( D 2 CO 3 ) in a hybrid clamped cell ( Russian alloy / copper-beryllium ) at 1.85 GPa, the molecules are planar and form dimers joined by pairs of hydrogen bonds . All three C-O bonds are nearly equidistant at 1.34 Å , intermediate between typical C-O and C=O distances (respectively 1.43 and 1.23 Å). The unusual C-O bond lengths are attributed to delocalized π bonding in the molecule's center and extraordinarily strong hydrogen bonds. The same effects also induce a very short O—O separation (2.13 Å), through the 136° O-H-O angle imposed by the doubly hydrogen-bonded 8-membered rings. [ 4 ] Longer O—O distances are observed in strong intramolecular hydrogen bonds, e.g. in oxalic acid , where the distances exceed 2.4 Å. [ 11 ]
In even a slight presence of water, carbonic acid dehydrates to carbon dioxide and water , which then catalyzes further decomposition. [ 6 ] For this reason, carbon dioxide can be considered the carbonic acid anhydride .
The hydration equilibrium constant at 25 °C is [ H 2 CO 3 ]/[CO 2 ] ≈ 1.7×10 −3 in pure water [ 12 ] and ≈ 1.2×10 −3 in seawater . [ 13 ] Hence the majority of carbon dioxide at geophysical or biological air-water interfaces does not convert to carbonic acid, remaining dissolved CO 2 gas. However, the uncatalyzed equilibrium is reached quite slowly: the rate constants are 0.039 s −1 for hydration and 23 s −1 for dehydration.
In the presence of the enzyme carbonic anhydrase , equilibrium is instead reached rapidly, and the following reaction takes precedence: [ 14 ] HCO 3 − + H + ↽ − − ⇀ CO 2 + H 2 O {\displaystyle {\ce {HCO3^- {+}H^+ <=> CO2 {+}H2O}}}
When the created carbon dioxide exceeds its solubility, gas evolves and a third equilibrium CO 2 ( soln ) ↽ − − ⇀ CO 2 ( g ) {\displaystyle {\ce {CO_2 (soln) <=> CO_2 (g)}}} must also be taken into consideration. The equilibrium constant for this reaction is defined by Henry's law .
The two reactions can be combined for the equilibrium in solution: HCO 3 − + H + ↽ − − ⇀ CO 2 ( soln ) + H 2 O K 3 = [ H + ] [ HCO 3 − ] [ CO 2 ( soln ) ] {\displaystyle {\begin{aligned}{\ce {HCO3^{-}{}+ H+{}<=> CO2(soln){}+ H2O}}&&K_{3}={\frac {[{\ce {H+}}][{\ce {HCO3^-}}]}{[{\ce {CO2(soln)}}]}}\end{aligned}}} When Henry's law is used to calculate the denominator care is needed with regard to units since Henry's law constant can be commonly expressed with 8 different dimensionalities. [ 15 ]
In wastewater treatment and agriculture irrigation, carbonic acid is used to acidify the water similar to sulfuric acid and sulfurous acid produced by sulfur burners. [ 16 ]
In the beverage industry , sparkling or "fizzy water" is usually referred to as carbonated water . It is made by dissolving carbon dioxide under a small positive pressure in water. Many soft drinks treated the same way effervesce .
Significant amounts of molecular H 2 CO 3 exist in aqueous solutions subjected to pressures of multiple gigapascals (tens of thousands of atmospheres) in planetary interiors. [ 17 ] [ 18 ] Pressures of 0.6–1.6 GPa at 100 K , and 0.75–1.75 GPa at 300 K are attained in the cores of large icy satellites such as Ganymede , Callisto , and Titan , where water and carbon dioxide are present. Pure carbonic acid, being denser, is expected to have sunk under the ice layers and separate them from the rocky cores of these moons. [ 19 ]
Carbonic acid is the formal Brønsted–Lowry conjugate acid of the bicarbonate anion, stable in alkaline solution . The protonation constants have been measured to great precision, but depend on overall ionic strength I . The two equilibria most easily measured are as follows: CO 3 2 − + H + ↽ − − ⇀ HCO 3 − β 1 = [ HCO 3 − ] [ H + ] [ CO 3 2 − ] CO 3 2 − + 2 H + ↽ − − ⇀ H 2 CO 3 β 2 = [ H 2 CO 3 ] [ H + ] 2 [ CO 3 2 − ] {\displaystyle {\begin{aligned}{\ce {CO3^{2-}{}+ H+{}<=> HCO3^-}}&&\beta _{1}={\frac {[{\ce {HCO3^-}}]}{[{\ce {H+}}][{\ce {CO3^{2-}}}]}}\\{\ce {CO3^{2-}{}+ 2H+{}<=> H2CO3}}&&\beta _{2}={\frac {[{\ce {H2CO3}}]}{[{\ce {H+}}]^{2}[{\ce {CO3^{2-}}}]}}\end{aligned}}} where brackets indicate the concentration of species . At 25 °C, these equilibria empirically satisfy [ 20 ] log ( β 1 ) = 0 .54 I 2 − 0 .96 I + 9 .93 log ( β 2 ) = − 2 .5 I 2 − 0 .043 I + 16 .07 {\displaystyle {\begin{alignedat}{6}\log(\beta _{1})=&&0&.54&I^{2}-0&.96&I+&&9&.93\\\log(\beta _{2})=&&-2&.5&I^{2}-0&.043&I+&&16&.07\end{alignedat}}} log( β 1 ) decreases with increasing I , as does log( β 2 ) . In a solution absent other ions (e.g. I = 0 ), these curves imply the following stepwise dissociation constants : p K 1 = log ( β 2 ) − log ( β 1 ) = 6.77 p K 2 = log ( β 1 ) = 9.93 {\displaystyle {\begin{alignedat}{3}p{\text{K}}_{1}&=\log(\beta _{2})-\log(\beta _{1})&=6.77\\p{\text{K}}_{2}&=\log(\beta _{1})&=9.93\end{alignedat}}} Direct values for these constants in the literature include p K 1 = 6.35 and p K 2 - p K 1 = 3.49 . [ 21 ]
To interpret these numbers, note that two chemical species in an acid equilibrium are equiconcentrated when p K = p H . In particular, the extracellular fluid ( cytosol ) in biological systems exhibits p H ≈ 7.2 , so that carbonic acid will be almost 50%-dissociated at equilibrium.
The Bjerrum plot shows typical equilibrium concentrations, in solution, in seawater , of carbon dioxide and the various species derived from it, as a function of pH . [ 8 ] [ 9 ] As human industrialization has increased the proportion of carbon dioxide in Earth's atmosphere , the proportion of carbon dioxide dissolved in sea- and freshwater as carbonic acid is also expected to increase. This rise in dissolved acid is also expected to acidify those waters, generating a decrease in pH. [ 22 ] [ 23 ] It has been estimated that the increase in dissolved carbon dioxide has already caused the ocean's average surface pH to decrease by about 0.1 from pre-industrial levels. | https://en.wikipedia.org/wiki/HO-COOH |
Dioxidanylium, which is protonated molecular oxygen, or just protonated oxygen, is an ion with formula HO + 2 .
It is formed when hydrogen containing substances combust , and exists in the ionosphere , and in plasmas that contain oxygen and hydrogen . [ 2 ] Oxidation by O 2 in superacids could be by way of the production of protonated molecular oxygen.
It is the conjugate acid of dioxygen . The proton affinity of dioxygen (O 2 ) is 4.4 eV. [ 3 ]
Protonated molecular oxygen is of interest in trying to detect dioxygen in space. Because Earth's atmosphere is full of O 2 , its spectrum from a space object is impossible to observe from the ground. However HO + 2 should be much more detectable. [ 4 ]
Reaction of dioxygenyl O + 2 with hydrogen: [ 5 ]
The reaction of the trihydrogen cation with dioxygen is approximately thermoneutral: [ 3 ]
When atomic hydrogen, created in an electric discharge is rapidly cooled with oxygen and condensed in solid neon, several reactive ions and molecules are produced. These include HO 2 ( hydroperoxyl ), HOHOH − , H 2 O(HO), HOHO − as well as HO + 2 . [ 6 ] This reaction also forms hydrogen peroxide (H 2 O 2 ) and hydrogen tetroxide (H 2 O 4 ). [ 7 ]
In the infrared spectrum HO + 2 the v 1 band due to vibrating O–H has a band head at 3016.73 cm −1 . [ 8 ]
A helium complex (He–O 2 H + ) also is known. [ 8 ]
HO + 2 appears to react rapidly with hydrogen: [ 9 ]
HO + 2 also reacts with dinitrogen and water: [ 9 ]
The protonated molecular oxygen dimer HO + 4 has a lower energy than that of protonated molecular oxygen. [ 3 ] | https://en.wikipedia.org/wiki/HO2+ |
Aspartic acid (symbol Asp or D ; [ 4 ] the ionic form is known as aspartate ), is an α- amino acid that is used in the biosynthesis of proteins. [ 5 ] The L -isomer of aspartic acid is one of the 22 proteinogenic amino acids , i.e., the building blocks of proteins . D -aspartic acid is one of two D -amino acids commonly found in mammals. [ 6 ] [ 7 ] Apart from a few rare exceptions, D -aspartic acid is not used for protein synthesis but is incorporated into some peptides and plays a role as a neurotransmitter / neuromodulator . [ 6 ]
Like all other amino acids, aspartic acid contains an amino group and a carboxylic acid. Its α-amino group is in the protonated –NH + 3 form under physiological conditions, while its α-carboxylic acid group is deprotonated −COO − under physiological conditions. Aspartic acid has an acidic side chain (CH 2 COOH) which reacts with other amino acids, enzymes and proteins in the body. [ 5 ] Under physiological conditions (pH 7.4) in proteins the side chain usually occurs as the negatively charged aspartate form, −COO − . [ 5 ] It is a non- essential amino acid in humans, meaning the body can synthesize it as needed. It is encoded by the codons GAU and GAC.
In proteins aspartate sidechains are often hydrogen bonded to form asx turns or asx motifs , which frequently occur at the N-termini of alpha helices .
Aspartic acid, like glutamic acid , is classified as an acidic amino acid, with a pK a of 3.9; however, in a peptide this is highly dependent on the local environment, and could be as high as 14.
The one-letter code D for aspartate was assigned arbitrarily, [ 8 ] with the proposed mnemonic aspar D ic acid. [ 9 ]
Aspartic acid was first discovered in 1827 by Auguste-Arthur Plisson and Étienne-Ossian Henry [ 10 ] [ 11 ] by hydrolysis of asparagine , which had been isolated from asparagus juice in 1806. [ 12 ] Their original method used lead hydroxide , but various other acids or bases are now more commonly used instead. [ citation needed ]
There are two forms or enantiomers of aspartic acid. The name "aspartic acid" can refer to either enantiomer or a mixture of two. [ 13 ] Of these two forms, only one, " L -aspartic acid", is directly incorporated into proteins. The biological roles of its counterpart, " D -aspartic acid" are more limited. Where enzymatic synthesis will produce one or the other, most chemical syntheses will produce both forms, " DL -aspartic acid", known as a racemic mixture . [ citation needed ]
In the human body, aspartate is most frequently synthesized through the transamination of oxaloacetate . The biosynthesis of aspartate is facilitated by an aminotransferase enzyme: the transfer of an amine group from another molecule such as alanine or glutamine yields aspartate and an alpha-keto acid. [ 5 ]
Industrially, aspartate is produced by amination of fumarate catalyzed by L- aspartate ammonia-lyase . [ 14 ]
Racemic aspartic acid can be synthesized from diethyl sodium phthalimidomalonate,
(C 6 H 4 (CO) 2 NC(CO 2 Et) 2 ). [ 15 ]
In plants and microorganisms , aspartate is the precursor to several amino acids, including four that are essential for humans: methionine , threonine , isoleucine , and lysine . The conversion of aspartate to these other amino acids begins with reduction of aspartate to its "semialdehyde", O 2 CCH(NH 2 )CH 2 CHO. [ 16 ] Asparagine is derived from aspartate via transamidation:
(where G C(O)NH 2 and G C(O)OH are glutamine and glutamic acid , respectively)
Aspartate has many other biochemical roles. It is a metabolite in the urea cycle [ 17 ] and participates in gluconeogenesis . It carries reducing equivalents in the malate-aspartate shuttle , which utilizes the ready interconversion of aspartate and oxaloacetate , which is the oxidized (dehydrogenated) derivative of malic acid . Aspartate donates one nitrogen atom in the biosynthesis of inosine , the precursor to the purine bases. In addition, aspartic acid acts as a hydrogen acceptor in a chain of ATP synthase. Dietary L-aspartic acid has been shown to act as an inhibitor of Beta-glucuronidase , which serves to regulate enterohepatic circulation of bilirubin and bile acids. [ 18 ]
Click on genes, proteins and metabolites below to link to respective articles. [ § 1 ]
Aspartate (the conjugate base of aspartic acid) stimulates NMDA receptors , though not as strongly as the amino acid neurotransmitter L-glutamate does. [ 19 ] Aspartate is the "A" in NMDA (N-methyl-D- aspartate receptor).
In 2014, the global market for aspartic acid was 39.3 thousand short tons (35.7 thousand tonnes ) [ 20 ] or about $117 million annually. [ 21 ] The three largest market segments include the U.S., Western Europe, and China. Current applications include biodegradable polymers ( polyaspartic acid ), low calorie sweeteners ( aspartame ), scale and corrosion inhibitors, and resins. [ citation needed ]
One area of aspartic acid market growth is biodegradable superabsorbent polymers (SAP), and hydrogels. [ 22 ] Around 75% of superabsorbent polymers are used in disposable diapers and an additional 20% is used for adult incontinence and feminine hygiene products. Polyaspartic acid , the polymerization product of aspartic acid, is a biodegradable substitute to polyacrylate . [ 22 ] [ 23 ] [ 24 ]
In addition to SAP, aspartic acid has applications in the fertilizer industry , where polyaspartate improves water retention and nitrogen uptake. [ 25 ]
Aspartic acid is not an essential amino acid , which means that it can be synthesized from central metabolic pathway intermediates in humans, and does not need to be present in the diet. In eukaryotic cells, roughly 1 in 20 amino acids incorporated into a protein is an aspartic acid, [ 26 ] and accordingly almost any source of dietary protein will include aspartic acid. Additionally, aspartic acid is found in: | https://en.wikipedia.org/wiki/HO2CCH(NH2)CH2CO2H |
Malic acid is an organic compound with the molecular formula HO 2 CCH(OH)CH 2 CO 2 H . It is a dicarboxylic acid that is made by all living organisms, contributes to the sour taste of fruits, and is used as a food additive . Malic acid has two stereoisomeric forms ( L - and D -enantiomers), though only the L -isomer exists naturally. The salts and esters of malic acid are known as malates . The malate anion is a metabolic intermediate in the citric acid cycle .
The word 'malic' is derived from Latin mālum , meaning 'apple'. The related Latin word mālus , meaning 'apple tree', is used as the name of the genus Malus , which includes all apples and crabapples; [ 5 ] and is the origin of other taxonomic classifications such as Maloideae , Malinae , and Maleae .
L -Malic acid is the naturally occurring form, whereas a mixture of L - and D -malic acid is produced synthetically.
Malate plays an important role in biochemistry . In the C4 carbon fixation process, malate is a source of CO 2 in the Calvin cycle . In the citric acid cycle , ( S )-malate is an intermediate, formed by the addition of an -OH group on the si face of fumarate. It can also be formed from pyruvate via anaplerotic reactions .
Malate is also synthesized by the carboxylation of phosphoenolpyruvate in the guard cells of plant leaves. Malate, as a double anion, often accompanies potassium cations during the uptake of solutes into the guard cells in order to maintain electrical balance in the cell. The accumulation of these solutes within the guard cell decreases the solute potential , allowing water to enter the cell and promote aperture of the stomata.
Malic acid was first isolated from apple juice by Carl Wilhelm Scheele in 1785. [ 6 ] Antoine Lavoisier in 1787 proposed the name acide malique , which is derived from the Latin word for apple, mālum —as is its genus name Malus . [ 7 ] [ 8 ] In German it is named Äpfelsäure (or Apfelsäure ) after plural or singular of a sour thing from the apple fruit, but the salt(s) are called Malat(e) .
Malic acid is the main acid in many fruits, including apricots , blackberries , blueberries , cherries , grapes , mirabelles , peaches , pears , plums , and quince , [ 9 ] and is present in lower concentrations in other fruits, such as citrus. It contributes to the sourness of unripe apples. Sour apples contain high proportions of the acid. It is present in grapes and in most wines with concentrations sometimes as high as 5 g/L. [ 10 ] It confers a tart taste to wine ; the amount decreases with increasing fruit ripeness . The taste of malic acid is very clear and pure in rhubarb , a plant for which it is the primary flavor. It is also the compound responsible for the tart flavor of sumac spice. It is also a component of some artificial vinegar flavors, such as "salt and vinegar" flavored potato chips. [ 11 ]
The process of malolactic fermentation converts malic acid to much milder lactic acid . Malic acid occurs naturally in all fruits and many vegetables, and is generated in fruit metabolism. [ 12 ]
Malic acid, when added to food products, is denoted by E number E296. It is sometimes used with or in place of the less sour citric acid in sour sweets. These sweets are sometimes labeled with a warning stating that excessive consumption can cause irritation of the mouth. It is approved for use as a food additive in the EU, [ 13 ] US [ 14 ] and Australia and New Zealand [ 15 ] (where it is listed by its INS number 296).
Malic acid contains 10 kJ (2.39 kilocalories) of energy per gram. [ 16 ]
Racemic malic acid is produced industrially by the double hydration of maleic anhydride . In 2000, American production capacity was 5,000 tons per year. The enantiomers may be separated by chiral resolution of the racemic mixture. S -Malic acid is obtained by fermentation of fumaric acid . [ 17 ]
Self-condensation of malic acid in the presence of fuming sulfuric acid gives the pyrone coumalic acid : [ 18 ]
Carbon monoxide and water are liberated during this reaction.
Malic acid was important in the discovery of the Walden inversion and the Walden cycle , in which (−)-malic acid first is converted into (+)-chlorosuccinic acid by action of phosphorus pentachloride . Wet silver oxide then converts the chlorine compound to (+)-malic acid, which then reacts with PCl 5 to the (−)-chlorosuccinic acid. The cycle is completed when silver oxide takes this compound back to (−)-malic acid.
L -malic acid is used to resolve α-phenylethylamine , a versatile resolving agent in its own right. [ 19 ]
Soil supplementation with molasses increases microbial synthesis of malic acid. This is thought to occur naturally as part of soil microbe suppression of disease , so soil amendment with molasses can be used as a crop treatment in horticulture. [ 20 ]
Click on genes, proteins and metabolites below to link to respective articles. [ § 1 ]
Acetyl-CoA
Oxaloacetate
Malate
Fumarate
Succinate
Succinyl-CoA
Citrate
cis- Aconitate
Isocitrate
Oxalosuccinate
2-oxoglutarate | https://en.wikipedia.org/wiki/HO2CCH2CHOHCO2H |
In chemistry , a phosphoric acid , in the general sense, is a phosphorus oxoacid in which each phosphorus (P) atom is in the oxidation state +5, and is bonded to four oxygen (O) atoms, one of them through a double bond , arranged as the corners of a tetrahedron . Two or more of these PO 4 tetrahedra may be connected by shared single-bonded oxygens, forming linear or branched chains , cycles , or more complex structures. The single-bonded oxygen atoms that are not shared are completed with acidic hydrogen atoms. The general formula of a phosphoric acid is H n +2−2 x P n O 3 n +1− x , where n is the number of phosphorus atoms and x is the number of fundamental cycles in the molecule's structure, between 0 and n + 2 / 2 .
Removal of protons ( H + ) from k hydroxyl groups –OH leaves anions generically called phosphates (if k = n − 2 x + 2 ) or hydrogen phosphates (if k is between 1 and n − 2 x + 1 ), with general formula [H n −2 x +2− k P n O 3 n +1− x ] k − . The fully dissociated anion ( k = n − 2 x + 2 ) has formula [P n O 3 n − x +1 ] ( n −2 x +2)− . The term phosphate is also used in organic chemistry for the functional groups that result when one or more of the hydrogens are replaced by bonds to other groups.
These acids, together with their salts and esters , include some of the best-known compounds of phosphorus, of high importance in biochemistry , mineralogy , agriculture , pharmacy , chemical industry , and chemical research .
The simplest and most commonly encountered of the phosphoric acids is orthophosphoric acid , H 3 PO 4 . Indeed, the term phosphoric acid often means this compound specifically (and this is also the current IUPAC nomenclature). [ citation needed ]
Two or more orthophosphoric acid molecules can be joined by condensation into larger molecules by elimination of water . Condensation of a few units yields the oligophosphoric acids , while larger molecules are called polyphosphoric acids . (However, the distinction between the two terms is not well defined.)
For example, pyrophosphoric , triphosphoric and tetraphosphoric acids can be obtained by the reactions 2 H 3 PO 4 ⟶ H 4 P 2 O 7 + H 2 O H 4 P 2 O 7 + H 3 PO 4 ⟶ H 5 P 3 O 10 + H 2 O H 5 P 3 O 10 + H 3 PO 4 ⟶ H 6 P 4 O 13 + H 2 O {\displaystyle {\begin{aligned}{\ce {2 H3PO4}}&\longrightarrow {\ce {H4P2O7 + H2O}}\\[2pt]{\ce {H4P2O7 + H3PO4}}&\longrightarrow {\ce {H5P3O10 + H2O}}\\[2pt]{\ce {H5P3O10 + H3PO4}}&\longrightarrow {\ce {H6P4O13 + H2O}}\end{aligned}}}
The "backbone" of a polyphosphoric acid molecule is a chain of alternating P and O atoms. Each extra orthophosphoric unit that is condensed adds 1 extra H ( hydrogen ) atom, 1 extra P ( phosphorus ) atom, and 3 extra O ( oxygen ) atoms. The general formula of a polyphosphoric acid is H n +2 P n O 3 n +1 or HO[−P(O)(OH)−O−] n H .
Polyphosphoric acids are used in organic synthesis for cyclizations and acylations ; an alternative is Eaton's reagent . [ 1 ] [ 2 ] [ 3 ]
Metaphosphoric acid ( HPO 3 ) is a colorless, vitreous, deliquescent solid, density 2.2 to 2.5 g/cc, which sublimes upon heating. It is soluble in ethanol. [ 4 ]
Phosphoric acid units can be bonded together in rings (cyclic structures). The simplest such compound is trimetaphosphoric acid or cyclo-triphosphoric acid having the formula H 3 P 3 O 9 . Its structure is shown in the illustration. Since the ends are condensed, its formula has one less H 2 O (water) than tripolyphosphoric acid.
The general formula of a phosphoric acid is H n −2 x +2 P n O 3 n − x +1 , where n is the number of phosphorus atoms and x is the number of fundamental cycles in the molecule's structure; that is, the minimum number of bonds that would have to be broken to eliminate all cycles.
The limiting case of internal condensation, where all oxygen atoms are shared and there are no hydrogen atoms ( x = n +2 / 2 ) is an anhydride P 2 n O 5 n , phosphorus pentoxide P 4 O 10 .
Removal of the hydrogen atoms as protons H + turns a phosphoric acid into a phosphate anion. Partial removal yields various hydrogen phosphate anions.
The anions of orthophosphoric acid H 3 PO 4 are orthophosphate (commonly called simply "phosphate") PO 3− 4 , monohydrogen phosphate HPO 2− 4 , and dihydrogen phosphate H 2 PO − 4 .
Dissociation of pyrophosphoric acid H 4 P 2 O 7 generates four anions, [H 4− k P 2 O 7 ] k − , where the charge k ranges from 1 to 4. The last one is pyrophosphate [P 2 O 7 ] 4− . The pyrophosphates are mostly water-soluble.
Likewise, tripolyphosphoric acid H 5 P 3 O 10 yields at least five anions [H 5− k P 3 O 10 ] k − , where k ranges from 1 to 5, including tripolyphosphate [P 3 O 10 ] 5− . Tetrapolyphosphoric acid H 6 P 4 O 13 yields at least six anions, including tetrapolyphosphate [P 4 O 13 ] 6− , and so on. Note that each extra phosphoric unit adds one extra P atom, three extra O atoms, and either one extra hydrogen atom or an extra negative charge.
Branched polyphosphoric acids give similarly branched polyphosphate anions. The simplest example of this is triphosphono phosphate [OP(OPO 3 ) 3 ] 9− and its partially dissociated versions.
The general formula for such (non-cyclic) polyphosphate anions, linear or branched, is [H n +2− k P n O 3 n +1 ] k − , where the charge k may vary from 1 to n + 2 . Generally in an aqueous solution, the degree or percentage of dissociation depends on the pH of the solution.
Salts or esters of cyclic polyphosphoric acids are often called "metaphosphates". What are commonly called trimetaphosphates actually have a mixture of ring sizes. A general formula for such cyclic compounds is [HPO 3 ] x where x = number of phosphoric units in the molecule.
When metaphosphoric acids lose their hydrogens as H + , cyclic anions called metaphosphates are formed. An example of a compound with such an anion is sodium hexametaphosphate ( Na 6 P 6 O 18 ), used as a sequestrant and a food additive .
These phosphoric acids series are generally water - soluble considering the polarity of the molecules. Ammonium and alkali phosphates are also quite soluble in water. The alkaline earth salts start becoming less soluble and phosphate salts of various other metals are even less soluble.
In aqueous solutions (solutions of water), water gradually (over the course of hours) hydrolyzes polyphosphates into smaller phosphates and finally into ortho-phosphate, given enough water. Higher temperature or acidic conditions can speed up the hydrolysis reactions considerably. [ 5 ]
Conversely, polyphosphoric acids or polyphosphates are often formed by dehydrating a phosphoric acid solution; in other words, removing water from it often by heating and evaporating the water off.
Ortho-, pyro-, and tripolyphosphate compounds, such as sodium tripolyphosphate , have been commonly used in detergents (i. e. cleaners) formulations. Sometimes pyrophosphate, tripolyphosphate, tetrapolyphosphate, etc. are called diphosphate , triphosphate , tetraphosphate , etc., especially when they are part of phosphate esters in biochemistry . They are also used for scale and corrosion control by potable water providers . [ 6 ] As a corrosion inhibitor, polyphosphates work by forming a protective film on the interior surface of pipes. [ 7 ]
The −OH groups in phosphoric acids can also condense with the hydroxyl groups of alcohols to form phosphate esters . Since orthophosphoric acid has three −OH groups, it can esterify with one, two, or three alcohol molecules to form a mono-, di-, or triester. See the general structure image of an ortho- (or mono-) phosphate ester below on the left, where any of the R groups can be a hydrogen or an organic radical . Di- and tripoly- (or tri-) phosphate esters, etc. are also possible. Any −OH groups on the phosphates in these ester molecules may lose H + ions to form anions, again depending on the pH in a solution. In the biochemistry of living organisms, there are many kinds of (mono)phosphate, diphosphate, and triphosphate compounds (essentially esters ), many of which play a significant role in metabolism such as adenosine diphosphate (ADP) and triphosphate (ATP) . | https://en.wikipedia.org/wiki/HO3P |
L -Tyrosine or tyrosine (symbol Tyr or Y ) [ 2 ] or 4-hydroxyphenylalanine is one of the 20 standard amino acids that are used by cells to synthesize proteins . It is a conditionally essential amino acid with a polar side group . The word "tyrosine" is from the Greek tyrós , meaning cheese , as it was first discovered in 1846 by German chemist Justus von Liebig in the protein casein from cheese. [ 3 ] [ 4 ] It is called tyrosyl when referred to as a functional group or side chain. While tyrosine is generally classified as a hydrophobic amino acid, it is more hydrophilic than phenylalanine . [ 5 ] It is encoded by the codons UAC and UAU in messenger RNA .
The one-letter symbol Y was assigned to tyrosine for being alphabetically nearest of those letters available. Note that T was assigned to the structurally simpler threonine, U was avoided for its similarity with V for valine, W was assigned to tryptophan, while X was reserved for undetermined or atypical amino acids. [ 6 ] The mnemonic t Y rosine was also proposed. [ 7 ]
Aside from being a proteinogenic amino acid , tyrosine has a special role by virtue of the phenol functionality. Its hydroxy group is able to form the ester linkage , with phosphate in particular. Phosphate groups are transferred to tyrosine residues by way of protein kinases . This is one of the post-translational modifications . Phosphorylated tyrosine occurs in proteins that are part of signal transduction processes.
Similar functionality is also presented in serine and threonine , whose side chains have a hydroxy group, but are alcohols . Phosphorylation of these three amino acids' moieties (including tyrosine) creates a negative charge on their ends, that is greater than the negative charge of the only negatively charged aspartic and glutamic acids. Phosphorylated proteins keep these same properties—which are useful for more reliable protein-protein interactions—by means of phosphotyrosine, phosphoserine and phosphothreonine. [ 8 ]
Binding sites for a signalling phosphoprotein may be diverse in their chemical structure. [ 9 ]
Phosphorylation of the hydroxyl group can change the activity of the target protein, or may form part of a signaling cascade via SH2 domain binding. [ 10 ]
A tyrosine residue also plays an important role in photosynthesis . In chloroplasts ( photosystem II ), it acts as an electron donor in the reduction of oxidized chlorophyll . In this process, it loses the hydrogen atom of its phenolic OH-group. This radical is subsequently reduced in the photosystem II by the four core manganese clusters . [ 11 ]
The Dietary Reference Intake for tyrosine is usually estimated together with phenylalanine . It varies depending on an estimate method, however the ideal proportion of these two amino acids is considered to be 60:40 (phenylalanine:tyrosine) as a human body has such composition. [ 12 ] Tyrosine, which can also be synthesized in the body from phenylalanine, is found in many high- protein food products such as meat , fish , cheese , cottage cheese , milk , yogurt , peanuts , almonds , pumpkin seeds , sesame seeds , soy protein and lima beans . [ 13 ] [ 14 ] For example, the white of an egg has about 250 mg per egg, [ 15 ] while beef, lamb, pork, tuna, salmon, chicken, and turkey contain about 500–1000 mg per 3 ounces (85 g) portion. [ 15 ] [ 16 ]
In plants and most microorganisms, tyrosine is produced via prephenate , an intermediate on the shikimate pathway . Prephenate is oxidatively decarboxylated with retention of the hydroxyl group to give p -hydroxyphenylpyruvate, which is transaminated using glutamate as the nitrogen source to give tyrosine and α-ketoglutarate .
Mammals synthesize tyrosine from the essential amino acid phenylalanine (Phe), which is derived from food. The conversion of Phe to Tyr is catalyzed by the enzyme phenylalanine hydroxylase , a monooxygenase. This enzyme catalyzes the reaction causing the addition of a hydroxyl group to the end of the 6-carbon aromatic ring of phenylalanine , such that it becomes tyrosine.
Some of the tyrosine residues can be tagged (at the hydroxyl group) with a phosphate group ( phosphorylated ) by protein kinases . In its phosphorylated form, tyrosine is called phosphotyrosine . Tyrosine phosphorylation is considered to be one of the key steps in signal transduction and regulation of enzymatic activity. Phosphotyrosine can be detected through specific antibodies . Tyrosine residues may also be modified by the addition of a sulfate group, a process known as tyrosine sulfation . [ 17 ] Tyrosine sulfation is catalyzed by tyrosylprotein sulfotransferase (TPST). Like the phosphotyrosine antibodies mentioned above, antibodies have recently been described that specifically detect sulfotyrosine. [ 18 ]
In dopaminergic cells in the brain , tyrosine is converted to L-DOPA by the enzyme tyrosine hydroxylase (TH). TH is the rate-limiting enzyme involved in the synthesis of the neurotransmitter dopamine . Dopamine can then be converted into other catecholamines , such as norepinephrine (noradrenaline) and epinephrine (adrenaline).
The thyroid hormones triiodothyronine (T 3 ) and thyroxine (T 4 ) in the colloid of the thyroid are also derived from tyrosine.
The latex of Papaver somniferum , the opium poppy, has been shown to convert tyrosine into the alkaloid morphine and the bio-synthetic pathway has been established from tyrosine to morphine by using Carbon-14 radio-labelled tyrosine to trace the in-vivo synthetic route. [ 22 ] Tyrosine ammonia lyase (TAL) is an enzyme in the natural phenols biosynthesis pathway. It transforms L -tyrosine into p -coumaric acid . Tyrosine is also the precursor to the pigment melanin . Tyrosine (or its precursor phenylalanine) is needed to synthesize the benzoquinone structure which forms part of coenzyme Q10 . [ 23 ] [ 24 ]
[ citation needed ]
The decomposition of L -tyrosine (syn. para -hydroxyphenylalanine) begins with an α-ketoglutarate dependent transamination through the tyrosine transaminase to para -hydroxyphenylpyruvate . The positional description para , abbreviated p , mean that the hydroxyl group and side chain on the phenyl ring are across from each other (see the illustration below).
The next oxidation step catalyzes by p -hydroxyphenylpyruvate dioxygenase and splitting off CO 2 homogentisate (2,5-dihydroxyphenyl-1-acetate). [ 25 ] In order to split the aromatic ring of homogentisate, a further dioxygenase, homogentisate 1,2-dioxygenase is required. Thereby, through the incorporation of a further O 2 molecule, maleylacetoacetate is created.
Fumarylacetoacetate is created by maleylacetoacetate cis - trans -isomerase through rotation of the carboxyl group created from the hydroxyl group via oxidation. This cis-trans -isomerase contains glutathione as a coenzyme . Fumarylacetoacetate is finally split by the enzyme fumarylacetoacetate hydrolase through the addition of a water molecule.
Thereby fumarate (also a metabolite of the citric acid cycle) and acetoacetate (3-ketobutyroate) are liberated. Acetoacetate is a ketone body , which is activated with succinyl-CoA, and thereafter it can be converted into acetyl-CoA , which in turn can be oxidized by the citric acid cycle or be used for fatty acid synthesis .
Phloretic acid is also a urinary metabolite of tyrosine in rats. [ 26 ]
Three structural isomers of L -tyrosine are known. In addition to the common amino acid L -tyrosine, which is the para isomer ( para -tyr, p -tyr or 4-hydroxyphenylalanine), there are two additional regioisomers, namely meta -tyrosine (also known as 3-hydroxyphenylalanine , L- m -tyrosine , and m -tyr) and ortho -tyrosine ( o -tyr or 2-hydroxyphenylalanine), that occur in nature. The m -tyr and o -tyr isomers, which are rare, arise through non-enzymatic free-radical hydroxylation of phenylalanine under conditions of oxidative stress . [ 27 ] [ 28 ]
Tyrosine is a precursor to neurotransmitters and increases plasma neurotransmitter levels (particularly dopamine and norepinephrine), [ 29 ] but has little if any effect on mood in normal subjects. [ 30 ] [ 31 ] [ 32 ]
A 2015 systematic review found that "tyrosine loading acutely counteracts decrements in working memory and information processing that are induced by demanding situational conditions such as extreme weather or cognitive load " and therefore "tyrosine may benefit healthy individuals exposed to demanding situational conditions". [ 33 ]
L -Tyrosine is used in pharmaceuticals , dietary supplements , and food additives . Two methods were formerly used to manufacture L -tyrosine. The first involves the extraction of the desired amino acid from protein hydrolysates using a chemical approach. The second utilizes enzymatic synthesis from phenolics, pyruvate, and ammonia through the use of tyrosine phenol-lyase . [ 34 ] Advances in genetic engineering and the advent of industrial fermentation have shifted the synthesis of L-tyrosine to the use of engineered strains of E. coli . [ 35 ] [ 34 ] | https://en.wikipedia.org/wiki/HOC6H4CH2CH(NH2)COOH |
1,4-Butynediol is an organic compound that is an alkyne and a diol . It is a colourless, hygroscopic solid that is soluble in water and polar organic solvents . It is a commercially significant compound in its own right and as a precursor to other products.
1,4-Butynediol can be produced in the Reppe synthesis , where formaldehyde and acetylene are the reactants: [ 3 ]
Several patented production methods use copper bismuth catalysts coated on an inert material. The normal temperature range for the reaction is 90 °C up to 150 °C, depending on the pressure used for the reaction which can range from 1 to 20 bar. [ 4 ]
1,4-Butynediol is a precursor to 1,4-butanediol and 2-butene-1,4-diol by hydrogenation . It is also used in the manufacture of certain herbicides, textile additives, corrosion inhibitors, plasticizers, synthetic resins, and polyurethanes . It is the major raw material used in the synthesis of vitamin B 6 . [ 5 ] It is also used for brightening, preserving, and inhibiting nickel plating. [ 3 ]
It reacts with a mixture of chlorine and hydrochloric acid to give mucochloric acid, HO 2 CC(Cl)=C(Cl)CHO (see mucobromic acid ).
1,4-Butynediol is corrosive and irritates the skin, eyes, and respiratory tract. | https://en.wikipedia.org/wiki/HOCH2CCCH2OH |
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/HOCL |
Carbonic acid is a chemical compound with the chemical formula H 2 C O 3 . The molecule rapidly converts to water and carbon dioxide in the presence of water. However, in the absence of water, it is quite stable at room temperature . [ 5 ] [ 6 ] The interconversion of carbon dioxide and carbonic acid is related to the breathing cycle of animals and the acidification of natural waters . [ 4 ]
In biochemistry and physiology, the name "carbonic acid" is sometimes applied to aqueous solutions of carbon dioxide . These chemical species play an important role in the bicarbonate buffer system , used to maintain acid–base homeostasis . [ 7 ]
In chemistry , the term "carbonic acid" strictly refers to the chemical compound with the formula H 2 CO 3 . Some biochemistry literature effaces the distinction between carbonic acid and carbon dioxide dissolved in extracellular fluid.
In physiology , carbon dioxide excreted by the lungs may be called volatile acid or respiratory acid .
At ambient temperatures, pure carbonic acid is a stable gas. [ 6 ] There are two main methods to produce anhydrous carbonic acid: reaction of hydrogen chloride and potassium bicarbonate at 100 K in methanol and proton irradiation of pure solid carbon dioxide . [ 3 ] Chemically, it behaves as a diprotic Brønsted acid . [ 8 ] [ 9 ]
Carbonic acid monomers exhibit three conformational isomers : cis–cis, cis–trans, and trans–trans. [ 10 ]
At low temperatures and atmospheric pressure , solid carbonic acid is amorphous and lacks Bragg peaks in X-ray diffraction . [ 11 ] But at high pressure, carbonic acid crystallizes, and modern analytical spectroscopy can measure its geometry.
According to neutron diffraction of dideuterated carbonic acid ( D 2 CO 3 ) in a hybrid clamped cell ( Russian alloy / copper-beryllium ) at 1.85 GPa, the molecules are planar and form dimers joined by pairs of hydrogen bonds . All three C-O bonds are nearly equidistant at 1.34 Å , intermediate between typical C-O and C=O distances (respectively 1.43 and 1.23 Å). The unusual C-O bond lengths are attributed to delocalized π bonding in the molecule's center and extraordinarily strong hydrogen bonds. The same effects also induce a very short O—O separation (2.13 Å), through the 136° O-H-O angle imposed by the doubly hydrogen-bonded 8-membered rings. [ 4 ] Longer O—O distances are observed in strong intramolecular hydrogen bonds, e.g. in oxalic acid , where the distances exceed 2.4 Å. [ 11 ]
In even a slight presence of water, carbonic acid dehydrates to carbon dioxide and water , which then catalyzes further decomposition. [ 6 ] For this reason, carbon dioxide can be considered the carbonic acid anhydride .
The hydration equilibrium constant at 25 °C is [ H 2 CO 3 ]/[CO 2 ] ≈ 1.7×10 −3 in pure water [ 12 ] and ≈ 1.2×10 −3 in seawater . [ 13 ] Hence the majority of carbon dioxide at geophysical or biological air-water interfaces does not convert to carbonic acid, remaining dissolved CO 2 gas. However, the uncatalyzed equilibrium is reached quite slowly: the rate constants are 0.039 s −1 for hydration and 23 s −1 for dehydration.
In the presence of the enzyme carbonic anhydrase , equilibrium is instead reached rapidly, and the following reaction takes precedence: [ 14 ] HCO 3 − + H + ↽ − − ⇀ CO 2 + H 2 O {\displaystyle {\ce {HCO3^- {+}H^+ <=> CO2 {+}H2O}}}
When the created carbon dioxide exceeds its solubility, gas evolves and a third equilibrium CO 2 ( soln ) ↽ − − ⇀ CO 2 ( g ) {\displaystyle {\ce {CO_2 (soln) <=> CO_2 (g)}}} must also be taken into consideration. The equilibrium constant for this reaction is defined by Henry's law .
The two reactions can be combined for the equilibrium in solution: HCO 3 − + H + ↽ − − ⇀ CO 2 ( soln ) + H 2 O K 3 = [ H + ] [ HCO 3 − ] [ CO 2 ( soln ) ] {\displaystyle {\begin{aligned}{\ce {HCO3^{-}{}+ H+{}<=> CO2(soln){}+ H2O}}&&K_{3}={\frac {[{\ce {H+}}][{\ce {HCO3^-}}]}{[{\ce {CO2(soln)}}]}}\end{aligned}}} When Henry's law is used to calculate the denominator care is needed with regard to units since Henry's law constant can be commonly expressed with 8 different dimensionalities. [ 15 ]
In wastewater treatment and agriculture irrigation, carbonic acid is used to acidify the water similar to sulfuric acid and sulfurous acid produced by sulfur burners. [ 16 ]
In the beverage industry , sparkling or "fizzy water" is usually referred to as carbonated water . It is made by dissolving carbon dioxide under a small positive pressure in water. Many soft drinks treated the same way effervesce .
Significant amounts of molecular H 2 CO 3 exist in aqueous solutions subjected to pressures of multiple gigapascals (tens of thousands of atmospheres) in planetary interiors. [ 17 ] [ 18 ] Pressures of 0.6–1.6 GPa at 100 K , and 0.75–1.75 GPa at 300 K are attained in the cores of large icy satellites such as Ganymede , Callisto , and Titan , where water and carbon dioxide are present. Pure carbonic acid, being denser, is expected to have sunk under the ice layers and separate them from the rocky cores of these moons. [ 19 ]
Carbonic acid is the formal Brønsted–Lowry conjugate acid of the bicarbonate anion, stable in alkaline solution . The protonation constants have been measured to great precision, but depend on overall ionic strength I . The two equilibria most easily measured are as follows: CO 3 2 − + H + ↽ − − ⇀ HCO 3 − β 1 = [ HCO 3 − ] [ H + ] [ CO 3 2 − ] CO 3 2 − + 2 H + ↽ − − ⇀ H 2 CO 3 β 2 = [ H 2 CO 3 ] [ H + ] 2 [ CO 3 2 − ] {\displaystyle {\begin{aligned}{\ce {CO3^{2-}{}+ H+{}<=> HCO3^-}}&&\beta _{1}={\frac {[{\ce {HCO3^-}}]}{[{\ce {H+}}][{\ce {CO3^{2-}}}]}}\\{\ce {CO3^{2-}{}+ 2H+{}<=> H2CO3}}&&\beta _{2}={\frac {[{\ce {H2CO3}}]}{[{\ce {H+}}]^{2}[{\ce {CO3^{2-}}}]}}\end{aligned}}} where brackets indicate the concentration of species . At 25 °C, these equilibria empirically satisfy [ 20 ] log ( β 1 ) = 0 .54 I 2 − 0 .96 I + 9 .93 log ( β 2 ) = − 2 .5 I 2 − 0 .043 I + 16 .07 {\displaystyle {\begin{alignedat}{6}\log(\beta _{1})=&&0&.54&I^{2}-0&.96&I+&&9&.93\\\log(\beta _{2})=&&-2&.5&I^{2}-0&.043&I+&&16&.07\end{alignedat}}} log( β 1 ) decreases with increasing I , as does log( β 2 ) . In a solution absent other ions (e.g. I = 0 ), these curves imply the following stepwise dissociation constants : p K 1 = log ( β 2 ) − log ( β 1 ) = 6.77 p K 2 = log ( β 1 ) = 9.93 {\displaystyle {\begin{alignedat}{3}p{\text{K}}_{1}&=\log(\beta _{2})-\log(\beta _{1})&=6.77\\p{\text{K}}_{2}&=\log(\beta _{1})&=9.93\end{alignedat}}} Direct values for these constants in the literature include p K 1 = 6.35 and p K 2 - p K 1 = 3.49 . [ 21 ]
To interpret these numbers, note that two chemical species in an acid equilibrium are equiconcentrated when p K = p H . In particular, the extracellular fluid ( cytosol ) in biological systems exhibits p H ≈ 7.2 , so that carbonic acid will be almost 50%-dissociated at equilibrium.
The Bjerrum plot shows typical equilibrium concentrations, in solution, in seawater , of carbon dioxide and the various species derived from it, as a function of pH . [ 8 ] [ 9 ] As human industrialization has increased the proportion of carbon dioxide in Earth's atmosphere , the proportion of carbon dioxide dissolved in sea- and freshwater as carbonic acid is also expected to increase. This rise in dissolved acid is also expected to acidify those waters, generating a decrease in pH. [ 22 ] [ 23 ] It has been estimated that the increase in dissolved carbon dioxide has already caused the ocean's average surface pH to decrease by about 0.1 from pre-industrial levels. | https://en.wikipedia.org/wiki/HOCOOH |
HOCPCA ( 3-hydroxycyclopent-1-enecarboxylic acid ) is a compound with an affinity for the GHB receptor 39 times greater than that of GHB itself. [ 1 ]
This drug article relating to the nervous system is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HOCPCA |
Water ( H 2 O ) is a polar inorganic compound that is at room temperature a tasteless and odorless liquid , which is nearly colorless apart from an inherent hint of blue . It is by far the most studied chemical compound [ 20 ] and is described as the "universal solvent " [ 21 ] and the "solvent of life". [ 22 ] It is the most abundant substance on the surface of Earth [ 23 ] and the only common substance to exist as a solid , liquid, and gas on Earth's surface. [ 24 ] It is also the third most abundant molecule in the universe (behind molecular hydrogen and carbon monoxide ). [ 23 ]
Water molecules form hydrogen bonds with each other and are strongly polar. This polarity allows it to dissociate ions in salts and bond to other polar substances such as alcohols and acids, thus dissolving them. Its hydrogen bonding causes its many unique properties, such as having a solid form less dense than its liquid form, a relatively high boiling point of 100 °C for its molar mass , and a high heat capacity .
Water is amphoteric , meaning that it can exhibit properties of an acid or a base , depending on the pH of the solution that it is in; it readily produces both H + and OH − ions. [ c ] Related to its amphoteric character, it undergoes self-ionization . The product of the activities , or approximately, the concentrations of H + and OH − is a constant, so their respective concentrations are inversely proportional to each other. [ 25 ]
Water is the chemical substance with chemical formula H 2 O ; one molecule of water has two hydrogen atoms covalently bonded to a single oxygen atom. [ 26 ] Water is a tasteless, odorless liquid at ambient temperature and pressure . Liquid water has weak absorption bands at wavelengths of around 750 nm which cause it to appear to have a blue color. [ 4 ] This can easily be observed in a water-filled bath or wash-basin whose lining is white. Large ice crystals, as in glaciers , also appear blue.
Under standard conditions , water is primarily a liquid, unlike other analogous hydrides of the oxygen family , which are generally gaseous. This unique property of water is due to hydrogen bonding . The molecules of water are constantly moving concerning each other, and the hydrogen bonds are continually breaking and reforming at timescales faster than 200 femtoseconds (2 × 10 −13 seconds). [ 27 ] However, these bonds are strong enough to create many of the peculiar properties of water, some of which make it integral to life.
Within the Earth's atmosphere and surface, the liquid phase is the most common and is the form that is generally denoted by the word "water". The solid phase of water is known as ice and commonly takes the structure of hard, amalgamated crystals , such as ice cubes , or loosely accumulated granular crystals, like snow . Aside from common hexagonal crystalline ice , other crystalline and amorphous phases of ice are known. The gaseous phase of water is known as water vapor (or steam ). Visible steam and clouds are formed from minute droplets of water suspended in the air.
Water also forms a supercritical fluid . The critical temperature is 647 K and the critical pressure is 22.064 MPa . In nature, this only rarely occurs in extremely hostile conditions. A likely example of naturally occurring supercritical water is in the hottest parts of deep water hydrothermal vents , in which water is heated to the critical temperature by volcanic plumes and the critical pressure is caused by the weight of the ocean at the extreme depths where the vents are located. This pressure is reached at a depth of about 2200 meters: much less than the mean depth of the ocean (3800 meters). [ 28 ]
Water has a very high specific heat capacity of 4184 J/(kg·K) at 20 °C (4182 J/(kg·K) at 25 °C)—the second-highest among all the heteroatomic species (after ammonia ), as well as a high heat of vaporization (40.65 kJ/mol or 2257 kJ/kg at the normal boiling point), both of which are a result of the extensive hydrogen bonding between its molecules. These unusual properties allow water to moderate Earth's climate by buffering large fluctuations in temperature. Most of the additional energy stored in the climate system since 1970 has accumulated in the oceans . [ 29 ]
The specific enthalpy of fusion (more commonly known as latent heat) of water is 333.55 kJ/kg at 0 °C: the same amount of energy is required to melt ice as to warm ice from −160 °C up to its melting point or to heat the same amount of water by about 80 °C. Of common substances, only that of ammonia is higher. This property confers resistance to melting on the ice of glaciers and drift ice . Before and since the advent of mechanical refrigeration , ice was and still is in common use for retarding food spoilage.
The specific heat capacity of ice at −10 °C is 2030 J/(kg·K) [ 30 ] and the heat capacity of steam at 100 °C is 2080 J/(kg·K). [ 31 ]
The density of water is about 1 gram per cubic centimetre (62 lb/cu ft): this relationship was originally used to define the gram. [ 32 ] The density varies with temperature, but not linearly: as the temperature increases, the density rises to a peak at 3.98 °C (39.16 °F) and then decreases; [ 33 ] the initial increase is unusual because most liquids undergo thermal expansion so that the density only decreases as a function of temperature. The increase observed for water from 0 °C (32 °F) to 3.98 °C (39.16 °F) and for a few other liquids [ d ] is described as negative thermal expansion . Regular, hexagonal ice is also less dense than liquid water—upon freezing, the density of water decreases by about 9%. [ 36 ] [ e ]
These peculiar effects are due to the highly directional bonding of water molecules via the hydrogen bonds: ice and liquid water at low temperature have comparatively low-density, low-energy open lattice structures. The breaking of hydrogen bonds on melting with increasing temperature in the range 0–4 °C allows for a denser molecular packing in which some of the lattice cavities are filled by water molecules. [ 33 ] [ 37 ] Above 4 °C, however, thermal expansion becomes the dominant effect, [ 37 ] and water near the boiling point (100 °C) is about 4% less dense than water at 4 °C (39 °F). [ 36 ] [ f ]
Under increasing pressure, ice undergoes a number of transitions to other polymorphs with higher density than liquid water, such as ice II , ice III , high-density amorphous ice (HDA), and very-high-density amorphous ice (VHDA). [ 38 ] [ 39 ]
The unusual density curve and lower density of ice than of water is essential for much of the life on earth—if water were most dense at the freezing point, then in winter the cooling at the surface would lead to convective mixing. Once 0 °C are reached, the water body would freeze from the bottom up, and all life in it would be killed. [ 36 ] Furthermore, given that water is a good thermal insulator (due to its heat capacity), some frozen lakes might not completely thaw in summer. [ 36 ] As it is, the inversion of the density curve leads to a stable layering for surface temperatures below 4 °C, and with the layer of ice that floats on top insulating the water below, [ 40 ] even e.g., Lake Baikal in central Siberia freezes only to about 1 m thickness in winter. In general, for deep enough lakes, the temperature at the bottom stays constant at about 4 °C (39 °F) throughout the year (see diagram). [ 36 ]
The density of saltwater depends on the dissolved salt content as well as the temperature. Ice still floats in the oceans, otherwise, they would freeze from the bottom up. However, the salt content of oceans lowers the freezing point by about 1.9 °C [ 41 ] (due to freezing-point depression of a solvent containing a solute ) and lowers the temperature of the density maximum of water to the former freezing point at 0 °C. This is why, in ocean water, the downward convection of colder water is not blocked by an expansion of water as it becomes colder near the freezing point. The oceans' cold water near the freezing point continues to sink. So creatures that live at the bottom of cold oceans like the Arctic Ocean generally live in water 4 °C colder than at the bottom of frozen-over fresh water lakes and rivers.
As the surface of saltwater begins to freeze (at −1.9 °C [ 41 ] for normal salinity seawater , 3.5%) the ice that forms is essentially salt-free, with about the same density as freshwater ice. This ice floats on the surface, and the salt that is "frozen out" adds to the salinity and density of the seawater just below it, in a process known as brine rejection . This denser saltwater sinks by convection and the replacing seawater is subject to the same process. This produces essentially freshwater ice at −1.9 °C [ 41 ] on the surface. The increased density of the seawater beneath the forming ice causes it to sink towards the bottom. On a large scale, the process of brine rejection and sinking cold salty water results in ocean currents forming to transport such water away from the Poles, leading to a global system of currents called the thermohaline circulation .
Water is miscible with many liquids, including ethanol in all proportions. Water and most oils are immiscible, usually forming layers according to increasing density from the top. This can be predicted by comparing the polarity . Water being a relatively polar compound will tend to be miscible with liquids of high polarity such as ethanol and acetone , whereas compounds with low polarity will tend to be immiscible and poorly soluble such as with hydrocarbons .
As a gas, water vapor is completely miscible with air. On the other hand, the maximum water vapor pressure that is thermodynamically stable with the liquid (or solid) at a given temperature is relatively low compared with total atmospheric pressure. For example, if the vapor's partial pressure is 2% of atmospheric pressure and the air is cooled from 25 °C, starting at about 22 °C, water will start to condense, defining the dew point , and creating fog or dew . The reverse process accounts for the fog burning off in the morning. If the humidity is increased at room temperature, for example, by running a hot shower or a bath, and the temperature stays about the same, the vapor soon reaches the pressure for phase change and then condenses out as minute water droplets, commonly referred to as steam.
A saturated gas or one with 100% relative humidity is when the vapor pressure of water in the air is at equilibrium with vapor pressure due to (liquid) water; water (or ice, if cool enough) will fail to lose mass through evaporation when exposed to saturated air. Because the amount of water vapor in the air is small, relative humidity, the ratio of the partial pressure due to the water vapor to the saturated partial vapor pressure, is much more useful. Vapor pressure above 100% relative humidity is called supersaturated and can occur if the air is rapidly cooled, for example, by rising suddenly in an updraft. [ g ]
The compressibility of water is a function of pressure and temperature. At 0 °C, at the limit of zero pressure, the compressibility is 5.1 × 10 −10 Pa −1 . At the zero-pressure limit, the compressibility reaches a minimum of 4.4 × 10 −10 Pa −1 around 45 °C before increasing again with increasing temperature. As the pressure is increased, the compressibility decreases, being 3.9 × 10 −10 Pa −1 at 0 °C and 100 megapascals (1,000 bar). [ 42 ]
The bulk modulus of water is about 2.2 GPa. [ 43 ] The low compressibility of non-gasses, and of water in particular, leads to their often being assumed as incompressible. The low compressibility of water means that even in the deep oceans at 4 kilometres (2.5 mi) depth, where pressures are 40 MPa, there is only a 1.8% decrease in volume. [ 43 ]
The bulk modulus of water ice ranges from 11.3 GPa at 0 K up to 8.6 GPa at 273 K. [ 44 ] The large change in the compressibility of ice as a function of temperature is the result of its relatively large thermal expansion coefficient compared to other common solids.
The temperature and pressure at which ordinary solid, liquid, and gaseous water coexist in equilibrium is a triple point of water. Since 1954, this point had been used to define the base unit of temperature, the kelvin , [ 45 ] [ 46 ] but, starting in 2019 , the kelvin is now defined using the Boltzmann constant , rather than the triple point of water. [ 47 ]
Due to the existence of many polymorphs (forms) of ice, water has other triple points, which have either three polymorphs of ice or two polymorphs of ice and liquid in equilibrium. [ 46 ] Gustav Heinrich Johann Apollon Tammann in Göttingen produced data on several other triple points in the early 20th century. Kamb and others documented further triple points in the 1960s. [ 48 ] [ 49 ] [ 50 ]
The melting point of ice is 0 °C (32 °F; 273 K) at standard pressure; however, pure liquid water can be supercooled well below that temperature without freezing if the liquid is not mechanically disturbed. It can remain in a fluid state down to its homogeneous nucleation point of about 231 K (−42 °C; −44 °F). [ 52 ] The melting point of ordinary hexagonal ice falls slightly under moderately high pressures, by 0.0073 °C (0.0131 °F)/atm [ h ] or about 0.5 °C (0.90 °F)/70 atm [ i ] [ 53 ] as the stabilization energy of hydrogen bonding is exceeded by intermolecular repulsion, but as ice transforms into its polymorphs (see crystalline states of ice ) above 209.9 MPa (2,072 atm), the melting point increases markedly with pressure , i.e., reaching 355 K (82 °C) at 2.216 GPa (21,870 atm) (triple point of Ice VII [ 54 ] ).
Pure water containing no exogenous ions is an excellent electronic insulator , but not even "deionized" water is completely free of ions. Water undergoes autoionization in the liquid state when two water molecules form one hydroxide anion ( OH − ) and one hydronium cation ( H 3 O + ). Because of autoionization, at ambient temperatures pure liquid water has a similar intrinsic charge carrier concentration to the semiconductor germanium and an intrinsic charge carrier concentration three orders of magnitude greater than the semiconductor silicon, hence, based on charge carrier concentration, water can not be considered to be a completely dielectric material or electrical insulator but to be a limited conductor of ionic charge. [ 55 ]
Because water is such a good solvent, it almost always has some solute dissolved in it, often a salt . If water has even a tiny amount of such an impurity, then the ions can carry charges back and forth, allowing the water to conduct electricity far more readily.
It is known that the theoretical maximum electrical resistivity for water is approximately 18.2 MΩ·cm (182 kΩ ·m) at 25 °C. [ 56 ] This figure agrees well with what is typically seen on reverse osmosis , ultra-filtered and deionized ultra-pure water systems used, for instance, in semiconductor manufacturing plants. A salt or acid contaminant level exceeding even 100 parts per trillion (ppt) in otherwise ultra-pure water begins to noticeably lower its resistivity by up to several kΩ·m. [ citation needed ]
In pure water, sensitive equipment can detect a very slight electrical conductivity of 0.05501 ± 0.0001 μS / cm at 25.00 °C. [ 56 ] Water can also be electrolyzed into oxygen and hydrogen gases but in the absence of dissolved ions this is a very slow process, as very little current is conducted. In ice, the primary charge carriers are protons (see proton conductor ). [ 57 ] Ice was previously thought to have a small but measurable conductivity of 1 × 10 −10 S/cm, but this conductivity is now thought to be almost entirely from surface defects, and without those, ice is an insulator with an immeasurably small conductivity. [ 33 ]
An important feature of water is its polar nature. The structure has a bent molecular geometry for the two hydrogens from the oxygen vertex. The oxygen atom also has two lone pairs of electrons. One effect usually ascribed to the lone pairs is that the H–O–H gas-phase bend angle is 104.48°, [ 58 ] which is smaller than the typical tetrahedral angle of 109.47°. The lone pairs are closer to the oxygen atom than the electrons sigma bonded to the hydrogens, so they require more space. The increased repulsion of the lone pairs forces the O–H bonds closer to each other. [ 59 ]
Another consequence of its structure is that water is a polar molecule . Due to the difference in electronegativity , a bond dipole moment points from each H to the O, making the oxygen partially negative and each hydrogen partially positive. A large molecular dipole , points from a region between the two hydrogen atoms to the oxygen atom. The charge differences cause water molecules to aggregate (the relatively positive areas being attracted to the relatively negative areas). This attraction, hydrogen bonding , explains many of the properties of water, such as its solvent properties. [ 60 ]
Although hydrogen bonding is a relatively weak attraction compared to the covalent bonds within the water molecule itself, it is responsible for several of the water's physical properties. These properties include its relatively high melting and boiling point temperatures: more energy is required to break the hydrogen bonds between water molecules. In contrast, hydrogen sulfide ( H 2 S ), has much weaker hydrogen bonding due to sulfur's lower electronegativity. H 2 S is a gas at room temperature , despite hydrogen sulfide having nearly twice the molar mass of water. The extra bonding between water molecules also gives liquid water a large specific heat capacity . This high heat capacity makes water a good heat storage medium (coolant) and heat shield.
Water molecules stay close to each other ( cohesion ), due to the collective action of hydrogen bonds between water molecules. These hydrogen bonds are constantly breaking, with new bonds being formed with different water molecules; but at any given time in a sample of liquid water, a large portion of the molecules are held together by such bonds. [ 61 ]
Water also has high adhesion properties because of its polar nature. On clean, smooth glass the water may form a thin film because the molecular forces between glass and water molecules (adhesive forces) are stronger than the cohesive forces. [ citation needed ] In biological cells and organelles , water is in contact with membrane and protein surfaces that are hydrophilic ; that is, surfaces that have a strong attraction to water. Irving Langmuir observed a strong repulsive force between hydrophilic surfaces. To dehydrate hydrophilic surfaces—to remove the strongly held layers of water of hydration—requires doing substantial work against these forces, called hydration forces. These forces are very large but decrease rapidly over a nanometer or less. [ 62 ] They are important in biology, particularly when cells are dehydrated by exposure to dry atmospheres or to extracellular freezing. [ 63 ]
Water has an unusually high surface tension of 71.99 mN/m at 25 °C [ 64 ] which is caused by the strength of the hydrogen bonding between water molecules. [ 65 ] This allows insects to walk on water. [ 65 ]
Because water has strong cohesive and adhesive forces, it exhibits capillary action. [ 66 ] Strong cohesion from hydrogen bonding and adhesion allows trees to transport water more than 100 m upward. [ 65 ]
Water is an excellent solvent due to its high dielectric constant. [ 67 ] Substances that mix well and dissolve in water are known as hydrophilic ("water-loving") substances, while those that do not mix well with water are known as hydrophobic ("water-fearing") substances. [ 68 ] The ability of a substance to dissolve in water is determined by whether or not the substance can match or better the strong attractive forces that water molecules generate between other water molecules. If a substance has properties that do not allow it to overcome these strong intermolecular forces, the molecules are precipitated out from the water. Contrary to the common misconception, water and hydrophobic substances do not "repel", and the hydration of a hydrophobic surface is energetically, but not entropically, favorable.
When an ionic or polar compound enters water, it is surrounded by water molecules ( hydration ). The relatively small size of water molecules (~3 angstroms) allows many water molecules to surround one molecule of solute . The partially negative dipole ends of the water are attracted to positively charged components of the solute, and vice versa for the positive dipole ends.
In general, ionic and polar substances such as acids , alcohols , and salts are relatively soluble in water, and nonpolar substances such as fats and oils are not. Nonpolar molecules stay together in water because it is energetically more favorable for the water molecules to hydrogen bond to each other than to engage in van der Waals interactions with non-polar molecules.
An example of an ionic solute is table salt ; the sodium chloride, NaCl, separates into Na + cations and Cl − anions , each being surrounded by water molecules. The ions are then easily transported away from their crystalline lattice into solution. An example of a nonionic solute is table sugar . The water dipoles make hydrogen bonds with the polar regions of the sugar molecule ( OH groups ) and allow it to be carried away into solution.
The quantum tunneling dynamics in water was reported as early as 1992. At that time it was known that there are motions which destroy and regenerate the weak hydrogen bond by internal rotations of the substituent water monomers . [ 69 ] On 18 March 2016, it was reported that the hydrogen bond can be broken by quantum tunneling in the water hexamer . Unlike previously reported tunneling motions in water, this involved the concerted breaking of two hydrogen bonds. [ 70 ] Later in the same year, the discovery of the quantum tunneling of water molecules was reported. [ 71 ]
Water is relatively transparent to visible light , near ultraviolet light, and far-red light, but it absorbs most ultraviolet light , infrared light , and microwaves . Most photoreceptors and photosynthetic pigments utilize the portion of the light spectrum that is transmitted well through water. Microwave ovens take advantage of water's opacity to microwave radiation to heat the water inside of foods. Water's light blue color is caused by weak absorption in the red part of the visible spectrum . [ 4 ] [ 72 ]
A single water molecule can participate in a maximum of four hydrogen bonds because it can accept two bonds using the lone pairs on oxygen and donate two hydrogen atoms. Other molecules like hydrogen fluoride , ammonia, and methanol can also form hydrogen bonds. However, they do not show anomalous thermodynamic , kinetic , or structural properties like those observed in water because none of them can form four hydrogen bonds: either they cannot donate or accept hydrogen atoms, or there are steric effects in bulky residues. In water, intermolecular tetrahedral structures form due to the four hydrogen bonds, thereby forming an open structure and a three-dimensional bonding network, resulting in the anomalous decrease in density when cooled below 4 °C. This repeated, constantly reorganising unit defines a three-dimensional network extending throughout the liquid. This view is based upon neutron scattering studies and computer simulations, and it makes sense in the light of the unambiguously tetrahedral arrangement of water molecules in ice structures.
However, there is an alternative theory for the structure of water. In 2004, a controversial paper from Stockholm University suggested that water molecules in the liquid state typically bind not to four but only two others; thus forming chains and rings. The term "string theory of water" (which is not to be confused with the string theory of physics) was coined. These observations were based upon X-ray absorption spectroscopy that probed the local environment of individual oxygen atoms. [ 73 ]
The repulsive effects of the two lone pairs on the oxygen atom cause water to have a bent , not linear , molecular structure, [ 74 ] allowing it to be polar. The hydrogen–oxygen–hydrogen angle is 104.45°, which is less than the 109.47° for ideal sp 3 hybridization . The valence bond theory explanation is that the oxygen atom's lone pairs are physically larger and therefore take up more space than the oxygen atom's bonds to the hydrogen atoms. [ 75 ] The molecular orbital theory explanation ( Bent's rule ) is that lowering the energy of the oxygen atom's nonbonding hybrid orbitals (by assigning them more s character and less p character) and correspondingly raising the energy of the oxygen atom's hybrid orbitals bonded to the hydrogen atoms (by assigning them more p character and less s character) has the net effect of lowering the energy of the occupied molecular orbitals because the energy of the oxygen atom's nonbonding hybrid orbitals contributes completely to the energy of the oxygen atom's lone pairs while the energy of the oxygen atom's other two hybrid orbitals contributes only partially to the energy of the bonding orbitals (the remainder of the contribution coming from the hydrogen atoms' 1s orbitals).
In liquid water there is some self-ionization giving hydronium ions and hydroxide ions.
The equilibrium constant for this reaction, known as the ionic product of water, K w = [ H 3 O + ] [ O H − ] {\displaystyle K_{\rm {w}}=[{\rm {H_{3}O^{+}}}][{\rm {OH^{-}}}]} , has a value of about 10 −14 at 25 °C. At neutral pH , the concentration of the hydroxide ion ( OH − ) equals that of the (solvated) hydrogen ion ( H + ), with a value close to 10 −7 mol L −1 at 25 °C. [ 76 ] See data page for values at other temperatures.
The thermodynamic equilibrium constant is a quotient of thermodynamic activities of all products and reactants including water:
However, for dilute solutions, the activity of a solute such as H 3 O + or OH − is approximated by its concentration, and the activity of the solvent H 2 O is approximated by 1, so that we obtain the simple ionic product K e q ≈ K w = [ H 3 O + ] [ O H − ] {\displaystyle K_{\rm {eq}}\approx K_{\rm {w}}=[{\rm {H_{3}O^{+}}}][{\rm {OH^{-}}}]}
The action of water on rock over long periods of time typically leads to weathering and water erosion , physical processes that convert solid rocks and minerals into soil and sediment, but under some conditions chemical reactions with water occur as well, resulting in metasomatism or mineral hydration , a type of chemical alteration of a rock which produces clay minerals . It also occurs when Portland cement hardens.
Water ice can form clathrate compounds , known as clathrate hydrates , with a variety of small molecules that can be embedded in its spacious crystal lattice. The most notable of these is methane clathrate , 4 CH 4 ·23H 2 O , naturally found in large quantities on the ocean floor.
Rain is generally mildly acidic, with a pH between 5.2 and 5.8 if not having any acid stronger than carbon dioxide. [ 77 ] If high amounts of nitrogen and sulfur oxides are present in the air, they too will dissolve into the cloud and raindrops, producing acid rain .
Several isotopes of both hydrogen and oxygen exist, giving rise to several known isotopologues of water. Vienna Standard Mean Ocean Water is the current international standard for water isotopes. Naturally occurring water is almost completely composed of the neutron-less hydrogen isotope protium . Only 155 ppm include deuterium ( 2 H or D), a hydrogen isotope with one neutron, and fewer than 20 parts per quintillion include tritium ( 3 H or T), which has two neutrons. Oxygen also has three stable isotopes, with 16 O present in 99.76%, 17 O in 0.04%, and 18 O in 0.2% of water molecules. [ 78 ]
Deuterium oxide, D 2 O , is also known as heavy water because of its higher density. It is used in nuclear reactors as a neutron moderator . Tritium is radioactive , decaying with a half-life of 4500 days; THO exists in nature only in minute quantities, being produced primarily via cosmic ray-induced nuclear reactions in the atmosphere. Water with one protium and one deuterium atom HDO occur naturally in ordinary water in low concentrations (~0.03%) and D 2 O in far lower amounts (0.000003%) and any such molecules are temporary as the atoms recombine.
The most notable physical differences between H 2 O and D 2 O , other than the simple difference in specific mass, involve properties that are affected by hydrogen bonding, such as freezing and boiling, and other kinetic effects. This is because the nucleus of deuterium is twice as heavy as protium, and this causes noticeable differences in bonding energies. The difference in boiling points allows the isotopologues to be separated. The self-diffusion coefficient of H 2 O at 25 °C is 23% higher than the value of D 2 O . [ 79 ] Because water molecules exchange hydrogen atoms with one another, hydrogen deuterium oxide (DOH) is much more common in low-purity heavy water than pure dideuterium monoxide D 2 O .
Consumption of pure isolated D 2 O may affect biochemical processes—ingestion of large amounts impairs kidney and central nervous system function. Small quantities can be consumed without any ill-effects; humans are generally unaware of taste differences, [ 80 ] but sometimes report a burning sensation [ 81 ] or sweet flavor. [ 82 ] Very large amounts of heavy water must be consumed for any toxicity to become apparent. Rats, however, are able to avoid heavy water by smell, and it is toxic to many animals. [ 83 ]
Light water refers to deuterium-depleted water (DDW), water in which the deuterium content has been reduced below the standard 155 ppm level.
Water is the most abundant substance on Earth's surface and also the third most abundant molecule in the universe, after H 2 and CO . [ 23 ] 0.23 ppm of the earth's mass is water and 97.39% of the global water volume of 1.38 × 10 9 km 3 is found in the oceans. [ 84 ]
Water is far more prevalent in the outer Solar System, beyond a point called the frost line , where the Sun's radiation is too weak to vaporize solid and liquid water (as well as other elements and chemical compounds with relatively low melting points, such as methane and ammonia ). In the inner Solar System, planets, asteroids, and moons formed almost entirely of metals and silicates. Water has since been delivered to the inner Solar System via an as-yet unknown mechanism, theorized to be the impacts of asteroids or comets carrying water from the outer Solar System, where bodies contain much more water ice. [ 85 ] The difference between planetary bodies located inside and outside the frost line can be stark. Earth's mass is 0.000023% water, while Tethys , a moon of Saturn, is almost entirely made of water. [ 86 ]
Water is amphoteric : it has the ability to act as either an acid or a base in chemical reactions. [ 87 ] According to the Brønsted-Lowry definition, an acid is a proton ( H + ) donor and a base is a proton acceptor. [ 88 ] When reacting with a stronger acid, water acts as a base; when reacting with a stronger base, it acts as an acid. [ 88 ] For instance, water receives an H + ion from HCl when hydrochloric acid is formed:
In the reaction with ammonia , NH 3 , water donates a H + ion, and is thus acting as an acid:
Because the oxygen atom in water has two lone pairs , water often acts as a Lewis base , or electron-pair donor, in reactions with Lewis acids , although it can also react with Lewis bases, forming hydrogen bonds between the electron pair donors and the hydrogen atoms of water. HSAB theory describes water as both a weak hard acid and a weak hard base, meaning that it reacts preferentially with other hard species:
When a salt of a weak acid or of a weak base is dissolved in water, water can partially hydrolyze the salt, producing the corresponding base or acid, which gives aqueous solutions of soap and baking soda their basic pH:
Water's Lewis base character makes it a common ligand in transition metal complexes, examples of which include metal aquo complexes such as Fe(H 2 O) 2+ 6 to perrhenic acid , which contains two water molecules coordinated to a rhenium center. In solid hydrates , water can be either a ligand or simply lodged in the framework, or both. Thus, FeSO 4 ·7H 2 O consists of [Fe(H 2 O) 6 ] 2+ centers and one "lattice water". Water is typically a monodentate ligand, i.e., it forms only one bond with the central atom. [ 89 ]
As a hard base, water reacts readily with organic carbocations ; for example in a hydration reaction , a hydroxyl group ( OH − ) and an acidic proton are added to the two carbon atoms bonded together in the carbon-carbon double bond, resulting in an alcohol. When the addition of water to an organic molecule cleaves the molecule in two, hydrolysis is said to occur. Notable examples of hydrolysis are the saponification of fats and the digestion of proteins and polysaccharides . Water can also be a leaving group in S N 2 substitution and E2 elimination reactions; the latter is then known as a dehydration reaction .
Water contains hydrogen in the oxidation state +1 and oxygen in the oxidation state −2. [ 90 ] It oxidizes chemicals such as hydrides , alkali metals , and some alkaline earth metals . [ 91 ] [ 92 ] One example of an alkali metal reacting with water is: [ 93 ]
Some other reactive metals, such as aluminium and beryllium , are oxidized by water as well, but their oxides adhere to the metal and form a passive protective layer. [ 94 ] Note that the rusting of iron is a reaction between iron and oxygen [ 95 ] that is dissolved in water, not between iron and water.
Water can be oxidized to emit oxygen gas, but very few oxidants react with water even if their reduction potential is greater than the potential of O 2 /H 2 O . Almost all such reactions require a catalyst . [ 96 ] An example of the oxidation of water is:
Water can be split into its constituent elements, hydrogen and oxygen, by passing an electric current through it. [ 97 ] This process is called electrolysis. The cathode half reaction is:
The anode half reaction is:
The gases produced bubble to the surface, where they can be collected or ignited with a flame above the water if this was the intention. The required potential for the electrolysis of pure water is 1.23 V at 25 °C. [ 97 ] The operating potential is actually 1.48 V or higher in practical electrolysis.
Henry Cavendish showed that water was composed of oxygen and hydrogen in 1781. [ 98 ] The first decomposition of water into hydrogen and oxygen, by electrolysis , was done in 1800 by English chemist William Nicholson and Anthony Carlisle . [ 98 ] [ 99 ] In 1805, Joseph Louis Gay-Lussac and Alexander von Humboldt showed that water is composed of two parts hydrogen and one part oxygen. [ 100 ]
Gilbert Newton Lewis isolated the first sample of pure heavy water in 1933. [ 101 ]
The properties of water have historically been used to define various temperature scales . Notably, the Kelvin , Celsius , Rankine , and Fahrenheit scales were, or currently are, defined by the freezing and boiling points of water. The less common scales of Delisle , Newton , Réaumur , and Rømer were defined similarly. The triple point of water is a more commonly used standard point today.
The accepted IUPAC name of water is oxidane or simply water , [ 102 ] or its equivalent in different languages, although there are other systematic names which can be used to describe the molecule. Oxidane is only intended to be used as the name of the mononuclear parent hydride used for naming derivatives of water by substituent nomenclature . [ 103 ] These derivatives commonly have other recommended names. For example, the name hydroxyl is recommended over oxidanyl for the –OH group. The name oxane is explicitly mentioned by the IUPAC as being unsuitable for this purpose, since it is already the name of a cyclic ether also known as tetrahydropyran . [ 3 ] [ 104 ]
The simplest systematic name of water is hydrogen oxide . This is analogous to related compounds such as hydrogen peroxide , hydrogen sulfide , and deuterium oxide (heavy water). Using chemical nomenclature for type I ionic binary compounds , water would take the name hydrogen monoxide , [ 105 ] but this is not among the names published by the International Union of Pure and Applied Chemistry (IUPAC). [ 102 ] Another name is dihydrogen monoxide , which is a rarely used name of water, and mostly used in the dihydrogen monoxide parody .
Other systematic names for water include hydroxic acid , hydroxylic acid , and hydrogen hydroxide , using acid and base names. [ j ] None of these exotic names are used widely. The polarized form of the water molecule, H + OH − , is also called hydron hydroxide by IUPAC nomenclature. [ 106 ]
Water substance is a rare term used for H 2 O when one does not wish to specify the phase of matter (liquid water, water vapor , some form of ice , or a component in a mixture) though the term water is also used with this general meaning.
Oxygen dihydride is another way of referring to water, but modern usage often restricts the term " hydride " to ionic compounds (which water is not). | https://en.wikipedia.org/wiki/HOH |
HOME STAR , (also spelled HOMESTAR ), informally known as Cash for Caulkers , is a United States government program proposed in November 2009 to encourage economic growth by offering incentives to homeowners and retailers for improving the energy efficiency of existing homes. [ 1 ]
In late 2009 there was a broad perception that the United States economy was beginning to recover from the Late-2000s recession . There was a broad perception that government spending authorized by the American Recovery and Reinvestment Act of 2009 had contributed to the recovery, and some desire for the government to do more to encourage job growth and a faster recovery. [ 2 ]
In mid-November former president Bill Clinton , and John Doerr of Barack Obama 's President's Economic Recovery Advisory Board , proposed different versions of an economic stimulus program by which the government would offer tax incentives to encourage people to improve the energy efficiency of their homes. [ 2 ] Doerr, in public speeches, called the proposal "cash for caulkers". Separately U.S. Representative Peter Welch proposed a system of energy rebates to Rahm Emanuel , Obama’s Chief of Staff . [ 3 ] Obama, in turn, proposed the idea as part of a larger new stimulus program, at a speech at the Brookings Institution on December 8, 2009. [ 4 ]
The stated goals of the proposed program are to reduce pollution, particularly greenhouse gases , by reducing household energy use, to save consumers money in the long term through lower power bills, and to stimulate American businesses through the money spent on appliances, materials, and installation. Improving the energy efficiency of "fixed infrastructure", which accounts for approximately 40% of all energy use in the United States, is considered the "low hanging fruit" of energy conservation - a step that achieves results relatively inexpensively and does not require any new technologies or changes to production or consumption methods. [ 5 ]
The name "Homestar" is a reference to the popular energy star electronic device efficiency rating system, and the nickname "Cash for Caulkers" is a play on the earlier cash for clunkers automobile trade-in incentive. [ 3 ]
As of December 2009, no proposed legislation had been released, and there were few specific details of how the program would be administered, which federal agencies would be involved, or how the tax incentives would be paid (or to whom). [ 3 ] The program is expected to involve preliminary energy audits by private contractor energy experts, who then recommend a series of steps for each homeowner to upgrade their home's energy efficiency. [ 6 ] As proposed the plan was for the government to pay 50% of the cost of each home improvement project through a rebate, tax credit , or funds paid to manufacturers and retailers, up to a maximum of $12,000 (~$16,568 in 2023) paid for each home. [ 6 ] Alternatively, there was speculation that the federal government might give funds to local governments to run their own programs. There was no limitation on eligibility based on tax bracket or income . [ 6 ]
Items under consideration for the program included weatherization of home by installing additional insulation, new doors, and windows, and replacing old appliances with more energy-efficient new ones. Expensive items such as washing machines, dishwashers, refrigerators, air conditioners, and heaters, would be covered. [ 6 ]
The program was expected to cost approximately $10 billion over the course of one year, paid for out of unspent Troubled Asset Relief Program funds, and would reduce energy consumption of homes that took full advantage of the program by up to 20%. To become effective it would have to be part of a bill passed by the United States Congress . [ 6 ] | https://en.wikipedia.org/wiki/HOME_STAR |
In the mathematical field of knot theory , the HOMFLY polynomial or HOMFLYPT polynomial , sometimes called the generalized Jones polynomial , is a 2-variable knot polynomial , i.e. a knot invariant in the form of a polynomial of variables m and l .
A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. One tool used to answer such questions is a knot polynomial, which is computed from a diagram of the knot and can be shown to be an invariant of the knot , i.e. diagrams representing the same knot have the same polynomial . The converse may not be true. The HOMFLY polynomial is one such invariant and it generalizes two polynomials previously discovered, the Alexander polynomial and the Jones polynomial , both of which can be obtained by appropriate substitutions from HOMFLY. The HOMFLY polynomial is also a quantum invariant .
The name HOMFLY combines the initials of its co-discoverers: Jim Hoste , Adrian Ocneanu , Kenneth Millett , Peter J. Freyd , W. B. R. Lickorish , and David N. Yetter. [ 1 ] The addition of PT recognizes independent work carried out by Józef H. Przytycki and Paweł Traczyk. [ 2 ]
The polynomial is defined using skein relations :
where L + , L − , L 0 {\displaystyle L_{+},L_{-},L_{0}} are links formed by crossing and smoothing changes on a local region of a link diagram, as indicated in the figure.
The HOMFLY polynomial of a link L that is a split union of two links L 1 {\displaystyle L_{1}} and L 2 {\displaystyle L_{2}} is given by
See the page on skein relation for an example of a computation using such relations.
This polynomial can be obtained also using other skein relations:
The Jones polynomial, V ( t ), and the Alexander polynomial, Δ ( t ) {\displaystyle \Delta (t)\,} can be computed in terms of the HOMFLY polynomial (the version in α {\displaystyle \alpha } and z {\displaystyle z} variables) as follows: | https://en.wikipedia.org/wiki/HOMFLY_polynomial |
In chemistry , HOMO and LUMO are types of molecular orbitals . The acronyms stand for highest occupied molecular orbital and lowest unoccupied molecular orbital , respectively. HOMO and LUMO are sometimes collectively called the frontier orbitals , such as in the frontier molecular orbital theory .
The energy difference between the HOMO and LUMO is the HOMO–LUMO gap . Its size can be used to predict the strength and stability of transition metal complexes , as well as the colors they produce in solution. [ 1 ] As a rule of thumb, the smaller a compound's HOMO–LUMO gap, the less stable the compound. [ 2 ]
The HOMO level is to organic semiconductors roughly what the maximum valence band is to inorganic semiconductors and quantum dots . The same analogy can be made between the LUMO level and the conduction band minimum. [ 3 ]
In organometallic chemistry, the size of the LUMO lobe can help predict where addition to pi ligands will occur.
A SOMO is a singly occupied molecular orbital such as half-filled HOMO of a radical . [ 4 ] This abbreviation may also be extended to semi occupied molecular orbital .
If existent, the molecular orbitals at one energy level below the HOMO and one energy level above the LUMO are also found to play a role in frontier molecular orbital theory. They are named NHOMO for next-to-highest occupied molecular orbital and SLUMO for second lowest unoccupied molecular orbital . [ 5 ] These are also commonly referred to as HOMO−1 and LUMO+1 respectively. [ 6 ]
This quantum chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HOMO_and_LUMO |
Hydroxylamine (also known as hydroxyammonia ) is an inorganic compound with the chemical formula N H 2 O H . The compound exists as hygroscopic colorless crystals . [ 4 ] Hydroxylamine is almost always provided and used as an aqueous solution or more often as one of its salts such as hydroxylammonium sulfate , a water-soluble solid.
Hydroxylamine and its salts are consumed almost exclusively to produce Nylon-6 . The oxidation of NH 3 to hydroxylamine is a step in biological nitrification . [ 5 ]
Hydroxylamine was first prepared as hydroxylammonium chloride in 1865 by the German chemist Wilhelm Clemens Lossen (1838-1906); he reacted tin and hydrochloric acid in the presence of ethyl nitrate . [ 6 ] It was first prepared in pure form in 1891 by the Dutch chemist Lobry de Bruyn and by the French chemist Léon Maurice Crismer (1858-1944). [ 7 ] [ 8 ] The coordination complex ZnCl 2 (NH 2 OH) 2 (zinc dichloride di(hydroxylamine)), known as Crismer's salt, releases hydroxylamine upon heating. [ 9 ]
Hydroxylamine and its N -substituted derivatives are pyramidal at nitrogen, with bond angles very similar to those of amines. The conformation of hydroxylamine places the NOH anti to the lone pair on nitrogen, seeming to minimize lone pair-lone pair interactions. [ 10 ]
Hydroxylamine or its salts (salts containing hydroxylammonium cations [NH 3 OH] + ) can be produced via several routes but only two are commercially viable. It is also produced naturally as discussed in a section on biochemistry .
NH 2 OH is mainly produced as its sulfuric acid salt , hydroxylammonium sulfate ( [NH 3 OH][SO 4 ] ), by the hydrogenation of nitric oxide over platinum catalysts in the presence of sulfuric acid. [ 11 ]
Another route to NH 2 OH is the Raschig process : aqueous ammonium nitrite is reduced by HSO − 3 and SO 2 at 0 °C to yield a hydroxylamido- N , N -disulfonate anion :
This ammonium hydroxylamine disulfonate anion is then hydrolyzed to give hydroxylammonium sulfate :
Julius Tafel discovered that hydroxylamine hydrochloride or sulfate salts can be produced by electrolytic reduction of nitric acid with HCl or H 2 SO 4 respectively: [ 12 ] [ 13 ]
Hydroxylamine can also be produced by the reduction of nitrous acid or potassium nitrite with bisulfite :
Hydrochloric acid disproportionates nitromethane to hydroxylamine hydrochloride and carbon monoxide via the hydroxamic acid . [ citation needed ]
A direct lab synthesis of hydroxylamine from molecular nitrogen in water plasma was demonstrated in 2024. [ 14 ]
Solid NH 2 OH can be collected by treatment with liquid ammonia . Ammonium sulfate , [NH 4 ] 2 SO 4 , a side-product insoluble in liquid ammonia, is removed by filtration; the liquid ammonia is evaporated to give the desired product. [ 4 ] The net reaction is:
Base, such as sodium butoxide, can be used to free the hydroxylamine from hydroxylammonium chloride : [ 4 ]
Hydroxylamine is a base with a pKa of 6.03:
Hydroxylamine reacts with alkylating agents usually at the nitrogen atom:
The reaction of NH 2 OH with an aldehyde or ketone produces an oxime .
This reaction can be useful in the purification of ketones and aldehydes: if hydroxylamine is added to an aldehyde or ketone in solution, an oxime forms, which generally precipitates from solution; heating the precipitate with aqueous acid then restores the original aldehyde or ketone. [ 15 ]
NH 2 OH reacts with chlorosulfonic acid to give hydroxylamine- O -sulfonic acid : [ 16 ]
It isomerizes to the amine oxide H 3 N + −O − . [ 17 ]
Hydroxylamine derivatives substituted in place of the hydroxyl or amine hydrogen are (respectively) called O - or N ‑hydroxylamines. In general N ‑hydroxylamines are more common. Examples are N ‑ tert ‑butylhydroxylamine or the glycosidic bond in calicheamicin . N , O ‑Dimethylhydroxylamine is a precursor to Weinreb amides .
Similarly to amines, one can distinguish hydroxylamines by their degree of substitution: primary, secondary and tertiary. When stored exposed to air for weeks, secondary hydroxylamines degrade to nitrones . [ 18 ]
N ‑organylhydroxylamines, R−NH−OH , where R is an organyl group, can be reduced to amines R−NH 2 : [ 19 ]
Oximes such as dimethylglyoxime are also employed as ligands .
The hydrolysis of N-substituted oximes, hydroxamic acids, and nitrones easily provides hydroxylamines.
Alkylating of hydroxylamine or N-alkylhydroxylamines proceeds usually at nitrogen. One challenge is dialkylation when only monoalkylation is desired.
For O-alkylation of hydroxylamines, strong base such as sodium hydride is required to first deprotonate the OH group: [ 20 ]
Amine oxidation with benzoyl peroxide is a common method to synthesize hydroxylamines. Care must be taken to prevent over-oxidation to a nitrone . Other methods include:
Approximately 95% of hydroxylamine is used in the synthesis of cyclohexanone oxime , a precursor to Nylon 6 . [ 11 ] The treatment of this oxime with acid induces the Beckmann rearrangement to give caprolactam . [ 21 ] The latter can then undergo a ring-opening polymerization to yield Nylon 6. [ 22 ]
Hydroxylamine and its salts are commonly used as reducing agents in myriad organic and inorganic reactions. They can also act as antioxidants for fatty acids.
High concentrations of hydroxylamine are used by biologists to introduce mutations by acting as a DNA nucleobase amine-hydroxylating agent. [ 23 ] In is thought to mainly act via hydroxylation of cytidine to hydroxyaminocytidine, which is misread as thymidine, thereby inducing C:G to T:A transition mutations. [ 24 ] But high concentrations or over-reaction of hydroxylamine in vitro are seemingly able to modify other regions of the DNA & lead to other types of mutations. [ 24 ] This may be due to the ability of hydroxylamine to undergo uncontrolled free radical chemistry in the presence of trace metals and oxygen, in fact in the absence of its free radical affects Ernst Freese noted hydroxylamine was unable to induce reversion mutations of its C:G to T:A transition effect and even considered hydroxylamine to be the most specific mutagen known. [ 25 ] Practically, it has been largely surpassed by more potent mutagens such as EMS , ENU , or nitrosoguanidine , but being a very small mutagenic compound with high specificity, it found some specialized uses such as mutation of DNA packed within bacteriophage capsids, [ 26 ] and mutation of purified DNA in vitro . [ 27 ]
An alternative industrial synthesis of paracetamol developed by Hoechst – Celanese involves the conversion of ketone to a ketoxime with hydroxylamine.
Some non-chemical uses include removal of hair from animal hides and photographic developing solutions. [ 2 ] In the semiconductor industry, hydroxylamine is often a component in the "resist stripper", which removes photoresist after lithography.
Hydroxylamine can also be used to better characterize the nature of a post-translational modification onto proteins. For example, poly(ADP-Ribose) chains are sensitive to hydroxylamine when attached to glutamic or aspartic acids but not sensitive when attached to serines. [ 28 ] Similarly, Ubiquitin molecules bound to serines or threonines residues are sensitive to hydroxylamine, but those bound to lysine (isopeptide bond) are resistant. [ 29 ]
In biological nitrification, the oxidation of NH 3 to hydroxylamine is mediated by the ammonia monooxygenase (AMO). [ 5 ] Hydroxylamine oxidoreductase (HAO) further oxidizes hydroxylamine to nitrite. [ 30 ]
Cytochrome P460, an enzyme found in the ammonia-oxidizing bacteria Nitrosomonas europea , can convert hydroxylamine to nitrous oxide , a potent greenhouse gas . [ 31 ]
Hydroxylamine can also be used to highly selectively cleave asparaginyl - glycine peptide bonds in peptides and proteins. [ 32 ] It also bonds to and permanently disables (poisons) heme-containing enzymes . It is used as an irreversible inhibitor of the oxygen-evolving complex of photosynthesis on account of its similar structure to water.
Hydroxylamine is a skin irritant but is of low toxicity.
A detonator can easily explode aqueous solutions concentrated above 80% by weight, and even 50% solution might prove detonable if tested in bulk. [ 33 ] [ 34 ] In air, the combustion is rapid and complete:
Absent air, pure hydroxylamine requires stronger heating and the detonation does not complete combustion:
At least two factories dealing in hydroxylamine have been destroyed since 1999 with loss of life. [ 35 ] It is known, however, that ferrous and ferric iron salts accelerate the decomposition of 50% NH 2 OH solutions. [ 36 ] Hydroxylamine and its derivatives are more safely handled in the form of salts .
It is an irritant to the respiratory tract , skin, eyes, and other mucous membranes . It may be absorbed through the skin, is harmful if swallowed, and is a possible mutagen . [ 37 ] | https://en.wikipedia.org/wiki/HONH2 |
Aspartic acid (symbol Asp or D ; [ 4 ] the ionic form is known as aspartate ), is an α- amino acid that is used in the biosynthesis of proteins. [ 5 ] The L -isomer of aspartic acid is one of the 22 proteinogenic amino acids , i.e., the building blocks of proteins . D -aspartic acid is one of two D -amino acids commonly found in mammals. [ 6 ] [ 7 ] Apart from a few rare exceptions, D -aspartic acid is not used for protein synthesis but is incorporated into some peptides and plays a role as a neurotransmitter / neuromodulator . [ 6 ]
Like all other amino acids, aspartic acid contains an amino group and a carboxylic acid. Its α-amino group is in the protonated –NH + 3 form under physiological conditions, while its α-carboxylic acid group is deprotonated −COO − under physiological conditions. Aspartic acid has an acidic side chain (CH 2 COOH) which reacts with other amino acids, enzymes and proteins in the body. [ 5 ] Under physiological conditions (pH 7.4) in proteins the side chain usually occurs as the negatively charged aspartate form, −COO − . [ 5 ] It is a non- essential amino acid in humans, meaning the body can synthesize it as needed. It is encoded by the codons GAU and GAC.
In proteins aspartate sidechains are often hydrogen bonded to form asx turns or asx motifs , which frequently occur at the N-termini of alpha helices .
Aspartic acid, like glutamic acid , is classified as an acidic amino acid, with a pK a of 3.9; however, in a peptide this is highly dependent on the local environment, and could be as high as 14.
The one-letter code D for aspartate was assigned arbitrarily, [ 8 ] with the proposed mnemonic aspar D ic acid. [ 9 ]
Aspartic acid was first discovered in 1827 by Auguste-Arthur Plisson and Étienne-Ossian Henry [ 10 ] [ 11 ] by hydrolysis of asparagine , which had been isolated from asparagus juice in 1806. [ 12 ] Their original method used lead hydroxide , but various other acids or bases are now more commonly used instead. [ citation needed ]
There are two forms or enantiomers of aspartic acid. The name "aspartic acid" can refer to either enantiomer or a mixture of two. [ 13 ] Of these two forms, only one, " L -aspartic acid", is directly incorporated into proteins. The biological roles of its counterpart, " D -aspartic acid" are more limited. Where enzymatic synthesis will produce one or the other, most chemical syntheses will produce both forms, " DL -aspartic acid", known as a racemic mixture . [ citation needed ]
In the human body, aspartate is most frequently synthesized through the transamination of oxaloacetate . The biosynthesis of aspartate is facilitated by an aminotransferase enzyme: the transfer of an amine group from another molecule such as alanine or glutamine yields aspartate and an alpha-keto acid. [ 5 ]
Industrially, aspartate is produced by amination of fumarate catalyzed by L- aspartate ammonia-lyase . [ 14 ]
Racemic aspartic acid can be synthesized from diethyl sodium phthalimidomalonate,
(C 6 H 4 (CO) 2 NC(CO 2 Et) 2 ). [ 15 ]
In plants and microorganisms , aspartate is the precursor to several amino acids, including four that are essential for humans: methionine , threonine , isoleucine , and lysine . The conversion of aspartate to these other amino acids begins with reduction of aspartate to its "semialdehyde", O 2 CCH(NH 2 )CH 2 CHO. [ 16 ] Asparagine is derived from aspartate via transamidation:
(where G C(O)NH 2 and G C(O)OH are glutamine and glutamic acid , respectively)
Aspartate has many other biochemical roles. It is a metabolite in the urea cycle [ 17 ] and participates in gluconeogenesis . It carries reducing equivalents in the malate-aspartate shuttle , which utilizes the ready interconversion of aspartate and oxaloacetate , which is the oxidized (dehydrogenated) derivative of malic acid . Aspartate donates one nitrogen atom in the biosynthesis of inosine , the precursor to the purine bases. In addition, aspartic acid acts as a hydrogen acceptor in a chain of ATP synthase. Dietary L-aspartic acid has been shown to act as an inhibitor of Beta-glucuronidase , which serves to regulate enterohepatic circulation of bilirubin and bile acids. [ 18 ]
Click on genes, proteins and metabolites below to link to respective articles. [ § 1 ]
Aspartate (the conjugate base of aspartic acid) stimulates NMDA receptors , though not as strongly as the amino acid neurotransmitter L-glutamate does. [ 19 ] Aspartate is the "A" in NMDA (N-methyl-D- aspartate receptor).
In 2014, the global market for aspartic acid was 39.3 thousand short tons (35.7 thousand tonnes ) [ 20 ] or about $117 million annually. [ 21 ] The three largest market segments include the U.S., Western Europe, and China. Current applications include biodegradable polymers ( polyaspartic acid ), low calorie sweeteners ( aspartame ), scale and corrosion inhibitors, and resins. [ citation needed ]
One area of aspartic acid market growth is biodegradable superabsorbent polymers (SAP), and hydrogels. [ 22 ] Around 75% of superabsorbent polymers are used in disposable diapers and an additional 20% is used for adult incontinence and feminine hygiene products. Polyaspartic acid , the polymerization product of aspartic acid, is a biodegradable substitute to polyacrylate . [ 22 ] [ 23 ] [ 24 ]
In addition to SAP, aspartic acid has applications in the fertilizer industry , where polyaspartate improves water retention and nitrogen uptake. [ 25 ]
Aspartic acid is not an essential amino acid , which means that it can be synthesized from central metabolic pathway intermediates in humans, and does not need to be present in the diet. In eukaryotic cells, roughly 1 in 20 amino acids incorporated into a protein is an aspartic acid, [ 26 ] and accordingly almost any source of dietary protein will include aspartic acid. Additionally, aspartic acid is found in: | https://en.wikipedia.org/wiki/HOOCCH(NH2)CH2COOH |
Citric acid is an organic compound with the formula C 6 H 8 O 7 . [ 10 ] It is a colorless weak organic acid . [ 10 ] It occurs naturally in citrus fruits . In biochemistry , it is an intermediate in the citric acid cycle , which occurs in the metabolism of all aerobic organisms . [ 10 ]
More than two million tons of citric acid are manufactured every year. It is used widely as acidifier , flavoring , preservative , and chelating agent . [ 11 ]
A citrate is a derivative of citric acid; that is, the salts , esters , and the polyatomic anion found in solutions and salts of citric acid. An example of the former, a salt is trisodium citrate ; an ester is triethyl citrate . When citrate trianion is part of a salt, the formula of the citrate trianion is written as C 6 H 5 O 3− 7 or C 3 H 5 O(COO) 3− 3 .
Citric acid occurs in a variety of fruits and vegetables, most notably citrus fruits . Lemons and limes have particularly high concentrations of the acid; it can constitute as much as 8% of the dry weight of these fruits (about 47 g/L in the juices [ 12 ] ). [ a ] The concentrations of citric acid in citrus fruits range from 0.005 mol/L for oranges and grapefruits to 0.30 mol/L in lemons and limes; these values vary within species depending upon the cultivar and the circumstances under which the fruit was grown. [ citation needed ]
Citric acid was first isolated in 1784 by the chemist Carl Wilhelm Scheele , who crystallized it from lemon juice. [ 13 ] [ 14 ]
Industrial-scale citric acid production first began in 1890 based on the Italian citrus fruit industry, where the juice was treated with hydrated lime ( calcium hydroxide ) to precipitate calcium citrate , which was isolated and converted back to the acid using diluted sulfuric acid . [ 15 ] In 1893, C. Wehmer discovered Penicillium mold could produce citric acid from sugar. [ 16 ] However, microbial production of citric acid did not become industrially important until World War I disrupted Italian Citrus exports. [ citation needed ]
In 1917, American food chemist James Currie discovered that certain strains of the mold Aspergillus niger could be efficient citric acid producers, [ 17 ] and the pharmaceutical company Pfizer began industrial-level production using this technique two years later, followed by Citrique Belge in 1929. In this production technique, which is still the major industrial route to citric acid used today, cultures of Aspergillus niger are fed on a sucrose or glucose -containing medium to produce citric acid. The source of sugar is corn steep liquor , molasses , hydrolyzed corn starch , or other inexpensive, carbohydrate solution. [ 18 ] After the mold is filtered out of the resulting suspension , citric acid is isolated by precipitating it with calcium hydroxide to yield calcium citrate salt, from which citric acid is regenerated by treatment with sulfuric acid, as in the direct extraction from citrus fruit juice.
In 1977, a patent was granted to Lever Brothers for the chemical synthesis of citric acid starting either from aconitic or isocitrate (also called alloisocitrate) calcium salts under high pressure conditions; this produced citric acid in near quantitative conversion under what appeared to be a reverse, non-enzymatic Krebs cycle reaction . [ 19 ]
Global production was in excess of 2,000,000 tons in 2018. [ 20 ] More than 50% of this volume was produced in China. More than 50% was used as an acidity regulator in beverages, some 20% in other food applications, 20% for detergent applications, and 10% for applications other than food, such as cosmetics, pharmaceuticals, and in the chemical industry. [ 15 ]
Citric acid can be obtained as an anhydrous (water-free) form or as a monohydrate . The anhydrous form crystallizes from hot water, while the monohydrate forms when citric acid is crystallized from cold water. The monohydrate can be converted to the anhydrous form at about 78 °C. Citric acid also dissolves in absolute (anhydrous) ethanol (76 parts of citric acid per 100 parts of ethanol) at 15 °C. It decomposes with loss of carbon dioxide above about 175 °C.
Citric acid is a triprotic acid , with pK a values, extrapolated to zero ionic strength, of 3.128, 4.761, and 6.396 at 25 °C. [ 21 ] The pK a of the hydroxyl group has been found, by means of 13 C NMR spectroscopy , to be 14.4. [ 22 ] The speciation diagram shows that solutions of citric acid are buffer solutions between about pH 2 and pH 8. In biological systems around pH 7, the two species present are the citrate ion and mono-hydrogen citrate ion. The SSC 20X hybridization buffer is an example in common use. [ 23 ] [ 24 ] Tables compiled for biochemical studies are available. [ 25 ]
Conversely, the pH of a 1 mM solution of citric acid will be about 3.2. The pH of fruit juices from citrus fruits like oranges and lemons depends on the citric acid concentration, with a higher concentration of citric acid resulting in a lower pH.
Acid salts of citric acid can be prepared by careful adjustment of the pH before crystallizing the compound. See, for example, sodium citrate .
The citrate ion forms complexes with metallic cations. The stability constants for the formation of these complexes are quite large because of the chelate effect . Consequently, it forms complexes even with alkali metal cations. However, when a chelate complex is formed using all three carboxylate groups, the chelate rings have 7 and 8 members, which are generally less stable thermodynamically than smaller chelate rings. In consequence, the hydroxyl group can be deprotonated, forming part of a more stable 5-membered ring, as in ammonium ferric citrate , [NH + 4 ] 5 Fe 3+ (C 6 H 4 O 4− 7 ) 2 ·2H 2 O . [ 26 ]
Citric acid can be esterified at one or more of its three carboxylic acid groups to form any of a variety of mono-, di-, tri-, and mixed esters. [ 27 ]
Citrate is an intermediate in the citric acid cycle , also known as the tricarboxylic acid ( TCA ) cycle or the Krebs cycle , a central metabolic pathway for animals, plants, and bacteria. In the Krebs cycle, citrate synthase catalyzes the condensation of oxaloacetate with acetyl CoA to form citrate. Citrate then acts as the substrate for aconitase and is converted into aconitic acid . The cycle ends with regeneration of oxaloacetate. This series of chemical reactions is the source of two-thirds of the food-derived energy in higher organisms. The chemical energy released is available under the form of Adenosine triphosphate (ATP). Hans Adolf Krebs received the 1953 Nobel Prize in Physiology or Medicine for the discovery.
Citrate can be transported out of the mitochondria and into the cytoplasm, then broken down into acetyl-CoA for fatty acid synthesis , and into oxaloacetate. Citrate is a positive modulator of this conversion, and allosterically regulates the enzyme acetyl-CoA carboxylase , which is the regulating enzyme in the conversion of acetyl-CoA into malonyl-CoA (the commitment step in fatty acid synthesis). In short, citrate is transported into the cytoplasm, converted into acetyl-CoA, which is then converted into malonyl-CoA by acetyl-CoA carboxylase, which is allosterically modulated by citrate.
High concentrations of cytosolic citrate can inhibit phosphofructokinase , the catalyst of a rate-limiting step of glycolysis . This effect is advantageous: high concentrations of citrate indicate that there is a large supply of biosynthetic precursor molecules, so there is no need for phosphofructokinase to continue to send molecules of its substrate, fructose 6-phosphate , into glycolysis. Citrate acts by augmenting the inhibitory effect of high concentrations of ATP , another sign that there is no need to carry out glycolysis. [ 28 ]
Citrate is a vital component of bone, helping to regulate the size of apatite crystals. [ 29 ]
Because it is one of the stronger edible acids, the dominant use of citric acid is as a flavoring and preservative in food and beverages, especially soft drinks and candies. [ 15 ] Within the European Union it is denoted by E number E330 . Citrate salts of various metals are used to deliver those minerals in a biologically available form in many dietary supplements . Citric acid has 247 kcal per 100 g. [ 30 ] In the United States the purity requirements for citric acid as a food additive are defined by the Food Chemicals Codex , which is published by the United States Pharmacopoeia (USP). [ citation needed ]
Citric acid can be added to ice cream as an emulsifying agent to keep fats from separating, to caramel to prevent sucrose crystallization, or in recipes in place of fresh lemon juice. Citric acid is used with sodium bicarbonate in a wide range of effervescent formulae, both for ingestion (e.g., powders and tablets) and for personal care ( e.g. , bath salts , bath bombs , and cleaning of grease ). Citric acid sold in a dry powdered form is commonly sold in markets and groceries as "sour salt", due to its physical resemblance to table salt. It has use in culinary applications, as an alternative to vinegar or lemon juice, where a pure acid is needed. Citric acid can be used in food coloring to balance the pH level of a normally basic dye. [ citation needed ]
Citric acid is an excellent chelating agent , binding metals by making them soluble. It is used to remove and discourage the buildup of limescale from boilers and evaporators. [ 15 ] It can be used to treat water, which makes it useful in improving the effectiveness of soaps and laundry detergents. By chelating the metals in hard water , it lets these cleaners produce foam and work better without need for water softening. Citric acid is the active ingredient in some bathroom and kitchen cleaning solutions. A solution with a six percent concentration of citric acid will remove hard water stains from glass without scrubbing. Citric acid can be used in shampoo to wash out wax and coloring from the hair. Illustrative of its chelating abilities, citric acid was the first successful eluant used for total ion-exchange separation of the lanthanides , during the Manhattan Project in the 1940s. [ 33 ] In the 1950s, it was replaced by the far more efficient [ 34 ] EDTA .
In industry, it is used to dissolve rust from steel, and to passivate stainless steels . [ 35 ]
Citric acid is used as an acidulant in creams, gels, and liquids. Used in foods and dietary supplements, it may be classified as a processing aid if it was added for a technical or functional effect (e.g. acidulent, chelator, viscosifier, etc.). If it is still present in insignificant amounts, and the technical or functional effect is no longer present, it may be exempt from labeling <21 CFR §101.100(c)>.
Citric acid is an alpha hydroxy acid and is an active ingredient in chemical skin peels. [ 36 ]
Citric acid is commonly used as a buffer to increase the solubility of brown heroin . [ 37 ]
Citric acid is used as one of the active ingredients in the production of facial tissues with antiviral properties. [ 38 ]
The buffering properties of citrates are used to control pH in household cleaners and pharmaceuticals . [ 39 ] [ 40 ]
Citric acid is used as an odorless alternative to white vinegar for fabric dyeing with acid dyes . [ 41 ] It can enhance the mordanting process, crosslinking fabrics and dyes through an esterification reaction. [ 42 ]
Sodium citrate is a component of Benedict's reagent , used for both qualitative and quantitative identification of reducing sugars. [ 43 ]
Citric acid can be used as an alternative to nitric acid in passivation of stainless steel . [ 44 ]
Citric acid can be used as a lower-odor stop bath as part of the process for developing photographic film . Photographic developers are alkaline, so a mild acid is used to neutralize and stop their action quickly, but commonly used acetic acid leaves a strong vinegar odor in the darkroom. [ 45 ]
Citric acid is an excellent soldering flux , [ 46 ] either dry or as a concentrated solution in water. It should be removed after soldering, especially with fine wires, as it is mildly corrosive. It dissolves and rinses quickly in hot water.
Alkali citrate can be used as an inhibitor of kidney stones by increasing urine citrate levels, useful for prevention of calcium stones, and increasing urine pH, useful for preventing uric acid and cystine stones. [ 47 ]
Citric acid is a versatile precursor to many other organic compounds. Dehydration routes give itaconic acid and its anhydride. [ 48 ] Citraconic acid can be produced via thermal isomerization of itaconic acid anhydride. [ 49 ] The required itaconic acid anhydride is obtained by dry distillation of citric acid. Aconitic acid can be synthesized by dehydration of citric acid using sulfuric acid : [ 50 ]
Acetonedicarboxylic acid can also be prepared by decarboxylation of citric acid in fuming sulfuric acid. [ 51 ]
Although a weak acid, exposure to pure citric acid can cause adverse effects. Inhalation may cause cough, shortness of breath, or sore throat. Over-ingestion may cause abdominal pain and sore throat. Exposure of concentrated solutions to skin and eyes can cause redness and pain. [ 52 ] Long-term or repeated consumption may cause erosion of tooth enamel . [ 52 ] [ 53 ] [ 54 ] | https://en.wikipedia.org/wiki/HOOCCH2(OH)C(COOH)CH2COOH |
HORTA is an underground geographic positioning technology utilized in the mining industry and being considered for extraterrestrial space mining applications. The technology utilizes a gyroscope and an accelerometer , together called an inertial navigation system or INS, to aid in 3D -position determination.
It was developed by Canadian mining company Inco in the late 1990s, based on an earlier technology that had been originally developed for the United States Armed Forces . It provides an automated solution to the problem of positioning and location in underground mines . [ 1 ]
The term is a backronym for the Horta, an alien species seen in the Star Trek episode " The Devil in the Dark "; the aliens were excellent miners. [ 2 ] As Inco uses the term, HORTA stands for Honeywell Ore Retrieval and Tunneling Aid. [ 1 ]
A mining vehicle, "with a HORTA mounted, can survey much faster and more accurately than manual surveys. It takes the truck 120 minutes to survey a 1.6-km-long drift, recording 1,500 points every 60 cm. This compares with a manual survey of the same distance that takes 180 hours, and records only five points every 6 m. Added benefits from such a detailed survey would be to allow engineers to design more effective ventilation systems , or to regularly check ground stability." [ 1 ]
HORTA units may be fitted onto all mobile underground equipment, including drills, [ 1 ] so their position may be determined with acceptable engineering accuracy.
This article about mining is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HORTA_(mining) |
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/HOSCN |
Hexafluorophosphoric acid refers to a family of salts produced by combining phosphorus pentafluoride and hydrofluoric acid . The idealized chemical formula for hexafluorophosphoric acid
is HPF 6 , which also is written H[PF 6 ] . [ 3 ] Hexafluorophosphoric acid is only stable in solution, decomposing to HF and PF 5 when dry. [ 4 ] It exothermically reacts with water to produce oxonium hexafluorophosphate ( [H 3 O] + [PF 6 ] − ) and hydrofluoric acid. Additionally, such solutions often contain products derived from hydrolysis of the P-F bonds, including HPO 2 F 2 , H 2 PO 3 F , and H 3 PO 4 , and their conjugate bases. [ 5 ] Hexafluorophosphoric acid attacks glass. Upon heating, it decomposes to generate HF. Crystalline HPF 6 has been obtained as the hexahydrate, wherein PF − 6 is enclosed in truncated octahedral cages defined by the water and protons. NMR spectroscopy indicates that solutions derived from this hexahydrate contain significant amounts of HF. [ 5 ]
Whereas a species with the formula HPF 6 remains unknown, the analogous molecular hexafluoroarsenic acid (HAsF 6 ) has been crystallized. [ 6 ] | https://en.wikipedia.org/wiki/HPF6 |
hPG80 refers to the extracellular and oncogenic version of progastrin . This name first appeared in a scientific publication in January 2020. [ 1 ] Until that date, scientific publications only mention ' progastrin ', without necessarily explicitly specifying whether it is intracellular (in the context of digestion ) or extracellular (circulating and detectable in plasma) in the tumor pathological setting.
For more clarity, the remainder of this article uses exclusively the name hPG80 to refer to extracellular progastrin.
A link between this protein and cancer has been known for more than 30 years. hPG80 is involved in most of the biological functions that ensure the existence of cancer . [ 2 ] The peptide is secreted by tumor cells and found in the plasma of cancer patients from early stages. [ 1 ] It then has functions that are independent of digestion and totally different from progastrin and its only role as an intracellular precursor of gastrin .
In the name hPG80, the "h" describes the human species: human; "PG" is a common script for the progastrin protein and the number 80 corresponds to the size of the protein: 80 amino acids .
The name hPG80 was thus proposed in the publication resulting from the work of Professor Benoît You under the management of Dominique Joubert and Alexandre Prieur in order to remove ambiguities between the intracellular version of the protein (in the function of digestion) and its extracellular version of the protein (in the case of cancer patients) which is no longer, despite its name, the precursor of gastrin . [ 1 ]
Moreover, the existence of a phonetically identical peptide, the Pro-Gastrin Releasing Peptide (proGRP), accentuated a possible confusion around the name progastrin and the need for a specific name.
1990: hPG80 is secreted by pancreatic cancer cells. [ 3 ]
1993 - 1994: hPG80 is secreted by ovarian and colon cancer cells. [ 4 ] [ 5 ]
1996 - 1997: hPG80 is identified as necessary for the proliferation and tumorigenesis of colon cancer cells. [ 6 ]
2000 - 2001: The GAST gene is a target of the β-catenin/Tcf4 pathway. [ 7 ] The presence of hPG80 is demonstrated in the plasma of colorectal cancer patients. [ 8 ]
2003: hPG80 is involved in the dissociation regulation of adherent and tight junctions. [ 2 ] Src mediates the effects of hPG80 on cell growth. [ 9 ]
2005: Ras and β-catenin/Tcf4 pathways induce synergistic activation of the GAST gene, contributing to possible neoplastic progression. [ 10 ]
2007: Inhibition of hPG80 expression inhibits the Wnt /β-catenin pathway inducing decreased growth and tumor differentiation in intestinal tumor models. [ 11 ]
2012: p53 gene mutation increases hPG80-dependent colonic proliferation and cancer formation. [ 12 ]
2014: hPG80 is identified as a new pro-angiogenic factor. [ 13 ]
2016: Autocrine secretion of hPG80 promotes survival and self-renewal of stem cells in colon cancer. [ 14 ]
2017: The use of antibodies directed against hPG80 to target the Wnt pathway and cancer stem cells represents a new therapeutic track for cancer. [ 15 ]
2020: hPG80 is detected in the plasma of patients with 11 different types of cancer. An association between longitudinal variations in hPG80 levels and the efficacy of anti-cancer treatments has been demonstrated. [ 1 ]
Through a variety of mechanisms, all crucial for tumor growth and survival, research has demonstrated the major role that hPG80 plays in tumor initiation and progression, generally using colorectal cancer as a model. Bardram was the first to hypothesize the presence of hPG80 in the early stages of the disease. [ 3 ] He evaluated the presence of hPG80 and its maturation products in the serum of patients with Zollinger-Ellison syndrome . This work showed that hPG80 measurement more accurately reflected tumor than the conventional measurement of amide gastrin. Indeed, hPG80 is more than 700 times more abundant than amide gastrin in colorectal tumors. [ 16 ]
In the early 90s, it was shown that hPG80 was not fully matured in human colon cancer cell lines and, more importantly, that it was secreted by in vitro cells. [ 5 ] These observations led to the study of autocrine and paracrine function of hPG80 in tumor cells. [ 17 ] Generally, it has been shown that hPG80 does not mature properly in cancer cells, particularly in colorectal cancer, because maturation enzymes are either absent or non-functional. [ 4 ] [ 5 ] [ 16 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ]
In 1996, it was demonstrated that GAST gene expression is required for human colon cancer cell tumorigenesis. [ 6 ] 60 to 80% of colon cancers express the GAST gene.
Through different experimental configurations, alteration of the GAST gene or neutralization of hPG80 resulted in a decrease in the number of tumors in mice with a tumor predisposition (mutation on the APC gene). Conversely, a significant increase in tumor formation was observed in mice overexpressing progastrin and treated with azoxymethane (AOM), a chemical carcinogen. [ 7 ] [ 11 ] [ 15 ] [ 22 ] [ 23 ]
When a tumor develops, its need for oxygen and nutrients causes creation of new blood vessels. This process is called neo-angiogenesis . In 2015, hPG80 was shown to be a pro-angiogenic factor. [ 13 ] Indeed, hPG80 stimulates endothelial cells proliferation and migration and increases their ability to form capillary-like structures in vitro. Blocking the production of hPG80 (with shRNA ) in xenograft cells in nude mice reduces tumor neovascularization .
Treatment of intestinal epithelial cells with hPG80 results in a significant loss of caspase 9 and caspase 3 activation and a decrease in DNA fragmentation. Therefore, the effect of hPG80 on cell survival results from both increased proliferation and decreased apoptosis . [ 24 ]
Cell migration is based on their ability to become independent of adjacent cells. Intercellular contacts integrity is essential for electrolyte uptake regulation as well as for tumor metastasis prevention. In 2003, it was demonstrated that blocking hPG80 secretion by an antisense construction directed against progastrin mRNA allows restoration of membrane localization of tight and adherent junctions constituent proteins in a human colorectal carcinoma cell line DLD-1. [ 2 ] hPG80 thus plays a role on cell contacts integrity.
Cancer stem cells (CSCs) constitute a small proportion of the tumor, usually between 1 and 5%. But they are essential for tumor survival because they act as a "reactor". Giraud and al. have demonstrated the major role played by hPG80 in CSCs. [ 14 ] These authors have shown that hPG80 expression is strongly increased in colorectal cancer cells cultured under conditions where CSCs are enriched. They then showed that hPG80 was able to regulate CSCs frequency (survival and self-renewal) in vitro and in vivo. Subsequently, Prieur and al. demonstrated that when a neutralizing antibody is added to a cell culture or when human colorectal cancer cells implanted mice are treated in vivo with such an antibody, CSCs frequency is decreased in the same proportions. [ 15 ] These two scientific articles clearly show that hPG80 is a survival factor for CSCs. Moreover, hPG80 inhibition would induce CSC differentiation, opening the possibility of a differentiation therapy rather than a classical anti-proliferative therapy. Its main function is to help CSCs survive and spread to form metastases , which probably explains why this peptide can be considered as a potential predictive marker for the presence of liver metastasis in colorectal cancer. [ 25 ]
The first event leading to colon cancer is in 80 to 90% of cases a constitutive activation of the Wnt/β-catenin oncogenic pathway induced by mutations in the APC ( Adenomatous polyposis coli ) coding gene or the β-catenin coding gene. Mutations induction into normal intestinal stem cells is sufficient to trigger tumorigenesis . [ 26 ] GAST gene which encodes hPG80 is activated by the Wnt oncogenic pathway. It is a downstream target of the β-catenin/Tcf-4 signaling pathway. [ 7 ]
Demonstration of the link between hPG80 and an oncogenic pathway has been described for K-Ras . Cell lines and colon cancer tissues with K-Ras mutations all had significantly higher levels of GAST mRNA than wild type K-Ras. [ 27 ] K-Ras effects on GAST expression are produced by activation of the Raf-MEK-ERK signal transduction pathway, final step being activation of the GAST gene promoter.
Since both K-Ras and the Wnt pathway induce GAST expression, the hypothesis of a possible cooperation between these two pathways to regulate hPG80 expression was investigated. [ 10 ] Chakadar and al. found significant synergistic stimulation of the GAST gene promoter (by a factor of 25–40) by a combination of oncogenic β-catenin and K-Ras overexpression. Activation of the GAST gene promoter was also shown to be dependent on other signalling signals: enhanced or suppressed by co-expression of wild-type SMAD4 or by a dominant negative mutant of SMAD4 , respectively, and abrogated by inhibition of PI3K. Thus, constitutive activation of the Wnt pathway, considered to be at the onset of tumorigenesis in the colon, and the K-Ras oncogene, present in 50% of human colorectal tumors, synergistically stimulate the production of hPG80, a tumorigenesis promoter. Tumorigenesis induced by activation of the Wnt pathway is partially dependent on hPG80.
The oncogene pp60 (c-Src) is activated in colon cancer cells and leads to increased amounts of hPG80. [ 9 ] This means that hPG80 production, which occurs during early tumorigenesis, could play a role in this activation, which is known as an early event in colon tumorigenesis. [ 11 ] [ 28 ] [ 29 ] The PI3K/Akt pathway, which is particularly involved in proliferation, is also activated by hPG80. NF-kappaB is another important signaling messenger regulated by hPG80. [ 11 ] [ 30 ] Its involvement in mechanisms responsible for the anti-apoptotic effect of hPG80 has been demonstrated in pancreatic cancer cells in vitro and in vivo in mice overexpressing the GAST gene. [ 31 ] [ 32 ] JAK2 (Janus-activated kinase 2), STAT3 and kinases increases regulated by extracellular signals have also been observed in the colon mucosa of hGAS mice. [ 30 ]
It has been shown that colon tumor cells which do not express hPG80 return to a "normal" state. This is due to the fact that when the Wnt pathway is inactivated, the JAG1 gene is repressed, inducing inactivation of the Notch pathway which plays a major role in the acquisition of a differentiated cell phenotype. [ 33 ]
In 2012, the P53 gene mutation was shown to increase hPG80-dependent colon cells proliferation and colon cancer formation in mice. [ 12 ]
An identification of the hPG80 receptor has been the subject of several studies in recent years. However, hPG80 receptor identity remains a real issue in the scientific community. The receptor can activate a number of signaling pathways, either directly or indirectly, which is rather unusual for a receptor. This could indicate a peculiarity of this receptor and why it is difficult to identify it. The unidentified hPG80 receptor transduces a progastrin signal via various intracellular intermediates known to be involved in tumorigenesis.
High affinity binding sites have been described for the first time in intestinal epithelial cells using recombinant human progastrin iodine. [ 34 ] Affinity was in the range of 0.5-1 nM, which is receptor compatible. When biotinylated progastrin binding was evaluated by flow cytometry, strong and specific binding of progastrin to certain cell lines (IEC-6, IEC-18, HT-29, COLO320) was also detected. [ 35 ] A specificity of binding was confirmed by competition with cold, unlabelled hPG80, but not with carboxy-terminal glycine-containing gastrin or amidated gastrin-17. Binding was not influenced by the presence of the classical CCK-2 receptor.
It is clear from these two studies that there is a binding site/receptor for hPG80 that is distinct from binding to gastrin-17 amidated and to gastrin 17 with carboxy-terminal glycine (G17-Gly). The sequence of hPG80 interacting with this receptor is likely located in the last 26 amino acid residues of hPG80 carboxy-terminal end, which have been shown to be sufficient for its function. [ 36 ] However, this putative receptor identity is unknown.
One candidate is Annexin A2, identified as being able of binding progastrin and derived peptides. [ 37 ] Annexin A2 is a partial mediator of the effect of progastrin/gastrins. In particular, Annexin A2 mediates NF-kappaB upregulation and β-catenin in response to progastrin in mice and HEK-293 cells. [ 38 ] In addition, annexin A2 may be involved in progastrin-dependent clathrin endocytosis. However, progastrin affinity for Annexin A2 is not what would be expected for a specific receptor. And, although Annexin A2 plays a role in progastrin functions, it does not fit a receptor function.
Another candidate is the G protein-coupled receptor 56 (GPCR56), expressed on both colon stem cells and cancer cells. [ 39 ] While human recombinant hPG80 promotes in vitro growth and survival of wild mice colon organoids , those from GPCR56-deficient mice (GPCR56-/-) are resistant to hPG80. However, although hPG80 has been shown to bind to cells expressing GPCR56, authors did not provide direct evidence of a hPG80 bound to GPCR56 itself. GPCR56 is a good candidate, but evidence that it is hPG80 receptor is to this day not established.
hPG80 through various mechanisms can be considered as a major promoter of tumorigenesis. hPG80 is found in the plasma of cancer patients and its neutralization induces tumor reversion.
Colorectal cancer is not the only type of cancer to express hPG80. Its expression has also been demonstrated in ovarian cancers , liver tumors and pancreatic tumors . [ 4 ] [ 40 ] [ 41 ] Thus, several types of tumors express the unmatured peptide. hPG80 can be detected and quantified in the blood of cancer patients. A first demonstration has been made in colorectal cancer showing an increase of hPG80 and non-amide gastrin levels in plasma in these patients compared to a control series (healthy individuals). [ 8 ] In addition, an hPG80 increase has been observed in patients with adenomatous polyps. [ 15 ] hPG80 is therefore expressed at all stages by the tumor, from early stages to metastasis.
hPG80 is found in different tumor types and secreted in vitro by certain cancer cells. A study has shown its presence in the blood of patients with 11 different types of cancer: breast cancer , colorectal cancer , stomach/ esophageal cancer , kidney cancer , liver cancer , non-small cell lung cancer , skin melanoma , ovarian cancer , pancreatic cancer , prostate cancer and uterine cancer (endometrial/cervical). [ 1 ]
Pre- and post-operative plasma assays of hPG80 in colorectal cancer patients show that hPG80 presence reflects tumor production. [ 42 ]
It has been observed that hPG80 concentrations are increased in patients at risk of developing colorectal carcinoma . [ 43 ] In addition, an increase in hPG80 has been observed in hyperplastic polyps that have progressed to cancer. [ 44 ] [ 45 ]
hPG80 may also be a biomarker of liver metastasis in colorectal cancer. [ 25 ]
In addition, You and al. observed a decrease in hPG80 levels after surgery in a patients cohort with gastrointestinal cancers with peritoneal involvement treated with post-operative chemotherapy and cytoreductive surgery. [ 1 ]
In addition, earlier detection of small lesions and monitoring of recurrence can be improved by measuring hPG80 levels as a complementary blood biomarker in a cohort of patients with hepatocellular carcinoma treated with local or systemic therapies (Fig. 3). [ 1 ] Measured hPG80 levels are relevant in patients for whom alpha-fetoprotein (AFP) is below 20 ng/ml, an established threshold in clinical practice. [ 46 ] Depending on disease management, patients in remission have lower levels of hPG80 than those in whom the cancer is still active.
To date, no drug is able to target CSCs. Humanized anti-hPG80 antibodies, alone or in combination with chemotherapy , appears to be a promising approach. [ 15 ] The use of anti-hPG80 antibodies has also been discussed as a potential treatment in colorectal cancer patients with a mutation in the KRAS gene. Targeting of hPG80 with the humanized anti-hPG80 antibody has been shown:
1. a decrease in the self-renewal capacity of CSCs of various origins;
2. prolongation of in vitro and in vivo chemosensitivity and delayed relapse after treatment of T84 xenografted mouse cells;
3. decreased tumor burden and increased cell differentiation in the remaining tumors in transgenic mice developing Wnt-induced intestinal neoplasia.
This has recently been confirmed for ovarian, breast, esophageal, liver and gastric cancers making this therapeutic antibody a potential multi-cancer drug. [ 1 ]
It has been shown that hPG80 is a radioresistant factor that can be targeted to sensitize rectum radiation-resistant cancers. [ 47 ] hPG80 decreased expression increases sensitivity to irradiation in colorectal cancer cell lines leading to increased radiation-induced DNA damage and apoptosis . In the same lineage, hPG80 targeting also results in radiation-induced survival pathways inhibition, Akt and ERK. | https://en.wikipedia.org/wiki/HPG80 |
In chemistry , a phosphoric acid , in the general sense, is a phosphorus oxoacid in which each phosphorus (P) atom is in the oxidation state +5, and is bonded to four oxygen (O) atoms, one of them through a double bond , arranged as the corners of a tetrahedron . Two or more of these PO 4 tetrahedra may be connected by shared single-bonded oxygens, forming linear or branched chains , cycles , or more complex structures. The single-bonded oxygen atoms that are not shared are completed with acidic hydrogen atoms. The general formula of a phosphoric acid is H n +2−2 x P n O 3 n +1− x , where n is the number of phosphorus atoms and x is the number of fundamental cycles in the molecule's structure, between 0 and n + 2 / 2 .
Removal of protons ( H + ) from k hydroxyl groups –OH leaves anions generically called phosphates (if k = n − 2 x + 2 ) or hydrogen phosphates (if k is between 1 and n − 2 x + 1 ), with general formula [H n −2 x +2− k P n O 3 n +1− x ] k − . The fully dissociated anion ( k = n − 2 x + 2 ) has formula [P n O 3 n − x +1 ] ( n −2 x +2)− . The term phosphate is also used in organic chemistry for the functional groups that result when one or more of the hydrogens are replaced by bonds to other groups.
These acids, together with their salts and esters , include some of the best-known compounds of phosphorus, of high importance in biochemistry , mineralogy , agriculture , pharmacy , chemical industry , and chemical research .
The simplest and most commonly encountered of the phosphoric acids is orthophosphoric acid , H 3 PO 4 . Indeed, the term phosphoric acid often means this compound specifically (and this is also the current IUPAC nomenclature). [ citation needed ]
Two or more orthophosphoric acid molecules can be joined by condensation into larger molecules by elimination of water . Condensation of a few units yields the oligophosphoric acids , while larger molecules are called polyphosphoric acids . (However, the distinction between the two terms is not well defined.)
For example, pyrophosphoric , triphosphoric and tetraphosphoric acids can be obtained by the reactions 2 H 3 PO 4 ⟶ H 4 P 2 O 7 + H 2 O H 4 P 2 O 7 + H 3 PO 4 ⟶ H 5 P 3 O 10 + H 2 O H 5 P 3 O 10 + H 3 PO 4 ⟶ H 6 P 4 O 13 + H 2 O {\displaystyle {\begin{aligned}{\ce {2 H3PO4}}&\longrightarrow {\ce {H4P2O7 + H2O}}\\[2pt]{\ce {H4P2O7 + H3PO4}}&\longrightarrow {\ce {H5P3O10 + H2O}}\\[2pt]{\ce {H5P3O10 + H3PO4}}&\longrightarrow {\ce {H6P4O13 + H2O}}\end{aligned}}}
The "backbone" of a polyphosphoric acid molecule is a chain of alternating P and O atoms. Each extra orthophosphoric unit that is condensed adds 1 extra H ( hydrogen ) atom, 1 extra P ( phosphorus ) atom, and 3 extra O ( oxygen ) atoms. The general formula of a polyphosphoric acid is H n +2 P n O 3 n +1 or HO[−P(O)(OH)−O−] n H .
Polyphosphoric acids are used in organic synthesis for cyclizations and acylations ; an alternative is Eaton's reagent . [ 1 ] [ 2 ] [ 3 ]
Metaphosphoric acid ( HPO 3 ) is a colorless, vitreous, deliquescent solid, density 2.2 to 2.5 g/cc, which sublimes upon heating. It is soluble in ethanol. [ 4 ]
Phosphoric acid units can be bonded together in rings (cyclic structures). The simplest such compound is trimetaphosphoric acid or cyclo-triphosphoric acid having the formula H 3 P 3 O 9 . Its structure is shown in the illustration. Since the ends are condensed, its formula has one less H 2 O (water) than tripolyphosphoric acid.
The general formula of a phosphoric acid is H n −2 x +2 P n O 3 n − x +1 , where n is the number of phosphorus atoms and x is the number of fundamental cycles in the molecule's structure; that is, the minimum number of bonds that would have to be broken to eliminate all cycles.
The limiting case of internal condensation, where all oxygen atoms are shared and there are no hydrogen atoms ( x = n +2 / 2 ) is an anhydride P 2 n O 5 n , phosphorus pentoxide P 4 O 10 .
Removal of the hydrogen atoms as protons H + turns a phosphoric acid into a phosphate anion. Partial removal yields various hydrogen phosphate anions.
The anions of orthophosphoric acid H 3 PO 4 are orthophosphate (commonly called simply "phosphate") PO 3− 4 , monohydrogen phosphate HPO 2− 4 , and dihydrogen phosphate H 2 PO − 4 .
Dissociation of pyrophosphoric acid H 4 P 2 O 7 generates four anions, [H 4− k P 2 O 7 ] k − , where the charge k ranges from 1 to 4. The last one is pyrophosphate [P 2 O 7 ] 4− . The pyrophosphates are mostly water-soluble.
Likewise, tripolyphosphoric acid H 5 P 3 O 10 yields at least five anions [H 5− k P 3 O 10 ] k − , where k ranges from 1 to 5, including tripolyphosphate [P 3 O 10 ] 5− . Tetrapolyphosphoric acid H 6 P 4 O 13 yields at least six anions, including tetrapolyphosphate [P 4 O 13 ] 6− , and so on. Note that each extra phosphoric unit adds one extra P atom, three extra O atoms, and either one extra hydrogen atom or an extra negative charge.
Branched polyphosphoric acids give similarly branched polyphosphate anions. The simplest example of this is triphosphono phosphate [OP(OPO 3 ) 3 ] 9− and its partially dissociated versions.
The general formula for such (non-cyclic) polyphosphate anions, linear or branched, is [H n +2− k P n O 3 n +1 ] k − , where the charge k may vary from 1 to n + 2 . Generally in an aqueous solution, the degree or percentage of dissociation depends on the pH of the solution.
Salts or esters of cyclic polyphosphoric acids are often called "metaphosphates". What are commonly called trimetaphosphates actually have a mixture of ring sizes. A general formula for such cyclic compounds is [HPO 3 ] x where x = number of phosphoric units in the molecule.
When metaphosphoric acids lose their hydrogens as H + , cyclic anions called metaphosphates are formed. An example of a compound with such an anion is sodium hexametaphosphate ( Na 6 P 6 O 18 ), used as a sequestrant and a food additive .
These phosphoric acids series are generally water - soluble considering the polarity of the molecules. Ammonium and alkali phosphates are also quite soluble in water. The alkaline earth salts start becoming less soluble and phosphate salts of various other metals are even less soluble.
In aqueous solutions (solutions of water), water gradually (over the course of hours) hydrolyzes polyphosphates into smaller phosphates and finally into ortho-phosphate, given enough water. Higher temperature or acidic conditions can speed up the hydrolysis reactions considerably. [ 5 ]
Conversely, polyphosphoric acids or polyphosphates are often formed by dehydrating a phosphoric acid solution; in other words, removing water from it often by heating and evaporating the water off.
Ortho-, pyro-, and tripolyphosphate compounds, such as sodium tripolyphosphate , have been commonly used in detergents (i. e. cleaners) formulations. Sometimes pyrophosphate, tripolyphosphate, tetrapolyphosphate, etc. are called diphosphate , triphosphate , tetraphosphate , etc., especially when they are part of phosphate esters in biochemistry . They are also used for scale and corrosion control by potable water providers . [ 6 ] As a corrosion inhibitor, polyphosphates work by forming a protective film on the interior surface of pipes. [ 7 ]
The −OH groups in phosphoric acids can also condense with the hydroxyl groups of alcohols to form phosphate esters . Since orthophosphoric acid has three −OH groups, it can esterify with one, two, or three alcohol molecules to form a mono-, di-, or triester. See the general structure image of an ortho- (or mono-) phosphate ester below on the left, where any of the R groups can be a hydrogen or an organic radical . Di- and tripoly- (or tri-) phosphate esters, etc. are also possible. Any −OH groups on the phosphates in these ester molecules may lose H + ions to form anions, again depending on the pH in a solution. In the biochemistry of living organisms, there are many kinds of (mono)phosphate, diphosphate, and triphosphate compounds (essentially esters ), many of which play a significant role in metabolism such as adenosine diphosphate (ADP) and triphosphate (ATP) . | https://en.wikipedia.org/wiki/HPO3 |
Phosphonite
A phosphite ion in inorganic chemistry usually refers to [HPO 3 ] 2− but includes [H 2 PO 3 ] − ([HPO 2 (OH)] − ). These anions are the conjugate bases of phosphorous acid (H 3 PO 3 ). The corresponding salts, e.g. sodium phosphite (Na 2 HPO 3 ) are reducing in character.
The IUPAC recommended name for phosphorous acid is phosphonic acid . Correspondingly, the IUPAC-recommended name for the HPO 2− 3 ion is phosphonate . In the US the IUPAC naming conventions for inorganic compounds are taught at high school, but not as a 'required' part of the curriculum. [ 2 ] A well-known university-level textbook follows the IUPAC recommendations. [ 3 ] In practice any reference to "phosphite" should be investigated to determine the naming convention being employed.
From the commercial perspective, the most important phosphite salt is basic lead phosphite . Many salts containing the phosphite ion have been investigated structurally, these include sodium phosphite pentahydrate (Na 2 HPO 3 ·5H 2 O). (NH 4 ) 2 HPO 3 ·H 2 O, CuHPO 3 ·H 2 O, SnHPO 3 and Al 2 (HPO 3 ) 3 ·4H 2 O. [ 4 ] The structure of HPO 2− 3 is approximately tetrahedral. [ 5 ] [ 6 ]
HPO 2− 3 has a number of canonical resonance forms making it isoelectronic with bisulfite ion, HSO − 3 , which has a similar structure. [ 7 ]
Acid or hydrogen phosphites are called hydrogenphosphonates or acid phosphites. IUPAC recommends the name hydrogenphosphonates). They are anions HP(O) 2 OH − . A typical derivative is the salt [NH 4 ][HP(O) 2 OH]. [ 7 ] [ 6 ] Many related salts are known, e.g., RbHPHO 3 , CsHPHO 3 , TlHPHO 3 . These salts are prepared by treating phosphorous acid with the metal carbonate . These compounds contain a layer polymeric anion consisting of HPO 3 tetrahedra linked by hydrogen bonds. These layers are interleaved by layers of metal cations. [ 8 ]
Organic esters of hydrogen phosphites are anions with the formula HP(O) 2 OR − (R = organic group). One commercial example is the fungicide fosetyl-Al with the formula [C 2 H 5 OP(H)O 2 ] 3 Al. [ 9 ]
Pyrophosphites (diphosphites) can be produced by gently heating acid phosphites under reduced pressure. They contain the ion H 2 P 2 O 2− 5 , which can be formulated [HP(O) 2 O−P(O) 2 H] 2− . [ 7 ] [ 6 ]
In contrast to the paucity of evidence for PO 3− 3 , the corresponding arsenic ion, ortho- arsenite , AsO 3− 3 is known. An example is Ag 3 AsO 3 as well as the polymeric meta-arsenite (AsO − 2 ) n . [ 7 ] The iso-electronic sulfite ion, SO 2− 3 is known from its salts. [ 7 ]
Inorganic phosphites (containing HPO 2− 3 ) have been applied to crops to combat fungus-like pathogens of the order oomycetes (water molds). The situation is confusing because of the similarity in name between phosphite and phosphate (a major plant nutrient and fertilizer ingredient), and controversial because phosphites have sometimes been advertised as fertilizers, even though they are converted to phosphate too slowly to serve as a plant's main phosphorus source. In fact, phosphites may cause phytotoxicity when a plant is starved of phosphates. [ 10 ] Lemoynie [ 11 ] and others have described this complicated situation and noted that calling phosphites fertilizers avoided the regulatory complication and negative public perceptions that might have been incurred by registering them as fungicides. [ 10 ]
A major form of inorganic phosphite used in agriculture is monopotassium phosphite . This compound does serve as a potassium fertilizer. | https://en.wikipedia.org/wiki/HPO32- |
Phosphoric acid (orthophosphoric acid, monophosphoric acid or phosphoric(V) acid) is a colorless, odorless phosphorus -containing solid , and inorganic compound with the chemical formula H 3 P O 4 . It is commonly encountered as an 85% aqueous solution , which is a colourless, odourless, and non- volatile syrupy liquid. It is a major industrial chemical, being a component of many fertilizers.
The compound is an acid . Removal of all three H + ions gives the phosphate ion PO 3− 4 . Removal of one or two protons gives dihydrogen phosphate ion H 2 PO − 4 , and the hydrogen phosphate ion HPO 2− 4 , respectively. Phosphoric acid forms esters , called organophosphates . [ 17 ]
The name "orthophosphoric acid" can be used to distinguish this specific acid from other " phosphoric acids ", such as pyrophosphoric acid . Nevertheless, the term "phosphoric acid" often means this specific compound; and that is the current IUPAC nomenclature .
Phosphoric acid is produced industrially by one of two routes, wet processes and dry. [ 18 ] [ 19 ] [ 20 ]
In the wet process, a phosphate-containing mineral such as calcium hydroxyapatite and fluorapatite are treated with sulfuric acid . [ 21 ]
Calcium sulfate (gypsum, CaSO 4 ) is a by-product, which is removed as phosphogypsum . The hydrogen fluoride (HF) gas is streamed into a wet (water) scrubber producing hydrofluoric acid . In both cases the phosphoric acid solution usually contains 23–33% P 2 O 5 (32–46% H 3 PO 4 ). It may be concentrated to produce commercial- or merchant-grade phosphoric acid, which contains about 54–62% P 2 O 5 (75–85% H 3 PO 4 ). Further removal of water yields superphosphoric acid with a P 2 O 5 concentration above 70% (corresponding to nearly 100% H 3 PO 4 ). The phosphoric acid from both processes may be further purified by removing compounds of arsenic and other potentially toxic impurities.
To produce food-grade phosphoric acid, phosphate ore is first reduced with coke in an electric arc furnace , to give elemental phosphorus . This process is also known as the thermal process or the electric furnace process. Silica is also added, resulting in the production of calcium silicate slag. Elemental phosphorus is distilled out of the furnace and burned with air to produce high-purity phosphorus pentoxide , which is dissolved in water to make phosphoric acid. [ 22 ] The thermal process produces phosphoric acid with a very high concentration of P 2 O 5 (about 85%) and a low level of impurities.
However, this process is more expensive and energy-intensive than the wet process, which produces phosphoric acid with a lower concentration of P 2 O 5 (about 26–52%) and a higher level of impurities. The wet process is the most common method of producing phosphoric acid for fertilizer use. [ 23 ] Even in China, where the thermal process is still used quite widely due to relatively cheap coal as opposed to the sulfuric acid, over 7/8 of phosphoric acid is produced with wet process. [ 24 ]
Phosphoric acids produced from phosphate rock or thermal processes often requires purification. A common purification methods is liquid–liquid extraction, which involves the separation of phosphoric acids from water and other impurities using organic solvents, such as tributyl phosphate (TBP), methyl isobutyl ketone (MIBK), or n -octanol . Nanofiltration involves the use of a premodified nanofiltration membrane, which is functionalized by a deposit of a high molecular weight polycationic polymer of polyethyleneimines. Nanofiltration has been shown to significantly reduce the concentrations of various impurities, including cadmium, aluminum, iron, and rare earth elements. The laboratory and industrial pilot scale results showed that this process allows the production of food-grade phosphoric acid. [ 25 ]
Fractional crystallization can achieve highest purities typically used for semiconductor applications. Usually a static crystallizer is used. A static crystallizer uses vertical plates, which are suspended in the molten feed and which are alternatingly cooled and heated by a heat transfer medium. The process begins with the slow cooling of the heat transfer medium below the freezing point of the stagnant melt. This cooling causes a layer of crystals to grow on the plates. Impurities are rejected from the growing crystals and are concentrated in the remaining melt. After the desired fraction has been crystallized, the remaining melt is drained from the crystallizer. The purer crystalline layer remains adhered to the plates. In a subsequent step, the plates are heated again to liquify the crystals and the purified phosphoric acid drained into the product vessel. The crystallizer is filled with feed again and the next cooling cycle is started. [ 26 ]
In aqueous solution phosphoric acid behaves as a triprotic acid.
The difference between successive p K a values is sufficiently large so that salts of either monohydrogen phosphate, HPO 2− 4 or dihydrogen phosphate, H 2 PO − 4 , can be prepared from a solution of phosphoric acid by adjusting the pH to be mid-way between the respective p K a values.
Aqueous solutions up to 62.5% H 3 PO 4 are eutectic , exhibiting freezing-point depression as low as −85 °C. When the concentration of acid rises above 62.5% the freezing-point increases, reaching 21 °C by 85% H 3 PO 4 (w/w; the monohydrate ). Beyond this the phase diagram becomes complicated, with significant local maxima and minima. For this reason phosphoric acid is rarely sold above 85%, as beyond this adding or removing small amounts of moisture risks the entire mass freezing solid, which would be a major problem on a large scale. A local maximum at 91.6% which corresponds to the hemihydrate 2H 3 PO 4 •H 2 O, freezing at 29.32 °C. [ 27 ] [ 28 ] There is a second smaller eutectic depression at a concentration of 94.75% with a freezing point of 23.5 °C. At higher concentrations the freezing point rapidly increases. Concentrated phosphoric acid tends to supercool before crystallization occurs, and may be relatively resistant to crystallisation even when stored below the freezing point. [ 13 ]
Phosphoric acid is commercially available as aqueous solutions of various concentrations, not usually exceeding 85%. If concentrated further it undergoes slow self-condensation, forming an equilibrium with pyrophosphoric acid :
Even at 90% concentration the amount of pyrophosphoric acid present is negligible, but beyond 95% it starts to increase, reaching 15% at what would have otherwise been 100% orthophosphoric acid. [ 29 ]
As the concentration is increased higher acids are formed, culminating in the formation of polyphosphoric acids . [ 30 ] It is not possible to fully dehydrate phosphoric acid to phosphorus pentoxide , instead the polyphosphoric acid becomes increasingly polymeric and viscous. Due to the self-condensation, pure orthophosphoric acid can only be obtained by a careful fractional freezing/melting process. [ 13 ] [ 12 ]
The dominant use of phosphoric acid is for fertilizers , consuming approximately 90% of production. [ 31 ]
Food-grade phosphoric acid (additive E338 [ 32 ] ) is used to acidify foods and beverages such as various colas and jams, providing a tangy or sour taste. The phosphoric acid also serves as a preservative . [ 33 ] Soft drinks containing phosphoric acid, which would include Coca-Cola , are sometimes called phosphate sodas or phosphates. Phosphoric acid in soft drinks has the potential to cause dental erosion. [ 34 ] Phosphoric acid also has the potential to contribute to the formation of kidney stones , especially in those who have had kidney stones previously. [ 35 ]
Specific applications of phosphoric acid include:
Phosphoric acid may also be used for chemical polishing ( etching ) of metals like aluminium or for passivation of steel products in a process called phosphatization . [ 41 ]
Phosphoric acid is not a strong acid . However, at moderate concentrations phosphoric acid solutions are irritating to the skin. Contact with concentrated solutions can cause severe skin burns and permanent eye damage. [ 42 ]
A link has been shown between long-term regular cola intake and osteoporosis in later middle age in women (but not men). [ 43 ] | https://en.wikipedia.org/wiki/HPO4 |
HPTE , also known as hydroxychlor , p,p' -hydroxy-DDT , or 2,2-bis(4-hydroxyphenyl)-1,1,1-trichloroethane , is a metabolite of methoxychlor , a synthetic insecticide related to DDT . [ 1 ] Like bisphenol A with similar chemical structure , HPTE is an endocrine disruptor which has estrogenic activity, [ 2 ] and also inhibits Cholesterol side-chain cleavage enzyme (P450scc, CYP11A1) [ 3 ] and 3α-hydroxysteroid dehydrogenase (3α-HSD). [ 4 ]
This pharmacology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HPTE |
HP Vectra was a line of business-oriented personal computers manufactured by Hewlett-Packard (now HP Inc. ). It was introduced in October 1985 as HP's first IBM-compatible PC . [ 1 ]
Hewlett-Packard, which originally made its name through selling test equipment, made its move into the computing field in 1967 with HP 1000 / 2100 minicomputers. Further minicomputer and terminal products followed in the coming years, and in 1983, the company finally released a microcomputer, the HP 150 series. It only lasted two years before HP embraced the IBM PC standard with the Vectra line. Mainly targeted at business and professional fields, the Vectra was HP's top-of-the-line family of computers for over 15 years.
InfoWorld stated that HP was "responding to demands from its customers for full IBM PC compatibility". [ 2 ] Vectras were not entirely IBM-compatible , and in the early years, had a considerable amount of non-standard hardware features, including hard disk types, keyboards, and the mouse interface, and corresponding BIOS extensions named EX-BIOS, [ 3 ] thus requiring their own custom OEM version of MS-DOS . Software that used strictly BIOS calls, would work, but anything that performed low-level hardware access, often had problems. Vectras notably failed to pass the most popular compatibility test of the day, which involved running Lotus 123 and Microsoft Flight Simulator . By the time 486 PCs became commonplace, however, most of the proprietary hardware in HP machines had been dropped.
In 1995, HP added the Pavilion line as a lower-end range designed for the consumer markets (which the company had ignored up to this point), including both desktop PCs and the company's early laptops. In 2002 (following the HP- Compaq merger and the release of the VL420 and e-pc 42 models a year prior), the Vectra family was discontinued, and was replaced by the Evo , which was originally developed by Compaq.
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HP_Vectra |
HRDetect [ 1 ] ( H omologous R ecombination D eficiency D etect ) is a whole-genome sequencing (WGS)-based classifier designed to predict BRCA1 and BRCA2 deficiency based on six mutational signatures . Additionally, the classifier is able to identify similarities in mutational profiles of tumors to that of tumors with BRCA1 and BRCA2 defects, also known as BRCAness. This classifier can be applied to assess the implementation of PARP [ 1 ] inhibitors in patients with BRCA1/BRCA2 deficiency. The final output is a probability of BRCA1/2 mutation.
BRCA1 and BRCA2 play crucial roles in maintaining genome integrity, mainly through homologous recombination (HR) for DNA double-strand breaks (DSB)repair. The mutations of BRCA1 and BRCA2 can lead to a reduced capacity of HR machinery, increased genomic instability , and elicit a predisposition to malignancies. [ 2 ] People with BRCA1 and BRCA2 deficiency have higher risks of developing certain cancers such as breast and ovarian cancers. Germline defects in BRCA1/BRCA2 genes account for up to 5% of breast cancer cases. [ 1 ]
Poly (ADP ribose) polymerase (PARP) inhibitors are designed to treat BRCA1- and BRCA2- defect tumors owing to their homologous recombination deficiency. [ 4 ] These drugs have been majorly implemented in breast and ovarian cancers, [ 5 ] and their clinical efficacy among patients with other types of cancers, such as pancreatic cancer, is still being investigated. [ 6 ] It is vital to identify adequate patients with BRCA1/BRCA2 deficiency to utilize PARP inhibitors optimally. PARP inhibitors operate on the concept of synthetic lethality where by selectively causing cell death in BRCA-mutant cells while sparing normal cells.
HRDetect was implemented to detect tumors with BRCA1/BRCA2 deficiency using the data from whole-genome sequencing. This model quantitatively aggregates six HRD-associated signatures into a single score called HRDetect to accurately classify breast cancers by their BRCA1 and BRCA2 status. The machine learning algorithm assigns weight values to these signatures prior to computing the final score. The six signatures, ranked by decreasing weight, include microhomology-mediated indels, the HRD index, base- substitution signature 3, rearrangement signature 3, rearrangement signature 5, and base- substitution signature 8. Additionally, this weighted approach is able to identify BRCAness, which refers to mutational phenotypes displaying homologous recombination deficiency similar to tumors with BRCA1/BRCA2 germline defects. [ 7 ]
HRDetect requires four types of inputs:
It is based on a supervised learning method using a lasso logistic regression model to distinguish samples into those with and without BRCA 1/2 deficiency. Optimal coefficients are obtained by minimizing the objective function.
To account for a high substitution count in samples, the genomic data is first log transformed:
x = ln ( x + 1 ) {\displaystyle x=\ln(x+1)}
The transformed data is then standardized to make mutational class values comparable giving each object a mean of 0 and a standard deviation (sd) of 1:
x = x − mean ( x ) s d ⋅ ( x ) {\displaystyle \mathrm {x} ={\frac {x-\operatorname {mean} \left(x\right)}{\mathrm {s} \mathrm {d} \cdot \left(x\right)}}}
To be able to distinguish between those affected and not affected by BRCA1/BRCA2 deficiency, a lasso logistic regression model is used:
min ( ( β 0 , β ) ) ∈ R p + 1 ( − [ 1 N ∑ i = 1 N y i ⋅ ( β 0 + x i T β ) − log ( 1 + e ( β 0 + x i T β ) ) ] + λ ‖ β ‖ 1 ) {\displaystyle \min _{((\beta _{0},\,\beta ))\in \mathbb {R} ^{p+1}}{\left(-\left[{\frac {1}{N}}\sum _{i=1}^{N}y_{i}\cdot \left(\beta _{0}+x_{i}^{T}\beta \right)-\log \left(1+e^{\left(\beta _{0}+x_{i}^{T}\beta \right)}\right)\right]+\lambda \|\beta \|_{1}\right)}}
where:
y i {\displaystyle y_{i}} : BRCA status of a sample || y i = 1 for BRCA1/BRCA2-null samples || y i = 0 otherwise β 0 {\displaystyle \beta _{0}} : Intercept, interpreted as the log of odds of y i {\displaystyle y_{i}} = 1 when x i T {\displaystyle x_{i}^{T}} = 0 β {\displaystyle \beta } : Vector of weights p {\displaystyle p} : Number of features characterizing each sample N {\displaystyle N} : Number of samples x i T {\displaystyle x_{i}^{T}} : Vector of features characterizing the i th sample λ {\displaystyle \lambda } : Penalty promoting the sparseness of the weights ‖ β ‖ {\displaystyle \|\beta \|} : L1 norm of the vector of weights
The β weights are constrained to be positive to reflect the presence of mutational actions due to BRCA1/BRCA2 defects. Setting the constraint of nonnegative weights ensures that all samples would be scored on the basis of the presence of relevant mutational signatures associated with BRCA1/BRCA2 deficiency, irrespective of whether these signatures are the dominant mutational process in the cancer.
Lastly, the weights obtained from the lasso regression are used to give a new sample a probabilistic score using the normalized mutational data x i T {\displaystyle x_{i}^{T}} and application of the model parameters( β {\displaystyle \beta } , β 0 {\displaystyle \beta _{0}} ):
P ( C i = B R C A ) = 1 1 + e − ( β 0 + x i T β ) {\displaystyle P\left(C_{i}=BRCA\right)={\frac {1}{1+e^{-\left(\beta _{0}+x_{i}^{T}\beta \right)}}}}
where:
C i {\displaystyle C_{i}} : variable encoding the status of the i th sample β 0 {\displaystyle \beta _{0}} : Intercept weight x i T {\displaystyle x_{i}^{T}} : Vector encoding features of the i th sample β {\displaystyle \beta } : Vector of weights
The probability value quantifies the degree of BRCA1/BRCA2 defectiveness. A cut-off probability value should be chosen while maintaining a high sensitivity. These scores can be utilized to guide therapy.
Mutations in genes responsible for HR are prevalent among human cancers. The BRCA1 and BRCA2 genes are centrally involved in HR, DNAdamage repair, end resection, and checkpoint signaling. Mutational signatures of HRD have been identified in over 20% of breast cancers, as well as pancreatic, ovarian, and gastric cancers. BRCA1/2 mutations confer sensitivity to platinum-based chemotherapies. HRDetect can independently trained to predict BRCA1/2 status, and has the capacity to predict outcomes on platinum-based chemotherapies. [ 8 ]
HRDetect was initially developed to detect tumors with BRCA1 and BRCA2 deficiency based on the data from whole-genome sequencing of a cohort of 560 breast cancer samples. Within this cohort, 22 patients were known to carry germline BRCA1/BRCA2 mutations. BRCA1/BRCA2- deficiency mutational signatures were found in more breast cancer patients than previously known. This model was able to identify 124 (22%) breast cancer patients showing BRCA1/2 mutational signatures in this cohort of 560 samples. Apart from the 22 known cases, an additional 33 patients showed deficiency with germline BRCA1/2 mutations, 22 patients displayed somatic mutation of BRCA1/2, and 47 were recognized to show functional defect without detected BRCA1/2 mutation. As a result, with an application of a probabilistic cut-off 0.7, HRDetect was able to demonstrate a 98.7% sensitivity recognizing BRCA1/2- deficient cases.
In contrast, germline mutations of BRCA1/2 are present in only 1~5% of breast cancer cases. Furthermore, these findings suggest that more breast cancer patients, as many as 1 in 5 (20%), may benefit from PARP inhibitors than a small percentage of patients currently given with the treatment.
Cohort of 80 Breast cancer patients. 6 out of 7 are above HRDetect score 0.7.
Cohort of 80 Breast Cancer Samples
HRDetect was tested in 80 breast cancer cases with mainly ER positive and HER2 negative. The tool was able to find ones that exceed HRDetect score 0.7, including one germline BRCA1 mutation carrier, four germline BRCA2 mutation carriers and one somatic BRCA2 mutation carrier. The sensitivity of this tool also reached 86%.
HRDetect can be applied to other cancer types and yields adequate sensitivity. [ 6 ]
In a cohort of 73 patients with ovarian cancer, 30 patients were known to carry BRCA1/BRCA2 mutations and 46 (63%) patients were assessed by HRDetect to have HRDetect score over 0.7. The sensitivity of detecting BRCA1/2-deficient cancer was almost 100%, with an additional 16 cases identified.
In a cohort of 96 patients with pancreatic cancers, 6 cases were known to have mutation or allele loss and 11 (11.5%) patients were identified by HRDetect to an exceed cutoff of 0.7. The study observed a similar result of sensitivity approaching 100%, with five other cases identified.
Advantages
Limitations
While it can be used with WES data, the sensitivity of detection falls considerably when not trained with such data. The sensitivity increases when training is performed with WES data however false-positive's are still identified. | https://en.wikipedia.org/wiki/HRDetect |
A HRG gyrocompass is a compass and instrument of navigation . It is the latest [ when? ] generation of maintenance-free instruments.
It uses a hemispherical resonant gyroscope , accelerometers and computers to compute true north . The HRG gyrocompass is a complete unit, which unlike a conventional compass, has no rotating or other moving parts. It has an outstanding reliability. [ 1 ] Its operational Mean Time Between Failure (MTBF) values are improved over a Fiber Optic Gyrocompass and also conventional mechanical gyrocompass. [ 2 ]
It is also immune to severe environmental conditions. [ which? ] | https://en.wikipedia.org/wiki/HRG_gyrocompass |
Bisulfide (or bisulphide in British English) is an inorganic anion with the chemical formula HS − (also written as SH − ). It contributes no color to bisulfide salts, and its salts may have a distinctive putrid smell. It is a strong base. Bisulfide solutions are corrosive and attack the skin.
It is an important chemical reagent and an industrial chemical, mainly used in paper pulp industry ( Kraft process ), textiles, synthetic flavors, coloring brasses, and iron control.
A variety of salts are known, including sodium hydrosulfide and potassium hydrosulfide . Ammonium hydrosulfide , a component of "stink bombs" has not been isolated as a pure solid. Some compounds described as salts of the sulfide dianion contain primarily hydrosulfide. For example, the hydrated form of sodium sulfide , nominally with the formula Na 2 S · 9 H 2 O , is better described as NaSH · NaOH · 8 H 2 O .
Aqueous bisulfide absorbs light at around 230 nm in the UV–visible spectrum . [ 1 ] Using this approach, bisulfide has been detected in the ocean [ 2 ] [ 3 ] and in sewage. [ 4 ] Bisulfide should not be confused with the disulfide dianion, S 2− 2 , or − S–S − .
The bisulfide anion can accept a proton:
Because of its affinity to accept a proton (H + ), bisulfide has a basic character. In aqueous solution, it has a corresponding p K a value of 6.9. Its conjugate acid is hydrogen sulfide ( H 2 S ). However, bisulfide's basicity stems from its behavior as an Arrhenius base . A solution containing spectator-only counter ions, has a basic pH according to the following acid-base reaction:
Upon treatment with an acid, bisulfide converts to hydrogen sulfide . With strong acids, it can be doubly protonated to give H 3 S + . Oxidation of bisulfide gives sulfate. When strongly heated, bisulfide salts decompose to produce sulfide salts and hydrogen sulfide.
At physiological pH, hydrogen sulfide is usually fully ionized to bisulfide (HS − ). Therefore, in biochemical settings, "hydrogen sulfide" is often used to mean, bisulfide. Hydrosulfide has been identified as the third gasotransmitter along with nitric oxide and carbon monoxide. [ 5 ]
SH − is a soft anionic ligand that forms complexes with most metal ions. Examples include [Au(SH) 2 ] − and (C 5 H 5 ) 2 Ti(SH) 2 , derived from gold(I) chloride and titanocene dichloride , respectively. [ 6 ]
Bisulfide salts are corrosive , strongly alkaline and release toxic hydrogen sulfide upon acidification. | https://en.wikipedia.org/wiki/HS- |
Sulfuric(IV) acid ( United Kingdom spelling: sulphuric(IV) acid ), also known as sulfurous (UK: sulphurous ) acid and thionic acid , [ citation needed ] is the chemical compound with the formula H 2 SO 3 .
Raman spectra of solutions of sulfur dioxide in water show only signals due to the SO 2 molecule and the bisulfite ion, HSO − 3 . [ 2 ] The intensities of the signals are consistent with the following equilibrium :
17 O NMR spectroscopy provided evidence that solutions of sulfurous acid and protonated sulfites contain a mixture of isomers, which is in equilibrium: [ 3 ]
Attempts to concentrate the solutions of sulfurous acid simply reverse the equilibrium, producing sulfur dioxide and water vapor. A clathrate with the formula 4SO 2 ·23H 2 O has been crystallised. It decomposes above 7 °C.
Sulfurous acid is commonly known not to exist in its free state, and owing to this, it is stated in textbooks that it cannot be isolated in the water-free form. [ 4 ] However, the molecule has been detected in the gas phase in 1988 by the dissociative ionization of diethyl sulfite . [ 5 ] The conjugate bases of this elusive acid are, however, common anions, bisulfite (or hydrogen sulfite) and sulfite . Sulfurous acid is an intermediate species in the formation of acid rain from sulfur dioxide. [ 6 ]
Aqueous solutions of sulfur dioxide, which sometimes are referred to as sulfurous acid, are used as reducing agents and as disinfectants, as are solutions of bisulfite and sulfite salts. They are oxidised to sulfuric acid or sulfate by accepting another oxygen atom. [ 7 ] | https://en.wikipedia.org/wiki/HS2O3 |
HSAB is an acronym for "hard and soft (Lewis) acids and bases ". HSAB is widely used in chemistry for explaining the stability of compounds , reaction mechanisms and pathways. It assigns the terms 'hard' or 'soft', and 'acid' or 'base' to chemical species . 'Hard' applies to species which are small, have high charge states (the charge criterion applies mainly to acids, to a lesser extent to bases), and are weakly polarizable . 'Soft' applies to species which are big, have low charge states and are strongly polarizable. [ 1 ]
The theory is used in contexts where a qualitative, rather than quantitative, description would help in understanding the predominant factors which drive chemical properties and reactions. This is especially so in transition metal chemistry , where numerous experiments have been done to determine the relative ordering of ligands and transition metal ions in terms of their hardness and softness.
HSAB theory is also useful in predicting the products of metathesis reactions. In 2005 it was shown that even the sensitivity and performance of explosive materials can be explained on basis of HSAB theory. [ 2 ]
Ralph Pearson introduced the HSAB principle in the early 1960s [ 3 ] [ 4 ] [ 5 ] as an attempt to unify inorganic and organic reaction chemistry. [ 6 ]
Essentially, the theory states that soft acids prefer to form bonds with soft bases, whereas hard acids prefer to form bonds with hard bases, all other factors being equal. [ 7 ] It can also be said that hard acids bind strongly to hard bases and soft acids bind strongly to soft bases. The HSAB classification in the original work was largely based on equilibrium constants of Lewis acid/base reactions with a reference base for comparison. [ 8 ]
Borderline cases are also identified: borderline acids are trimethylborane , sulfur dioxide and ferrous Fe 2+ , cobalt Co 2+ caesium Cs + and lead Pb 2+ cations. Borderline bases are: aniline , pyridine , nitrogen N 2 and the azide , chloride , bromide , nitrate and sulfate anions.
Generally speaking, acids and bases interact and the most stable interactions are hard–hard ( ionogenic character) and soft–soft ( covalent character).
An attempt to quantify the 'softness' of a base consists in determining the equilibrium constant for the following equilibrium:
where CH 3 Hg + ( methylmercury ion) is a very soft acid and H + (proton) is a hard acid, which compete for B (the base to be classified).
Some examples illustrating the effectiveness of the theory:
In 1983 Pearson together with Robert Parr extended the qualitative HSAB theory with a quantitative definition of the chemical hardness ( η ) as being proportional to the second derivative of the total energy of a chemical system with respect to changes in the number of electrons at a fixed nuclear environment: [ 11 ]
The factor of one-half is arbitrary and often dropped as Pearson has noted. [ 12 ]
An operational definition for the chemical hardness is obtained by applying a three-point finite difference approximation to the second derivative: [ 13 ]
where I is the ionization potential and A the electron affinity . This expression implies that the chemical hardness is proportional to the band gap of a chemical system, when a gap exists.
The first derivative of the energy with respect to the number of electrons is equal to the chemical potential , μ , of the system,
from which an operational definition for the chemical potential is obtained from a finite difference approximation to the first order derivative as
which is equal to the negative of the electronegativity ( χ ) definition on the Mulliken scale : μ = − χ .
The hardness and Mulliken electronegativity are related as
and in this sense hardness is a measure for resistance to deformation or change. Likewise a value of zero denotes maximum softness , where softness is defined as the reciprocal of hardness.
In a compilation of hardness values only that of the hydride anion deviates. Another discrepancy noted in the original 1983 article are the apparent higher hardness of Tl 3+ compared to Tl + .
If the interaction between acid and base in solution results in an equilibrium mixture the strength of the interaction can be quantified in terms of an equilibrium constant . An alternative quantitative measure is the heat ( enthalpy ) of formation of the Lewis acid-base adduct in a non-coordinating solvent. The ECW model is quantitative model that describes and predicts the strength of Lewis acid base interactions, -ΔH . The model assigned E and C parameters to many Lewis acids and bases. Each acid is characterized by an E A and a C A . Each base is likewise characterized by its own E B and C B . The E and C parameters refer, respectively, to the electrostatic and covalent contributions to the strength of the bonds that the acid and base will form. The equation is
The W term represents a constant energy contribution for acid–base reaction such as the cleavage of a dimeric acid or base. The equation predicts reversal of acids and base strengths. The graphical presentations of the equation show that there is no single order of Lewis base strengths or Lewis acid strengths. [ 14 ] The ECW model accommodates the failure of single parameter descriptions of acid-base interactions.
A related method adopting the E and C formalism of Drago and co-workers quantitatively predicts the formation constants for complexes of many metal ions plus the proton with a wide range of unidentate Lewis acids in aqueous solution, and also offered insights into factors governing HSAB behavior in solution. [ 15 ]
Another quantitative system has been proposed, in which Lewis acid strength toward Lewis base fluoride is based on gas-phase affinity for fluoride . [ 16 ] Additional one-parameter base strength scales have been presented. [ 17 ] However, it has been shown that to define the order of Lewis base strength (or Lewis acid strength) at least two properties must be considered. [ 18 ] For Pearson's qualitative HSAB theory the two properties are hardness and strength while for Drago's quantitative ECW model the two properties are electrostatic and covalent .
An application of HSAB theory is the so-called Kornblum's rule (after Nathan Kornblum ) which states that in reactions with ambident nucleophiles (nucleophiles that can attack from two or more places), the more electronegative atom reacts when the reaction mechanism is S N 1 and the less electronegative one in a S N 2 reaction. This rule (established in 1954) [ 19 ] predates HSAB theory but in HSAB terms its explanation is that in a S N 1 reaction the carbocation (a hard acid) reacts with a hard base (high electronegativity) and that in a S N 2 reaction tetravalent carbon (a soft acid) reacts with soft bases.
According to findings, electrophilic alkylations at free CN − occur preferentially at carbon, regardless of whether the S N 1 or S N 2 mechanism is involved and whether hard or soft electrophiles are employed. Preferred N attack, as postulated for hard electrophiles by the HSAB principle, could not be observed with any alkylating agent. Isocyano compounds are only formed with highly reactive electrophiles that react without an activation barrier because the diffusion limit is approached. It is claimed that the knowledge of absolute rate constants and not of the hardness of the reaction partners is needed to predict the outcome of alkylations of the cyanide ion. [ 20 ]
Reanalysis of a large number of various most typical ambident organic system reveals that thermodynamic/kinetic control describes reactivity of organic compounds perfectly, whereas the HSAB principle fails and should be abandoned in the rationalization of ambident reactivity of organic compounds. [ 21 ] | https://en.wikipedia.org/wiki/HSAB_theory |
HSC Sim is a process simulator based on the HSC Chemistry software and databases. It has been implemented as a module to HSC Chemistry 6.0 published in June 2006 and can be used primarily for static process simulation . HSC stands for H ([enthalpy]), S ([entropy]) and Cp([heat capacity]).
HSC Sim has been primarily developed for the use in the mining and mineral industry , though other use such as modelling of biochemical and organic chemistry processes is possible as well.
In mineral industry the simulator is used for process operator training as an OTS (operator training simulator). | https://en.wikipedia.org/wiki/HSC_Sim |
The bisulfite ion ( IUPAC -recommended nomenclature: hydrogensulfite ) is the ion HSO − 3 . Salts containing the HSO − 3 ion are also known as "sulfite lyes". [ 1 ] Sodium bisulfite is used interchangeably with sodium metabisulfite (Na 2 S 2 O 5 ). Sodium metabisulfite dissolves in water to give a solution of Na + HSO − 3 .
The bisulfite anion exists in solution as a mixture of two tautomers . One tautomer has the proton attached to one of the three oxygen atoms. In the second tautomer the proton resides on sulfur. The S-protonated tautomer has C 3v symmetry . The O-protonated tautomer has only C s symmetry.
There exist two tautomers of bisulfite. They interconvert readily but can be characterized individually by various spectroscopic methods. They have been observed by 17 O NMR spectroscopy: [ 1 ] [ 2 ]
Solutions of bisulfite are typically prepared by treatment of sulfur dioxide with aqueous base: [ 3 ]
HSO − 3 is the conjugate base of sulfurous acid , (H 2 SO 3 ).
HSO − 3 is a weak acidic species with a p K a of 6.97. Its conjugate base is sulfite , SO 2− 3 :
Attempted isolation of the common salts of bisulfite results in dehydration of the anion with formation of metabisulfite ( S 2 O 2− 5 ), also known as disulfite:
Because of this equilibrium, anhydrous sodium and potassium salts of bisulfite cannot be obtained. However, there are some reports of anhydrous bisulfites with large counter ions . [ 4 ]
Bisulfite is a good reducing agent, especially for oxygen scrubbing:
Its reducing properties are exploited to precipitate gold from auric acid (gold dissolved in aqua regia ) and reduce chromium(VI) to chromium(III). In water chlorination , sodium bisulfite is used to reduce the residual 'chlorine' which can have a negative impact on aquatic life.
In organic chemistry , sodium bisulfite is used to form adducts with aldehyde and with certain cyclic ketones . These adducts are α-hydroxy sulfonic acids . [ 6 ] This reaction is useful for the separation and purification of aldehydes. [ 7 ] The bisulfite adducts are charged and so are more soluble in polar solvents. The reaction can be reversed in base or strong acid. [ 8 ] Examples of such procedures are described for benzaldehyde , [ 9 ] 2-tetralone , [ 10 ] citral , [ 11 ] the ethyl ester of pyruvic acid [ 12 ] and glyoxal . [ 13 ] In the ring-expansion reaction of cyclohexanone with diazald , the bisulfite reaction is reported to allow differentiation between the primary reaction product cycloheptanone and the main contaminant cyclooctanone. [ 14 ]
Another use of bisulfite in organic chemistry is as a mild reducing agent , for example to remove traces or excess amounts of chlorine , bromine , iodine , hypochlorite salts, osmate esters, chromium trioxide and potassium permanganate . Sodium bisulfite is a decoloration agent in purification procedures because it reduces strongly coloured oxidizing agents, conjugated alkenes and carbonyl compounds.
Bisulfite is also the key ingredient in the Bucherer reaction . In this reaction an aromatic hydroxyl group is converted to the corresponding amine group. This is a reversible reaction . The first step in this reaction is an addition reaction of sodium bisulfite to an aromatic double bond . The Bucherer carbazole synthesis is a related organic reaction that uses sodium bisulfite as a reagent.
Sodium bisulfite is used in the analysis of the methylation status of cytosines in DNA .
In this technique, sodium bisulfite deaminates cytosine into uracil , but does not affect 5-methylcytosine , a methylated form of cytosine with a methyl group attached to carbon 5.
When the bisulfite-treated DNA is amplified via polymerase chain reaction , the uracil is amplified as thymine and the methylated cytosines are amplified as cytosine. DNA sequencing techniques are then used to read the sequence of the bisulfite-treated DNA. Those cytosines that are read as cytosines after sequencing represent methylated cytosines, while those that are read as thymines represent unmethylated cytosines in the genomic DNA. [ 15 ] | https://en.wikipedia.org/wiki/HSO3 |
Chlorosulfuric acid ( IUPAC name: sulfurochloridic acid ) is the inorganic compound with the formula HSO 3 Cl. It is also known as chlorosulfonic acid , being the sulfonic acid of chlorine . It is a distillable, colorless liquid which is hygroscopic and a powerful lachrymator . Commercial samples usually are pale brown or straw colored. [ 3 ]
Salts and esters of chlorosulfuric acid are known as chlorosulfates .
Chlorosulfuric acid is a tetrahedral molecule . Its structure was debated for many decades until in 1941 Shrinivasa Dharmatti proved by magnetic susceptibility that chlorine is directly bonded to sulfur. [ 4 ] [ 5 ]
The formula is more descriptively written SO 2 (OH)Cl, but HSO 3 Cl is traditional. It is an intermediate, chemically and conceptually, between sulfuryl chloride (SO 2 Cl 2 ) and sulfuric acid (H 2 SO 4 ). [ 6 ] The compound is rarely obtained pure. Upon standing with excess sulfur trioxide, it decomposes to pyrosulfuryl chlorides: [ 7 ]
The industrial synthesis entails the reaction of hydrogen chloride with a solution of sulfur trioxide in sulfuric acid : [ 7 ]
It can also be prepared by the method originally used by acid's discoverer Alexander William Williamson in 1854, [ 4 ] namely chlorination of sulfuric acid, written here for pedagogical purposes as HSO 3 (OH) vs. the usual format H 2 SO 4 :
The latter method is more suited for laboratory-scale operations.
Williamson's discovery disproved then-popular hypothesis that sulfuric acid is a compound of water (which was incorrectly assumed to have formula of HO) and sulfur trioxide . [ 8 ]
ClSO 2 OH is used to prepare alkyl sulfates , which are useful as detergents and as chemical intermediates: [ 7 ]
One historical synthesis of saccharin begins with the reaction of toluene with ClSO 2 OH to give the ortho - and para -toluenesulfonyl chloride derivatives:
Oxidation of the ortho isomer gives the benzoic acid derivative that then is cyclized with ammonia and neutralized with base to afford saccharin.
Chlorosulfonic acid has been used as an anti- contrail agent in Ryan Model 147 reconnaissance drones, [ 9 ] and to produce smoke screens . [ 10 ] [ 11 ]
ClSO 3 H reacts violently with water to yield sulfuric acid and hydrogen chloride, which are corrosive: | https://en.wikipedia.org/wiki/HSO3Cl |
Fluorosulfuric acid ( IUPAC name: sulfurofluoridic acid ) is the inorganic compound with the chemical formula HSO 3 F . It is one of the strongest acids commercially available. It is a tetrahedral molecule and is closely related to sulfuric acid , H 2 SO 4 , substituting a fluorine atom for one of the hydroxyl groups. It is a colourless liquid, although commercial samples are often yellow. [ 2 ]
Fluorosulfuric acid is a free-flowing colorless liquid. It is soluble in polar organic solvents (e.g. nitrobenzene , acetic acid , and ethyl acetate ), but poorly soluble in nonpolar solvents such as alkanes.
HSO 3 F is one of the strongest known simple Brønsted acids . [ 3 ] It has an H 0 value of −15.1 compared to −12 for sulfuric acid. The combination of HSO 3 F and the Lewis acid antimony pentafluoride produces " Magic acid ", which is a far stronger protonating agent. These acids are categorized as " superacids ", acids stronger than 100% sulfuric acid.
Reflecting its strong acidity, HSO 3 F dissolves almost all organic compounds that are even weak proton acceptors. [ 4 ] HSO 3 F hydrolyzes slowly to hydrogen fluoride (HF) and sulfuric acid . The related triflic acid ( CF 3 SO 3 H ) retains the high acidity of HSO 3 F but is more hydrolytically stable. The self-ionization of fluorosulfonic acid also occurs:
HSO 3 F isomerizes alkanes and catalyzes the alkylation of hydrocarbons with alkenes, [ 5 ] although it is unclear if such applications are of commercial importance. It can also be used as a laboratory fluorinating agent. [ 6 ]
Fluorosulfuric acid is prepared by the reaction of HF and sulfur trioxide : [ 2 ]
Alternatively, KHF 2 or CaF 2 can be treated with oleum at 250 °C. Once freed from HF by sweeping with an inert gas, HSO 3 F can be distilled in a glass apparatus. [ 6 ]
Fluorosulfuric acid is considered to be highly toxic and extremely corrosive. It hydrolyzes to release HF. Addition of water to HSO 3 F is similar to, and even more violent than, the addition of water to sulfuric acid . | https://en.wikipedia.org/wiki/HSO3F |
The sulfate or sulphate ion is a polyatomic anion with the empirical formula SO 2− 4 . Salts, acid derivatives, and peroxides of sulfate are widely used in industry. Sulfates occur widely in everyday life. Sulfates are salts of sulfuric acid and many are prepared from that acid.
"Sulfate" is the spelling recommended by IUPAC , but "sulphate" was traditionally used in British English .
The sulfate anion consists of a central sulfur atom surrounded by four equivalent oxygen atoms in a tetrahedral arrangement. The symmetry of the isolated anion is the same as that of methane. The sulfur atom is in the +6 oxidation state while the four oxygen atoms are each in the −2 state. The sulfate ion carries an overall charge of −2 and it is the conjugate base of the bisulfate (or hydrogensulfate) ion, HSO − 4 , which is in turn the conjugate base of H 2 SO 4 , sulfuric acid . Organic sulfate esters , such as dimethyl sulfate , are covalent compounds and esters of sulfuric acid. The tetrahedral molecular geometry of the sulfate ion is as predicted by VSEPR theory .
The first description of the bonding in modern terms was by Gilbert Lewis in his groundbreaking paper of 1916, where he described the bonding in terms of electron octets around each atom. There are two double bonds, and there is a formal charge of +2 on the sulfur atom and -1 on each oxygen atom. [ 1 ] [ a ]
Later, Linus Pauling used valence bond theory to propose that the most significant resonance canonicals had two pi bonds involving d orbitals. His reasoning was that the charge on sulfur was thus reduced, in accordance with his principle of electroneutrality . [ 2 ] The S−O bond length of 149 pm is shorter than the bond lengths in sulfuric acid of 157 pm for S−OH. The double bonding was taken by Pauling to account for the shortness of the S−O bond.
Pauling's use of d orbitals provoked a debate on the relative importance of pi bonding and bond polarity ( electrostatic attraction ) in causing the shortening of the S−O bond. The outcome was a broad consensus that d orbitals play a role, but are not as significant as Pauling had believed. [ 3 ] [ 4 ]
A widely accepted description involving pπ – dπ bonding was initially proposed by Durward William John Cruickshank . In this model, fully occupied p orbitals on oxygen overlap with empty sulfur d orbitals (principally the d z 2 and d x 2 – y 2 ). [ 5 ] However, in this description, despite there being some π character to the S−O bonds, the bond has significant ionic character. For sulfuric acid, computational analysis (with natural bond orbitals ) confirms a clear positive charge on sulfur (theoretically +2.45) and a low 3d occupancy. Therefore, the representation with four single bonds is the optimal Lewis structure rather than the one with two double bonds (thus the Lewis model, not the Pauling model). [ 6 ]
In this model, the structure obeys the octet rule and the charge distribution is in agreement with the electronegativity of the atoms. The discrepancy between the S−O bond length in the sulfate ion and the S−OH bond length in sulfuric acid is explained by donation of p-orbital electrons from the terminal S=O bonds in sulfuric acid into the antibonding S−OH orbitals, weakening them resulting in the longer bond length of the latter.
However, Pauling's representation for sulfate and other main group compounds with oxygen is still a common way of representing the bonding in many textbooks. [ 5 ] [ 7 ] The apparent contradiction can be clarified if one realizes that the covalent double bonds in the Lewis structure actually represent bonds that are strongly polarized by more than 90% towards the oxygen atom. On the other hand, in the structure with a dipolar bond , the charge is localized as a lone pair on the oxygen. [ 6 ]
Typically metal sulfates are prepared by treating metal oxides, metal carbonates, or the metal itself with sulfuric acid : [ 7 ]
Although written with simple anhydrous formulas, these conversions generally are conducted in the presence of water. Consequently the product sulfates are hydrated , corresponding to zinc sulfate ZnSO 4 ·7H 2 O , copper(II) sulfate CuSO 4 ·5H 2 O , and cadmium sulfate CdSO 4 ·H 2 O .
Some metal sulfides can be oxidized to give metal sulfates.
There are numerous examples of ionic sulfates, many of which are highly soluble in water . Exceptions include calcium sulfate , strontium sulfate , lead(II) sulfate , barium sulfate , silver sulfate , and mercury sulfate , which are poorly soluble. Radium sulfate is the most insoluble sulfate known. The barium derivative is useful in the gravimetric analysis of sulfate: if one adds a solution of most barium salts, for instance barium chloride , to a solution containing sulfate ions, barium sulfate will precipitate out of solution as a whitish powder. This is a common laboratory test to determine if sulfate anions are present.
The sulfate ion can act as a ligand attaching either by one oxygen (monodentate) or by two oxygens as either a chelate or a bridge. [ 7 ] An example is the complex Co ( en ) 2 (SO 4 )] + Br − [ 7 ] or the neutral metal complex Pt SO 4 ( PPh 3 ) 2 ] where the sulfate ion is acting as a bidentate ligand. The metal–oxygen bonds in sulfate complexes can have significant covalent character.
Sulfates are widely used industrially. Major compounds include:
Sulfate-reducing bacteria , some anaerobic microorganisms, such as those living in sediment or near deep sea thermal vents, use the reduction of sulfates coupled with the oxidation of organic compounds or hydrogen as an energy source for chemosynthesis.
Some sulfates were known to alchemists. The vitriol salts, from the Latin vitreolum , glassy, were so-called because they were some of the first transparent crystals known. [ 8 ] Green vitriol is iron (II) sulfate heptahydrate, FeSO 4 ·7H 2 O ; blue vitriol is copper (II) sulfate pentahydrate, CuSO 4 ·5H 2 O and white vitriol is zinc sulfate heptahydrate, ZnSO 4 ·7H 2 O . Alum , a double sulfate of potassium and aluminium with the formula K 2 Al 2 (SO 4 ) 4 ·24H 2 O , figured in the development of the chemical industry.
Sulfates occur as microscopic particles ( aerosols ) resulting from fossil fuel and biomass combustion. They increase the acidity of the atmosphere and form acid rain . The anaerobic sulfate-reducing bacteria Desulfovibrio desulfuricans and D. vulgaris can remove the black sulfate crust that often tarnishes buildings. [ 9 ]
After 1990, the global dimming trend had clearly switched to global brightening. [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ] This followed measures taken to combat air pollution by the developed nations , typically through flue-gas desulfurization installations at thermal power plants , such as wet scrubbers or fluidized bed combustion . [ 24 ] [ 25 ] [ 26 ] In the United States, sulfate aerosols have declined significantly since 1970 with the passage of the Clean Air Act , which was strengthened in 1977 and 1990. According to the EPA , from 1970 to 2005, total emissions of the six principal air pollutants, including sulfates, dropped by 53% in the US. [ 27 ] By 2010, this reduction in sulfate pollution led to estimated healthcare cost savings valued at $50 billion annually. [ 28 ] Similar measures were taken in Europe, [ 27 ] such as the 1985 Helsinki Protocol on the Reduction of Sulfur Emissions under the Convention on Long-Range Transboundary Air Pollution , and with similar improvements. [ 29 ]
Since changes in aerosol concentrations already have an impact on the global climate, they would necessarily influence future projections as well. In fact, it is impossible to fully estimate the warming impact of all greenhouse gases without accounting for the counteracting cooling from aerosols. [ 32 ] [ 33 ]
Regardless of the current strength of aerosol cooling, all future climate change scenarios project decreases in particulates and this includes the scenarios where 1.5 °C (2.7 °F) and 2 °C (3.6 °F) targets are met: their specific emission reduction targets assume the need to make up for lower dimming. [ 34 ] Since models estimate that the cooling caused by sulfates is largely equivalent to the warming caused by atmospheric methane (and since methane is a relatively short-lived greenhouse gas), it is believed that simultaneous reductions in both would effectively cancel each other out. [ 35 ]
On regional and global scale, air pollution can affect the water cycle , in a manner similar to some natural processes. One example is the impact of Sahara dust on hurricane formation: air laden with sand and mineral particles moves over the Atlantic Ocean, where they block some of the sunlight from reaching the water surface, slightly cooling it and dampening the development of hurricanes. [ 43 ] Likewise, it has been suggested since the early 2000s that since aerosols decrease solar radiation over the ocean and hence reduce evaporation from it, they would be "spinning down the hydrological cycle of the planet." [ 44 ] [ 45 ]
As the real world had shown the importance of sulfate aerosol concentrations to the global climate, research into the subject accelerated. Formation of the aerosols and their effects on the atmosphere can be studied in the lab, with methods like ion-chromatography and mass spectrometry [ 47 ] Samples of actual particles can be recovered from the stratosphere using balloons or aircraft, [ 48 ] and remote satellites were also used for observation. [ 49 ] This data is fed into the climate models , [ 50 ] as the necessity of accounting for aerosol cooling to truly understand the rate and evolution of warming had long been apparent, with the IPCC Second Assessment Report being the first to include an estimate of their impact on climate, and every major model able to simulate them by the time IPCC Fourth Assessment Report was published in 2007. [ 51 ] Many scientists also see the other side of this research, which is learning how to cause the same effect artificially. [ 52 ] While discussed around the 1990s, if not earlier, [ 53 ] stratospheric aerosol injection as a solar geoengineering method is best associated with Paul Crutzen 's detailed 2006 proposal. [ 54 ] Deploying in the stratosphere ensures that the aerosols are at their most effective, and that the progress of clean air measures would not be reversed: more recent research estimated that even under the highest-emission scenario RCP 8.5 , the addition of stratospheric sulfur required to avoid 4 °C (7.2 °F) relative to now (and 5 °C (9.0 °F) relative to the preindustrial) would be effectively offset by the future controls on tropospheric sulfate pollution, and the amount required would be even less for less drastic warming scenarios. [ 55 ] This spurred a detailed look at its costs and benefits, [ 56 ] but even with hundreds of studies into the subject completed by the early 2020s, some notable uncertainties remain. [ 57 ]
The hydrogensulfate ion ( HSO − 4 ), also called the bisulfate ion, is the conjugate base of sulfuric acid ( H 2 SO 4 ). [ 59 ] [ b ] Sulfuric acid is classified as a strong acid; in aqueous solutions it ionizes completely to form hydronium ( H 3 O + ) and hydrogensulfate ( HSO − 4 ) ions. In other words, the sulfuric acid behaves as a Brønsted–Lowry acid and is deprotonated to form hydrogensulfate ion. Hydrogensulfate has a valency of 1. An example of a salt containing the HSO − 4 ion is sodium bisulfate , NaHSO 4 . In dilute solutions the hydrogensulfate ions also dissociate, forming more hydronium ions and sulfate ions ( SO 2− 4 ). | https://en.wikipedia.org/wiki/HSO4 |
Fluoroantimonic acid is a mixture of hydrogen fluoride and antimony pentafluoride , containing various cations and anions (the simplest being H 2 F + and SbF − 6 ). This mixture is a superacid stronger than pure sulfuric acid , by many orders of magnitude, according to its Hammett acidity function . It even protonates some hydrocarbons to afford pentacoordinate carbocations ( carbonium ions ). [ 1 ] Like its precursor hydrogen fluoride , it attacks glass, but can be stored in containers lined with PTFE (Teflon) or PFA .
Fluoroantimonic acid is formed by combining hydrogen fluoride and antimony pentafluoride :
The speciation (i.e., the inventory of components) of fluoroantimonic acid is complex. Spectroscopic measurements show that fluoroantimonic acid consists of a mixture of HF-solvated protons, [ (HF) n H] + (such as H 3 F + 2 ), and SbF 5 -adducts of fluoride, [(SbF 5 ) n F] – (such as Sb 4 F − 21 ). Thus, the formula " [H 2 F] + [SbF 6 ] − " is a convenient but oversimplified approximation of the true composition. [ 2 ] Nevertheless, the extreme acidity of this mixture is evident from the inferior proton-accepting ability of the species present in the solution. Hydrogen fluoride, a weak acid in aqueous solution that is normally not thought to have any appreciable Brønsted basicity at all, is in fact the strongest Brønsted base in the mixture, protonating to H 2 F + in the same way water protonates to H 3 O + in aqueous acid. It is the fluoronium ion that accounts for fluoroantimonic acid's extreme acidity. The protons easily migrate through the solution, moving from H 2 F + to HF, when present, by the Grotthuss mechanism . [ 3 ]
Two related products have been crystallized from HF-SbF 5 mixtures, and both have been analyzed by single crystal X-ray crystallography . These salts have the formulas [H 2 F + ] [Sb 2 F − 11 ] and [H 3 F + 2 ] [Sb 2 F − 11 ] . In both salts, the anion is Sb 2 F − 11 . [ 4 ] As mentioned above, SbF − 6 is weakly basic; the larger anion Sb 2 F − 11 is expected to be a still weaker base.
Fluoroantimonic acid is the strongest superacid based on the measured value of its Hammett acidity function ( H 0 ), which has been determined for various ratios of HF:SbF 5 . The H 0 of HF is −15. [ 5 ] A solution of HF containing 1 mol % of SbF 5 is −20. The H 0 is −21 for 10 mol%. For > 50 mol % SbF 5 , the H 0 is between −21 and −23. The lowest attained H 0 is about −28 (although some sources have reported to reach below −31.) [ 6 ] [ 7 ] [ 8 ] The following H 0 values show that fluoroantimonic acid is stronger than other superacids. [ 9 ] Increased acidity is indicated by lower (in this case, more negative) values of H 0 .
Of the above, only the carborane acids , whose H 0 could not be directly determined due to their high melting points, may be stronger acids than fluoroantimonic acid. [ 9 ] [ 10 ]
The H 0 value measures the protonating ability of the bulk, liquid acid, and this value has been directly determined or estimated for various compositions of the mixture. The p K a on the other hand, measures the equilibrium of proton dissociation of a discrete chemical species when dissolved in a particular solvent. Since fluoroantimonic acid is not a single chemical species, its p K a value is not well-defined. [ citation needed ]
The gas-phase acidity (GPA) of individual species present in the mixture have been calculated using density functional theory methods. [ 2 ] (Solution-phase p K a s of these species can, in principle, be estimated by taking into account solvation energies, but do not appear to be reported in the literature as of 2019.) For example, the ion-pair [H 2 F] + · SbF – 6 was estimated to have a GPA of 254 kcal/mol. For comparison, the commonly encountered superacid triflic acid , TfOH, is a substantially weaker acid by this measure, with a GPA of 299 kcal/mol. [ 11 ] However, certain carborane superacids have GPAs lower than that of [H 2 F] + · SbF – 6 . For example, H(CHB 11 Cl 11 ) has an experimentally determined GPA of 241 kcal/mol. [ 12 ]
Fluoroantimonic acid solution is so reactive that it is challenging to identify media with which it is unreactive. Materials compatible with fluoroantimonic acid as a solvent include SO 2 ClF , and sulfur dioxide ; some chlorofluorocarbons have also been used. Containers for HF/SbF 5 are made of PTFE . [ citation needed ]
Fluoroantimonic acid solutions decompose when heated, generating free hydrogen fluoride gas and liquid antimony pentafluoride at a temperature of 40 °C. [ 13 ]
As a superacid , fluoroantimonic acid solutions protonate nearly all organic compounds , often causing dehydrogenation, or dehydration. In 1967, Bickel and Hogeveen showed that 2HF·SbF 5 reacts with isobutane and neopentane to form carbenium ions: [ 14 ] [ 15 ]
It is also used in the synthesis of tetraxenonogold complexes. [ 16 ]
HF/SbF 5 is a highly corrosive substance that reacts violently with water. Heating it is dangerous as well, as it decomposes into toxic hydrogen fluoride . With superacids that are fuming and toxic, proper personal protective equipment should be used. In addition to the obligatory gloves and goggles , the use of a face shield and respirator are also required. Regular lab gloves are not recommended, as this acid can react with the gloves. [ 10 ] Safety gear must be worn at all times when handling or going anywhere near the substance, as fluoroantimonic acid can protonate every compound in the human body. [ 17 ] | https://en.wikipedia.org/wiki/HSbF6 |
HT-TALENS ( HIV-targeted transcription activator-like effector nucleases ) is an engineered plant protein that is a proposed cure for AIDS . [ 1 ] [ 2 ]
The HIV genome is made from RNA rather than DNA . The enzyme that converts RNA to DNA and then inserts it into a cell makes between one and 10 mistakes every time it copies itself. This high error rate means that the virus population that inhabits each HIV patients is genetically diverse. [ 1 ]
When the HIV virus infects someone, it copies its DNA and inserts into the DNA of white blood cells , making the virus part of its host. Even if these genes could be silenced with drugs, (later) stopping the drugs sets the viral DNA free to attack the patient. [ 1 ]
HT-TALENs binds to that sequence and cuts the HIV DNA, but not human DNA. When that cut gets fixed by the cell's DNA repair system, it makes a scar that leaves the virus unable to return and make HIV DNA cells. 60% of the cells making the protein damage the viral DNA. [ 1 ]
This genetics article is a stub . You can help Wikipedia by expanding it .
This article about biological engineering is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HT-TALENS |
HTML5test.com is a discontinued [ 3 ] web app for evaluating a web browser 's implementation some of common web standards , including HTML5 , Web SQL Database , Scalable Vector Graphics (SVG), and WebGL . [ 4 ] [ 1 ]
The test suite was developed by Dutch web programmer Niels Leenheer, and published in March 2010. [ 5 ] The app returns an integer score out of a possible 555 points. The point total has changed multiple times through the evolution of the software. Leenheer introduced the present scoring system as part of a major redesign of the test introduced in November 2013. [ 6 ] On 9 January 2024, Leenheer announced a problem with app's server and added that he has no incentives to work on it anymore. [ 3 ] Since then third-party mirrors have been set up at html5test .co and html5test .opensuse .org .
HTML5Test.com evaluates the browser's support for Web storage , the W3C Geolocation API , HTML5-specific HTML elements (including the canvas element ), and other features. [ 7 ] [ 8 ] It does not evaluate a browser's conformance to other web standards, such as Cascading Style Sheets , ECMAScript , or the Document Object Model . Conformance testing for those standards is within the purview of Acid3 , an automated test published by Ian Hickson in 2008. [ 9 ] Similarly, Acid3 does not evaluate a browser's HTML5 conformance. The test scope of HTML5Test.com and the test scope of Acid3 are mutually exclusive. | https://en.wikipedia.org/wiki/HTML5test |
HTML video is a subject of the HTML specification as the standard way of playing video via the web. Introduced in HTML5 , [ 1 ] it is designed to partially replace the object element and the previous de facto standard of using the proprietary Adobe Flash plugin, though early adoption was hampered by lack of agreement as to which video coding formats and audio coding formats should be supported in web browsers. As of 2020, HTML video is the only widely supported video playback technology in modern browsers, with the Flash plugin being phased out.
The <video> element started being discussed by the WHATWG in October 2006. [ 2 ] The <video> element was proposed by Opera Software in February 2007. [ 3 ] Opera also released a preview build that was showcased the same day, [ 4 ] [ 5 ] and a manifesto that called for video to become a first-class citizen of the web. [ 6 ]
The following HTML code fragment will embed a WebM video into a web page.
The "controls" attribute enables the browser's own user interface for controlling playback. Alternatively, playback can be controlled with JavaScript , which the web designer can use to create a custom user interface. The optional "poster" attribute specifies an image to show in the video's place before playback is started. Its purpose is to be representative of the video.
Video format support varies among browsers (see below), so a web page can provide video in multiple formats. For other features, browser sniffing is used sometimes, which may be error-prone: any web developer's knowledge of browsers will inevitably be incomplete or not up-to-date. The browser in question "knows best" what formats it can use. The "video" element supports fallback through specification of multiple sources. Using any number of <source> elements, as shown below, the browser will choose automatically which file to download. Alternatively, the JavaScript canPlayType() function can be used to achieve the same. The "type" attribute specifies the MIME type and possibly a list of codecs, which helps the browser to determine whether it can decode the file without beginning to download it. The MIME type denotes the container format of the file, and the container format defines the interpretation of the codec string. [ 7 ]
The HTML specification does not specify which video and audio formats browsers should support. User agents are free to support any video formats they feel are appropriate, but content authors cannot assume that any video will be accessible by all complying user agents, since user agents have no minimal set of video and audio formats to support.
The HTML5 Working Group considered it desirable to specify at least one video format which all user agents (browsers) should support. The ideal format in this regard would:
Initially, Ogg Theora was the recommended standard video format in HTML5, because it was not affected by any known patents. But on 10 December 2007, the HTML5 specification was updated, [ 8 ] replacing the reference to concrete formats:
User agents should support Theora video and Vorbis audio, as well as the Ogg container format.
with a placeholder: [ 9 ]
It would be helpful for interoperability if all browsers could support the same codecs. However, there are no known codecs that satisfy all the current players: we need a codec that is known to not require per-unit or per-distributor licensing, that is compatible with the open source development model, that is of sufficient quality as to be usable, and that is not an additional submarine patent risk for large companies. This is an ongoing issue and this section will be updated once more information is available. [ 10 ]
The result was a polarisation of HTML video between industry-standard , ISO-defined but patent -encumbered formats, and open formats . The new AV1 format by Alliance for Open Media aims to be both industry standard, royalty-free, and open, and has wide industry support.
Although Theora is not affected by known non-free patents, Apple [ 11 ] has expressed concern about unknown patents that might affect it, whose owners might be waiting for a corporation with extensive financial resources to use the format before suing. [ 12 ] [ 13 ] Formats like H.264 might also be subject to unknown patents in principle, but they have been deployed much more widely and so it is presumed that any patent-holders would have already made themselves known. Apple has also opposed requiring Ogg format support in the HTML standard (even as a "should" requirement) on the grounds that some devices might support other formats much more easily, and that HTML has historically not required particular formats for anything. [ 13 ]
Some web developers criticized the removal of the Ogg formats from the specification. [ 14 ] A follow-up discussion also occurred on the W3C questions and answers blog. [ 15 ]
Mozilla and Opera support only the open formats of Theora and WebM . Google stated its intention to remove support for H.264 in 2011, specifically for the HTML video tag. [ 16 ] Although it has been removed from Chromium , as of January 2021 [update] it has yet to be removed from Google Chrome ten years later. [ 17 ] [ 18 ]
The adaptive bitrate streaming standard MPEG-DASH can be used in Web browsers via the Media Source Extensions (MSE) [ 19 ] and JavaScript-based DASH players. Such players are, e.g., the open-source project dash.js [ 19 ] of the DASH Industry Forum, but there are also products such as the HTML5 Video Player of Bitmovin [ 20 ] (using HTML with JavaScript, but also a Flash-based DASH players for legacy Web browsers not supporting the MSE).
Google 's acquisition of On2 in 2010 resulted in its acquisition of the VP8 video format. Google has provided a royalty-free license to use VP8. [ 21 ] Google also started WebM , which combines the standardized open source VP8 video codec with Vorbis audio in a Matroska based container. The opening of VP8 was welcomed by the Free Software Foundation . [ 22 ]
When Google announced in January 2011 that it would end native support of H.264 in Chrome, [ 23 ] criticism came from many quarters including Peter Bright of Ars Technica [ 24 ] and Microsoft web evangelist Tim Sneath, who compared Google's move to declaring Esperanto the official language of the United States. [ 25 ] However, Haavard Moen of Opera Software strongly criticized the Ars Technica article [ 26 ] and Google responded to the reaction by clarifying its intent to promote WebM in its products on the basis of openness. [ 16 ]
After the launch of WebM, Mozilla and Opera have called for the inclusion of VP8 in HTML. [ 27 ]
On 7 March 2013, Google Inc. and MPEG LA , LLC announced agreements covering techniques that "may be essential" to VP8, with Google receiving a license from MPEG LA and 11 patent holders, and MPEG LA ending its efforts to form a VP8 patent pool. [ 28 ] [ 29 ] [ 30 ] [ 31 ]
In 2012, VP9 was released by Google as a successor to VP8, also open and royalty free.
At the end of 2017 the new AV1 format developed by the Alliance for Open Media (AOMedia) as the evolution of VP9 has reached the feature freeze, and the bitstream freeze is expected for January 2018. Firefox nightly builds already include support for AV1. [ 32 ]
H.264/MPEG-4 AVC is widely used, and has good speed, compression, hardware decoders, and video quality, but is patent-encumbered. [ 33 ] Users of H.264 need licenses either from the individual patent holders, or from the MPEG LA , a group of patent holders including Microsoft and Apple, except for some Internet broadcast video uses. [ 34 ] H.264 is usually used in the MP4 container format, together with Advanced Audio Coding (AAC) audio. AAC is also covered by patents in itself, so users of MP4 will have to license both H.264 and AAC.
In June 2009, the WHATWG concluded that no existing format was suitable as a specified requirement. [ 35 ]
Apple still only supports H.264, but Microsoft now supports VP9 and WebM, and has pledged support for AV1 .
On 30 October 2013, Cisco announced that it was making a binary H.264 module available for download. Cisco will pay the costs of patent licensing for those binary modules when downloaded by the using software while it is being installed , making H.264 free to use in that specific case. [ 36 ]
In the announcement, Cisco cited its desire of furthering the use of the WebRTC project as the reason, since WebRTC's video chat feature will benefit from having a video format supported in all browsers. [ 37 ] The H.264 module will be available on "all popular or feasibly supportable platforms, which can be loaded into any application". [ 38 ]
Cisco is also planning to publish source code for those modules under BSD license , but without paying the royalties, [ 36 ] so the code will practically be free software only in countries without H.264 software patents , which has already been true about other existing implementations.
Also on 30 October 2013, Mozilla's Brendan Eich announced that Firefox would automatically download Cisco's H.264 module when needed by default. He also noted that the binary module is not a perfect solution, since users do not have full free software rights to "modify, recompile, and redistribute without license agreements or fees". Thus Xiph and Mozilla continue the development of Daala . [ 38 ] [ 39 ]
OpenH264 only supports the baseline profile of H.264, and does not by itself address the need for an AAC decoder. Therefore, it is not considered sufficient for typical MP4 web video, which is typically in the high profile with AAC audio. [ 40 ] [ 41 ] [ 42 ] However, for use in WebRTC, the omission of AAC was justified in the release announcement: "the standards bodies have aligned on Opus and G.711 as the common audio codecs for WebRTC". [ 37 ] There is doubt as to whether a capped global licensing of AAC, like Cisco's for H.264, is feasible after AAC's licensing bureau removed the price cap shortly after the release of OpenH264. [ 43 ]
This table shows which video formats are likely to be supported by a given user agent . Most of the browsers listed here use a multimedia framework for decoding and display of video, instead of incorporating such software components. It is not generally possible to tell the set of formats supported by a multimedia framework without querying it, because that depends on the operating system and third party codecs. [ 44 ] In these cases, video format support is an attribute of the framework, not the browser (or its layout engine), assuming the browser properly queries its multimedia framework before rejecting unknown video formats. In some cases, the support listed here is not a function of either codecs available within the operating system's underlying media framework, or of codec capabilities built into the browser, but rather could be by a browser add-on that might, for example, bypass the browser's normal HTML parsing of the <video> tag to embed a plug-in based video player.
Note that a video file normally contains both video and audio content, each encoded in its own format. The browser has to support both the video and audio formats. See HTML audio for a table of which audio formats are supported by each browser.
The video format can be specified by MIME type in HTML (see example ). MIME types are used for querying multimedia frameworks for supported formats. [ 45 ]
Of these browsers, only Firefox and Opera employ libraries for built-in decoding. In practice, Internet Explorer and Safari can also guarantee certain format support, because their manufacturers also make their multimedia frameworks. At the other end of the scale, Konqueror has identical format support to Internet Explorer when run on Windows, and Safari when run on Mac, but the selected support here for Konqueror is the typical for Linux , where Konqueror has most of its users. In general, the format support of browsers is much dictated by conflicting interests of vendors, specifically that Media Foundation and QuickTime support commercial standards, whereas GStreamer and Phonon cannot legally support other than free formats by default on the free operating systems that they are intended for. [ 46 ]
Since 107 (hardware decoding; needs hardware decoder)
(Chromium)
Since 17.0 (supports <video> tag with Web Media Extensions and VP9 Video Extensions ) [ 71 ] [ 72 ] [ 73 ]
These indicate the level of support for the given item in each engine. By default, the most recent version of the engine is implied. However, a specific version number can be listed; when this indicates full support, it's the initial version of the engine fully supporting the item.
Transparent video, that is video with an alpha channel , has multiple design advantages: [ 114 ]
HTML has support for digital rights management (DRM, restricting how content can be used) via the Encrypted Media Extensions (EME). The addition of DRM is controversial because it allows restricting users' freedom to use media restricted by DRM, even where fair use gives users the legal right to do so. [ 119 ] A main argument in W3C's approval of EME was that the video content would otherwise be delivered in plugins and apps, and not in the web browser. [ 120 ]
In 2013 Netflix added support for HTML video using EME, beside their old delivery method using a Silverlight plugin (also with DRM). [ 121 ]
In 2010, in the wake of Apple iPad launch and after Steve Jobs announced that Apple mobile devices would not support Flash , a number of high-profile sites began to serve H.264 HTML video instead of Adobe Flash for user-agents identifying as iPad. [ 122 ] HTML video was not as widespread as Flash videos, though there were rollouts of experimental HTML-based video players from DailyMotion (using Ogg Theora and Vorbis format), [ 123 ] YouTube (using the H.264 and WebM formats), [ 124 ] and Vimeo (using the H.264 format). [ 125 ]
Support for HTML video has been steadily increasing. In June 2013, Netflix added support for HTML video. [ 126 ] In January 2015, YouTube switched to using HTML video instead of Flash by default. [ 127 ] In December 2015, Facebook switched from Flash to HTML video for all video content. [ 128 ]
As of 2016, Flash is still widely installed on desktops, while generally not being supported on mobile devices such as smartphones. [ 129 ] The Flash plugin is widely assumed, including by Adobe, [ 129 ] [ 130 ] to be destined to be phased out, [ 131 ] [ 132 ] which will leave HTML video as the only widely supported method to play video on the World Wide Web. Chrome, [ 133 ] [ 134 ] Firefox, [ 135 ] Safari, [ 136 ] and Edge, [ 137 ] have plans to make almost all flash content click to play in 2017. The only major browser which does not have announced plans to deprecate Flash is Internet Explorer. [ 138 ] Adobe announced on 25 July 2017 that they would be permanently ending development of Flash in 2020. [ 139 ] | https://en.wikipedia.org/wiki/HTML_video |
HTTP Status Code 402 , also known as "Payment Required," is a standard response code in the Hypertext Transfer Protocol (HTTP) . It is part of the HTTP/1.1 protocol defined by the Internet Engineering Task Force (IETF) in the RFC 7231 [ 1 ] specification.
The HTTP 402 status code indicates that the client must make a payment to access the requested resource. [ 2 ] It is typically used in situations where the server requires payment before granting access to the content or service. This code serves as a reminder that financial transaction or authorization is needed to proceed further.
The 402 status code is considered non-standard and was introduced to extend the HTTP protocol's capabilities beyond the standard set of status codes. It provides a clear indication to the client that they need to take action to complete the payment process before they can access the requested resource.
Client request:
Server response: [ 3 ]
The HTTP 402 status code is typically used in e-commerce and subscription-based systems where access to content or services is restricted until the user completes a payment. It can be employed in various scenarios, such as:
The HTTP status code 402 is currently classified as an experimental code within the HTTP protocol . Such experimental codes are introduced to assess new features or ideas and determine their practical application. The designation of the 402 status implies that a payment is mandated to obtain a particular resource or service. However, its tentative status indicates limited mainstream adoption. Web developers and institutions are advised to adhere to recognized HTTP norms and employ stable, thoroughly documented status codes. Even though the 402 code might be used on an experimental basis, caution is recommended because of potential discrepancies and compatibility challenges. [ 5 ]
The HTTP 402 response is accompanied by an entity body that provides additional information to the client regarding the payment requirements. This entity body can be in various formats, including HTML , XML , or JSON , and typically includes details such as the payment amount, payment methods accepted, and instructions on how to complete the transaction. [ 6 ]
The server may also include relevant headers in the response, such as Retry-After, which indicates the time duration the client should wait before retrying the request after completing the payment process. [ 6 ]
The HTTP 402 status code should not be confused with the more commonly used 403 Forbidden status code. [ 7 ] While both codes indicate that access to a resource is restricted, the distinction lies in the reason for the restriction. The 402 code specifically implies that payment is required, whereas the 403 code implies that access is forbidden due to other reasons, such as insufficient permissions or authentication failure. | https://en.wikipedia.org/wiki/HTTP_402 |
HTTP 403 is an HTTP status code meaning access to the requested resource is forbidden. The server understood the request, but will not fulfill it, if it was correct. [ 1 ]
HTTP 403 provides a distinct error case from HTTP 401; while HTTP 401 is returned when the client has not authenticated, and implies that a successful response may be returned following valid authentication, HTTP 403 is returned when the client is not permitted access to the resource despite providing authentication such as insufficient permissions of the authenticated account. [ a ]
Error 403: "The server understood the request, but is refusing to authorize it." [ 2 ] : §15.5.4
Error 401: "The 401 (Unauthorized) status code indicates that the request has not been applied because it lacks valid authentication credentials for the target resource." [ 2 ] : §15.5.2
The Apache web server returns 403 Forbidden in response to requests for URL [ 3 ] paths that corresponded to file system directories when directory listings have been disabled in the server and there is no Directory Index directive to specify an existing file to be returned to the browser. Some administrators configure the Mod proxy extension to Apache to block such requests and this will also return 403 Forbidden. Microsoft IIS responds in the same way when directory listings are denied in that server. In WebDAV , the 403 Forbidden response will be returned by the server if the client issued a PROPFIND request but did not also issue the required Depth header or issued a Depth header of infinity. [ 3 ]
A 403 status code can occur for the following reasons: [ 4 ]
Client request: [ 5 ]
Server response: [ 5 ] | https://en.wikipedia.org/wiki/HTTP_403 |
HTTP Live Streaming (also known as HLS ) is an HTTP -based adaptive bitrate streaming communications protocol developed by Apple Inc. and released in 2009. Support for the protocol is widespread in media players, web browsers, mobile devices, and streaming media servers. As of 2022 [update] , an annual video industry survey has consistently found it to be the most popular streaming format. [ 2 ]
HLS resembles MPEG-DASH in that it works by breaking the overall stream into a sequence of small HTTP-based file downloads, each downloading one short chunk of an overall potentially unbounded transport stream. A list of available streams, encoded at different bit rates, is sent to the client using an extended M3U playlist . [ 3 ]
Based on standard HTTP transactions, HTTP Live Streaming can traverse any firewall or proxy server that lets through standard HTTP traffic, unlike UDP-based protocols such as RTP . This also allows content to be offered from conventional HTTP servers and delivered over widely available HTTP-based content delivery networks . [ 4 ] [ 5 ] [ 6 ] The standard also includes a standard encryption mechanism [ 7 ] and secure-key distribution using HTTPS , which together provide a simple DRM system. Later versions of the protocol also provide for trick-mode fast-forward and rewind and for integration of subtitles.
Apple has documented HTTP Live Streaming as an Internet Draft (Individual Submission), the first stage in the process of publishing it as a Request for Comments (RFC). As of December 2015, the authors of that document have requested the RFC Independent Stream Editor (ISE) to publish the document as an informational (non-standard) RFC outside of the IETF consensus process. [ 8 ] In August 2017, RFC 8216 was published to describe version 7 of the protocol. [ 9 ]
HTTP Live Streaming uses a conventional web server , that implements support for HTTP Live Streaming (HLS), to distribute audiovisual content and requires specific software, such as OBS to fit the content into a proper format ( codec ) for transmission in real time over a network .
The service architecture comprises:
HTTP Live Streaming provides mechanisms for players to adapt to unreliable network conditions without causing user-visible playback stalling. For example, on an unreliable wireless network, HLS allows the player to use a lower quality video, thus reducing bandwidth usage. HLS videos can be made highly available by providing multiple servers for the same video, allowing the player to swap seamlessly if one of the servers fails.
To enable a player to adapt to the bandwidth of the network, the original video is encoded in several distinct quality levels . The server serves an index, called a master playlist , of these encodings , called variant streams . The player can then choose between the variant streams during playback, changing back and forth seamlessly as network conditions change.
At WWDC 2016 Apple announced [ 11 ] the inclusion of byte-range addressing for fragmented MP4 files, or fMP4, allowing content to be played via HLS without the need to multiplex it into MPEG-2 Transport Stream . The industry considered this as a step towards compatibility between HLS and MPEG-DASH . [ 12 ] [ 13 ]
Two unrelated HLS extensions with a Low Latency name and corresponding acronym exist:
The remainder of this section describes Apple's ALHLS. It reduces the glass-to-glass delay when streaming via HLS by reducing the time to start live stream playbacks and maintain that time during a live-streaming event.
It works by adding partial media segment files into the mix, much like MPEG-CMAF's fMP4. Unlike CMAF, ALHLS also supports partial MPEG-2 TS transport files. A partial media segment is a standard segment (e.g. 6 seconds) split into equal segments of less than a second (e.g. 200 milliseconds). The standard first segment is replaced by the series of partial segments. Subsequent segments are of the standard size. [ 16 ] HTTP/2 is required to push the segments along with the playlist, reducing the overhead of establishing repeated HTTP/TCP connections.
Other features include:
Apple also added new tools: tsrecompressor produces and encodes a continuous low latency stream of audio and video. The mediastreamsegmenter tool is now available in a low-latency version. It is an HLS segmenter that takes in a UDP/MPEG-TS stream from tsrecompressor and generates a media playlist, including the new tags above.
Support for low-latency HLS is available in tvOS 13 beta, and iOS & iPadOS 14. [ 17 ] On April 30, 2020, Apple added the low latency specifications to the second edition of the main HLS specification. [ 18 ]
Dynamic ad insertion is supported in HLS using splice information based on SCTE-35 specification. The SCTE-35 splice message is inserted into the media playlist file using the EXT-X-DATERANGE tag. Each SCTE-35 splice_info_section() is represented by an EXT-X-DATERANGE tag with a SCTE35-CMD attribute. A SCTE-35 splice out/in pair signaled by the splice_insert() commands is represented by one or more EXT-X-DATERANGE tags carrying the same ID attribute. The SCTE-35 splice out command should have the SCTE35-OUT attribute and the splice in command should have the SCTE35-IN attribute.
Between the two EXT-X-DATERANGE tags that contain the SCTE35-OUT and SCTE35-IN attributes respectively, there may be a sequence of media segment URIs. These media segments normally represent ad programs that can be replaced by the local or customized ad. The ad replacement does not require the replacement of the media files, only the URIs in the playlist need to be changed to point to different ad programs. The ad replacement can be done on the origin server or on the client's media-playing device.
Notable server implementations supporting HTTP Live Streaming include:
HTTP Live Streaming is natively supported in the following operating systems:
Windows 10 used to have native support for HTTP Live Streaming in EdgeHTML , a proprietary browser engine that was used in Microsoft Edge (now referred to as Edge Legacy) before the transition to the Chromium-based Blink browser engine. Edge Legacy was included in Windows 10 up till version 2004. It was replaced by Edge Chromium in version 20H2. Along with Windows 11 , Microsoft released an updated Media Player that supports HLS natively.
Has full HLS support.
Support via Media Source Extensions on Edge Chromium.
No native support on Edge Chromium from version 79 to present. [ 34 ]
Support via Media Source Extensions on other OS.
Android and iOS have OS-dependent native support.
Other platforms require Media Source Extensions.
Support via Media Source Extensions on other OS.
Other platforms require Media Source Extensions.
Has full HLS support.
Has full HLS support.
To play a HLS stream, go to File > Open Stream and replace "http://" with "itls://" (for video streams) or "itals://" (for audio streams) in the stream URL.
iPhone, iPad, and AppleTV
Plays Internet Radio Streams
HLS Audio - 100% Compliant AAC-LC/HE-AAC/xHE-AAC 2.0 Stereo/5.1-7.1 Surround ES - Elementary Stream ADTS fMP4 - Fragmented ISO MP4 Displays Synchronous Realtime Metadata and Graphics
VLC 3.0 has full HLS support.
Supported protocols IN only: SDVoE and NDI | https://en.wikipedia.org/wiki/HTTP_Live_Streaming |
HTTP Parameter Pollution ( HPP ) is a web application vulnerability exploited by injecting encoded query string delimiters in already existing parameters . The vulnerability occurs if user input is not correctly encoded for output by a web application. [ 1 ] This vulnerability allows the injection of parameters into web application-created URLs. It was first brought forth to the public in 2009 by Stefano di Paola and Luca Carettoni, in the conference OWASP EU09 Poland. [ 1 ] The impact of such vulnerability varies, and it can range from "simple annoyance" to complete disruption of the intended behavior of a web application. Overriding HTTP parameters to alter a web application's behavior, bypassing input and access validation checkpoints, as well as other indirect vulnerabilities, are possible consequences of a HPP attack. [ 1 ]
There is no RFC standard on what should be done when it has passed multiple parameters. HPP could be used for cross channel pollution, bypassing CSRF protection and WAF input validation checks. [ 2 ]
When they are passed multiple parameters with the same name, here is how various back ends behave. [ 3 ]
Proper input validation and awareness about web technology on HPP is protection against HTTP Parameter Pollution. [ 5 ]
This World Wide Web –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/HTTP_parameter_pollution |
Hydrogen ditelluride or ditellane is an unstable hydrogen dichalcogenide containing two tellurium atoms per molecule, with structure H−Te−Te−H or (TeH) 2 . Hydrogen ditelluride is interesting to theorists because its molecule is simple yet asymmetric (with no centre of symmetry ) and is predicted to be one of the easiest to detect parity violation , in which the left handed molecule has differing properties to the right handed one due to the effects of the weak force .
Hydrogen ditelluride can possibly be formed at the tellurium cathode in electrolysis in acid. [ 2 ] When electrolysed in alkaline solutions, a tellurium cathode produces ditelluride Te 2− 2 ions, as well as Te 2− and a red polytelluride. The greatest amount of ditelluride is made when pH is over 12. [ 3 ]
Apart from its speculative detection in electrolysis , ditellane has been detected in the gas phase produced from di- sec -butylditellane. [ 1 ] [ 4 ]
Hydrogen ditelluride has been investigated theoretically, with various properties predicted. The molecule is twisted with a C 2 symmetry . There are two enantiomers . Hydrogen ditelluride is one of the simplest possible unsymmetrical molecules; any simpler molecule will not have the required low symmetry. The equilibrium geometry (not counting zero point energy or vibrational energy) has bond lengths of 2.879 Å between the tellurium atoms and 1.678 Å between hydrogen and tellurium. The H−Te−Te angle is 94.93°. The angle of lowest energy between the two H−Te bonds (the dihedral angle between the H a −Te−Te and Te−Te−H b planes) is 89.32°. The trans configuration is higher in energy (3.71 kcal/mol), and the cis would be even higher (4.69 kcal/mol). [ 5 ]
Being chiral , the molecule is predicted to show evidence of parity violation , though this may get interference from stereomutation tunneling , where the P enantiomer and M enantiomer spontaneously convert into each other by quantum tunneling . The parity violation effect on energy comes about from virtual Z boson exchanges between the nucleus and electrons. [ 6 ] It is proportional to the cube of the atomic number, so is stronger in tellurium molecules than others higher up in the periodic table (O, S, Se). Because of parity violation, the energy of the two enantiomers differs, and is likely to be higher in this molecule than most molecules, so an effort is underway to observe this so-far undetected effect. The tunneling effect is reduced by higher masses, so that the deuterium form, D 2 Te 2 will show less tunneling. In a torsional vibrational mode, the molecule can twist back and forward storing energy. Seven different quantum vibration levels are predicted below the energy to jump to the other enantiomer. The levels are numbered v t = 0 up to 6. The sixth level is predicted to be split into two energy levels because of quantum tunneling. [ 7 ] The parity violation energy is calculated as 3 × 10 −9 cm −1 or 90 Hz. [ 7 ]
The different vibrational modes for H 2 Te are symmetrical stretch of H−Te , symmetrical bend of H−Te−Te , torsion, stretch Te−Te , asymmetrical stretch H−Te , asymmetrical bend of H−Te−Te . [ 7 ] The time to tunnel between enantiomers is only 0.6 ms for 1 H 2 Te 2 , but is 66 000 seconds (18 h 20 min) for the tritium isotopomer T 2 Te 2 . [ 7 ]
There are organic derivatives, in which the hydrogen is replaced by organic groups. One example is bis(2,4,6-tributylphenyl)ditellane. [ 8 ] Others are diphenyl ditelluride and 1,2-bis(cyclohexylmethyl)ditellane. A ligand -TeTeH is known in some transition metal complexes. IUPAC nomenclature calls this "ditellanido". | https://en.wikipedia.org/wiki/HTeTeH |
The HUGO Gene Nomenclature Committee ( HGNC ) is a committee of the Human Genome Organisation (HUGO) that sets the standards for human gene nomenclature . The HGNC approves a unique and meaningful name for every known human gene , [ 4 ] [ 5 ] based on a query of experts. In addition to the name, which is usually 1 to 10 words long, the HGNC also assigns a symbol (a short group of characters) to every gene. As with an SI symbol, a gene symbol is like an abbreviation but is more than that, being a second unique name that can stand on its own just as much as substitute for the longer name. It may not necessarily "stand for" the initials of the name, although many gene symbols do reflect that origin.
Full gene names, and especially gene abbreviations and symbols, are often not specific to a single gene. A marked example is CAP which can refer to any of 6 different genes ( BRD4 Archived 2013-10-27 at the Wayback Machine , CAP1 Archived 2013-11-02 at the Wayback Machine , HACD1 Archived 2013-10-07 at the Wayback Machine , LNPEP Archived 2012-09-13 at the Wayback Machine , SERPINB6 Archived 2013-10-08 at the Wayback Machine , and SORBS1 Archived 2012-10-12 at the Wayback Machine ).
The HGNC short gene names, or gene symbols, unlike previously used or published symbols, are specifically assigned to one gene only. This can result in less common abbreviations being selected but reduces confusion as to which gene is referred to.
The HGNC published its latest human gene naming guidelines in 2020. [ 5 ] These may be summarized as: [ 6 ]
The HGNC states that "gene nomenclature should evolve with new technology rather than be restrictive, as sometimes occurs when historical and single gene nomenclature systems are applied." [ 7 ] The HGNC has also issued guides to specific locus types such as endogenous retroviral loci, [ 8 ] structural variants [ 9 ] and non-coding RNAs. [ 10 ] [ 11 ] [ 12 ]
When assigning new gene nomenclature the HGNC make efforts to contact authors who have published on the human gene in question by email, and their responses to the proposed nomenclature are requested. HGNC also coordinates with the related Mouse and Rat Genomic Nomenclature Committees, other database curators, and experts for given specific gene families or sets of genes.
The gene name revision procedure is similar to the naming procedure, but changing a standardized gene name after establishment of a consensus can create confusion, therefore the merit of this is controversial. For this reason the HGNC aims to change a gene name only if agreement for that change can be reached among a majority of researchers working on that gene.
A complete list of all HGNC-approved gene symbols for protein-coding genes: | https://en.wikipedia.org/wiki/HUGO_Gene_Nomenclature_Committee |
HUMARA assay is one of the most widely used methods to determine the clonal origin of a tumor. [ 1 ] [ 2 ] The method is based on X chromosome inactivation and it takes advantage of the different methylation status of the gene HUMARA (short for human androgen receptor ) located on the X chromosome . Considering the fact that once one X chromosome is inactivated in a cell, [ 3 ] all other cells derived from it will have the same X chromosome inactivated, this approach becomes a tool to differentiate a monoclonal population from a polyclonal one in a female tissue. The HUMARA gene, in particular, has three important features that make it highly convenient for the purpose:
Due to these qualities of the HUMARA gene, clonal origin of any tissue from a female mammalian organism can be determined.
The basic process is as follows:
If two bands are apparent, the tissue studied is most likely of polyclonal origin. If a single band is observed, the tissue is monoclonal unless two alleles have exactly the same numbers of CAG repeats or different cells with the same inactivated initiated the tumor; so, seemingly monoclonal although it is actually polyclonal.
In order to make a conclusion about the clonality of a tumor, the DNA from a normal tissue of the same person is taken, and a sample without enzyme treatment is amplified as a control. If a single band is observed even in normal tissues without enzyme treatment, it may be explained as follows: this person has the genetic pattern XO (this possibility can be excluded if a single band is observed after enzyme treatment because, if XO is indeed the genetic pattern of the sample, then there will be no methylation, and therefore no band should be visible after digesting with the enzyme. If a band is observed after enzyme treatment, the person most likely has two X chromosomes with the exact same CAG repeats.) When two bands appear for normal tissue (both enzyme treated and untreated), and two bands are observed for both the enzyme-treated tumor sample and for untreated tumor DNA, the tumor is polyclonal. However, if the same number of bands are observed with a single band after enzyme treatment, there is a high chance for the tumor to be monoclonal, though this is not certain as it is possible for both alleles to have the exact same CAG repeats. | https://en.wikipedia.org/wiki/HUMARA_assay |
In infrared astronomy , the H band refers to an atmospheric transmission window centred on 1.65 micrometres with a Full width at half maximum of 0.35 micrometres [ 1 ] (in the near-infrared ).
Save for a limited amount of absorption by water vapor, Earth's atmosphere is highly translucent at the wavelengths covered by the H band. [ 2 ] The window is also notably less likely to be contaminated by infrared excess than other bands. [ 3 ]
The band is useful for a range of infrared observations including the imaging of sunspots , spectroscopic investigation of late-type stars , and imaging planetary phenomena such as extraterrestrial vortices or volcanic activity in the Solar System . [ 4 ] In addition stellar atmospheres are highly transparent in the H band and stellar light in the window originates from deeper in the stellar atmosphere than any other band. It also includes within it access to several sets of spectral lines including for carbon monoxide and cyanide . [ 5 ]
This astronomy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/H_band_(infrared) |
In mathematics and control theory , H 2 , or H-square is a Hardy space with square norm. It is a subspace of L 2 space , and is thus a Hilbert space . In particular, it is a reproducing kernel Hilbert space .
In general, elements of L 2 on the unit circle are given by
whereas elements of H 2 are given by
The projection from L 2 to H 2 (by setting a n = 0 when n < 0) is orthogonal.
The Laplace transform L {\displaystyle {\mathcal {L}}} given by
can be understood as a linear operator
where L 2 ( 0 , ∞ ) {\displaystyle L^{2}(0,\infty )} is the set of square-integrable functions on the positive real number line, and C + {\displaystyle \mathbb {C} ^{+}} is the right half of the complex plane. It is more; it is an isomorphism , in that it is invertible, and it isometric , in that it satisfies
The Laplace transform is "half" of a Fourier transform; from the decomposition
one then obtains an orthogonal decomposition of L 2 ( R ) {\displaystyle L^{2}(\mathbb {R} )} into two Hardy spaces
This is essentially the Paley-Wiener theorem . | https://en.wikipedia.org/wiki/H_square |
The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors . | https://en.wikipedia.org/wiki/Ha_(function_prefix) |
Haar-like features are digital image features used in object recognition . They owe their name to their intuitive similarity with Haar wavelets and were used in the first real-time face detector. [ 1 ]
Working with only image intensities (i.e., the RGB pixel values at each and every pixel of image) made the task of feature calculation computationally expensive . A publication by Papageorgiou et al. [ 2 ] discussed working with an alternate feature set based on Haar wavelets instead of the usual image intensities. Paul Viola and Michael Jones [ 1 ] adapted the idea of using Haar wavelets and developed the so-called Haar-like features. A Haar-like feature considers adjacent rectangular regions at a specific location in a detection window, sums up the pixel intensities in each region and calculates the difference between these sums. This difference is then used to categorize subsections of an image.
For example, with a human face, it is a common observation that among all faces the region of the eyes is darker than the region of the cheeks. Therefore, a common Haar feature for face detection is a set of two adjacent rectangles that lie above the eye and the cheek region. The position of these rectangles is defined relative to a detection window that acts like a bounding box to the target object (the face in this case).
In the detection phase of the Viola–Jones object detection framework , a window of the target size is moved over the input image, and for each subsection of the image the Haar-like feature is calculated. This difference is then compared to a learned threshold that separates non-objects from objects. Because such a Haar-like feature is only a weak learner or classifier (its detection quality is slightly better than random guessing) a large number of Haar-like features are necessary to describe an object with sufficient accuracy. In the Viola–Jones object detection framework, the Haar-like features are therefore organized in something called a classifier cascade to form a strong learner or classifier.
The key advantage of a Haar-like feature over most other features is its calculation speed. Due to the use of integral images , a Haar-like feature of any size can be calculated in constant time (approximately 60 microprocessor instructions for a 2-rectangle feature).
A simple rectangular Haar-like feature can be defined as the difference of the sum of pixels of areas inside the rectangle, which can be at any position and scale within the original image. This modified feature set is called 2-rectangle feature . Viola and Jones also defined 3-rectangle features and 4-rectangle features. The values indicate certain characteristics of a particular area of the image. Each feature type can indicate the existence (or absence) of certain characteristics in the image, such as edges or changes in texture. For example, a 2-rectangle feature can indicate where the border lies between a dark region and a light region.
One of the contributions of Viola and Jones was to use summed-area tables , [ 3 ] which they called integral images . Integral images can be defined as two-dimensional lookup tables in the form of a matrix with the same size of the original image. Each element of the integral image contains the sum of all pixels located on the up-left region of the original image (in relation to the element's position). This allows to compute sum of rectangular areas in the image, at any position or scale, using only four lookups:
where points A , B , C , D {\displaystyle A,B,C,D} belong to the integral image I {\displaystyle I} , as shown in the figure.
Each Haar-like feature may need more than four lookups, depending on how it was defined. Viola and Jones's 2-rectangle features need six lookups, 3-rectangle features need eight lookups, and 4-rectangle features need nine lookups.
Lienhart and Maydt [ 4 ] introduced the concept of a tilted (45°) Haar-like feature. This was used to increase the dimensionality of the set of features in an attempt to improve the detection of objects in images. This was successful, as some of these features are able to describe the object in a better way. For example, a 2-rectangle tilted Haar-like feature can indicate the existence of an edge at 45°.
Messom and Barczak [ 5 ] extended the idea to a generic rotated Haar-like feature. Although the idea is sound mathematically, practical problems prevent the use of Haar-like features at any angle. In order to be fast, detection algorithms use low resolution images introducing rounding errors . For this reason rotated Haar-like features are not commonly used. | https://en.wikipedia.org/wiki/Haar-like_feature |
In toxicology , Haber's rule or Haber's law is a mathematical statement of the relationship between the concentration of a poisonous gas and how long the gas must be breathed to produce death, or other toxic effect. The rule was formulated by German chemist Fritz Haber in the early 1900s.
Haber's rule states that, for a given poisonous gas, t C = k {\displaystyle tC=k} , where C {\displaystyle C} is the concentration of the gas (mass per unit volume), t {\displaystyle t} is the amount of time necessary to breathe the gas to produce a given toxic effect, and k {\displaystyle k} is a constant, depending on both the gas and the effect. Thus, the rule states that doubling the concentration will halve the time, for example.
It makes equivalent any two groupings of dose concentration and exposure time that have equivalent mathematical products . For instance, if we assign dose concentration the symbol C, and time the classic t, then for any two dose schema , if C 1 t 1 =C 2 t 2 , then under Haber's rule the two dose schema are equivalent.
Haber's rule is an approximation, useful with certain inhaled poisons under certain conditions, and Haber himself acknowledged that it was not always applicable. If a substance is efficiently eliminated in the host, for example, then Haber's Law breaks down in the limit of t approaching the order of the half-life of the drug , rewriting the equation as the integral ∫Cdt = constant for arbitrary varying C and elapsed time T. It is very convenient, however, because its relationship between C {\displaystyle C} and t {\displaystyle t} appears as a straight line in a log-log plot .
In 1940, statistician C. I. Bliss published a study of toxicity in insecticides in which he proposed more complex models , for example, expressing the relationship between C {\displaystyle C} and t {\displaystyle t} as two straight line segments in a log-log plot . [ 1 ] However, because of its simplicity, Haber's rule continued to be widely used. Recently, some researchers have argued that it is time to move beyond the simple relationship expressed by Haber's rule and to make regular use of more sophisticated models. [ 2 ] | https://en.wikipedia.org/wiki/Haber's_rule |
The Haber process , [ 1 ] also called the Haber–Bosch process , is the main industrial procedure for the production of ammonia . [ 2 ] [ 3 ] It converts atmospheric nitrogen (N 2 ) to ammonia (NH 3 ) by a reaction with hydrogen (H 2 ) using finely divided iron metal as a catalyst:
N 2 + 3 H 2 ↽ − − ⇀ 2 NH 3 Δ H 298 K ∘ = − 92.28 kJ per mole of N 2 {\displaystyle {\ce {N2 + 3H2 <=> 2NH3}}\qquad {\Delta H_{\mathrm {298~K} }^{\circ }=-92.28~{\text{kJ per mole of }}{\ce {N2}}}}
This reaction is exothermic but disfavored in terms of entropy because four equivalents of reactant gases are converted into two equivalents of product gas. As a result, high pressures and temperatures that are not too high are needed to drive the reaction forward .
The German chemists Fritz Haber and Carl Bosch developed the process in the first decade of the 20th century, and its improved efficiency over existing methods such as the Birkeland-Eyde and Frank-Caro processes was a major advancement in the industrial production of ammonia. [ 4 ] [ 5 ] [ 6 ]
The Haber process can be combined with steam reforming to produce ammonia with just three chemical inputs: water, natural gas , and atmospheric nitrogen. Both Haber and Bosch were eventually awarded the Nobel Prize in Chemistry : Haber in 1918 for ammonia synthesis specifically, and Bosch in 1931 for related contributions to high-pressure chemistry .
During the 19th century, the demand rapidly increased for nitrates and ammonia for use as fertilizers, which supply plants with the nutrients they need to grow, and for industrial feedstocks. The main source was mining niter deposits and guano from tropical islands. [ 7 ] At the beginning of the 20th century these reserves were thought insufficient to satisfy future demands, [ 8 ] and research into new potential sources of ammonia increased. Although atmospheric nitrogen (N 2 ) is abundant, comprising ~78% of the air, it is exceptionally stable and does not readily react with other chemicals.
Haber, with his assistant Robert Le Rossignol [ citation needed ] , developed the high-pressure devices and catalysts needed to demonstrate the Haber process at a laboratory scale. [ 9 ] [ 10 ] They demonstrated their process in the summer of 1909 by producing ammonia from the air, drop by drop, at the rate of about 125 mL (4 US fl oz) per hour. The process was purchased by the German chemical company BASF , which assigned Carl Bosch the task of scaling up Haber's tabletop machine to industrial scale. [ 5 ] [ 11 ] He succeeded in 1910. Haber and Bosch were later awarded Nobel Prizes, in 1918 and 1931 respectively, for their work in overcoming the chemical and engineering problems of large-scale, continuous-flow, high-pressure technology. [ 5 ]
Ammonia was first manufactured using the Haber process on an industrial scale in 1913 in BASF's Oppau plant in Germany, reaching 20 tonnes/day in 1914. [ 12 ] During World War I , the production of munitions required large amounts of nitrate. The Allied powers had access to large deposits of sodium nitrate in Chile (Chile saltpetre ) controlled by British companies. India had large supplies too, but it was also controlled by the British. [ 13 ] Moreover, even if German commercial interests had nominal legal control of such resources, the Allies controlled the sea lanes and imposed a highly effective blockade which would have prevented such supplies from reaching Germany. The Haber process proved so essential to the German war effort [ 5 ] [ 14 ] that it is considered virtually certain Germany would have been defeated in a matter of months without it. Synthetic ammonia from the Haber process was used for the production of nitric acid , a precursor to the nitrates used in explosives.
The original Haber–Bosch reaction chambers used osmium as the catalyst , but this was available in extremely small quantities. Haber noted that uranium was almost as effective and easier to obtain than osmium. In 1909, BASF researcher Alwin Mittasch discovered a much less expensive iron-based catalyst that is still used. A major contributor to the discovery of this catalysis was Gerhard Ertl . [ 15 ] [ 16 ] [ 17 ] [ 18 ] The most popular catalysts are based on iron promoted with K 2 O , CaO , SiO 2 , and Al 2 O 3 .
During the interwar years , alternative processes were developed, most notably the Casale process, the Claude process, and the Mont-Cenis process developed by the Friedrich Uhde Ingenieurbüro. [ 19 ] Luigi Casale and Georges Claude proposed to increase the pressure of the synthesis loop to 80–100 MPa (800–1,000 bar ; 12,000–15,000 psi ), thereby increasing the single-pass ammonia conversion and making nearly complete liquefaction at ambient temperature feasible. Claude proposed to have three or four converters with liquefaction steps in series, thereby avoiding recycling. Most plants continue to use the original Haber process (20 MPa (200 bar; 2,900 psi) and 500 °C (932 °F)), albeit with improved single-pass conversion and lower energy consumption due to process and catalyst optimization.
Combined with the energy needed to produce hydrogen and purified atmospheric nitrogen, ammonia production is energy-intensive, accounting for 1% to 2% of global energy consumption , 3% of global carbon emissions , [ 20 ] and 3% to 5% of natural gas consumption. [ 21 ] Hydrogen required for ammonia synthesis is most often produced through gasification of carbon-containing material, mostly natural gas, but other potential carbon sources include coal, petroleum, peat, biomass, or waste. As of 2012, the global production of ammonia produced from natural gas using the steam reforming process was 72%, [ 22 ] however in China as of 2022 natural gas and coal were responsible for 20% and 75% respectively. [ 23 ] Hydrogen can also be produced from water and electricity using electrolysis : at one time, most of Europe's ammonia was produced from the Hydro plant at Vemork . Other possibilities include biological hydrogen production or photolysis , but at present, steam reforming of natural gas is the most economical means of mass-producing hydrogen.
The choice of catalyst is important for synthesizing ammonia. In 2012, Hideo Hosono 's group found that Ru -loaded calcium-aluminium oxide C12A7: e − electride works well as a catalyst and pursued more efficient formation. [ 24 ] [ 25 ] This method is implemented in a small plant for ammonia synthesis in Japan. [ 26 ] [ 27 ] In 2019, Hosono's group found another catalyst, a novel perovskite oxynitride-hydride BaCeO 3− x N y H z , that works at lower temperature and without costly ruthenium. [ 28 ]
The major source of hydrogen is methane . Steam reforming of natural gas extracts hydrogen from methane in a high-temperature and pressure tube inside a reformer with a nickel catalyst. Other fossil fuel sources include coal, heavy fuel oil and naphtha .
Green hydrogen is produced without fossil fuels or carbon dioxide emissions from biomass , water electrolysis and thermochemical (solar or another heat source) water splitting. [ 29 ] [ 30 ] [ 31 ]
Starting with a natural gas ( CH 4 ) feedstock, the steps are as follows;
The hydrogen is catalytically reacted with nitrogen (derived from air separation [ clarification needed ] ) to form anhydrous liquid ammonia . It is difficult and expensive, as lower temperatures result in slower reaction kinetics (hence a slower reaction rate ) [ 32 ] and high pressure requires high-strength pressure vessels [ 33 ] that resist hydrogen embrittlement . Diatomic nitrogen is bound together by a triple bond , which makes it relatively inert. [ 34 ] [ 35 ] Yield and efficiency are low, meaning that the ammonia must be extracted and the gases reprocessed for the reaction to proceed at an acceptable pace. [ 36 ]
This step is known as the ammonia synthesis loop:
The gases (nitrogen and hydrogen) are passed over four beds of catalyst , with cooling between each pass to maintain a reasonable equilibrium constant . On each pass, only about 15% conversion occurs, but unreacted gases are recycled, and eventually conversion of 97% is achieved. [ 3 ]
Due to the nature of the (typically multi-promoted magnetite ) catalyst used in the ammonia synthesis reaction, only low levels of oxygen-containing (especially CO, CO 2 and H 2 O) compounds can be tolerated in the hydrogen/nitrogen mixture. Relatively pure nitrogen can be obtained by air separation , but additional oxygen removal may be required.
Because of relatively low single pass conversion rates (typically less than 20%), a large recycle stream is required. This can lead to the accumulation of inerts in the gas.
Nitrogen gas (N 2 ) is unreactive because the atoms are held together by triple bonds . The Haber process relies on catalysts that accelerate the scission of these bonds.
Two opposing considerations are relevant: the equilibrium position and the reaction rate . At room temperature, the equilibrium is in favor of ammonia, but the reaction does not proceed at a detectable rate due to its high activation energy. Because the reaction is exothermic , the equilibrium constant decreases with increasing temperature following Le Châtelier's principle . It becomes unity at around 150–200 °C (302–392 °F). [ 3 ]
Above this temperature, the equilibrium quickly becomes unfavorable at atmospheric pressure, according to the Van 't Hoff equation . Lowering the temperature is unhelpful because the catalyst requires a temperature of at least 400 °C to be efficient. [ 3 ]
Increased pressure favors the forward reaction because 4 moles of reactant produce 2 moles of product, and the pressure used (15–25 MPa (150–250 bar; 2,200–3,600 psi)) alters the equilibrium concentrations to give a substantial ammonia yield. The reason for this is evident in the equilibrium relationship:
K = y NH 3 2 y H 2 3 y N 2 ϕ ^ NH 3 2 ϕ ^ H 2 3 ϕ ^ N 2 ( P ∘ P ) 2 , {\displaystyle K={\frac {y_{{\ce {NH3}}}^{2}}{y_{{\ce {H2}}}^{3}y_{{\ce {N2}}}}}{\frac {{\hat {\phi }}_{{\ce {NH3}}}^{2}}{{\hat {\phi }}_{{\ce {H2}}}^{3}{\hat {\phi }}_{{\ce {N2}}}}}\left({\frac {P^{\circ }}{P}}\right)^{2},}
where ϕ ^ i {\displaystyle {\hat {\phi }}_{i}} is the fugacity coefficient of species i {\displaystyle i} , y i {\displaystyle y_{i}} is the mole fraction of the same species, P {\displaystyle P} is the reactor pressure, and P ∘ {\displaystyle P^{\circ }} is standard pressure, typically 1 bar (0.10 MPa).
Economically, reactor pressurization is expensive: pipes, valves, and reaction vessels need to be strong enough, and safety considerations affect operating at 20 MPa. Compressors take considerable energy, as work must be done on the (compressible) gas. Thus, the compromise used gives a single-pass yield of around 15%. [ 3 ]
While removing the ammonia from the system increases the reaction yield, this step is not used in practice, since the temperature is too high; instead it is removed from the gases leaving the reaction vessel. The hot gases are cooled under high pressure, allowing the ammonia to condense and be removed as a liquid. Unreacted hydrogen and nitrogen gases are returned to the reaction vessel for another round. [ 3 ] While most ammonia is removed (typically down to 2–5 mol.%), some ammonia remains in the recycle stream. In academic literature, a more complete separation of ammonia has been proposed by absorption in metal halides , metal-organic frameworks or zeolites . [ 38 ] Such a process is called an absorbent-enhanced Haber process or adsorbent-enhanced Haber–Bosch process . [ 39 ]
The steam reforming, shift conversion, carbon dioxide removal , and methanation steps each operate at absolute pressures of about 25 to 35 bar, while the ammonia synthesis loop operates at temperatures of 300–500 °C (572–932 °F) and pressures ranging from 60 to 180 bar depending upon the method used. The resulting ammonia must then be separated from the residual hydrogen and nitrogen at temperatures of −20 °C (−4 °F). [ 40 ] [ 3 ]
The Haber–Bosch process relies on catalysts to accelerate N 2 hydrogenation. The catalysts are heterogeneous solids that interact with gaseous reagents. [ 41 ]
The catalyst typically consists of finely divided iron bound to an iron oxide carrier containing promoters possibly including aluminium oxide , potassium oxide , calcium oxide , potassium hydroxide, [ 42 ] molybdenum, [ 43 ] and magnesium oxide .
The iron catalyst is obtained from finely ground iron powder, which is usually obtained by reduction of high-purity magnetite (Fe 3 O 4 ). The pulverized iron is oxidized to give magnetite or wüstite (FeO, ferrous oxide) particles of a specific size. The magnetite (or wüstite) particles are then partially reduced, removing some of the oxygen . The resulting catalyst particles consist of a core of magnetite, encased in a shell of wüstite , which in turn is surrounded by an outer shell of metallic iron. The catalyst maintains most of its bulk volume during the reduction, resulting in a highly porous high-surface-area material, which enhances its catalytic effectiveness. Minor components include calcium and aluminium oxides , which support the iron catalyst and help it maintain its surface area. These oxides of Ca, Al, K, and Si are unreactive to reduction by hydrogen. [ 3 ]
The production of the catalyst requires a particular melting process in which used raw materials must be free of catalyst poisons and the promoter aggregates must be evenly distributed in the magnetite melt. Rapid cooling of the magnetite, which has an initial temperature of about 3500 °C, produces the desired precursor. Unfortunately, the rapid cooling ultimately forms a catalyst of reduced abrasion resistance. Despite this disadvantage, the method of rapid cooling is often employed. [ 3 ]
The reduction of the precursor magnetite to α-iron is carried out directly in the production plant with synthesis gas . The reduction of the magnetite proceeds via the formation of wüstite (FeO) so that particles with a core of magnetite become surrounded by a shell of wüstite. The further reduction of magnetite and wüstite leads to the formation of α-iron, which forms together with the promoters the outer shell. [ 44 ] The involved processes are complex and depend on the reduction temperature: At lower temperatures, wüstite disproportionates into an iron phase and a magnetite phase; at higher temperatures, the reduction of the wüstite and magnetite to iron dominates. [ 45 ]
The α-iron forms primary crystallites with a diameter of about 30 nanometers. These crystallites form a bimodal pore system with pore diameters of about 10 nanometers (produced by the reduction of the magnetite phase) and of 25 to 50 nanometers (produced by the reduction of the wüstite phase). [ 44 ] With the exception of cobalt oxide , the promoters are not reduced.
During the reduction of the iron oxide with synthesis gas, water vapor is formed. This water vapor must be considered for high catalyst quality as contact with the finely divided iron would lead to premature aging of the catalyst through recrystallization , especially in conjunction with high temperatures. The vapor pressure of the water in the gas mixture produced during catalyst formation is thus kept as low as possible, target values are below 3 gm −3 . For this reason, the reduction is carried out at high gas exchange, low pressure, and low temperatures. The exothermic nature of the ammonia formation ensures a gradual increase in temperature. [ 3 ]
The reduction of fresh, fully oxidized catalyst or precursor to full production capacity takes four to ten days. [ 3 ] The wüstite phase is reduced faster and at lower temperatures than the magnetite phase (Fe 3 O 4 ). After detailed kinetic, microscopic, and X-ray spectroscopic investigations it was shown that wüstite reacts first to metallic iron. This leads to a gradient of iron(II) ions, whereby these diffuse from the magnetite through the wüstite to the particle surface and precipitate there as iron nuclei. A high-activity novel catalyst based on this phenomenon was discovered in the 1980s at the Zhejiang University of Technology and commercialized by 2003. [ 46 ]
Pre-reduced, stabilized catalysts occupy a significant market share . They are delivered showing the fully developed pore structure, but have been oxidized again on the surface after manufacture and are therefore no longer pyrophoric . The reactivation of such pre-reduced catalysts requires only 30 to 40 hours instead of several days. In addition to the short start-up time, they have other advantages such as higher water resistance and lower weight. [ 3 ]
Many efforts have been made to improve the Haber–Bosch process. Many metals were tested as catalysts. The requirement for suitability is the dissociative adsorption of nitrogen (i. e. the nitrogen molecule must be split into nitrogen atoms upon adsorption). If the binding of the nitrogen is too strong, the catalyst is blocked and the catalytic ability is reduced (self-poisoning). The elements in the periodic table to the left of the iron group show such strong bonds. Further, the formation of surface nitrides makes, for example, chromium catalysts ineffective. Metals to the right of the iron group, in contrast, adsorb nitrogen too weakly for ammonia synthesis. Haber initially used catalysts based on osmium and uranium . Uranium reacts to its nitride during catalysis, while osmium oxide is rare. [ 48 ]
According to theoretical and practical studies, improvements over pure iron are limited. The activity of iron catalysts is increased by the inclusion of cobalt. [ 49 ]
Ruthenium forms highly active catalysts. Allowing milder operating pressures and temperatures, Ru-based materials are referred to as second-generation catalysts. Such catalysts are prepared by the decomposition of triruthenium dodecacarbonyl on graphite . [ 3 ] A drawback of activated-carbon-supported ruthenium-based catalysts is the methanation of the support in the presence of hydrogen. Their activity is strongly dependent on the catalyst carrier and the promoters. A wide range of substances can be used as carriers, including carbon , magnesium oxide , aluminium oxide , zeolites , spinels , and boron nitride . [ 50 ]
Ruthenium-activated carbon-based catalysts have been used industrially in the KBR Advanced Ammonia Process (KAAP) since 1992. [ 51 ] The carbon carrier is partially degraded to methane ; however, this can be mitigated by a special treatment of the carbon at 1500 °C, thus prolonging the catalyst lifetime. In addition, the finely dispersed carbon poses a risk of explosion. For these reasons and due to its low acidity , magnesium oxide has proven to be a good choice of carrier. Carriers with acidic properties extract electrons from ruthenium, make it less reactive, and have the undesirable effect of binding ammonia to the surface. [ 50 ]
Catalyst poisons lower catalyst activity. They are usually impurities in the synthesis gas . Permanent poisons cause irreversible loss of catalytic activity, while temporary poisons lower the activity while present. Sulfur compounds, phosphorus compounds, arsenic compounds, and chlorine compounds are permanent poisons. Oxygenic compounds like water, carbon monoxide , carbon dioxide , and oxygen are temporary poisons. [ 3 ] [ 52 ]
Although chemically inert components of the synthesis gas mixture such as noble gases or methane are not strictly poisons, they accumulate through the recycling of the process gases and thus lower the partial pressure of the reactants, which in turn slows conversion. [ 53 ]
The reaction is:
The reaction is an exothermic equilibrium reaction in which the gas volume is reduced. The equilibrium constant K eq of the reaction (see table) and obtained from:
Since the reaction is exothermic , the equilibrium of the reaction shifts at lower temperatures to the ammonia side. Furthermore, four volumetric units of the raw materials produce two volumetric units of ammonia. According to Le Chatelier's principle , higher pressure favours ammonia. High pressure is necessary to ensure sufficient surface coverage of the catalyst with nitrogen. [ 56 ] For this reason, a ratio of nitrogen to hydrogen of 1 to 3, a pressure of 250 to 350 bar, a temperature of 450 to 550 °C and α iron are optimal.
The catalyst ferrite (α-Fe) is produced in the reactor by the reduction of magnetite with hydrogen. The catalyst has its highest efficiency at temperatures of about 400 to 500 °C. Even though the catalyst greatly lowers the activation energy for the cleavage of the triple bond of the nitrogen molecule, high temperatures are still required for an appropriate reaction rate. At the industrially used reaction temperature of 450 to 550 °C an optimum between the decomposition of ammonia into the starting materials and the effectiveness of the catalyst is achieved. [ 57 ] The formed ammonia is continuously removed from the system. The volume fraction of ammonia in the gas mixture is about 20%.
The inert components, especially the noble gases such as argon , should not exceed a certain content in order not to reduce the partial pressure of the reactants too much. To remove the inert gas components, part of the gas is removed and the argon is separated in a gas separation plant . The extraction of pure argon from the circulating gas is carried out using the Linde process . [ 58 ]
Modern ammonia plants produce more than 3000 tons per day in one production line. The following diagram shows the set-up of a modern (designed in the early 1960s by Kellogg [ 59 ] ) "single-train" Haber–Bosch plant:
Depending on its origin, the synthesis gas must first be freed from impurities such as hydrogen sulfide or organic sulfur compounds, which act as a catalyst poison . High concentrations of hydrogen sulfide, which occur in synthesis gas from carbonization coke, are removed in a wet cleaning stage such as the sulfosolvan process , while low concentrations are removed by adsorption on activated carbon . [ 60 ] Organosulfur compounds are separated by pressure swing adsorption together with carbon dioxide after CO conversion.
To produce hydrogen by steam reforming, methane reacts with water vapor using a nickel oxide-alumina catalyst in the primary reformer to form carbon monoxide and hydrogen. The energy required for this, the enthalpy ΔH, is 206 kJ/mol. [ 61 ]
The methane gas reacts in the primary reformer only partially. To increase the hydrogen yield and keep the content of inert components (i. e. methane) as low as possible, the remaining methane gas is converted in a second step with oxygen to hydrogen and carbon monoxide in the secondary reformer. The secondary reformer is supplied with air as the oxygen source. Also, the required nitrogen for the subsequent ammonia synthesis is added to the gas mixture.
In the third step, the carbon monoxide is oxidized to carbon dioxide , which is called CO conversion or water-gas shift reaction .
Carbon monoxide and carbon dioxide would form carbamates with ammonia, which would clog (as solids) pipelines and apparatus within a short time. In the following process step, the carbon dioxide must therefore be removed from the gas mixture. In contrast to carbon monoxide, carbon dioxide can easily be removed from the gas mixture by gas scrubbing with triethanolamine . The gas mixture then still contains methane and noble gases such as argon, which, however, behave inertly. [ 53 ]
The gas mixture is then compressed to operating pressure by turbo compressors . The resulting compression heat is dissipated by heat exchangers ; it is used to preheat raw gases.
The actual production of ammonia takes place in the ammonia reactor. The first reactors were bursting under high pressure because the atomic hydrogen in the carbonaceous steel partially recombined into methane and produced cracks in the steel. Bosch, therefore, developed tube reactors consisting of a pressure-bearing steel tube in which a low-carbon iron lining tube was inserted and filled with the catalyst. Hydrogen that diffused through the inner steel pipe escaped to the outside via thin holes in the outer steel jacket, the so-called Bosch holes. [ 55 ] A disadvantage of the tubular reactors was the relatively high-pressure loss, which had to be applied again by compression. The development of hydrogen-resistant chromium-molybdenum steels made it possible to construct single-walled pipes. [ 62 ]
Modern ammonia reactors are designed as multi-storey reactors with a low-pressure drop, in which the catalysts are distributed as fills over about ten storeys one above the other. The gas mixture flows through them one after the other from top to bottom. Cold gas is injected from the side for cooling. A disadvantage of this reactor type is the incomplete conversion of the cold gas mixture in the last catalyst bed. [ 62 ]
Alternatively, the reaction mixture between the catalyst layers is cooled using heat exchangers, whereby the hydrogen-nitrogen mixture is preheated to the reaction temperature. Reactors of this type have three catalyst beds. In addition to good temperature control, this reactor type has the advantage of better conversion of the raw material gases compared to reactors with cold gas injection.
Uhde has developed and is using an ammonia converter with three radial flow catalyst beds and two internal heat exchangers instead of axial flow catalyst beds. This further reduces the pressure drop in the converter. [ 63 ]
The reaction product is continuously removed for maximum yield. The gas mixture is cooled to 450 °C in a heat exchanger using water, freshly supplied gases, and other process streams. The ammonia also condenses and is separated in a pressure separator. Unreacted nitrogen and hydrogen are then compressed back to the process by a circulating gas compressor , supplemented with fresh gas, and fed to the reactor. [ 62 ] In a subsequent distillation, the product ammonia is purified.
The mechanism of ammonia synthesis contains the following seven elementary steps :
Transport and diffusion (the first and last two steps) are fast compared to adsorption, reaction, and desorption because of the shell structure of the catalyst. It is known from various investigations that the rate-determining step of the ammonia synthesis is the dissociation of nitrogen. [ 3 ] In contrast, exchange reactions between hydrogen and deuterium on the Haber–Bosch catalysts still take place at temperatures of −196 °C (−320.8 °F) at a measurable rate; the exchange between deuterium and hydrogen on the ammonia molecule also takes place at room temperature. Since the adsorption of both molecules is rapid, it cannot determine the speed of ammonia synthesis. [ 64 ]
In addition to the reaction conditions, the adsorption of nitrogen on the catalyst surface depends on the microscopic structure of the catalyst surface. Iron has different crystal surfaces, whose reactivity is very different. The Fe(111) and Fe(211) surfaces have by far the highest activity. The explanation for this is that only these surfaces have so-called C7 sites – these are iron atoms with seven closest neighbours. [ 3 ]
The dissociative adsorption of nitrogen on the surface follows the following scheme, where S* symbolizes an iron atom on the surface of the catalyst: [ 44 ]
The adsorption of nitrogen is similar to the chemisorption of carbon monoxide. On a Fe(111) surface, the adsorption of nitrogen first leads to an adsorbed γ-species with an adsorption energy of 24 kJmol −1 and an N-N stretch vibration of 2100 cm −1 . Since the nitrogen is isoelectronic to carbon monoxide, it adsorbs in an on-end configuration in which the molecule is bound perpendicular to the metal surface at one nitrogen atom. [ 17 ] [ 65 ] [ 3 ] This has been confirmed by photoelectron spectroscopy . [ 66 ]
Ab-initio-MO calculations have shown that, in addition to the σ binding of the free electron pair of nitrogen to the metal, there is a π binding from the d orbitals of the metal to the π* orbitals of nitrogen, which strengthens the iron-nitrogen bond. The nitrogen in the α state is more strongly bound with 31 kJmol −1 . The resulting N–N bond weakening could be experimentally confirmed by a reduction of the wave numbers of the N–N stretching oscillation to 1490 cm −1 . [ 65 ]
Further heating of the Fe(111) area covered by α-N 2 leads to both desorption and the emergence of a new band at 450 cm −1 . This represents a metal-nitrogen oscillation, the β state. A comparison with vibration spectra of complex compounds allows the conclusion that the N 2 molecule is bound "side-on", with an N atom in contact with a C7 site. This structure is called "surface nitride". The surface nitride is very strongly bound to the surface. [ 66 ] Hydrogen atoms (H ads ), which are very mobile on the catalyst surface, quickly combine with it.
Infrared spectroscopically detected surface imides (NH ad ), surface amides (NH 2,ad ) and surface ammoniacates (NH 3,ad ) are formed, the latter decay under NH 3 release ( desorption ). [ 55 ] The individual molecules were identified or assigned by X-ray photoelectron spectroscopy (XPS), high-resolution electron energy loss spectroscopy (HREELS) and Ir Spectroscopy .
On the basis of these experimental findings, the reaction mechanism is believed to involve the following steps (see also figure): [ 67 ]
Reaction 5 occurs in three steps, forming NH, NH 2 , and then NH 3 . Experimental evidence points to reaction 2 as being slow, rate-determining step . This is not unexpected, since that step breaks the nitrogen triple bond, the strongest of the bonds broken in the process.
As with all Haber–Bosch catalysts, nitrogen dissociation is the rate-determining step for ruthenium-activated carbon catalysts. The active center for ruthenium is a so-called B5 site, a 5-fold coordinated position on the Ru(0001) surface where two ruthenium atoms form a step edge with three ruthenium atoms on the Ru(0001) surface. [ 68 ] The number of B5 sites depends on the size and shape of the ruthenium particles, the ruthenium precursor and the amount of ruthenium used. [ 50 ] The reinforcing effect of the basic carrier used in the ruthenium catalyst is similar to the promoter effect of alkali metals used in the iron catalyst. [ 50 ]
An energy diagram can be created based on the Enthalpy of Reaction of the individual steps. The energy diagram can be used to compare homogeneous and heterogeneous reactions: Due to the high activation energy of the dissociation of nitrogen, the homogeneous gas phase reaction is not realizable. The catalyst avoids this problem as the energy gain resulting from the binding of nitrogen atoms to the catalyst surface overcompensates for the necessary dissociation energy so that the reaction is finally exothermic. Nevertheless, the dissociative adsorption of nitrogen remains the rate-determining step: not because of the activation energy, but mainly because of the unfavorable pre-exponential factor of the rate constant. Although hydrogenation is endothermic, this energy can easily be applied by the reaction temperature (about 700 K). [ 3 ]
When first invented, the Haber process competed against another industrial process, the cyanamide process . However, the cyanamide process consumed large amounts of electrical power and was more labor-intensive than the Haber process. [ 5 ] : 137–143
As of 2018, the Haber process produced 230 million tonnes of anhydrous ammonia per year . [ 69 ] The ammonia is used mainly as a nitrogen fertilizer as ammonia itself, in the form of ammonium nitrate , and as urea . The Haber process consumes 3–5% of the world's natural gas production (around 1–2% of the world's energy supply). [ 4 ] [ 70 ] [ 71 ] [ 72 ] In combination with advances in breeding, herbicides, and pesticides, these fertilizers have helped to increase the productivity of agricultural land:
With average crop yields remaining at the 1900 level the crop harvest in the year 2000 would have required nearly four times more land and the cultivated area would have claimed nearly half of all ice-free continents, rather than under 15% of the total land area that is required today. [ 73 ]
The energy-intensity of the process contributes to climate change and other environmental problems such as the leaching of nitrates into groundwater, rivers, ponds, and lakes; expanding dead zones in coastal ocean waters, resulting from recurrent eutrophication ; atmospheric deposition of nitrates and ammonia affecting natural ecosystems; higher emissions of nitrous oxide (N 2 O), now the third most important greenhouse gas following CO 2 and CH 4 . [ 73 ] The Haber–Bosch process is one of the largest contributors to a buildup of reactive nitrogen in the biosphere , causing an anthropogenic disruption to the nitrogen cycle . [ 74 ]
Since nitrogen use efficiency is typically less than 50%, [ 75 ] farm runoff from heavy use of fixed industrial nitrogen disrupts biological habitats. [ 4 ] [ 76 ]
Nearly 50% of the nitrogen found in human tissues originated from the Haber–Bosch process. [ 77 ] Thus, the Haber process serves as the "detonator of the population explosion ", enabling the global population to increase from 1.6 billion in 1900 to 7.7 billion by November 2018. [ 78 ]
Reverse fuel cell [ 79 ] technology converts electric energy, water and nitrogen into ammonia without a separate hydrogen electrolysis process. [ 80 ]
The use of synthetic nitrogen fertilisers reduces the incentive for farmers to use more sustainable crop rotations which include legumes for their natural nitrogen-fixing ability. | https://en.wikipedia.org/wiki/Haber_process |
The Haber–Weiss reaction generates •OH ( hydroxyl radicals ) from H 2 O 2 ( hydrogen peroxide ) and superoxide (•O 2 − ) catalyzed by iron ions. It was first proposed by Fritz Haber and his student Joseph Joshua Weiss in 1932. [ 1 ]
This reaction has long been studied and revived in different contexts, including organic chemistry , free radicals , radiochemistry , and water radiolysis . In the 1970, with the emerging interest for the effect of free radicals onto the ageing mechanisms of living cells due to oxygen (O 2 ), it was proposed that the Haber–Weiss reaction was a source of radicals responsible for cellular oxidative stress . However, this hypothesis was later disproved by several research works. [ 2 ] The oxidative stress toxicity is not caused by the Haber–Weiss reaction as a whole, but by the Fenton reaction , which is one specific part of it.
The reaction is kinetically slow, but is catalyzed by dissolved iron ions. The first step of the catalytic cycle involves the reduction of the ferric (Fe 3+ ) ion into the ferrous (Fe 2+ ) ion:
The second step is the Fenton reaction :
Net reaction:
The main finding of Haber and Weiss was that hydrogen peroxide (H 2 O 2 ) is decomposed by a chain reaction. [ 2 ]
The Haber–Weiss reaction chain proceeds by successive steps: (i) initiation, (ii) propagation and (iii) termination.
The chain is initiated by the Fenton reaction:
Then, the reaction chain propagates by means of two successive steps:
Finally, the chain is terminated when the hydroxyl radical is scavenged by a ferrous ion:
George showed in 1947 that, in water, step 3 cannot compete with the spontaneous disproportionation of superoxide, and proposed an improved mechanism for the disappearance of hydrogen peroxide. See [ 3 ] for a summary. The reactions proposed therein are:
With time, various chemical notations for the hydroperoxyl (perhydroxyl) radical coexist in the literature. Haber, Wilstätter and Weiss simply wrote HO 2 or O 2 H, but sometimes HO 2 • or • O 2 H can also be found to stress the radical character of the species.
The hydroperoxyl radical is a weak acid and gives rise to the superoxide radical (O 2 •– ) when it loses a proton:
A first pK a value of 4.88 for the dissociation of the hydroperoxyl radical was determined in 1970. [ 4 ] The presently accepted value is 4.7. [ 5 ] This pK a value is close to that of acetic acid . Below a pH of 4.7, the protonated hydroperoxyl radical will dominate in solution while at pH above 4.7 the superoxide radical anion will be the main species.
As the Haber–Weiss reaction depends on the presence of both Fe 3+ and Fe 2+ in solution, its kinetics is influenced by the respective solubilities of both species whose are directly function of the solution pH . As Fe 3+ is about 100 times less soluble than Fe 2+ in natural waters at near-neutral pH, the ferric ion concentration is the limiting factor for the reaction rate. The reaction can only proceed with a fast enough rate under sufficiently acidic conditions. At high pH, under alkaline conditions, the reaction considerably slows down because of the precipitation of Fe(OH) 3 which notably lowers the concentration of the Fe 3+ species in solution.
Moreover, the pH value also directly influences the acid-base dissociation equilibrium involving the hydroperoxyl and the superoxide radicals (pK a = 4.7) [ 5 ] as mentioned above. | https://en.wikipedia.org/wiki/Haber–Weiss_reaction |
Habit , equivalent to habitus in some applications in biology , refers variously to aspects of behaviour or structure, as follows:
In zoology , habit (not to be confused with habitus as described below) usually refers to a specific behavior pattern, either adopted, learned , pathological, innate , or directly related to physiology . For example:
Mode of life (or lifestyle , modus vivendi ) is a concept related to habit , and it is sometimes referred to as the habit of an animal. It may refer to the locomotor capabilities, as in "( motile habit ", sessile , errant, sedentary), feeding behaviour and mechanisms, nutrition mode (free-living, parasitic , holozoic , saprotrophic , trophic type ), type of habitat ( terrestrial , arboreal , aquatic , marine , freshwater, seawater, benthic , pelagic , nektonic , planktonic , etc.), period of activity ( diurnal , nocturnal ), types of ecological interaction , etc.
The habits of plants and animals often change responding to changes in their environment . For example: if a species develops a disease or there is a drastic change of habitat or local climate, or it is removed to a different region, then the normal habits may change. Such changes may be either pathological , or adaptive . [ 4 ]
In botany , habit is the general appearance, growth form, or architecture . For example:
Plants may be woody or herbaceous . The main types of woody plants are trees , shrubs and lianas . Climbing plants ( vines ) can be woody (lianas) or herbaceous (nonwoody vines). Plants can also be categorized in terms of their habit as subshrubs (dwarf shrub, bush), cushion plants and succulents . [ 5 ]
There is some overlap between the classifications of plants according to their habit and their life-form .
Other terms in biology refer similarly to various taxa ; for example:
Since the distinction between the concepts – mode of behavior and morphological form – are significant in zoology, the term habitus (from which the word habit derives) is used to describe form as distinct from behaviour ( habit ). The term habitus also occurs in botanical texts, but there it is used almost interchangeably with habit , because plant behaviour generally does not correspond closely to the concept of habits in the zoological sense. [ 6 ] | https://en.wikipedia.org/wiki/Habit_(biology) |
F-type main-sequence stars are thought to be the hottest and more massive stars capable of hosting a planet with extraterrestrial life. Compared to cooler main-sequence stars of G , K and M types, F stars have shorter lifetimes and higher levels of ultraviolet radiation, which can hinder the development of life. Stars hotter than F stars have shorter lifetimes and higher UV incidency, which make life development not possible.
One study on planets and their moons orbiting stars from F5 to F9.5 concluded that exoplanets/moons around exoplanets orbiting in habitable zones of F-type stars would receive excessive UV damage as compared to the Earth. [ 1 ] If half a billion years is assumed as the amount of time it took for life to evolve, then the highest spectral type considerable for life-bearing planets' stars would be around A0. However, it took life on Earth some 3 billion years to establish complexity, which probably rules out all the A-type main sequence stars . Therefore, F0 stars may be the hottest stars that live long enough to allow for the development of complex life. Putting lifetime concerns aside, life on primordial Earth likely started in an underwater (and far underwater) environment anyway, and the water keeps the UV from reaching life-forms. In fact, it is possible that more UV could jumpstart the genesis and evolution of life, fulfilling main-sequence deadlines. [ 2 ] In addition, hotter stars would have wider habitable zones (2.0–3.7 AU for an F0 star and 1.1–2.2 AU for an F8 star as opposed to 0.8–1.7 AU for the Solar System ), which would be another advantage of looking for habitable planets around F-type stars. [ 1 ] If UV does indeed prove to be primarily problematic, then according to Sato et al. (2014) a planet orbiting at the Early Mars limit around an F8 star would actually be better off than Earth, receiving only 95% of the Earth's UV irradiation, and atmospheric attenuation would decrease even a Venus-like (in terms of stellar flux) planet around an F0 star's UV irradiation to less than 1/4 that of Earth. The best case would be an Earth-like planet at the Early Mars limit with attenuation around an F8-type star, where UV irradiance is 3.7% Earth's. [ 3 ]
The greatest variation in UV irradiance occurs in a planet orbiting an F0 star with >1.5 solar masses ( M ☉ ), as opposed to an F8 or F9 star with ≤1.2 M ☉ . The most dangerous phase in a star's life for orbiting habitable planets would be the first 500 million years. In some cases such as a planet at the outer edge of the habitable zone around an old F5 or F8 star, a planet can receive less UV than Earth receive. [ 3 ]
According to the Kepler data, M-type stars supposedly had more Earth-sized planets than larger, Sunlike (where the term is broad, meaning any FG K star) stars. However, in recent years, the Gaia space telescope has exposed Kepler's flaws, making it apparent that Earth-sized planets around red dwarfs are no more common than around FGK stars. As a result, the habitability of F-type stars is not impaired by the overall frequency of Earth-sized planets around them. However, it does show that Earth-size planets should be extremely uncommon (<0.1%) in the habitable zones of their stars. [ 4 ] So, instead of exoplanets, some studies focus mainly on exomoons orbiting Jupiter-like planets that fall within the habitable zone. [ 1 ] Alternatively, a study done by NASA with the same telescope gave a result saying that up to 50% of stars with temperatures between 4,300 (K6) and 7,300 (F0) K had habitable planets, and the number increased to 75% when the optimistic habitable zone was used. [ 5 ]
The habitability of F-type systems may be impaired, though, by the fact that they make up only 3% of the stars in the Milky way, compared to 6–8% for G-types, 12–13% for K-types, and ~70% for red dwarfs. Further study is required to make decisive conclusions about the frequency of habitable planets around F-type stars. [ 3 ] [ 5 ]
As of 2023 [update] , there are no confirmed potentially habitable exoplanets around F-type stars, but some unconfirmed Kepler candidates may be potentially habitable, including KOI-4878.01 , [ 6 ] KOI-7040.01, KOI-6676.01, KOI-5202.01, and KOI-5236.01. Upsilon Andromedae has a Jupiter-like planet in the habitable zone and could therefore have habitable exomoons. [ 7 ] HD 10647 also has such a planet , which has a mass of >0.94 Jupiter masses and orbits at the outer frontier of the habitable zone. [ 8 ]
KOI-4878.01 is a potentially habitable exoplanet candidate orbiting an F8-type star. It is Earth-sized, with a period of 449 days and a semi-major axis of 1.137 AU. The equilibrium temperature is 258 K (−15 °C; 5 °F), and it gets just 1.04 times the light that Earth gets from the Sun. It could be the most Earth-like planet ever found ( ESI = 0.98) if it is confirmed, despite its hotter and more massive star (stellar properties are not taken into account in ESI calculation). With a purely watery composition, the mass would be ~4 Mars masses (0.4 Earths), and with a pure iron composition, the mass would be 3 Earths. [ 6 ] [ 9 ]
Upsilon Andromedae is another F8-type star. It has 3 confirmed Jovian planets, and Upsilon Andromedae d orbits in the star's extended habitable zone on a 1267-day year. It orbits near the outer edge, at 2.5 AU, and has a minimum mass of 4.6 Jupiters. [ 7 ] The habitability potential is therefore in possible Earth-like exomoons and not in the planet itself. It was the first multiple-planet system to be found around a main-sequence star (as well as, consequently, an F star) and is shown to be dynamically stable in all scenarios. [ 7 ] | https://en.wikipedia.org/wiki/Habitability_of_F-type_main-sequence_star_systems |
K-type main-sequence stars , also known as orange dwarfs, may be candidates for supporting extraterrestrial life . These stars are known as "Goldilocks stars" as they emit enough radiation in the non- UV ray spectrum [ 1 ] to provide a temperature that allows liquid water to exist on the surface of a planet; they also remain stable in the main sequence longer than the Sun by burning their hydrogen slower, [ 2 ] allowing more time for life to form on a planet around a K-type main-sequence star. [ 3 ] The planet's habitable zone, ranging from 0.1–0.4 to 0.3–1.3 astronomical units (AU), [ 4 ] [ better source needed ] depending on the size of the star, is often far enough from the star so as not to be tidally locked to the star, and to have a sufficiently low solar flare activity not to be lethal to life. In comparison, red dwarf stars have too much solar activity and quickly tidally lock the planets in their habitable zones, making them less suitable for life. The odds of complex life arising may be better on planets around K-type main-sequence stars than around Sun-like stars, given the suitable temperature and extra time available for it to evolve. [ 5 ] Some planets around K-type main-sequence stars are potential candidates for extraterrestrial life. [ 2 ]
A K-type star's habitable zone approximately ranges between 0.1–0.4 to 0.3–1.3 AU from the star. Here, exoplanets will receive only a relatively small amount of ultraviolet radiation, especially so towards the outer edge. This is favorable to support life, as it means that there is enough radiated energy to allow liquid water to exist on the surface, but not so much, especially ionizing radiation, as to destroy life. [ 4 ]
The habitable zone is also very stable, lasting for most of the K-type main-sequence star's main sequence phase and with little instability of luminosity during that phase. [ 6 ]
Despite K-stars' lower total UV output, in order for their planets to have habitable temperatures, they must orbit much nearer to their K-star hosts, offsetting or reversing any advantage of a lower total UV output. There is also growing evidence that K-type dwarf stars emit dangerously high levels of X-rays and far ultraviolet (FUV) radiation for considerably longer into their early main sequence phase than do either heavier G-type stars or lighter early M-type dwarf stars. [ 7 ] This prolonged radiation saturation period may sterilise, destroy the atmospheres of, or at least delay the emergence of life for Earth-like planets orbiting inside the habitable zones around K-type dwarf stars. [ 7 ] [ 8 ]
The super-Earth HD 40307 g around the K2.5V star HD 40307 orbits in the circumstellar habitable zone (CHZ), although it has a reasonably elliptical orbit ( e =0.22). There may be many more, and the Kepler space telescope (now retired) was one of the main sources of information of these exoplanets. [ 9 ] Kepler-62 and Kepler-442 are examples of discoveries by Kepler of systems consisting of a K-type dwarf with potentially habitable planets orbiting it.
HD 85512 b was originally thought to be a super-Earth with habitability potential orbiting a K-type main-sequence star, [ 10 ] [ 11 ] but it is now considered to be a false positive detection, [ 12 ] an artifact caused by stellar rotation . [ 13 ] | https://en.wikipedia.org/wiki/Habitability_of_K-type_main-sequence_star_systems |
The habitability of neutron star systems is the potential of planets and moons orbiting a neutron star to provide suitable habitats for life . [ 1 ] Of the roughly 3000 neutron stars known, only a handful have sub-stellar companions. The most famous of these are the low-mass planets around the millisecond pulsar PSR B1257+12 .
Habitability is conventionally defined by the equilibrium temperature of a planet, which is a function of the amount of incoming radiation; a planet is defined "habitable" if liquid water can exist on its surface although even planets with little external energy can harbour underground life. Pulsars do not emit large quantities of radiation given their small size; the habitable zone can easily end up lying so close to the star that tidal effects destroy the planets. Additionally, it is often unclear how much radiation a given pulsar emits and how much of it can actually reach a hypothetical planet's surface; of the known pulsar planets, only those of PSR B1257+12 are close to the habitable zone and as of 2015, no known pulsar planet is likely to be habitable.
A habitable planet orbiting a neutron star must be between one and 10 times the mass of the Earth. If the planet were lighter, its atmosphere would be lost. Its atmosphere must also be thick enough to convert the intense X-ray radiation from the neutron star into heat on its surface allowing it to have a temperature suitable for life. [ 1 ]
A magnetic field strong enough — the magnetosphere — would protect the planet from the strong solar winds . This could preserve the planet's atmosphere for several billion years. Such a planet could have liquid water on its surface. [ 1 ]
A Dutch research team published an article on the subject in the journal Astronomy & Astrophysics in December 2017. [ 2 ] [ 3 ] | https://en.wikipedia.org/wiki/Habitability_of_neutron_star_systems |
The Habitable Exoplanet Observatory ( HabEx ) is a space telescope concept that would be optimized to search for and image Earth-size habitable exoplanets in the habitable zones of their stars, where liquid water can exist. HabEx would aim to understand how common terrestrial worlds beyond the Solar System may be and determine the range of their characteristics. It would be an optical, UV and infrared telescope that would also use spectrographs to study planetary atmospheres and eclipse starlight with either an internal coronagraph or an external starshade . [ 3 ]
The proposal, first made in 2016, is for a large strategic science missions NASA mission. It would operate at the Lagrange point L2 .
In January 2023, a new space telescope concept was proposed called the Habitable Worlds Observatory (HWO), which draws upon HabEx and the Large Ultraviolet Optical Infrared Surveyor (LUVOIR). [ 4 ]
In 2016, NASA began considering four different space telescopes as the next Flagship ( Large strategic science missions ) following the James Webb Space Telescope and Nancy Grace Roman Space Telescope . [ 3 ] They are the Habitable Exoplanet Observatory (HabEx), Large Ultraviolet Optical Infrared Surveyor (LUVOIR), Origins Space Telescope , and Lynx X-ray Surveyor . In 2019, the four teams turned their final reports over to the National Academy of Sciences , whose independent Decadal Survey committee advises NASA on which mission should take top priority. [ 3 ]
The Habitable Exoplanet Imaging Mission (HabEx) is a concept for a mission to directly image planetary systems around Sun-like stars. [ 5 ] [ 6 ] HabEx will be sensitive to all types of planets; however its main goal is to directly image Earth-size rocky exoplanets, and characterize their atmospheric content . By measuring the spectra of these planets, HabEx will search for signatures of habitability such as water, and be sensitive to gases in the atmosphere potentially indicative of biological activity, such as oxygen or ozone. [ 6 ]
In 2021, the National Academy of Sciences released its final recommendations in the Decadal Survey. It recommended that NASA consider a new 6-meter (20-foot) aperture telescope combining design elements of LUVOIR and HabEx. The new telescope would be called the Habitable Worlds Observatory (HWO). A preliminary launch date was set for 2040, and the budget was estimated to be $11 billion. [ 7 ] [ 8 ] [ 9 ]
HabEx's prime science goal is the discovery and characterization of Earth-sized planets in the habitable zones of nearby main sequence stars, it will also study the full range of exoplanets within the systems and also enable a wide range of general astrophysics science.
In particular, the mission will be designed to search for signs of habitability and biosignatures in the atmospheres of Earth-sized rocky planets located in the habitable zone of nearby solar type stars. [ 10 ] Absorption features from CH 4 , H 2 O , NH 3 , and CO , and emission features from Na and K , are all within the wavelength range of anticipated HabEx observations.
With a contrast that is 1000 times better than that achievable with the Hubble Space Telescope , [ 10 ] HabEx could resolve large dust structures , tracing the gravitational effect of planets. By imaging several faint protoplanetary disks for the first time, HabEx will enable comparative studies of dust inventory and properties across a broad range of stellar classifications . [ 5 ] This will put the Solar System in perspective not only in terms of exoplanet populations, but also in terms of dust belt morphologies. [ 10 ]
General astrometry and astrophysics observations may be performed if justified by a high science return while still being compatible with top exoplanet science goals and preferred architecture. A wide variety of investigations are currently being considered for HabEx general astrophysics program. They range from studies of galaxy leakiness and inter-galactic medium reionization through measurements of the escape fraction of ionizing photons , to studies of the life cycle of baryons as they flow in and out of galaxies, to resolved stellar population studies, including the impact of massive stars and other local environment conditions on star formation rate and history. [ 10 ] More exotic applications include astrometric observations of local dwarf galaxies to help constrain the nature of dark matter , and precision measurement of the local value of the Hubble Constant . [ 10 ]
The following table summarizes the possible investigations currently suggested for HabEx general astrophysics: [ 10 ]
Based on the science drivers and purpose, the researchers are considering direct imaging and spectroscopy of reflected starlight in the visible spectrum , with potential extensions to the UV and the near infrared parts of the spectrum . The telescope has a primary monolithic mirror that is 4 metres (13 ft) in diameter.
An absolute minimum continuous wavelength range is 0.4 to 1 μm, with possible short wavelength extensions down below 0.3 μm and near infrared extensions to 1.7 μm or even 2.5 μm, depending on the cost and complexity. [ 10 ]
For characterization of extraterrestrial atmospheres , going to longer wavelengths would require a 52 m (171 ft) starshade that would launch separately on a Falcon Heavy , [ 1 ] or a larger telescope in order to reduce the amount of background light. An alternative would be to keep the coronagraph small. Characterizing exoplanets at wavelengths shorter than ~350 nm would require a fully UV-sensitive high contrast optical train to preserve throughput, and will make all wavefront requirements more stringent, whether for a starshade or a coronagraph architecture. [ 10 ] Such high spatial resolution, high contrast observations would also open up unique capabilities for studying the formation and evolution of stars and galaxies.
HabEx would search for potential biosignature gases in exoplanets' atmospheres, such as O 2 (0.69 and 0.76 μm) and its photolytic product ozone ( O 3 ). On the long wavelength side, extending the observations to 1.7 μm would make it possible to search for strong additional water signatures (at 1.13 and 1.41 μm), and would also allow to search for evidence that the detected O 2 and O 3 gases were created by abiotic processes (e.g., by looking for features from CO 2 , CO, O 4 ). A further infrared capability to ~2.5 μm would allow to search for secondary features such as methane ( CH 4 ) that may be consistent with biological processes. Pushing even further in the UV may also allow distinction between a biotic, high-O 2 atmosphere from an abiotic, CO 2 -rich atmosphere based on the ozone absorption of 0.3 μm. [ 10 ]
Molecular oxygen ( O 2 ) can be produced by geophysical processes, as well as a byproduct of photosynthesis by life forms , so although encouraging, O 2 is not a definite biosignature, unless it is considered in its environmental context. I.e., while O2 production to ~20% of atmospheric content seems to be part of life on Earth, too much oxygen is actually poisonous to life as humans know it and could easily be created by planetary situations like a incredibly deep world spanning ocean. [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] | https://en.wikipedia.org/wiki/Habitable_Exoplanets_Observatory |
The Habitable Worlds Observatory (HWO) is a proposed next generation space telescope , a successor of the flagship Hubble , Webb and Roman projects. It would have a large 6–8 meter mirror and be able to detect infrared , optical , and ultraviolet wavelengths. Its primary mission would be to search for and image Earth-size habitable exoplanets in the habitable zones of their stars, where liquid water can exist, by using a coronagraph or a starshade to block out the light of their stars. Beyond planets, it will also observe galaxies. [ 1 ] The proposed launch date is 2041, a tentative date because U.S. President Donald Trump has promised to defund and dismantle the Roman telescope only a year away from launch. [ 2 ]
HWO’s main objective would be to identify and directly image at least 25 potentially habitable worlds. It would then use spectroscopy to search for chemical biosignatures in these planets’ atmospheres, including gases such as oxygen and methane, which could serve as critical evidence for life. HWO would also use its high sensitivity and resolution capabilities to trace the evolution of galaxies and other cosmic structures. [ 3 ]
The main science themes for HWO are: [ 1 ]
The concept for HWO came out of two earlier ideas called the Large Ultraviolet Optical Infrared Surveyor and Habitable Exoplanets Observatory . HWO was officially recommended in 2020 by the National Academies ’ Decadal Survey on Astronomy and Astrophysics . [ 4 ] In 2023, the National Aeronautics and Space Administration (NASA) established a Great Observatory Maturation Program (GOMAP) to unite government, industry, and academia to develop the technologies needed for HWO. [ 3 ] GOMAP aims to draw on lessons from previous NASA missions to streamline development of the HWO concept and decrease budget and schedule risks for the future mission.
The HWO is designed to be launched on a super heavy-lift launch vehicle such as SpaceX 's Starship , Blue Origin 's New Glenn or the SLS . [ 5 ] The design for the HWO includes a 6–8 meter mirror, however it would allow for a larger mirror if launch vehicle technology allows by the time of its launch in the 2040s. [ 5 ] | https://en.wikipedia.org/wiki/Habitable_Worlds_Observatory |
In astronomy and astrobiology , the habitable zone ( HZ ), or more precisely the circumstellar habitable zone ( CHZ ), is the range of orbits around a star within which a planetary surface can support liquid water given sufficient atmospheric pressure . [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] The bounds of the HZ are based on Earth 's position in the Solar System and the amount of radiant energy it receives from the Sun . Due to the importance of liquid water to Earth's biosphere , the nature of the HZ and the objects within it may be instrumental in determining the scope and distribution of planets capable of supporting Earth-like extraterrestrial life and intelligence . As such, it is considered by many to be a major factor of planetary habitability , and the most likely place to find extraterrestrial liquid water and biosignatures elsewhere in the universe.
The habitable zone is also called the Goldilocks zone , a metaphor , allusion and antonomasia of the children's fairy tale of " Goldilocks and the Three Bears ", in which a little girl chooses from sets of three items, rejecting the ones that are too extreme (large or small, hot or cold, etc.), and settling on the one in the middle, which is "just right".
Since the concept was first presented many stars have been confirmed to possess an HZ planet, including some systems that consist of multiple HZ planets. [ 7 ] Most such planets, being either super-Earths or gas giants , are more massive than Earth, because massive planets are easier to detect . [ 8 ] On November 4, 2013, astronomers reported, based on Kepler space telescope data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of Sun-like stars and red dwarfs in the Milky Way . [ 9 ] [ 10 ] About 11 billion of these may be orbiting Sun-like stars. [ 11 ] Proxima Centauri b , located about 4.2 light-years (1.3 parsecs ) from Earth in the constellation of Centaurus , is the nearest known exoplanet, and is orbiting in the habitable zone of its star. [ 12 ] The HZ is also of particular interest to the emerging field of habitability of natural satellites because planetary mass moons in the HZ might outnumber planets. [ 13 ]
In subsequent decades, the HZ concept began to be challenged as a primary criterion for life, so the concept is still evolving. [ 14 ] Since the discovery of evidence for extraterrestrial liquid water, substantial quantities of it are now thought to occur outside the circumstellar habitable zone. The concept of deep biospheres , like Earth's, that exist independently of stellar energy, are now generally accepted in astrobiology given the large amount of liquid water known to exist in lithospheres and asthenospheres of the Solar System. [ 15 ] Sustained by other energy sources, such as tidal heating [ 16 ] [ 17 ] or radioactive decay [ 18 ] or pressurized by non-atmospheric means, liquid water may be found even on rogue planets , or their moons. [ 19 ] Liquid water can also exist at a wider range of temperatures and pressures as a solution , for example with sodium chlorides in seawater on Earth, chlorides and sulphates on equatorial Mars , [ 20 ] or ammoniates, [ 21 ] due to its different colligative properties . In addition, other circumstellar zones, where non-water solvents favorable to hypothetical life based on alternative biochemistries could exist in liquid form at the surface, have been proposed. [ 22 ]
An estimate of the range of distances from the Sun allowing the existence of liquid water appears in Newton's Principia (Book III, Section 1, corol. 4). [ 23 ] The philosopher Louis Claude de Saint-Martin speculated in his 1802 work Man: His True Nature and Ministry , "... we may presume, that, being susceptible of vegetation, it [the Earth] has been placed, in the series of planets, in the rank which was necessary, and at exactly the right distance from the sun, to accomplish its secondary object of vegetation; and from this we might infer that the other planets are either too near or too remote from the sun, to vegetate." [ 24 ]
Possibly the earliest use of the term habitable zone was in 1913, [ 25 ] by Edward Maunder in his book "Are The Planets Inhabited?". [ 26 ] Hubertus Strughold 's 1953 treatise The Green and the Red Planet: A Physiological Study of the Possibility of Life on Mars used the term "ecosphere" and referred to various "zones" in which life could emerge. [ 27 ] [ 28 ] In the same year, Harlow Shapley wrote "Liquid Water Belt", which described the same concept in further scientific detail. Both works stressed the importance of liquid water to life. [ 29 ] Su-Shu Huang , an American astrophysicist argued in 1960 that circumstellar habitable zones, and by extension extraterrestrial life, would be uncommon in multiple star systems , given the gravitational instabilities of those systems. [ 30 ] [ 31 ] [ 32 ]
The concept of habitable zones was further developed in 1964 by Stephen H. Dole in his book Habitable Planets for Man , in which he discussed the concept of the circumstellar habitable zone as well as various other determinants of planetary habitability, eventually estimating the number of habitable planets in the Milky Way to be about 600 million. [ 3 ] At the same time, science-fiction author Isaac Asimov introduced the concept of a circumstellar habitable zone to the general public through his various explorations of space colonization . [ 33 ] The term " Goldilocks zone " emerged in the 1970s, referencing specifically a region around a star whose temperature is "just right" for water to be present in the liquid phase. [ 34 ] In 1993, astronomer James Kasting introduced the term "circumstellar habitable zone" to refer more precisely to the region then (and still) known as the habitable zone. [ 30 ] Kasting was the first to present a detailed model for the habitable zone for exoplanets. [ 4 ] [ 35 ]
An update to the habitable zone concept came in 2000 when astronomers Peter Ward and Donald Brownlee introduced the idea of the " galactic habitable zone ", which they later developed with Guillermo Gonzalez . [ 36 ] [ 37 ] The galactic habitable zone, defined as the region where life is most likely to emerge in a galaxy, encompasses those regions close enough to a galactic center that stars there are enriched with heavier elements , but not so close that star systems, planetary orbits, and the emergence of life would be frequently disrupted by the intense radiation and enormous gravitational forces commonly found at galactic centers. [ 36 ]
Subsequently, some astrobiologists propose that the concept be extended to other solvents, including dihydrogen, sulfuric acid, dinitrogen, formamide, and methane, among others, which would support hypothetical life forms that use an alternative biochemistry . [ 22 ] In 2013, further developments in habitable zone concepts were made with the proposal of a circum- planetary habitable zone, also known as the "habitable edge", to encompass the region around a planet where the orbits of natural satellites would not be disrupted, and at the same time tidal heating from the planet would not cause liquid water to boil away. [ 38 ]
It has been noted that the current term of 'circumstellar habitable zone' poses confusion as the name suggests that planets within this region will possess a habitable environment. [ 39 ] [ 40 ] However, surface conditions are dependent on a host of different individual properties of that planet. [ 39 ] [ 40 ] This misunderstanding is reflected in excited reports of 'habitable planets'. [ 41 ] [ 42 ] [ 43 ] Since it is completely unknown whether conditions on these distant HZ worlds could host life, different terminology is needed. [ 40 ] [ 42 ] [ 44 ] [ 45 ]
Whether a body is in the circumstellar habitable zone of its host star is dependent on the radius of the planet's orbit (for natural satellites, the host planet's orbit), the mass of the body itself, and the radiative flux of the host star. Given the large spread in the masses of planets within a circumstellar habitable zone, coupled with the discovery of super-Earth planets that can sustain thicker atmospheres and stronger magnetic fields than Earth, circumstellar habitable zones are now split into two separate regions—a "conservative habitable zone" in which lower-mass planets like Earth can remain habitable, complemented by a larger "extended habitable zone" in which a planet like Venus, with stronger greenhouse effects , can have the right temperature for liquid water to exist at the surface. [ 46 ]
Estimates for the habitable zone within the Solar System range from 0.38 to 10.0 astronomical units , [ 48 ] [ 49 ] [ 50 ] [ 51 ] though arriving at these estimates has been challenging for a variety of reasons. Numerous planetary mass objects orbit within, or close to, this range and as such receive sufficient sunlight to raise temperatures above the freezing point of water. However, their atmospheric conditions vary substantially.
The aphelion of Venus, for example, touches the inner edge of the zone in most estimates and, while atmospheric pressure at the surface is sufficient for liquid water, a strong greenhouse effect raises surface temperatures to 462 °C (864 °F) at which water can only exist as vapor. [ 52 ] The entire orbits of the Moon , [ 53 ] Mars , [ 54 ] and numerous asteroids also lie within various estimates of the habitable zone. Only at Mars' lowest elevations (less than 30% of the planet's surface) is atmospheric pressure and temperature sufficient for water to, if present, exist in liquid form for short periods. [ 55 ] At Hellas Basin , for example, atmospheric pressures can reach 1,115 Pa and temperatures above zero Celsius (about the triple point for water) for 70 days in the Martian year. [ 55 ] Despite indirect evidence in the form of seasonal flows on warm Martian slopes , [ 56 ] [ 57 ] [ 58 ] [ 59 ] no confirmation has been made of the presence of liquid water at the surface. While other objects orbit partly within this zone, including comets, Ceres [ 60 ] is the only one of planetary mass.
Despite this, studies indicate the strong possibility of past liquid water on the surface of Venus , [ 61 ] the Moon , [ 62 ] [ 63 ] Mars , [ 64 ] [ 65 ] [ 66 ] Vesta [ 67 ] and Ceres, [ 68 ] [ 69 ] suggesting a more common phenomenon than previously thought. Since sustainable liquid water is thought to be essential to support complex life, most estimates, therefore, are inferred from the effect that a repositioned orbit would have on the habitability of Earth or Venus as their surface gravity allows sufficient atmosphere to be retained for several billion years.
According to the extended habitable zone concept, planetary-mass objects with atmospheres capable of inducing sufficient radiative forcing could possess liquid water farther out from the Sun. Such objects could include those whose atmospheres contain a high component of greenhouse gas and terrestrial planets much more massive than Earth ( super-Earth class planets), that have retained atmospheres with surface pressures of up to 100 kbar. There are no examples of such objects in the Solar System to study; not enough is known about the nature of atmospheres of these kinds of extrasolar objects, and their position in the habitable zone cannot determine the net temperature effect of such atmospheres including induced albedo , anti-greenhouse or other possible heat sources.
For reference, the average distance from the Sun of some major bodies within the various estimates of the habitable zone is: Mercury, 0.39 AU; Venus, 0.72 AU; Earth, 1.00 AU; Mars, 1.52 AU; Vesta, 2.36 AU; Ceres and Pallas, 2.77 AU; Jupiter, 5.20 AU; Saturn, 9.58 AU. In the most conservative estimates, only Earth lies within the zone; in the most permissive estimates, even Saturn at perihelion, or Mercury at aphelion, might be included.
Astronomers use stellar flux and the inverse-square law to extrapolate circumstellar habitable zone models created for the Solar System to other stars. For example, according to Kopparapu's habitable zone estimate, although the Solar System has a circumstellar habitable zone centered at 1.34 AU from the Sun, [ 5 ] a star with 0.25 times the luminosity of the Sun would have a habitable zone centered at 0.25 {\displaystyle {\sqrt {0.25}}} , or 0.5, the distance from the star, corresponding to a distance of 0.67 AU. Various complicating factors, though, including the individual characteristics of stars themselves, mean that extrasolar extrapolation of the HZ concept is more complex.
Some scientists argue that the concept of a circumstellar habitable zone is actually limited to stars in certain types of systems or of certain spectral types . Binary systems, for example, have circumstellar habitable zones that differ from those of single-star planetary systems, in addition to the orbital stability concerns inherent with a three-body configuration. [ 81 ] If the Solar System were such a binary system, the outer limits of the resulting circumstellar habitable zone could extend as far as 2.4 AU. [ 82 ] [ 83 ]
With regard to spectral types, Zoltán Balog proposes that O-type stars cannot form planets due to the photoevaporation caused by their strong ultraviolet emissions. [ 84 ] Studying ultraviolet emissions, Andrea Buccino found that only 40% of stars studied (including the Sun) had overlapping liquid water and ultraviolet habitable zones. [ 85 ] Stars smaller than the Sun, on the other hand, have distinct impediments to habitability. For example, Michael Hart proposed that only main-sequence stars of spectral class K0 or brighter could offer habitable zones, an idea which has evolved in modern times into the concept of a tidal locking radius for red dwarfs . Within this radius, which is coincidental with the red-dwarf habitable zone, it has been suggested that the volcanism caused by tidal heating could cause a "tidal Venus" planet with high temperatures and no hospitable environment for life. [ 86 ]
Others maintain that circumstellar habitable zones are more common and that it is indeed possible for water to exist on planets orbiting cooler stars. Climate modeling from 2013 supports the idea that red dwarf stars can support planets with relatively constant temperatures over their surfaces despite tidal locking. [ 87 ] Astronomy professor Eric Agol argues that even white dwarfs may support a relatively brief habitable zone through planetary migration. [ 88 ] At the same time, others have written in similar support of semi-stable, temporary habitable zones around brown dwarfs . [ 86 ] Also, a habitable zone in the outer parts of stellar systems may exist during the pre-main-sequence phase of stellar evolution, especially around M-dwarfs, potentially lasting for billion-year timescales. [ 89 ]
Circumstellar habitable zones change over time with stellar evolution. For example, hot O-type stars, which may remain on the main sequence for fewer than 10 million years, [ 90 ] would have rapidly changing habitable zones not conducive to the development of life. Red dwarf stars, on the other hand, which can live for hundreds of billions of years on the main sequence, would have planets with ample time for life to develop and evolve. [ 91 ] [ 92 ] Even while stars are on the main sequence, though, their energy output steadily increases, pushing their habitable zones farther out; our Sun, for example, was 75% as bright in the Archaean as it is now, [ 93 ] and in the future, continued increases in energy output will put Earth outside the Sun's habitable zone, even before it reaches the red giant phase. [ 94 ] In order to deal with this increase in luminosity, the concept of a continuously habitable zone has been introduced. As the name suggests, the continuously habitable zone is a region around a star in which planetary-mass bodies can sustain liquid water for a given period. Like the general circumstellar habitable zone, the continuously habitable zone of a star is divided into a conservative and extended region. [ 94 ]
In red dwarf systems, gigantic stellar flares which could double a star's brightness in minutes [ 95 ] and huge starspots which can cover 20% of the star's surface area, [ 96 ] have the potential to strip an otherwise habitable planet of its atmosphere and water. [ 97 ] As with more massive stars, though, stellar evolution changes their nature and energy flux, [ 98 ] so by about 1.2 billion years of age, red dwarfs generally become sufficiently constant to allow for the development of life. [ 97 ] [ 99 ]
Once a star has evolved sufficiently to become a red giant, its circumstellar habitable zone will change dramatically from its main-sequence size. [ 100 ] For example, the Sun is expected to engulf the previously habitable Earth as a red giant. [ 101 ] [ 102 ] However, once a red giant star reaches the horizontal branch , it achieves a new equilibrium and can sustain a new circumstellar habitable zone, which in the case of the Sun would range from 7 to 22 AU. [ 103 ] At such stage, Saturn's moon Titan would likely be habitable in Earth's temperature sense. [ 104 ] Given that this new equilibrium lasts for about 1 Gyr , and because life on Earth emerged by 0.7 Gyr from the formation of the Solar System at latest, life could conceivably develop on planetary mass objects in the habitable zone of red giants. [ 103 ] However, around such a helium-burning star, important life processes like photosynthesis could only happen around planets where the atmosphere has carbon dioxide, as by the time a solar-mass star becomes a red giant, planetary-mass bodies would have already absorbed much of their free carbon dioxide. [ 105 ] Moreover, as Ramirez and Kaltenegger (2016) [ 102 ] showed, intense stellar winds would completely remove the atmospheres of such smaller planetary bodies, rendering them uninhabitable anyway. Thus, Titan would not be habitable even after the Sun becomes a red giant. [ 102 ] Nevertheless, life need not originate during this stage of stellar evolution for it to be detected. Once the star becomes a red giant, and the habitable zone extends outward, the icy surface would melt, forming a temporary atmosphere that can be searched for signs of life that may have been thriving before the start of the red giant stage. [ 102 ]
A planet's atmospheric conditions influence its ability to retain heat so that the location of the habitable zone is also specific to each type of planet: desert planets (also known as dry planets), with very little water, will have less water vapor in the atmosphere than Earth and so have a reduced greenhouse effect , meaning that a desert planet could maintain oases of water closer to its star than Earth is to the Sun. The lack of water also means there is less ice to reflect heat into space, so the outer edge of desert-planet habitable zones is further out. [ 106 ] [ 107 ]
A planet cannot have a hydrosphere —a key ingredient for the formation of carbon-based life—unless there is a source for water within its stellar system. The origin of water on Earth is still not completely understood; possible sources include the result of impacts with icy bodies, outgassing , mineralization , leakage from hydrous minerals from the lithosphere , and photolysis . [ 108 ] [ 109 ] For an extrasolar system, an icy body from beyond the frost line could migrate into the habitable zone of its star, creating an ocean planet with seas hundreds of kilometers deep [ 110 ] such as GJ 1214 b [ 111 ] [ 112 ] or Kepler-22b may be. [ 113 ]
Maintenance of liquid surface water also requires a sufficiently thick atmosphere. Possible origins of terrestrial atmospheres are currently theorized to outgassing, impact degassing, and ingassing. [ 114 ] Atmospheres are thought to be maintained through similar processes along with biogeochemical cycles and the mitigation of atmospheric escape . [ 115 ] In a 2013 study led by Italian astronomer Giovanni Vladilo , it was shown that the size of the circumstellar habitable zone increased with greater atmospheric pressure. [ 77 ] Below an atmospheric pressure of about 15 millibars, it was found that habitability could not be maintained [ 77 ] because even a small shift in pressure or temperature could render water unable to form as a liquid. [ 116 ]
Although traditional definitions of the habitable zone assume that carbon dioxide and water vapor are the most important greenhouse gases (as they are on the Earth), [ 30 ] a study [ 50 ] led by Ramses Ramirez and co-author Lisa Kaltenegger has shown that the size of the habitable zone is greatly increased if prodigious volcanic outgassing of hydrogen is also included along with the carbon dioxide and water vapor. The outer edge in the Solar System would extend out as far as 2.4 AU in that case. Similar increases in the size of the habitable zone were computed for other stellar systems. An earlier study by Ray Pierrehumbert and Eric Gaidos [ 49 ] had eliminated the CO 2 -H 2 O concept entirely, arguing that young planets could accrete many tens to hundreds of bars of hydrogen from the protoplanetary disc, providing enough of a greenhouse effect to extend the solar system outer edge to 10 AU. In this case, though, the hydrogen is not continuously replenished by volcanism and is lost within millions to tens of millions of years.
In the case of planets orbiting in the HZs of red dwarf stars, the extremely close distances to the stars cause tidal locking , an important factor in habitability. For a tidally locked planet, the sidereal day is as long as the orbital period , causing one side to permanently face the host star and the other side to face away. In the past, such tidal locking was thought to cause extreme heat on the star-facing side and bitter cold on the opposite side, making many red dwarf planets uninhabitable; however, three-dimensional climate models in 2013 showed that the side of a red dwarf planet facing the host star could have extensive cloud cover, increasing its bond albedo and reducing significantly temperature differences between the two sides. [ 87 ]
Planetary mass natural satellites have the potential to be habitable as well. However, these bodies need to fulfill additional parameters, in particular being located within the circumplanetary habitable zones of their host planets. [ 38 ] More specifically, moons need to be far enough from their host giant planets that they are not transformed by tidal heating into volcanic worlds like Io , [ 38 ] but must remain within the Hill radius of the planet so that they are not pulled out of the orbit of their host planet. [ 117 ] Red dwarfs that have masses less than 20% of that of the Sun cannot have habitable moons around giant planets, as the small size of the circumstellar habitable zone would put a habitable moon so close to the star that it would be stripped from its host planet. In such a system, a moon close enough to its host planet to maintain its orbit would have tidal heating so intense as to eliminate any prospects of habitability. [ 38 ]
A planetary object that orbits a star with high orbital eccentricity may spend only some of its year in the HZ and experience a large variation in temperature and atmospheric pressure. This would result in dramatic seasonal phase shifts where liquid water may exist only intermittently. It is possible that subsurface habitats could be insulated from such changes and that extremophiles on or near the surface might survive through adaptions such as hibernation ( cryptobiosis ) and/or hyperthermostability . Tardigrades , for example, can survive in a dehydrated state temperature between 0.150 K (−273 °C) [ 118 ] and 424 K (151 °C). [ 119 ] Life on a planetary object orbiting outside HZ might hibernate on the cold side as the planet approaches the apastron where the planet is coolest and become active on approach to the periastron when the planet is sufficiently warm. [ 120 ]
A 2015 review concluded that the exoplanets Kepler-62f , Kepler-186f and Kepler-442b were likely the best candidates for being potentially habitable. [ 121 ] These are at a distance of 990, 490 and 1,120 light-years away, respectively. Of these, Kepler-186f is closest in size to Earth with 1.2 times Earth's radius, and it is located towards the outer edge of the habitable zone around its red dwarf star. Among nearest terrestrial exoplanet candidates , Tau Ceti e is 11.9 light-years away. It is in the inner edge of its planetary system's habitable zone, giving it an estimated average surface temperature of 68 °C (154 °F). [ 122 ]
Studies that have attempted to estimate the number of terrestrial planets within the circumstellar habitable zone tend to reflect the availability of scientific data. A 2013 study by Ravi Kumar Kopparapu put η e , the fraction of stars with planets in the HZ, at 0.48, [ 5 ] meaning that there may be roughly 95–180 billion habitable planets in the Milky Way. [ 123 ] However, this is merely a statistical prediction; only a small fraction of these possible planets have yet been discovered. [ 124 ]
Previous studies have been more conservative. In 2011, Seth Borenstein concluded that there are roughly 500 million habitable planets in the Milky Way. [ 125 ] NASA's Jet Propulsion Laboratory 2011 study, based on observations from the Kepler mission, raised the number somewhat, estimating that about "1.4 to 2.7 percent" of all stars of spectral class F , G , and K are expected to have planets in their HZs. [ 126 ] [ 127 ]
The first discoveries of extrasolar planets in the HZ occurred just a few years after the first extrasolar planets were discovered. However, these early detections were all gas giant-sized, and many were in eccentric orbits. Despite this, studies indicate the possibility of large, Earth-like moons around these planets supporting liquid water. [ 128 ] One of the first discoveries was 70 Virginis b , a gas giant initially nicknamed "Goldilocks" due to it being neither "too hot" nor "too cold". Later study revealed temperatures analogous to Venus, ruling out any potential for liquid water. [ 129 ] 16 Cygni Bb , also discovered in 1996, has an extremely eccentric orbit that spends only part of its time in the HZ, such an orbit would causes extreme seasonal effects. In spite of this, simulations have suggested that a sufficiently large companion could support surface water year-round. [ 130 ]
Gliese 876 b , discovered in 1998, and Gliese 876 c , discovered in 2001, are both gas giants discovered in the habitable zone around Gliese 876 that may also have large moons. [ 131 ] Another gas giant, Upsilon Andromedae d was discovered in 1999 orbiting Upsilon Andromidae's habitable zone.
Announced on April 4, 2001, HD 28185 b is a gas giant found to orbit entirely within its star's circumstellar habitable zone [ 132 ] and has a low orbital eccentricity, comparable to that of Mars in the Solar System. [ 133 ] Tidal interactions suggest it could harbor habitable Earth-mass satellites in orbit around it for many billions of years, [ 134 ] though it is unclear whether such satellites could form in the first place. [ 135 ]
HD 69830 d , a gas giant with 17 times the mass of Earth, was found in 2006 orbiting within the circumstellar habitable zone of HD 69830 , 41 light years away from Earth. [ 136 ] The following year, 55 Cancri f was discovered within the HZ of its host star 55 Cancri A . [ 137 ] [ 138 ] Hypothetical satellites with sufficient mass and composition are thought to be able to support liquid water at their surfaces. [ 139 ]
Though, in theory, such giant planets could possess moons, the technology did not exist to detect moons around them, and no extrasolar moons had been discovered. Planets within the zone with the potential for solid surfaces were therefore of much higher interest.
The 2007 discovery of Gliese 581c , the first super-Earth in the circumstellar habitable zone, created significant interest in the system by the scientific community, although the planet was later found to have extreme surface conditions that may resemble Venus. [ 140 ] Gliese 581 d, another planet in the same system and thought to be a better candidate for habitability, was also announced in 2007. Its existence was later disconfirmed in 2014, but only for a short time. As of 2015, the planet has no newer disconfirmations. Gliese 581 g , yet another planet thought to have been discovered in the circumstellar habitable zone of the system, was considered to be more habitable than both Gliese 581 c and d. However, its existence was also disconfirmed in 2014, [ 141 ] and astronomers are divided about its existence.
Discovered in August 2011, HD 85512 b was initially speculated to be habitable, [ 142 ] but the new circumstellar habitable zone criteria devised by Kopparapu et al. in 2013 place the planet outside the circumstellar habitable zone. [ 124 ]
Kepler-22 b , discovered in December 2011 by the Kepler space probe, [ 143 ] is the first transiting exoplanet discovered around a Sun-like star . With a radius 2.4 times that of Earth, Kepler-22b has been predicted by some to be an ocean planet. [ 144 ] Gliese 667 Cc , discovered in 2011 but announced in 2012, [ 145 ] is a super-Earth orbiting in the circumstellar habitable zone of Gliese 667 C . It is one of the most Earth-like planets known.
Gliese 163 c , discovered in September 2012 in orbit around the red dwarf Gliese 163 [ 146 ] is located 49 light years from Earth. The planet has 6.9 Earth masses and 1.8–2.4 Earth radii, and with its close orbit receives 40 percent more stellar radiation than Earth, leading to surface temperatures of about 60° C . [ 147 ] [ 148 ] [ 149 ] HD 40307 g , a candidate planet tentatively discovered in November 2012, is in the circumstellar habitable zone of HD 40307 . [ 150 ] In December 2012, Tau Ceti e and Tau Ceti f were found in the circumstellar habitable zone of Tau Ceti , a Sun-like star 12 light years away. [ 151 ] Although more massive than Earth, they are among the least massive planets found to date orbiting in the habitable zone; [ 152 ] however, Tau Ceti f, like HD 85512 b, did not fit the new circumstellar habitable zone criteria established by the 2013 Kopparapu study. [ 153 ] It is now considered as uninhabitable.
Recent discoveries have uncovered planets that are thought to be similar in size or mass to Earth. "Earth-sized" ranges are typically defined by mass. The lower range used in many definitions of the super-Earth class is 1.9 Earth masses; likewise, sub-Earths range up to the size of Venus (~0.815 Earth masses). An upper limit of 1.5 Earth radii is also considered, given that above 1.5 R 🜨 the average planet density rapidly decreases with increasing radius, indicating these planets have a significant fraction of volatiles by volume overlying a rocky core. [ 154 ] A genuinely Earth-like planet – an Earth analog or "Earth twin" – would need to meet many conditions beyond size and mass; such properties are not observable using current technology.
A solar analog (or "solar twin") is a star that resembles the Sun. No solar twin with an exact match as that of the Sun has been found. However, some stars are nearly identical to the Sun and are considered solar twins. An exact solar twin would be a G2V star with a 5,778 K temperature, be 4.6 billion years old, with the correct metallicity and a 0.1% solar luminosity variation. [ 155 ] Stars with an age of 4.6 billion years are at the most stable state. Proper metallicity and size are also critical to low luminosity variation. [ 156 ] [ 157 ] [ 158 ]
Using data collected by NASA's Kepler space telescope and the W. M. Keck Observatory , scientists have estimated that 22% of solar-type stars in the Milky Way galaxy have Earth-sized planets in their habitable zone. [ 159 ]
On 7 January 2013, astronomers from the Kepler team announced the discovery of Kepler-69c (formerly KOI-172.02 ), an Earth-size exoplanet candidate (1.7 times the radius of Earth) orbiting Kepler-69 , a star similar to the Sun, in the HZ and expected to offer habitable conditions. [ 160 ] [ 161 ] [ 162 ] [ 163 ] The discovery of two planets orbiting in the habitable zone of Kepler-62 , by the Kepler team was announced on April 19, 2013. The planets, named Kepler-62e and Kepler-62f , are likely solid planets with sizes 1.6 and 1.4 times the radius of Earth, respectively. [ 162 ] [ 163 ] [ 164 ]
With a radius estimated at 1.1 Earth, Kepler-186f , discovery announced in April 2014, is the closest yet size to Earth of an exoplanet confirmed by the transit method [ 165 ] [ 166 ] [ 167 ] though its mass remains unknown and its parent star is not a Solar analog.
Kapteyn b , discovered in June 2014, was thought to is a possible rocky world of about 4.8 Earth masses and about 1.5 Earth radii orbiting the habitable zone of the red subdwarf Kapteyn's Star , 12.8 light-years away. [ 168 ] However, further analysis concluded that this claim was an artefact of stellar rotation and activity. [ 169 ]
On 6 January 2015, NASA announced the 1000th confirmed exoplanet discovered by the Kepler Space Telescope. Three of the newly confirmed exoplanets were found to orbit within habitable zones of their related stars : two of the three, Kepler-438b and Kepler-442b , are near-Earth-size and likely rocky ; the third, Kepler-440b , is a super-Earth . [ 170 ] However, Kepler-438b is found to be a subject of powerful flares, so it is now considered uninhabitable. 16 January, K2-3d a planet of 1.5 Earth radii was found orbiting within the habitable zone of K2-3 , receiving 1.4 times the intensity of visible light as Earth. [ 171 ]
Kepler-452b , announced on 23 July 2015 is 50% bigger than Earth, likely rocky and takes approximately 385 Earth days to orbit the habitable zone of its G-class (solar analog) star Kepler-452 . [ 172 ] [ 173 ]
The discovery of a system of three tidally locked planets orbiting the habitable zone of an ultracool dwarf star, TRAPPIST-1 , was announced in May 2016. [ 174 ] The discovery is considered significant because it dramatically increases the possibility of smaller, cooler, more numerous and closer stars possessing habitable planets.
Two potentially habitable planets, discovered by the K2 mission in July 2016 orbiting around the M dwarf K2-72 around 227 light years from the Sun: K2-72c and K2-72e are both of similar size to Earth and receive similar amounts of stellar radiation. [ 175 ]
Announced on the 20 April 2017, LHS 1140b is a super-dense super-Earth 39 light years away, 6.6 times Earth's mass and 1.4 times radius, its star 15% the mass of the Sun but with much less observable stellar flare activity than most M dwarfs. [ 176 ] The planet is one of few observable by both transit and radial velocity that's mass is confirmed with an atmosphere may be studied.
Discovered by radial velocity in June 2017, with approximately three times the mass of Earth, Luyten b orbits within the habitable zone of Luyten's Star just 12.2 light-years away. [ 177 ]
At 11 light-years away, the second closest planet, Ross 128 b , was announced in November 2017 following a decade's radial velocity study of relatively "quiet" red dwarf star Ross 128. At 1.35 times Earth's mass, is it roughly Earth-sized and likely rocky in composition. [ 178 ]
Discovered in March 2018, K2-155d is about 1.64 times the radius of Earth, is likely rocky and orbits in the habitable zone of its red dwarf star 203 light years away. [ 179 ] [ 180 ] [ 181 ]
One of the earliest discoveries by the Transiting Exoplanet Survey Satellite (TESS) announced on July 31, 2019, is a Super-Earth planet GJ 357 d orbiting the outer edge of a red dwarf 31 light years away. [ 182 ]
K2-18b is an exoplanet 124 light-years away, orbiting in the habitable zone of the K2-18 , a red dwarf. This planet is significant for water vapor found in its atmosphere; this was announced on September 17, 2019.
In September 2020, astronomers identified 24 superhabitable planet (planets better than Earth) contenders, from among more than 4000 confirmed exoplanets at present, based on astrophysical parameters , as well as the natural history of known life forms on the Earth . [ 183 ]
Liquid-water environments have been found to exist in the absence of atmospheric pressure and at temperatures outside the HZ temperature range. For example, Saturn 's moons Titan and Enceladus and Jupiter 's moons Europa and Ganymede , all of which are outside the habitable zone, may hold large volumes of liquid water in subsurface oceans . [ 184 ]
Outside the HZ, tidal heating and radioactive decay are two possible heat sources that could contribute to the existence of liquid water. [ 16 ] [ 17 ] Abbot and Switzer (2011) put forward the possibility that subsurface water could exist on rogue planets as a result of radioactive decay-based heating and insulation by a thick surface layer of ice. [ 19 ]
With some theorising that life on Earth may have actually originated in stable, subsurface habitats, [ 185 ] [ 186 ] it has been suggested that it may be common for wet subsurface extraterrestrial habitats such as these to 'teem with life'. [ 187 ] On Earth itself, living organisms may be found more than 6 km (3.7 mi) below the surface. [ 188 ]
Another possibility is that outside the HZ organisms may use alternative biochemistries that do not require water at all. Astrobiologist Christopher McKay , has suggested that methane ( CH 4 ) may be a solvent conducive to the development of "cryolife", with the Sun's "methane habitable zone" being centered on 1,610,000,000 km (1.0 × 10 9 mi; 11 AU) from the star. [ 22 ] This distance is coincident with the location of Titan, whose lakes and rain of methane make it an ideal location to find McKay's proposed cryolife. [ 22 ] In addition, testing of a number of organisms has found some are capable of surviving in extra-HZ conditions. [ 189 ]
The Rare Earth hypothesis argues that complex and intelligent life is uncommon and that the HZ is one of many critical factors. According to Ward & Brownlee (2004) and others, not only is a HZ orbit and surface water a primary requirement to sustain life but a requirement to support the secondary conditions required for multicellular life to emerge and evolve. The secondary habitability factors are both geological (the role of surface water in sustaining necessary plate tectonics) [ 36 ] and biochemical (the role of radiant energy in supporting photosynthesis for necessary atmospheric oxygenation). [ 190 ] But others, such as Ian Stewart and Jack Cohen in their 2002 book Evolving the Alien argue that complex intelligent life may arise outside the HZ. [ 191 ] Intelligent life outside the HZ may have evolved in subsurface environments, from alternative biochemistries [ 191 ] or even from nuclear reactions. [ 192 ]
On Earth, several complex multicellular life forms (or eukaryotes ) have been identified with the potential to survive conditions that might exist outside the conservative habitable zone. Geothermal energy sustains ancient circumvent ecosystems, supporting large complex life forms such as Riftia pachyptila . [ 193 ] Similar environments may be found in oceans pressurised beneath solid crusts, such as those of Europa and Enceladus, outside of the habitable zone. [ 194 ] Numerous microorganisms have been tested in simulated conditions and in low Earth orbit, including eukaryotes. An animal example is the Milnesium tardigradum , which can withstand extreme temperatures well above the boiling point of water and the cold vacuum of outer space. [ 195 ] A desert moss, Syntrichia caninervis is one of few plants believed capable of surviving on Mars. [ 196 ] In addition, the lichens Rhizocarpon geographicum and Rusavskia elegans have been found to survive in an environment where the atmospheric pressure is far too low for surface liquid water and where the radiant energy is also much lower than that which most plants require to photosynthesize. [ 197 ] [ 198 ] [ 199 ] The fungi Cryomyces antarcticus and Cryomyces minteri are also able to survive and reproduce in Mars-like conditions. [ 199 ]
Species, including humans , known to possess animal cognition require large amounts of energy, [ 200 ] and have adapted to specific conditions, including an abundance of atmospheric oxygen and the availability of large quantities of chemical energy synthesized from radiant energy. If humans are to colonize other planets, true Earth analogs in the HZ are most likely to provide the closest natural habitat; this concept was the basis of Stephen H. Dole's 1964 study. With suitable temperature, gravity, atmospheric pressure and the presence of water, the necessity of spacesuits or space habitat analogs on the surface may be eliminated, and complex Earth life can thrive. [ 3 ]
Planets in the HZ remain of paramount interest to researchers looking for intelligent life elsewhere in the universe. [ 201 ] The Drake equation , sometimes used to estimate the number of intelligent civilizations in our galaxy, contains the factor or parameter n e , which is the average number of planetary-mass objects orbiting within the HZ of each star. A low value lends support to the Rare Earth hypothesis, which posits that intelligent life is a rarity in the Universe, whereas a high value provides evidence for the Copernican mediocrity principle , the view that habitability—and therefore life—is common throughout the Universe. [ 36 ] A 1971 NASA report by Drake and Bernard Oliver proposed the " water hole ", based on the spectral absorption lines of the hydrogen and hydroxyl components of water, as a good, obvious band for communication with extraterrestrial intelligence [ 202 ] [ 203 ] that has since been widely adopted by astronomers involved in the search for extraterrestrial intelligence. According to Jill Tarter , Margaret Turnbull and many others, HZ candidates are the priority targets to narrow waterhole searches [ 204 ] [ 205 ] and the Allen Telescope Array now extends Project Phoenix to such candidates. [ 206 ]
Because the HZ is considered the most likely habitat for intelligent life, METI efforts have also been focused on systems likely to have planets there. The 2001 Teen Age Message and 2003 Cosmic Call 2 , for example, were sent to the 47 Ursae Majoris system, known to contain three Jupiter-mass planets and possibly with a terrestrial planet in the HZ. [ 207 ] [ 208 ] [ 209 ] [ 210 ] The Teen Age Message was also directed to the 55 Cancri system, which has a gas giant in its HZ. [ 137 ] A Message from Earth in 2008, [ 211 ] and Hello From Earth in 2009, were directed to the Gliese 581 system, containing three planets in the HZ—Gliese 581 c, d, and the unconfirmed g. | https://en.wikipedia.org/wiki/Habitable_zone |
A Habitable Zone for Complex Life (HZCL) is a range of distances from a star suitable for complex aerobic life . Different types of limitations preventing complex life give rise to different zones. [ 1 ] Conventional habitable zones are based on compatibility with water. [ 2 ] Most zones start at a distance from the host star and then end at a distance farther from the star. A planet would need to orbit inside the boundaries of this zone. With multiple zonal constraints, the zones would need to overlap for the planet to support complex life. The requirements for bacterial life produce much larger zones than those for complex life, which requires a very narrow zone. [ 3 ] [ 4 ] [ 5 ]
The first confirmed exoplanets was discovered in 1992, several planets orbiting the pulsar PSR B1257+12 . [ 6 ] Since then the list of exoplanets has grown to the thousands. [ 7 ] Most exoplanets are hot Jupiter planets, that orbit very close the star. [ 8 ] Many exoplanets are super-Earths , that could be a gas dwarf or large rocky planet , like Kepler-442b at a mass 2.36 times Earths. [ 9 ]
Unstable stars are young and old stars, or very large or small stars. Unstable stars have changing solar luminosity that changes the size of the life habitable zones. Unstable stars also produce extreme solar flares and coronal mass ejections . Solar flares and coronal mass ejections can strip away a planet's atmosphere that is not replaceable. Thus life habitable zones require and very stable star like the Sun , at ±0.1% solar luminosity change. [ 10 ] [ 11 ] Finding a stable star, like the Sun, is the search for a solar twin , with solar analogs that have been found. [ 12 ] Star metallicity , mass , age , color , and temperature all effect luminosity variations. [ 13 ] [ 14 ] [ 15 ] The Sun, a G2V star, has a mid-range metallicity optimal for the formation of rocky planets. [ 16 ] Dwarf stars ( red dwarf / orange dwarf / brown dwarf / subdwarf ) are not only unstable, but also emit low energy, so the habitable zone is very close to the star and planets become tidally locked on the timescales needed for the development of life. [ 17 ] Giant stars ( subgiant / giant star / red giant / red supergiant ) are unstable and emit high energy, so the habitable zone is very far from the star. [ 18 ] Multiple-star systems are also very common and are not suitable for complex life, as the planet orbit would be unstable due to multiple gravitational forces and solar radiation. Liquid water is possible in Multiple-star systems. [ 19 ] [ 20 ] [ 21 ] [ 22 ]
A conventional habitable zone is defined by liquid water.
Over time and with more research , astronomers , cosmologists and astrobiologist have discovered more parameters needed for life. Each parameter could have a corresponding zone. Some of the named zones include: [ 29 ] [ 30 ]
Some factors that depend on planetary distance and may limit complex aerobic life have not been given zone names. These include:
Life on Earth is carbon-based . However, some theories suggest that life could be based on other elements in the periodic table . [ 101 ] Other elements proposed have been silicon , boron , arsenic , ammonia , methane and others. As more research has been done on life on Earth, it has been found that only carbon 's organic molecules have the complexity and stability to form life. [ 102 ] [ 103 ] [ 104 ] Carbon properties allows for complex chemical bonding that produces covalent bonds needed for organic chemistry . Carbon molecules are lightweight and relatively small in size. Carbon's ability to bond to oxygen , hydrogen , nitrogen , phosphorus , and sulfur (called CHNOPS ) is key to life. [ 105 ] [ 106 ] [ 107 ] | https://en.wikipedia.org/wiki/Habitable_zone_for_complex_life |
Habitat fragmentation describes the emergence of discontinuities (fragmentation) in an organism's preferred environment ( habitat ), causing population fragmentation and ecosystem decay . [ 2 ] Causes of habitat fragmentation include geological processes that slowly alter the layout of the physical environment [ 3 ] (suspected of being one of the major causes of speciation [ 3 ] ), and human activity such as land conversion , which can alter the environment much faster and causes the extinction of many species. More specifically, habitat fragmentation is a process by which large and contiguous habitats get divided into smaller, isolated patches of habitats. [ 4 ] [ 5 ]
The term habitat fragmentation includes five discrete phenomena:
"fragmentation ... not only causes loss of the amount of habitat but by creating small, isolated patches it also changes the properties of the remaining habitat" (van den Berg et al. 2001) [ failed verification ] . Habitat fragmentation is the landscape level of the phenomenon, and patch level process. Thus meaning, it covers; the patch areas, edge effects, and patch shape complexity. [ 6 ]
In scientific literature, there is some debate whether the term "habitat fragmentation" applies in cases of habitat loss , or whether the term primarily applies to the phenomenon of habitat being cut into smaller pieces without significant reduction in habitat area. Scientists who use the stricter definition of "habitat fragmentation" per se [ 5 ] would refer to the loss of habitat area as "habitat loss" and explicitly mention both terms if describing a situation where the habitat becomes less connected and there is less overall habitat.
Furthermore, habitat fragmentation is considered as an invasive threat to biodiversity , due to its implications of affecting large number of species than biological invasions , overexploitation , or pollution . [ 7 ]
Additionally, the effects of habitat fragmentation damage the ability for species, such as native plants , to be able to effectively adapt to their changing environments. Ultimately, this prevents gene flow from one generation of population to the next, especially for species living in smaller population sizes. Whereas, for species of larger populations have more genetic mutations which can arise and genetic recombination impacts which can increase species survival in those environments. Overall, habitat fragmentation results in habitat disintegration and habitat loss which both tie into destructing biodiversity as a whole.
Evidence of habitat destruction through natural processes such as volcanism , fire, and climate change is found in the fossil record. [ 3 ] [ failed verification ] Studies have demonstrated the impacts of individual species at the landscape level [ 8 ] For example, From research the results show that the impact of deer herbivory on forest plant communities can be observed at the landscape level at the Rondeau Provincial park for the period of 1955-1978 [ 8 ] and also, habitat fragmentation of tropical rainforests in Euramerica 300 million years ago led to a great loss of amphibian diversity, but simultaneously the drier climate spurred on a burst of diversity among reptiles. [ 3 ]
Habitat fragmentation is frequently caused by humans when native plants are cleared for human activities such as agriculture , rural development , urbanization and the creation of hydroelectric reservoirs. Habitats which were once continuous become divided into separate fragments. Due to human activities, many tropical and temperate habitats have already been severely fragmented, and in the near future, the degree of fragmentation will significantly rise. [ 9 ] After intensive clearing, the separate fragments tend to be very small islands isolated from each other by cropland, pasture, pavement, or even barren land. The latter is often the result of slash and burn farming in tropical forests . In the wheat belt of central-western New South Wales , Australia , 90% of the native vegetation has been cleared and over 99% of the tall grass prairie of North America has been cleared, resulting in extreme habitat fragmentation.
The two types of processes that can lead to habitat fragmentation are known as endogenous processes and exogenous processes. Endogenous is a process that develops as a part of species biology so they typically include changes in biology, behavior, and interactions within or between species. Endogenous threats can result in changes to breeding patterns or migration patterns and are often triggered by exogenous processes. Exogenous processes are independent of species biology and can include habitat degradation, habitat subdivision or habitat isolation. These processes can have a substantial impact on endogenous processes by fundamentally altering species behavior. Habitat subdivision or isolation can lead to changes in dispersal or movement of species including changes to seasonal migration. These changes can lead to a decrease in a density of species, increased competition or even increased predation. [ 10 ]
One of the major ways that habitat fragmentation affects biodiversity is by reducing the amount of suitable habitat available for organisms. Habitat fragmentation often involves both habitat destruction and the subdivision of previously continuous habitat. [ 11 ] Plants and other sessile organisms are disproportionately affected by some types of habitat fragmentation because they cannot respond quickly to the altered spatial configuration of the habitat. [ 12 ] Habitat fragmentation consistently reduces biodiversity by 13 to 75% and impairs key ecosystem functions by decreasing biomass and altering nutrient cycles . This underscores the severe and lasting ecological impacts of fragmentation, which could be highlighted in the sections discussing the consequences of fragmentation. [ 13 ]
Habitat loss, which can occur through the process of habitat fragmentation, is considered to be the greatest threat to species. [ 14 ] But, the effect of the configuration of habitat patches within the landscape, independent of the effect of the amount of habitat within the landscape (referred to as fragmentation per se [ 5 ] ), has been suggested to be small. [ 15 ] A review of empirical studies found that, of the 381 reported significant effect of habitat fragmentation per se on species occurrences, abundances or diversity in the scientific literature, 76% were positive whereas 24% were negative. [ 16 ] Despite these results, the scientific literature tends to emphasize negative effects more than positive effects. [ 17 ] Positive effects of habitat fragmentation per se imply that several small patches of habitat can have higher conservation value than a single large patch of equivalent size. [ 16 ] Land sharing strategies could therefore have more positive impacts on species than land sparing strategies. [ 16 ] Although the negative effects of habitat loss are generally viewed to be much larger than that of habitat fragmentation, the two events are heavily connected and observations are not usually independent of one another. [ 18 ]
Area is the primary determinant of the number of species in a fragment [ 19 ] and the relative contributions of demographic and genetic processes to the risk of global population extinction depend on habitat configuration, stochastic environmental variation and species features. [ 20 ] Minor fluctuations in climate, resources, or other factors that would be unremarkable and quickly corrected in large populations can be catastrophic in small, isolated populations. Thus fragmentation of habitat is an important cause of species extinction. [ 19 ] Population dynamics of subdivided populations tend to vary asynchronously . In an unfragmented landscape a declining population can be "rescued" by immigration from a nearby expanding population. In fragmented landscapes, the distance between fragments may prevent this from happening. Additionally, unoccupied fragments of habitat that are separated from a source of immigrants by some barrier are less likely to be repopulated than adjoining fragments. Even small species such as the Columbia spotted frog are reliant on the rescue effect . Studies showed 25% of juveniles travel a distance over 200m compared to 4% of adults. Of these, 95% remain in their new locale, demonstrating that this journey is necessary for survival. [ 21 ]
Additionally, habitat fragmentation leads to edge effects . Microclimatic changes in light, temperature, and wind can alter the ecology around the fragment, and in the interior and exterior portions of the fragment. [ 22 ] Fires become more likely in the area as humidity drops and temperature and wind levels rise. Exotic and pest species may establish themselves easily in such disturbed environments, and the proximity of domestic animals often upsets the natural ecology. Also, habitat along the edge of a fragment has a different climate and favours different species from the interior habitat. Small fragments are therefore unfavourable for species that require interior habitat. The percentage preservation of contiguous habitats is closely related to both genetic and species biodiversity preservation. Generally a 10% remnant contiguous habitat will result in a 50% biodiversity loss . [ 23 ]
Much of the remaining terrestrial wildlife habitat in many third world countries has experienced fragmentation through the development of urban expansion such as roads interfering with habitat loss . Aquatic species’ habitats have been fragmented by dams and water diversions . [ 24 ] These fragments of habitat may not be large or connected enough to support species that need a large territory where they can find mates and food. The loss and fragmentation of habitats makes it difficult for migratory species to find places to rest and feed along their migration routes. [ 24 ]
The effects of current fragmentation will continue to emerge for decades. Extinction debts are likely to come due, although the counteracting immigration debts may never fully be paid. Indeed, the experiments here reveal ongoing losses of biodiversity and ecosystem functioning two decades or longer after fragmentation occurred. Understanding the relationship between transient and long-term dynamics is a substantial challenge that ecologists must tackle, and fragmentation experiments will be central for relating observation to theory. [ 7 ]
Habitat fragmentation is often a cause of species becoming threatened or endangered . [ 25 ] The existence of viable habitat is critical to the survival of any species, and in many cases, the fragmentation of any remaining habitat can lead to difficult decisions for conservation biologists. Given a limited amount of resources available for conservation is it preferable to protect the existing isolated patches of habitat or to buy back land to get the largest possible contiguous piece of land. In rare cases, a conservation reliant species may gain some measure of disease protection by being distributed in isolated habitats, and when controlled for overall habitat loss some studies have shown a positive relationship between species richness and fragmentation; this phenomenon has been called the habitat amount hypothesis, though the validity of this claim has been disputed. [ 15 ] [ 26 ] The ongoing debate of what size fragments are most relevant for conservation is often referred to as SLOSS (Single Large or Several Small). Habitat loss in a biodiversity hotspot can result in a localized extinction crisis, generally speaking habitat loss in a hotspot location can be a good indicator or predictor of the number of threatened and extinct endemic species. [ 27 ]
One solution to the problem of habitat fragmentation is to link the fragments by preserving or planting corridors of native vegetation. In some cases, a bridge or underpass may be enough to join two fragments. [ 28 ] This has the potential to mitigate the problem of isolation but not the loss of interior habitat. Wildlife corridors can help animals to move and occupy new areas when food sources or other natural resources are lacking in their core habitat, and animals can find new mates in neighbouring regions so that genetic diversity can increase. Species that relocate seasonally can do so more safely and effectively when it does not interfere with human development barriers.
Due to the continuous expansion of urban landscapes, current research is looking at green roofs being possible vectors of habitat corridors. A recent study has found that green roofs are beneficial in connecting the habitats of arthropods, specifically bees and weevils. [ 29 ]
Another mitigation measure is the enlargement of small remnants to increase the amount of interior habitat. This may be impractical since developed land is often more expensive and could require significant time and effort to restore.
The best solution is generally dependent on the particular species or ecosystem that is being considered. More mobile species, like most birds, do not need connected habitat while some smaller animals, like rodents, may be more exposed to predation in open land. These questions generally fall under the headings of metapopulations island biogeography .
As the remaining habitat patches are smaller, they tend to support smaller populations of fewer species. [ 30 ] Small populations are at an increased risk of a variety of genetic consequences that influence their long-term survival. [ 31 ] Remnant populations often contain only a subset of the genetic diversity found in the previously continuous habitat. In these cases, processes that act upon underlying genetic diversity, such as adaptation , have a smaller pool of fitness-maintaining alleles to survive in the face of environmental change. However, in some scenarios, where subsets of genetic diversity are partitioned among multiple habitat fragments, almost all original genetic diversity can be maintained despite each individual fragment displaying a reduced subset of diversity. [ 32 ] [ 33 ]
Gene flow occurs when individuals of the same species exchange genetic information through reproduction. Populations can maintain genetic diversity through migration . When a habitat becomes fragmented and reduced in area, gene flow and migration are typically reduced. Fewer individuals will migrate into the remaining fragments, and small disconnected populations that may have once been part of a single large population will become reproductively isolated. Scientific evidence that gene flow is reduced due to fragmentation depends on the study species. While trees that have long-range pollination and dispersal mechanisms may not experience reduced gene flow following fragmentation, [ 34 ] most species are at risk of reduced gene flow following habitat fragmentation. [ 12 ]
Reduced gene flow, and reproductive isolation can result in inbreeding between related individuals. Inbreeding does not always result in negative fitness consequences, but when inbreeding is associated with fitness reduction it is called inbreeding depression . Inbreeding becomes of increasing concern as the level of homozygosity increases, facilitating the expression of deleterious alleles that reduce the fitness. Habitat fragmentation can lead to inbreeding depression for many species due to reduced gene flow. [ 35 ] [ 36 ] Inbreeding depression is associated with conservation risks, like local extinction. [ 37 ]
Small populations are more susceptible to genetic drift . Genetic drift is random changes to the genetic makeup of populations and leads to reductions in genetic diversity. The smaller the population is, the more likely genetic drift will be a driving force of evolution rather than natural selection. Because genetic drift is a random process, it does not allow species to become more adapted to their environment. Habitat fragmentation is associated with increases to genetic drift in small populations which can have negative consequences for the genetic diversity of the populations. [ 35 ] However, research suggests that some tree species may be resilient to the negative consequences of genetic drift until population size is as small as ten individuals or less. [ 32 ]
Habitat fragmentation decreases the size and increases plant populations' spatial isolation. With genetic variation and increased methods of inter-population genetic divergence due to increased effects of random genetic drift , elevating inbreeding and reducing gene flow within plant species. While genetic variation may decrease with remnant population size, not all fragmentation events lead to genetic losses and different types of genetic variation. Rarely, fragmentation can also increase gene flow among remnant populations, breaking down local genetic structure. [ 38 ]
In order for populations to evolve in response to natural selection, they must be large enough that natural selection is a stronger evolutionary force than genetic drift. Recent studies on the impacts of habitat fragmentation on adaptation in some plant species have suggested that organisms in fragmented landscapes may be able to adapt to fragmentation. [ 39 ] [ 40 ] However, there are also many cases where fragmentation reduces adaptation capacity because of small population size. [ 41 ]
Some species that have experienced genetic consequences due to habitat fragmentation are listed below:
Although the way habitat fragmentation affects the genetics and extinction rates of species has been heavily studied, fragmentation has also been shown to affect species' behaviours and cultures as well. This is important because social interactions can determine and have an effect on a species' fitness and survival. Habitat fragmentation alters the resources available and the structure of habitats, as a result, alters the behaviours of species and the dynamics between differing species. Behaviours affected can be within a species such as reproduction, mating, foraging, species dispersal, communication and movement patterns or can be behaviours between species such as predator-prey relationships. [ 47 ] In addition, when animals happen to venture into unknown areas in between fragmented forests or landscapes, they can supposedly come into contact with humans which puts them at a great risk and further decreases their chances of survival. [ 7 ]
Habitat fragmentation due to anthropogenic activities has been shown to greatly affect the predator-prey dynamics of many species by altering the number of species and the members of those species. [ 47 ] This affects the natural predator-prey relationships between animals in a given community [ 47 ] and forces them to alter their behaviours and interactions, therefore resetting the so-called "behavioral space race". [ 48 ] The way in which fragmentation changes and re-shapes these interactions can occur in many different forms. Most prey species have patches of land that are a refuge from their predators, allowing them the safety to reproduce and raise their young. Human introduced structures such as roads and pipelines alter these areas by facilitating predator activity in these refuges, increasing predator-prey overlap. [ 48 ] The opposite could also occur in the favour of prey, increasing prey refuge and subsequently decreasing predation rates. Fragmentation may also increase predator abundance or predator efficiency and therefore increase predation rates in this manner. [ 48 ] Several other factors can also increase or decrease the extent to which the shifting predator-prey dynamics affect certain species, including how diverse a predators diet is and how flexible habitat requirements are for predators and prey. [ 47 ] Depending on which species are affected and these other factors, fragmentation and its effects on predator-prey dynamics may contribute to species extinction. [ 47 ] In response to these new environmental pressures, new adaptive behaviours may be developed. Prey species may adapt to increased risk of predation with strategies such as altering mating tactics or changing behaviours and activities related to food and foraging. [ 47 ]
In the boreal woodland caribous of British Columbia, the effects of fragmentation are demonstrated. The species refuge area is peatland bog which has been interrupted by linear features such as roads and pipelines. [ 49 ] These features have allowed their natural predators, the wolf, and the black bear to more efficiently travel over landscapes and between patches of land. [ 49 ] Since their predators can more easily access the caribous' refuge, the females of the species attempt to avoid the area, affecting their reproductive behaviours and offspring produced. [ 49 ]
Fragmentation affecting the communication behaviours of birds has been well studied in Dupont's Lark. The Larks primarily reside in regions of Spain and are a small passerine bird which uses songs as a means of cultural transmission between members of the species. [ 49 ] The Larks have two distinct vocalizations, the song, and the territorial call. The territorial call is used by males to defend and signal territory from other male Larks and is shared between neighbouring territories when males respond to a rivals song. [ 50 ] Occasionally it is used as a threat signal to signify an impending attack on territory. [ 51 ] A large song repertoire can enhance a male's ability to survive and reproduce as he has a greater ability to defend his territory from other males, and a larger number of males in the species means a larger variety of songs being transmitted. [ 50 ] Fragmentation of the Dupont's Lark territory from agriculture, forestry and urbanization appears to have a large effect on their communication structures. [ 51 ] Males only perceive territories of a certain distance to be rivals and so isolation of territory from others due to fragmentation leads to a decrease in territorial calls as the males no longer have any reason to use it or have any songs to match. [ 51 ]
Humans have also brought on varying implications into ecosystems which in turn affect animal behaviour and responses generated. [ 52 ] Although there are some species which are able to survive these kinds of harsh conditions, such as, cutting down wood in the forests for pulp and paper industries, there are animals which can survive this change but some that cannot. An example includes, varying aquatic insects are able to identify appropriate ponds to lay their eggs with the aid of polarized light to guide them, however, due to ecosystem modifications caused by humans they are led onto artificial structures which emit artificial light which are induced by dry asphalt dry roads for an example. [ 53 ]
While habitat fragmentation is often associated with its effects on large plant and animal populations and biodiversity, due to the interconnectedness of ecosystems there are also significant effects that it has on the microbiota of an environment. Increased fragmentation has been linked to reduced populations and diversity of fungi responsible for decomposition, as well as the insects they are host to. [ 54 ] [ 55 ] This has been linked to simplified food webs in highly fragmented areas compared to old growth forests. [ 56 ] Furthermore, edge effects have been shown to result in significantly varied microenvironments compared to interior forest due to variations in light availability, presence of wind, changes in precipitation, and overall moisture content of leaf litter. [ 57 ] These microenvironments are often not conducive to overall forest health as they enable generalist species to thrive at the expense of specialists that depend on specific environments. [ 54 ]
A metadata analysis has found that habitat fragmentation greatly affects mutualistic relationships while affecting antagonistic relationships, such as predation and herbivory , to a less degree. [ 58 ] For example, the mutualistic relationship between Mesogyne insignis and Megachile . A study has found greater pollination and increased fruit production of M. insignis in unfragmented forests verses fragmented forests. [ 59 ] As for an example of an antagonistic relationship of nest predation, a study found that there is no increase in nest predation on fragmented forests - thus not supporting the edge effect hypothesis. [ 60 ]
Habitat fragmentation has profound effects on ecosystem services , impacting nutrient retention, species richness, and local biophysical conditions. Fragmentation-mediated processes cause generalizable responses at the population , community , and ecosystem levels, resulting in decreased nutrient retention. [ 61 ] Furthermore, habitat fragmentation alters relationships between biodiversity and ecosystem functioning across multiple scales, affecting both the local loss of biodiversity and the local loss of function. [ 13 ] Moreover, fragmentation can change the microclimate at both local and regional scales, influencing biodiversity through interactions with anthropogenic climate change . [ 62 ] Overall, habitat fragmentation significantly disrupts ecosystem services by altering nutrient retention, biodiversity, and ecosystem functioning at various spatial and temporal scales.
Forest fragmentation is a form of habitat fragmentation where forests are reduced (either naturally or man-made) to relatively small, isolated patches of forest known as forest fragments or forest remnants. [ 3 ] The intervening matrix that separates the remaining woodland patches can be natural open areas, farmland , or developed areas. Following the principles of island biogeography , remnant woodlands act like islands of forest in a sea of pastures, fields, subdivisions, shopping malls, etc. These fragments will then begin to undergo the process of ecosystem decay .
Forest fragmentation also includes less subtle forms of discontinuities such as utility right-of-ways (ROWs). Utility ROWs are of ecological interest because they have become pervasive in many forest communities, spanning areas as large as 5 million acres in the United States. [ 63 ] Utility ROWs include electricity transmission ROWs, gas pipeline and telecommunication ROWs. Electricity transmission ROWs are created to prevent vegetation interference with transmission lines. Some studies have shown that electricity transmission ROWs harbor more plant species than adjoining forest areas, [ 64 ] due to alterations in the microclimate in and around the corridor. Discontinuities in forest areas associated with utility right-of-ways can serve as biodiversity havens for native bees [ 63 ] and grassland species, [ 65 ] as the right-of-ways are preserved in an early successional stage.
Forest fragmentation reduces food resources and habitat sources for animals thus splitting these species apart. Thus, making these animals become much more susceptible to effects of predation and making them less likely to perform interbreeding - lowering genetic diversity. [ 66 ]
Additionally, forest fragmentation affects the native plant species present within the area by dividing large populations into smaller ones. In turn, smaller populations are more inclined to be affected by genetic drift and population performance, as well as experience increases in inbreeding activities. [ 67 ] Moreover, fragmentation can affect the relationship present between animals and plants, such as the relationships regarding seed-dispersal or pollinator-plant relationship. [ 67 ] [ 68 ]
Forest fragmentation is one of the greatest threats to biodiversity in forests, especially in the tropics. [ 69 ] The problem of habitat destruction that caused the fragmentation in the first place is compounded by:
The effect of fragmentation on the flora and fauna of a forest patch depends on a) the size of the patch, and b) its degree of isolation. [ 71 ] Isolation depends on the distance to the nearest similar patch, and the contrast with the surrounding areas. For example, if a cleared area is reforested or allowed to regenerate , the increasing structural diversity of the vegetation will lessen the isolation of the forest fragments. However, when formerly forested lands are converted permanently to pastures, agricultural fields, or human-inhabited developed areas, the remaining forest fragments, and the biota within them, are often highly isolated.
Forest patches that are smaller or more isolated will lose species faster than those that are larger or less isolated. A large number of small forest "islands" typically cannot support the same biodiversity that a single contiguous forest would hold, even if their combined area is much greater than the single forest. However, forest islands in rural landscapes greatly increase their biodiversity. [ 72 ] In the Maulino forest of Chile fragmentation appear to not affect overall plant diversity much, and tree diversity is indeed higher in fragments than in large continuous forests. [ 73 ] [ 74 ]
McGill University in Montreal , Quebec , Canada released a university based newspaper statement stating that 70% of the world's remaining forest stands within one kilometre of a forest edge putting biodiversity at an immense risk based on research conducted by international scientists. [ 75 ]
Reduced fragment area, increased isolation, and increased edge initiate changes that percolate through all ecosystems. Habitat fragmentation is able to formulate persistent outcomes which can also become unexpected such as an abundance of some species and the pattern that long temporal scales are required to discern many strong system responses. [ 7 ]
The presence of forest fragments influences the supply of various ecosystems in adjacent agricultural fields (Mitchell et al. 2014). Mitchell et al. (2014), researched on six varying ecosystem factors such as crop production, decomposition , pesticide regulation , carbon storage, soil fertility , and water quality regulation in soybean fields through separate distances by nearby forest fragments which all varied in isolation and size across an agricultural landscape in Quebec, Canada . Sustainable forest management can be achieved in several ways including by managing forests for ecosystem services (beyond simple provisioning), through government compensation schemes, and through effective regulation and legal frameworks. [ 76 ] The only realistic method of conserving forests is to apply and practice sustainable forest management to risk further loss.
There is a high industrial demand for wood , pulp , paper , and other resources which the forest can provide with, thus businesses which will want more access to the cutting of forests to gain those resources. The rainforest alliance has efficiently been able to put into place an approach to sustainable forest management, and they established this in the late 1980s. Their conservation was deemed successful as it has saved over nearly half a billion acres of land around the world. [ 77 ]
A few approaches and measures which can be taken in order to conserve forests are methods by which erosion can be minimized, waste is properly disposed, conserve native tree species to maintain genetic diversity , and setting aside forestland (provides habitat for critical wildlife species ). [ 77 ] Additionally, forest fires can also occur frequently and measures can also be taken to further prevent forest fires from occurring. For example, in Guatemala ’s culturally and ecologically significant Petén region, researchers were able to find over a 20-year period, actively managed FSC -certified forests experienced substantially lower rates of deforestation than nearby protected areas, and forest fires only affected 0.1 percent of certified land area, compared to 10.4 percent of protected areas. [ 77 ] However, it must be duly noted that short term decisions regarding forest sector employment and harvest practices can have long-term effects on biodiversity. [ 78 ] Planted forests become increasingly important as they supply approximately a quarter of global industrial roundwood production and are predicted to account for 50% of global output within two decades (Brown, 1998; Jaakko Poyry, 1999). [ 79 ] Although there have been many difficulties, the implementation of forest certification has been quite prominent in being able to raise effective awareness and disseminating knowledge on a holistic concept, embracing economic, environmental and social issues, worldwide. While also providing a tool for a range of other applications than assessment of sustainability , such as e.g. verifying carbon sinks. [ 80 ]
Two approaches are typically used to understand habitat fragmentation and its ecological impacts.
The species-oriented approach focuses specifically on individual species and how they each respond to their environment and habitat changes with in it. This approach can be limited because it does only focus on individual species and does not allow for a broad view of the impacts of habitat fragmentation across species. [ 81 ]
The pattern-oriented approach is based on land cover and its patterning in correlation with species occurrences. One model of study for landscape patterning is the patch-matrix-corridor model developed by Richard Forman The pattern-oriented approach focuses on land cover defined by human means and activities. This model has stemmed from island biogeography and tries to infer causal relationships between the defined landscapes and the occurrence of species or groups of species within them. The approach has limitations in its collective assumptions across species or landscapes which may not account for variations amongst them. [ 82 ]
The other model is the variegation model. Variegated landscapes retain much of their natural vegetation but are intermixed with gradients of modified habitat [ 83 ] This model of habitat fragmentation typically applies to landscapes that are modified by agriculture. In contrast to the fragmentation model that is denoted by isolated patches of habitat surrounded by unsuitable landscape environments, the variegation model applies to landscapes modified by agriculture where small patches of habitat remain near the remnant original habitat. In between these patches are a matrix of grassland that is often modified versions of the original habitat. These areas do not present as much of a barrier to native species. [ 84 ] | https://en.wikipedia.org/wiki/Habitat_fragmentation |
In mathematics Haboush's theorem , often still referred to as the Mumford conjecture , states that for any semisimple algebraic group G over a field K , and for any linear representation ρ of G on a K - vector space V , given v ≠ 0 in V that is fixed by the action of G , there is a G -invariant polynomial F on V , without constant term, such that
The polynomial can be taken to be homogeneous , in other words an element of a symmetric power of the dual of V , and if the characteristic is p >0 the degree of the polynomial can be taken to be a power of p .
When K has characteristic 0 this was well known; in fact Weyl's theorem on the complete reducibility of the representations of G implies that F can even be taken to be linear. Mumford's conjecture about the extension to prime characteristic p was proved by W. J. Haboush (1975) , about a decade after the problem had been posed by David Mumford , in the introduction to the first edition of his book Geometric Invariant Theory .
Haboush's theorem can be used to generalize results of geometric invariant theory from characteristic 0, where they were already known, to characteristic p >0. In particular Nagata's earlier results together with Haboush's theorem show that if a reductive group (over an algebraically closed field) acts on a finitely generated algebra then the fixed subalgebra is also finitely generated.
Haboush's theorem implies that if G is a reductive algebraic group acting regularly on an affine algebraic variety, then disjoint closed invariant sets X and Y can be separated by an invariant function f (this means that f is 0 on X and 1 on Y ).
C.S. Seshadri (1977) extended Haboush's theorem to reductive groups over schemes.
It follows from the work of Nagata (1963) , Haboush, and Popov that the following conditions are equivalent for an affine algebraic group G over a field K :
The theorem is proved in several steps as follows: | https://en.wikipedia.org/wiki/Haboush's_theorem |
Habr (since 2018; formerly Habrahabr ) ( Russian : Хабр, Хабрахабр ) is a Russian collaborative blog about IT , computer science and anything related to the Internet , owned by TechMedia. [ 1 ] Habrahabr was founded in June 2006, and the English section of Habr was launched in 2019.
Habr is often compared to other technology sites, such as Engadget or Hacker News . The parent company of the site, Habr Blockchain Publishing, developed a group of websites ("Habr Q&A" qna.habr.com, "Habr Career" career.habr.com, "Habr Freelance" freelance.habr.com after they developed habrahabr.ru).
In 2007, Habrahabr received two nominations in the ROTOR contest ( Russian : РОТОР ), which awards prizes to Russian-language web projects. It was nominated for Discovery of the Year ( Russian : Открытие года ) and Online Community of the Year ( Russian : Интернет-сообщество года ) prizes. The website's author, Denis Kryuchkov, was nominated for the Producer of the Year prize ( Russian : Продюсер года ). In 2009, the website was again nominated for the Online Community of the Year prize.
The blogs comprise three sections: theme-specific, personal and corporate blogs. [ 2 ] Each team blog consists of two sections, both of which contain entries that go by the moniker "habratopiki" (in Russian, "хабратопики") in the Habr environment.
The first section, titled "zahabrennye" (in Russian, "захабренные"), broadcasts entries that have received high approval from users of the website. The second section, called "othabrennye" (in Russian, "отхабренные"), contains habratopiki that have received disapproval by users of the Habr platform.
Topic-specific blogs, which go by the name "Haby" (the plural form of the Russian adaptation of the word "hub"), include sections devoted to programming , IT security , DIY projects , self-care , popular science , open source software , vintage hardware , game development , transportation , programming language -specific threads, and others.
Habr's corporate blogs are authored by companies that include Google , Yandex , Intel , Microsoft , Samsung , and ABBYY , among others.
Since the autumn of 2010, Habr has hosted a questions and answers service, similar to Google's services FAQ. In this section, any user can ask questions about IT-related topics and receive answers from other members of the project.
In 2013, the Q&A section separated from the main portal Habrahbr, and can now be found under a section that is separated from the main Habr portal.
The "people" section provides statistics on registered users (distribution by country and region, the number of registered and active users) and includes user rating, built on the basis of their habrasily. In the present karmagraf - a graph showing the cumulative change indicators karma users.
Rating companies, one way or another connected with the sphere of high technologies. Basis rating - the assessment by users of a particular company.
The section devoted to industry job boards. All resumes and vacancies divided by sector ("consulting, outsourcing," "Optimizing sites (SEO)», «Media", etc.). Only users with non-negative karma can post. Summaries from users with negative karma will not appear in the list.
The Sandbox is designed for posts from read-only users. Posts get there from users who have not yet received access to commenting and creating posts without pre-moderation. After hitting the post in the sandbox it is to see someone from "zahabrennyh," and if he is interested in the post, it will be added to the main section. | https://en.wikipedia.org/wiki/Habr |
Hachimoji DNA (from Japanese 八文字 hachimoji , "eight letters") is a synthetic nucleic acid analog that uses four synthetic nucleotides in addition to the four present in the natural nucleic acids , DNA and RNA. This leads to four allowed base pairs : two unnatural base pairs formed by the synthetic nucleobases in addition to the two normal pairs. Hachimoji bases have been demonstrated in both DNA and RNA analogs, using deoxyribose and ribose respectively as the backbone sugar. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]
Benefits of such a nucleic acid system may include an enhanced ability to store data , as well as insights into what may be possible in the search for extraterrestrial life . [ 5 ] [ 6 ]
The hachimoji DNA system produced one type of catalytic RNA ( ribozyme or aptamer ) in vitro .
Natural DNA is a molecule carrying the genetic instructions used in the growth, development, functioning, and reproduction of all known living organisms and many viruses . DNA and ribonucleic acid (RNA) are nucleic acids ; alongside proteins , lipids and complex carbohydrates ( polysaccharides ), nucleic acids are one of the four major types of macromolecules that are essential for all known forms of life . DNA is a polynucleotide as it is composed of simpler monomeric units called nucleotides ; when double-stranded, the two chains coil around each other to form a double helix . [ 7 ] [ 8 ]
In natural DNA, each nucleotide is composed of one of four nucleobases ( cytosine [C], guanine [G], adenine [A] or thymine [T]), a sugar called deoxyribose , and a phosphate group . The nucleotides are joined to one another in a chain by covalent bonds between the sugar of one nucleotide and the phosphate of the next, resulting in an alternating sugar-phosphate backbone . The nitrogenous bases of the two separate polynucleotide strands are bound to each other with hydrogen bonds , according to base pairing rules (A with T and C with G), to make double-stranded DNA.
Hachimoji DNA is similar to natural DNA but differs in the number, and type, of nucleobases. [ 1 ] [ 5 ] Unnatural nucleobases, more hydrophobic than natural bases , [ 9 ] [ 10 ] are used in successful hachimoji DNA. Such a DNA always formed the standard double helix , no matter what sequence of bases were used. An enzyme ( T7 polymerase ) was adapted by the researchers to be used in vitro to transcribe hachimoji DNA into hachimoji RNA, which, in turn, produced chemical activity in the form of a glowing green fluorophore . [ 4 ] [ 5 ]
DNA and RNA are naturally composed of four nucleotide bases that form hydrogen bonds in order to pair. Hachimoji DNA uses an additional four synthetic nucleotides to form four types of base pairs, two of which are unnatural: P binds with Z and B binds with S ( dS in DNA , rS in RNA ). [ 1 ]
2-amino-8-(1′-b-D-2′-deoxyribofuranosyl)-imidazo-[1,2a]-1,3,5-triazin-[8H]-4-one [ 1 ]
6-amino-3-(1′-b-D-2′-deoxyribofuranosyl)-5-nitro-1H-pyridin-2-one [ 1 ]
6-amino-9[(1′-b-D-2′-deoxyribofuranosyl)-4-hydroxy-5-(hydroxymethyl)-oxolan-2-yl]-1H-purin-2-one [ 1 ]
3-methyl-6-amino-5-(1′-b-D-2′-deoxyribofuranosyl)-pyrimidin-2-one [ 1 ]
Earlier, the research group responsible for the hachimoji DNA system, headed by Harvard University chemist Steven Benner , had studied a synthetic DNA analog system, named Artificially Expanded Genetic Information System (AEGIS), that used twelve different nucleotides, including the four found in DNA. [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ]
Scripps Research chemist Floyd Romesberg , noted for creating the first Unnatural Base Pair (UBP) , and expanding the genetic alphabet of four letters to six in 2012, [ 16 ] stated that the invention of the hachimoji DNA system is an example of the fact that the natural bases (G, C, A and T) "are not unique". [ 17 ] [ 18 ] Creating new life forms may be possible, at least theoretically, [ 9 ] with the new DNA system. [ 18 ] For now, however, the hachimoji DNA system is not self-sustaining; the system needs a steady supply of unique building blocks and proteins found only in the laboratory. As a result, "Hachimoji DNA can go nowhere if it escapes the laboratory." [ 4 ]
NASA funded this research to "expand[s] the scope of the structures that we might encounter as we search for life in the cosmos". [ 1 ] According to Lori Glaze of the Planetary Science Division of NASA, "Life detection is an increasingly important goal of NASA's planetary science missions, and this new work [with hachimoji DNA] will help us to develop effective instruments and experiments that will expand the scope of what we look for." [ 3 ] [ 19 ] Research team leader Steven Benner notes, "By carefully analyzing the roles of shape, size and structure in hachimoji DNA, this work expands our understanding of the types of molecules that might store information in extraterrestrial life on alien worlds." [ 20 ]
According to researchers, [ 1 ] hachimoji DNA could also be used "to develop clean diagnostics for human diseases , in DNA digital data storage , DNA barcoding , self-assembling nanostructures , and to make proteins with unusual amino acids . Parts of this hachimoji DNA are already being commercially produced by Firebird Biomolecular Sciences LLC". [ 1 ] [ 4 ] | https://en.wikipedia.org/wiki/Hachimoji_DNA |
Hack's law is an empirical relationship between the length of streams and the area of their basins . If L is the length of the longest stream in a basin, and A is the area of the basin, then Hack's law may be written as
for some constant C where the exponent h is slightly less than 0.6 in most basins. h varies slightly from region to region and slightly decreases for larger basins (>8,000 mi 2 , or 20,720 km 2 ). In addition to the catchment-scales, Hack's law was observed on unchanneled small-scale surfaces when the morphology measured at high resolutions (Cheraghi et al., 2018).
The law is named after American geomorphologist John Tilton Hack .
This geomorphology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hack's_law |
The Hack Computer is a theoretical computer design created by Noam Nisan and Shimon Schocken and described in their book, The Elements of Computing Systems: Building a Modern Computer from First Principles. [ 1 ] In using the term “modern”, the authors refer to a digital, binary machine that is patterned according to the von Neumann architecture model.
The Hack computer is intended for hands-on virtual construction in a hardware simulator application as a part of a basic, but comprehensive, course in computer organization and architecture . [ 2 ] One such course, created by the authors and delivered in two parts, is freely available as a massive open online course (MOOC) called Build a Modern Computer From First Principles: From Nand to Tetris. [ 3 ] In the twelve projects included in the course, learners start with a two input Nand gate and end up with a fully operational virtual computer, including both hardware (memory and CPU) and software (assembler, VM, Java-like programming language, and OS). In addition to the hardware simulator used for initial implementation of the computer hardware, a complete Hack computer emulator program and assembler that supports the projects described in the book and the on-line course is also available at the author's web site. [ 4 ]
The Hack computer hardware consists of three basic elements as shown in the block diagram. There are two separate 16- bit memory units and a central processing unit (CPU). Because data is moved and processed by the computer in 16-bit words, the Hack computer is classified as a 16-bit architecture .
The instruction memory, implemented as read-only memory from the viewpoint of the computer and designated ROM, holds assembled binary program code for execution. The random access memory , called RAM, provides storage for an executing program’s data and provides services and storage areas for the computer’s memory-mapped I/O mechanism. Data processing and program control management are provided by the CPU.
The three units are connected by parallel buses. The address buses (15-bit), as well as the data and instruction busses (16-bit) for the ROM and RAM units are completely independent. Therefore, the Hack design follows the Harvard architecture model with respect to bus communication between the memory units and the CPU. All memory is word addressable only.
The Hack computer’s ROM module is presented as a linear array of individually addressable , sequential, 16-bit memory registers. Addresses start at 0 (0x0000). Since the memory elements are sequential devices, a system clock signal is supplied by the simulation application and the computer emulator application. The ROM address bus is 15 bits wide, so a total of 32,768 individual words are available for program instructions. The address of the currently active word is supplied by a program counter register within the CPU (see below). The value in the ROM memory register identified by the address placed on the instruction address bus in a particular clock cycle is available as the "current" instruction at the beginning of the next cycle. There is no instruction register ; instructions are decoded in each cycle from the currently active ROM register.
Although the RAM module is also viewed as a continuous linear array of individually addressable sequential, read-write, 16-bit memory registers, it is functionally organized by address range into three segments. Addresses 0 (0x000) through 16383 (0x3FFF) contain conventional 16-bit, read-write registers and are meant for use as general-purpose program data storage.
The registers at addresses 16384 (0x4000) through 24575 (0x5FFF) are essentially like data RAM, but they are also designated for use by a built-in screen I/O subsystem. Data written to addresses in this range have the side effect of producing output on the computer’s virtual 256 x 512 screen (see I/O). If a program does not require screen output, registers in this range may be used for general program data.
The final address in the RAM address space, at 24576 (0x6000), contains a single one word register whose current value is controlled by the output of a keyboard attached to the computer hosting the Hack emulator program. This keyboard memory map register is read-only (see I/O).
Data memory addresses in the range 24577 (0x6001) through 32767 (0x7FFF) are invalid. State transitions of the selected RAM memory register is also coordinated by the system clock signal.
As illustrated in the accompanying diagram, the Hack computer central processing unit (CPU) is an integrated logic unit with internal structure. It provides many of the functions found in simple, commercially available CPUs. The most complex element of the CPU is the arithmetic logic unit (ALU) which provides the computational functionality of the computer. The ALU is a combinational logic device having two 16-bit input operands and a single 16-bit output. The computation produced as output from the operands is specified by a set of six ordered, single-bit inputs to the ALU. The ALU also emits two single-bit status flags which indicate whether a computation result is zero (zr flag) or negative (ng flag).
The CPU also contains two 16-bit registers , labeled D and A. The D (Data) register is a general-purpose register whose current value always supplies the ALU x operand, although for some instructions its value is ignored. While the A (Address) register may also provide its current value as the y operand to the ALU when so directed by an instruction, its value may also be used for data memory addressing and as a target address in instruction memory for branching instructions. To facilitate this function, the A register is directly associated with a "pseudo-register" designated as M which is not explicitly implemented in hardware. This M register therefore represents the value contained in RAM having the address of the current value contained in the A register.
The final important element in the CPU is the program counter (PC) register. The PC is a 16-bit binary counter whose low 15 bits specify the address in instruction memory of the next instruction for execution. Unless directed otherwise by a branching instruction, the PC increments its value at the end of each clock cycle. The CPU also includes logic to change, under program control, the order of the computer's instruction execution, by setting the PC to a non-sequential value. The PC also implements a single-bit reset input that initializes the PC value to 0 (0x0000) when it is cycled from logic 0 to logic 1 and back. Unlike many actual CPU designs, there is no program accessible hardware mechanism provided to implement CPU external or internal interrupts or support for function calls.
The Hack computer employs a memory-mapped approach to I/O. Bitmapped, black and white output to a virtual 256 x 512 screen is effected by writing a bitmap of the desired output to data memory locations 16384 (0x4000) through 24575 (0x5FFF). The data words in this address range are viewed as a linear array of bits with each bit value representing the black/white state of a single pixel on the computer emulator's virtual screen. The least significant bit of the word in the first memory address of the screen RAM segment sets the pixel in the upper left corner of the screen to white if it is 0 and black if it is 1. The next-most significant bit in the first word controls the next pixel to the right, and so on. After the first 512-pixel row is described by the first 32 words of screen memory, the mapping is continued in the same fashion for the second row with the next 32 words. Logic external to the computer reads the screen RAM memory map segment and updates the virtual screen.
If a keyboard is attached to the computer hosting the CPU emulator program, the emulator puts a 16-bit bit scan code corresponding to a key depressed during program execution into the keyboard register at RAM address 24576 (0x6000). If no key is depressed, this register contains the value 0. The emulator provides a toggle button to enable/disable the keyboard. The encoding scheme closely follows ASCII encoding for printable characters. The effect of the Shift key is generally honored. Codes are also provided for other keys often present on a standard PC keyboard; for example, direction control keys (←, ↑, ↓, →) and Fn keys.
Step-wise operation of the CPU and memory units is controlled by a clock that is built-in to both the hardware simulator and the computer emulator programs. At the beginning of a clock cycle the instruction at the ROM address emitted by the current value of the program counter is decoded. The ALU operands specified in the instruction are marshalled where needed. The computation specified is performed by the ALU and the appropriate status flags are set. The computation result is saved as specified by the instruction. Finally, the program counter is updated to the value of the next required program instruction. If no branching was specified by the current instruction, the PC value is simply incremented. If branching was specified, the PC is loaded (from the A register) with the address of the next instruction to be executed. The cycle then repeats using the now current PC value.
Because of its Harvard memory architecture model, the Hack computer is designed to execute the current instruction and “fetch” the next instruction in a single, two-part clock cycle. The speed of the clock may be varied by a control element in both the hardware simulator and the CPU emulator. Independent of the selected speed however, each instruction is completely executed in one cycle. The user may also single-step through a program.
Execution of a program loaded in ROM is controlled by the CPU's reset bit. If the value of the reset bit is 0, execution proceeds according to the operating cycle described above. Setting the reset bit to 1 sets the PC to 0. Setting the reset bit value back to zero then begins execution of the current program at the first instruction; however, RAM contains the values from any previous activity on reset.
There is no hardware or machine language support for interrupts of any kind.
Values stored in ROM memory must represent valid Hack machine language instructions as described in the Instruction Set Architecture section.
Any 16-bit value may be stored in RAM. The data type of value stored in RAM is inferred by its location and/or its use within a program. The primary hardware supported data type is the 16-bit signed integer, which is represented in 2’s complement format. Signed integers therefore have the range -32768 through 32767. The lower 15 bits of a value in RAM may also represent an address in ROM or RAM in the sense of a pointer .
For values in the RAM memory registers assigned for screen I/O, the value will be interpreted as a 16 pixel map of the 256 row x 512 column virtual screen by the computer's independent I/O subsystem if the screen is "turned on".
The code value in keyboard memory may be read programmatically and interpreted for use by a program.
There is no hardware support for floating-point types.
The Hack computer's instruction set architecture (ISA) and derived machine language is sparse compared to many other architectures. Although the 6 bits used to specify a computation by the ALU could allow for 64 distinct instructions, only 18 are officially implemented in the Hack computer's ISA. Since the Hack computer hardware has direct support for neither integer multiplication (and division) or function calls, there are no corresponding machine language instructions in the ISA for these operations.
Hack machine language has only two types of instructions, each encoded in 16 binary digits.
Instructions whose most significant bit is “0” are called A-instructions or address instructions. The A-instruction is bit-field encoded as follows:
0 b 14 b 13 b 12 b 11 b 10 b 9 b 8 b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0
0 – the most significant bit of a A-instruction is “0”
b 14 - b 0 - these bits provide the binary representation of a non-negative integer in the decimal range 0 through 32767
When this instruction is executed, the remaining 15 bits are left-zero extended and loaded into the CPU's A-register. As a side-effect, the RAM register having the address represented by that value is enabled for subsequent read/write action in the next clock cycle.
The other instruction type, known as C-instructions (computation instructions) is the programming working horse. It has “1” as the most significant bit. The remaining 15 bits are bit-field encoded to define the operands, computation performed, and storage location for the specified computation result. This instruction may also specify a program branch based on the most recent computation result. he format is
C-instruction: dest = comp ; jump , either the dest or jump may be empty giving two options dest = comp or comp ; jump
The C-instruction is bit-field encoded as follows:
111 a c 1 c 2 c 3 c 4 c 5 c 6 d 1 d 2 d 3 j 1 j 2 j 3
1 – the most significant bit of a C-instruction is “1”
11 – these second two bits are ignored by the CPU and, by convention, are each always set to “1”
a – this bit specifies the source of the “y” operand of the ALU when it is used in a computation
c 1 -c 6 – these six control bits specify the operands and computation to be performed by the ALU
d 1 -d 3 – these three bits specify the destination(s) for storing the current ALU output
j 1 -j 3 – these three bits specify an arithmetic branch condition, an unconditional branch (jump), or no branching
The Hack computer encoding scheme of the C-instruction is shown in the following tables.
In these tables,
The Hack computer has a text-based assembly language to create programs for the hardware platform that implements the Hack computer ISA. Hack assembly language programs may be stored in text files having the file name extension “.asm”. Hack assembly language source files are case sensitive. Each line of text contains one of the following elements:
Each of these line types has a specific syntax and may contain predefined or user defined symbols or numeric constants. Blank lines and comments are ignored by the assembler. Label declarations, A-instructions, and C-instructions, as defined below, may not include any internal white-space characters, although leading or trailing whitespace is permitted (and ignored).
Any text beginning with the two-character sequence “//” is a comment. Comments may appear on a source code line alone, or may also be placed at the end of any other program source line. All text following the comment identifier character sequence to end of line is completely ignored by the assembler; consequently, they produce no machine code.
Hack assembly language allows the use of alphanumeric symbols for number of different specific purposes. A symbol may be any sequence of alphabetic (upper and lower case) or numeric digits. Symbols may also contain any of the following characters: under bar (“_”), period(“.”), dollar sign (“$”), and colon (“:”). Symbols may not begin with a digit character. Symbols are case sensitive. User defined symbols are used to create variable names and labels (see below).
The Hack assembly language assembler recognizes some predefined symbols for use in assembly language programs. The symbols R0, R1, …, R15 are bound respectively to the integers 0 through 15. These symbols are meant to represent general purpose registers and the symbols values therefore represent data memory addresses 0 through 15. Predefined symbols SCREEN and KBD are also specified to represent the data memory address of the start of memory-mapped virtual screen output (16384) and keyboard input (24756). There are a few other symbols (SP, LCL, ARG, THIS, and THAT) that are used in building the operating system software stack.
A string of decimal (0-9) digits may be used to represent a non-negative, decimal constant in the range 0 through 32,767. The use of the minus sign to indicate a negative number is not allowed. Binary or octal representation is not supported.
User defined symbols may be created in an assembly language program to represent variables; that is, a named RAM register. The symbol is bound at assembly to a RAM address chosen by the assembler. Therefore, variables must be treated as addresses when appearing in assembly language source code.
Variables are implicitly defined in assembly language source code when they are first referenced in an A-instruction. When the source code is processed by the assembler, the variable symbol is bound to a unique positive integer value in beginning at address 16. Addresses are sequentially bound to variable symbols in the order of their first appearance in the source code. By convention, user-defined symbols that identify program variables are written in all lower case.
Labels are symbols delimited by left "(" and right ")" parenthesis. They are defined on a separate source program line and are bound by the assembler to the address of the instruction memory location of the next instruction in the source code. Labels may be defined only once, but they may be used multiple times anywhere within the program, even before the line on which they are defined. By convention, labels are expressed in all-caps. They are used to identify the target address of branch C-instructions.
The A-instruction has the syntax “@ xxxx ”, where xxxx is either a numeric decimal constant in the range 0 through 32767, a label, or a variable (predefined or user defined). When executed, this instruction sets the value of the A register and the M pseudo-register to a 15-bit binary value represented by “ xxxx ”. The 15-bit value is left-zero extended to 16-bits in the A register.
The A-instruction may be used for one of three purposes. It is the only means to introduce a (non-negative) numeric value into the computer under program control; that is, it may be used to create program constants. Secondly, it is used to specify a RAM memory location using the M pseudo-register mechanism for subsequent reference by a C-instruction. Finally, a C-instruction which specifies a branch uses the current value of the A register as the branch target address. The A-instruction is used to set that target address prior to the branch instruction, usually by reference to a label.
C-instructions direct the ALU computation engine and program flow control capabilities of the Hack computer. The instruction syntax is defined by three fields, referred to as “comp”, “dest”, and “jump”. The comp field is required in every C-instruction. The C-instruction syntax is “dest = comp ; jump”. The “=” and “;” characters are used to delimit the fields of the instruction. If the dest field is not used, the “=” character is omitted. If the jump field is not used, the “;” character is omitted. The C-instruction allows no internal spaces.
The comp field must be one of the 28 documented mnemonic codes defined in the table above. These codes are considered distinct units; they must be expressed in all-caps with no internal spaces. It is noted that the 6 ALU control bits could potentially specify 64 computational functions; however, only the 18 presented in the table are officially documented for recognition by the assembler.
The dest field may be used to specify one or more locations to store the result of the specified computation. If this field is omitted, along with the “=” delimiter, the computed value is not stored. The allowed storage location combinations are specified by the mnemonic codes defined in the table above.
The jump field may be used to specify the address in ROM of the next instruction to be executed. If the field is omitted, along with the “;” delimiter, execution continues with the instruction immediately following the current instruction. The branch address target, in ROM, is provided by the current value of the A register if the specified branch condition is satisfied. If the branch condition fails, execution continues with the next instruction in ROM. Mnemonic codes are provided for six different comparisons based on the value of the current computation. Additionally, an unconditional branch is provided as a seventh option. Because the comp field must always be supplied, even though the value is not required for the unconditional branch, the syntax of this instruction is given as “0;JMP”. The branch conditions supported are specified in the table above.
Freely available software supporting the Hack computer includes a command line assembler application. The assembler reads Hack assembly language source tiles (*.asm) and produces Hack machine language output files (*.hack). The machine language file is also a text file. Each line of this file is a 16-character string of binary digits that represents the encoding of each corresponding executable line of the source text file according to the specification described in the section "Instruction set architecture (ISA) and machine language". The file created may be loaded into the Hack computer emulator by a facility provided by the emulator user interface.
Following is an annotated example program written in Hack assembly language. This program sums the first 100 consecutive integers and places the result of the calculation in a user-defined variable called “sum”. It implements a “while” loop construct to iterate though the integer values 1 through 100 and adds each integer to a “sum” variable. The user-defined variable “cnt” maintains the current integer value through the loop. This program illustrates all of the features of the “documented” assembly language capabilities of Hack Computer except memory-mapped I/O. It is Hack Assembly translation of the C fragment:
The contents of the Hack assembly language source file are shown in the second column in bold font. Line numbers are provided for reference in the following discussion but do not appear in the source code. The Hack machine code produced by the assembler is shown in the last column with the assigned ROM address in the preceding column. Note that full-line comments, blank lines, and label definition statements generate no machine language code. Also, the comments provided at the end of each line containing an assembly language instruction are ignored by the assembler.
The assembler output, shown in the last column, is a text string of 16 binary characters, not 16-bit binary integer representation.
Nbr
Type
Addr
Code
Note that the instruction sequence follows the pattern of A-instruction, C-instruction, A-instruction, C-instruction, ... . This is typical for Hack assembly language programs. The A-instruction specifies a constant or memory address that is used in the subsequent C-instruction.
All three variations of the A-instruction are illustrated. In line 11 (@100), the constant value 100 is loaded into the A register. This value is used in line 12 (D=D-A) to compute the value used to test the loop branch condition.
Since line 4 (@cnt) contains the first appearance of the user-defined variable "cnt", this statement binds the symbol to the next unused RAM address. In this instance, the address is 16, and that value is loaded into the A register. Also, the M pseudo-register also now references this address, and RAM[16] is made the active RAM memory location.
The third use of the A-instruction is seen in line 21 (@LOOP). Here the instruction loads the bound label value, representing an address in ROM memory, into the A register and M pseudo-register. The subsequent unconditional branch instruction in line 22 (0;JMP) loads the M register value into the CPU's program counter register to effect control transfer to the beginning of the loop.
The Hack computer provides no machine language instruction to halt program execution. The final two lines of the program (@END and 0;JMP) create an infinite loop condition which Hack assembly programs conventionally use to terminate programs designed to run in the CPU emulator. | https://en.wikipedia.org/wiki/Hack_computer |
The glider is a pattern that travels across the board in Conway's Game of Life . It was first discovered by Richard K. Guy in 1969, while John Conway's group was attempting to track the evolution of the R- pentomino . Gliders are the smallest spaceships , and they travel diagonally at a speed of one cell every four generations, or c / 4 {\displaystyle c/4} . The glider is often produced from randomly generated starting configurations. [ 1 ]
The name comes from the fact that, after two steps, the glider pattern repeats its configuration with a glide reflection symmetry. After four steps and two glide reflections, it returns to its original orientation. [ 2 ] John Conway remarked that he wished he hadn't called it the glider. The game was developed before the widespread use of interactive computers, and after seeing it animated, he feels the glider looks more like an ant walking across the plane. [ 3 ]
Gliders are important to the Game of Life because they are easily produced, can be collided with each other to form more complicated objects, and can be used to transmit information over long distances. Instances of this second advantage are called glider syntheses . For instance, eight gliders can be positioned so that they collide to form a Gosper glider gun . [ 4 ] Glider collisions designed to result in certain patterns are also called glider syntheses. Patterns such as blocks, beehives, blinkers, traffic lights, even the uncommon Eater, can be synthesized with just two gliders. It takes three gliders to build the three other basic spaceships, and even the pentadecathlon oscillator .
Some patterns require a very large number (sometimes hundreds) of glider collisions; some oscillators, exotic spaceships, puffer trains, guns, etc. Whether the construction of an exotic pattern from gliders can possibly mean it can occur naturally, is still conjecture.
Gliders can also be collided with other patterns with interesting results. For example, if two gliders are shot at a block in just the right way, the block moves closer to the source of the gliders. If three gliders are shot in just the right way, the block moves farther away. This "sliding block memory" can be used to simulate a counter , which would be modified by firing gliders at it. It is possible to construct logic gates such as AND , OR and NOT using gliders. One may also build a pattern that acts like a finite-state machine connected to two counters. This has the same computational power as a universal Turing machine , so, using the glider, the Game of Life is theoretically as powerful as any computer with unlimited memory and no time constraints: it is Turing complete . [ 5 ] [ 6 ]
It was conjectured that any still life could be synthesized by gliders, with the details of the structure encoded by the positions and phases of the gliders. This has been disproven by a still life with 306 cells, constructed by Ilkka Törmä and Ville Salo in 2022, which can only be descended from itself without change. [ 7 ] [ 8 ] Also, anything that can be synthesized with gliders, can be synthesized with certain constructions called " universal constructors ". There is a universal constructor that starts with only 15 gliders, with a construction algorithm published in 2022. [ 9 ]
Eric S. Raymond has proposed the glider as an emblem to represent the hacker subculture, as the Game of Life appeals to hackers, and the concept of the glider was "born at almost the same time as the Internet and Unix ". [ 10 ] The emblem is in use in various places within the subculture. [ 11 ] [ 12 ] | https://en.wikipedia.org/wiki/Hacker_Emblem |
Hacker News ( HN ) is a social news website focusing on computer science and entrepreneurship . It is run by the investment fund and startup incubator Y Combinator . In general, content that can be submitted is defined as "anything that gratifies one's intellectual curiosity." [ 1 ]
The word hacker in "Hacker News" is used in its original meaning and refers to the hacker culture which consists of people who enjoy tinkering with technology. [ 2 ]
The site was created by Paul Graham in February 2007. [ 3 ] Initially called Startup News or occasionally News.YC., it became known by its current name on August 14, 2007. [ 4 ] It developed as a project of Graham's company Y Combinator , functioning as a real-world application of the Arc programming language which Graham co-developed. [ 5 ]
At the end of March 2014, Graham stepped away from his leadership role at Y Combinator, leaving Hacker News administration in the hands of other staff members. [ 6 ] [ 7 ] The site is currently moderated by Daniel Gackle who posts under the username dang . [ 8 ] Gackle co-moderated Hacker News with Scott Bell (username sctb ) until 2019 when Bell stopped working on the site. [ 9 ]
The intention was to recreate a community similar to the early days of Reddit . [ 3 ] [ 10 ] However, unlike Reddit where new users can immediately both upvote and downvote content, Hacker News does not allow users to downvote content until they have accumulated 501 "karma" points. Karma points are calculated as the number of upvotes a given user's content has received minus the number of downvotes. [ 3 ] "Flagging" comments, likewise, is not permitted until a user has 30 karma points. [ 11 ]
Graham stated he hopes to avoid the Eternal September that results in the general decline of intelligent discourse within a community. [ 5 ] The site has a proactive attitude in moderating content, including automated flame and spam detectors and active human moderation. It also practices stealth banning in which user posts stop appearing for others to see, unbeknownst to the user. [ 12 ] Additional software is used to detect "voting rings to purposefully vote up stories". [ 3 ]
According to a 2013 TechCrunch article: "Graham says that Hacker News gets a lot of complaints that it has a bias toward featuring stories about Y Combinator startups, but he says there is no such bias. [...] Graham adds that he gets a lot of vitriol from users personally with accusations of bias or censoring." [ 3 ] | https://en.wikipedia.org/wiki/Hacker_News |
The hacker ethic is a philosophy and set of moral values within hacker culture . Practitioners believe that sharing information and data with others is an ethical imperative. [ 1 ] The hacker ethic is related to the concept of freedom of information , as well as the political theories of anti-authoritarianism , anarchism , and libertarianism . [ 2 ] [ 3 ] [ 4 ]
While some tenets of the hacker ethic were described in other texts like Computer Lib/Dream Machines (1974) by Ted Nelson , the term hacker ethic is generally attributed to journalist Steven Levy , who appears to have been the first to document both the philosophy and the founders of the philosophy in his 1984 book titled Hackers: Heroes of the Computer Revolution .
The hacker ethic originated at the Massachusetts Institute of Technology in the 1950s–1960s. The term " hacker " has long been used there to describe college pranks that MIT students would regularly devise, and was used more generally to describe a project undertaken or a product built to fulfill some constructive goal, but also out of pleasure for mere involvement. [ 5 ]
MIT housed an early IBM 704 computer inside the Electronic Accounting Machinery (EAM) room in 1959. This room became the staging grounds for early hackers, as MIT students from the Tech Model Railroad Club sneaked inside the EAM room after hours to attempt programming the 30-ton, 9-foot-tall (2.7 m) computer.
The hacker ethic was described as a "new way of life, with a philosophy, an ethic and a dream". However, the elements of the hacker ethic were not openly debated and discussed; rather they were implicitly accepted and silently agreed upon. [ 6 ]
The free software movement was born in the early 1980s from followers of the hacker ethic. Its founder, Richard Stallman , is referred to by Steven Levy as "the last true hacker". [ 7 ]
Richard Stallman describes:
"The hacker ethic refers to the feelings of right and wrong, to the ethical ideas this community of people had—that knowledge should be shared with other people who can benefit from it, and that important resources should be utilized rather than wasted." [ 8 ]
and states more precisely that hacking (which Stallman defines as playful cleverness) and ethics are two separate issues:
"Just because someone enjoys hacking does not mean he has an ethical commitment to treating other people properly. Some hackers care about ethics—I do, for instance—but that is not part of being a hacker, it is a separate trait. [...] Hacking is not primarily about an ethical issue. [...] hacking tends to lead a significant number of hackers to think about ethical questions in a certain way. I would not want to completely deny all connection between hacking and views on ethics." [ 9 ]
The hacker culture has been compared to early Protestantism [ citation needed ] . Protestant sectarians emphasized individualism and loneliness, similar to hackers who have been considered loners and nonjudgmental individuals. The notion of moral indifference between hackers characterized the persistent actions of computer culture in the 1970s and early 1980s. According to Kirkpatrick, author of The Hacker Ethic , the "computer plays the role of God, whose requirements took priority over the human ones of sentiment when it came to assessing one's duty to others."
According to Kirkpatrick's The Hacker Ethic:
"Exceptional single-mindedness and determination to keep plugging away at a problem until the optimal solution had been found are well-documented traits of the early hackers. Willingness to work right through the night on a single programming problem are widely cited as features of the early 'hacker' computer culture."
The hacker culture is placed in the context of 1960s youth culture when American youth culture challenged the concept of capitalism and big, centralized structures. The hacker culture was a subculture within 1960s counterculture. The hackers' main concern was challenging the idea of technological expertise and authority. The 1960s hippy period attempted to "overturn the machine." Although hackers appreciated technology, they wanted regular citizens, and not big corporations, to have power over technology "as a weapon that might actually undermine the authority of the expert and the hold of the monolithic system."
As Levy summarized in the preface of Hackers , the general tenets or principles of hacker ethic include: [ 10 ]
In addition to those principles, Levy also described more specific hacker ethics and beliefs in chapter 2, The Hacker Ethic : [ 11 ] The ethics he described in chapter 2 are:
From the early days of modern computing through to the 1970s, it was far more common for computer users to have the freedoms that are provided by an ethic of open sharing and collaboration. Software , including source code, was commonly shared by individuals who used computers. Most companies had a business model based on hardware sales, and provided or bundled the associated software free of charge. According to Levy's account, sharing was the norm and expected within the non-corporate hacker culture. The principle of sharing stemmed from the open atmosphere and informal access to resources at MIT. During the early days of computers and programming, the hackers at MIT would develop a program and share it with other computer users.
If the hack was deemed particularly good, then the program might be posted on a board somewhere near one of the computers. Other programs that could be built upon it and improved it were saved to tapes and added to a drawer of programs, readily accessible to all the other hackers. At any time, a fellow hacker might reach into the drawer, pick out the program, and begin adding to it or "bumming" it to make it better. Bumming referred to the process of making the code more concise so that more can be done in fewer instructions, saving precious memory for further enhancements.
In the second generation of hackers, sharing was about sharing with the general public in addition to sharing with other hackers. A particular organization of hackers that was concerned with sharing computers with the general public was a group called Community Memory . This group of hackers and idealists put computers in public places for anyone to use. The first community computer was placed outside of Leopold's Records in Berkeley, California .
Another sharing of resources occurred when Bob Albrecht provided considerable resources for a non-profit organization called the People's Computer Company (PCC). PCC opened a computer center where anyone could use the computers there for fifty cents per hour.
This second generation practice of sharing contributed to the battles of free and open software. In fact, when Bill Gates ' version of BASIC for the Altair was shared among the hacker community, Gates claimed to have lost a considerable sum of money because few users paid for the software. As a result, Gates wrote an Open Letter to Hobbyists . [ 22 ] [ 23 ] This letter was published by several computer magazines and newsletters, most notably that of the Homebrew Computer Club where much of the sharing occurred.
According to Brent K. Jesiek in "Democratizing Software: Open Source, the Hacker Ethic, and Beyond, " technology is being associated with social views and goals. Jesiek refers to Gisle Hannemyr's views on open source vs. commercialized software. Hannemyr concludes that when a hacker constructs software, the software is flexible, tailorable, modular in nature and is open-ended. A hacker's software contrasts mainstream hardware which favors control, a sense of being whole, and be immutable (Hannemyr, 1999).
Furthermore, he concludes that 'the difference between the hacker’s approach and those of the industrial programmer is one of outlook: between an agoric, integrated and holistic attitude towards the creation of artifacts and a proprietary, fragmented and reductionist one' (Hannemyr, 1999). As Hannemyr’s analysis reveals, the characteristics of a given piece of software frequently reflect the attitude and outlook of the programmers and organizations from which it emerges."
As copyright and patent laws limit the ability to share software, opposition to software patents is widespread in the hacker and free software community .
Many of the principles and tenets of hacker ethic contribute to a common goal: the Hands-On Imperative. As Levy described in Chapter 2, "Hackers believe that essential lessons can be learned about the systems—about the world—from taking things apart, seeing how they work, and using this knowledge to create new and more interesting things." [ 24 ]
Employing the Hands-On Imperative requires free access, open information, and the sharing of knowledge. To a true hacker, if the Hands-On Imperative is restricted, then the ends justify the means to make it unrestricted so that improvements can be made . When these principles are not present, hackers tend to work around them. For example, when the computers at MIT were protected either by physical locks or login programs, the hackers there systematically worked around them in order to have access to the machines. Hackers assumed a "willful blindness" in the pursuit of perfection. [ 14 ]
This behavior was not malicious in nature: the MIT hackers did not seek to harm the systems or their users. This deeply contrasts with the modern, media-encouraged image of hackers who crack secure systems in order to steal information or complete an act of cyber-vandalism.
Throughout writings about hackers and their work processes, a common value of community and collaboration is present. For example, in Levy's Hackers , each generation of hackers had geographically based communities where collaboration and sharing occurred. For the hackers at MIT, it was the labs where the computers were running. For the hardware hackers (second generation) and the game hackers (third generation) the geographic area was centered in Silicon Valley where the Homebrew Computer Club and the People's Computer Company helped hackers network, collaborate, and share their work.
The concept of community and collaboration is still relevant today, although hackers are no longer limited to collaboration in geographic regions. Now collaboration takes place via the Internet . Eric S. Raymond identifies and explains this conceptual shift in The Cathedral and the Bazaar : [ 25 ]
Before cheap Internet, there were some geographically compact communities where the culture encouraged Weinberg's egoless programming, and a developer could easily attract a lot of skilled kibitzers and co-developers. Bell Labs, the MIT AI and LCS labs, UC Berkeley: these became the home of innovations that are legendary and still potent.
Raymond also notes that the success of Linux coincided with the wide availability of the World Wide Web . The value of community is still in high practice and use today.
Levy identifies several "true hackers" who significantly influenced the hacker ethic. Some well-known "true hackers" include:
Levy also identified the "hardware hackers" (the "second generation", mostly centered in Silicon Valley ) and the "game hackers" (or the "third generation"). All three generations of hackers, according to Levy, embodied the principles of the hacker ethic. Some of Levy's "second-generation" hackers include:
Levy's "third generation" practitioners of hacker ethic include:
In 2001, Finnish philosopher Pekka Himanen promoted the hacker ethic in opposition to the Protestant work ethic . In Himanen's opinion, the hacker ethic is more closely related to the virtue ethics found in the writings of Plato and of Aristotle . Himanen explained these ideas in a book, The Hacker Ethic and the Spirit of the Information Age , with a prologue contributed by Linus Torvalds and an epilogue by Manuel Castells .
In this manifesto, the authors wrote about a hacker ethic centering on passion, hard work, creativity and joy in creating software. Both Himanen and Torvalds were inspired by the Sampo in Finnish mythology . The Sampo, described in the Kalevala saga, was a magical artifact constructed by Ilmarinen , the blacksmith god, that brought good fortune to its holder; nobody knows exactly what it was supposed to be. The Sampo has been interpreted in many ways: a world pillar or world tree , a compass or astrolabe , a chest containing a treasure, a Byzantine coin die , a decorated Vendel period shield, a Christian relic, etc. Kalevala saga compiler Lönnrot interpreted it to be a " quern " or mill of some sort that made flour, salt, and wealth. [ 26 ] [ 27 ] | https://en.wikipedia.org/wiki/Hacker_ethic |
Hackpad is a web-based collaborative real-time text editor forked from Etherpad . [ 1 ]
It was used as the company wikis by multiple prominent startups of the 2010s, such as Airbnb , Stripe , and Upworthy . [ 2 ]
In April 2014, Hackpad was acquired by Dropbox . [ 3 ] [ 4 ] In April 2015, it was announced that Hackpad would be released as open source [ 5 ] and source code was published on GitHub in August 2015, [ 6 ] under the Apache license 2.0. [ 7 ] On April 25, 2017, Dropbox announced that it would shut down on July 19, 2017, with users being permanently migrated to Dropbox Paper . [ 8 ]
This content management system article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hackpad |
The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors . | https://en.wikipedia.org/wiki/Hacovercosine |
The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors . | https://en.wikipedia.org/wiki/Hacoversed_cosine |
The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors . | https://en.wikipedia.org/wiki/Hacoversed_sine |
The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors . | https://en.wikipedia.org/wiki/Hacoversine |
The hadal zone , also known as the hadopelagic zone , is the deepest region of the ocean , lying within oceanic trenches . The hadal zone ranges from around 6 to 11 km (3.7 to 6.8 mi; 20,000 to 36,000 ft) below sea level , and exists in long, narrow, topographic V-shaped depressions. [ 1 ] [ 2 ]
The cumulative area occupied by the 46 individual hadal habitats worldwide is less than 0.25% of the world's seafloor , yet trenches account for over 40% of the ocean's depth range. [ 3 ] Most hadal habitat is found in the Pacific Ocean , the deepest of the conventional oceanic divisions. [ 3 ]
Historically, the hadal zone was not recognized as distinct from the abyssal zone , although the deepest sections were sometimes called "ultra-abyssal". During the early 1950s, the Danish Galathea II and Soviet Vityaz expeditions separately discovered a distinct shift in the life at depths of 6,000–7,000 m (20,000–23,000 ft) not recognized by the broad definition of the abyssal zone. [ 4 ] [ 5 ] The term "hadal" was first proposed in 1956 by Anton Frederik Bruun to describe the parts of the ocean deeper than 6,000 m (20,000 ft), leaving abyssal for the parts at 4,000–6,000 m (13,000–20,000 ft). [ 6 ] The name refers to Hades , the ancient Greek god of the underworld . [ 6 ] About 94% of the hadal zone is found in subduction trenches. [ 7 ]
Depths in excess of 6,000 m (20,000 ft) are generally in ocean trenches , but there are also trenches at shallower depths. These shallower trenches lack the distinct shift in lifeforms and are therefore not hadal. [ 8 ] [ 9 ] [ 10 ] Although the hadal zone has gained widespread recognition and many continue to use the first proposed limit of 6,000 m (20,000 ft), it has been observed that 6,000–7,000 m (20,000–23,000 ft) represents a gradual transition between the abyssal and hadal zones, [ 10 ] leading to the suggestion of placing the limit in the middle, at 6,500 m (21,300 ft). Among others, this intermediate limit has been adopted by UNESCO . [ 11 ] [ 12 ] Similar to other depth ranges, the fauna of the hadal zone can be broadly placed into two groups: the hadobenthic species (compare benthic ) living on or at the seabottom/sides of trenches, and the hadopelagic species (compare pelagic ) living in the open water. [ 13 ] [ 14 ]
The deepest ocean trenches are considered the least explored and most extreme marine ecosystems . They are characterized by complete lack of sunlight, low temperatures, nutrient scarcity, and extremely high hydrostatic pressures. The major sources of nutrients and carbon are fallout from upper layers, drifts of fine sediment, and landslides. Most organisms are scavengers and detrivores . As of 2020, over 400 species are known from hadal ecosystems, many of which possess physiological adaptations to the extreme environmental conditions. There are high levels of endemism , and noteworthy examples of gigantism in amphipods , mysids , and isopods and dwarfism in nematodes , copepods , and kinorhynchs . [ 15 ]
Marine life decreases with depth, both in abundance and biomass , but there is a wide range of metazoan organisms in the hadal zone, mostly benthos , including fish , sea cucumber , bristle worms , bivalves , isopods , sea anemones , amphipods , copepods , decapod crustaceans and gastropods . Most of these trench communities probably originated from the abyssal plains . Although they have evolved adaptations to high pressure and low temperatures such as lower metabolism, intra-cellular protein-stabilising osmolytes , and unsaturated fatty acids in cell membrane phospholipids , there is no consistent relationship between pressure and metabolic rate in these communities. Increased pressure can instead constrain the ontogenic or larval stages of organisms. Pressure increases ten-fold as an organism moves from sea level to a depth of 90 m (300 ft), whilst pressure only doubles as an organism moves from 6,000 to 11,000 m (20,000 to 36,000 ft).
Over a geological time scale , trenches can become accessible as previously stenobathic (limited to a narrow depth range) fauna evolve to become eurybathic (adapted to a wider range of depths), such as grenadiers and natantian prawns. Trench communities do, nevertheless, display a contrasting degree of intra-trench endemism and inter-trench similarities at a higher taxonomic level. [ 5 ]
Only a relatively small number of fish species are known from the hadal zone, including certain grenadiers, cutthroat eels , pearlfish , cusk-eels , snailfish and eelpouts . [ 16 ] [ 17 ] Due to the extreme pressure, the theoretical maximum depth for vertebral fish may be about 8,000–8,500 m (26,200–27,900 ft), below which teleosts would be hyperosmotic , assuming trimethylamine N-oxide requirements follow the observed approximate linear relationship with depth. [ 18 ] [ 19 ] Some invertebrates do occur deeper, such as bigfin squid , [ 20 ] [ 21 ] certain polynoid worms, myriotrochid sea cucumbers, turrid snails and pardaliscid amphipods in excess of 10,000 m (33,000 ft). [ 9 ] In addition, giant protists known as Xenophyophora ( foraminifera ) live at these depths. [ 22 ]
The only known primary producers in the hadal zone are certain bacteria that are able to metabolize hydrogen and methane released by rock and seawater reactions ( serpentinization ), [ 23 ] or hydrogen sulfide released from cold seeps . Some of these bacteria are symbiotic , for example living inside the mantle of certain thyasirid and vesicomyid bivalves. [ 24 ] Otherwise the first link in the hadal food web are heterotroph organisms that feed on marine snow , both fine particles and the occasional carcass. [ 23 ] [ 25 ]
The hadal zone can reach far below 6,000 m (20,000 ft) deep; the deepest known extends to 10,911 m (35,797 ft). [ 26 ] At such depths, the pressure in the hadal zone exceeds 1,100 standard atmospheres (110 MPa ; 16,000 psi ). Lack of light and extreme pressure makes this part of the ocean difficult to explore.
The exploration of the hadal zone requires the use of instruments that are able to withstand pressures of up to a thousand or more atmospheres. A few haphazard and non-standard tools have been used to collect limited, but valuable, information about the basic biology of a few hadal organisms. [ 27 ] Manned and unmanned submersibles , however, can be used to study the depths in greater detail. Unmanned robotic submersibles may be remotely operated (connected to the research vessel by a cable) or autonomous (freely moving). Cameras and manipulators on submersibles allow researchers to observe and take samples of sediment and organisms. Failures of submersibles under the immense pressure at hadal zone depths have occurred. HROV Nereus is thought to have imploded at a depth of 9,990 meters while exploring the Kermadec Trench in 2014. [ 28 ]
The first manned exploration to reach Challenger Deep , the deepest known part of the ocean located in the Mariana Trench , was accomplished in 1960 by Jacques Piccard and Don Walsh . [ 29 ] They reached a maximum depth of 10,911 metres (35,797 ft) in the bathyscaphe Trieste . [ 30 ] [ 27 ]
James Cameron also reached the bottom of Mariana Trench in March 2012 using the Deepsea Challenger . [ 31 ] The descent of the Deepsea Challenger reached a depth of 10,908 metres (35,787 ft), slightly less than the deepest dive record set by Piccard and Walsh. [ 32 ] Cameron holds the record for the deepest solo dive. [ 30 ]
In June 2012, the Chinese manned submersible Jiaolong was able to reach 7,020 m (23,030 ft) deep in the Mariana Trench, making it the deepest diving manned research submersible. [ 33 ] [ 34 ] This range surpasses that of the previous record holder, the Japanese-made Shinkai , whose maximum depth is 6,500 m (21,300 ft). [ 35 ]
Few unmanned submersibles are capable of descending to maximum hadal depths. The deepest diving unmanned submersibles have included the Kaikō (lost at sea in 2003), [ 36 ] the ABISMO , [ 37 ] the Nereus (lost at sea in 2014), [ 28 ] and the Haidou-1 . [ 38 ] | https://en.wikipedia.org/wiki/Hadal_zone |
In mathematics , Hadamard's inequality (also known as Hadamard's theorem on determinants [ 1 ] ) is a result first published by Jacques Hadamard in 1893. [ 2 ] It is a bound on the determinant of a matrix whose entries are complex numbers in terms of the lengths of its column vectors. In geometrical terms, when restricted to real numbers , it bounds the volume in Euclidean space of n dimensions marked out by n vectors v i for 1 ≤ i ≤ n in terms of the lengths of these vectors || v i ||.
Specifically, Hadamard's inequality states that if N is the matrix having columns [ 3 ] v i , then
If the n vectors are non-zero, equality in Hadamard's inequality is achieved if and only if the vectors are orthogonal .
A corollary is that if the entries of an n by n matrix N are bounded by B , so | N ij | ≤ B for all i and j , then
In particular, if the entries of N are +1 and −1 only then [ 4 ]
In combinatorics , matrices N for which equality holds, i.e. those with orthogonal columns, are called Hadamard matrices .
More generally, suppose that N is a complex matrix of order n , whose entries are bounded by | N ij | ≤ 1, for each i , j between 1 and n . Then Hadamard's inequality states that
Equality in this bound is attained for a real matrix N if and only if N is a Hadamard matrix.
A positive-semidefinite matrix P can be written as N * N , where N * denotes the conjugate transpose of N (see Decomposition of a semidefinite matrix ). Then
So, the determinant of a positive definite matrix is less than or equal to the product of its diagonal entries. Sometimes this is also known as Hadamard's inequality. [ 2 ] [ 5 ]
The result is trivial if the matrix N is singular , so assume the columns of N are linearly independent . By dividing each column by its Euclidean norm, it can be seen that the result is equivalent to the special case where each column has norm 1, in other words if e i are unit vectors and M is the matrix having the e i as columns then
and equality is achieved if and only if the vectors are an orthogonal set . The general result now follows:
To prove (1) , consider P = M * M where M * is the conjugate transpose of M , and let the eigenvalues of P be λ 1 , λ 2 , … λ n . Since the length of each column of M is 1, each entry in the diagonal of P is 1, so the trace of P is n . Applying the inequality of arithmetic and geometric means ,
so
If there is equality then each of the λ i 's must all be equal and their sum is n , so they must all be 1. The matrix P is Hermitian , therefore diagonalizable , so it is the identity matrix —in other words the columns of M are an orthonormal set and the columns of N are an orthogonal set. [ 6 ] Many other proofs can be found in the literature. | https://en.wikipedia.org/wiki/Hadamard's_inequality |
In mathematics , Hadamard's lemma , named after Jacques Hadamard , is essentially a first-order form of Taylor's theorem , in which we can express a smooth, real-valued function exactly in a convenient manner.
Hadamard's lemma [ 1 ] — Let f {\displaystyle f} be a smooth, real-valued function defined on an open, star-convex neighborhood U {\displaystyle U} of a point a {\displaystyle a} in n {\displaystyle n} -dimensional Euclidean space. Then f ( x ) {\displaystyle f(x)} can be expressed, for all x ∈ U , {\displaystyle x\in U,} in the form: f ( x ) = f ( a ) + ∑ i = 1 n ( x i − a i ) g i ( x ) , {\displaystyle f(x)=f(a)+\sum _{i=1}^{n}\left(x_{i}-a_{i}\right)g_{i}(x),} where each g i {\displaystyle g_{i}} is a smooth function on U , {\displaystyle U,} a = ( a 1 , … , a n ) , {\displaystyle a=\left(a_{1},\ldots ,a_{n}\right),} and x = ( x 1 , … , x n ) . {\displaystyle x=\left(x_{1},\ldots ,x_{n}\right).}
Let x ∈ U . {\displaystyle x\in U.} Define h : [ 0 , 1 ] → R {\displaystyle h:[0,1]\to \mathbb {R} } by h ( t ) = f ( a + t ( x − a ) ) for all t ∈ [ 0 , 1 ] . {\displaystyle h(t)=f(a+t(x-a))\qquad {\text{ for all }}t\in [0,1].}
Then h ′ ( t ) = ∑ i = 1 n ∂ f ∂ x i ( a + t ( x − a ) ) ( x i − a i ) , {\displaystyle h'(t)=\sum _{i=1}^{n}{\frac {\partial f}{\partial x_{i}}}(a+t(x-a))\left(x_{i}-a_{i}\right),} which implies h ( 1 ) − h ( 0 ) = ∫ 0 1 h ′ ( t ) d t = ∫ 0 1 ∑ i = 1 n ∂ f ∂ x i ( a + t ( x − a ) ) ( x i − a i ) d t = ∑ i = 1 n ( x i − a i ) ∫ 0 1 ∂ f ∂ x i ( a + t ( x − a ) ) d t . {\displaystyle {\begin{aligned}h(1)-h(0)&=\int _{0}^{1}h'(t)\,dt\\&=\int _{0}^{1}\sum _{i=1}^{n}{\frac {\partial f}{\partial x_{i}}}(a+t(x-a))\left(x_{i}-a_{i}\right)\,dt\\&=\sum _{i=1}^{n}\left(x_{i}-a_{i}\right)\int _{0}^{1}{\frac {\partial f}{\partial x_{i}}}(a+t(x-a))\,dt.\end{aligned}}}
But additionally, h ( 1 ) − h ( 0 ) = f ( x ) − f ( a ) , {\displaystyle h(1)-h(0)=f(x)-f(a),} so by letting g i ( x ) = ∫ 0 1 ∂ f ∂ x i ( a + t ( x − a ) ) d t , {\displaystyle g_{i}(x)=\int _{0}^{1}{\frac {\partial f}{\partial x_{i}}}(a+t(x-a))\,dt,} the theorem has been proven. ◼ {\displaystyle \blacksquare }
Corollary [ 1 ] — If f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } is smooth and f ( 0 ) = 0 {\displaystyle f(0)=0} then f ( x ) / x {\displaystyle f(x)/x} is a smooth function on R . {\displaystyle \mathbb {R} .} Explicitly, this conclusion means that the function R → R {\displaystyle \mathbb {R} \to \mathbb {R} } that sends x ∈ R {\displaystyle x\in \mathbb {R} } to { f ( x ) / x if x ≠ 0 lim t → 0 f ( t ) / t if x = 0 {\displaystyle {\begin{cases}f(x)/x&{\text{ if }}x\neq 0\\\lim _{t\to 0}f(t)/t&{\text{ if }}x=0\\\end{cases}}} is a well-defined smooth function on R . {\displaystyle \mathbb {R} .}
By Hadamard's lemma, there exists some g ∈ C ∞ ( R ) {\displaystyle g\in C^{\infty }(\mathbb {R} )} such that f ( x ) = f ( 0 ) + x g ( x ) {\displaystyle f(x)=f(0)+xg(x)} so that f ( 0 ) = 0 {\displaystyle f(0)=0} implies f ( x ) / x = g ( x ) . {\displaystyle f(x)/x=g(x).} ◼ {\displaystyle \blacksquare }
Corollary [ 1 ] — If y , z ∈ R n {\displaystyle y,z\in \mathbb {R} ^{n}} are distinct points and f : R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } is a smooth function that satisfies f ( z ) = 0 = f ( y ) {\displaystyle f(z)=0=f(y)} then there exist smooth functions g i , h i ∈ C ∞ ( R n ) {\displaystyle g_{i},h_{i}\in C^{\infty }\left(\mathbb {R} ^{n}\right)} ( i = 1 , … , 3 n − 2 {\displaystyle i=1,\ldots ,3n-2} ) satisfying g i ( z ) = 0 = h i ( y ) {\displaystyle g_{i}(z)=0=h_{i}(y)} for every i {\displaystyle i} such that f = ∑ i g i h i . {\displaystyle f=\sum _{i}^{}g_{i}h_{i}.}
By applying an invertible affine linear change in coordinates, it may be assumed without loss of generality that z = ( 0 , … , 0 ) {\displaystyle z=(0,\ldots ,0)} and y = ( 0 , … , 0 , 1 ) . {\displaystyle y=(0,\ldots ,0,1).} By Hadamard's lemma, there exist g 1 , … , g n ∈ C ∞ ( R n ) {\displaystyle g_{1},\ldots ,g_{n}\in C^{\infty }\left(\mathbb {R} ^{n}\right)} such that f ( x ) = ∑ i = 1 n x i g i ( x ) . {\displaystyle f(x)=\sum _{i=1}^{n}x_{i}g_{i}(x).} For every i = 1 , … , n , {\displaystyle i=1,\ldots ,n,} let α i := g i ( y ) {\displaystyle \alpha _{i}:=g_{i}(y)} where 0 = f ( y ) = ∑ i = 1 n y i g i ( y ) = g n ( y ) {\displaystyle 0=f(y)=\sum _{i=1}^{n}y_{i}g_{i}(y)=g_{n}(y)} implies α n = 0. {\displaystyle \alpha _{n}=0.} Then for any x = ( x 1 , … , x n ) ∈ R n , {\displaystyle x=\left(x_{1},\ldots ,x_{n}\right)\in \mathbb {R} ^{n},} f ( x ) = ∑ i = 1 n x i g i ( x ) = ∑ i = 1 n [ x i ( g i ( x ) − α i ) ] + ∑ i = 1 n − 1 [ x i α i ] using g i ( x ) = ( g i ( x ) − α i ) + α i and α n = 0 = [ ∑ i = 1 n x i ( g i ( x ) − α i ) ] + [ ∑ i = 1 n − 1 x i x n α i ] + [ ∑ i = 1 n − 1 x i ( 1 − x n ) α i ] using x i = x n x i + x i ( 1 − x n ) . {\displaystyle {\begin{alignedat}{8}f(x)&=\sum _{i=1}^{n}x_{i}g_{i}(x)&&\\&=\sum _{i=1}^{n}\left[x_{i}\left(g_{i}(x)-\alpha _{i}\right)\right]+\sum _{i=1}^{n-1}\left[x_{i}\alpha _{i}\right]&&\quad {\text{ using }}g_{i}(x)=\left(g_{i}(x)-\alpha _{i}\right)+\alpha _{i}{\text{ and }}\alpha _{n}=0\\&=\left[\sum _{i=1}^{n}x_{i}\left(g_{i}(x)-\alpha _{i}\right)\right]+\left[\sum _{i=1}^{n-1}x_{i}x_{n}\alpha _{i}\right]+\left[\sum _{i=1}^{n-1}x_{i}\left(1-x_{n}\right)\alpha _{i}\right]&&\quad {\text{ using }}x_{i}=x_{n}x_{i}+x_{i}\left(1-x_{n}\right).\\\end{alignedat}}} Each of the 3 n − 2 {\displaystyle 3n-2} terms above has the desired properties. ◼ {\displaystyle \blacksquare } | https://en.wikipedia.org/wiki/Hadamard's_lemma |
The Hadamard code is an error-correcting code named after the French mathematician Jacques Hadamard that is used for error detection and correction when transmitting messages over very noisy or unreliable channels. In 1971, the code was used to transmit photos of Mars back to Earth from the NASA space probe Mariner 9 . [ 1 ] Because of its unique mathematical properties, the Hadamard code is not only used by engineers, but also intensely studied in coding theory , mathematics , and theoretical computer science .
The Hadamard code is also known under the names Walsh code , Walsh family , [ 2 ] and Walsh–Hadamard code [ 3 ] in recognition of the American mathematician Joseph Leonard Walsh .
The Hadamard code is an example of a linear code of length 2 m {\displaystyle 2^{m}} over a binary alphabet .
Unfortunately, this term is somewhat ambiguous as some references assume a message length k = m {\displaystyle k=m} while others assume a message length of k = m + 1 {\displaystyle k=m+1} .
In this article, the first case is called the Hadamard code while the second is called the augmented Hadamard code .
The Hadamard code is unique in that each non-zero codeword has a Hamming weight of exactly 2 k − 1 {\displaystyle 2^{k-1}} , which implies that the distance of the code is also 2 k − 1 {\displaystyle 2^{k-1}} .
In standard coding theory notation for block codes , the Hadamard code is a [ 2 k , k , 2 k − 1 ] 2 {\displaystyle [2^{k},k,2^{k-1}]_{2}} -code, that is, it is a linear code over a binary alphabet , has block length 2 k {\displaystyle 2^{k}} , message length (or dimension) k {\displaystyle k} , and minimum distance 2 k / 2 {\displaystyle 2^{k}/2} .
The block length is very large compared to the message length, but on the other hand, errors can be corrected even in extremely noisy conditions.
The augmented Hadamard code is a slightly improved version of the Hadamard code; it is a [ 2 k , k + 1 , 2 k − 1 ] 2 {\displaystyle [2^{k},k+1,2^{k-1}]_{2}} -code and thus has a slightly better rate while maintaining the relative distance of 1 / 2 {\displaystyle 1/2} , and is thus preferred in practical applications.
In communication theory, this is simply called the Hadamard code and it is the same as the first order Reed–Muller code over the binary alphabet. [ 4 ]
Normally, Hadamard codes are based on Sylvester's construction of Hadamard matrices , but the term “Hadamard code” is also used to refer to codes constructed from arbitrary Hadamard matrices , which are not necessarily of Sylvester type.
In general, such a code is not linear.
Such codes were first constructed by Raj Chandra Bose and Sharadchandra Shankar Shrikhande in 1959. [ 5 ] If n is the size of the Hadamard matrix, the code has parameters ( n , 2 n , n / 2 ) 2 {\displaystyle (n,2n,n/2)_{2}} , meaning it is a not-necessarily-linear binary code with 2 n codewords of block length n and minimal distance n /2. The construction and decoding scheme described below apply for general n , but the property of linearity and the identification with Reed–Muller codes require that n be a power of 2 and that the Hadamard matrix be equivalent to the matrix constructed by Sylvester's method.
The Hadamard code is a locally decodable code, which provides a way to recover parts of the original message with high probability, while only looking at a small fraction of the received word. This gives rise to applications in computational complexity theory and particularly in the design of probabilistically checkable proofs .
Since the relative distance of the Hadamard code is 1/2, normally one can only hope to recover from at most a 1/4 fraction of error. Using list decoding , however, it is possible to compute a short list of possible candidate messages as long as fewer than 1 2 − ϵ {\displaystyle {\frac {1}{2}}-\epsilon } of the bits in the received word have been corrupted.
In code-division multiple access (CDMA) communication, the Hadamard code is referred to as Walsh Code, and is used to define individual communication channels . It is usual in the CDMA literature to refer to codewords as “codes”. Each user will use a different codeword, or “code”, to modulate their signal. Because Walsh codewords are mathematically orthogonal , a Walsh-encoded signal appears as random noise to a CDMA capable mobile terminal , unless that terminal uses the same codeword as the one used to encode the incoming signal . [ 6 ]
Hadamard code is the name that is most commonly used for this code in the literature. However, in modern use these error correcting codes are referred to as Walsh–Hadamard codes.
There is a reason for this:
Jacques Hadamard did not invent the code himself, but he defined Hadamard matrices around 1893, long before the first error-correcting code , the Hamming code , was developed in the 1940s.
The Hadamard code is based on Hadamard matrices, and while there are many different Hadamard matrices that could be used here, normally only Sylvester's construction of Hadamard matrices is used to obtain the codewords of the Hadamard code.
James Joseph Sylvester developed his construction of Hadamard matrices in 1867, which actually predates Hadamard's work on Hadamard matrices. Hence the name Hadamard code is disputed and sometimes the code is called Walsh code , honoring the American mathematician Joseph Leonard Walsh .
An augmented Hadamard code was used during the 1971 Mariner 9 mission to correct for picture transmission errors. The binary values used during this mission were 6 bits long, which represented 64 grayscale values.
Because of limitations of the quality of the alignment of the transmitter at the time (due to Doppler Tracking Loop issues) the maximum useful data length was about 30 bits. Instead of using a repetition code , a [32, 6, 16] Hadamard code was used.
Errors of up to 7 bits per 32-bit word could be corrected using this scheme. Compared to a 5- repetition code , the error correcting properties of this Hadamard code are much better, yet its rate is comparable. The efficient decoding algorithm was an important factor in the decision to use this code.
The circuitry used was called the "Green Machine". It employed the fast Fourier transform which can increase the decoding speed by a factor of three. Since the 1990s use of this code by space programs has more or less ceased, and the NASA Deep Space Network does not support this error correction scheme for its dishes that are greater than 26 m.
While all Hadamard codes are based on Hadamard matrices, the constructions differ in subtle ways for different scientific fields, authors, and uses. Engineers, who use the codes for data transmission, and coding theorists , who analyse extremal properties of codes, typically want the rate of the code to be as high as possible, even if this means that the construction becomes mathematically slightly less elegant.
On the other hand, for many applications of Hadamard codes in theoretical computer science it is not so important to achieve the optimal rate, and hence simpler constructions of Hadamard codes are preferred since they can be analyzed more elegantly.
When given a binary message x ∈ { 0 , 1 } k {\displaystyle x\in \{0,1\}^{k}} of length k {\displaystyle k} , the Hadamard code encodes the message into a codeword Had ( x ) {\displaystyle {\text{Had}}(x)} using an encoding function Had : { 0 , 1 } k → { 0 , 1 } 2 k . {\displaystyle {\text{Had}}:\{0,1\}^{k}\to \{0,1\}^{2^{k}}.} This function makes use of the inner product ⟨ x , y ⟩ {\displaystyle \langle x,y\rangle } of two vectors x , y ∈ { 0 , 1 } k {\displaystyle x,y\in \{0,1\}^{k}} , which is defined as follows:
Then the Hadamard encoding of x {\displaystyle x} is defined as the sequence of all inner products with x {\displaystyle x} :
As mentioned above, the augmented Hadamard code is used in practice since the Hadamard code itself is somewhat wasteful.
This is because, if the first bit of y {\displaystyle y} is zero, y 1 = 0 {\displaystyle y_{1}=0} , then the inner product contains no information whatsoever about x 1 {\displaystyle x_{1}} , and hence, it is impossible to fully decode x {\displaystyle x} from those positions of the codeword alone.
On the other hand, when the codeword is restricted to the positions where y 1 = 1 {\displaystyle y_{1}=1} , it is still possible to fully decode x {\displaystyle x} .
Hence it makes sense to restrict the Hadamard code to these positions, which gives rise to the augmented Hadamard encoding of x {\displaystyle x} ; that is, pHad ( x ) = ( ⟨ x , y ⟩ ) y ∈ { 1 } × { 0 , 1 } k − 1 {\displaystyle {\text{pHad}}(x)={\Big (}\langle x,y\rangle {\Big )}_{y\in \{1\}\times \{0,1\}^{k-1}}} .
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix G {\displaystyle G} . This is a matrix such that Had ( x ) = x ⋅ G {\displaystyle {\text{Had}}(x)=x\cdot G} holds for all x ∈ { 0 , 1 } k {\displaystyle x\in \{0,1\}^{k}} , where the message x {\displaystyle x} is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field F 2 {\displaystyle \mathbb {F} _{2}} . In particular, an equivalent way to write the inner product definition for the Hadamard code arises by using the generator matrix whose columns consist of all strings y {\displaystyle y} of length k {\displaystyle k} , that is,
where y i ∈ { 0 , 1 } k {\displaystyle y_{i}\in \{0,1\}^{k}} is the i {\displaystyle i} -th binary vector in lexicographical order .
For example, the generator matrix for the Hadamard code of dimension k = 3 {\displaystyle k=3} is:
The matrix G {\displaystyle G} is a ( k × 2 k ) {\displaystyle (k\times 2^{k})} -matrix and gives rise to the linear operator Had : { 0 , 1 } k → { 0 , 1 } 2 k {\displaystyle {\text{Had}}:\{0,1\}^{k}\to \{0,1\}^{2^{k}}} .
The generator matrix of the augmented Hadamard code is obtained by restricting the matrix G {\displaystyle G} to the columns whose first entry is one.
For example, the generator matrix for the augmented Hadamard code of dimension k = 3 {\displaystyle k=3} is:
Then pHad : { 0 , 1 } k → { 0 , 1 } 2 k − 1 {\displaystyle {\text{pHad}}:\{0,1\}^{k}\to \{0,1\}^{2^{k-1}}} is a linear mapping with pHad ( x ) = x ⋅ G ′ {\displaystyle {\text{pHad}}(x)=x\cdot G'} .
For general k {\displaystyle k} , the generator matrix of the augmented Hadamard code is a parity-check matrix for the extended Hamming code of length 2 k − 1 {\displaystyle 2^{k-1}} and dimension 2 k − 1 − k {\displaystyle 2^{k-1}-k} , which makes the augmented Hadamard code the dual code of the extended Hamming code.
Hence an alternative way to define the Hadamard code is in terms of its parity-check matrix: the parity-check matrix of the Hadamard code is equal to the generator matrix of the Hamming code.
Hadamard codes are obtained from an n -by- n Hadamard matrix H . In particular, the 2 n codewords of the code are the rows of H and the rows of − H . To obtain a code over the alphabet {0,1}, the mapping −1 ↦ 1, 1 ↦ 0, or, equivalently, x ↦ (1 − x )/2, is applied to the matrix elements. That the minimum distance of the code is n /2 follows from the defining property of Hadamard matrices, namely that their rows are mutually orthogonal. This implies that two distinct rows of a Hadamard matrix differ in exactly n /2 positions, and, since negation of a row does not affect orthogonality, that any row of H differs from any row of − H in n /2 positions as well, except when the rows correspond, in which case they differ in n positions.
To get the augmented Hadamard code above with n = 2 k − 1 {\displaystyle n=2^{k-1}} , the chosen Hadamard matrix H has to be of Sylvester type, which gives rise to a message length of log 2 ( 2 n ) = k {\displaystyle \log _{2}(2n)=k} .
The distance of a code is the minimum Hamming distance between any two distinct codewords, i.e., the minimum number of positions at which two distinct codewords differ. Since the Walsh–Hadamard code is a linear code , the distance is equal to the minimum Hamming weight among all of its non-zero codewords. All non-zero codewords of the Walsh–Hadamard code have a Hamming weight of exactly 2 k − 1 {\displaystyle 2^{k-1}} by the following argument.
Let x ∈ { 0 , 1 } k {\displaystyle x\in \{0,1\}^{k}} be a non-zero message. Then the following value is exactly equal to the fraction of positions in the codeword that are equal to one:
The fact that the latter value is exactly 1 / 2 {\displaystyle 1/2} is called the random subsum principle . To see that it is true, assume without loss of generality that x 1 = 1 {\displaystyle x_{1}=1} .
Then, when conditioned on the values of y 2 , … , y k {\displaystyle y_{2},\dots ,y_{k}} , the event is equivalent to y 1 ⋅ x 1 = b {\displaystyle y_{1}\cdot x_{1}=b} for some b ∈ { 0 , 1 } {\displaystyle b\in \{0,1\}} depending on x 2 , … , x k {\displaystyle x_{2},\dots ,x_{k}} and y 2 , … , y k {\displaystyle y_{2},\dots ,y_{k}} . The probability that y 1 = b {\displaystyle y_{1}=b} happens is exactly 1 / 2 {\displaystyle 1/2} . Thus, in fact, all non-zero codewords of the Hadamard code have relative Hamming weight 1 / 2 {\displaystyle 1/2} , and thus, its relative distance is 1 / 2 {\displaystyle 1/2} .
The relative distance of the augmented Hadamard code is 1 / 2 {\displaystyle 1/2} as well, but it no longer has the property that every non-zero codeword has weight exactly 1 / 2 {\displaystyle 1/2} since the all 1 {\displaystyle 1} s vector 1 2 k − 1 {\displaystyle 1^{2^{k-1}}} is a codeword of the augmented Hadamard code. This is because the vector x = 10 k − 1 {\displaystyle x=10^{k-1}} encodes to pHad ( 10 k − 1 ) = 1 2 k − 1 {\displaystyle {\text{pHad}}(10^{k-1})=1^{2^{k-1}}} . Furthermore, whenever x {\displaystyle x} is non-zero and not the vector 10 k − 1 {\displaystyle 10^{k-1}} , the random subsum principle applies again, and the relative weight of Had ( x ) {\displaystyle {\text{Had}}(x)} is exactly 1 / 2 {\displaystyle 1/2} .
A locally decodable code is a code that allows a single bit of the original message to be recovered with high probability by only looking at a small portion of the received word.
A code is q {\displaystyle q} -query locally decodable if a message bit, x i {\displaystyle x_{i}} , can be recovered by checking q {\displaystyle q} bits of the received word. More formally, a code, C : { 0 , 1 } k → { 0 , 1 } n {\displaystyle C:\{0,1\}^{k}\rightarrow \{0,1\}^{n}} , is ( q , δ ≥ 0 , ϵ ≥ 0 ) {\displaystyle (q,\delta \geq 0,\epsilon \geq 0)} -locally decodable, if there exists a probabilistic decoder, D : { 0 , 1 } n → { 0 , 1 } k {\displaystyle D:\{0,1\}^{n}\rightarrow \{0,1\}^{k}} , such that (Note: Δ ( x , y ) {\displaystyle \Delta (x,y)} represents the Hamming distance between vectors x {\displaystyle x} and y {\displaystyle y} ) :
∀ x ∈ { 0 , 1 } k , ∀ y ∈ { 0 , 1 } n {\displaystyle \forall x\in \{0,1\}^{k},\forall y\in \{0,1\}^{n}} , Δ ( y , C ( x ) ) ≤ δ n {\displaystyle \Delta (y,C(x))\leq \delta n} implies that P r [ D ( y ) i = x i ] ≥ 1 2 + ϵ , ∀ i ∈ [ k ] {\displaystyle Pr[D(y)_{i}=x_{i}]\geq {\frac {1}{2}}+\epsilon ,\forall i\in [k]}
Theorem 1: The Walsh–Hadamard code is ( 2 , δ , 1 2 − 2 δ ) {\displaystyle (2,\delta ,{\frac {1}{2}}-2\delta )} -locally decodable for all 0 ≤ δ ≤ 1 4 {\displaystyle 0\leq \delta \leq {\frac {1}{4}}} .
Lemma 1: For all codewords, c {\displaystyle c} in a Walsh–Hadamard code, C {\displaystyle C} , c i + c j = c i + j {\displaystyle c_{i}+c_{j}=c_{i+j}} , where c i , c j {\displaystyle c_{i},c_{j}} represent the bits in c {\displaystyle c} in positions i {\displaystyle i} and j {\displaystyle j} respectively, and c i + j {\displaystyle c_{i+j}} represents the bit at position ( i + j ) {\displaystyle (i+j)} .
Let C ( x ) = c = ( c 0 , … , c 2 n − 1 ) {\displaystyle C(x)=c=(c_{0},\dots ,c_{2^{n}-1})} be the codeword in C {\displaystyle C} corresponding to message x {\displaystyle x} .
Let G = ( ↑ ↑ ↑ g 0 g 1 … g 2 n − 1 ↓ ↓ ↓ ) {\displaystyle G={\begin{pmatrix}\uparrow &\uparrow &&\uparrow \\g_{0}&g_{1}&\dots &g_{2^{n}-1}\\\downarrow &\downarrow &&\downarrow \end{pmatrix}}} be the generator matrix of C {\displaystyle C} .
By definition, c i = x ⋅ g i {\displaystyle c_{i}=x\cdot g_{i}} . From this, c i + c j = x ⋅ g i + x ⋅ g j = x ⋅ ( g i + g j ) {\displaystyle c_{i}+c_{j}=x\cdot g_{i}+x\cdot g_{j}=x\cdot (g_{i}+g_{j})} . By the construction of G {\displaystyle G} , g i + g j = g i + j {\displaystyle g_{i}+g_{j}=g_{i+j}} . Therefore, by substitution, c i + c j = x ⋅ g i + j = c i + j {\displaystyle c_{i}+c_{j}=x\cdot g_{i+j}=c_{i+j}} .
To prove theorem 1 we will construct a decoding algorithm and prove its correctness.
Input: Received word y = ( y 0 , … , y 2 n − 1 ) {\displaystyle y=(y_{0},\dots ,y_{2^{n}-1})}
For each i ∈ { 1 , … , n } {\displaystyle i\in \{1,\dots ,n\}} :
Output: Message x = ( x 1 , … , x n ) {\displaystyle x=(x_{1},\dots ,x_{n})}
For any message, x {\displaystyle x} , and received word y {\displaystyle y} such that y {\displaystyle y} differs from c = C ( x ) {\displaystyle c=C(x)} on at most δ {\displaystyle \delta } fraction of bits, x i {\displaystyle x_{i}} can be decoded with probability at least 1 2 + ( 1 2 − 2 δ ) {\displaystyle {\frac {1}{2}}+({\frac {1}{2}}-2\delta )} .
By lemma 1, c j + c k = c j + k = x ⋅ g j + k = x ⋅ e i = x i {\displaystyle c_{j}+c_{k}=c_{j+k}=x\cdot g_{j+k}=x\cdot e_{i}=x_{i}} . Since j {\displaystyle j} and k {\displaystyle k} are picked uniformly, the probability that y j ≠ c j {\displaystyle y_{j}\not =c_{j}} is at most δ {\displaystyle \delta } . Similarly, the probability that y k ≠ c k {\displaystyle y_{k}\not =c_{k}} is at most δ {\displaystyle \delta } . By the union bound , the probability that either y j {\displaystyle y_{j}} or y k {\displaystyle y_{k}} do not match the corresponding bits in c {\displaystyle c} is at most 2 δ {\displaystyle 2\delta } . If both y j {\displaystyle y_{j}} and y k {\displaystyle y_{k}} correspond to c {\displaystyle c} , then lemma 1 will apply, and therefore, the proper value of x i {\displaystyle x_{i}} will be computed. Therefore, the probability x i {\displaystyle x_{i}} is decoded properly is at least 1 − 2 δ {\displaystyle 1-2\delta } . Therefore, ϵ = 1 2 − 2 δ {\displaystyle \epsilon ={\frac {1}{2}}-2\delta } and for ϵ {\displaystyle \epsilon } to be positive, 0 ≤ δ ≤ 1 4 {\displaystyle 0\leq \delta \leq {\frac {1}{4}}} .
Therefore, the Walsh–Hadamard code is ( 2 , δ , 1 2 − 2 δ ) {\displaystyle (2,\delta ,{\frac {1}{2}}-2\delta )} locally decodable for 0 ≤ δ ≤ 1 4 {\displaystyle 0\leq \delta \leq {\frac {1}{4}}} .
For k ≤ 7 the linear Hadamard codes have been proven optimal in the sense of minimum distance. [ 7 ] | https://en.wikipedia.org/wiki/Hadamard_code |
In quantum computation , the Hadamard test is a method used to create a random variable whose expected value is the expected real part R e ⟨ ψ | U | ψ ⟩ {\displaystyle \mathrm {Re} \langle \psi |U|\psi \rangle } , where | ψ ⟩ {\displaystyle |\psi \rangle } is a quantum state and U {\displaystyle U} is a unitary gate acting on the space of | ψ ⟩ {\displaystyle |\psi \rangle } . [ 1 ] The Hadamard test produces a random variable whose image is in { ± 1 } {\displaystyle \{\pm 1\}} and whose expected value is exactly R e ⟨ ψ | U | ψ ⟩ {\displaystyle \mathrm {Re} \langle \psi |U|\psi \rangle } . It is possible to modify the circuit to produce a random variable whose expected value is I m ⟨ ψ | U | ψ ⟩ {\displaystyle \mathrm {Im} \langle \psi |U|\psi \rangle } by applying an S † {\displaystyle S^{\dagger }} gate after the first Hadamard gate. [ 1 ]
To perform the Hadamard test we first calculate the state 1 2 ( | 0 ⟩ + | 1 ⟩ ) ⊗ | ψ ⟩ {\displaystyle {\frac {1}{\sqrt {2}}}\left(\left|0\right\rangle +\left|1\right\rangle \right)\otimes \left|\psi \right\rangle } . We then apply the unitary operator on | ψ ⟩ {\displaystyle \left|\psi \right\rangle } conditioned on the first qubit to obtain the state 1 2 ( | 0 ⟩ ⊗ | ψ ⟩ + | 1 ⟩ ⊗ U | ψ ⟩ ) {\displaystyle {\frac {1}{\sqrt {2}}}\left(\left|0\right\rangle \otimes \left|\psi \right\rangle +\left|1\right\rangle \otimes U\left|\psi \right\rangle \right)} . We then apply the Hadamard gate to the first qubit, yielding 1 2 ( | 0 ⟩ ⊗ ( I + U ) | ψ ⟩ + | 1 ⟩ ⊗ ( I − U ) | ψ ⟩ ) {\displaystyle {\frac {1}{2}}\left(\left|0\right\rangle \otimes (I+U)\left|\psi \right\rangle +\left|1\right\rangle \otimes (I-U)\left|\psi \right\rangle \right)} .
Measuring the first qubit, the result is | 0 ⟩ {\displaystyle \left|0\right\rangle } with probability 1 4 ⟨ ψ | ( I + U † ) ( I + U ) | ψ ⟩ {\displaystyle {\frac {1}{4}}\langle \psi |(I+U^{\dagger })(I+U)|\psi \rangle } , in which case we output 1 {\displaystyle 1} . The result is | 1 ⟩ {\displaystyle \left|1\right\rangle } with probability 1 4 ⟨ ψ | ( I − U † ) ( I − U ) | ψ ⟩ {\displaystyle {\frac {1}{4}}\langle \psi |(I-U^{\dagger })(I-U)|\psi \rangle } , in which case we output − 1 {\displaystyle -1} . The expected value of the output will then be the difference between the two probabilities, which is 1 2 ⟨ ψ | ( U † + U ) | ψ ⟩ = R e ⟨ ψ | U | ψ ⟩ {\displaystyle {\frac {1}{2}}\langle \psi |(U^{\dagger }+U)|\psi \rangle =\mathrm {Re} \langle \psi |U|\psi \rangle }
To obtain a random variable whose expectation is I m ⟨ ψ | U | ψ ⟩ {\displaystyle \mathrm {Im} \langle \psi |U|\psi \rangle } follow exactly the same procedure but start with 1 2 ( | 0 ⟩ − i | 1 ⟩ ) ⊗ | ψ ⟩ {\displaystyle {\frac {1}{\sqrt {2}}}\left(\left|0\right\rangle -i\left|1\right\rangle \right)\otimes \left|\psi \right\rangle } . [ 2 ]
The Hadamard test has many applications in quantum algorithms such as the Aharonov-Jones-Landau algorithm .
Via a very simple modification it can be used to compute inner product between two states | ϕ 1 ⟩ {\displaystyle |\phi _{1}\rangle } and | ϕ 2 ⟩ {\displaystyle |\phi _{2}\rangle } : [ 3 ] instead of starting from a state | ψ ⟩ {\displaystyle |\psi \rangle } it suffice to start from the ground state | 0 ⟩ {\displaystyle |0\rangle } , and perform two controlled operations on the ancilla qubit. Controlled on the ancilla register being | 0 ⟩ {\displaystyle |0\rangle } , we apply the unitary that produces | ϕ 1 ⟩ {\displaystyle |\phi _{1}\rangle } in the second register, and controlled on the ancilla register being in the state | 1 ⟩ {\displaystyle |1\rangle } , we create | ϕ 2 ⟩ {\displaystyle |\phi _{2}\rangle } in the second register. The expected value of the measurements of the ancilla qubits leads to an estimate of ⟨ ϕ 1 | ϕ 2 ⟩ {\displaystyle \langle \phi _{1}|\phi _{2}\rangle } . The number of samples needed to estimate the expected value with absolute error ϵ {\displaystyle \epsilon } is O ( 1 ϵ 2 ) {\displaystyle O\left({\frac {1}{\epsilon ^{2}}}\right)} , because of a Chernoff bound . This value can be improved to O ( 1 ϵ ) {\displaystyle O\left({\frac {1}{\epsilon }}\right)} using amplitude estimation techniques. [ 3 ]
, | https://en.wikipedia.org/wiki/Hadamard_test |
In complex analysis , a branch of mathematics , the Hadamard three-circle theorem is a result about the behavior of holomorphic functions .
Hadamard three-circle theorem: Let f ( z ) {\displaystyle f(z)} be a holomorphic function on the annulus r 1 ≤ | z | ≤ r 3 {\displaystyle r_{1}\leq \left|z\right|\leq r_{3}} . Let M ( r ) {\displaystyle M(r)} be the maximum of | f ( z ) | {\displaystyle |f(z)|} on the circle | z | = r . {\displaystyle |z|=r.} Then, log M ( r ) {\displaystyle \log M(r)} is a convex function of the logarithm log ( r ) . {\displaystyle \log(r).} Moreover, if f ( z ) {\displaystyle f(z)} is not of the form c z λ {\displaystyle cz^{\lambda }} for some constants λ {\displaystyle \lambda } and c {\displaystyle c} , then log M ( r ) {\displaystyle \log M(r)} is strictly convex as a function of log ( r ) . {\displaystyle \log(r).}
The conclusion of the theorem can be restated as
for any three concentric circles of radii r 1 < r 2 < r 3 . {\displaystyle r_{1}<r_{2}<r_{3}.}
The three circles theorem follows from the fact that for any real a , the function Re log( z a f ( z )) is harmonic between two circles, and therefore takes its maximum value on one of the circles. The theorem follows by choosing the constant a so that this harmonic function has the same maximum value on both circles.
The theorem can also be deduced directly from Hadamard's three-line theorem . [ 1 ]
A statement and proof for the theorem was given by J.E. Littlewood in 1912, but he attributes it to no one in particular, stating it as a known theorem. Harald Bohr and Edmund Landau attribute the theorem to Jacques Hadamard , writing in 1896; Hadamard published no proof. [ 2 ]
This article incorporates material from Hadamard three-circle theorem on PlanetMath , which is licensed under the Creative Commons Attribution/Share-Alike License . | https://en.wikipedia.org/wiki/Hadamard_three-circle_theorem |
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