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Heme A (or haem A ) is a heme , a coordination complex consisting of a macrocyclic ligand called a porphyrin , chelating an iron atom. Heme A is a biomolecule and is produced naturally by many organisms. Heme A, often appears a dichroic green/red when in solution, is a structural relative of heme B , a component of hemoglobin , the red pigment in blood.
Heme A differs from heme B in that a methyl side chain at ring position 8 is oxidized to a formyl group and a hydroxyethylfarnesyl group , an isoprenoid chain, has been attached to the vinyl side chain at ring position 2 of the iron tetrapyrrole heme . Heme A is similar to heme o , in that both have this farnesyl addition at position 2 but heme O does not have the formyl group at position 8, still containing the methyl group. The correct structure of heme A, based upon NMR and IR experiments of the reduced, Fe(II) form of the heme, was published in 1975. [ 1 ] The structure was confirmed by synthesis of the dimethyl ester of the iron-free form. [ 2 ]
Heme A was first isolated by the German biochemist Otto Warburg in 1951 and shown by him to be the active component of the integral membrane metalloprotein cytochrome c oxidase. [ 3 ]
The final structural question of the exact geometric configuration about the first carbon at ring position 3 of ring I, the carbon bound to the hydroxyl group, has been shown to be the chiral S configuration. [ 4 ]
Like heme B, heme A is often attached to the apoprotein through a coordinate bond between the heme iron and a conserved amino acid side-chain. In the important respiratory protein cytochrome c oxidase (CCO) this ligand 5 for the heme A at the oxygen reaction center is a histidyl group. [ 5 ] Histidine is a common ligand for many hemeproteins including hemoglobin and myoglobin .
Heme A in the cytochrome a portion of cytochrome c oxidase, bound by two histidine residues (shown in pink) [ 6 ]
An example of a metalloprotein that contains heme A is cytochrome c oxidase. This very complicated protein contains heme A at two different sites, each with a different function. The iron of the heme A of cytochrome a is hexacoordinated, that is bound with 6 other atoms. The iron of the heme A of cytochrome a3 is sometimes bound by 5 other atoms leaving the sixth site available to bind dioxygen (molecular oxygen ). [ 6 ] In addition, this enzyme binds 3 copper, magnesium, zinc, and several potassium and sodium ions. The two heme A groups in CCO are thought to readily exchange electrons between each other, the copper ions and the closely associated protein cytochrome c.
Both the formyl group and the isoprenoid side chain are thought to play important roles in conservation of the energy of oxygen reduction by cytochrome c oxidase . CCO is thought to be responsible for conserving the energy of dioxygen reduction by pumping protons into the inter-membrane mitochondrial space. Both the formyl and hydroxyethylfarnesyl groups of heme A are thought to play important roles in this critical process, as published by the influential group of S. Yoshikawa. [ 7 ] | https://en.wikipedia.org/wiki/Heme_A |
Heme B or haem B (also known as protoheme IX ) is the most abundant heme . [ 1 ] Hemoglobin and myoglobin are examples of oxygen transport proteins that contain heme B. The peroxidase family of enzymes also contain heme B. The COX-1 and COX-2 enzymes (cyclooxygenase) of recent fame, also contain heme B at one of two active sites.
Generally, heme B is attached to the surrounding protein matrix (known as the apoprotein ) through a single coordination bond between the heme iron and an amino-acid side-chain.
Both hemoglobin and myoglobin have a coordination bond to an evolutionarily-conserved histidine , while nitric oxide synthase and cytochrome P450 have a coordination bond to an evolutionarily-conserved cysteine bound to the iron center of heme B.
Since the iron in heme B containing proteins is bound to the four nitrogens of the porphyrin (forming a plane) and a single electron donating atom of the protein, the iron is often in a pentacoordinate state. When oxygen or the toxic carbon monoxide is bound the iron becomes hexacoordinated.
The correct structures of heme B and heme S were first elucidated by German chemist Hans Fischer . [ 2 ] | https://en.wikipedia.org/wiki/Heme_B |
Heme C (or haem C ) is an important kind of heme .
The correct structure of heme C was published in mid 20th century by the Swedish biochemist K.-G. Paul. [ 1 ] This work confirmed the structure first inferred by the great Swedish biochemist Hugo Theorell . The structure of heme C, based upon NMR and IR experiments of the reduced Fe(II) form of the heme, was confirmed in 1975. [ 2 ] The structure of heme C including the absolute stereochemical configuration about the thioether bonds was first presented for the vertebrate protein, cytochrome c [ 3 ] and is now extended to many other heme C containing proteins.
Heme C differs from heme B in that the two vinyl side chains of heme B are replaced by covalent, thioether linkages to the apoprotein . The two thioether linkages are typically made by cysteine residues of the protein. These linkages do not allow the heme C to easily dissociate from the holoprotein , cytochrome c , compared with the more easily dissociated heme B that may dissociate from the holoprotein, the heme-protein complex, even under mild conditions. This allows a very wide range of cytochrome c structure and function, with myriad c type cytochromes acting primarily as electron carriers. The redox potential for cytochrome c can also be "fine-tuned" by small changes in protein structure and solvent interaction. [ 4 ]
The number of heme C units bound to a holoprotein is highly variable. For vertebrate cells one heme C per protein is the rule but for bacteria this number is often 2, 4, 5, 6 or even 16 heme C groups per holoprotein. It is generally agreed the number and arrangement of heme C groups are related and even required for proper holoprotein function. For instance, those proteins containing several heme C groups are involved with multiple electron transfer reactions, particularly important is the 6 electron reduction required to reduce atmospheric nitrogen into two organic ammonia molecules. It is common for the heme C to amino acid ratio to be high for bacterial hemeproteins , so the interiors of some cytochrome c proteins appear packed with many heme C groups compared with other hemeproteins. Some hemeproteins, often from single cell organisms , may contain five hemes C. [ 5 ] The bc 1 complex is another important enzyme that contains a C type heme.
The thioether linkages seem to allow a great freedom of function for the holoproteins. In general, the c type cytochromes can be "fine tuned" over a wider range of oxidation-reduction potential than cytochromes b. This may be an important reason why cytochrome c is nearly ubiquitous throughout life. Heme C also plays an important role in apoptosis where just a few molecules of cytoplasmic cytochrome c, which must still contain heme C, leads to programmed cell death. [ 6 ] Cytochrome c can be measured in human serum and can be used as a marker for inflammation. [ 7 ]
In addition to these equatorial covalent bonds, the heme iron is also usually axially coordinated to the side chains of two amino acids , making the iron hexacoordinate. For example, mammalian and tuna cytochrome c contain a single heme C that is axially coordinated to side chains of both histidine and methionine . [ 8 ] Perhaps because of the two covalent bonds holding the heme to the protein, the iron of heme C is sometimes axially ligated to the amino group of lysine or even water. | https://en.wikipedia.org/wiki/Heme_C |
Heme O (or haem O ) differs from the closely related heme A by having a methyl group at ring position 8 instead of the formyl group . The isoprenoid chain at position 2 is the same.
Heme O, found in the bacterium Escherichia coli , [ 1 ] functions in a similar manner to heme A in mammalian oxygen reduction. | https://en.wikipedia.org/wiki/Heme_O |
A heme transporter is a protein that delivers heme to the various parts of a biological cell that require it.
Heme is a major source of dietary iron in humans and other mammals, and its synthesis in the body is well understood, but heme pathways are not as well understood. It is likely that heme is tightly regulated for two reasons: the toxic nature of iron in cells, and the lack of a regulated excretory system for excess iron. Understanding heme pathways is therefore important in understanding diseases such as hemochromatosis and anemia .
Members of the SLC48 and SLC49 solute carrier family participate in heme transport across cellular membranes ( heme-transporting ATPase ). [ 1 ]
SLC48A1 [ 2 ] —also known as Heme-Responsive Gene 1 (HRG1)—and its orthologues were first identified as a heme transporter family through a genetic screen in C.elegans . [ 3 ] The protein plays a role in mobilizing heme from the lysosome to the cytoplasm . [ 4 ] Deletion of the gene in mice leads to accumulation of heme crystals called hemozoin within the lysosomes of bone marrow, liver and splenic macrophages, [ 5 ] [ 6 ] but the gene is not known to be associated with human disease.
FLVCR1 [ 7 ] was originally identified as the receptor for the feline leukemia virus , whose genetic disruption leads to anemia and disruption of heme transport. [ 8 ] [ 9 ] It appears to protect cells at the CFU-E stage by exporting heme to prevent heme toxicity. Rare homozygous mutations result in autosomal recessive posterior column ataxia with retinitis pigmentosa . [ 10 ] [ 11 ]
FLVCR2 [ 12 ] is closely related to FLCVR1, and genetic transfection experiments indicate that it transports heme. [ 13 ] Mutations in the gene are associated with proliferative vasculopathy and hydranencephaly-hydrocephaly syndrome (PVHH, also known as Fowler syndrome). [ 14 ] [ 15 ]
Related genes SLC49A3 [ 16 ] and SLC49A4 [ 17 ] are less well characterized [ 1 ] functionally, although SLC49A4 is also known as Disrupted In Renal Cancer Protein 2 or RCC4 due to an association with renal cell cancer . [ 18 ] [ 19 ]
This molecular or cell biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Heme_transporter |
Hemeroby , or hemerochora is a term used in botanical and ecological sciences . It is often associated to naturalness as the complementary term, [ 1 ] with a high degree of hemeroby equating to a high human influence on a natural environment. [ 2 ] However, the two terms are not inversely related. [ 3 ]
The term is derived from the Greek hémeros and bíos .
The word hemero-, hemer- means tame, cultivated. Bios is life. Hemeroby literally means "tamed life".
Various scales for quantifying hemeroby have been devised. [ 2 ]
This botany article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hemeroby |
Hemerochory (Ancient Greek ἥμερος, hemeros: 'tame, ennobled, cultivated, cultivated' and Greek χωρίς choris: separate, isolated), or anthropochory , [ 1 ] [ 2 ] is the distribution of cultivated plants or their seeds and cuttings , consciously or unconsciously, by humans into an area that they could not colonize through their natural mechanisms of spread, but are able to maintain themselves without specific human help in their new habitat. [ 3 ]
Hemerochory is one of the main propagation mechanisms of a plant. Hemerochoric plants can both increase and decrease the biodiversity of a habitat. [ 4 ]
Hemerochoric plants are classified according to the manner of introduction into, for example:
Chronologically the hemerochoric plants are divided in:
Anthropochory is often used synonymously but does not mean exactly the same. Anthropochory is the spread by humans. The spread through domestic animals does not belong to the anthropochoric, but to the hemerochoric, because domestic animals belong to the human culture. Strictly speaking, anthropochoric means the spread through humans as a transport medium. These can also be native species that were either adapted from the outset to locations created by human cultural activity or have adapted to them afterwards; As a result, their area of distribution has often, but not always, increased.
Hemerochorous spread of plants through human cultural activity very likely already happened in the Stone Age , but demonstrably at the latest in antiquity , namely along old trade routes . Fruits such as apples and pears gradually made their way along the Silk Road from the area around the Altai Mountains to Greece and from there to the gardens of the Romans , who in turn brought these cultivated plants to Central Europe, and some of these plants were eventually able to survive outside the culture. Many useful plants, such as tomato, potato, pumpkin and French bean did not reach Central Europe until the 16th century, after the American continent was discovered, and are now grown worldwide.
In the last 400 to 500 years the spread has expanded through trade and military campaigns, through explorers and missionaries . The latter brought countless plants with them from their travels both out of an interest in exotic plants , which were often included in the plant collections of princely courts, and for purely scientific purposes. In the context of botanical studies, the interest was often in the possible healing effects of these plants, but also in the expansion of botanical knowledge, or the plants were only used for collecting ( herbaria ).
Some ornamental plants also came to Europe because they promised a lucrative business. This applies, for example, to the camellias , one of which is also grown as a tea plant in Japan and China. While this species turned out to be not cultivable in Central Europe, people very quickly discovered the aesthetic appeal of the other camellia species as an ornamental plant. Botanical gardens played a major role in the acclimatization of such plants from distant habitats. [ 6 ]
Agochoric plants are those that are spread through accidental transport. Unlike speirochoric plants, they are usually not sown on human-prepared soil. On land, agochoric plants used to be common in harbors, at train stations or along railway lines . [ 7 ]
However, mainly aquatic plants are spread through agochory. Ballast water plays a major role in the agochoric spread of aquatic plants. Around the world, around ten billion tons of seawater and the organisms it contains are shipped in this way. Exporting countries in particular are affected by the spread of organisms through ballast water. The ships arrive at the ports with empty cargo hold , but fully pumped ballast tanks. In the draining of this ballast water, these ports receive thousands of cubic meters of seawater brimming with alien creatures now in a new environment. The seaweed Undaria pinnatifida , which is native to the Japanese coast, reached the Tasmanian coast via ballast water and has formed dense kelp forests along the coast since 1988, displacing the native flora and fauna. Caulerpa taxifolia is one of those plants that are often spread by ballast water. It is also spread by the fact that ships tear off parts of the algae with their anchors.
Australia was the first country to introduce a ballast water policy back in 1990 and is now the most determined to address this problem. Ships were asked not to take in ballast water in shallow and polluted bays and not to refuel with ballast water during the night, since then many marine organisms that are otherwise on the seabed rise to the surface of the water. Ships should also exchange their ballast water 200 kilometers away from the coastal waters, so that on the one hand the offshore species are not introduced into the more sensitive coastal waters and, on the other hand, no inhabitants of the coastal zone are transported to other continents. [ 8 ]
Ethelochory is intentional transportation of plants or seeds to different regions for agricultural and gardening purposes. [ 9 ] Numerous crops that are important for human nutrition have been willingly spread by humans. Wheat , barley , lentil , beans , flax and poppy seeds, for example, are not typical plants for Central Europe , although they are all archaeotypes. People brought them after the beginning of the Neolithic (about 6,500 years ago) gradually from the eastern Mediterranean to central Europe and the rest of the world through the upcoming centuries. In central Europe, it is especially Cyperus esculentus which has been classified since the 1980s among the invasive species , because their tubers have been spread en masse, by sticking to vehicles or machines. [ 10 ]
Many of the old cultivated plants have spread around the world, primarily through emigrants from Europe. Grown for at least 4,000 years, wheat was introduced to America in the 16th century and Australia in the 19th century. Orange, lemons, apricots and peaches were originally native to China. They probably came via the Silk Road as early as the 3rd century BC . In Asia Minor and from there through the Romans to the Mediterranean. European settlers, in turn, used these species to grow fruit in suitable regions of America.
From the 16th century, ornamental plants were grown more and more. Species native to Europe were first introduced as garden plants . These include, for example, the gladioli , the ornamental onion , European bluebell , the snowdrop native to southeast Europe and the common clematis . Ornamental plants from more distant regions were added later. From East Asia in particular, a number of plants were introduced to Europe as exotic or for economic reasons.
Some plants were unintentionally introduced in this process; this unwanted hemerochory as a seed companion is called speirochory . Since every seed also contains seeds of the herbs of the field from which it comes, their competitors, the " weeds ", were also sold through the trade in the seeds of the useful plant. The real chamomile is one of the plants that were unintentionally spread as a companion to seeds. [ 11 ]
Speirochoric plants are sown on human-prepared soil and are competitors of the crops . Plants that are considered to be archaeophytes, such as the poppy, native to the Mediterranean area, the real chamomile, the cornflower and field buttercup , spread through the seeds with the grain in Central Europe. In the meantime, the seeds are cleaned more thoroughly using modern methods and the cultivation is hardly contaminated by pesticides or other control techniques.
In spite of this, Cuscuta campestris , which is classified as a problematic weed in Australia , was accidentally imported into the country together with basil seeds in 1981, 1988 and 1990. | https://en.wikipedia.org/wiki/Hemerochory |
The Hemetsberger indole synthesis (also called the Hemetsberger–Knittel synthesis ) is a chemical reaction that thermally decomposes a 3-aryl-2-azido-propenoic ester into an indole -2-carboxylic ester . [ 1 ] [ 2 ]
Yields are typically above 70%. However, this is not a popular reaction, due to the lack of stability and difficulty in synthesizing the starting material.
The mechanism is unknown. However, azirine [ 3 ] intermediates have been isolated. The mechanism is postulated to proceed via a nitrene intermediate. [ 4 ] | https://en.wikipedia.org/wiki/Hemetsberger_indole_synthesis |
In organic chemistry , a hemiacetal is a functional group the general formula R 1 R 2 C(OH)OR , where R 1 , R 2 is a hydrogen atom or an organic substituent . They generally result from the nucleophilic addition of an alcohol (a compound with at least one hydroxy group ) to an aldehyde ( R−CH=O ) or a ketone ( R 2 C=O ) under acidic conditions. The addition of an alcohol to a ketone is more commonly referred to as a hemiketal . Common examples of hemiacetals include cyclic monosaccharides . Hemiacetals have use as a protecting group and in synthesizing oxygenated heterocycles like tetrahydrofurans .
According to the IUPAC definition of a hemiacetal, the R 1 and R 2 groups may or may not be hydrogen. In a hemiketal, both of these R-groups must not be hydrogen. Thus, hemiketals are regarded as a subclass of hemiacetals. [ 1 ] The prefix hemi, meaning half, refers to the one alcohol added to the carbonyl group . This is half of the required alcohols to form acetals or ketals . [ 2 ] Cyclic hemiacetals can sometimes be referred to as lactols . [ 3 ]
Hemiacetals form in the reaction between alcohols and aldehydes or ketones. Using an acid catalyst, the reaction proceeds via nucleophilic attack of the carbonyl group by the alcohol. [ 4 ] A subsequent nucleophilic attack of the hemiacetal by the alcohol results in an acetal . [ 2 ] Solutions of simple aldehydes in alcohols mainly consist of the hemiacetal. The equilibrium is dynamic and can be easily reversed via hydrolysis . The equilibrium is sensitive to steric effects. [ 5 ]
Cyclic hemiacetals often form readily, especially when they are 5- and 6-membered rings. In this case, a hydroxy group reacts with a carbonyl group within the same molecule to undergo an intramolecular cyclization reaction . [ 6 ]
Hemiacetals commonly exist in nature as aldoses such as glucose , and hemiketals commonly exist in nature as ketoses such as fructose . The favorability of the formation of a strain-free six-membered ring and the electrophilicity of an aldehyde combine to strongly favor the acetal form. [ 8 ]
Tetrahydrofurans can be synthesized from nucleophilic addition to hemiacetals with high stereoselectivity, which can be further used to form polymers such as lignans . [ 9 ]
Hemiacetals can also undergo acid-catalyzed spirocyclization or metal-catalyzed addition/elimination to afford spiroacetals. These reactions are moderately stereoselective, although the thermodynamically-favoured isomer is often produced. [ 10 ] Drug discovery programs synthesize spiroacetal scaffolds to generate libraries of spiroacetal-containing molecules. These spiroacetal derivatives have potential use in treating diseases such as CLL leukemia . [ 11 ]
One method of producing linear hemiacetal esters is through the condensation of stabilized hemiacetals by anhydrides; this creates a stable hemiketal intermediate that subsequently undergoes acetylation into the hemiacetal ester. Hemiacetal esters are primarily used in polymer chemistry as a polymerization initiator and as a protecting group for carboxylic acids. [ 12 ] | https://en.wikipedia.org/wiki/Hemiacetal |
In organic chemistry , a hemiaminal (also carbinolamine ) is a functional group or type of chemical compound that has a hydroxyl group and an amine attached to the same carbon atom: −C(OH)(NR 2 )− . R can be hydrogen or an alkyl group. Hemiaminals are intermediates in imine formation from an amine and a carbonyl by alkylimino-de-oxo-bisubstitution . [ 1 ] Hemiaminals can be viewed as a blend of aminals and geminal diol . They are a special case of amino alcohols .
Hemiaminals form from the reaction of an amine and a ketone or aldehyde. The hemiaminal is sometimes isolable, but often they spontaneously dehydrate to give imines. [ 2 ]
The adducts formed by the addition of ammonia to aldehydes have long been studied. [ 3 ] Compounds containing both a primary amino group and a hydroxyl group bonded to the same carbon atom are rarely stable ("The hemiaminal [derived from primary amines] is, except in very special cases... not observed"), [ 4 ] as they tend to dehydrate to form imines which polymerise to hexamethylenetetramine . A rare stable example is the adduct of ammonia and hexafluoroacetone , (CF 3 ) 2 C(OH)NH 2 . [ 5 ]
The C-substituted derivatives are obtained by reaction of aldehydes and ammonia: [ 6 ]
N-substituted derivatives are somewhat stable. They are invoked but rarely observed as intermediates in the Mannich reaction . These N,N',N''-trisubstituted hexahydro-1,3,5-triazines arise from the condensation of the amine and formaldehyde as illustrated by the route to 1,3,5-trimethyl-1,3,5-triazacyclohexane :
Although adducts generated from primary amines or ammonia are usually unstable, the hemiaminals have been trapped in a cavity. [ 7 ]
One of the simplest reactions entails condensation of formaldehyde and dimethylamine. This reaction produces first the carbinolamine (a hemiaminal) and bis(dimethylamino)methane ( Me = CH 3 ): [ 8 ] [ 9 ]
The reaction of formaldehyde with carbazole , which is weakly basic, proceed similarly: [ 10 ]
Again, this carbinol converts readily to the methylene-linked bis(carbazole).
Hemiaminal ethers have the following structure: R‴-C(NR' 2 )(OR")-R⁗. The glycosylamines are examples of cyclic hemiaminal ethers.
Hemiaminal formation is a key step in an asymmetric total synthesis of saxitoxin : [ 11 ]
In this reaction step the alkene group is first oxidized to an intermediate acyloin by action of osmium(III) chloride, oxone ( sacrificial catalyst ) and sodium carbonate (base). | https://en.wikipedia.org/wiki/Hemiaminal |
In mycology a tissue or feature is said to be amyloid if it has a positive amyloid reaction when subjected to a crude chemical test using iodine as an ingredient of either Melzer's reagent or Lugol's solution , producing a blue to blue-black staining. The term "amyloid" is derived from the Latin amyloideus ("starch-like"). [ 1 ] It refers to the fact that starch gives a similar reaction, also called an amyloid reaction. The test can be on microscopic features, such as spore walls or hyphal walls, or the apical apparatus or entire ascus wall of an ascus , or be a macroscopic reaction on tissue where a drop of the reagent is applied. Negative reactions, called inamyloid or nonamyloid , are for structures that remain pale yellow-brown or clear. A reaction producing a deep reddish to reddish-brown staining is either termed a dextrinoid reaction ( pseudoamyloid is a synonym) or a hemiamyloid reaction.
Melzer's is used by exposing fungal tissue or cells to the reagent, typically in a microscope slide preparation, and looking for any of three color reactions:
Among the amyloid reaction, two types can be distinguished:
Melzer's reactions are typically almost immediate, though in some cases the reaction may take up to 20 minutes to develop. [ 2 ]
The function of the chemicals that make up Melzer's reagent are several. The chloral hydrate is a clearing agent , bleaching and improving the transparency of various dark-colored microscopic materials. The potassium iodide is used to improve the solubility of the iodine, which is otherwise only semi-soluble in water. Iodine is thought to be the main active staining agent in Melzer's; it is thought to react with starch-like polysaccharides in the cell walls of amyloid material, however, its mechanism of action is not entirely understood. It has been observed that hemiamyloid material reacts differently when exposed to Melzer's than it does when exposed to other IKI solutions such as Lugol's, and that in some cases an amyloid reaction is shown in material that had prior exposure to KOH, but an inamyloid reaction without such pretreatment. [ 3 ] [ 4 ]
An experiment in which spores from 35 species of basidiomycetes were tested for reactions to both Melzer's and Lugol's showed that spores in a large percentage of the species tested display very different reactions between the two reagents. These varied from being weakly or non-reactive in Lugols, to giving iodine-positive reactions in Lugol's but not in Melzer's, to even giving dextrinoid reactions in Lugol's while giving amyloid reactions in Melzer's. [ 5 ]
Melzer's degrades into a cloudy precipitate when combined with alkaline solutions, [ 2 ] hence it cannot be used in combination or in direct series with such common mycological reagents such as potassium hydroxide or ammonium hydroxide solutions. When potassium hydroxide is used as a pretreatment, the alkalinity must be first neutralized before adding Melzer's.
Hemiamyloidity in mycology refers to a special case of cell wall amyloidity where the blue staining by iodine only occurs when the tissue was pretreated with potassium hydroxide solution (KOH) or other strong bases, whereas direct application of iodine causes a red reaction when using Lugol's solution , but no reaction when using Melzer's reagent . [ 6 ] [ 7 ] Hemiamyloidity is so far only known in Ascomycota , but here widespread and an important taxonomic distinction criterion. [ 6 ] [ 8 ] If cell walls stain blue by iodine reagents without pretreatment with KOH, this is called euamyloid. The term amyloid comprises both variants.
A hemiamyloid element of the cell wall does not directly stain blue with iodine reagents added to a water preparation, but only when it has been pretreated with potassium hydroxide solution (KOH). Without KOH pretreatment, the result depends much on the type of iodine reagent: with Lugol's solution (IKI), hemiamyloid structures react red to reddish-brown, whereas any reaction is suppressed when using Melzer's reagent (MLZ). This masking effect (false inamyloidity) is due to the high chloral hydrate concentration in MLZ. The alternative to hemiamyloid is called euamyloid. Euamyloid and KOH-pretreated hemiamyloid structures react blue regardless of the type of iodine reagent. Hemiamyloid and euamyloid reactions may occur at a time, either at spatially separated sites of the cell wall (e.g., ascus apical ring euamyloid, lateral wall hemiamyloid), or as an intermediate type of the same wall region. In the latter case, an overlay of blue and red can be observed in Lugol's solution without KOH pretreatment: a color change from blue to dirty reddish-brown occurs when the iodine reagent slowly diffuses into the water preparation, because the euamyloid reaction appears at lower iodine concentrations than the hemiamyloid reaction. Asci with entirely reactive walls of this type of hemiamyloidity show rainbow-like colours when low-concentrated IKI is applied.
Hemiamyloid (red) reaction in IKI prior to KOH, in comparison with euamyloid (blue) and inamyloid (negative). Only the hemiamyloid reaction strongly depends on the applied iodine reagent (IKI, MLZ) and pretreatment with KOH, being negative in MLZ and blue when KOH-pretreated (in IKI or MLZ). Direct application of IKI to a water munt (without KOH, highlighted) is the easiest way to recognize hemiamyloidity.
Iodine reaction of hemiamyloid ascus apical rings of Hysteropezizella (Helotiales) in dependence of iodine reagent (IKI, MLZ) and pretreatment with KOH.
Hemiamyloidity occurs in many groups of ascomycetes . In most members of Lecanorales and Ostropales, whether lichenized or not, the entire outer ascus wall layer reacts hemiamyloid. Roughly 20% of Helotiales have hemiamyloid ascus apical rings compared to estimated 50% with euamyloid apical rings. In Pezizomycetes and different classes of pyrenomycetes hemiamyloid reactions are rare. Although hemiamyloidity is a very valuable taxonomic marker that permits differentiation between species or genera, this type of reaction, in particular the red reaction in IKI, is often overlooked. This neglect occurred since mycologists switched to Melzer's reagent, which was introduced in 1924 and almost completely displaced the previously used Lugol's solution. Hemiamyloidity was first reported by applying Melzer's reagent which gave a negative result without KOH, but a blue reaction when treated with KOH beforehand. [ 9 ] Because of the frequency of hemiamyloidity in lichens, lichenologists generally did not join this change but continued using Lugol's solution. The widespread usage of swelling herborized fungi in KOH before study further contributes to the frequent overlooking of hemiamyloidity.
The chemical background of hemiamyloidity is not clear. A hypothesis claims that short helical sections of a carbohydrate chain alternate with shorter or longer linear sections. The short helical sections, similar to dextrinoidity of glycogen , would cause the red reaction by inclusion of iodine atoms into the spiral, and the linear sections might curl up under the influence of KOH, resulting in long helical chains which cause a blue stain upon iodine inclusion. The hypothetical spiral structure of these macromolecules seems to be related to the extensibility of the ascus wall, which is a prerequisite for the active, explosive ejection of ascospores from an ascus when its high cell turgor is released. A high cell wall extensibility is particularly required at the area of the apical pore-like opening (apical ring), through which the ascospores are pressed when the ascus bursts. | https://en.wikipedia.org/wiki/Hemiamyloidity |
Hemiboreal means halfway between the temperate and subarctic (or boreal ) zones. The term is most frequently used in the context of climates and ecosystems .
A hemiboreal forest has some characteristics of a boreal forest to the north, and also shares features with temperate-zone forests to the south. A significant number of nut species, such as aspens , oaks , maples , ash trees , birches , beeches , hazels , and hornbeams , can be found here.
The term sometimes denotes the form of climate characteristic of the zone of hemiboreal forests—specifically, the climates designated Dfb , Dwb and Dsb in the Köppen climate classification scheme. On occasion, it is applied to all areas that have long, cold winters and warm (but not hot) summers—which also including areas that are semiarid ( BS ) and arid ( BW ) based on average annual precipitation . It can also be applied to some areas with a subpolar oceanic climate ( Cfc ), particularly those with continental climate characteristics.
Examples of locations with hemiboreal climates or ecosystems include:
This article about atmospheric science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hemiboreal |
A hemicellulose (also known as polyose ) is one of a number of heteropolymers (matrix polysaccharides), such as arabinoxylans , present along with cellulose in almost all terrestrial plant cell walls . [ 1 ] Cellulose is crystalline, strong, and resistant to hydrolysis . Hemicelluloses are branched, shorter in length than cellulose, and also show a propensity to crystallize. [ 2 ] They can be hydrolyzed by dilute acid or base as well as a myriad of hemicellulase enzymes.
Diverse kinds of hemicelluloses are known. Important examples include xylan , glucuronoxylan , arabinoxylan , glucomannan , and xyloglucan .
Hemicelluloses are polysaccharides often associated with cellulose , but with distinct compositions and structures. Whereas cellulose is derived exclusively from glucose , hemicelluloses are composed of diverse sugars, and can include the five-carbon sugars xylose and arabinose , the six-carbon sugars glucose, mannose and galactose , and the six-carbon deoxy sugar rhamnose . Hemicelluloses contain most of the D- pentose sugars, and occasionally small amounts of L-sugars as well. Xylose is in most cases the sugar monomer present in the largest amount, although in softwoods mannose can be the most abundant sugar. Not only regular sugars can be found in hemicellulose, but also their acidified forms, for instance glucuronic acid and galacturonic acid can be present. [ 3 ] [ 4 ]
Unlike cellulose, hemicelluloses consist of shorter chains – 500–3,000 sugar units. In contrast, each polymer of cellulose comprises 7,000–15,000 glucose molecules. [ 5 ] In addition, hemicelluloses may be branched polymers , while cellulose is unbranched. Hemicelluloses are embedded in the cell walls of plants, sometimes in chains that form a ' ground ' – they bind with pectin to cellulose to form a network of cross-linked fibres. [ 6 ]
Based on the structural difference, like backbone linkages and side groups, as well as other factors, like abundance and distributions in plants, hemicelluloses can be categorized into four groups as following: [ 4 ] 1) xylans, 2) mannans ; 3) mixed linkage β-glucans ; 4) xyloglucans.
Xylans usually consist of a backbone of β-(1→4)-linked xylose residues and can be further divided into homoxylans and heteroxylans. Homoxylans have a backbone of D-xylopyranose residues linked by β(1→4) glycosidic linkages. Homoxylans mainly have structural functions. Heteroxylans such as glucuronoxylans, glucuronoarabinoxylans, and complex heteroxylans, have a backbone of D-xylopyranose and short carbohydrate branches. For example, glucuronoxylan has a substitution with α-(1→2)-linked glucuronosyl and 4-O-methyl glucuronosyl residues. Arabinoxylans and glucuronoarabinoxylans contain arabinose residues attached to the backbone [ 7 ]
The mannan-type hemicellulose can be classified into two types based on their main chain difference, galactomannans and glucomannans. Galactomannans have only β-(1→4) linked D-mannopyranose residues in linear chains. Glucomannans consist of both β-(1→4) linked D-mannopyranose and β-(1→4) linked D-glucopyranose residues in the main chains. As for the side chains, D-galactopyranose residues tend to be 6-linked to both types as the single side chains with various amount. [ 1 ]
The conformation of the mixed linkage glucan chains usually contains blocks of β-(1→4) D-Glucopyranose separated by single β-(1→3) D-Glucopyranose. The population of β-(1→4) and β-(1→3) are about 70% and 30%. These glucans primarily consist of cellotriosyl (C 18 H 32 O 16 ) and cellotraosyl (C 24 H 42 O 21 )segments in random order. There are some study show the molar ratio of cellotriosyl/cellotraosyl for oat (2.1-2.4), barley (2.8-3.3), and wheat (4.2-4.5). [ 1 ] [ 5 ]
Xyloglucans have a backbone similar to cellulose with α-D-xylopyranose residues at position 6. To better describe different side chains, a single letter code notation is used for each side chain type. G -- unbranched Glc residue; X -- α-d-Xyl-(1→6)-Glc. L -- β-Gal , S -- α-l-Araf, F-- α-l-Fuc. These are the most common side chains. [ 5 ]
The two most common types of xyloglucans in plant cell walls are identified as XXXG and XXGG. [ 1 ]
Hemicelluloses are synthesised from sugar nucleotides in the cell's Golgi apparatus . [ 9 ] Two models explain their synthesis: 1) a '2 component model' where modification occurs at two transmembrane proteins, and 2) a '1 component model' where modification occurs only at one transmembrane protein. After synthesis, hemicelluloses are transported to the plasma membrane via Golgi vesicles.
Each kind of hemicellulose is biosynthesized by specialized enzymes. [ 9 ] [ 10 ]
Mannan chain backbones are synthesized by cellulose synthase-like protein family A (CSLA) and possibly enzymes in cellulose synthase-like protein family D (CSLD). [ 9 ] [ 10 ] Mannan synthase, a particular enzyme in CSLA, is responsible for the addition of mannose units to the backbone. [ 9 ] [ 10 ] The galactose side-chains of some mannans are added by galactomannan galactosyltransferase. [ 9 ] [ 10 ] Acetylation of mannans is mediated by a mannan O-acetyltransferase, however, this enzyme has not been definitively identified. [ 10 ]
Xyloglucan backbone synthesis is mediated by cellulose synthase-like protein family C (CSLC), particularly glucan synthase , which adds glucose units to the chain. [ 9 ] [ 10 ] Backbone synthesis of xyloglucan is also mediated in some way by xylosyltransferase , but this mechanism is separate to its transferase function and remains unclear. [ 10 ] Xylosyltransferase in its transferase function is, however, utilized for the addition of xylose to the side-chain. [ 9 ] [ 10 ] Other enzymes utilized for side-chain synthesis of xyloglucan include galactosyltransferase (which is responsible for the addition of [galactose and of which two different forms are utilized), fucosyltransferase (which is responsible for the addition of fucose), and acetyltransferase (which is responsible for acetylation). [ 9 ] [ 10 ]
Xylan backbone synthesis, unlike that of the other hemicelluloses, is not mediated by any cellulose synthase-like proteins. [ 10 ] Instead, xylan synthase is responsible for backbone synthesis, facilitating the addition of xylose. [ 10 ] Several genes for xylan synthases have been identified. [ 10 ] Several other enzymes are utilized for the addition and modification of the side-chain units of xylan, including glucuronosyltransferase (which adds [glucuronic acid units), xylosyltransferase (which adds additional xylose units), arabinosyltransferase (which adds arabinose), methyltransferase (responsible for methylation ), and acetyltransferase] (responsible for acetylation). [ 10 ] Given that mixed-linkage glucan is a non-branched homopolymer of glucose, there is no side-chain synthesis, only the addition of glucose to the backbone in two linkages, β1-3 and β1-4. [ 10 ] Backbone synthesis is mediated by enzymes in cellulose synthase-like protein families F and H (CSLF and CSLH), specifically glucan synthase. [ 9 ] [ 10 ] Several forms of glucan synthase from CSLF and CSLH have been identified. [ 9 ] [ 10 ] All of them are responsible for addition of glucose to the backbone and all are capable of producing both β1-3 and β1-4 linkages, however, it is unknown how much each specific enzyme contributes to the distribution of β1-3 and β1-4 linkages. [ 9 ] [ 10 ]
In the sulfite pulp process the hemicellulose is largely hydrolysed by the acid pulping liquor ending up in the brown liquor where the fermentable hexose sugars (around 2%) can be used for producing ethanol . This process was primarily applied to calcium sulfite brown liquors. [ 11 ]
It is also abundantly found in cereal hull/husk, bran, and straw. A number of proposed processes aim to break it down into the above-mentioned parts for utilization. [ 18 ]
As a polysaccharide compound in plant cell walls similar to cellulose, hemicellulose helps cellulose in the strengthening of plant cell walls. [ 7 ] Hemicellulose interacts with the cellulose by providing cross-linking of cellulose microfibrils : hemicellulose will search for voids in the cell wall during its formation and provide support around cellulose fibrils in order to equip the cell wall with the maximum possible strength it can provide. [ 7 ] Hemicellulose dominates the middle lamella of the plant cell, unlike cellulose which is primarily found in the secondary layers. This allows for hemicellulose to provide middle-ground support for the cellulose on the outer layers of the plant cell. In few cell walls, hemicellulose will also interact with lignin to provide structural tissue support of more vascular plants. [ 3 ] [ 19 ]
There are many ways to obtain hemicellulose; all of these rely on extraction methods through hardwood or softwood trees milled into smaller samples. In hardwoods the main hemicellulose extract is glucuronoxlyan (acetylated xylans), while galactoglucomannan is found in softwoods. [ 20 ] [ 21 ] Prior to extraction the wood typically must be milled into wood chips of various sizes depending on the reactor used. Following this, a hot water extraction process, also known as autohydrolysis or hydrothermal treatment, is utilized with the addition of acids and bases to change the yield size and properties. [ 20 ] [ 21 ] The main advantage to hot water extraction is that it offers a method where the only chemical that is needed is water, making this environmentally friendly and cheap. [ 22 ]
The goal of hot water treatment is to remove as much hemicellulose from the wood as possible. This is done through the hydrolysis of the hemicellulose to achieve smaller oligomers and xylose. Xylose when dehydrated becomes furfural. [ 23 ] When xylose and furfural [ check spelling ] are the goal, acid catalysts, such as formic acid, are added to increase the transition of polysaccharide to monosaccharides. This catalyst also has been shown to also utilize a solvent effect to be aid the reaction. [ 23 ]
One method of pretreatment is to soak the wood with diluted acids (with concentrations around 4%). This converts the hemicellulose into monosaccharides. When pretreatment is done with bases (for instance sodium or potassium hydroxide) this destroys the structure of the lignin. [ 21 ] This changes the structure from crystalline to amorphous. Hydrothermal pretreatment is another method. [ further explanation needed ] This offers advantages such as no toxic or corrosive solvents are needed, nor are special reactors, and no extra costs to dispose of hazardous chemicals. [ 20 ]
The hot water extraction process is done in batch reactors, semi-continuous reactors, or slurry continuous reactors. For batch and semi-continuous reactors wood samples can be used in conditions such as chips or pellets while a slurry reactor must have particles as small as 200 to 300 micrometers. [ 21 ] While the particle size decreases the yield production decreases as well. [ 24 ] This is due to the increase of cellulose. [ citation needed ]
The hot water process is operated at a temperature range of 160 to 240 degrees Celsius in order to maintain the liquid phase. This is done above the normal boiling point of water to increase the solubilization of the hemicellulose and the depolymerization of polysaccharides. [ 23 ] This process can take several minutes to several hours depending on the temperature and pH of the system. [ 21 ] Higher temperatures paired with higher extraction times lead to higher yields. A maximum yield is obtained at a pH of 3.5. [ 20 ] If below, the extraction yield exponentially decreases. In order to control pH, sodium bicarbonate is generally added. [ 20 ] The sodium bicarbonate inhibits the autolysis of acetyl groups as well as inhibiting glycosyl bonds. Depending on the temperature and time the hemicellulose can be further converted into oligomers, monomers and lignin. [ 20 ]
Solid bits of wood remain after autohydrolysis, as the lignin is largely untouched. A proper degree of autohydrolysis can preserve the lignin well enough to be used for paper production. This is useful for the Kraft process , which normally does not recover wood hemicellulose into useful products. [ 25 ] | https://en.wikipedia.org/wiki/Hemicellulose |
A hemichrome ( FeIII ) is a form of low-spin methemoglobin (metHb).
Hemichromes, which precede the denaturation processes of hemoglobin (Hb), are mainly produced by partially denaturated hemoglobins and form histidine complexes.
Hemichromes are usually associated with blood disorders . [ 1 ]
Hemichromes can be classified in two main categories: reversible and irreversible .
Reversible hemichromes (Hch-1) have the ability to return to their native formation (hemoglobin). Some hemichromes can be reduced to the high-spin state of deoxyhemoglobin , while others are first being reduced to hemochromes (FeII) and then to deoxyhemoglobin through anaerobic dialysis. Photolysis, in the presence of oxygen from CO and its reaction with the hemochrome, can quickly convert a hemichrome to oxyhemoglobin (HbO2). [ 2 ] Irreversible hemichromes (Hch-2) cannot be converted to their native form.
Both the reversible and irreversible hemichromes have a similar rate during proteolytic degradation and they both have a lower percentage of alpha helixes . [ 2 ]
Upon blood exiting the body, hemoglobin in blood transits from bright red to dark brown, which is attributed to oxidation of oxy-hemoglobin (HbO 2 ) to methemoglobin (met-Hb) and ending up in hemichrome (HC). For forensic purposes, the fractions of HbO 2 , met-Hb and HC in a bloodstain can be used for age determination of bloodstains when measured with Reflectance Spectroscopy [1] .
Hemichromes form an insoluble macromolecule (macromolecular aggregate) by copolymerization with the cytoplasm of band 3 . Covalent bonds reinforce the aggregate interactions of the hemichromes which are accumulated on the surface of the membrane. [ 3 ] However, hemichromes are less stable than their native form. [ 2 ]
Hemoglobin A in humans can form hemichromes even under physiological conditions as a result of pH and temperature alterations, and the autoxidation of oxyhemoglobin. Hemichrome formation, followed by a band 3 clustering and the formation of Heinz bodies , can take place during the physiological clearance of damaged red blood cells. [ 4 ] The difference between a normal red blood cell (RBC) and a red blood cell with unstable hemoglobin (such as in the case of hemolytic anaemia ) is that, in a normal RBC, the formation of Heinz bodies is significantly delayed. In cells with unstable hemoglobin, hemichromes are formed soon after the cell has been released into the bloodstream and they precipitate on the membrane's surface. [ 5 ]
Source: [ 2 ]
When hemoglobin is exposed to certain conditions, reversible or irreversible hemichromes are formed.
Reversible hemichrome formation occurs in the presence of:
Irreversible hemichrome formation occurs in the presence of: | https://en.wikipedia.org/wiki/Hemichrome |
In mathematics , upper hemicontinuity and lower hemicontinuity are extensions of the notions of upper and lower semicontinuity of single-valued functions to set-valued functions .
A set-valued function that is both upper and lower hemicontinuous is said to be continuous in an analogy to the property of the same name for single-valued functions.
To explain both notions, consider a sequence a of points in a domain, and a sequence b of points in the range. We say that b corresponds to a if each point in b is contained in the image of the corresponding point in a .
The image on the right shows a function that is not lower hemicontinuous at x . To see this, let a be a sequence that converges to x from the left. The image of x is a vertical line that contains some point ( x , y ). But every sequence b that corresponds to a is contained in the bottom horizontal line, so it cannot converge to y . In contrast, the function is upper hemicontinuous everywhere. For example, considering any sequence a that converges to x from the left or from the right, and any corresponding sequence b , the limit of b is contained in the vertical line that is the image of the limit of a .
The image on the left shows a function that is not upper hemicontinuous at x . To see this, let a be a sequence that converges to x from the right. The image of a contains vertical lines, so there exists a corresponding sequence b in which all elements are bounded away from f ( x ). The image of the limit of a contains a single point f ( x ), so it does not contain the limit of b . In contrast, that function is lower hemicontinuous everywhere. For example, for any sequence a that converges to x , from the left or from the right, f ( x ) contains a single point, and there exists a corresponding sequence b that converges to f ( x ).
A set-valued function Γ : A ⇉ B {\displaystyle \Gamma :A\rightrightarrows B} is said to be upper hemicontinuous at a point a ∈ A {\displaystyle a\in A} if, for every open V ⊂ B {\displaystyle V\subset B} with Γ ( a ) ⊂ V , {\displaystyle \Gamma (a)\subset V,} there exists a neighbourhood U {\displaystyle U} of a {\displaystyle a} such that for all x ∈ U , {\displaystyle x\in U,} Γ ( x ) {\displaystyle \Gamma (x)} is a subset of V . {\displaystyle V.}
A set-valued function Γ : A ⇉ B {\displaystyle \Gamma :A\rightrightarrows B} is said to be lower hemicontinuous at the point a ∈ A {\displaystyle a\in A} if for every open set V {\displaystyle V} intersecting Γ ( a ) , {\displaystyle \Gamma (a),} there exists a neighbourhood U {\displaystyle U} of a {\displaystyle a} such that Γ ( x ) {\displaystyle \Gamma (x)} intersects V {\displaystyle V} for all x ∈ U . {\displaystyle x\in U.} (Here V {\displaystyle V} intersects S {\displaystyle S} means nonempty intersection V ∩ S ≠ ∅ {\displaystyle V\cap S\neq \varnothing } ).
If a set-valued function is both upper hemicontinuous and lower hemicontinuous, it is said to be continuous.
Theorem — For a set-valued function Γ : A ⇉ B {\displaystyle \Gamma :A\rightrightarrows B} with closed values, if Γ {\displaystyle \Gamma } is upper hemicontinuous at a ∈ A , {\displaystyle a\in A,} then for every sequence a ∙ = ( a m ) m = 1 ∞ {\displaystyle a_{\bullet }=\left(a_{m}\right)_{m=1}^{\infty }} in A {\displaystyle A} and every sequence ( b m ) m = 1 ∞ {\displaystyle \left(b_{m}\right)_{m=1}^{\infty }} such that b m ∈ Γ ( a m ) , {\displaystyle b_{m}\in \Gamma \left(a_{m}\right),}
If B {\displaystyle B} is compact, then the converse is also true.
As an example, look at the image at the right, and consider sequence a in the domain that converges to x (either from the left or from the right). Then, any sequence b that satisfies the requirements converges to some point in f ( x ).
The graph of a set-valued function Γ : A ⇉ B {\displaystyle \Gamma :A\rightrightarrows B} is the set defined by G r ( Γ ) = { ( a , b ) ∈ A × B : b ∈ Γ ( a ) } . {\displaystyle Gr(\Gamma )=\{(a,b)\in A\times B:b\in \Gamma (a)\}.} The graph of Γ {\displaystyle \Gamma } is the set of all a ∈ A {\displaystyle a\in A} such that Γ ( a ) {\displaystyle \Gamma (a)} is not empty.
Theorem — If Γ : A ⇉ B {\displaystyle \Gamma :A\rightrightarrows B} is an upper hemicontinuous set-valued function with closed domain (that is, the domain of Γ {\displaystyle \Gamma } is closed) and closed values (i.e. Γ ( a ) {\displaystyle \Gamma (a)} is closed for all a ∈ A {\displaystyle a\in A} ), then Gr ( Γ ) {\displaystyle \operatorname {Gr} (\Gamma )} is closed.
If B {\displaystyle B} is compact, then the converse is also true. [ 1 ]
Theorem — Γ : A ⇉ B {\displaystyle \Gamma :A\rightrightarrows B} is lower hemicontinuous at a ∈ A {\displaystyle a\in A} if and only if for every sequence a ∙ = ( a m ) m = 1 ∞ {\displaystyle a_{\bullet }=\left(a_{m}\right)_{m=1}^{\infty }} in A {\displaystyle A} such that a ∙ → a {\displaystyle a_{\bullet }\to a} in A {\displaystyle A} and all b ∈ Γ ( a ) , {\displaystyle b\in \Gamma (a),} there exists a subsequence ( a m k ) k = 1 ∞ {\displaystyle \left(a_{m_{k}}\right)_{k=1}^{\infty }} of a ∙ {\displaystyle a_{\bullet }} and also a sequence b ∙ = ( b k ) k = 1 ∞ {\displaystyle b_{\bullet }=\left(b_{k}\right)_{k=1}^{\infty }} such that b ∙ → b {\displaystyle b_{\bullet }\to b} and b k ∈ Γ ( a m k ) {\displaystyle b_{k}\in \Gamma \left(a_{m_{k}}\right)} for every k . {\displaystyle k.}
A set-valued function Γ : A → B {\displaystyle \Gamma :A\to B} is said to have open lower sections if the set Γ − 1 ( b ) = { a ∈ A : b ∈ Γ ( a ) } {\displaystyle \Gamma ^{-1}(b)=\{a\in A:b\in \Gamma (a)\}} is open in A {\displaystyle A} for every b ∈ B . {\displaystyle b\in B.} If Γ {\displaystyle \Gamma } values are all open sets in B , {\displaystyle B,} then Γ {\displaystyle \Gamma } is said to have open upper sections .
If Γ {\displaystyle \Gamma } has an open graph Gr ( Γ ) , {\displaystyle \operatorname {Gr} (\Gamma ),} then Γ {\displaystyle \Gamma } has open upper and lower sections and if Γ {\displaystyle \Gamma } has open lower sections then it is lower hemicontinuous. [ 2 ]
Open Graph Theorem — If Γ : A → P ( R n ) {\displaystyle \Gamma :A\to P\left(\mathbb {R} ^{n}\right)} is a set-valued function with convex values and open upper sections, then Γ {\displaystyle \Gamma } has an open graph in A × R n {\displaystyle A\times \mathbb {R} ^{n}} if and only if Γ {\displaystyle \Gamma } is lower hemicontinuous. [ 2 ]
Set-theoretic, algebraic and topological operations on set-valued functions (like union, composition, sum, convex hull, closure) usually preserve the type of continuity. But this should be taken with appropriate care since, for example, there exists a pair of lower hemicontinuous set-valued functions whose intersection is not lower hemicontinuous.
This can be fixed upon strengthening continuity properties: if one of those lower hemicontinuous multifunctions has open graph then their intersection is again lower hemicontinuous.
Crucial to set-valued analysis (in view of applications) are the investigation of single-valued selections and approximations to set-valued functions.
Typically lower hemicontinuous set-valued functions admit single-valued selections ( Michael selection theorem , Bressan–Colombo directionally continuous selection theorem, Fryszkowski decomposable map selection).
Likewise, upper hemicontinuous maps admit approximations (e.g. Ancel–Granas–Górniewicz–Kryszewski theorem).
The upper and lower hemicontinuity might be viewed as usual continuity:
Theorem — A set-valued map Γ : A → B {\displaystyle \Gamma :A\to B} is lower [resp. upper] hemicontinuous if and only if the mapping Γ : A → P ( B ) {\displaystyle \Gamma :A\to P(B)} is continuous where the hyperspace P(B) has been endowed with the lower [resp. upper] Vietoris topology .
(For the notion of hyperspace compare also power set and function space ).
Using lower and upper Hausdorff uniformity we can also define the so-called upper and lower semicontinuous maps in the sense of Hausdorff (also known as metrically lower / upper semicontinuous maps ). | https://en.wikipedia.org/wiki/Hemicontinuity |
A hemiepiphyte is a plant that spends part of its life cycle as an epiphyte . The seeds of primary hemiepiphytes germinate in the canopy and initially live epiphytically. They send roots downward, and these roots eventually make contact with the ground. Secondary hemiepiphytes are root-climbers [ 1 ] that begin as rooted vines growing upward from the forest floor , but later break their connection to the ground. [ 2 ] When this happens, they may send down long roots to the ground. [ 1 ]
Strangler figs are hemiepiphytic – they may begin life as epiphytes but after making contact with the ground they encircle their host tree and "strangle" it. This usually results in the death of the host tree, either through girdling or through competition for light. [ 3 ] Strangler figs can also germinate and develop as independent trees, not reliant on the support of a host.
This botany article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hemiepiphyte |
A hemihelix is a curved geometric shape consisting of a series of helices with alternating chirality , connected by a perversion at the reversals. [ 1 ] [ 2 ]
The formation of hemihelices with periodic distributions of perversions in slender structures is understood in terms of competing buckling instabilities generated by in-plane stresses . [ 3 ]
This geometry-related article is a stub . You can help Wikipedia by expanding it .
This physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hemihelix |
In chemistry , a hemihydrate (or semihydrate ) is a hydrate whose solid contains one molecule of water of crystallization per two other molecules, or per two unit cells . This is sometimes characterized as a solid that has one "half molecule" of water per unit cell. [ 1 ] An example of this is calcium sulfate hemihydrate ( CaSO 4 ·0.5H 2 O or 2CaSO 4 ·H 2 O ), which is the hemihydrate of calcium sulfate ( CaSO 4 ).
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hemihydrate |
In coordination chemistry and catalysis hemilability ( hemi - half, lability - a susceptibility to change) refers to a property of many polydentate ligands which contain at least two electronically different coordinating groups, such as hard and soft donors . These hybrid or heteroditopic ligands form complexes where one coordinating group is easily displaced from the metal centre while the other group remains firmly bound; a behaviour which has been found to increase the reactivity of catalysts when compared to the use of more traditional ligands. [ 1 ] [ 2 ]
In general, catalytic cycles can be divided into 3 stages:
Traditionally the focus of catalytic research has been on the reaction taking place in the second stage, however there will be energy changes associated with the beginning and end steps due to their effect on the coordination sphere and geometry of the complex, as well as its oxidation number in cases of oxidative addition and reductive elimination . When these energy changes are large they can dictate the turn-over rate of the catalyst and hence its effectiveness.
Hemilabile ligands reduce the activation energy of these changes by readily undergoing partial and reversible displacement from the metal centre. Hence a co-ordinately saturated hemilabile complex will readily reorganise to allow the coordination of reagents but will also promote the ejection of products due to re-coordination of the labile section of the ligand. The low energy barrier between the fully and hemi coordinated states results in frequent inverconvertion between the two, which promotes a fast catalytic turn-over rate.
Hemilabile ligands dissociate in one of three main ways; an "on/off" mechanism where they are constantly dissociating and re-associating, a displacement mechanism where they dissociate easily when exposed to a competing substrate, or redox switching where the oxidation state of the ligand is used to tune its affinity for the metal center. [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/Hemilability |
In music , hemiola (also hemiolia ) is the ratio 3:2. The equivalent Latin term is sesquialtera . In rhythm , hemiola refers to three beats of equal value in the time normally occupied by two beats. In pitch, hemiola refers to the interval of a perfect fifth .
The word hemiola comes from the Greek adjective ἡμιόλιος, hemiolios , meaning "containing one and a half," "half as much again," "in the ratio of one and a half to one (3:2), as in musical sounds." [ 1 ] The words "hemiola" and "sesquialtera" both signify the ratio 3:2, and in music were first used to describe relations of pitch. Dividing the string of a monochord in this ratio produces the interval of a perfect fifth . Beginning in the 15th century, both words were also used to describe rhythmic relationships, specifically the substitution (usually through the use of coloration —red notes in place of black ones, or black in place of "white", hollow noteheads) of three imperfect notes (divided into two parts) for two perfect ones (divided into three parts) in tempus perfectum or in prolatio maior . [ 2 ] [ 3 ]
In rhythm , hemiola refers to three beats of equal value in the time normally occupied by two beats. [ 4 ]
The Oxford Dictionary of Music illustrates hemiola with a superimposition of three notes in the time of two and vice versa. [ 5 ]
One textbook states that, although the word "hemiola" is commonly used for both simultaneous and successive durational values, describing a simultaneous combination of three against two is less accurate than for successive values and the "preferred term for a vertical two against three … is sesquialtera ." [ 6 ] The New Harvard Dictionary of Music states that in some contexts, a sesquialtera is equivalent to a hemiola. [ 7 ] Grove's Dictionary , on the other hand, has maintained from the first edition of 1880 down to the most recent edition of 2001 that the Greek and Latin terms are equivalent and interchangeable, both in the realms of pitch and rhythm, [ 8 ] [ 3 ] although David Hiley , E. Thomas Stanford, and Paul R. Laird hold that, though similar in effect, hemiola properly applies to a momentary occurrence of three duple values in place of two triple ones, whereas sesquialtera represents a proportional metric change between successive sections. [ 9 ]
A repeating vertical hemiola is known as polyrhythm , or more specifically, cross-rhythm . The most basic rhythmic cell of sub-Saharan Africa is the 3:2 cross-rhythm. Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics." [ 10 ] Agawu states: "[The] resultant [3:2] rhythm holds the key to understanding ... there is no independence here, because 2 and 3 belong to a single Gestalt ." [ 11 ]
In the following example, a Ghanaian gyil plays a hemiola as the basis of an ostinato melody. The left hand (lower notes) sounds the two main beats, while the right hand (upper notes) sounds the three cross-beats. [ 12 ]
In compound time ( 6 8 or 6 4 ), where a regular pattern of two beats to a measure is established at the start of a phrase, this changes to a pattern of three beats at the end of the phrase.
The minuet from J. S. Bach 's keyboard Partita No. 5 in G major articulates groups of 2 times 3 quavers that are really in 6 8 time, despite the 3 4 metre stated in the initial time-signature. [ 13 ] The latter time is restored only at the cadences (bars 4 and 11–12):
Later in the same piece, Bach creates a conflict between the two metres ( 6 8 against 3 4 ):
Hemiola is found in many Renaissance pieces in triple rhythm. One composer who exploited this characteristic was the 16th-century French composer Claude Le Jeune , a leading exponent of musique mesurée à l'antique . One of his best-known chansons is "Revoici venir du printemps", where the alternation of compound-duple and simple-triple metres with a common counting unit for the beat subdivisions can be clearly heard:
The hemiola was commonly used in baroque music , particularly in dances , such as the courante and minuet . Other composers who have used the device extensively include Corelli , Handel , Weber and Beethoven . A spectacular example from Beethoven comes in the scherzo from his String Quartet No. 6 . As Philip Radcliffe puts it, "The constant cross-rhythms shifting between 3 4 and 6 8 , more common at certain earlier and later periods, were far from usual in 1800, and here they are made to sound especially eccentric owing to frequent sforzandi on the last quaver of the bar... it looks ahead to later works and must have sounded very disconcerting to contemporary audiences." [ 14 ]
Later in the nineteenth century, Tchaikovsky frequently used hemiolas in his waltzes, as did Richard Strauss in the waltzes from Der Rosenkavalier , and the third movement of Robert Schumann 's Piano Concerto is noted for the ambiguity of its rhythm. John Daverio says that the movement's "fanciful hemiolas... serve to legitimize the dance-like material as a vehicle for symphonic elaboration." [ 15 ]
Johannes Brahms was particularly famous for exploiting the hemiola's potential for large-scale thematic development. Writing about the rhythm and meter of Brahms's Symphony No. 3 , Frisch says "Perhaps in no other first movement by Brahms does the development of these elements play so critical a role. The first movement of the third is cast in 6 4 meter that is also open, through internal recasting as 3 2 (a so-called hemiola). Metrical ambiguity arises in the very first appearance of the motto [opening theme]." [ 16 ]
At the beginning of the second movement, Assez vif – très rythmé , of his String Quartet (1903), Ravel "uses the pizzicato as a vehicle for rhythmic interplay between 6 8 and 3 4 ." [ 17 ]
Peter Manuel, in the context of an analysis of the flamenco soleá song form, refers to the following figure as a horizontal hemiola or "sesquialtera" (which mistranslates as: "six that alters"). It is "a cliché of various Spanish and Latin American musics ... well established in Spain since the sixteenth century", a twelve-beat scheme with internal accents, consisting of a 6 8 bar followed by one in 3 4 , for a 3 + 3 + 2 + 2 + 2 pattern. [ 18 ]
This figure is a common African bell pattern , used by the Hausa people of Nigeria , in Haitian Vodou drumming , Cuban palo , and many other drumming systems. The horizontal hemiola suggests metric modulation ( 6 8 changing to 3 4 ). This interpretational switch has been exploited, for example, by Leonard Bernstein , in the song "America" from West Side Story , as can be heard in the prominent motif (suggesting a duple beat scheme, followed by a triple beat scheme):
Hemiola can be used to describe the ratio of the lengths of two strings as three-to-two (3:2), that together sound a perfect fifth . [ 2 ] The early Pythagoreans, such as Hippasus and Philolaus , used this term in a music-theoretic context to mean a perfect fifth . [ 19 ]
The justly tuned pitch ratio of a perfect fifth means that the upper note makes three vibrations in the same amount of time that the lower note makes two. In the cent system of pitch measurement, the 3:2 ratio corresponds to approximately 702 cents, or 2% of a semitone wider than seven semitones. The just perfect fifth can be heard when a violin is tuned: if adjacent strings are adjusted to the exact ratio of 3:2, the result is a smooth and consonant sound, and the violin sounds in tune. Just perfect fifths are the basis of Pythagorean tuning , and are employed together with other just intervals in just intonation . The 3:2 just perfect fifth arises in the justly tuned C major scale between C and G. [ 20 ]
Later Greek authors such as Aristoxenus and Ptolemy use the word to describe smaller intervals as well, such as the hemiolic chromatic pyknon , which is one-and-a-half times the size of the semitone comprising the enharmonic pyknon . [ 21 ]
Sources | https://en.wikipedia.org/wiki/Hemiola |
The hemispherical resonator gyroscope (HRG), also called wine-glass gyroscope or mushroom gyro , is a compact, low-noise, high-performance angular rate or rotation sensor. An HRG is made using a thin solid-state hemispherical shell, anchored by a thick stem. This shell is driven to a flexural resonance by electrostatic forces generated by electrodes which are deposited directly onto separate fused-quartz structures that surround the shell. The gyroscopic effect is obtained from the inertial property of the flexural standing waves. Although the HRG is a mechanical system, it has no moving parts, and can be very compact.
The HRG makes use of a small thin solid-state hemispherical shell, anchored by a thick stem. This shell is driven to a flexural resonance by dedicated electrostatic forces generated by electrodes which are deposited directly onto separate fused quartz structures that surround the shell.
For a single-piece design (i.e., the hemispherical shell and stem form a monolithic part [ 1 ] ) made from high-purity fused quartz , it is possible to reach a Q factor of over 30-50 million in vacuum, thus the corresponding random walks are extremely low. The Q factor is limited by the coating (extremely thin film of gold or platinum) and by fixture losses. [ 2 ] Such resonators have to be fine-tuned by ion-beam micro-erosion of the glass or by laser ablation in order to be perfectly dynamically balanced. When coated, tuned, and assembled within the housing, the Q factor remains over 10 million.
In application to the HRG shell, Coriolis forces cause a precession of vibration patterns around the axis of rotation . It causes a slow precession of a standing wave around this axis, with an angular rate that differs from input one. This is the wave inertia effect, discovered in 1890 by British scientist George Hartley Bryan (1864–1928). [ 3 ] Therefore, when subject to rotation around the shell symmetry axis, the standing wave does not rotate exactly with the shell, but the difference between both rotations is nevertheless perfectly proportional to the input rotation. The device is then able to sense rotation.
The electronics which sense the standing waves are also able to drive them. Therefore, the gyros can operate in either a "whole angle mode" that sense the standing waves' position or a "force rebalance mode" that holds the standing wave in a fixed orientation with respect to the gyro.
Originally used in space applications (attitude and orbit control systems for spacecraft), [ 4 ] HRG is now used in advanced inertial navigation systems , in attitude and heading reference systems , and HRG gyrocompasses . [ 5 ]
The HRG is extremely reliable [ 6 ] [ 7 ] because of its very simple hardware (two or three pieces of machined fused quartz). It has no moving parts; its core is made of a monolithic part which includes the hemispherical shell and its stem. [ 8 ] They have demonstrated outstanding reliability since their initial use in 1996 on the NEAR Shoemaker spacecraft. [ 9 ] [ 10 ]
The HRG is highly accurate [ 8 ] [ 11 ] and is not sensitive to external environmental perturbations. The resonating shell weighs only a few grams and it is perfectly balanced, which makes it insensitive to vibrations, accelerations, and shocks.
The HRG exhibits superior SWAP (size, weight, and power) characteristics compared to other gyroscope technologies.
The HRG generates neither acoustic nor radiated noise because the resonating shell is perfectly balanced and operates under vacuum.
The material of the resonator, the fused quartz , is naturally radiation hard in any space environment. [ 12 ] This confers intrinsic immunity to deleterious space radiation effects to the HRG resonator. Thanks to the extremely high Q factor of the resonating shell, the HRG has an ultra-low angular random walk [ 9 ] and extremely low power dissipation.
The HRG, unlike optical gyros ( fibre-optic gyroscope and ring laser gyroscope ), has inertial memory: if the power is lost for a short period of time (typically a few seconds), the sensitive element continues to integrate the input motion (angular rate) so that when the power returns, the HRG signals the angle turned while power was off.
The HRG is a very high-tech device which requires sophisticated manufacturing tools and processes. The control electronics required to sense and drive the standing waves are sophisticated. This high level of sophistication limits the availability of this technology; few companies were able to produce it. Currently three companies are manufacturing HRG: Northrop Grumman , [ 9 ] Safran Electronics & Defense [ 13 ] and Raytheon Anschütz . [ 14 ]
Classical HRG is relatively expensive due to the cost of the precision ground and polished hollow quartz hemispheres. This manufacturing cost restricts its use to high-added-value applications such as satellites and spacecraft. [ 9 ] Nevertheless manufacturing costs can be dramatically reduced by design changes and engineering controls. Rather than depositing electrodes on an internal hemisphere that must perfectly match the shape of the outer resonating hemisphere, electrodes are deposited on a flat plate that matches the equatorial plane of the resonating hemisphere. In such configuration, HRG becomes very cost effective and is well suitable for high grade but cost sensitive applications. [ 15 ] | https://en.wikipedia.org/wiki/Hemispherical_resonator_gyroscope |
In organic chemistry , hemithioacetals (or thiohemiacetals ) are organosulfur compounds with the general formula R−CH(−OH)−SR’ . They are the sulfur analogues of the acetals , R−CH(−OH)−OR’ , with an oxygen atom replaced by sulfur (as implied by the thio- prefix). Because they consist of four differing substituents on a single carbon , hemithioacetals are chiral . A related family of compounds are the dithiohemiacetals , with the formula R−CH(−SH)−SR’ . [ 1 ] Although they can be important intermediates , hemithioacetals are usually not isolated, since they exist in equilibrium with thiols ( −SH ) and aldehydes ( −CH=O ).
Hemithioacetals are formed by the reaction of a thiol ( R−SH ) and an aldehyde ( R−CH=O ):
Hemithioacetals usually arise via acid catalysis . They typically are intermediates in the formation of dithioacetals ( R−CH(S−R’) 2 ):
Hemithioacetals ordinarily readily dissociate into thiol and aldehyde, however, some have been isolated. In general, these isolable hemithioacetals are cyclic, which disfavors dissociation, and can often be further stabilized by the presence of acid. [ 2 ] An important class are S-glycosides , such as octylthioglucoside , which are formed by a reaction between thiols and sugars. Other examples include 2-hydroxy tetrahydrothiophene [ 3 ] and the anti-HIV drug Lamivudine . [ 4 ] Another class of isolable hemithioacetals are derived from carbonyl groups that form stable hydrates. For example, thiols react with hexafluoroacetone trihydrate to give hemithioacetals, which can be isolated. [ 5 ]
Glyoxalase I , which is part of the glyoxalase system present in the cytosol , catalyzes the conversion of α-oxoaldehyde (RC(O)CHO) and the thiol glutathione (abbreviated GSH) to S-2-hydroxyacylglutathione derivatives [RCH(OH)CO-SG]. The catalytic mechanism involves an intermediate hemithioacetal adduct [RCOCH(OH)-SG]. The spontaneous reaction forms methylglyoxal -glutathione hemithioacetal and human glyoxalase I. [ 6 ]
A hemithioacetal is also invoked in the mechanism of prenylcysteine lyase . In catalytic mechanism, S-farnesylcysteine is oxidized by a flavin to a thiocarbenium ion. The thiocarbenium ion hydrolyzes to form the hemithioacetal:
After formation, the hemithioacetal breaks into hydrogen peroxide , farnesal, and cysteine . [ 7 ] | https://en.wikipedia.org/wiki/Hemithioacetal |
A hemocyte is a cell that plays a role in the immune system of invertebrates . It is found within the hemolymph .
Hemocytes are phagocytes of invertebrates.
Hemocytes in Drosophila melanogaster can be divided into two categories: embryonic and larval. Embryonic hemocytes are derived from head mesoderm and enter the hemolymph as circulating cells. Larval hemocytes, on the other hand, are responsible for tissue remodeling during development. Specifically, they are released during the pupa stage in order to prepare the fly for the transition into an adult and the massive associated tissue reorganization that must occur.
There are four basic types of hemocytes found in fruit flies: secretory, plasmatocytes, crystal cells, and lamellocytes. Secretory cells are never released into the hemolymph and instead send out signalling molecules responsible for cell differentiation. Plasmatocytes are the hemocytes responsible for cell ingestion (phagocytosis) and represent about 95% of circulating hemocytes. Crystal cells are involved in melanization, a process by which microbes/pathogens are engulfed in a hardened gel and destroyed via anti-microbial peptides and other proteins involved in the humoral response. They constitute about 5% of circulating hemocytes. [ 1 ] Lamellocytes are flat cells that are never found in adult cells, and instead are only present in larval cells for their ability to encapsulate invading pathogens. They specifically act on parasitic wasp eggs that bind to the surfaces of cells, and are incapable of being phagocytosed by host cells. [ 2 ]
In mosquitoes , hemocytes are functionally divided into three populations: granulocytes, oenocytoids and prohemocytes. [ 3 ] Granulocytes are the most abundant cell type. They rapidly attach to foreign surfaces and readily engage in phagocytosis . Oenocytoids do not readily spread on foreign surfaces and are the major producers of phenoloxidase, which is the major enzyme of the melanization immune pathway. Prohemocytes are small cells of unknown function, which may result from the asymmetric mitosis of granulocytes.
This zoology –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hemocyte_(invertebrate_immune_system_cell) |
Hemodialysis , also spelled haemodialysis , or simply dialysis , is a process of filtering the blood of a person whose kidneys are not working normally. This type of dialysis achieves the extracorporeal removal of waste products such as creatinine and urea and free water from the blood when the kidneys are in a state of kidney failure . Hemodialysis is one of three renal replacement therapies (the other two being kidney transplant and peritoneal dialysis ). An alternative method for extracorporeal separation of blood components such as plasma or cells is apheresis .
Hemodialysis can be an outpatient or inpatient therapy. Routine hemodialysis is conducted in a dialysis outpatient facility, either a purpose-built room in a hospital or a dedicated, stand-alone clinic. Less frequently hemodialysis is done at home . Dialysis treatments in a clinic are initiated and managed by specialized staff made up of nurses and technicians; dialysis treatments at home can be self-initiated and managed or done jointly with the assistance of a trained helper who is usually a family member. [ 1 ]
Hemodialysis is the choice of renal replacement therapy for patients who need dialysis acutely, and for many patients as maintenance therapy. It provides excellent, rapid clearance of solutes. [ 2 ]
A nephrologist (a medical kidney specialist) decides when hemodialysis is needed and the various parameters for a dialysis treatment. These include frequency (how many treatments per week), length of each treatment, and the blood and dialysis solution flow rates, as well as the size of the dialyzer. The composition of the dialysis solution is also sometimes adjusted in terms of its sodium, potassium, and bicarbonate levels. In general, the larger the body size of an individual, the more dialysis they will need. In North America and the UK , 3–4 hour treatments (sometimes up to 5 hours for larger patients) given 3 times a week are typical. For some patients, nephrologists may suggest an incremental approach, especially for those with substantial residual kidney function at the time of dialysis initiation. With "incremental hemodialysis", the initial dialysis prescription begins with fewer and/or shorter sessions per week—usually one or two 3 hour session—and gradually increases frequency and duration as kidney function declines. [ 3 ] Four sessions per week may be prescribed for larger patients, as well as patients who have trouble with fluid overload .
There is growing interest in short daily home hemodialysis , which is 1.5 – 4 hr sessions given 5–7 times per week, usually at home. There is also interest in nocturnal dialysis , which involves dialyzing a patient, usually at home, for 8–10 hours per night, 3–6 nights per week. Nocturnal in-center dialysis, 3–4 times per week, was first described more than 40 years ago, and is offered at some dialysis units. [ 4 ] [ 5 ] [ 6 ]
Hemodialysis often involves fluid removal (through ultrafiltration ), because most patients with renal failure pass little or no urine. Side effects caused by removing too much fluid and/or removing fluid too rapidly include low blood pressure , fatigue , chest pains, leg-cramps, nausea and headaches . These symptoms can occur during the treatment and can persist post treatment; they are sometimes collectively referred to as the dialysis hangover or dialysis washout. The severity of these symptoms is usually proportionate to the amount and speed of fluid removal. However, the impact of a given amount or rate of fluid removal can vary greatly from person to person and day to day. These side effects can be avoided and/or their severity lessened by limiting fluid intake between treatments or increasing the dose of dialysis e.g. dialyzing more often or longer per treatment than the standard three times a week, 3–4 hours per treatment schedule.
Since hemodialysis requires access to the circulatory system, patients undergoing hemodialysis may expose their circulatory system to microbes , which can lead to bacteremia , an infection affecting the heart valves ( endocarditis ) or an infection affecting the bones ( osteomyelitis ). The risk of infection varies depending on the type of access used (see below). Bleeding may also occur, again the risk varies depending on the type of access used. Infections can be minimized by strictly adhering to infection control best practices.
Venous needle dislodgement (VND) is a fatal complication of hemodialysis where the patient experiences rapid blood loss due to a faltering attachment of the needle to the venous access point. [ 7 ]
Unfractioned heparin (UHF) is the most commonly used anticoagulant in hemodialysis, as it is generally well tolerated and can be quickly reversed with protamine sulfate . Low-molecular weight heparin (LMWH) is however, becoming increasingly popular and is now the norm in western Europe. [ 8 ] Compared to UHF, LMWH has the advantage of an easier mode of administration and reduced bleeding but the effect cannot be easily reversed. [ 9 ] Heparin can infrequently cause a low platelet count due to a reaction called heparin-induced thrombocytopenia (HIT) . The risk of HIT is lower with LMWH compared to UHF. In such patients, alternative anticoagulants may be used. Even though HIT causes a low platelet count it can paradoxically predispose thrombosis. [ 10 ] When comparing UHF to LMWH for the risk of adverse effects, the evidence is uncertain as to which treatment approach to thin blood has the least side effects and what is the ideal treatment strategy for preventing blood clots during hemodialysis. [ 11 ] In patients at high risk of bleeding, dialysis can be done without anticoagulation. [ 12 ]
First-use syndrome is a rare but severe anaphylactic reaction to the artificial kidney . Its symptoms include sneezing, wheezing, shortness of breath, back pain, chest pain, or sudden death. It can be caused by residual sterilant in the artificial kidney or the material of the membrane itself. In recent years, the incidence of first-use syndrome has decreased, due to an increased use of gamma irradiation , steam sterilization, or electron-beam radiation instead of chemical sterilants, and the development of new semipermeable membranes of higher biocompatibility . New methods of processing previously acceptable components of dialysis must always be considered. For example, in 2008, a series of first-use type of reactions, including deaths, occurred due to heparin contaminated during the manufacturing process with oversulfated chondroitin sulfate . [ 13 ]
Long term complications of hemodialysis include hemodialysis-associated amyloidosis , neuropathy and various forms of heart disease . Increasing the frequency and length of treatments has been shown to improve fluid overload and enlargement of the heart that is commonly seen in such patients. [ 14 ] [ 15 ]
Folate deficiency can occur in some patients having hemodialysis. [ 16 ]
Although a dialysate fluid, which is a solution containing diluted electrolytes, is employed for the filtration of blood, haemodialysis can cause an electrolyte imbalance. These imbalances can derive from abnormal concentrations of potassium ( hypokalemia , hyperkalemia ), and sodium ( hyponatremia , hypernatremia ). These electrolyte imbalances are associated with increased cardiovascular mortality. [ 17 ]
The principle of hemodialysis is the same as other methods of dialysis ; it involves diffusion of solutes across a semipermeable membrane. Hemodialysis utilizes counter current flow , where the dialysate is flowing in the opposite direction to blood flow in the extracorporeal circuit. Counter-current flow maintains the concentration gradient across the membrane at a maximum and increases the efficiency of the dialysis.
Fluid removal ( ultrafiltration ) is achieved by altering the hydrostatic pressure of the dialysate compartment, causing free water and some dissolved solutes to move across the membrane along a created pressure gradient.
The dialysis solution that is used may be a sterilized solution of mineral ions and is called dialysate. Urea and other waste products including potassium , and phosphate diffuse into the dialysis solution. However, concentrations of sodium and chloride are similar to those of normal plasma to prevent loss. Sodium bicarbonate is added in a higher concentration than plasma to correct blood acidity. A small amount of glucose is also commonly used. The concentration of electrolytes in the dialysate is adjusted depending on the patient's status before the dialysis. If a high concentration of sodium is added to the dialysate, the patient can become thirsty and end up accumulating body fluids, which can lead to heart damage. On the contrary, low concentrations of sodium in the dialysate solution have been associated with a low blood pressure and intradialytic weight gain, which are markers of improved outcomes. However, the benefits of using a low concentration of sodium have not been demonstrated yet, since these patients can also develop cramps, intradialytic hypotension and low sodium in serum, which are symptoms associated with a high mortality risk. [ 18 ]
Note that this is a different process to the related technique of hemofiltration .
Three primary methods are used to gain access to the blood for hemodialysis: an intravenous catheter, an arteriovenous fistula (AV) and a synthetic graft. The type of access is influenced by factors such as the expected time course of a patient's renal failure and the condition of their vasculature. Patients may have multiple access procedures, usually because an AV fistula or graft is maturing and a catheter is still being used. The placement of a catheter is usually done under light sedation, while fistulas and grafts require an operation.
There are three types of hemodialysis: conventional hemodialysis, daily hemodialysis, and nocturnal hemodialysis. Below is an adaptation and summary from a brochure of The Ottawa Hospital.
Conventional hemodialysis is usually done three times per week, for about three to four hours for each treatment (Sometimes five hours for larger patients), during which the patient's blood is drawn out through a tube at a rate of 200–400 mL/min. The tube is connected to a 15, 16, or 17 gauge needle inserted in the dialysis fistula or graft, or connected to one port of a dialysis catheter . The blood is then pumped through the dialyzer, and then the processed blood is pumped back into the patient's bloodstream through another tube (connected to a second needle or port). During the procedure, the patient's blood pressure is closely monitored, and if it becomes low, or the patient develops any other signs of low blood volume such as nausea, the dialysis attendant can administer extra fluid through the machine. During the treatment, the patient's entire blood volume (about 5 L) circulates through the machine every 15 minutes. During this process, the dialysis patient is exposed to a week's worth of water for the average person.
Daily hemodialysis is typically used by those patients who do their own dialysis at home. It is less stressful (more gentle) but does require more frequent access. This is simple with catheters, but more problematic with fistulas or grafts. The " buttonhole technique " can be used for fistulas, but not grafts, requiring frequent access. Daily hemodialysis is usually done for 2 hours six days a week.
The procedure of nocturnal hemodialysis is similar to conventional hemodialysis except it is performed three to six nights a week and between six and ten hours per session while the patient sleeps. [ 19 ]
The hemodialysis machine pumps the patient's blood and the dialysate through the dialyzer. [ 20 ] The newest dialysis machines on the market are highly computerized and continuously monitor an array of safety-critical parameters, including blood (QB) and dialysate QD) flow rates; [ 21 ] dialysis solution conductivity, temperature, and pH; and analysis of the dialysate for evidence of blood leakage or presence of air. Any reading that is out of normal range triggers an audible alarm to alert the patient-care technician who is monitoring the patient. [ 22 ] Manufacturers of dialysis machines include companies such as Nipro , Fresenius , Gambro , Baxter, B. Braun , NxStage and Bellco. [ citation needed ] QB to QD flow rates have to reach 1:2 ratio where QB is set around 250 ml/min and QD is set around 500 ml/min to ensure good dialysis efficiency. [ 21 ]
An extensive water purification system is critical for hemodialysis. Since dialysis patients are exposed to vast quantities of water, which is mixed with dialysate concentrate to form the dialysate, even trace mineral contaminants or bacterial endotoxins can filter into the patient's blood. Because the damaged kidneys cannot perform their intended function of removing impurities, molecules introduced into the bloodstream from improperly purified water can build up to hazardous levels, causing numerous symptoms or death. Aluminum , chlorine and or chloramines , fluoride , copper , and zinc , as well as bacterial fragments and endotoxins , have all caused problems in this regard.
For this reason, water used in hemodialysis is carefully purified before use. A common water purification system includes a multi stage system.
The water is first softened. Next the water is run through a tank containing activated charcoal to adsorb organic contaminants, and chlorine and chloramines. The water may then be temperature-adjusted if needed. Primary purification is then done by forcing water through a membrane with very tiny pores, a so-called reverse osmosis membrane. This lets the water pass, but holds back even very small solutes such as electrolytes. Final removal of leftover electrolytes is done in some water systems by passing the water through an electrodeionization (EDI) device, which removes any leftover anions or cations and replace them with hydroxyl and hydrogen ions, respectively, leaving ultrapure water.
Even this degree of water purification may be insufficient. The trend lately is to pass this final purified water (after mixing with dialysate concentrate) through an ultrafiltration membrane or absolute filter. This provides another layer of protection by removing impurities, especially those of bacterial origin, that may have accumulated in the water after its passage through the original water purification system.
Once purified water is mixed with dialysate (also called dialysis fluid) concentrate consisting of: sodium , potassium , calcium , magnesium and dextrose mixed in an acid solution; this solution is mixed with the purified water and a chemical buffer . This forms the dialysate solution, which contains the basic electrolytes found in human blood. This dialysate solution contains charged ions that conducts electricity. During dialysis, the conductivity of dialysis solution is continuously monitored to ensure that the water and dialysate concentrate are being mixed in the proper proportions. Both excessively concentrated dialysis solution and excessively dilute solution can cause severe clinical problems.
Chemical buffers such as bicarbonate or lactate can alternatively be added to regulate the pH of the dialysate. Both buffers can stabilize the pH of the solution at a physiological level with no negative impacts on the patient. There is some evidence of a reduction in the incidence of heart and blood problems and high blood pressure events when using bicarbonate as the pH buffer compared to lactate. However, the mortality rates after using both buffers do not show a significative difference. [ 23 ]
The dialyzer is the piece of equipment that filters the blood. Almost all dialyzers in use today are of the hollow-fiber variety. A cylindrical bundle of hollow fibers, whose walls are composed of semi-permeable membrane, is anchored at each end into potting compound (a sort of glue). This assembly is then put into a clear plastic cylindrical shell with four openings. One opening or blood port at each end of the cylinder communicates with each end of the bundle of hollow fibers. This forms the "blood compartment" of the dialyzer. Two other ports are cut into the side of the cylinder. These communicate with the space around the hollow fibers, the "dialysate compartment." Blood is pumped via the blood ports through this bundle of very thin capillary -like tubes, and the dialysate is pumped through the space surrounding the fibers. Pressure gradients are applied when necessary to move fluid from the blood to the dialysate compartment.
Dialyzer membranes come with different pore sizes. Those with smaller pore size are called "low-flux" and those with larger pore sizes are called "high-flux." Some larger molecules, such as beta-2-microglobulin, are not removed at all with low-flux dialyzers; lately, the trend has been to use high-flux dialyzers. However, such dialyzers require newer dialysis machines and high-quality dialysis solution to control the rate of fluid removal properly and to prevent backflow of dialysis solution impurities into the patient through the membrane.
Dialyzer membranes used to be made primarily of cellulose (derived from cotton linter). The surface of such membranes was not very biocompatible, because exposed hydroxyl groups would activate complement in the blood passing by the membrane. Therefore, the basic, "unsubstituted" cellulose membrane was modified. One change was to cover these hydroxyl groups with acetate groups (cellulose acetate); another was to mix in some compounds that would inhibit complement activation at the membrane surface (modified cellulose). The original "unsubstituted cellulose" membranes are no longer in wide use, whereas cellulose acetate and modified cellulose dialyzers are still used. Cellulosic membranes can be made in either low-flux or high-flux configuration, depending on their pore size.
Another group of membranes is made from synthetic materials, using polymers such as polyarylethersulfone , polyamide , polyvinylpyrrolidone , polycarbonate , and polyacrylonitrile . These synthetic membranes activate complement to a lesser degree than unsubstituted cellulose membranes. However, they are in general more hydrophobic which leads to increased adsorption of proteins to the membrane surface which in turn can lead to complement system activation. [ 24 ] [ 25 ] Synthetic membranes can be made in either low- or high-flux configuration, but most are high-flux.
Nanotechnology is being used in some of the most recent high-flux membranes to create a uniform pore size. The goal of high-flux membranes is to pass relatively large molecules such as beta-2-microglobulin (MW 11,600 daltons), but not to pass albumin (MW ~66,400 daltons). Every membrane has pores in a range of sizes. As pore size increases, some high-flux dialyzers begin to let albumin pass out of the blood into the dialysate. This is thought to be undesirable, although one school of thought holds that removing some albumin may be beneficial in terms of removing protein-bound uremic toxins.
Whether using a high-flux dialyzer improves patient outcomes is somewhat controversial, but several important studies have suggested that it has clinical benefits. The NIH-funded HEMO trial compared survival and hospitalizations in patients randomized to dialysis with either low-flux or high-flux membranes. Although the primary outcome (all-cause mortality) did not reach statistical significance in the group randomized to use high-flux membranes, several secondary outcomes were better in the high-flux group. [ 26 ] [ 27 ] A recent Cochrane analysis concluded that benefit of membrane choice on outcomes has not yet been demonstrated. [ 28 ] A collaborative randomized trial from Europe, the MPO (Membrane Permeabilities Outcomes) study, [ 29 ] comparing mortality in patients just starting dialysis using either high-flux or low-flux membranes, found a nonsignificant trend to improved survival in those using high-flux membranes, and a survival benefit in patients with lower serum albumin levels or in diabetics.
High-flux dialysis membranes and/or intermittent internal on-line hemodiafiltration (iHDF) may also be beneficial in reducing complications of beta-2-microglobulin accumulation. Because beta-2-microglobulin is a large molecule, with a molecular weight of about 11,600 daltons, it does not pass at all through low-flux dialysis membranes. Beta-2-M is removed with high-flux dialysis, but is removed even more efficiently with IHDF. After several years (usually at least 5–7), patients on hemodialysis begin to develop complications from beta-2-M accumulation, including carpal tunnel syndrome, bone cysts, and deposits of this amyloid in joints and other tissues. Beta-2-M amyloidosis can cause very serious complications, including spondyloarthropathy , and often is associated with shoulder joint problems. Observational studies from Europe and Japan have suggested that using high-flux membranes in dialysis mode, or IHDF, reduces beta-2-M complications in comparison to regular dialysis using a low-flux membrane. [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ]
Dialyzers come in many different sizes. A larger dialyzer with a larger membrane area (A) will usually remove more solutes than a smaller dialyzer, especially at high blood flow rates. This also depends on the membrane permeability coefficient K 0 for the solute in question. So dialyzer efficiency is usually expressed as the K 0 A – the product of permeability coefficient and area. Most dialyzers have membrane surface areas of 0.8 to 2.2 square meters, and values of K 0 A ranging from about 500 to 1500 mL/min. K 0 A , expressed in mL/min, can be thought of as the maximum clearance of a dialyzer at very high blood and dialysate flow rates.
The dialyzer may either be discarded after each treatment or be reused. Reuse requires an extensive procedure of high-level disinfection. Reused dialyzers are not shared between patients. There was an initial controversy about whether reusing dialyzers worsened patient outcomes. The consensus today is that reuse of dialyzers, if done carefully and properly, produces similar outcomes to single use of dialyzers. [ 35 ]
Dialyzer Reuse is a practice that has been around since the invention of the product. This practice includes the cleaning of a used dialyzer to be reused multiple times for the same patient. Dialysis clinics reuse dialyzers to become more economical and reduce the high costs of "single-use" dialysis which can be extremely expensive and wasteful. Single used dialyzers are initiated just once and then thrown out creating a large amount of bio- medical waste with no mercy for cost savings. If done right, dialyzer reuse can be very safe for dialysis patients.
There are two ways of reusing dialyzers, manual and automated. Manual reuse involves the cleaning of a dialyzer by hand. The dialyzer is semi-disassembled then flushed repeatedly before being rinsed with water. It is then stored with a liquid disinfectant(PAA) for 18+ hours until its next use. Although many clinics outside the USA use this method, some clinics are switching toward a more automated/streamlined process as the dialysis practice advances. The newer method of automated reuse is achieved by means of a medical device that began in the early 1980s. These devices are beneficial to dialysis clinics that practice reuse – especially for large dialysis clinical entities – because they allow for several back to back cycles per day. The dialyzer is first pre-cleaned by a technician, then automatically cleaned by machine through a step-cycles process until it is eventually filled with liquid disinfectant for storage. Although automated reuse is more effective than manual reuse, newer technology has sparked even more advancement in the process of reuse. When reused over 15 times with current methodology, the dialyzer can lose B2m, middle molecule clearance and fiber pore structure integrity, which has the potential to reduce the effectiveness of the patient's dialysis session. Currently, as of 2010, newer, more advanced reprocessing technology has proven the ability to eliminate the manual pre-cleaning process altogether and has also proven the potential to regenerate (fully restore) all functions of a dialyzer to levels that are approximately equivalent to single-use for more than 40 cycles. [ 36 ] As medical reimbursement rates begin to fall even more, many dialysis clinics are continuing to operate effectively with reuse programs especially since the process is easier and more streamlined than before.
Hemodialysis was one of the most common procedures performed in U.S. hospitals in 2011, occurring in 909,000 stays (a rate of 29 stays per 10,000 population). This was an increase of 68 percent from 1997, when there were 473,000 stays. It was the fifth most common procedure for patients aged 45–64 years. [ 37 ]
Many have played a role in developing dialysis as a practical treatment for renal failure, starting with Thomas Graham of Glasgow , who first presented the principles of solute transport across a semipermeable membrane in 1854. [ 38 ] The artificial kidney was first developed by Abel , Rountree, and Turner in 1913, [ 39 ] the first hemodialysis in a human being was by Haas (February 28, 1924) [ 40 ] and the artificial kidney was developed into a clinically useful apparatus by Kolff in 1943 to 1945. [ 41 ] This research showed that life could be prolonged in patients dying of kidney failure .
Willem Kolff was the first to construct a working dialyzer in 1943. The first successfully treated patient was a 67-year-old woman in uremic coma who regained consciousness after 11 hours of hemodialysis with Kolff's dialyzer in 1945. At the time of its creation, Kolff's goal was to provide life support during recovery from acute renal failure. After World War II ended, Kolff donated the five dialyzers he had made to hospitals around the world, including Mount Sinai Hospital, New York . Kolff gave a set of blueprints for his hemodialysis machine to George Thorn at the Peter Bent Brigham Hospital in Boston . This led to the manufacture of the next generation of Kolff's dialyzer, a stainless steel Kolff-Brigham dialysis machine.
According to McKellar (1999), a significant contribution to renal therapies was made by Canadian surgeon Gordon Murray with the assistance of two doctors, an undergraduate chemistry student, and research staff. Murray's work was conducted simultaneously and independently from that of Kolff. Murray's work led to the first successful artificial kidney built in North America in 1945–46, which was successfully used to treat a 26-year-old woman out of a uraemic coma in Toronto. The less-crude, more compact, second-generation "Murray-Roschlau" dialyser was invented in 1952–53, whose designs were stolen by German immigrant Erwin Halstrup, and passed off as his own (the "Halstrup–Baumann artificial kidney"). [ 42 ]
By the 1950s, Willem Kolff's invention of the dialyzer was used for acute renal failure, but it was not seen as a viable treatment for patients with stage 5 chronic kidney disease (CKD). At the time, doctors believed it was impossible for patients to have dialysis indefinitely for two reasons. First, they thought no man-made device could replace the function of kidneys over the long term. In addition, a patient undergoing dialysis developed damaged veins and arteries, so that after several treatments, it became difficult to find a vessel to access the patient's blood.
The original Kolff kidney was not very useful clinically, because it did not allow for removal of excess fluid. Swedish professor Nils Alwall [ 43 ] encased a modified version of this kidney inside a stainless steel canister, to which a negative pressure could be applied, in this way effecting the first truly practical application of hemodialysis, which was done in 1946 at the University of Lund . Alwall also was arguably the inventor of the arteriovenous shunt for dialysis. He reported this first in 1948 where he used such an arteriovenous shunt in rabbits. Subsequently, he used such shunts, made of glass, as well as his canister-enclosed dialyzer, to treat 1500 patients in renal failure between 1946 and 1960, as reported to the First International Congress of Nephrology held in Evian in September 1960. Alwall was appointed to a newly created Chair of Nephrology at the University of Lund in 1957. Subsequently, he collaborated with Swedish businessman Holger Crafoord to found one of the key companies that would manufacture dialysis equipment in the past 50 years, Gambro . The early history of dialysis has been reviewed by Stanley Shaldon . [ 44 ]
Belding H. Scribner , working with the biomechanical engineer Wayne Quinton , modified the glass shunts used by Alwall by making them from Teflon . Another key improvement was to connect them to a short piece of silicone elastomer tubing. This formed the basis of the so-called Scribner shunt, perhaps more properly called the Quinton-Scribner shunt. After treatment, the circulatory access would be kept open by connecting the two tubes outside the body using a small U-shaped Teflon tube, which would shunt the blood from the tube in the artery back to the tube in the vein. [ 45 ]
In 1962, Scribner started the world's first outpatient dialysis facility, the Seattle Artificial Kidney Center, later renamed the Northwest Kidney Centers . Immediately the problem arose of who should be given dialysis, since demand far exceeded the capacity of the six dialysis machines at the center. Scribner decided that he would not make the decision about who would receive dialysis and who would not. Instead, the choices would be made by an anonymous committee, which could be viewed as one of the first bioethics committees.
For a detailed history of successful and unsuccessful attempts at dialysis, including pioneers such as Abel and Roundtree, Haas, and Necheles, see this review by Kjellstrand. [ 46 ] | https://en.wikipedia.org/wiki/Hemodialysis |
Hemodynamics or haemodynamics are the dynamics of blood flow . The circulatory system is controlled by homeostatic mechanisms of autoregulation , just as hydraulic circuits are controlled by control systems . The hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Hemodynamics explains the physical laws that govern the flow of blood in the blood vessels .
Blood flow ensures the transportation of nutrients , hormones , metabolic waste products, oxygen , and carbon dioxide throughout the body to maintain cell-level metabolism , the regulation of the pH , osmotic pressure and temperature of the whole body, and the protection from microbial and mechanical harm. [ 1 ]
Blood is a non-Newtonian fluid , and is most efficiently studied using rheology rather than hydrodynamics. Because blood vessels are not rigid tubes, classic hydrodynamics and fluids mechanics based on the use of classical viscometers are not capable of explaining haemodynamics. [ 2 ]
The study of the blood flow is called hemodynamics, and the study of the properties of the blood flow is called hemorheology .
Blood is a complex liquid. Blood is composed of plasma and formed elements . The plasma contains 91.5% water, 7% proteins and 1.5% other solutes. The formed elements are platelets , white blood cells , and red blood cells . The presence of these formed elements and their interaction with plasma molecules are the main reasons why blood differs so much from ideal Newtonian fluids. [ 1 ]
Normal blood plasma behaves like a Newtonian fluid at physiological rates of shear. Typical values for the viscosity of normal human plasma at 37 °C is 1.4 mN·s/m 2 . [ 3 ] The viscosity of normal plasma varies with temperature in the same way as does that of its solvent water [ 4 ] ;a 3°C change in temperature in the physiological range (36.5°C to 39.5°C)reduces plasma viscosity by about 10%. [ 5 ]
The osmotic pressure of solution is determined by the number of particles present and by the temperature . For example, a 1 molar solution of a substance contains 6.022 × 10 23 molecules per liter of that substance and at 0 °C it has an osmotic pressure of 2.27 MPa (22.4 atm). The osmotic pressure of the plasma affects the mechanics of the circulation in several ways. An alteration of the osmotic pressure difference across the membrane of a blood cell causes a shift of water and a change of cell volume. The changes in shape and flexibility affect the mechanical properties of whole blood. A change in plasma osmotic pressure alters the hematocrit, that is, the volume concentration of red cells in the whole blood by redistributing water between the intravascular and extravascular spaces. This in turn affects the mechanics of the whole blood. [ 6 ]
The red blood cell is highly flexible and biconcave in shape. Its membrane has a Young's modulus in the region of 106 Pa . Deformation in red blood cells is induced by shear stress. When a suspension is sheared, the red blood cells deform and spin because of the velocity gradient, with the rate of deformation and spin depending on the shear rate and the concentration.
This can influence the mechanics of the circulation and may complicate the measurement of blood viscosity . It is true that in a steady state flow of a viscous fluid through a rigid spherical body immersed in the fluid, where we assume the inertia is negligible in such a flow, it is believed that the downward gravitational force of the particle is balanced by the viscous drag force. From this force balance the speed of fall can be shown to be given by Stokes' law [ citation needed ]
Where a is the particle radius, ρ p , ρ f are the respectively particle and fluid density μ is the fluid viscosity, g is the gravitational acceleration. From the above equation we can see that the sedimentation velocity of the particle depends on the square of the radius. If the particle is released from rest in the fluid , its sedimentation velocity U s increases until it attains the steady value called the terminal velocity (U), as shown above. [ citation needed ]
Hemodilution is the dilution of the concentration of red blood cells and plasma constituents by partially substituting the blood with colloids or crystalloids . It is a strategy to avoid exposure of patients to the potential hazards of homologous blood transfusions. [ 7 ] [ 8 ]
Hemodilution can be normovolemic, which implies the dilution of normal blood constituents by the use of expanders. During acute normovolemic hemodilution (ANH), blood subsequently lost during surgery contains proportionally fewer red blood cells per milliliter, thus minimizing intraoperative loss of the whole blood. Therefore, blood lost by the patient during surgery is not actually lost by the patient, for this volume is purified and redirected into the patient. [ citation needed ]
On the other hand, hypervolemic hemodilution (HVH) uses acute preoperative volume expansion without any blood removal. In choosing a fluid, however, it must be assured that when mixed, the remaining blood behaves in the microcirculation as in the original blood fluid, retaining all its properties of viscosity . [ 9 ]
In presenting what volume of ANH should be applied one study suggests a mathematical model of ANH which calculates the maximum possible RCM savings using ANH, given the patients weight H i and H m . [ citation needed ]
To maintain the normovolemia, the withdrawal of autologous blood must be simultaneously replaced by a suitable hemodilute. Ideally, this is achieved by isovolemia exchange transfusion of a plasma substitute with a colloid osmotic pressure (OP). A colloid is a fluid containing particles that are large enough to exert an oncotic pressure across the micro-vascular membrane.
When debating the use of colloid or crystalloid, it is imperative to think about all the components of the starling equation:
To identify the minimum safe hematocrit desirable for a given patient the following equation is useful: [ citation needed ]
where EBV is the estimated blood volume; 70 mL/kg was used in this model and H i (initial hematocrit) is the patient's initial hematocrit.
From the equation above it is clear that the volume of blood removed during the ANH to the H m is the same as the BL s .
How much blood is to be removed is usually based on the weight, not the volume. The number of units that need to be removed to hemodilute to the maximum safe hematocrit (ANH) can be found by
This is based on the assumption that each unit removed by hemodilution has a volume of 450 mL (the actual volume of a unit will vary somewhat since completion of collection is dependent on weight and not volume).
The model assumes that the hemodilute value is equal to the H m prior to surgery, therefore, the re-transfusion of blood obtained by hemodilution must begin when SBL begins.
The RCM available for retransfusion after ANH (RCMm) can be calculated from the patient's H i and the final hematocrit after hemodilution( H m )
The maximum SBL that is possible when ANH is used without falling below Hm(BLH) is found by assuming that all the blood removed during ANH is returned to the patient at a rate sufficient to maintain the hematocrit at the minimum safe level
If ANH is used as long as SBL does not exceed BL H there will not be any need for blood transfusion. We can conclude from the foregoing that H should therefore not exceed s .
The difference between the BL H and the BL s therefore is the incremental surgical blood loss ( BL i ) possible when using ANH.
When expressed in terms of the RCM
Where RCM i is the red cell mass that would have to be administered using homologous blood to maintain the H m if ANH is not used and blood loss equals BLH. [ citation needed ]
The model used assumes ANH used for a 70 kg patient with an estimated blood volume of 70 ml/kg (4900 ml). A range of H i and H m was evaluated to understand conditions where hemodilution is necessary to benefit the patient. [ 10 ] [ 11 ]
The result of the model calculations are presented in a table given in the appendix for a range of H i from 0.30 to 0.50 with ANH performed to minimum hematocrits from 0.30 to 0.15. Given a H i of 0.40, if the H m is assumed to be 0.25.then from the equation above the RCM count is still high and ANH is not necessary, if BL s does not exceed 2303 ml, since the hemotocrit will not fall below H m , although five units of blood must be removed during hemodilution. Under these conditions, to achieve the maximum benefit from the technique if ANH is used, no homologous blood will be required to maintain the H m if blood loss does not exceed 2940 ml. In such a case, ANH can save a maximum of 1.1 packed red blood cell unit equivalent, and homologous blood transfusion is necessary to maintain H m , even if ANH is used. [ citation needed ] This model can be used to identify when ANH may be used for a given patient and the degree of ANH necessary to maximize that benefit. [ citation needed ]
For example, if H i is 0.30 or less it is not possible to save a red cell mass equivalent to two units of homologous PRBC even if the patient is hemodiluted to an H m of 0.15. That is because from the RCM equation the patient RCM falls short from the equation giving above.
If H i is 0.40 one must remove at least 7.5 units of blood during ANH, resulting in an H m of 0.20 to save two units equivalence. Clearly, the greater the H i and the greater the number of units removed during hemodilution, the more effective ANH is for preventing homologous blood transfusion. The model here is designed to allow doctors to determine where ANH may be beneficial for a patient based on their knowledge of the H i , the potential for SBL, and an estimate of the H m . Though the model used a 70 kg patient, the result can be applied to any patient. To apply these result to any body weight, any of the values BLs, BLH and ANHH or PRBC given in the table need to be multiplied by the factor we will call T
Basically, the model considered above is designed to predict the maximum RCM that can save ANH. [ citation needed ]
In summary, the efficacy of ANH has been described mathematically by means of measurements of surgical blood loss and blood volume flow measurement. This form of analysis permits accurate estimation of the potential efficiency of the techniques and shows the application of measurement in the medical field. [ 10 ]
The heart is the driver of the circulatory system, pumping blood through rhythmic contraction and relaxation. The rate of blood flow out of the heart (often expressed in L/min) is known as the cardiac output (CO).
Blood being pumped out of the heart first enters the aorta , the largest artery of the body. It then proceeds to divide into smaller and smaller arteries, then into arterioles , and eventually capillaries , where oxygen transfer occurs. The capillaries connect to venules , and the blood then travels back through the network of veins to the venae cavae into the right heart . The micro-circulation — the arterioles, capillaries, and venules —constitutes most of the area of the vascular system and is the site of the transfer of O 2 , glucose , and enzyme substrates into the cells. The venous system returns the de-oxygenated blood to the right heart where it is pumped into the lungs to become oxygenated and CO 2 and other gaseous wastes exchanged and expelled during breathing. Blood then returns to the left side of the heart where it begins the process again.
In a normal circulatory system, the volume of blood returning to the heart each minute is approximately equal to the volume that is pumped out each minute (the cardiac output). [ 12 ] Because of this, the velocity of blood flow across each level of the circulatory system is primarily determined by the total cross-sectional area of that level.
Cardiac output is determined by two methods. One is to use the Fick equation:
C O = V O 2 / C a O 2 − C v O 2 {\displaystyle CO=VO2/C_{a}O_{2}-C_{v}O_{2}}
The other thermodilution method is to sense the temperature change from a liquid injected in the proximal port of a Swan-Ganz to the distal port.
Cardiac output is mathematically expressed by the following equation:
where
The normal human cardiac output is 5-6 L/min at rest. Not all blood that enters the left ventricle exits the heart. What is left at the end of diastole (EDV) minus the stroke volume make up the end systolic volume (ESV). [ 13 ]
Circulatory system of species subjected to orthostatic blood pressure (such as arboreal snakes) has evolved with physiological and morphological features to overcome the circulatory disturbance. For instance, in arboreal snakes the heart is closer to the head, in comparison with aquatic snakes. This facilitates blood perfusion to the brain. [ 14 ] [ 15 ]
Blood flow is also affected by the smoothness of the vessels, resulting in either turbulent (chaotic) or laminar (smooth) flow. Smoothness is reduced by the buildup of fatty deposits on the arterial walls.
The Reynolds number (denoted NR or Re) is a relationship that helps determine the behavior of a fluid in a tube, in this case blood in the vessel.
The equation for this dimensionless relationship is written as: [ 16 ]
The Reynolds number is directly proportional to the velocity and diameter of the tube. Note that NR is directly proportional to the mean velocity as well as the diameter. A Reynolds number of less than 2300 is laminar fluid flow, which is characterized by constant flow motion, whereas a value of over 4000, is represented as turbulent flow. [ 16 ] Due to its smaller radius and lowest velocity compared to other vessels, the Reynolds number at the capillaries is very low, resulting in laminar instead of turbulent flow. [ 17 ]
Often expressed in cm/s. This value is inversely related to the total cross-sectional area of the blood vessel and also differs per cross-section, because in normal condition the blood flow has laminar characteristics . For this reason, the blood flow velocity is the fastest in the middle of the vessel and slowest at the vessel wall. In most cases, the mean velocity is used. [ 18 ] There are many ways to measure blood flow velocity, like videocapillary microscoping with frame-to-frame analysis, or laser Doppler anemometry . [ 19 ] Blood velocities in arteries are higher during systole than during diastole . One parameter to quantify this difference is the pulsatility index ( PI ), which is equal to the difference between the peak systolic velocity and the minimum diastolic velocity divided by the mean velocity during the cardiac cycle . This value decreases with distance from the heart. [ 20 ]
Resistance is also related to vessel radius, vessel length, and blood viscosity.
In a first approach based on fluids, as indicated by the Hagen–Poiseuille equation . [ 16 ] The equation is as follows:
In a second approach, more realistic of the vascular resistance and coming from experimental observations on blood flows, according to Thurston, [ 22 ] there is a plasma release-cell layering at the walls surrounding a plugged flow. It is a fluid layer in which at a distance δ, viscosity η is a function of δ written as η(δ), and these surrounding layers do not meet at the vessel centre in real blood flow. Instead, there is the plugged flow which is hyperviscous because holding high concentration of RBCs. Thurston assembled this layer to the flow resistance to describe blood flow by means of a viscosity η(δ) and thickness δ from the wall layer.
The blood resistance law appears as R adapted to blood flow profile :
where
Blood resistance varies depending on blood viscosity and its plugged flow (or sheath flow since they are complementary across the vessel section) size as well, and on the size of the vessels.
Assuming steady, laminar flow in the vessel, the blood vessels behavior is similar to that of a pipe. For instance if p1 and p2 are pressures are at the ends of the tube, the pressure drop/gradient is: [ 23 ]
The larger arteries, including all large enough to see without magnification, are conduits with low vascular resistance (assuming no advanced atherosclerotic changes) with high flow rates that generate only small drops in pressure. The smaller arteries and arterioles have higher resistance, and confer the main blood pressure drop across major arteries to capillaries in the circulatory system.
In the arterioles blood pressure is lower than in the major arteries. This is due to bifurcations, which cause a drop in pressure. The more bifurcations, the higher the total cross-sectional area, therefore the pressure across the surface drops. This is why [ citation needed ] the arterioles have the highest pressure-drop. The pressure drop of the arterioles is the product of flow rate and resistance: ∆P=Q xresistance. The high resistance observed in the arterioles, which factor largely in the ∆ P is a result of a smaller radius of about 30 μm. [ 24 ] The smaller the radius of a tube, the larger the resistance to fluid flow.
Immediately following the arterioles are the capillaries. Following the logic observed in the arterioles, we expect the blood pressure to be lower in the capillaries compared to the arterioles. Since pressure is a function of force per unit area, ( P = F / A ), the larger the surface area, the lesser the pressure when an external force acts on it. Though the radii of the capillaries are very small, the network of capillaries has the largest surface area in the vascular network. They are known to have the largest surface area (485 mm^2) in the human vascular network. The larger the total cross-sectional area, the lower the mean velocity as well as the pressure. [ 25 ]
Substances called vasoconstrictors can reduce the size of blood vessels, thereby increasing blood pressure. Vasodilators (such as nitroglycerin ) increase the size of blood vessels, thereby decreasing arterial pressure.
If the blood viscosity increases (gets thicker), the result is an increase in arterial pressure. Certain medical conditions can change the viscosity of the blood. For instance, anemia (low red blood cell concentration) reduces viscosity, whereas increased red blood cell concentration increases viscosity. It had been thought that aspirin and related " blood thinner " drugs decreased the viscosity of blood, but instead studies found that they act by reducing the tendency of the blood to clot. [ 26 ]
To determine the systemic vascular resistance (SVR) the formula for calculating all resistance is used.
R = ( Δ p r e s s u r e ) / f l o w . {\displaystyle R=(\Delta pressure)/flow.}
This translates for SVR into:
S V R = ( M A P − C V P ) / C O {\displaystyle SVR=(MAP-CVP)/CO}
Where
To get this in Wood units the answer is multiplied by 80.
Normal systemic vascular resistance is between 900 and 1440 dynes/sec/cm−5. [ 28 ]
Regardless of site, blood pressure is related to the wall tension of the vessel according to the Young–Laplace equation (assuming that the thickness of the vessel wall is very small as compared to the diameter of the lumen ):
where
For the thin-walled assumption to be valid the vessel must have a wall thickness of no more than about one-tenth (often cited as one twentieth) of its radius.
The cylinder stress , in turn, is the average force exerted circumferentially (perpendicular both to the axis and to the radius of the object) in the cylinder wall, and can be described as:
where:
When force is applied to a material it starts to deform or move. As the force needed to deform a material (e.g. to make a fluid flow) increases with the size of the surface of the material A., [ 6 ] the magnitude of this force F is proportional to the area A of the portion of the surface. Therefore, the quantity (F/A) that is the force per unit area is called the stress. The shear stress at the wall that is associated with blood flow through an artery depends on the artery size and geometry and can range between 0.5 and 4 Pa . [ 29 ]
Under normal conditions, to avoid atherogenesis, thrombosis, smooth muscle proliferation and endothelial apoptosis, shear stress maintains its magnitude and direction within an acceptable range. In some cases occurring due to blood hammer, shear stress reaches larger values. While the direction of the stress may also change by the reverse flow, depending on the hemodynamic conditions. Therefore, this situation can lead to atherosclerosis disease. [ 30 ]
Veins are described as the "capacitance vessels" of the body because over 70% of the blood volume resides in the venous system. Veins are more compliant than arteries and expand to accommodate changing volume. [ 31 ]
The blood pressure in the circulation is principally due to the pumping action of the heart. [ 32 ] The pumping action of the heart generates pulsatile blood flow, which is conducted into the arteries, across the micro-circulation and eventually, back via the venous system to the heart. During each heartbeat, systemic arterial blood pressure varies between a maximum ( systolic ) and a minimum ( diastolic ) pressure. [ 33 ] In physiology, these are often simplified into one value, the mean arterial pressure (MAP) , which is calculated as follows:
M A P = D P + 1 / 3 ( P P ) {\displaystyle MAP=DP+1/3(PP)}
where:
Differences in mean blood pressure are responsible for blood flow from one location to another in the circulation. The rate of mean blood flow depends on both blood pressure and the resistance to flow presented by the blood vessels. Mean blood pressure decreases as the circulating blood moves away from the heart through arteries and capillaries due to viscous losses of energy. Mean blood pressure drops over the whole circulation, although most of the fall occurs along the small arteries and arterioles . [ 35 ] Gravity affects blood pressure via hydrostatic forces (e.g., during standing), and valves in veins, breathing , and pumping from contraction of skeletal muscles also influence blood pressure in veins. [ 32 ]
The relationship between pressure, flow, and resistance is expressed in the following equation: [ 12 ]
When applied to the circulatory system, we get:
where
A simplified form of this equation assumes right atrial pressure is approximately 0:
The ideal blood pressure in the brachial artery , where standard blood pressure cuffs measure pressure, is <120/80 mmHg. Other major arteries have similar levels of blood pressure recordings indicating very low disparities among major arteries. In the innominate artery, the average reading is 110/70 mmHg, the right subclavian artery averages 120/80 and the abdominal aorta is 110/70 mmHg. [ 25 ] The relatively uniform pressure in the arteries indicate that these blood vessels act as a pressure reservoir for fluids that are transported within them.
Pressure drops gradually as blood flows from the major arteries, through the arterioles, the capillaries until blood is pushed up back into the heart via the venules, the veins through the vena cava with the help of the muscles. At any given pressure drop, the flow rate is determined by the resistance to the blood flow. In the arteries, with the absence of diseases, there is very little or no resistance to blood. The vessel diameter is the most principal determinant to control resistance. Compared to other smaller vessels in the body, the artery has a much bigger diameter (4 mm), therefore the resistance is low. [ 25 ]
The arm–leg (blood pressure) gradient is the difference between the blood pressure measured in the arms and that measured in the legs. It is normally less than 10 mm Hg, [ 36 ] but may be increased in e.g. coarctation of the aorta . [ 36 ]
Hemodynamic monitoring is the observation of hemodynamic parameters over time, such as blood pressure and heart rate . Blood pressure can be monitored either invasively through an inserted blood pressure transducer assembly (providing continuous monitoring), or noninvasively by repeatedly measuring the blood pressure with an inflatable blood pressure cuff .
Hypertension is diagnosed by the presence of arterial blood pressures of 140/90 or greater for two clinical visits. [ 27 ]
Pulmonary Artery Wedge Pressure can show if there is congestive heart failure, mitral and aortic valve disorders, hypervolemia , shunts, or cardiac tamponade. [ 37 ]
Noninvasive hemodynamic monitoring of eye fundus vessels can be performed by Laser Doppler holography, with near infrared light. The eye offers a unique opportunity for the non-invasive exploration of cardiovascular diseases . Laser Doppler imaging by digital holography can measure blood flow in the retina and choroid , whose Doppler responses exhibit a pulse -shaped profile with time [ 38 ] [ 39 ] This technique enables non invasive functional microangiography by high-contrast measurement of Doppler responses from endoluminal blood flow profiles in vessels in the posterior segment of the eye. Differences in blood pressure drive the flow of blood throughout the circulation. The rate of mean blood flow depends on both blood pressure and the hemodynamic resistance to flow presented by the blood vessels.
The word hemodynamics ( / ˌ h iː m ə d aɪ ˈ n æ m ɪ k s , - m oʊ -/ [ 40 ] ) uses combining forms of hemo- (which comes from the ancient Greek haima , meaning blood) and dynamics , thus "the dynamics of blood ". The vowel of the hemo- syllable is variously written according to the ae/e variation . | https://en.wikipedia.org/wiki/Hemodynamics |
Hemofiltration , also haemofiltration , is a renal replacement therapy which is used in the intensive care setting. It is usually used to treat acute kidney injury (AKI), but may be of benefit in multiple organ dysfunction syndrome or sepsis . [ 1 ] During hemofiltration, a patient's blood is passed through a set of tubing (a filtration circuit ) via a machine to a semipermeable membrane (the filter ) where waste products and water (collectively called ultrafiltrate ) are removed by convection . Replacement fluid is added and the blood is returned to the patient. [ 2 ]
As in dialysis , in hemofiltration one achieves movement of solutes across a semi-permeable membrane . However, solute movement with hemofiltration is governed by convection rather than by diffusion. With hemofiltration, dialysate is not used. Instead, a positive hydrostatic pressure drives water and solutes across the filter membrane from the blood compartment to the filtrate compartment, from which it is drained. Solutes, both small and large, get dragged through the membrane at a similar rate by the flow of water that has been engendered by the hydrostatic pressure. Thus convection overcomes the reduced removal rate of larger solutes (due to their slow speed of diffusion) seen in hemodialysis.
Hemofiltration is sometimes used in combination with hemodialysis, when it is termed hemodiafiltration. Blood is pumped through the blood compartment of a high flux dialyzer, and a high rate of ultrafiltration is used, so there is a high rate of movement of water and solutes from blood to dialysate that must be replaced by substitution fluid that is infused directly into the blood line. However, dialysis solution is also run through the dialysate compartment of the dialyzer. The combination is theoretically useful because it results in good removal of both large and small molecular weight solutes. [ citation needed ]
These treatments can be given intermittently, or continuously. The latter is usually done in an intensive care unit setting. There may be little difference in clinical and health economic outcome between the two in the context of acute kidney failure. [ 3 ] [ 4 ]
Either of these treatments can be given in outpatient dialysis units, three or more times a week, usually 3–5 hours per treatment. IHDF is used almost exclusively, with only a few centers using IHF. With both IHF or IHDF, the substitution fluid is prepared on-line from dialysis solution by running dialysis solution through a set of two membranes to purify it before infusing it directly into the blood line. In the United States, regulatory agencies have not yet approved on-line creation of substitution fluid because of concerns about its purity. For this reason, hemodiafiltration, had historically never been used in an outpatient setting in the United States. [ citation needed ]
Continuous hemofiltration (CHF) was first described in a 1977 paper by Kramer et al. as a treatment for fluid overload. [ 5 ] Hemofiltration is most commonly used in an intensive care unit setting, where it is either given as 8- to 12-hour treatments, so called SLEF (slow extended hemofiltration), or as CHF (continuous hemofiltration), also sometimes called continuous veno-venous hemofiltration (CVVH) or continuous renal replacement therapy (CRRT). [ 6 ] [ 7 ] Hemodiafiltration (SLED-F or CHDF or CVVHDF) also is widely used in this fashion. In the United States, the substitution fluid used in CHF or CHDF is commercially prepared, prepackaged, and sterile (or sometimes is prepared in the local hospital pharmacy), avoiding regulatory issues of on-line creation of replacement fluid from dialysis solution.
With slow continuous therapies, the blood flow rates are usually in the range of 100-200 ml/min, and access is usually achieved through a central venous catheter placed in one of the large central veins . In such cases a blood pump is used to drive blood flow through the filter. Native access for hemodialysis (e.g. AV fistulas or grafts) are unsuitable for CHF because the prolonged residence of the access needles required might damage such accesses.
The length of time before the circuit clots and becomes unusable, often referred to as circuit life , can vary depending on the medication used to keep blood from clotting. Heparin and regional citrate are often used, though heparin carries a higher risk of bleeding. [ 8 ] However, a comprehensive analysis of audit data from intensive care units in the UK revealed that, compared with heparin, citrate-based drugs were not associated with fewer deaths among patients with acute kidney injury after 90 days of treatment. Citrate-based drugs were, however, associated with a substantially higher cost of treatment. [ 9 ] [ 10 ]
Before implementing continuous renal replacement therapy (CRRT), acute renal failure (ARF) in critically ill, multiple organ failure patients was managed by intermittent hemodialysis and the mortality rate was very high. [ 11 ] Hemodialysis is effective in clearance and ultrafiltration, but it has deleterious effects on hemodynamic stability. [ 12 ] In 1971, Lee Henderson described the basis for convective transport in blood purification techniques. Subsequently, in 1974 he described hemodiafiltration combining convection and diffusion. These seminal papers represented the basis for the development of chronic hemodiafiltration by Leber and continuous arteriovenous hemofiltration (CAVH) by Peter Kramer. [ 13 ]
With his team, Peter Kramer (Died unexpectedly in 1984), had actually first reported the use of continuous hemofiltration in Germany in 1977. [ 14 ] Peter Kramer in ASAIO presented a paper describing the use of arteriovenous hemofiltration in the management of ARF. [ 15 ] Kramer tried that as a mean of managing diuretic-resistant fluid overload. Kramer described his experience of attaching a microporous hemofilter to the femoral artery and vein, and flowing blood through it at around 100 ml/minute. Liters of plasma filtrate poured out. He replaced it with an infusion of electrolyte solution. [ 16 ] Kramer explained that this could be done continuously, avoiding the volume shifts and other problems of intermittent hemodialysis. For those in the audience who cared for patients with anuric ARF, this was an epiphany of thunderbolt proportions. [ 17 ] He used a hollow fiber “haemofilter” that originally designed as an alternative to HD for chronic renal failure and produced 300-600 ml/hour of ultrafiltrate by convection. The simple, pumpless system made use of temporary dialysis catheters sited in the patient’s femoral artery and vein and could be rapidly established in critically ill patients. [ 18 ] Kramer explained that this could be done continuously, avoiding the volume shifts and other problems of intermittent hemodialysis. For those in the audience who cared for patients with anuric ARF, this was an epiphany of thunderbolt proportions. [ 19 ] He used a hollow fiber “haemofilter” that originally designed as an alternative to HD for chronic renal failure and produced 300-600 ml/hour of ultrafiltrate by convection. The simple, pumpless system made use of temporary dialysis catheters sited in the patient’s femoral artery and vein and could be rapidly established in critically ill patients. Using an isotonic salt solution for fluid replacement, continuous arteriovenous hemofiltration (CAVH) was soon extended to the management of ARF. In 1982, Kramer presented his experience with its use in more than 150 intensive care patients at a meeting of the American Society for Artificial Internal Organs(ASAIO). [ 20 ] Before that, Henderson et al and Knopp, had studied hemofiltration in animals and as an alternative to dialysis in chronic renal failure, but it was really Peter Kramer’s report in ASAIO meeting in 1982 that stimulated many of nephrologists and intensivists to undertake the serious evaluation of CAVH in ARF in the ICU. [ 21 ]
At first, in CAVH, the prescribed ultrafiltration rate was achieved manually by arranging the filtrate bag at the right height, thereby changing the negative pressure caused by the filtrate column. The replacement fluid was also regulated manually. Few years later, CAVH was developed in several centers for managing ARF in critically ill patients with multiple organ failure. In 1986, it has been reported that CAVH improve the patient survival from 9% to 38% with full nutrition in ARF. [ 22 ] Moreover, a workshop presented at ASAIO in 1988 summarized the development and role of continuous hemofiltration. [ 23 ] Since late 1980s, continuous renal replacement therapy (CRRT) has been studied extensively. In 1982, the use of CAVH in Vicenza was extended for the first time to a neonate with the application of specific minifilters . Two years later, CAVH began to be used to treat septic patients, burn patients and patients after transplantation and cardiac surgery, even with regional citrate anticoagulation. [ 24 ] In 1986, the term continuous renal replacement therapy was applied to all these continuous approaches. [ 25 ] The technology and terminology were expanded to include slow continuous ultrafiltration for fluid removal without replacement, continuous arteriovenous hemodialysis (CAVHD), and continuous arteriovenous hemodiafiltration. [ 26 ] Meanwhile, clinical and technical limitations of CAVH spurred new research and the discovery of new treatments, leading to the development of continuous veno-venous hemofiltration (CVVH), continuous veno-venous hemodialysis (CVVHD) and continuous veno-venous hemodiafiltration (CVVHDF). The low depurative efficiency was overcome by applying filters with two ports in the dialysate/filtrate compartment and through the use of counter-current dialysate flow, allowing the addition of diffusion and the birth of continuous arteriovenous hemodiafiltration or hemodialysis (CAVHDF or CAVHD). [ 27 ]
Development of double-lumen venous catheters and peristaltic blood pumps was invented in the mid-1980s, when CVVH was proposed. The presence of a pump that generated negative pressure in part of the circuit made it necessary to add a device to detect the presence of air and a sensor to monitor the pressure in the circuit, to avoid, respectively, air embolisms and circuit explosion in case of coagulation or obstruction of the venous line. Later, ultrafiltrate and replacement pumps and a heater were added to the circuit. [ 28 ] The development of CVVH allows to increase the exchange volumes, and subsequently, the depurative efficiency. The use of counter-current dialysate flow led to further improvements and the birth of CVVHD and CVVHDF. [ 29 ] Now Continuous renal replacement therapy has become the mainstay of management of renal failure for multiple organ failure patients in the ICU. [ 30 ]
Information technology and precision medicine have recently furthered the evolution of CRRT, providing the possibility of collecting data in large databases and evaluating policies and practice patterns. The application of artificial intelligence and enhanced human intelligence programs to the analysis of big data has further moved the front of research ahead, providing the possibility of creating silica-trials and finding answers to patients’ unmet clinical needs. The opportunity to evaluate the endophenotype of the patient makes it possible to adjust treatments and techniques by implementing the concept of precision CRRT. This allows clinicians to normalize outcomes and results among different populations or individuals and establish optimal and personalized care [ 31 ] | https://en.wikipedia.org/wiki/Hemofiltration |
Hemogenic endothelium or haemogenic endothelium [ 1 ] is a special subset of endothelial cells scattered within blood vessels that can differentiate into haematopoietic cells. [ 2 ]
The development of hematopoietic cells in the embryo proceeds sequentially from mesoderm through the hemangioblast to the hemogenic endothelium and hematopoietic progenitors. [ 3 ] The relationship between the hemogenic endothelium and the hemangioblast is not clearly understood. [ 1 ]
This molecular or cell biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hemogenic_endothelium |
Hemoglobin ( haemoglobin , [ a ] Hb or Hgb ) is a protein containing iron that facilitates the transportation of oxygen in red blood cells . Almost all vertebrates contain hemoglobin, [ 3 ] with the sole exception of the fish family Channichthyidae . [ 4 ] Hemoglobin in the blood carries oxygen from the respiratory organs ( lungs or gills ) to the other tissues of the body, where it releases the oxygen to enable aerobic respiration which powers an animal's metabolism . A healthy human has 12 to 20 grams of hemoglobin in every 100 mL of blood. Hemoglobin is a metalloprotein , a chromoprotein , and a globulin .
In mammals , hemoglobin makes up about 96% of a red blood cell's dry weight (excluding water), and around 35% of the total weight (including water). [ 5 ] Hemoglobin has an oxygen-binding capacity of 1.34 mL of O 2 per gram, [ 6 ] which increases the total blood oxygen capacity seventy-fold compared to dissolved oxygen in blood plasma alone. [ 7 ] The mammalian hemoglobin molecule can bind and transport up to four oxygen molecules. [ 8 ]
Hemoglobin also transports other gases. It carries off some of the body's respiratory carbon dioxide (about 20–25% of the total) [ 9 ] as carbaminohemoglobin , in which CO 2 binds to the heme protein . The molecule also carries the important regulatory molecule nitric oxide bound to a thiol group in the globin protein, releasing it at the same time as oxygen. [ 10 ]
Hemoglobin is also found in other cells, including in the A9 dopaminergic neurons of the substantia nigra , macrophages , alveolar cells , lungs, retinal pigment epithelium, hepatocytes, mesangial cells of the kidney, endometrial cells, cervical cells, and vaginal epithelial cells. [ 11 ] In these tissues, hemoglobin absorbs unneeded oxygen as an antioxidant , and regulates iron metabolism . [ 12 ] Excessive glucose in the blood can attach to hemoglobin and raise the level of hemoglobin A1c. [ 13 ]
Hemoglobin and hemoglobin-like molecules are also found in many invertebrates, fungi, and plants. [ 14 ] In these organisms, hemoglobins may carry oxygen, or they may transport and regulate other small molecules and ions such as carbon dioxide, nitric oxide, hydrogen sulfide and sulfide. A variant called leghemoglobin serves to scavenge oxygen away from anaerobic systems such as the nitrogen-fixing nodules of leguminous plants, preventing oxygen poisoning.
The medical condition hemoglobinemia , a form of anemia , is caused by intravascular hemolysis , in which hemoglobin leaks from red blood cells into the blood plasma .
In 1825, Johann Friedrich Engelhart discovered that the ratio of iron to protein is identical in the hemoglobins of several species. [ 16 ] [ 17 ] From the known atomic mass of iron, he calculated the molecular mass of hemoglobin to n × 16000 ( n =number of iron atoms per hemoglobin molecule, now known to be 4), the first determination of a protein's molecular mass. This "hasty conclusion" drew ridicule from colleagues who could not believe that any molecule could be so large. However, Gilbert Smithson Adair confirmed Engelhart's results in 1925 by measuring the osmotic pressure of hemoglobin solutions. [ 18 ]
Although blood had been known to carry oxygen since at least 1794, [ 19 ] [ 20 ] the oxygen-carrying property of hemoglobin was described by Hünefeld in 1840. [ 21 ] In 1851, German physiologist Otto Funke published a series of articles in which he described growing hemoglobin crystals by successively diluting red blood cells with a solvent such as pure water, alcohol or ether, followed by slow evaporation of the solvent from the resulting protein solution. [ 22 ] [ 23 ] Hemoglobin's reversible oxygenation was described a few years later by Felix Hoppe-Seyler . [ 24 ]
With the development of X-ray crystallography , it became possible to solve protein structures. [ 25 ] In 1959, Max Perutz determined the molecular structure of hemoglobin. [ 26 ] [ 27 ] For this work he shared the 1962 Nobel Prize in Chemistry with John Kendrew , who sequenced the globular protein myoglobin . [ 25 ] [ 28 ]
The role of hemoglobin in the blood was elucidated by French physiologist Claude Bernard .
The name hemoglobin (or haemoglobin ) is derived from the words heme (or haem ) and globin , reflecting the fact that each subunit of hemoglobin is a globular protein with an embedded heme group. Each heme group contains one iron atom, that can bind one oxygen molecule through ion-induced dipole forces. The most common type of hemoglobin in mammals contains four such subunits. [ 29 ]
Hemoglobin consists of protein subunits ( globin molecules), which are polypeptides , long folded chains of specific amino acids which determine the protein's chemical properties and function. The amino acid sequence of any polypeptide is translated from a segment of DNA, the corresponding gene .
There is more than one hemoglobin gene. In humans, hemoglobin A (the main form of hemoglobin in adults) is coded by genes HBA1 , HBA2 , and HBB . [ 30 ] Alpha 1 and alpha 2 subunits are respectively coded by genes HBA1 and HBA2 close together on chromosome 16, while the beta subunit is coded by gene HBB on chromosome 11. The amino acid sequences of the globin subunits usually differ between species, with the difference growing with evolutionary distance. For example, the most common hemoglobin sequences in humans, bonobos and chimpanzees are completely identical, with exactly the same alpha and beta globin protein chains. [ 31 ] [ 32 ] [ 33 ] Human and gorilla hemoglobin differ in one amino acid in both alpha and beta chains, and these differences grow larger between less closely related species. [ citation needed ]
Mutations in the genes for hemoglobin can result in variants of hemoglobin within a single species, although one sequence is usually "most common" in each species. [ 34 ] [ 35 ] Many of these mutations cause no disease, but some cause a group of hereditary diseases called hemoglobinopathies . The best known hemoglobinopathy is sickle-cell disease , which was the first human disease whose mechanism was understood at the molecular level. A mostly separate set of diseases called thalassemias involves underproduction of normal and sometimes abnormal hemoglobins, through problems and mutations in globin gene regulation . All these diseases produce anemia . [ 36 ]
Variations in hemoglobin sequences, as with other proteins, may be adaptive. For example, hemoglobin has been found to adapt in different ways to the thin air at high altitudes, where lower partial pressure of oxygen diminishes its binding to hemoglobin compared to the higher pressures at sea level. Recent studies of deer mice found mutations in four genes that can account for differences between high- and low-elevation populations. It was found that the genes of the two breeds are "virtually identical—except for those that govern the oxygen-carrying capacity of their hemoglobin. . . . The genetic difference enables highland mice to make more efficient use of their oxygen." [ 37 ] Mammoth hemoglobin featured mutations that allowed for oxygen delivery at lower temperatures, thus enabling mammoths to migrate to higher latitudes during the Pleistocene . [ 38 ] This was also found in hummingbirds that inhabit the Andes. Hummingbirds already expend a lot of energy and thus have high oxygen demands and yet Andean hummingbirds have been found to thrive in high altitudes. Non-synonymous mutations in the hemoglobin gene of multiple species living at high elevations ( Oreotrochilus, A. castelnaudii, C. violifer, P. gigas, and A. viridicuada ) have caused the protein to have less of an affinity for inositol hexaphosphate (IHP), a molecule found in birds that has a similar role as 2,3-BPG in humans; this results in the ability to bind oxygen in lower partial pressures. [ 39 ]
Birds' unique circulatory lungs also promote efficient use of oxygen at low partial pressures of O 2 . These two adaptations reinforce each other and account for birds' remarkable high-altitude performance. [ citation needed ]
Hemoglobin adaptation extends to humans, as well. There is a higher offspring survival rate among Tibetan women with high oxygen saturation genotypes residing at 4,000 m. [ 40 ] Natural selection seems to be the main force working on this gene because the mortality rate of offspring is significantly lower for women with higher hemoglobin-oxygen affinity when compared to the mortality rate of offspring from women with low hemoglobin-oxygen affinity. While the exact genotype and mechanism by which this occurs is not yet clear, selection is acting on these women's ability to bind oxygen in low partial pressures, which overall allows them to better sustain crucial metabolic processes. [ citation needed ]
Hemoglobin (Hb) is synthesized in a complex series of steps. The heme part is synthesized in a series of steps in the mitochondria and the cytosol of immature red blood cells, while the globin protein parts are synthesized by ribosomes in the cytosol. [ 41 ] Production of Hb continues in the cell throughout its early development from the proerythroblast to the reticulocyte in the bone marrow . At this point, the nucleus is lost in mammalian red blood cells, but not in birds and many other species. Even after the loss of the nucleus in mammals, residual ribosomal RNA allows further synthesis of Hb until the reticulocyte loses its RNA soon after entering the vasculature (this hemoglobin-synthetic RNA in fact gives the reticulocyte its reticulated appearance and name). [ 42 ]
Hemoglobin has a quaternary structure characteristic of many multi-subunit globular proteins. [ 43 ] Most of the amino acids in hemoglobin form alpha helices , and these helices are connected by short non-helical segments. Hydrogen bonds stabilize the helical sections inside this protein, causing attractions within the molecule, which then causes each polypeptide chain to fold into a specific shape. [ 44 ] Hemoglobin's quaternary structure comes from its four subunits in roughly a tetrahedral arrangement. [ 43 ]
In most vertebrates, the hemoglobin molecule is an assembly of four globular protein subunits. Each subunit is composed of a protein chain tightly associated with a non-protein prosthetic heme group. Each protein chain arranges into a set of alpha-helix structural segments connected together in a globin fold arrangement. Such a name is given because this arrangement is the same folding motif used in other heme/globin proteins such as myoglobin . [ 45 ] [ 46 ] This folding pattern contains a pocket that strongly binds the heme group. [ citation needed ]
A heme group consists of an iron (Fe) ion held in a heterocyclic ring, known as a porphyrin . This porphyrin ring consists of four pyrrole molecules cyclically linked together (by methine bridges) with the iron ion bound in the center. [ 47 ] The iron ion, which is the site of oxygen binding, coordinates with the four nitrogen atoms in the center of the ring, which all lie in one plane. The heme is bound strongly (covalently) to the globular protein via the N atoms of the imidazole ring of F8 histidine residue (also known as the proximal histidine) below the porphyrin ring. A sixth position can reversibly bind oxygen by a coordinate covalent bond , [ 48 ] completing the octahedral group of six ligands. This reversible bonding with oxygen is why hemoglobin is so useful for transporting oxygen around the body. [ 49 ] Oxygen binds in an "end-on bent" geometry where one oxygen atom binds to Fe and the other protrudes at an angle. When oxygen is not bound, a very weakly bonded water molecule fills the site, forming a distorted octahedron .
Even though carbon dioxide is carried by hemoglobin, it does not compete with oxygen for the iron-binding positions but is bound to the amine groups of the protein chains attached to the heme groups.
The iron ion may be either in the ferrous Fe 2+ or in the ferric Fe 3+ state, but ferrihemoglobin ( methemoglobin ) (Fe 3+ ) cannot bind oxygen. [ 50 ] In binding, oxygen temporarily and reversibly oxidizes (Fe 2+ ) to (Fe 3+ ) while oxygen temporarily turns into the superoxide ion, thus iron must exist in the +2 oxidation state to bind oxygen. If superoxide ion associated to Fe 3+ is protonated, the hemoglobin iron will remain oxidized and incapable of binding oxygen. In such cases, the enzyme methemoglobin reductase will be able to eventually reactivate methemoglobin by reducing the iron center.
In adult humans, the most common hemoglobin type is a tetramer (which contains four subunit proteins) called hemoglobin A , consisting of two α and two β subunits non-covalently bound, each made of 141 and 146 amino acid residues, respectively. This is denoted as α 2 β 2 . The subunits are structurally similar and about the same size. Each subunit has a molecular weight of about 16,000 daltons , [ 51 ] for a total molecular weight of the tetramer of about 64,000 daltons (64,458 g/mol). [ 52 ] Thus, 1 g/dL=0.1551 mmol/L. Hemoglobin A is the most intensively studied of the hemoglobin molecules. [ citation needed ]
In human infants, the fetal hemoglobin molecule is made up of 2 α chains and 2 γ chains. The γ chains are gradually replaced by β chains as the infant grows. [ 53 ]
The four polypeptide chains are bound to each other by salt bridges , hydrogen bonds , and the hydrophobic effect .
In general, hemoglobin can be saturated with oxygen molecules (oxyhemoglobin), or desaturated with oxygen molecules (deoxyhemoglobin). [ 54 ]
Oxyhemoglobin is formed during physiological respiration when oxygen binds to the heme component of the protein hemoglobin in red blood cells. This process occurs in the pulmonary capillaries adjacent to the alveoli of the lungs. The oxygen then travels through the blood stream to be dropped off at cells where it is utilized as a terminal electron acceptor in the production of ATP by the process of oxidative phosphorylation . It does not, however, help to counteract a decrease in blood pH. Ventilation , or breathing, may reverse this condition by removal of carbon dioxide , thus causing a shift up in pH. [ 55 ]
Hemoglobin exists in two forms, a taut (tense) form (T) and a relaxed form (R). Various factors such as low pH, high CO 2 and high 2,3 BPG at the level of the tissues favor the taut form, which has low oxygen affinity and releases oxygen in the tissues. Conversely, a high pH, low CO 2 , or low 2,3 BPG favors the relaxed form, which can better bind oxygen. [ 56 ] The partial pressure of the system also affects O 2 affinity where, at high partial pressures of oxygen (such as those present in the alveoli), the relaxed (high affinity, R) state is favoured. Inversely, at low partial pressures (such as those present in respiring tissues), the (low affinity, T) tense state is favoured. [ 57 ] Additionally, the binding of oxygen to the iron(II) heme pulls the iron into the plane of the porphyrin ring, causing a slight conformational shift. The shift encourages oxygen to bind to the three remaining heme units within hemoglobin (thus, oxygen binding is cooperative). [ citation needed ]
Classically, the iron in oxyhemoglobin is seen as existing in the iron(II) oxidation state. However, the complex of oxygen with heme iron is diamagnetic , whereas both oxygen and high-spin iron(II) are paramagnetic . Experimental evidence strongly suggests heme iron is in the iron(III) oxidation state in oxyhemoglobin, with the oxygen existing as superoxide anion (O 2 •− ) or in a covalent charge-transfer complex. [ 58 ]
Deoxygenated hemoglobin (deoxyhemoglobin) is the form of hemoglobin without the bound oxygen. The absorption spectra of oxyhemoglobin and deoxyhemoglobin differ. The oxyhemoglobin has significantly lower absorption of the 660 nm wavelength than deoxyhemoglobin, while at 940 nm its absorption is slightly higher. This difference is used for the measurement of the amount of oxygen in a patient's blood by an instrument called a pulse oximeter . This difference also accounts for the presentation of cyanosis , the blue to purplish color that tissues develop during hypoxia . [ 59 ]
Deoxygenated hemoglobin is paramagnetic ; it is weakly attracted to magnetic fields . [ 60 ] [ 61 ] In contrast, oxygenated hemoglobin exhibits diamagnetism , a weak repulsion from a magnetic field. [ 61 ]
Scientists agree that the event that separated myoglobin from hemoglobin occurred after lampreys diverged from jawed vertebrates . [ 62 ] This separation of myoglobin and hemoglobin allowed for the different functions of the two molecules to arise and develop: myoglobin has more to do with oxygen storage while hemoglobin is tasked with oxygen transport. [ 63 ] The α- and β-like globin genes encode the individual subunits of the protein. [ 30 ] The predecessors of these genes arose through another duplication event also after the gnathosome common ancestor derived from jawless fish, approximately 450–500 million years ago. [ 62 ] Ancestral reconstruction studies suggest that the preduplication ancestor of the α and β genes was a dimer made up of identical globin subunits, which then evolved to assemble into a tetrameric architecture after the duplication. [ 64 ] The development of α and β genes created the potential for hemoglobin to be composed of multiple distinct subunits, a physical composition central to hemoglobin's ability to transport oxygen. Having multiple subunits contributes to hemoglobin's ability to bind oxygen cooperatively as well as be regulated allosterically. [ 63 ] [ 64 ] Subsequently, the α gene also underwent a duplication event to form the HBA1 and HBA2 genes. [ 65 ] These further duplications and divergences have created a diverse range of α- and β-like globin genes that are regulated so that certain forms occur at different stages of development. [ 63 ]
Most ice fish of the family Channichthyidae have lost their hemoglobin genes as an adaptation to cold water. [ 4 ]
When oxygen binds to the iron complex, it causes the iron atom to move back toward the center of the plane of the porphyrin ring (see moving diagram). At the same time, the imidazole side-chain of the histidine residue interacting at the other pole of the iron is pulled toward the porphyrin ring. This interaction forces the plane of the ring sideways toward the outside of the tetramer, and also induces a strain in the protein helix containing the histidine as it moves nearer to the iron atom. This strain is transmitted to the remaining three monomers in the tetramer, where it induces a similar conformational change in the other heme sites such that binding of oxygen to these sites becomes easier.
As oxygen binds to one monomer of hemoglobin, the tetramer's conformation shifts from the T (tense) state to the R (relaxed) state. This shift promotes the binding of oxygen to the remaining three monomers' heme groups, thus saturating the hemoglobin molecule with oxygen. [ 66 ]
In the tetrameric form of normal adult hemoglobin, the binding of oxygen is, thus, a cooperative process . The binding affinity of hemoglobin for oxygen is increased by the oxygen saturation of the molecule, with the first molecules of oxygen bound influencing the shape of the binding sites for the next ones, in a way favorable for binding. This positive cooperative binding is achieved through steric conformational changes of the hemoglobin protein complex as discussed above; i.e., when one subunit protein in hemoglobin becomes oxygenated, a conformational or structural change in the whole complex is initiated, causing the other subunits to gain an increased affinity for oxygen. As a consequence, the oxygen binding curve of hemoglobin is sigmoidal , or S -shaped, as opposed to the normal hyperbolic curve associated with noncooperative binding.
The dynamic mechanism of the cooperativity in hemoglobin and its relation with low-frequency resonance has been discussed. [ 67 ]
Besides the oxygen ligand , which binds to hemoglobin in a cooperative manner, hemoglobin ligands also include competitive inhibitors such as carbon monoxide (CO) and allosteric ligands such as carbon dioxide (CO 2 ) and nitric oxide (NO). The carbon dioxide is bound to amino groups of the globin proteins to form carbaminohemoglobin ; this mechanism is thought to account for about 10% of carbon dioxide transport in mammals. Nitric oxide can also be transported by hemoglobin; it is bound to specific thiol groups in the globin protein to form an S-nitrosothiol, which dissociates into free nitric oxide and thiol again, as the hemoglobin releases oxygen from its heme site. This nitric oxide transport to peripheral tissues is hypothesized to assist oxygen transport in tissues, by releasing vasodilatory nitric oxide to tissues in which oxygen levels are low. [ 68 ]
The binding of oxygen is affected by molecules such as carbon monoxide (for example, from tobacco smoking , exhaust gas , and incomplete combustion in furnaces). CO competes with oxygen at the heme binding site. Hemoglobin's binding affinity for CO is 250 times greater than its affinity for oxygen. [ 69 ] [ 70 ] Since carbon monoxide is a colorless, odorless, and tasteless gas, and poses a potentially fatal threat, carbon monoxide detectors have become commercially available to warn of dangerous levels in residences. When hemoglobin combines with CO, it forms a very bright red compound called carboxyhemoglobin , which may cause the skin of CO poisoning victims to appear pink in death, instead of white or blue. When inspired air contains CO levels as low as 0.02%, headache and nausea occur; if the CO concentration is increased to 0.1%, unconsciousness will follow. In heavy smokers, up to 20% of the oxygen-active sites can be blocked by CO.
In similar fashion, hemoglobin also has competitive binding affinity for cyanide (CN − ), sulfur monoxide (SO), and sulfide (S 2− ), including hydrogen sulfide (H 2 S). All of these bind to iron in heme without changing its oxidation state, but they nevertheless inhibit oxygen-binding, causing grave toxicity.
The iron atom in the heme group must initially be in the ferrous (Fe 2+ ) oxidation state to support oxygen and other gases' binding and transport (it temporarily switches to ferric during the time oxygen is bound, as explained above). Initial oxidation to the ferric (Fe 3+ ) state without oxygen converts hemoglobin into "hem i globin" or methemoglobin , which cannot bind oxygen. Hemoglobin in normal red blood cells is protected by a reduction system to keep this from happening. Nitric oxide is capable of converting a small fraction of hemoglobin to methemoglobin in red blood cells. The latter reaction is a remnant activity of the more ancient nitric oxide dioxygenase function of globins.
Carbon di oxide occupies a different binding site on the hemoglobin. At tissues, where carbon dioxide concentration is higher, carbon dioxide binds to allosteric site of hemoglobin, facilitating unloading of oxygen from hemoglobin and ultimately its removal from the body after the oxygen has been released to tissues undergoing metabolism. This increased affinity for carbon dioxide by the venous blood is known as the Bohr effect . Through the enzyme carbonic anhydrase , carbon dioxide reacts with water to give carbonic acid , which decomposes into bicarbonate and protons :
Hence, blood with high carbon dioxide levels is also lower in pH (more acidic ). Hemoglobin can bind protons and carbon dioxide, which causes a conformational change in the protein and facilitates the release of oxygen. Protons bind at various places on the protein, while carbon dioxide binds at the α-amino group. [ 71 ] Carbon dioxide binds to hemoglobin and forms carbaminohemoglobin . [ 72 ] This decrease in hemoglobin's affinity for oxygen by the binding of carbon dioxide and acid is known as the Bohr effect . The Bohr effect favors the T state rather than the R state. (shifts the O 2 -saturation curve to the right ). Conversely, when the carbon dioxide levels in the blood decrease (i.e., in the lung capillaries), carbon dioxide and protons are released from hemoglobin, increasing the oxygen affinity of the protein. A reduction in the total binding capacity of hemoglobin to oxygen (i.e. shifting the curve down, not just to the right) due to reduced pH is called the root effect . This is seen in bony fish.
It is necessary for hemoglobin to release the oxygen that it binds; if not, there is no point in binding it. The sigmoidal curve of hemoglobin makes it efficient in binding (taking up O 2 in lungs), and efficient in unloading (unloading O 2 in tissues). [ 73 ]
In people acclimated to high altitudes, the concentration of 2,3-Bisphosphoglycerate (2,3-BPG) in the blood is increased, which allows these individuals to deliver a larger amount of oxygen to tissues under conditions of lower oxygen tension . This phenomenon, where molecule Y affects the binding of molecule X to a transport molecule Z, is called a heterotropic allosteric effect. Hemoglobin in organisms at high altitudes has also adapted such that it has less of an affinity for 2,3-BPG and so the protein will be shifted more towards its R state. In its R state, hemoglobin will bind oxygen more readily, thus allowing organisms to perform the necessary metabolic processes when oxygen is present at low partial pressures. [ 74 ]
Animals other than humans use different molecules to bind to hemoglobin and change its O 2 affinity under unfavorable conditions. Fish use both ATP and GTP . These bind to a phosphate "pocket" on the fish hemoglobin molecule, which stabilizes the tense state and therefore decreases oxygen affinity. [ 75 ] GTP reduces hemoglobin oxygen affinity much more than ATP, which is thought to be due to an extra hydrogen bond formed that further stabilizes the tense state. [ 76 ] Under hypoxic conditions, the concentration of both ATP and GTP is reduced in fish red blood cells to increase oxygen affinity. [ 77 ]
A variant hemoglobin, called fetal hemoglobin (HbF, α 2 γ 2 ), is found in the developing fetus , and binds oxygen with greater affinity than adult hemoglobin. This means that the oxygen binding curve for fetal hemoglobin is left-shifted (i.e., a higher percentage of hemoglobin has oxygen bound to it at lower oxygen tension), in comparison to that of adult hemoglobin. As a result, fetal blood in the placenta is able to take oxygen from maternal blood.
Hemoglobin also carries nitric oxide (NO) in the globin part of the molecule. This improves oxygen delivery in the periphery and contributes to the control of respiration. NO binds reversibly to a specific cysteine residue in globin; the binding depends on the state (R or T) of the hemoglobin. The resulting S-nitrosylated hemoglobin influences various NO-related activities such as the control of vascular resistance, blood pressure and respiration. NO is not released in the cytoplasm of red blood cells but transported out of them by an anion exchanger called AE1 . [ 78 ]
Hemoglobin variants are a part of the normal embryonic and fetal development. They may also be pathologic mutant forms of hemoglobin in a population , caused by variations in genetics. Some well-known hemoglobin variants, such as sickle-cell anemia , are responsible for diseases and are considered hemoglobinopathies . Other variants cause no detectable pathology , and are thus considered non-pathological variants. [ 34 ] [ 79 ]
In embryos :
In fetuses:
In neonates (newborns inmmediately after birth):
Abnormal forms that occur in diseases:
When red blood cells reach the end of their life due to aging or defects, they are removed from the circulation by the phagocytic activity of macrophages in the spleen or the liver or hemolyze within the circulation. Free hemoglobin is then cleared from the circulation via the hemoglobin transporter CD163 , which is exclusively expressed on monocytes or macrophages. Within these cells the hemoglobin molecule is broken up, and the iron gets recycled. This process also produces one molecule of carbon monoxide for every molecule of heme degraded. [ 80 ] Heme degradation is the only natural source of carbon monoxide in the human body, and is responsible for the normal blood levels of carbon monoxide in people breathing normal air. [ 81 ]
The other major final product of heme degradation is bilirubin . Increased levels of this chemical are detected in the blood if red blood cells are being destroyed more rapidly than usual. Improperly degraded hemoglobin protein or hemoglobin that has been released from the blood cells too rapidly can clog small blood vessels, especially the delicate blood filtering vessels of the kidneys , causing kidney damage. Iron is removed from heme and salvaged for later use, it is stored as hemosiderin or ferritin in tissues and transported in plasma by beta globulins as transferrins . When the porphyrin ring is broken up, the fragments are normally secreted as a yellow pigment called bilirubin, which is secreted into the intestines as bile. Intestines metabolize bilirubin into urobilinogen. Urobilinogen leaves the body in faeces, in a pigment called stercobilin. Globulin is metabolized into amino acids that are then released into circulation.
Hemoglobin deficiency can be caused either by a decreased amount of hemoglobin molecules, as in anemia , or by decreased ability of each molecule to bind oxygen at the same partial pressure of oxygen. Hemoglobinopathies (genetic defects resulting in abnormal structure of the hemoglobin molecule) [ 82 ] may cause both. In any case, hemoglobin deficiency decreases blood oxygen-carrying capacity . Hemoglobin deficiency is, in general, strictly distinguished from hypoxemia , defined as decreased partial pressure of oxygen in blood, [ 83 ] [ 84 ] [ 85 ] [ 86 ] although both are causes of hypoxia (insufficient oxygen supply to tissues).
Other common causes of low hemoglobin include loss of blood, nutritional deficiency, bone marrow problems, chemotherapy, kidney failure, or abnormal hemoglobin (such as that of sickle-cell disease).
The ability of each hemoglobin molecule to carry oxygen is normally modified by altered blood pH or CO 2 , causing an altered oxygen–hemoglobin dissociation curve . However, it can also be pathologically altered in, e.g., carbon monoxide poisoning .
Decrease of hemoglobin, with or without an absolute decrease of red blood cells, leads to symptoms of anemia. Anemia has many different causes, although iron deficiency and its resultant iron deficiency anemia are the most common causes in the Western world. As absence of iron decreases heme synthesis, red blood cells in iron deficiency anemia are hypochromic (lacking the red hemoglobin pigment) and microcytic (smaller than normal). Other anemias are rarer. In hemolysis (accelerated breakdown of red blood cells), associated jaundice is caused by the hemoglobin metabolite bilirubin, and the circulating hemoglobin can cause kidney failure .
Some mutations in the globin chain are associated with the hemoglobinopathies , such as sickle-cell disease and thalassemia . Other mutations, as discussed at the beginning of the article, are benign and are referred to merely as hemoglobin variants .
There is a group of genetic disorders, known as the porphyrias that are characterized by errors in metabolic pathways of heme synthesis. King George III of the United Kingdom was probably the most famous porphyria sufferer.
To a small extent, hemoglobin A slowly combines with glucose at the terminal valine (an alpha aminoacid) of each β chain. The resulting molecule is often referred to as Hb A 1c , a glycated hemoglobin . The binding of glucose to amino acids in the hemoglobin takes place spontaneously (without the help of an enzyme) in many proteins, and is not known to serve a useful purpose. However, as the concentration of glucose in the blood increases, the percentage of Hb A that turns into Hb A 1c increases. In diabetics whose glucose usually runs high, the percent Hb A 1c also runs high. Because of the slow rate of Hb A combination with glucose, the Hb A 1c percentage reflects a weighted average of blood glucose levels over the lifetime of red cells, which is approximately 120 days. [ 87 ] The levels of glycated hemoglobin are therefore measured in order to monitor the long-term control of the chronic disease of type 2 diabetes mellitus (T2DM). Poor control of T2DM results in high levels of glycated hemoglobin in the red blood cells. The normal reference range is approximately 4.0–5.9%. Though difficult to obtain, values less than 7% are recommended for people with T2DM. Levels greater than 9% are associated with poor control of the glycated hemoglobin, and levels greater than 12% are associated with very poor control. Diabetics who keep their glycated hemoglobin levels close to 7% have a much better chance of avoiding the complications that may accompany diabetes (than those whose levels are 8% or higher). [ 88 ] In addition, increased glycated of hemoglobin increases its affinity for oxygen, therefore preventing its release at the tissue and inducing a level of hypoxia in extreme cases. [ 89 ]
Elevated levels of hemoglobin are associated with increased numbers or sizes of red blood cells, called polycythemia . This elevation may be caused by congenital heart disease , cor pulmonale , pulmonary fibrosis , too much erythropoietin , or polycythemia vera . [ 90 ] High hemoglobin levels may also be caused by exposure to high altitudes, smoking, dehydration (artificially by concentrating Hb), advanced lung disease and certain tumors. [ 53 ]
Hemoglobin concentration measurement is among the most commonly performed blood tests , usually as part of a complete blood count . For example, it is typically tested before or after blood donation . Results are reported in g / L , g/ dL or mol /L. 1 g/dL equals about 0.6206 mmol/L, although the latter units are not used as often due to uncertainty regarding the polymeric state of the molecule. [ 91 ] This conversion factor, using the single globin unit molecular weight of 16,000 Da , is more common for hemoglobin concentration in blood. For MCHC (mean corpuscular hemoglobin concentration) the conversion factor 0.155, which uses the tetramer weight of 64,500 Da, is more common. [ 92 ] Normal levels are:
Normal values of hemoglobin in the 1st and 3rd trimesters of pregnant women must be at least 11 g/dL and at least 10.5 g/dL during the 2nd trimester. [ 95 ]
Dehydration or hyperhydration can greatly influence measured hemoglobin levels. Albumin can indicate hydration status.
If the concentration is below normal, this is called anemia. Anemias are classified by the size of red blood cells, the cells that contain hemoglobin in vertebrates. The anemia is called "microcytic" if red cells are small, "macrocytic" if they are large, and "normocytic" otherwise.
Hematocrit , the proportion of blood volume occupied by red blood cells, is typically about three times the hemoglobin concentration measured in g/dL. For example, if the hemoglobin is measured at 17 g/dL, that compares with a hematocrit of 51%. [ 96 ]
Laboratory hemoglobin test methods require a blood sample (arterial, venous, or capillary) and analysis on hematology analyzer and CO-oximeter. Additionally, a new noninvasive hemoglobin (SpHb) test method called Pulse CO-Oximetry is also available with comparable accuracy to invasive methods. [ 97 ]
Concentrations of oxy- and deoxyhemoglobin can be measured continuously, regionally and noninvasively using NIRS . [ 98 ] [ 99 ] [ 100 ] [ 101 ] [ 102 ] NIRS can be used both on the head and on muscles. This technique is often used for research in e.g. elite sports training, ergonomics, rehabilitation, patient monitoring, neonatal research, functional brain monitoring, brain–computer interface , urology (bladder contraction), neurology (Neurovascular coupling) and more.
Hemoglobin mass can be measured in humans using the non-radioactive, carbon monoxide (CO) rebreathing technique that has been used for more than 100 years. With this technique, a small volume of pure CO gas is inhaled and rebreathed for a few minutes. During rebreathing, CO binds to hemoglobin present in red blood cells. Based on the increase in blood CO after the rebreathing period, the hemoglobin mass can be determined through the dilution principle. [ 103 ]
Long-term control of blood sugar concentration can be measured by the concentration of Hb A 1c . Measuring it directly would require many samples because blood sugar levels vary widely through the day. Hb A 1c is the product of the irreversible reaction of hemoglobin A with glucose. A higher glucose concentration results in more Hb A 1c . Because the reaction is slow, the Hb A 1c proportion represents glucose level in blood averaged over the half-life of red blood cells, is typically ~120 days. An Hb A 1c proportion of 6.0% or less show good long-term glucose control, while values above 7.0% are elevated. This test is especially useful for diabetics. [ c ]
The functional magnetic resonance imaging (fMRI) machine uses the signal from deoxyhemoglobin, which is sensitive to magnetic fields since it is paramagnetic. Combined measurement with NIRS shows good correlation with both the oxy- and deoxyhemoglobin signal compared to the BOLD signal . [ 104 ]
Hemoglobin can be tracked noninvasively, to build an individual data set tracking the hemoconcentration and hemodilution effects of daily activities for better understanding of sports performance and training. Athletes are often concerned about endurance and intensity of exercise. The sensor uses light-emitting diodes that emit red and infrared light through the tissue to a light detector, which then sends a signal to a processor to calculate the absorption of light by the hemoglobin protein. [ 105 ] This sensor is similar to a pulse oximeter , which consists of a small sensing device that clips to the finger.
A variety of oxygen-transport and -binding proteins exist in organisms throughout the animal and plant kingdoms. Organisms including bacteria , protozoans , and fungi all have hemoglobin-like proteins whose known and predicted roles include the reversible binding of gaseous ligands . Since many of these proteins contain globins and the heme moiety (iron in a flat porphyrin support), they are often called hemoglobins, even if their overall tertiary structure is very different from that of vertebrate hemoglobin. In particular, the distinction of "myoglobin" and hemoglobin in lower animals is often impossible, because some of these organisms do not contain muscles . Or, they may have a recognizable separate circulatory system but not one that deals with oxygen transport (for example, many insects and other arthropods ). In all these groups, heme/globin-containing molecules (even monomeric globin ones) that deal with gas-binding are referred to as oxyhemoglobins. In addition to dealing with transport and sensing of oxygen, they may also deal with NO, CO 2 , sulfide compounds, and even O 2 scavenging in environments that must be anaerobic. [ 106 ] They may even deal with detoxification of chlorinated materials in a way analogous to heme-containing P450 enzymes and peroxidases.
The structure of hemoglobins varies across species. Hemoglobin occurs in all kingdoms of organisms, but not in all organisms. Primitive species such as bacteria, protozoa, algae , and plants often have single-globin hemoglobins. Many nematode worms, molluscs , and crustaceans contain very large multisubunit molecules, much larger than those in vertebrates. In particular, chimeric hemoglobins found in fungi and giant annelids may contain both globin and other types of proteins. [ 14 ]
One of the most striking occurrences and uses of hemoglobin in organisms is in the giant tube worm ( Riftia pachyptila , also called Vestimentifera), which can reach 2.4 meters length and populates ocean volcanic vents . Instead of a digestive tract , these worms contain a population of bacteria constituting half the organism's weight. The bacteria oxidize H 2 S from the vent with O 2 from the water to produce energy to make food from H 2 O and CO 2 . The worms' upper end is a deep-red fan-like structure ("plume"), which extends into the water and absorbs H 2 S and O 2 for the bacteria, and CO 2 for use as synthetic raw material similar to photosynthetic plants. The structures are bright red due to their content of several extraordinarily complex hemoglobins that have up to 144 globin chains, each including associated heme structures. These hemoglobins are remarkable for being able to carry oxygen in the presence of sulfide, and even to carry sulfide, without being completely "poisoned" or inhibited by it as hemoglobins in most other species are. [ 107 ] [ 108 ]
Some nonerythroid cells (i.e., cells other than the red blood cell line) contain hemoglobin. In the brain, these include the A9 dopaminergic neurons in the substantia nigra , astrocytes in the cerebral cortex and hippocampus , and in all mature oligodendrocytes . [ 12 ] It has been suggested that brain hemoglobin in these cells may enable the "storage of oxygen to provide a homeostatic mechanism in anoxic conditions, which is especially important for A9 DA neurons that have an elevated metabolism with a high requirement for energy production". [ 12 ] It has been noted further that "A9 dopaminergic neurons may be at particular risk of anoxic degeneration since in addition to their high mitochondrial activity they are under intense oxidative stress caused by the production of hydrogen peroxide via autoxidation and/or monoamine oxidase (MAO)-mediated deamination of dopamine and the subsequent reaction of accessible ferrous iron to generate highly toxic hydroxyl radicals". [ 12 ] This may explain the risk of degeneration of these cells in Parkinson's disease . [ 12 ] The hemoglobin-derived iron in these cells is not the cause of the post-mortem darkness of these cells (origin of the Latin name, substantia nigra ), but rather is due to neuromelanin .
Outside the brain, hemoglobin has non-oxygen-carrying functions as an antioxidant and a regulator of iron metabolism in macrophages , [ 109 ] alveolar cells , [ 110 ] and mesangial cells in the kidney. [ 111 ]
Historically, an association between the color of blood and rust occurs in the association of the planet Mars , with the Roman god of war, since the planet is an orange-red, which reminded the ancients of blood. Although the color of the planet is due to iron compounds in combination with oxygen in the Martian soil, it is a common misconception that the iron in hemoglobin and its oxides gives blood its red color. The color is actually due to the porphyrin moiety of hemoglobin to which the iron is bound, not the iron itself, [ 112 ] although the ligation and redox state of the iron can influence the pi to pi* or n to pi* electronic transitions of the porphyrin and hence its optical characteristics.
Artist Julian Voss-Andreae created a sculpture called Heart of Steel (Hemoglobin) in 2005, based on the protein's backbone. The sculpture was made from glass and weathering steel . The intentional rusting of the initially shiny work of art mirrors hemoglobin's fundamental chemical reaction of oxygen binding to iron. [ 113 ] [ 114 ]
Montreal artist Nicolas Baier created Lustre (Hémoglobine) , a sculpture in stainless steel that shows the structure of the hemoglobin molecule. It is displayed in the atrium of McGill University Health Centre 's research centre in Montreal. The sculpture measures about 10 metres × 10 metres × 10 metres. [ 115 ] [ 116 ] | https://en.wikipedia.org/wiki/Hemoglobin |
Hemoglycin (previously termed hemolithin ) is a space polymer that is the first polymer of amino acids found in meteorites . [ 2 ] [ 3 ] [ 4 ]
Structural work has determined that its 1,494- dalton core unit ( glycine 18 / hydroxy-glycine 4 / Fe 2 O 4 ) contains iron , but not lithium , leading to the more general term hemoglycin for these molecules. [ 1 ] [ 5 ] The hemoglycin core contains a total of 22 glycine residues in an anti-parallel beta-sheet chain that is terminated at each end by an iron atom plus two oxygens . Four of these glycine residues are oxidized to hydroxy-glycine with hydroxy groups (−OH) on the alpha carbon. This structure was determined by mass spectrometry of meteoritic solvent extracts [ 1 ] [ 2 ] [ 5 ] and has been confirmed in X-ray scattering by crystals of hemoglycin, [ 6 ] and also by optical absorption . [ 3 ] Crystals show a 480 nm characteristic absorption that can only exist when hydroxy-glycine residues have R chirality and are C-terminal bonded to iron. [ 6 ]
Because hemoglycin has now been found to be the dominant polymer of amino acids in 6 different meteorites ( Allende , [ 7 ] Acfer 086 , Efremovka , Kaba , Orgueil and Sutter's Mill ), each time with the same structure, it has been proposed [ 3 ] [ 6 ] that it is produced by a process of template replication . The measured 480 nm absorbance is larger than expected for a racemic distribution of R and S chirality in the hydroxy-glycine residues, indicating an R chirality excess in the polymer. Modeling of template replication that is assumed to depend on 480 nm absorption leads to an excess of R chirality and thus is consistent with this finding.
Hemoglycin is a completely abiotic molecule that forms in molecular clouds which go on to become protoplanetary disks , long before biochemistry on exoplanets like Earth begins. Hemoglycin via its glycine could seed an exoplanet (one able to support early biochemistry), but its main function appears to be the accretion of matter via formation of an extensive low-density lattice [ 6 ] in space in a protoplanetary disk. Besides being present in carbonaceous meteorites, hemoglycin has also been extracted and crystallized from a fossil stromatolite that formed on Earth 2.1 billion years ago. [ 8 ] Potentially this fossil hemoglycin was delivered to Earth during the Late Heavy Bombardment (LHB). Data to support this is that the hemoglycin in the fossil has extraterrestrial isotopes similar to that in meteorites.
The polymer on the precambrian Earth could have driven the Great Oxygenation Event (GOE) beginning 2.4 Gya by splitting water in response to ultraviolet irradiation. Also, it could have provided an energy source to early biochemistry and/or it could have simply delivered a source of polymer glycine .
A comment from the Harvard research leader on Hemoglycin JEMMc - Hemoglycin, a space polymer of glycine and iron has been extensively characterized [1-11] and now needs to be considered in the context of 4 areas of astronomy and planetary science:
1st in astronomy, the period between Pop III and Pop II stars, when the constituent elements of hemoglycin first formed even as early as 500My into cosmic time [1].
2nd in molecular clouds and protoplanetary disks where the polymer is likely to form and function in accretion [6,9,10]. Thus, the polymer could be a major player in solar system formation throughout the Universe.
3rd after in-fall to planets like Earth, where on Earth it could have kick-started "The Great Oxygenation Event" (GOE) [9].
4th on exo-planets that evolve biochemistry like Earth, it could be asked whether the formation of DNA involves hemoglycin as a template. Guanine and cytosine nucleotide bases could form and bind to the 5nm glycine rods of in-fall hemoglycin to start the coding of glycine [12].
Hemoglycin is not a biological molecule, being outside of biochemistry, that is, abiotic. It may have first formed 500 million years into cosmic time as a structure that could absorb photons from 0.2-15 μm [7,8,9,10], be available throughout the Universe, and provide energy to drive adjacent space chemistry. On its in-fall to exo-planets like Earth it could absorb solar ultraviolet and donate energy to early chemical systems. Hemoglycin could therefore be thought of as an abiotic absorber of light, a supplier of energy and an accretor of matter.
Synthetic hemoglycin synthesis will be attempted in 2025 to aid acquisition of a refined x-ray diffraction set for its structure. Hemoglycin crystals from meteorites, and stromatolites, to date are fiber-like or multiple [6,8,9]. A comparison of the MALDI mass spectrometry fragmentation patterns [5,11] of synthetic and extracted hemoglycin will be informative. | https://en.wikipedia.org/wiki/Hemoglycin |
Hemolin is an immunoglobulin -like protein exclusively found in Lepidoptera (moths and butterflies). It was first discovered in immune-challenged pupae of Hyalophora cecropia [ 1 ] and Manduca sexta . [ 2 ]
Hemolin has a horseshoe crystal structure [ 3 ] with four domains and resembles the developmental protein neuroglian .
Hemolin increases 18-fold up to 7 mg/ml following injection of bacteria in H. cecropia . Induction of Hemolin in moths after bacterial injection have been shown in several species including Antheraea pernyi , [ 4 ] Bombyx mori , Helicoverpa zea , [ 5 ] Heliothis virescens , [ 6 ] Hyphantria cunea , [ 7 ] and Samia cynthia . [ 8 ]
Hemolin has also been suggested to participate in the immune response to virus infection [ 9 ] and shown to bind to virus particles. [ 10 ] It is expressed in response to dsRNA in a dose-dependent manner. [ 11 ] Galleria melonella responds to caffeine intake by increased Hemolin protein expression. [ 12 ]
Hemolin is thought to be a gene duplication of the developmental protein neuroglian, [ 13 ] but has lost two of the protein domains that neuroglian contains. In the potential function as a developmental protein, Hemolin has been shown to increase close to pupation in Manduca sexta , [ 14 ] and is induced during diapause and by 20-Hydroxyecdysone in Lymantria dispar . [ 15 ] RNAi of Hemolin causes malformation in H. cecropia . [ 16 ] | https://en.wikipedia.org/wiki/Hemolin |
Hemolithin (sometimes confused with the similar space polymer hemoglycin ) is a proposed protein containing iron and lithium, of extraterrestrial origin, according to an unpublished preprint . [ 1 ] [ 6 ] [ 7 ] [ 8 ] The result has not been published in any peer-reviewed scientific journal . The protein was purportedly found inside two CV3 meteorites , Allende and Acfer-086, [ 1 ] [ 2 ] [ 4 ] by a team of scientists led by Harvard University biochemist Julie McGeoch. [ 1 ] [ 2 ] The report of the discovery was met with some skepticism and suggestions that the researchers had extrapolated too far from incomplete data. [ 9 ] [ 10 ]
The detected hemolithin protein was reported to have been found inside two CV3 meteorites Allende and Acfer 086. [ 4 ] Acfer-086, where the complete molecule was detected rather than fragments (Allende), was discovered in Agemour, Algeria in 1990. [ 2 ] [ 5 ]
According to the researchers' mass spectrometry , hemolithin is largely composed of glycine and hydroxyglycine amino acids . [ 10 ] The researchers noted that the protein was related to "very high extraterrestrial" ratios of Deuterium /Hydrogen (D/H); [ 2 ] such high D/H ratios are not found anywhere on Earth, but are "consistent with long-period comets" [ 3 ] and suggest, as reported, "that the protein was formed in the proto-solar disc or perhaps even earlier, in interstellar molecular clouds that existed long before the Sun's birth". [ 2 ]
A natural development of hemolithin may have started with glycine forming first, and then later linking with other glycine molecules into polymer chains , and later still, combining with iron and oxygen atoms. The iron and oxygen atoms reside at the end of the newly found molecule. The researchers speculate that the iron oxide grouping formed at the end of the molecule may be able to absorb photons , thereby enabling the molecule to split water (H 2 O) into hydrogen and oxygen and, as a result, produce a source of energy that might be useful to the development of life . [ 2 ]
Exobiologist and chemist Jeffrey Bada expressed concerns about the possible protein discovery commenting, "The main problem is the occurrence of hydroxyglycine , which, to my knowledge, has never before been reported in meteorites or in prebiotic experiments . Nor is it found in any proteins. ... Thus, this amino acid is a strange one to find in a meteorite, and I am highly suspicious of the results." [ 10 ] Likewise, Lee Cronin of the University of Glasgow stated, "The structure makes no sense." [ 9 ]
Hemolithin is the name given to a protein molecule isolated from two CV3 meteorites, Allende and Acfer-086. Its deuterium to hydrogen ratio is 26 times terrestrial which is consistent with it having formed in an interstellar molecular cloud , or later in the protoplanetary disk at the start of the Solar System 4.567 billion years ago. The elements hydrogen, lithium, carbon , oxygen, nitrogen and iron that it is composed of, were all available for the first time 13 billion years ago after the first generation of massive stars ended in nucleosynthetic events.
The research leading to the discovery of Hemolithin started in 2007 when another protein , one of the first to form on Earth, was observed to entrap water. [ 11 ] That property being useful to chemistry before biochemistry on earth developed, theoretical enthalpy calculations on the condensation of amino acids were performed in gas phase space asking: "whether amino acids could polymerize to protein in space?" - they could, and their water of condensation aided their polymerization. [ 12 ] This led to several manuscripts of isotope and mass information on Hemolithin. [ 1 ] [ 13 ] [ 14 ] [ 15 ]
A comment from the Harvard research leader on Hemolithin/Hemoglycin JEMMc – Hemolithin is now termed hemoglycin. Hemoglycin, a space polymer of glycine and iron has been extensively characterized [1-11] and it does contain lithium in some samples [5]. The research and now needs to be considered in the context of 4 areas of astronomy and planetary science:
1st in astronomy, the period between Pop III and Pop II stars, when the constituent elements of hemoglycin first formed even as early as 500My into cosmic time [1].
2nd in molecular clouds and protoplanetary disks where the polymer is likely to form and function in accretion [6,9,10]. Thus, the polymer could be a major player in solar system formation throughout the Universe.
3rd after in-fall to planets like Earth, where on Earth it could have kick-started "The Great Oxygenation Event" (GOE) [9].
4th on exo-planets that evolve biochemistry like Earth, it could be asked whether the formation of DNA involves hemoglycin as a template. Guanine and cytosine nucleotide bases could form and bind to the 5 nm glycine rods of in-fall hemoglycin to start the coding of glycine [12].
Hemoglycin is not a biological molecule, being outside of biochemistry, that is, abiotic. It may have first formed 500 million years into cosmic time as a structure that could absorb photons from 0.2-15 μm [7,8,9,10], be available throughout the Universe, and provide energy to drive adjacent space chemistry. On its in-fall to exo-planets like Earth it could absorb solar ultraviolet and donate energy to early chemical systems. Hemoglycin could therefore be thought of as an abiotic absorber of light, a supplier of energy and an accretor of matter.
Synthetic hemoglycin synthesis will be attempted in 2025 to aid acquisition of a refined x-ray diffraction set for its structure. Hemoglycin crystals from meteorites, and stromatolites, to date are fiber-like or multiple [6,8,9]. A comparison of the MALDI mass spectrometry fragmentation patterns [5,11] of synthetic and extracted hemoglycin will be informative. | https://en.wikipedia.org/wiki/Hemolithin |
Hemolysis is the breakdown of red blood cells . The ability of bacterial colonies to induce hemolysis when grown on blood agar is used to classify certain microorganisms . This is particularly useful in classifying streptococcal species. A substance that causes hemolysis is called a hemolysin .
When alpha-hemolysis (α-hemolysis) is present, the agar under the colon
y is light and greenish. Streptococcus pneumoniae and a group of oral streptococci ( Streptococcus viridans or viridans streptococci) display alpha-hemolysis. This is sometimes called green hemolysis because of the color change in the agar. Other synonymous terms are incomplete hemolysis and partial hemolysis . Alpha-hemolysis is caused by the bacteria's production of hydrogen peroxide , which oxidizes hemoglobin and produces the green oxidized derivative methemoglobin .
Beta-hemolysis (β-hemolysis), sometimes called complete hemolysis , is a complete lysis of red cells in the media around and under the colonies: the area appears lightened (yellow) and transparent. [ 1 ] Streptolysin , an exotoxin , is the enzyme produced by the bacteria which causes the complete lysis of red blood cells. There are two types of streptolysin: streptolysin O (SLO) and streptolysin S (SLS). Streptolysin O is an oxygen-sensitive cytotoxin secreted by most Group A streptococcus (GAS) and Streptococcus dysgalactiae ; it interacts with cholesterol in the membrane of eukaryotic cells (mainly red and white blood cells, macrophages, and platelets), usually resulting in β-hemolysis under the surface of blood agar. Streptolysin S is an oxygen-stable cytotoxin also produced by most GAS strains which results in clearing on the surface of blood agar. SLS affects immune cells, including polymorphonuclear leukocytes and lymphocytes, and is thought to prevent the host immune system from clearing infection. Streptococcus pyogenes , or Group A beta-hemolytic Strep (GAS), as well as Streptococcus agalactiae display beta-hemolysis.
The hemolysis of some weakly beta-hemolytic organisms is enhanced when streaked close to certain beta hemolytic strains of Staphylococcus aureus . This phenomenon is the mechanism behind the CAMP test , [ 2 ] a test that was historically used for the identification of Streptococcus agalactiae and Listeria monocytogenes . [ 3 ] A modified version of this test called the reverse CAMP test, utilizing S. agalactiae instead of S. aureus , can also be used to identify Clostridium perfringens .
If an organism does not induce hemolysis, the agar under and around the colony is unchanged and the organism is called non-hemolytic or said to display gamma-hemolysis (γ-hemolysis). Enterococcus faecalis (formerly called "Group D Strep"), Staphylococcus saprophyticus , and Staphylococcus epidermidis display gamma-hemolysis.
When some otherwise non-hemolytic bacteria, such as strains of the cholera-causing bacteria Vibrio cholerae , are plated on blood agar, no clearings are observed surrounding the isolated colonies, but the blood surrounding larger areas of growth turns green. This process, called hemodigestion, is caused by the metabolic by-products of the bacteria in aerobic conditions. [ 4 ] | https://en.wikipedia.org/wiki/Hemolysis_(microbiology) |
Hemophagocytosis is a dangerous form of phagocytosis in which histiocytes engulf red blood cells , white blood cells , platelets , and their precursors [ 1 ] in bone marrow and other tissues.
It is part of the presentation of hemophagocytic lymphohistiocytosis and macrophage activation syndrome . It has also been seen at autopsy of people who died of COVID-19 . [ 2 ]
This article related to pathology is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hemophagocytosis |
Hemorphin-4 is an endogenous opioid peptide of the hemorphin family which possesses antinociceptive properties and is derived from the β-chain of hemoglobin in the bloodstream. [ 1 ] [ 2 ] It contains a tetrapeptide core with the amino acid sequence Tyr-Pro-Trp-Thr. Hemorphin-4 serves as a opioid receptor ligand that has affinities for the μ- , δ- , and κ-opioid receptors in the same range as the structurally related β-casomorphins , although affinity to the κ-opioid receptor is markedly higher in comparison. [ 3 ] It acts as an agonist at these sites. [ 4 ] It presents high affinity for other receptors such as angiotensin IV, bombesin subtype 3 (hBRS-3), and the corticotropin releasing factor (CRF). [ 5 ] Even though it exhibits lower binding affinity for opioid receptors relative to traditional opioid peptides such as endorphins and enkephalins ; it may still influence opioid receptor systems due to its high tissue concentration.
Hemorphin-4 also has inhibitory effects on angiotensin-converting enzyme (ACE), [ 6 ] and as a result, may play a role in the regulation of blood pressure . [ 3 ] Notably, inhibition of ACE also reduces enkephalin catabolism . [ 7 ] Upon modifications with adamantane and cyclohexane , the Hemorphin-4 analog inhibits insulin-regulated aminopeptidase (IRAP) compared to other angiotensin IV inhibitors, making it a suitable candidate for pain, anxiety, and depression therapies. [ 5 ] In binding to the μ-opioid receptor, it has significant seizure-suppressing and pain-relieving properties and reduces involuntary bladder contractions in a similar manner to classic opioids. [ 8 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hemorphin-4 |
Haemozoin is a disposal product formed from the digestion of blood by some blood-feeding parasites . These hematophagous organisms such as malaria parasites ( Plasmodium spp. ), Rhodnius and Schistosoma digest haemoglobin and release high quantities of free heme , which is the non-protein component of haemoglobin. Heme is a prosthetic group consisting of an iron atom contained in the center of a heterocyclic porphyrin ring. Free heme is toxic to cells, so the parasites convert it into an insoluble crystalline form called hemozoin. In malaria parasites, hemozoin is often called malaria pigment .
Since the formation of hemozoin is essential to the survival of these parasites, it is an attractive target for developing drugs and is much-studied in Plasmodium as a way to find drugs to treat malaria (malaria's Achilles' heel ). Several currently used antimalarial drugs , such as chloroquine and mefloquine , are thought to kill malaria parasites by inhibiting haemozoin biocrystallization .
Black-brown pigment was observed by Johann Heinrich Meckel [ 1 ] in 1847, in the blood and spleen of a person suffering from insanity. [ 2 ] However, it was not until 1849 that the presence of this pigment was connected to infection with malaria. [ 3 ] Initially, it was thought that this pigment was produced by the body in response to infection, but Charles Louis Alphonse Laveran realized in 1880 that "malaria pigment" is, instead, produced by the parasites, as they multiplied within the red blood cell . [ 4 ] The link between pigment and malaria parasites was used by Ronald Ross to identify the stages in the Plasmodium life cycle that occur within the mosquito, since, although these forms of the parasite are different in appearance to the blood stages, they still contain traces of pigment. [ citation needed ]
Later, in 1891, T. Carbone and W.H. Brown (1911) published papers linking the hemoglobin degradation with pigment production, describing the malaria pigment as a form of hematin and disproving the widely held idea that it is related to melanin . Brown observed that all melanins were bleaching rapidly with potassium permanganate, while with this reagent malarial pigment manifests not the slightest sign of a true bleach reaction. [ 5 ] [ 6 ] The name "hemozoin" was proposed by Louis Westenra Sambon . [ 7 ] In the 1930s several authors identified hemozoin as a pure crystalline form of α-hematin and showed that the substance did not contain proteins within the crystals, [ 4 ] but no explanation for the solubility differences between malaria pigment and α-hematin crystals was given. [ citation needed ]
During its intraerythrocytic asexual reproduction cycle Plasmodium falciparum consumes up to 80% of the host cell hemoglobin . [ 8 ] [ 9 ] The digestion of hemoglobin releases monomeric α-hematin ( ferriprotoporphyrin IX). This compound is toxic, since it is a pro-oxidant and catalyzes the production of reactive oxygen species . Oxidative stress is believed to be generated during the conversion of heme (ferroprotoporphyrin) to hematin (ferriprotoporphyrin). Free hematin can also bind to and disrupt cell membranes , damaging cell structures and causing the lysis of the host erythrocyte. [ 10 ] The unique reactivity of this molecule has been demonstrated in several in vitro and in vivo experimental conditions. [ 11 ]
The malaria parasite, therefore, detoxifies the hematin, which it does by biocrystallization —converting it into insoluble and chemically inert β-hematin crystals (called hemozoin). [ 13 ] [ 14 ] [ 15 ] In Plasmodium the food vacuole fills with hemozoin crystals, which are about 100–200 nanometres long and each contain about 80,000 heme molecules. [ 4 ] Detoxification through biocrystallization is distinct from the detoxification process in mammals, where an enzyme called heme oxygenase instead breaks excess heme into biliverdin , iron , and carbon monoxide . [ 16 ]
Several mechanisms have been proposed for the production of hemozoin in Plasmodium , and the area is highly controversial, with membrane lipids , [ 17 ] [ 18 ] histidine-rich proteins, [ 19 ] or even a combination of the two, [ 20 ] being proposed to catalyse the formation of hemozoin. Other authors have described a heme detoxification protein, which is claimed to be more potent than either lipids or histidine-rich proteins. [ 12 ] It is possible that many processes contribute to the formation of hemozoin. [ 21 ] The formation of hemozoin in other blood-feeding organisms is not as well-studied as in Plasmodium . [ 22 ] However, studies on Schistosoma mansoni have revealed that this parasitic worm produces large amounts of hemozoin during its growth in the human bloodstream. Although the shapes of the crystals are different from those produced by malaria parasites, [ 23 ] chemical analysis of the pigment showed that it is made of hemozoin. [ 24 ] [ 25 ] In a similar manner, the crystals formed in the gut of the kissing bug Rhodnius prolixus during digestion of the blood meal also have a unique shape, but are composed of hemozoin. [ 26 ] Hz formation in R. prolixus midgut occurs at physiologically relevant physico-chemical conditions and lipids play an important role in heme biocrystallization. Autocatalytic heme crystallization to Hz is revealed to be an inefficient process and this conversion is further reduced as the Hz concentration increases. [ 27 ]
Several other mechanisms have been developed to protect a large variety of hematophagous organisms against the toxic effects of free heme. Mosquitoes digest their blood meals
extracellularly and do not produce hemozoin. Heme is retained in the peritrophic matrix , a layer of protein and polysaccharides that covers the midgut and separates gut cells from the blood bolus. [ 28 ]
Although β-hematin can be produced in assays spontaneously at low pH , the development of a simple and reliable method to measure the production of hemozoin has been difficult. This is in part due to the continued uncertainty over what molecules are involved in producing hemozoin, and partly from the difficulty in measuring the difference between aggregated or precipitated heme, and genuine hemozoin. [ 29 ] Current assays are sensitive and accurate, but require multiple washing steps so are slow and not ideal for high-throughput screening . [ 29 ] However, some screens have been performed with these assays. [ 30 ]
β-Hematin crystals are made of dimers of hematin molecules that are, in turn, joined together by hydrogen bonds to form larger structures. In these dimers, an iron - oxygen coordinate bond links the central iron of one hematin to the oxygen of the carboxylate side-chain of the adjacent hematin. These reciprocal iron–oxygen bonds are highly unusual and have not been observed in any other porphyrin dimer. β-Hematin can be either a cyclic dimer or a linear polymer , [ 31 ] a polymeric form has never been found in hemozoin, disproving the widely held idea that hemozoin is produced by the enzyme heme-polymerase. [ 32 ]
Hemozoin crystals have a distinct triclinic structure and are weakly magnetic . The difference between diamagnetic low-spin oxyhemoglobin and paramagnetic hemozoin can be used for isolation. [ 33 ] [ 34 ] They also exhibit optical dichroism , meaning they absorb light more strongly along their length than across their width, enabling the automated detection of malaria. [ 35 ] Hemozoin is produced in a form that, under the action of an applied magnetic field , gives rise to an induced optical dichroism characteristic of the hemozoin concentration; and precise measurement of this induced dichroism ( Magnetic circular dichroism ) may be used to determine the level of malarial infection. [ 36 ]
Hemozoin formation is an excellent drug target, since it is essential to malaria parasite survival and absent from the human host. The drug target hematin is host-derived and largely outside the genetic control of the parasite, which makes the development of drug resistance more difficult. Many clinically used drugs are thought to act by inhibiting the formation of hemozoin in the food vacuole. [ 37 ] This prevents the detoxification of the heme released in this compartment, and kills the parasite. [ 38 ]
The best-understood examples of such hematin biocrystallization inhibitors are quinoline drugs such as chloroquine and mefloquine . These drugs bind to both free heme and hemozoin crystals, [ 39 ] and therefore block the addition of new heme units onto the growing crystals. The small, most rapidly growing face is the face to which inhibitors are believed to bind. [ 40 ] [ 41 ]
Hemozoin is released into the circulation during reinfection and phagocytosed in vivo and in vitro by host phagocytes and alters important functions in those cells. Most functional alterations were long-term postphagocytic effects, [ 42 ] [ 43 ] including erythropoiesis inhibition shown in vitro. [ 44 ] [ 45 ] [ 46 ] In contrast, a powerful, short-term stimulation of oxidative burst by human monocytes was also shown to occur during phagocytosis of nHZ. [ 47 ] Lipid peroxidation non-enzymatically catalysed by hemozoin iron was described in immune cells. [ 48 ] [ 49 ] Lipoperoxidation products, as hydroxyeicosatetraenoic acids (HETEs) and 4-hydroxynonenal (4-HNE), are functionally involved in immunomodulation. [ 43 ] [ 46 ] [ 49 ] [ 50 ] [ 51 ] [ 52 ] | https://en.wikipedia.org/wiki/Hemozoin |
Hemp , or industrial hemp , is a plant in the botanical class of Cannabis sativa cultivars grown specifically for industrial and consumable use. It can be used to make a wide range of products. [ 1 ] Along with bamboo , hemp is among the fastest growing plants on Earth. [ 2 ] It was also one of the first plants to be spun into usable fiber 50,000 years ago. [ 3 ] It can be refined into a variety of commercial items, including paper , rope , textiles , clothing , biodegradable plastics , paint , insulation , biofuel , food , and animal feed . [ 4 ] [ 5 ]
Although chemotype I cannabis and hemp (types II, III, IV, V) are both Cannabis sativa and contain the psychoactive component tetrahydrocannabinol (THC), they represent distinct cultivar groups, typically with unique phytochemical compositions and uses. [ 6 ] Hemp typically has lower concentrations of total THC and may have higher concentrations of cannabidiol (CBD), which potentially mitigates the psychoactive effects of THC. [ 7 ] The legality of hemp varies widely among countries. Some governments regulate the concentration of THC and permit only hemp that is bred with an especially low THC content into commercial production. [ 8 ] [ 9 ]
The etymology is uncertain but there appears to be no common Proto-Indo-European source for the various forms of the word; the Greek term κάνναβις ( kánnabis ) is the oldest attested form, which may have been borrowed from an earlier Scythian or Thracian word. [ 10 ] [ 11 ] Then it appears to have been borrowed into Latin , and separately into Slavic and from there into Baltic , Finnish , and Germanic languages . [ 12 ]
In the Germanic languages, following Grimm's law , the "k" would have changed to "h" with the first Germanic sound shift, [ 10 ] [ 13 ] giving Proto-Germanic * hanapiz , after which it may have been adapted into the Old English form, hænep , henep . [ 10 ] Barber (1991) however, argued that the spread of the name "kannabis" was due to its historically more recent plant use, starting from the south, around Iran, whereas non-THC varieties of hemp are older and prehistoric. [ 12 ] Another possible source of origin is Assyrian qunnabu , which was the name for a source of oil, fiber , and medicine in the 1st millennium BC. [ 12 ]
Cognates of hemp in other Germanic languages include Dutch hennep , Danish and Norwegian hamp , Saterland Frisian Hoamp , German Hanf , Icelandic hampur and Swedish hampa . In those languages "hemp" can refer to either industrial fiber hemp or narcotic cannabis strains. [ 10 ]
Hemp is used to make a variety of commercial and industrial products, including rope, textiles, clothing , shoes, food, paper, bioplastics , insulation, and biofuel. [ 4 ] The bast fibers can be used to make textiles that are 100% hemp, but they are commonly blended with other fibers, such as flax , cotton or silk, as well as virgin and recycled polyester, to make woven fabrics for apparel and furnishings. The inner two fibers of the plant are woodier and typically have industrial applications, such as mulch, animal bedding, and litter. When oxidized (often erroneously referred to as "drying"), hemp oil from the seeds becomes solid and can be used in the manufacture of oil-based paints, in creams as a moisturizing agent, for cooking, and in plastics. Hemp seeds have been used in bird feed mix as well. A survey in 2003 showed that more than 95% of hemp seed sold in the European Union was used in animal and bird feed. [ 14 ]
Hemp seeds can be eaten raw, ground into hemp meal, sprouted or made into dried sprout powder. Hemp seeds can also be made into a slurry used for baking or for beverages, such as hemp milk and tisanes . [ 17 ] Hemp oil is cold-pressed from the seed and is high in unsaturated fatty acids . [ 18 ]
In the UK, the Department for Environment, Food and Rural Affairs treats hemp as a purely non-food crop , but with proper licensing and proof of less than 0.3% THC concentration, hemp seeds can be imported for sowing or for sale as a food or food ingredient. [ 19 ] In the US, hemp can be used legally in food products and, as of 2000 [update] , was typically sold in health food stores or through mail order . [ 18 ]
A 100-gram ( 3 + 1 ⁄ 2 -ounce) portion of hulled hemp seeds supplies 2,451 kilojoules (586 kilocalories) of food energy . They contain 5% water, 5% carbohydrates , 49% total fat, and 31% protein . [ 20 ]
The share of protein obtained from the hemp seeds can be increased by processing the seeds, such as by dehulling the seeds, or by using the meal or cake (also called hemp seed flour), [ 21 ] that is, the remaining fraction of hemp seed obtained after expelling its oil fraction. [ 22 ] [ 23 ] The proteins are mostly located in the inner layer of the seed, whereas the hull is poor in proteins, as it mostly contains the fiber. [ 23 ] [ 24 ]
Hemp seeds are notable in providing 64% of the Daily Value (DV) of protein per 100-gram serving. [ 20 ] The three main proteins in hemp seeds are edestin (83% of total protein content), albumin (13%) and ß-conglycinin (up to 5%). [ 25 ] [ 23 ] Hemp seed proteins are highly digestible compared to soy proteins when untreated (unheated). [ 26 ] [ 23 ] The amino acid profile of hemp seeds is comparable to the profiles of other protein-rich foods, such as meat, milk, eggs, and soy. [ 27 ] [ 24 ] [ 28 ] Protein digestibility-corrected amino acid scores were 0.49–0.53 for whole hemp seed, 0.46–0.51 for hemp seed meal, and 0.63–0.66 for hulled hemp seed. [ 21 ] [ 29 ] The most abundant amino acid in hemp seed is glutamic acid (3.74–4.58% of whole seed) followed by arginine (2.28–3.10% of whole seed). [ 22 ] [ 23 ] [ 24 ] The whole hemp seed can be considered a rich-protein source containing a protein amount higher or similar than other protein-rich products, such as quinoa (13.0%), chia seeds (18.2–19.7%), buckwheat seeds (27.8%) and linseeds (20.9%). Nutritionally, the protein fraction of hemp seed is highly digestible comparing to other plant-based proteins such as soy protein. Hemp seed protein has a good profile of essential amino acids, still, this profile of amino acids is inferior to that of soy or casein. [ 23 ] [ 24 ] [ 30 ]
Hemp seeds are a rich source of dietary fiber (20% DV), B vitamins , and the dietary minerals manganese (362% DV), phosphorus (236% DV), magnesium (197% DV), zinc (104% DV), and iron (61% DV). About 73% of the energy in hemp seeds is in the form of fats and essential fatty acids , [ 20 ] mainly polyunsaturated fatty acids , linoleic , oleic , and alpha-linolenic acids. [ 24 ] [ 28 ] The ratio of the 38.100 grams of polyunsaturated fats per 100 grams is 9.301 grams of omega-3 to 28.698 grams of omega-6. [ 31 ] Typically, the portion suggested on packages for an adult is 30 grams, approximately three tablespoons. [ 31 ]
With its gluten content as low as 4.78 ppm, hemp is attracting attention as a gluten-free (<20 ppm) food material. [ 25 ]
Despite the rich nutrient content of hemp seeds, the seeds contain antinutritional compounds , including phytic acid , [ 32 ] trypsin inhibitors, and tannins , in statistically significant concentrations. [ 26 ] [ 33 ]
Hemp oil oxidizes and turns rancid within a short period of time if not stored properly; [ 18 ] its shelf life is extended when it is stored in a dark airtight container and refrigerated. Both light and heat can degrade hemp oil.
Hemp fiber has been used extensively throughout history, with production climaxing soon after being introduced to the New World. For centuries, items ranging from rope, to fabrics, to industrial materials were made from hemp fiber. Hemp was also commonly used to make sail canvas . The word "canvas" is derived from the word cannabis . [ 34 ] [ 35 ] Pure hemp has a texture similar to linen . [ 36 ] Because of its versatility for use in a variety of products, today hemp is used in a number of consumer goods, including clothing, shoes, accessories, dog collars, and home wares. For clothing, in some instances, hemp is mixed with lyocell . [ 37 ] Its benefits in terms for sustainability also increase its appeal in industries, such as the clothing industry. [ 38 ] [ 39 ]
Hemp as a building construction material provides solutions to a variety of issues facing current building standards. Its light weight, mold resistance, breathability, etc. makes hemp products versatile in a multitude of uses. [ 40 ] Following the co-heating tests of NNFCC Renewable House at the Building Research Establishment (BRE), hemp is reported to be a more sustainable material of construction in comparison to most building methods used today. [ 41 ] In addition, its practical use in building construction could result in the reduction of both energy consumption costs and the creation of secondary pollutants. [ 41 ]
In 2022, hemp-lime, also known as hempcrete , was accepted as a building material, along with methodologies for its use, by the International Code Council , [ 42 ] and was included in the 2024 edition of the International Residential Code as an appendix: "Appendix BL Hemp-Lime (Hempcrete) Construction". [ 43 ] This inclusion in the IRC model code is expected to promote expansion of the use and legitimacy of hemp-lime in construction in the United States. [ 44 ]
The hemp market was at its largest during the 17th century. In the 19th century and onward, the market saw a decline during its rapid illegalization in many countries . [ 45 ] Hemp has resurfaced in green building construction, primarily in Europe. [ 46 ] The modern-day disputes regarding the legality of hemp lead to its main disadvantages: importing and regulating costs. Final Report on the Construction of the Hemp Houses at Haverhill , UK conducts that hemp construction exceeds the cost of traditional building materials by £48per square meter. [ 46 ]
Currently, the University of Bath researches the use of hemp-lime panel systems for construction. Funded by the European Union , the research tests panel design within their use in high-quality construction, on site assembly, humidity and moisture penetration, temperature change, daily performance and energy saving documentations. [ 47 ] The program, focusing on Britain, France, and Spain markets aims to perfect protocols of use and application, manufacturing, data gathering, certification for market use, as well as warranty and insurance. [ 47 ]
The most common use of hemp-lime in building is by casting the hemp-hurd and lime mix while wet around a timber frame with temporary shuttering and tamping the mix to form a firm mass. After the removal of the temporary shuttering, the solidified hemp mix is then ready to be plastered with lime plaster. [ 48 ]
Hemp is classified under the green category of building design, primarily due to its positive effects on the environment. [ 49 ] A few of its benefits include but are not limited to the suppression of weed growth, anti-erosion, reclamation properties, and the ability to remove poisonous substances and heavy metals from soil. [ 49 ]
The use of hemp is beginning to gain popularity alongside other natural materials. This is because cannabis processing is done mechanically with minimal harmful effects on the environment. A part of what makes hemp sustainable is its minimal water usage and non-reliance on pesticides for proper growth. It is recyclable, non- toxic , and biodegradable , making hemp a popular choice in green building construction. [ 49 ]
Hemp fiber is known to have high strength and durability, and has been known to be a good protector against vermin. The fiber has the capability to reinforce structures by embossing threads and cannabis shavers. Hemp has been involved more recently in the building industry, producing building construction materials including insulation , hempcrete , and varnishes. [ 40 ] [ 50 ] [ 51 ] [ 52 ] [ 53 ] [ 54 ]
Hemp made materials have low embodied energy. The plant has the ability to absorb large amounts of CO 2 , providing air quality, thermal balance, creating a positive environmental impact. [ 50 ]
Hemp's properties allow mold resistance, and its porous materiality makes the building materials made of it breathable. In addition hemp possesses the ability to absorb and release moisture without deteriorating. Hemp can be non-flammable if mixed with lime and could be applied on numerous aspects of the building (wall, roofs, etc.) due to its lightweight properties. [ 49 ] [ 50 ]
Hemp is commonly used as an insulation material. Its flexibility and toughness during compression allows for easier implementation within structural framing systems. The insulation material could also be easily adjusted to different sizes and shapes by being cut during the installation process. The ability to not settle and therefore avoiding cavity developments lowers its need for maintenance. [ 54 ]
Hemp insulation is naturally lightweight and non- toxic , allowing for an exposed installation in a variety of spaces, including flooring, walling, and roofing. Compared to mineral insulation, hemp absorbs roughly double the amount of heat and could be compared to wood, in some cases even overpassing some of its types. [ 54 ]
Hemp insulation's porous materiality allows for air and moisture penetration, with a bulk density going up to 20% without losing any thermal properties. In contrast, the commonly used mineral insulation starts to fail after 2%. The insulation evenly distributes vapor and allows for air circulation, constantly carrying out used air and replacing with fresh. Its use on the exterior of the structure, overlaid with breathable water-resistive barriers, eases the withdrawal of moisture from within the wall structure. [ 54 ]
In addition, the insulation doubles as a sound barrier, weakening airborne sound waves passing through it. [ 54 ]
In addition to the CO 2 absorbed during its growth period, hemp-lime, also known as hempcrete, continues absorption during the curing process. The mixture hardens when the silica contained in hemp shives mixes with hydraulic lime , resulting in the mineralization process called "carbonation". [ dubious – discuss ] [ 53 ] [ 55 ]
Though not a load-bearing material, [ 56 ] hempcrete is most commonly used as infill in building construction due to its light weight (roughly seven times lighter than common concrete) and vapor permeability. [ 57 ] The building material is made of hemp hurds (shiv or shives), hydraulic lime , and water mixed in varying ratios. [ 52 ] The mix depends on the use of the material within the structure and could differ in physical properties. Surfaces such as flooring interact with a multitude of loads and would have to be more resistive, while walls and roofs are required to be more lightweight. [ 52 ] The application of this material in construction requires minimal skill. [ 52 ]
Hempcrete can be formed in-situ or formed into blocks. Such blocks are not strong enough to be used for structural elements and must be supported by brick, wood, or steel framing. [ 41 ] In the end of the twentieth century, during his renovation of Maison de la Turquie in Nogent-sur-Seine, France , Charles Rasetti first invented and applied the use of hempcrete in construction. [ 58 ] Shortly after, in the 2000s, Modece Architects used hemp-lime for test designs in Haverhill . [ 59 ] The dwellings were studied and monitored for comparison with other building performances by BRE . Completed in 2009, the Center for the Built Environment's Renewable House was found to be among the most technologically advanced structures made of hemp-based material. A year later the first home made of hemp-based materials was completed in Asheville, North Carolina, US. [ 60 ]
Cannabis seeds have high-fat content and contain 30-35% of fatty acids. The extracted oil is suited for a variety of construction applications. [ 50 ] The biodegradable hemp oil acts as a wood varnish, protecting flooring from mold, pests, and wear. Its use prevents the water from penetrating the wood while still allowing air and vapor to pass through. [ 40 ] Its most common use can be seen in wood framing construction, one of the most common construction methods in the world. Because of its low UV-resistant rating, the finish is most often used indoors, on surfaces such as flooring and wood paneling. [ 54 ] [ 40 ]
Hemp-based insulating plaster is created by combining hemp fibers with calcium lime and sand . This material, when applied on internal walls, ceilings, and flooring, can be layered up to ten centimeters in thickness. Its porous materiality allows the created plaster to regulate air humidity and evenly distribute it. [ 40 ] The gradual absorption and release of water prevent the material from cracking and breaking apart. [ 61 ] [ 40 ] Similar to high-density fiber cement, hemp plaster can naturally vary in color and be manually pigmented. [ 62 ]
Hemp ropes can be woven in various diameters, possessing high amounts of strength making them suitable for a variety of uses for building construction purposes. [ 53 ] Some of these uses include installation of frames in building openings and connection of joints. The ropes also used in bridge construction, tunnels, traditional homes, etc. [ 53 ] One of the earliest examples of hemp rope and other textile use can be traced back to 1500 BC Egypt . [ 63 ]
Cannabis geotextiles could be put in both wet and dry conditions. Hemp-based bioplastic is a biodegradable alternative to regular plastic and can potentially replace polyvinyl chloride (PVC), a material used for plumbing pipes. [ 53 ]
Hemp growth lasts roughly 100 days, a much faster time period than an average tree used for construction purposes. While dry, the fibers could be pressed into tight wood alternatives to wood-frame construction, wall/ceiling paneling, and flooring. As an addition, hemp is flexible and versatile allowing it to be used in a greater number of ways than wood. [ 40 ] Similarly, hemp wood could also be made of recycled hemp-based paper. [ 64 ]
A mixture of fiberglass , hemp fiber, kenaf , and flax has been used since 2002 to make composite panels for automobiles. [ 65 ] The choice of which bast fiber to use is primarily based on cost and availability.
Various car makers are beginning to use hemp in their cars, including Audi , BMW , Ford , GM , Chrysler , Honda , Iveco , Lotus , Mercedes , Mitsubishi , Porsche , Saturn , Volkswagen [ 66 ] and Volvo. For example, the Lotus Eco Elise [ 67 ] and the Mercedes C-Class both contain hemp (up to 20 kg in each car in the case of the latter). [ 68 ]
Hemp paper are paper varieties consisting exclusively or to a large extent from pulp obtained from fibers of industrial hemp . The products are mainly specialty papers such as cigarette paper , [ 69 ] banknotes and technical filter papers . [ 70 ] Compared to wood pulp, hemp pulp offers a four to five times longer fiber, a significantly lower lignin fraction as well as a higher tear resistance and tensile strength . However, production costs are about four times higher than for paper from wood, [ 71 ] since the infrastructure for using hemp is underdeveloped. If the paper industry were to switch from wood to hemp for sourcing its cellulose fibers, the following benefits could be utilized:
However, hemp has had a hard time competing with paper from trees or recycled newsprint. Only the outer part of the stem consists mainly of fibers which are suitable for the production of paper. Numerous attempts have been made to develop machines that efficiently and inexpensively separate useful fibers from less useful fibers, but none have been completely successful. This has meant that paper from hemp is still expensive compared to paper from trees.
Hemp jewelry is the product of knotting hemp twine through the practice of macramé . Hemp jewelry includes bracelets, necklaces, anklets, rings, watches, and other adornments. Some jewelry features beads made from crystals, glass, stone , wood and bones . The hemp twine varies in thickness and comes in a variety of colors. There are many different stitches used to create hemp jewelry, however, the half knot and full knot stitches are most common.
Hemp rope was used in the age of sailing ships , though the rope had to be protected by tarring , since hemp rope has a propensity for breaking from rot , as the capillary effect of the rope-woven fibers tended to hold liquid at the interior, while seeming dry from the outside. [ 77 ] Tarring was a labor-intensive process, and earned sailors the nickname " Jack Tar ". Hemp rope was phased out when manila rope , which does not require tarring, became widely available. [ citation needed ] Manila is sometimes referred to as Manila hemp , but is not related to hemp; it is abacá , a species of banana.
Hemp shives are the core of the stem, hemp hurds are broken parts of the core. In the EU, they are used for animal bedding (horses, for instance), or for horticultural mulch. [ 78 ] Industrial hemp is much more profitable if both fibers and shives (or even seeds) can be used.
Hemp can be used as a "mop crop" to clear impurities out of wastewater, such as sewage effluent, excessive phosphorus from chicken litter, or other unwanted substances or chemicals. Additionally, hemp is being used to clean contaminants at the Chernobyl nuclear disaster site, by way of a process which is known as phytoremediation – the process of clearing radioisotopes and a variety of other toxins from the soil, water, and air. [ 79 ]
Hemp crops are tall, have thick foliage, and can be planted densely, and thus can be grown as a smother crop to kill tough weeds. [ 80 ] Using hemp this way can help farmers avoid the use of herbicides, gain organic certification , and gain the benefits of crop rotation . However, due to the plant's rapid and dense growth characteristics, some jurisdictions consider hemp a prohibited and noxious weed, much like Scotch Broom . [ 81 ]
Biodiesel can be made from the oils in hemp seeds and stalks; this product is sometimes called "hempoline". [ 82 ] Alcohol fuel (ethanol or, less commonly, methanol) can be made by fermenting the whole plant.
Filtered hemp oil can be used directly to power diesel engines . In 1892, Rudolf Diesel invented the diesel engine, which he intended to power "by a variety of fuels, especially vegetable and seed oils, which earlier were used for oil lamps , i.e. the Argand lamp ". [ 83 ] [ 84 ] [ 85 ]
Production of vehicle fuel from hemp is very small. Commercial biodiesel and biogas is typically produced from cereals, coconuts, palm seeds, and cheaper raw materials like garbage, wastewater, dead plant and animal material, animal feces and kitchen waste. [ 86 ]
Separation of hurd and bast fiber is known as decortication . Traditionally, hemp stalks would be water- retted first before the fibers were beaten off the inner hurd by hand, a process known as scutching . As mechanical technology evolved, separating the fiber from the core was accomplished by crushing rollers and brush rollers, or by hammer-milling, wherein a mechanical hammer mechanism beats the hemp against a screen until hurd, smaller bast fibers, and dust fall through the screen. After the Marijuana Tax Act was implemented in 1938, the technology for separating the fibers from the core remained "frozen in time". Recently, new high-speed kinematic decortication has come about, capable of separating hemp into three streams; bast fiber, hurd, and green microfiber.
Only in 1997, did Ireland, parts of the Commonwealth and other countries begin to legally grow industrial hemp again. Iterations of the 1930s decorticator have been met with limited success, along with steam explosion and chemical processing known as thermomechanical pulping . [ citation needed ]
Hemp is usually planted between March and May in the northern hemisphere, between September and November in the southern hemisphere. [ 87 ] It matures in about three to four months, depending on various conditions.
Millennia of selective breeding have resulted in varieties that display a wide range of traits; e.g. suited for particular environments/latitudes, producing different ratios and compositions of terpenoids and cannabinoids (CBD, THC, CBG, CBC, CBN...etc.), fiber quality, oil/seed yield, etc. Hemp grown for fiber is planted closely, resulting in tall, slender plants with long fibers. [ 88 ]
The use of industrial hemp plant and its cultivation was commonplace until the 1900s when it was associated with its genetic sibling a.k.a. Drug-Type Cannabis species (which contain higher levels of psychoactive THC). Influential groups misconstrued hemp as a dangerous "drug", [ 89 ] even though hemp is not a recreational drug and has the potential to be a sustainable and profitable crop for many farmers due to hemp's medical, structural and dietary uses. [ 90 ] [ 91 ] In the United States, the public's perception of hemp as marijuana has blocked hemp from becoming a useful crop and product," [ 90 ] in spite of its vital importance prior to World War II. [ 91 ]
Ideally, according to Britain's Department for Environment, Food and Rural Affairs , the herb should be desiccated and harvested toward the end of flowering. This early cropping reduces the seed yield but improves the fiber yield and quality. [ 92 ]
The seeds are sown with grain drills or other conventional seeding equipment to a depth of 13 to 25 mm ( 1 ⁄ 2 to 1 in). Greater seeding depths result in increased weed competition. Nitrogen should not be placed with the seed, but phosphate may be tolerated. The soil should have available 89 to 135 kg/ha of nitrogen, 46 kg/ha phosphorus, 67 kg/ha potassium, and 17 kg/ha sulfur. Organic fertilizers such as manure are one of the best methods of weed control. [ 93 ]
In contrast to cannabis for medical use, varieties grown for fiber and seed have less than 0.3% THC and are unsuitable for producing hashish and marijuana. [ 94 ] Present in industrial hemp, cannabidiol is a major constituent among some 560 compounds found in hemp. [ 95 ]
Cannabis sativa L. subsp. sativa var. sativa is the variety grown for industrial use, while C. sativa subsp. indica generally has poor fiber quality and female buds from this variety are primarily used for recreational and medicinal purposes. The major differences between the two types of plants are the appearance, and the amount of Δ 9 - tetrahydrocannabinol (THC) secreted in a resinous mixture by epidermal hairs called glandular trichomes , although they can also be distinguished genetically. [ 94 ] [ 96 ] Oilseed and fiber varieties of Cannabis approved for industrial hemp production produce only minute amounts of this psychoactive drug, not enough for any physical or psychological effects. Typically, hemp contains below 0.3% THC, while cultivars of Cannabis grown for medicinal or recreational use can contain anywhere from 2% to over 20%. [ 97 ]
Smallholder plots are usually harvested by hand. The plants are cut at 2 to 3 cm above the soil and left on the ground to dry. Mechanical harvesting is now common, using specially adapted cutter-binders or simpler cutters.
The cut hemp is laid in swathes to dry for up to four days. This was traditionally followed by retting , either water retting (the bundled hemp floats in water) or dew retting (the hemp remains on the ground and is affected by the moisture in dew and by molds and bacterial action).
Several arthropods can cause damage or injury to hemp plants, but the most serious species are associated with the Insecta class. The most problematic for outdoor crops are the voracious stem-boring caterpillars, which include the European corn borer , Ostrinia nubilalis, and the Eurasian hemp borer, Grapholita delineana. [ 98 ] A s the names imply, they target the stems reducing the structural integrity of the plant. [ 98 ] Another lepidopteran, the corn earworm, Helicoverpa zea , is known to damage flowering parts and can be challenging to control. [ 99 ] Other foliar pests, found in both indoor and outdoor crops, include the hemp russet mite, Aculops cannibicola, and cannabis aphid, Phorodon cannabis. [ 99 ] They cause injury by reducing plant vigor because they feed on the phloem of the plant. Root feeders can be difficult to detect and control because of their below surface habitat. A number of beetle grubs and chafers are known to cause damage to hemp roots, including the flea beetle and Japanese beetle , Popillia Japonica . [ 98 ] The rice root aphid , Rhopalosiphum rufiabdominale, has also been reported but primarily affects indoor growing facilities. [ 99 ] Integrated pest management strategies should be employed to manage these pests with prevention and early detection being the foundation of a resilient program. Cultural and physical controls should be employed in conjunction with biological pest controls , chemical applications should only be used as a last resort.
Hemp plants can be vulnerable to various pathogens , including bacteria, fungi, nematodes , viruses and other miscellaneous pathogens. Such diseases often lead to reduced fiber quality, stunted growth, and death of the plant. These diseases rarely affect the yield of a hemp field, so hemp production is not traditionally dependent on the use of pesticides.
Hemp is considered by a 1998 study in Environmental Economics to be environmentally friendly due to a decrease of land use and other environmental impacts, indicating a possible decrease of ecological footprint in a US context compared to typical benchmarks. [ 100 ] A 2010 study, however, that compared the production of paper specifically from hemp and eucalyptus concluded that "industrial hemp presents higher environmental impacts than eucalyptus paper"; however, the article also highlights that "there is scope for improving industrial hemp paper production". [ 101 ] Hemp is also claimed to require few pesticides and no herbicides, and it has been called a carbon negative raw material. [ 102 ] [ 103 ] Results indicate that high yield of hemp may require high total nutrient levels (field plus fertilizer nutrients) similar to a high yielding wheat crop. [ 104 ] A United Nations report endorses the versatility and sustainability of hemp and its productive potential in developing countries. Hemp uses a quarter of the water required by cotton, and absorbs more carbon dioxide than other crops and most trees. [ 105 ]
The world-leading producer of hemp is China, which produces more than 70% of the world output. France ranks second with about a quarter of the world production. Smaller production occurs in the rest of Europe, Chile, and North Korea . Over 30 countries produce industrial hemp, including Australia, Austria , Canada, Chile, China, Denmark , Egypt , Finland , Germany, Greece , [ 106 ] Hungary , India, Italy, Japan, Korea , Netherlands , New Zealand, Poland , Portugal , Romania , Russia, Slovenia , Spain, Sweden, Switzerland , Thailand , Turkey , the United Kingdom and Ukraine . [ 107 ] [ 108 ]
The United Kingdom and Germany resumed commercial production in the 1990s. British production is mostly used as bedding for horses; other uses are under development. Companies in Canada, the UK, the United States, and Germany, among many others, process hemp seed into a growing range of food products and cosmetics; many traditional growing countries continue to produce textile-grade fiber.
Air-dried stem yields in Ontario have from 1998 and onward ranged from 2.6 to 14.0 tons of dry, retted stalks per hectare (1–5.5 t/ac) at 12% moisture. Yields in Kent County, have averaged 8.75 t/ha (3.5 t/ac). Northern Ontario crops averaged 6.1 t/ha (2.5 t/ac) in 1998. Statistic for the European Union for 2008 to 2010 say that the average yield of hemp straw has varied between 6.3 and 7.3 ton per ha. [ 109 ] [ 110 ] Only a part of that is bast fiber. Around one ton of bast fiber and 2–3 tons of core material can be decorticated from 3–4 tons of good-quality, dry-retted straw. For an annual yield of this level is it in Ontario recommended to add nitrogen (N):70–110 kg/ha, phosphate (P 2 O 5 ): up to 80 kg/ha and potash (K 2 O): 40–90 kg/ha. [ 111 ] The average yield of dry hemp stalks in Europe was 6 ton/ha (2.4 ton/ac) in 2001 and 2002. [ 14 ]
FAO argue that an optimum yield of hemp fiber is more than 2 tons per ha, while average yields are around 650 kg/ha. [ 112 ]
In the Australian states of Tasmania , Victoria, Queensland , Western Australia , New South Wales , and most recently, South Australia , the state governments have issued licenses to grow hemp for industrial use. The first to initiate modern research into the potential of cannabis was the state of Tasmania, which pioneered the licensing of hemp during the early 1990s. The state of Victoria was an early adopter in 1998, and has reissued the regulation in 2008. [ 113 ]
Queensland has allowed industrial production under license since 2002, [ 114 ] where the issuance is controlled under the Drugs Misuse Act 1986. [ 115 ] Western Australia enabled the cultivation, harvest and processing of hemp under its Industrial Hemp Act 2004, [ 116 ] New South Wales now issues licenses [ 117 ] under a law, the Hemp Industry Regulations Act 2008 (No 58), that came into effect as of 6 November 2008. [ 118 ] Most recently, South Australia legalized industrial hemp under South Australia's Industrial Hemp Act 2017, which commenced on 12 November 2017. [ 119 ]
Commercial production (including cultivation) of industrial hemp has been permitted in Canada since 1998 under licenses and authorization issued by Health Canada. [ 120 ]
In the early 1990s, industrial hemp agriculture in North America began with the Hemp Awareness Committee at the University of Manitoba . The Committee worked with the provincial government to get research and development assistance and was able to obtain test plot permits from the Canadian government . Their efforts led to the legalization of industrial hemp (hemp with only minute amounts of tetrahydrocannabinol ) in Canada and the first harvest in 1998. [ 121 ] [ 122 ]
In 2017, the cultivated area for hemp in the Prairie provinces include Saskatchewan with more than 56,000 acres (23,000 ha), Alberta with 45,000 acres (18,000 ha), and Manitoba with 30,000 acres (12,000 ha). [ 123 ] Canadian hemp is cultivated mostly for its food value as hulled hemp seeds, hemp oils, and hemp protein powders, with only a small fraction devoted to production of hemp fiber used for construction and insulation. [ 123 ]
France is Europe's biggest producer (and the world's second largest producer) with 8,000 hectares (20,000 acres) cultivated. [ 124 ] 70–80% of the hemp fiber produced in 2003 was used for specialty pulp for cigarette papers and technical applications. About 15% was used in the automotive sector, and 5–6% was used for insulation mats. About 95% of hurds were used as animal bedding, while almost 5% was used in the building sector. [ 14 ] In 2010–2011, a total of 11,000 hectares (27,000 acres) was cultivated with hemp in the EU, a decline compared with previous year. [ 110 ] [ 125 ]
From the 1950s to the 1980s, the Soviet Union was the world's largest producer of hemp (3,000 square kilometres (1,200 sq mi) in 1970). The main production areas were in Ukraine , [ 126 ] the Kursk and Orel regions of Russia, and near the Polish border. Since its inception in 1931, the Hemp Breeding Department at the Institute of Bast Crops in Hlukhiv (Glukhov), Ukraine, has been one of the world's largest centers for developing new hemp varieties, focusing on improving fiber quality, per-hectare yields, and low THC content. [ 127 ]
After the collapse of the Soviet Union , the commercial cultivation of hemp declined sharply. However, at least an estimated 2.5 million acres of hemp grow wild in the Russian Far East and the Black Sea regions. [ 128 ]
In the United Kingdom, cultivation licenses are issued by the Home Office under the Misuse of Drugs Act 1971 . When grown for nondrug purposes, hemp is referred to as industrial hemp, and a common product is fiber for use in a wide variety of products, as well as the seed for nutritional aspects and the oil. Feral hemp or ditch weed is usually a naturalized fiber or oilseed strain of Cannabis that has escaped from cultivation and is self-seeding. [ 129 ]
In October 2019, hemp became legal to grow in 46 U.S. states under federal law. As of 2019, 47 states have enacted legislation to make hemp legal to grow at the state level, with several states implementing medical provisions regarding the growing of plants specifically for non-psychoactive CBD. [ 130 ]
The 2018 Farm Bill , which incorporated the Hemp Farming Act of 2018 , removed hemp as a Schedule I drug and instead made it an agricultural commodity. This legalized hemp at the federal level, which made it easier for hemp farmers to get production licenses, acquire loans, and receive federal crop insurance. [ 131 ]
The process to legalize hemp cultivation began in 2009, when Oregon began approving licenses for industrial hemp. [ 133 ] Then, in 2013, after the legalization of marijuana, several farmers in Colorado planted and harvested several acres of hemp, bringing in the first hemp crop in the United States in over half a century. [ 134 ] After that, the federal government created a Hemp Farming Pilot Program as a part of the Agricultural Act of 2014. [ 135 ] This program allowed institutions of higher education and state agricultural departments to begin growing hemp without the consent of the Drug Enforcement Administration (DEA). Hemp production in Kentucky , formerly the United States' leading producer, resumed in 2014. [ 136 ] Hemp production in North Carolina resumed in 2017, [ 137 ] and in Washington State the same year. [ 138 ] By the end of 2017, at least 34 U.S. states had industrial hemp programs. In 2018, New York began taking strides in industrial hemp production, along with hemp research pilot programs at Cornell University , Binghamton University and SUNY Morrisville . [ 139 ]
As of 2017, the hemp industry estimated that annual sales of hemp products were around $820 million annually; hemp-derived CBD have been the major force driving this growth. [ 140 ]
Despite this progress, hemp businesses in the US have had difficulties expanding as they have faced challenges in traditional marketing and sales approaches. According to a case study done by Forbes , hemp businesses and startups have had difficulty marketing and selling non-psychoactive hemp products, as majority of online advertising platforms and financial institutions do not distinguish between hemp and marijuana. [ 141 ]
Gathered hemp fiber was used to make cloth long before agriculture, nine to fifty thousand years ago. [ 3 ] It may also be one of the earliest plants to have been cultivated. [ 143 ] [ 144 ] An archeological site in the Oki Islands of Japan contained cannabis achenes from about 8000 BC, probably signifying use of the plant. [ 145 ] Hemp use archaeologically dates back to the Neolithic Age in China, with hemp fiber imprints found on Yangshao culture pottery dating from the 5th millennium BC . [ 142 ] [ 146 ] The Chinese later used hemp to make clothes, shoes, ropes, and an early form of paper. [ 142 ] The classical Greek historian Herodotus (ca. 480 BC) reported that the inhabitants of Scythia would often inhale the vapors of hemp-seed smoke, both as ritual and for their own pleasurable recreation. [ 147 ]
Textile expert Elizabeth Wayland Barber summarizes the historical evidence that Cannabis sativa , "grew and was known in the Neolithic period all across the northern latitudes, from Europe (Germany, Switzerland, Austria, Romania, Ukraine) to East Asia (Tibet and China)," but, "textile use of Cannabis sativa does not surface for certain in the West until relatively late, namely the Iron Age." [ 148 ] "I strongly suspect, however, that what catapulted hemp to sudden fame and fortune as a cultigen and caused it to spread rapidly westwards in the first millennium B.C. was the spread of the habit of pot-smoking from somewhere in south-central Asia, where the drug-bearing variety of the plant originally occurred. The linguistic evidence strongly supports this theory, both as to time and direction of spread and as to cause." [ 149 ]
Jews living in Palestine in the 2nd century were familiar with the cultivation of hemp, as witnessed by a reference to it in the Mishna ( Kil'ayim 2:5) as a variety of plant, along with arum , that sometimes takes as many as three years to grow from a seedling. In late medieval Holy Roman Empire (Germany) and Italy , hemp was employed in cooked dishes, as filling in pies and tortes , or boiled in a soup. [ 150 ] Hemp in later Europe was mainly cultivated for its fibers and was used for ropes on many ships, including those of Christopher Columbus . The use of hemp as a cloth was centered largely in the countryside, with higher quality textiles being available in the towns.
The Spaniards brought hemp to the Americas and cultivated it in Chile starting about 1545. [ 151 ] Similar attempts were made in Peru, Colombia, and Mexico, but only in Chile did the crop find success. [ 152 ] In July 1605, Samuel Champlain reported the use of grass and hemp clothing by the (Wampanoag) people of Cape Cod and the (Nauset) people of Plymouth Bay told him they harvested hemp in their region where it grew wild to a height of 4 to 5 ft. [ 153 ] In May 1607, "hempe" was among the crops Gabriel Archer observed being cultivated by the natives at the main Powhatan village, where Richmond, Virginia , is now situated; [ 154 ] and in 1613, Samuell Argall reported wild hemp "better than that in England" growing along the shores of the upper Potomac . As early as 1619, the first Virginia House of Burgesses passed an Act requiring all planters in Virginia to sow "both English and Indian" hemp on their plantations. [ 155 ] The Puritans are first known to have cultivated hemp in New England in 1645. [ 151 ]
George Washington pushed for the growth of hemp as it was a cash crop commonly used to make rope and fabric. In May 1765 he noted in his diary about the sowing of seeds each day until mid-April. Then he recounts the harvest in October which he grew 27 bushels that year.
It is sometimes supposed that an excerpt from Washington's diary, which reads "Began to seperate [ sic ] the Male from the Female hemp at Do.&—rather too late" is evidence that he was trying to grow female plants for the THC found in the flowers. However, the editorial remark accompanying the diary states that "This may arise from their [the male] being coarser, and the stalks larger" [ 156 ] In subsequent days, he describes soaking the hemp [ 157 ] (to make the fibers usable) and harvesting the seeds, [ 158 ] suggesting that he was growing hemp for industrial purposes, not recreational.
George Washington also imported the Indian hemp plant from Asia, which was used for fiber and, by some growers, for intoxicating resin production. In a 1796 letter to William Pearce who managed the plants for him, Washington says, "What was done with the Indian Hemp plant from last summer? It ought, all of it, to be sown again; that not only a stock of seed sufficient for my own purposes might have been raised, but to have disseminated seed to others; as it is more valuable than common hemp." [ 159 ] [ 160 ]
Other presidents known to have farmed hemp for alternative purposes include Thomas Jefferson , [ 161 ] James Madison , James Monroe , Andrew Jackson , Zachary Taylor , and Franklin Pierce . [ 162 ]
Historically, hemp production had made up a significant portion of antebellum Kentucky's economy. Before the American Civil War , many slaves worked on plantations producing hemp. [ 163 ]
In 1937, the Marihuana Tax Act of 1937 was passed in the United States, levying a tax on anyone who dealt commercially in cannabis, hemp, or marijuana. The passing of the Act to destroy the U.S. hemp industry has been reputed to involve businessmen Andrew Mellon , Randolph Hearst and the Du Pont family . [ 164 ] [ 165 ] [ 166 ]
One claim is that Hearst believed [ dubious – discuss ] that his extensive timber holdings were threatened by the invention of the decorticator that he feared would allow hemp to become a cheap substitute for the paper pulp used for newspaper. [ 164 ] [ 167 ] Historical research indicates this fear was unfounded because improvements of the decorticators in the 1930s – machines that separated the fibers from the hemp stem – could not make hemp fiber a cheaper substitute for fibers from other sources. Further, decorticators did not perform satisfactorily in commercial production. [ 168 ] [ 164 ]
Another claim is that Mellon, Secretary of the Treasury and the wealthiest man in America at that time, had invested heavily in DuPont 's new synthetic fiber, nylon , and believed [ dubious – discuss ] that the replacement of the traditional resource, hemp, was integral to the new product's success. [ 164 ] [ 169 ] [ 170 ] [ 171 ] [ 172 ] [ 173 ] [ 174 ] [ 175 ] DuPont and many industrial historians dispute a link between nylon and hemp, nylon became immediately a scarce commodity. [ clarification needed ] Nylon had characteristics that could be used for toothbrushes (sold from 1938) and very thin nylon fiber could compete with silk and rayon in various textiles normally not produced from hemp fiber, such as very thin stockings for women. [ 168 ] [ 176 ] [ 177 ] [ 178 ] [ 179 ]
While the Marijuana Tax Act of 1937 had just been signed into law, the United States Department of Agriculture lifted the tax on hemp cultivation during WWII. [ 180 ] Before WWII, the U.S. Navy used Jute and Manila Hemp from the Philippines and Indonesia for the cordage on their ships. During the war, Japan cut off those supply lines. [ 181 ] America was forced to turn inward and revitalize the cultivation of Hemp on U.S. soils.
Hemp was used extensively by the United States during World War II to make uniforms, canvas, and rope. [ 182 ] Much of the hemp used was cultivated in Kentucky and the Midwest . During World War II, the U.S. produced a short 1942 film, Hemp for Victory , promoting hemp as a necessary crop to win the war. [ 181 ] By the 1980s the film was largely forgotten, and the U.S. government even denied its existence. [ 183 ] The film, and the important historical role of hemp in U.S. agriculture and commerce was brought to light by hemp activist Jack Herer in the book The Emperor Wears No Clothes .
U.S. farmers participated in the campaign to increase U.S. hemp production to 36,000 acres in 1942. [ 184 ] This increase amounted to more than 20 times the production in 1941 before the war effort. [ 184 ]
In the United States, Executive Order 12919 (1994) identified hemp as a strategic national product that should be stockpiled. [ 185 ]
Hemp has been grown for millennia in Asia and the Middle East for its fiber. Commercial production of hemp in the West took off in the eighteenth century, but was grown in the sixteenth century in eastern England. [ 188 ] Because of colonial and naval expansion of the era, economies needed large quantities of hemp for rope and oakum . In the early 1940s, world production of hemp fiber ranged from 250,000 to 350,000 metric tons, Russia was the biggest producer. [ 168 ]
In Western Europe, the cultivation of hemp was not legally banned by the 1930s, but the commercial cultivation stopped by then, due to decreased demand compared to increasingly popular artificial fibers. [ 189 ] Speculation about the potential for commercial cultivation of hemp in large quantities has been criticized due to successful competition from other fibers for many products. The world production of hemp fiber fell from over 300,000 metric tons 1961 to about 75,000 metric tons in the early 1990s and has after that been stable at that level. [ 190 ]
In Japan, hemp was historically used as paper and a fiber crop. There is archaeological evidence cannabis was used for clothing and the seeds were eaten in Japan back to the Jōmon period (10,000 to 300 BC). Many Kimono designs portray hemp, or asa ( Japanese : 麻 ), as a beautiful plant. In 1948, marijuana was restricted as a narcotic drug. The ban on marijuana imposed by the United States authorities was alien to Japanese culture, as the drug had never been widely used in Japan before. Though these laws against marijuana are some of the world's strictest, allowing five years imprisonment for possession of the drug, they exempt hemp growers, whose crop is used to make robes for Buddhist monks and loincloths for Sumo wrestlers . Because marijuana use in Japan has doubled in the past decade, these exemptions have recently been called into question. [ 191 ]
The cultivation of hemp in Portuguese lands began around the fourteenth century. [ citation needed ] The raw material was used for the preparation of rope and plugs for the Portuguese ships. Portugal also utilized its colonies to support its hemp supply, including in certain parts of Brazil. [ 192 ]
In order to recover the ailing Portuguese naval fleet after the Restoration of Independence in 1640, King John IV put a renewed emphasis on the growing of hemp. He ordered the creation of the Royal Linen and Hemp Factory in the town of Torre de Moncorvo to increase production and support the effort. [ 193 ]
In 1971, the cultivation of hemp became illegal, and the production was substantially reduced. Because of EU regulations 1308–70, 619/71 and 1164–89, this law was revoked (for some certified seed varieties). [ 194 ] | https://en.wikipedia.org/wiki/Hemp |
The Henderson limit is the X-ray dose (energy per unit mass) a cryo-cooled crystal can absorb before the diffraction pattern decays to half of its original intensity. Its value is defined as 2 × 10 7 Gy (J/kg).
Although the process is still not fully understood, diffraction patterns of crystals typically decay with X-ray exposure due to a number of processes which non-uniformly and irreversibly modify molecules that compose the crystal. These modifications induce disorder and thus decrease the intensity of Bragg diffraction . The processes behind these modifications include primary damage via the photo electric effect , covalent modification by free radicals , oxidation ( methionine residues), reduction ( disulfide bonds ) and decarboxylation ( glutamate , aspartate residues).
Although generalizable, the limit is defined in the context of biomolecular X-ray crystallography , where a typical experiment consists of exposing a single frozen crystal of a macromolecule (generally protein , DNA or RNA ) to an intense X-ray beam. The beams that are diffracted are then analyzed towards obtaining an atomically resolved model of the crystal. Such decay presents itself as a problem for crystallographers who require that the diffraction intensities decay as little as possible, to maximize the signal to noise ratio in order to determine accurate atomic models that describe the crystal. | https://en.wikipedia.org/wiki/Henderson_limit |
In chemistry and biochemistry , the pH of weakly acidic chemical solutions can be estimated using the Henderson-Hasselbach Equation : pH = p K a + log 10 ( [ Base ] [ Acid ] ) {\displaystyle {\ce {pH}}={\ce {p}}K_{{\ce {a}}}+\log _{10}\left({\frac {[{\ce {Base}}]}{[{\ce {Acid}}]}}\right)}
The equation relates the pH of the weak acid to the numerical value of the acid dissociation constant , K a , of the acid , and the ratio of the concentrations of the acid and its conjugate base [ 1 ] .
Acid-base Equilibrium Reaction
H A ( a c i d ) ⇋ A − ( b a s e ) + H + {\displaystyle \mathrm {{\underset {(acid)}{HA}}\leftrightharpoons {\underset {(base)}{A^{-}}}+H^{+}} }
The Henderson-Hasselbalch equation is often used for estimating the pH of buffer solutions by approximating the actual concentration ratio as the ratio of the analytical concentrations of the acid and of a salt, MA. It is also useful for determining the volumes of the reagents needed before preparing buffer solutions, which prevents unncessary waste of chemical reagents that may need to be further neutralized by even more reagents before they are safe to expose.
For example, the acid may be carbonic acid
The equation can also be applied to bases by specifying the protonated form of the base as the acid. For example, with an amine , R N H 2 {\displaystyle \mathrm {RNH_{2}} }
The Henderson–Hasselbach buffer system also has many natural and biological applications, from physiological processes (e.g., metabolic acidosis) to geological phenomena.
The Henderson–Hasselbalch equation was developed by two scientists, Lawrence Joseph Henderson and Karl Albert Hasselbalch . [ 2 ] Lawrence Joseph Henderson was a biological chemist and Karl Albert Hasselbalch was a physiologist who studied pH. [ 2 ] [ 3 ]
In 1908, Lawrence Joseph Henderson [ 4 ] derived an equation to calculate the hydrogen ion concentration of a bicarbonate buffer solution, which rearranged looks like this:
In 1909 Søren Peter Lauritz Sørensen introduced the pH terminology, which allowed Karl Albert Hasselbalch to re-express Henderson's equation in logarithmic terms , [ 5 ] resulting in the Henderson–Hasselbalch equation.
A simple buffer solution consists of a solution of an acid and a salt of the conjugate base of the acid. For example, the acid may be acetic acid and the salt may be sodium acetate . The Henderson–Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant , K a of the acid, and the concentrations of the species in solution. [ 6 ]
To derive the equation a number of simplifying assumptions have to be made. [ 7 ]
Assumption 1 : The acid, HA, is monobasic and dissociates according to the equations
C A is the analytical concentration of the acid and C H is the concentration the hydrogen ion that has been added to the solution. The self-dissociation of water is ignored. A quantity in square brackets, [X], represents the concentration of the chemical substance X. It is understood that the symbol H + stands for the hydrated hydronium ion. K a is an acid dissociation constant .
The Henderson–Hasselbalch equation can be applied to a polybasic acid only if its consecutive p K values differ by at least 3. Phosphoric acid is such an acid.
Assumption 2 . The self-ionization of water can be ignored. This assumption is not, strictly speaking, valid with pH values close to 7, half the value of pK w , the constant for self-ionization of water . In this case the mass-balance equation for hydrogen should be extended to take account of the self-ionization of water.
However, the term K w / [ H + ] {\displaystyle \mathrm {K_{w}/[H^{+}]} } can be omitted to a good approximation. [ 7 ]
Assumption 3 : The salt MA is completely dissociated in solution. For example, with sodium acetate
the concentration of the sodium ion, [Na + ] can be ignored. This is a good approximation for 1:1 electrolytes, but not for salts of ions that have a higher charge such as magnesium sulphate , MgSO 4 , that form ion pairs .
Assumption 4 : The quotient of activity coefficients, Γ {\displaystyle \Gamma } , is a constant under the experimental conditions covered by the calculations.
The thermodynamic equilibrium constant, K ∗ {\displaystyle K^{*}} ,
is a product of a quotient of concentrations [ H + ] [ A − ] [ HA ] {\displaystyle {\frac {[{\ce {H+}}][{\ce {A^-}}]}{[{\ce {HA}}]}}} and a quotient, Γ {\displaystyle \Gamma } , of activity coefficients γ H + γ A − γ H A {\displaystyle {\frac {\gamma _{{\ce {H+}}}\gamma _{{\ce {A^-}}}}{\gamma _{HA}}}} . In these expressions, the quantities in square brackets signify the concentration of the undissociated acid, HA, of the hydrogen ion H + , and of the anion A − ; the quantities γ {\displaystyle \gamma } are the corresponding activity coefficients . If the quotient of activity coefficients can be assumed to be a constant which is independent of concentrations and pH, the dissociation constant, K a can be expressed as a quotient of concentrations.
Source: [ 8 ]
Following these assumptions, the Henderson–Hasselbalch equation is derived in a few logarithmic steps. K a = [ H + ] [ A − ] [ H A ] {\displaystyle K_{a}={[H^{+}][A^{-}] \over [HA]}}
Solve for [ H + ] {\displaystyle [H^{+}]} : [ H + ] = K a [ H A ] [ A − ] {\displaystyle [H^{+}]=K_{a}{[HA] \over [A^{-}]}}
On both sides, take the negative logarithm: − log [ H + ] = − log K a − log [ H A ] [ A − ] {\displaystyle -\log[H^{+}]=-\log K_{a}-\log {[HA] \over [A^{-}]}}
Based on previous assumptions, p H = − log [ H + ] {\displaystyle pH=-\log[H^{+}]} and p K a = − log K a {\displaystyle pK_{a}=-\log K_{a}} p H = p K a − log [ H A ] [ A − ] {\displaystyle pH=pK_{a}-\log {[HA] \over [A^{-}]}}
Inversion of − log [ H A ] [ A − ] {\displaystyle -\log {[HA] \over [A^{-}]}} by changing its sign, provides the Henderson–Hasselbalch equation p H = p K a + log [ A − ] [ H A ] {\displaystyle pH=pK_{a}+\log {[A^{-}] \over [HA]}}
The equilibrium constant for the protonation of a base, B,
is an association constant, K b , which is simply related to the dissociation constant of the conjugate acid, BH + .
The value of p K w {\displaystyle \mathrm {pK_{w}} } is ca. 14 at 25 °C. This approximation can be used when the correct value is not known. Thus, the Henderson–Hasselbalch equation can be used, without modification, for bases.
With homeostasis the pH of a biological solution is maintained at a constant value by adjusting the position of the equilibria
where H C O 3 − {\displaystyle \mathrm {HCO_{3}^{-}} } is the bicarbonate ion and H 2 C O 3 {\displaystyle \mathrm {H_{2}CO_{3}} } is carbonic acid . Carbonic acid is formed reversibly from carbon dioxide and water. However, the solubility of carbonic acid in water may be exceeded. When this happens carbon dioxide gas is liberated and the following equation may be used instead.
C O 2 ( g ) {\displaystyle \mathrm {CO_{2}(g)} } represents the carbon dioxide liberated as gas. In this equation, which is widely used in biochemistry, K m {\displaystyle K^{m}} is a mixed equilibrium constant relating to both chemical and solubility equilibria. It can be expressed as
where [HCO − 3 ] is the molar concentration of bicarbonate in the blood plasma and P CO 2 is the partial pressure of carbon dioxide in the supernatant gas. The concentration of H 2 C O 3 {\displaystyle \mathrm {H_{2}CO_{3}} } is dependent on the [ C O 2 ( a q ) ] {\displaystyle [\mathrm {CO_{2}(aq)} ]} which is also dependent on P CO 2 . [ 9 ]
One of the buffer systems present in the body is the blood plasma buffering system . This is formed from H 2 C O 3 {\displaystyle \mathrm {H_{2}CO_{3}} } , carbonic acid , working in conjunction with [HCO − 3 ] , bicarbonate , to form the bicarbonate system . [ 10 ] This is effective near physiological pH of 7.4 as carboxylic acid is in equilibrium with C O 2 ( g ) {\displaystyle \mathrm {CO_{2}(g)} } in the lungs. [ 9 ] As blood travels through the body, it gains and loses H+ from different processes including lactic acid fermentation and by NH3 protonation from protein catabolism. [ 9 ] Because of this the [ H 2 C O 3 ] {\displaystyle [\mathrm {H_{2}CO_{3}} ]} , changes in the blood as it passes through tissues. This correlates to a change in the partial pressure of C O 2 ( g ) {\displaystyle \mathrm {CO_{2}(g)} } in the lungs causing a change in the rate of respiration if more or less C O 2 ( g ) {\displaystyle \mathrm {CO_{2}(g)} } is necessary. [ 9 ] For example, a decreased blood pH will trigger the brain stem to perform more frequent respiration. The Henderson–Hasselbalch equation can be used to model these equilibria. It is important to maintain this pH of 7.4 to ensure enzymes are able to work optimally. [ 10 ]
Life threatening Acidosis (a low blood pH resulting in nausea, headaches, and even coma, and convulsions) is due to a lack of functioning of enzymes at a low pH. [ 10 ] As modelled by the Henderson–Hasselbalch equation, in severe cases this can be reversed by administering intravenous bicarbonate solution. If the partial pressure of C O 2 ( g ) {\displaystyle \mathrm {CO_{2}(g)} } does not change, this addition of bicarbonate solution will raise the blood pH.
The ocean contains a natural buffer system to maintain a pH between 8.1 and 8.3. [ 11 ] The ocean buffer system is known as the carbonate buffer system. [ 12 ] The carbonate buffer system is a series of reactions that uses carbonate as a buffer to convert C O 2 {\displaystyle \mathrm {CO_{2}} } into bicarbonate . [ 12 ] The carbonate buffer reaction helps maintain a constant H+ concentration in the ocean because it consumes hydrogen ions, [ 13 ] and thereby maintains a constant pH. [ 12 ] The ocean has been experiencing ocean acidification due to humans' increasing C O 2 {\displaystyle \mathrm {CO_{2}} } in the atmosphere. [ 14 ] About 30% of the C O 2 {\displaystyle \mathrm {CO_{2}} } that is released in the atmosphere is absorbed by the ocean, [ 14 ] and the increase in C O 2 {\displaystyle \mathrm {CO_{2}} } absorption results in an increase in H+ ion production. [ 15 ] The increase in atmospheric C O 2 {\displaystyle \mathrm {CO_{2}} } increases H+ ion production because in the ocean C O 2 {\displaystyle \mathrm {CO_{2}} } reacts with water and produces carbonic acid , and carbonic acid releases H+ ions and bicarbonate ions . [ 15 ] Overall, since the Industrial Revolution the ocean has experienced a pH decrease of about 0.1 pH units due to the increase in C O 2 {\displaystyle \mathrm {CO_{2}} } production. [ 12 ]
Ocean acidification affects marine life that have shells that are made up of carbonate . In a more acidic environment, it is harder for organisms to grow and maintain the carbonate shells. [ 12 ] The increase in ocean acidity can cause carbonate shell organisms to experience reduced growth and reproduction. [ 12 ]
Davenport, Horace W. (1974). The ABC of Acid-Base Chemistry: The Elements of Physiological Blood-Gas Chemistry for Medical Students and Physicians (Sixth ed.). Chicago: The University of Chicago Press. | https://en.wikipedia.org/wiki/Henderson–Hasselbalch_equation |
Hendrik Christoffel Ferreira (1954 – November 20, 2018, in Johannesburg ) was a professor in Digital Communications and Information Theory at the University of Johannesburg , Johannesburg , South Africa . [ 1 ]
He studied electrical engineering at the University of Pretoria , South Africa , where he obtained his Ph.D. in 1980. He worked as a visiting researcher at Linkabit in San Diego . He joined the Rand Afrikaans University in 1983, where, in 1989, he was appointed full professor. In recognition of his excellence in research and educating post-graduate students, he has been appointed as a research professor at the University of Johannesburg in 2007. He is a Fellow of the SAIEE , the South African Institute of Electrical Engineers.
Ferreira published close to 250 research papers on topics such as digital communications , power line communications , vehicular communication systems . [ 2 ] With his work he introduced and developed a new theme in Information Theory, namely coding techniques for constructing combined channel codes, where error correction and channel properties are considered jointly.
Ferreira was a pioneering initiator and stimulator of the research fields of Information Theory and Power Line Communications in South Africa . [ 3 ] He also was an organizer of the IEEE Information Theory Society and Power Line Communications within South Africa and Africa . He was a member of the Technical Committee for Power Line Communications of the IEEE Communications Society, and he served on the Technical Program Committee of several IEEE conferences, including the IEEE (ISIT) International Symposium on Information Theory, the IEEE (ISPLC) International Symposium on Power Line Communications, and the IEEE Africon and Chinacom conferences.
An obituary by his colleague Han Vinck was presented during a workshop in 2019. [ 4 ] | https://en.wikipedia.org/wiki/Hendrik_C._Ferreira |
Hendrik Johannes (Henny) van der Windt (born 22 August 1955, in Vlaardingen ) [ 1 ] is a Dutch associate professor at the Rijksuniversiteit Groningen , specialized in the relationship between sustainability and science , in particular the relationship between nature conservation and ecology and between energy technologies, locale energy-initiatives and the energy transition .
Van der Windt grew up in Vlaardingen where he went to high school (' Hogere Burgerschool -B'). He was active in the regional environmental group Centraal Aksiekomitee Rijnmond and various student committees on environmental protection. [ 2 ] After high school he studied biology at the Rijksuniversiteit Groningen (1972-1981).
He received his doctorate in 1995 with his PhD dissertation "En dan: wat is natuur nog in dit land?: natuurbescherming in Nederland 1880-1990" (After all, what is nature in this country, nature conservation in the Netherlands 1980–1990), with chapters on the rise of nature conservation , tensions between agriculture and nature conservation, forestry , ecological restoration and the management of the Wadden Sea .
At that time he worked as a junior scientist and lecturer at the Biology Department of the University of Groningen. After his doctorate, he worked several years as a researcher (post-doc) in Groningen within the Ethics and Policy research programme of NWO [ 3 ] Around 2000 he became associate professor at the Science & Society Group (later Integrated Research on Energy, Environment and Society (IREES)) of the University of Groningen.
He studied science-society interactions concerning genomics , food , ecological restoration , energy and sustainability , [ 4 ] combining approaches and insights from biology, environmental science , environmental history and science and technology studies .
His education tasks include various courses such as second year Bachelor programmes Science & Society , the minor Future Planet Innovation [ 5 ] and courses of the mastertrack Science, Business & Policy [ 6 ] and the master Energy and Environmental sciences. [ 7 ]
In addition to scientific papers, journalistic articles and policy reports [ 8 ] Van der Windt was author or editor of several books or chapters. [ 9 ] [ 10 ] A selection: | https://en.wikipedia.org/wiki/Henny_van_der_Windt |
Antoine Henri Becquerel ( / ˌ b ɛ k ə ˈ r ɛ l / ; [ 1 ] French: [ɑ̃twan ɑ̃ʁi bɛkʁɛl] ; 15 December 1852 – 25 August 1908) was a French physicist who shared the 1903 Nobel Prize in Physics with Marie Curie and Pierre Curie for his discovery of radioactivity . [ 2 ]
Becquerel was born in Paris, France, into a wealthy family which produced four generations of notable physicists, including Becquerel's grandfather ( Antoine César Becquerel ), father ( Edmond Becquerel ), and son ( Jean Becquerel ). [ 3 ] Henri started off his education by attending the Lycée Louis-le-Grand school, a prep school in Paris. [ 3 ] He studied engineering at the École polytechnique and the École des ponts et chaussées . [ 4 ]
Becquerel's earliest works centered on the subject of his doctoral thesis supervised by Charles Friedel [ 5 ] at the Faculty of Sciences of the Sorbonne : the plane polarization of light, with the phenomenon of phosphorescence and absorption of light by crystals. [ 6 ] He was awarded a Doctor of Science in 1888. [ 7 ]
Early in his career, Becquerel also studied the Earth's magnetic fields . [ 7 ] Becquerel became the third in his family to occupy the Chair of Applied Physics at the Muséum national d'histoire naturelle in 1892. Later on in 1894, Becquerel became chief engineer in the Department of Bridges and Highways before he started with his early experiments. In 1895, he was appointed as a professor at the École polytechnique. [ 8 ]
Becquerel's discovery of spontaneous radioactivity is a famous example of serendipity , of how chance favors the prepared mind. Becquerel had long been interested in phosphorescence , the emission of light of one color following the object's exposure to light of another color. In early 1896, there was a wave of excitement following Wilhelm Conrad Röntgen 's discovery of X-rays on 5 January. During the experiment, Röntgen "found that the Crookes tubes he had been using to study cathode rays emitted a new kind of invisible ray that was capable of penetrating through black paper". [ 9 ] Becquerel learned of Röntgen's discovery during a meeting of the French Academy of Sciences on 20 January where his colleague Henri Poincaré read out Röntgen's preprint paper. [ 10 ] : 43 Becquerel "began looking for a connection between the phosphorescence he had already been investigating and the newly discovered x-rays" [ 9 ] of Röntgen, and thought that phosphorescent materials might emit penetrating X-ray-like radiation when illuminated by bright sunlight; he had various phosphorescent materials including some uranium salts for his experiments. [ 10 ]
Throughout the first weeks of February, Becquerel layered photographic plates with coins or other objects then wrapped this in thick black paper, placed phosphorescent materials on top, placed these in bright sun light for several hours. The developed plate showed shadows of the objects. Already on 24 February he reported his first results. However, the 26 and 27 February were dark and overcast during the day, so Becquerel left his layered plates in a dark cabinet for these days. He nevertheless proceeded to develop the plates on 1 March and then made his astonishing discovery: the object shadows were just as distinct when left in the dark as when exposed to sunlight. Both William Crookes and Becquerel's 18 year old son Jean witnessed the discovery. [ 10 ] : 46
By May 1896, after other experiments involving non-phosphorescent uranium salts, he arrived at the correct explanation, namely that the penetrating radiation came from the uranium itself, without any need for excitation by an external energy source. [ 11 ] There followed a period of intense research into radioactivity, including the determination that the element thorium is also radioactive and the discovery of additional radioactive elements polonium and radium by Marie Skłodowska-Curie and her husband Pierre Curie . The intensive research of radioactivity led to Becquerel publishing seven papers on the subject in 1896. [ 4 ] Becquerel's other experiments allowed him to research more into radioactivity and figure out different aspects of the magnetic field when radiation is introduced into the magnetic field. "When different radioactive substances were put in the magnetic field, they deflected in different directions or not at all, showing that there were three classes of radioactivity: negative, positive, and electrically neutral." [ 12 ]
As simultaneity often happens in science, radioactivity came close to being discovered nearly four decades earlier in 1857, when Abel Niépce de Saint-Victor , who was investigating photography under Michel Eugène Chevreul , observed that uranium salts emitted radiation that could darken photographic emulsions. [ 13 ] [ 14 ] By 1861, Niepce de Saint-Victor realized that uranium salts produce "a radiation that is invisible to our eyes". [ 15 ] Niepce de Saint-Victor knew Edmond Becquerel, Henri Becquerel's father. In 1868, Edmond Becquerel published a book, La lumière: ses causes et ses effets (Light: Its causes and its effects). On page 50 of volume 2, Edmond noted that Niepce de Saint-Victor had observed that some objects that had been exposed to sunlight could expose photographic plates even in the dark. [ 16 ] Niepce further noted that on the one hand, the effect was diminished if an obstruction were placed between a photographic plate and the object that had been exposed to the sun, but " … d'un autre côté, l'augmentation d'effet quand la surface insolée est couverte de substances facilement altérables à la lumière, comme le nitrate d'urane … " ( ... on the other hand, the increase in the effect when the surface exposed to the sun is covered with substances that are easily altered by light, such as uranium nitrate ... ). [ 16 ]
Describing them to the French Academy of Sciences on 27 February 1896, he said:
One wraps a Lumière photographic plate with a bromide emulsion in two sheets of very thick black paper, such that the plate does not become clouded upon being exposed to the sun for a day. One places on the sheet of paper, on the outside, a slab of the phosphorescent substance, and one exposes the whole to the sun for several hours. When one then develops the photographic plate, one recognizes that the silhouette of the phosphorescent substance appears in black on the negative. If one places between the phosphorescent substance and the paper a piece of money or a metal screen pierced with a cut-out design, one sees the image of these objects appear on the negative ... One must conclude from these experiments that the phosphorescent substance in question emits rays which pass through the opaque paper and reduce silver salts. [ 17 ] [ 18 ]
But further experiments led him to doubt and then abandon this hypothesis. On 2 March 1896 he reported:
I will insist particularly upon the following fact, which seems to me quite important and beyond the phenomena which one could expect to observe: The same crystalline crusts [of potassium uranyl sulfate], arranged the same way with respect to the photographic plates, in the same conditions and through the same screens, but sheltered from the excitation of incident rays and kept in darkness, still produce the same photographic images. Here is how I was led to make this observation: among the preceding experiments, some had been prepared on Wednesday the 26th and Thursday the 27th of February, and since the sun was out only intermittently on these days, I kept the apparatuses prepared and returned the cases to the darkness of a bureau drawer, leaving in place the crusts of the uranium salt. Since the sun did not come out in the following days, I developed the photographic plates on the 1st of March, expecting to find the images very weak. Instead the silhouettes appeared with great intensity ... One hypothesis which presents itself to the mind naturally enough would be to suppose that these rays, whose effects have a great similarity to the effects produced by the rays studied by M. Lenard and M. Röntgen, are invisible rays emitted by phosphorescence and persisting infinitely longer than the duration of the luminous rays emitted by these bodies. However, the present experiments, without being contrary to this hypothesis, do not warrant this conclusion. I hope that the experiments which I am pursuing at the moment will be able to bring some clarification to this new class of phenomena. [ 19 ] [ 20 ]
Later in his life in 1900, Becquerel measured the properties of beta particles , and he realized that they had the same measurements as high speed electrons leaving the nucleus. [ 4 ] [ 21 ] In 1901 Becquerel made the discovery that radioactivity could be used for medicine. Henri made this discovery when he left a piece of radium in his vest pocket and noticed that he had been burnt by it. This discovery led to the development of radiotherapy , which is now used to treat cancer. [ 4 ] In 1908 Becquerel was elected president of Académie des Sciences , but he died on 25 August 1908, at the age of 55, in Le Croisic , France. [ 7 ] He died of a heart attack, [ 10 ] : 49 but it was reported that "he had developed serious burns on his skin, likely from the handling of radioactive materials." [ 22 ]
In 1889, Becquerel became a member of the Académie des Sciences . [ 4 ] In 1900, Becquerel won the Rumford Medal for his discovery of the radioactivity of uranium and he awarded the title of an Officer of the Legion of Honour . [ 23 ] [ 7 ] The Berlin-Brandenburg Academy of Sciences and Humanities awarded him the Helmholtz Medal in 1901. [ 24 ] In 1902, he was elected as a member of the American Philosophical Society . [ 25 ] In 1903, Henri shared a Nobel Prize in Physics with Pierre Curie and Marie Curie for the discovery of spontaneous radioactivity. [ 7 ] In 1905, he was awarded the Barnard Medal by the U.S. National Academy of Sciences. [ 26 ] In 1906, Henri was elected Vice Chairman of the academy, and in 1908, the year of his death, Becquerel was elected Permanent Secretary of the Académie des Sciences . [ 27 ] During his lifetime, Becquerel was honored with membership into the Accademia dei Lincei and the Royal Academy of Berlin . [ 7 ] Becquerel was elected a Foreign Member of the Royal Society (ForMemRS) in 1908 . [ 28 ] Becquerel has been honored with being the namesake of many different scientific discoveries. The SI unit for radioactivity, the becquerel (Bq), is named after him. [ 29 ]
There is a crater named Becquerel on the Moon and also a crater named Becquerel on Mars. [ 30 ] [ 31 ] The uranium-based mineral becquerelite was named after Henri. [ 32 ] Minor planet 6914 Becquerel is named in his honor. [ 33 ] | https://en.wikipedia.org/wiki/Henri_Becquerel |
Ferdinand Frédéric Henri Moissan ( French pronunciation: [fɛʁdinɑ̃ fʁedeʁik ɑ̃ʁi mwasɑ̃] ; 28 September 1852 – 20 February 1907) was a French chemist and pharmacist who won the 1906 Nobel Prize in Chemistry for his work in isolating fluorine from its compounds. [ a ] Among his other contributions, Moissan discovered moissanite and contributed to the development of the electric arc furnace . [ 1 ] Moissan was one of the original members of the International Atomic Weights Committee . [ 1 ] [ 3 ]
Moissan was born in Paris on 28 September 1852, the son of a minor officer of the Eastern Railway Company , Francis Ferdinand Moissan, and a seamstress, Joséphine Améraldine (née Mitel). [ 4 ] In 1864 they moved to Meaux , where he attended the local school. During this time, Moissan became an apprentice clockmaker. However, in 1870, Moissan and his family moved back to Paris due to war against Prussia. Moissan was unable to receive the grade universitaire necessary to attend university. After spending a year in the army, he enrolled at the Ecole Superieure de Pharmacie de Paris. [ 5 ]
Moissan became a trainee in pharmacy in 1871 and in 1872 he began working for a chemist in Paris, where he was able to save a person poisoned with arsenic . He decided to study chemistry and began first in the laboratory of Edmond Frémy at the Musée d’Histoire Naturelle, and later in that of Pierre Paul Dehérain at the École Pratique des Haute Études. [ 6 ] [ 5 ] Dehérain persuaded him to pursue an academic career. He passed the baccalauréat , which was necessary to study at university, in 1874 after an earlier failed attempt. He also became qualified as first-class pharmacist at the École Supérieure de Pharmacie in 1879, and received his doctoral degree there in 1880. [ 5 ]
He soon climbed through the ranks of the School of Pharmacy, and was appointed Assistant Lecturer, Senior Demonstrator, and finally Professor of Toxicology by 1886. He took the Chair of Inorganic Chemistry in 1899. The following year, he succeeded Louis Joseph Troost as Professor of Inorganic Chemistry at the Sorbonne . [ 7 ] During his time in Paris he became a friend of the chemist Alexandre Léon Étard and the botanist Vasque. [ 8 ] His marriage, to Léonie Lugan, took place in 1882. They had a son in 1885, named Louis Ferdinand Henri.
Moissan died suddenly in Paris in February 1907, shortly after his return from receiving the Nobel Prize in Stockholm . [ 7 ] His death was attributed to an acute case of appendicitis , however, there is speculation that repeated exposure to fluorine and carbon monoxide also contributed to his death. [ 5 ]
During his extensive career, Moissan authored more than three hundred publications, won the 1906 Nobel Prize in Chemistry for the first isolation of fluorine , in addition to the Prix Lucaze , the Davy Medal , the Hofmann Medal , and the Elliott Cresson Medal . He was elected fellow of the Royal Society and The Chemical Society of London , served on the International Atomic Weights Committee and made a commandeur in the Légion d'honneur . [ 7 ]
Moissan published his first scientific paper, about carbon dioxide and oxygen metabolism in plants, with Dehérain in 1874. He left plant physiology and then turned towards inorganic chemistry; subsequently his research on pyrophoric iron was well received by the two most prominent French inorganic chemists of that time, Henri Étienne Sainte-Claire Deville and Jules Henri Debray . After Moissan received his Ph.D. on cyanogen and its reactions to form cyanures in 1880, his friend Landrine offered him a position at an analytic laboratory. [ 4 ]
During the 1880s, Moissan focused on fluorine chemistry and especially the production of fluorine itself. The existence of the element had been well known for many years, but all attempts to isolate it had failed, and some experimenters had died in the attempt. [ 9 ] [ 10 ] He had no laboratory of his own, but borrowed lab space from others, including Charles Friedel . There he had access to a strong battery consisting of 90 Bunsen cells which made it possible to observe a gas produced by the electrolysis of molten arsenic trichloride ; the gas was reabsorbed by the arsenic trichloride.
Moissan eventually succeeded in isolating fluorine in 1886 by the electrolysis of a solution of potassium hydrogen difluoride (KHF 2 ) in liquid hydrogen fluoride (HF). The mixture was necessary because hydrogen fluoride is a nonconductor. The device was built with platinum - iridium electrodes in a platinum holder and the apparatus was cooled to −50 °C. The result was the complete separation of the hydrogen produced at the negative electrode from the fluorine produced at the positive one, first achieved on 26 June 1886. [ 11 ] [ 12 ] This remains the current standard method for commercial fluorine production. [ 13 ] The French Academy of Science sent three representatives, Marcellin Berthelot , Henri Debray , and Edmond Frémy , to verify the results, but Moissan was unable to reproduce them, owing to the absence from the hydrogen fluoride of traces of potassium fluoride present in the previous experiments. After resolving the problem and demonstrating the production of fluorine several times, he was awarded a prize of 10,000 francs. For the first successful isolation, he was awarded the 1906 Nobel Prize in Chemistry . [ 7 ] Following his grand achievement, his research focused on characterizing fluorine's chemistry. He discovered numerous fluorine compounds, such as (together with Paul Lebeau ) sulfur hexafluoride in 1901.
Moissan contributed to the development of the electric arc furnace , which opened several paths to developing and preparing new compounds, [ 14 ] and attempted to use pressure to produce synthetic diamonds [ 15 ] from the more common form of carbon . He also used the furnace to synthesize the borides and carbides of numerous elements. [ 6 ] Calcium carbide was a noticeable accomplishment as this paved the way for the development of the chemistry of acetylene. [ 1 ] In 1893, Moissan began studying fragments of a meteorite found in Meteor Crater near Diablo Canyon in Arizona . In these fragments he discovered minute quantities of a new mineral and, after extensive research, Moissan concluded that this mineral was made of silicon carbide . In 1905, this mineral was named moissanite , in his honor. In 1903 Moissan was elected member of the International Atomic Weights Committee where he served until his death. [ 16 ] | https://en.wikipedia.org/wiki/Henri_Moissan |
Jules Henri Poincaré [ 1 ] ( UK : / ˈ p w æ̃ k ɑːr eɪ / , US : / ˌ p w æ̃ k ɑː ˈ r eɪ / ; French: [ɑ̃ʁi pwɛ̃kaʁe] ⓘ ; [ 2 ] 29 April 1854 – 17 July 1912) was a French mathematician , theoretical physicist , engineer, and philosopher of science . He is often described as a polymath , and in mathematics as "The Last Universalist", [ 3 ] since he excelled in all fields of the discipline as it existed during his lifetime. He has further been called "the Gauss of modern mathematics ". [ 4 ] Due to his success in science, along with his influence and philosophy, he has been called "the philosopher par excellence of modern science." [ 5 ]
As a mathematician and physicist , he made many original fundamental contributions to pure and applied mathematics , mathematical physics , and celestial mechanics . [ 6 ] In his research on the three-body problem , Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory . Poincaré is regarded as the creator of the field of algebraic topology , and is further credited with introducing automorphic forms . He also made important contributions to algebraic geometry , number theory , complex analysis and Lie theory . [ 7 ] He famously introduced the concept of the Poincaré recurrence theorem , which states that a state will eventually return arbitrarily close to its initial state after a sufficiently long time, which has far-reaching consequences. [ 8 ] Early in the 20th century he formulated the Poincaré conjecture , which became, over time, one of the famous unsolved problems in mathematics . It was eventually solved in 2002–2003 by Grigori Perelman . Poincaré popularized the use of non-Euclidean geometry in mathematics as well. [ 9 ]
Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Hendrik Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations , an important step in the formulation of the theory of special relativity , for which he is also credited with laying down the foundations for, [ 10 ] further writing foundational papers in 1905. [ 11 ] He first proposed gravitational waves ( ondes gravifiques ) emanating from a body and propagating at the speed of light as being required by the Lorentz transformations, doing so in 1905. [ 12 ] In 1912, he wrote an influential paper which provided a mathematical argument for quantum mechanics . [ 13 ] [ 14 ] Poincaré also laid the seeds of the discovery of radioactivity through his interest and study of X-rays , which influenced physicist Henri Becquerel , who then discovered the phenomena. [ 15 ] The Poincaré group used in physics and mathematics was named after him, after he introduced the notion of the group. [ 16 ]
Poincaré was considered the dominant figure in mathematics and theoretical physics during his time, and was the most respected mathematician of his time, being described as "the living brain of the rational sciences" by mathematician Paul Painlevé . [ 17 ] Philosopher Karl Popper regarded Poincaré as the greatest philosopher of science of all time, [ 18 ] with Poincaré also originating the conventionalist view in science. [ 19 ] Poincaré was a public intellectual in his time, and personally, he believed in political equality for all, while wary of the influence of anti-intellectual positions that the Catholic Church held at the time. [ 20 ] He served as the president of the French Academy of Sciences (1906), the president of Société astronomique de France (1901–1903), and twice the president of Société mathématique de France (1886, 1900).
Poincaré was born on 29 April 1854 in Cité Ducale neighborhood, Nancy, Meurthe-et-Moselle , into an influential French family. [ 21 ] His father Léon Poincaré [ fr ] (1828–1892) was a professor of medicine at the University of Nancy . [ 22 ] His younger sister Aline married the spiritual philosopher Émile Boutroux . Another notable member of Henri's family was his cousin, Raymond Poincaré , a fellow member of the Académie française , who was President of France from 1913 to 1920, and three-time Prime Minister of France between 1913 and 1929. [ 23 ]
During his childhood he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugénie Launois (1830–1897).
In 1862, Henri entered the Lycée in Nancy (now renamed the Lycée Henri-Poincaré [ fr ] in his honour, along with Henri Poincaré University , also in Nancy). He spent eleven years at the Lycée and during this time he proved to be one of the top students in every topic he studied. He excelled in written composition. His mathematics teacher described him as a "monster of mathematics" and he won first prizes in the concours général , a competition between the top pupils from all the Lycées across France. His poorest subjects were music and physical education, where he was described as "average at best". [ 24 ] Poor eyesight and a tendency towards absentmindedness may explain these difficulties. [ 25 ] He graduated from the Lycée in 1871 with a baccalauréat in both letters and sciences.
During the Franco-Prussian War of 1870, he served alongside his father in the Ambulance Corps .
Poincaré entered the École Polytechnique as the top qualifier in 1873 and graduated in 1875. There he studied mathematics as a student of Charles Hermite , continuing to excel and publishing his first paper ( Démonstration nouvelle des propriétés de l'indicatrice d'une surface ) in 1874. From November 1875 to June 1878 he studied at the École des Mines , while continuing the study of mathematics in addition to the mining engineering syllabus, and received the degree of ordinary mining engineer in March 1879. [ 26 ]
As a graduate of the École des Mines, he joined the Corps des Mines as an inspector for the Vesoul region in northeast France. He was on the scene of a mining disaster at Magny in August 1879 in which 18 miners died. He carried out the official investigation into the accident.
At the same time, Poincaré was preparing for his Doctorate in Science in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of differential equations . It was named Sur les propriétés des fonctions définies par les équations aux différences partielles . Poincaré devised a new way of studying the properties of these equations. He not only faced the question of determining the integral of such equations, but also was the first person to study their general geometric properties. He realised that they could be used to model the behaviour of multiple bodies in free motion within the Solar System . He graduated from the University of Paris in 1879.
After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the University of Caen in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of automorphic functions .
There, in Caen , he met his future wife, Louise Poulain d'Andecy (1857–1934), granddaughter of Isidore Geoffroy Saint-Hilaire and great-granddaughter of Étienne Geoffroy Saint-Hilaire and on 20 April 1881, they married. [ 27 ] Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893).
Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the University of Paris ; he accepted the invitation. During the years 1883 to 1897, he taught mathematical analysis in the École Polytechnique .
In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations . He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in celestial mechanics and mathematical physics .
He never fully abandoned his career in the mining administration to mathematics. He worked at the Ministry of Public Services as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps des Mines in 1893 and inspector general in 1910.
Beginning in 1881 and for the rest of his career, he taught at the University of Paris (the Sorbonne ). He was initially appointed as the maître de conférences d'analyse (associate professor of analysis). [ 28 ] Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, [ 29 ] and Celestial Mechanics and Astronomy.
In 1887, at the young age of 32, Poincaré was elected to the French Academy of Sciences . He became its president in 1906, and was elected to the Académie française on 5 March 1908.
In 1887, he won Oscar II, King of Sweden 's mathematical competition for a resolution of the three-body problem concerning the free motion of multiple orbiting bodies. (See three-body problem section below.)
In 1893, Poincaré joined the French Bureau des Longitudes , which engaged him in the synchronisation of time around the world. In 1897 Poincaré backed an unsuccessful proposal for the decimalisation of circular measure , and hence time and longitude . [ 30 ] It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See work on relativity section below.)
In 1904, he intervened in the trials of Alfred Dreyfus , attacking the spurious scientific claims regarding evidence brought against Dreyfus.
Poincaré was the President of the Société Astronomique de France (SAF) , the French astronomical society, from 1901 to 1903. [ 31 ]
Poincaré had two notable doctoral students at the University of Paris, Louis Bachelier (1900) and Dimitrie Pompeiu (1905). [ 32 ]
In 1912, Poincaré underwent surgery for a prostate problem and subsequently died from an embolism on 17 July 1912, in Paris. He was 58 years of age. He is buried in the Poincaré family vault in the Cemetery of Montparnasse , Paris, in section 16 close to the gate Rue Émile-Richard.
A former French Minister of Education, Claude Allègre , proposed in 2004 that Poincaré be reburied in the Panthéon in Paris, which is reserved for French citizens of the highest honour. [ 33 ]
Poincaré made many contributions to different fields of pure and applied mathematics such as: celestial mechanics , fluid mechanics , optics , electricity , telegraphy , capillarity , elasticity , thermodynamics , potential theory , Quantum mechanics , theory of relativity and physical cosmology .
Among the specific topics he contributed to are the following:
The problem of finding the general solution to the motion of more than two orbiting bodies in the Solar System had eluded mathematicians since Newton's time. This was known originally as the three-body problem and later the n -body problem , where n is any number of more than two orbiting bodies. The n -body solution was considered very important and challenging at the close of the 19th century. Indeed, in 1887, in honour of his 60th birthday, Oscar II, King of Sweden , advised by Gösta Mittag-Leffler , established a prize for anyone who could find the solution to the problem. The announcement was quite specific:
Given a system of arbitrarily many mass points that attract each according to Newton's law , under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly .
In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prizeworthy. The prize was finally awarded to Poincaré, even though he did not solve the original problem. One of the judges, the distinguished Karl Weierstrass , said, "This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics." (The first version of his contribution even contained a serious error; for details see the article by Diacu [ 35 ] and the book by Barrow-Green [ 36 ] ). The version finally printed [ 37 ] contained many important ideas which led to the theory of chaos . The problem as stated originally was finally solved by Karl F. Sundman for n = 3 in 1912 and was generalised to the case of n > 3 bodies by Qiudong Wang in the 1990s. The series solutions have very slow convergence. It would take millions of terms to determine the motion of the particles for even very short intervals of time, so they are unusable in numerical work. [ 35 ]
Poincaré's work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the " luminiferous aether "), could be synchronised. At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" t ′ = t − v x / c 2 {\displaystyle t^{\prime }=t-vx/c^{2}\,} [ 38 ] and introduced the hypothesis of length contraction to explain the failure of optical and electrical experiments to detect motion relative to the aether (see Michelson–Morley experiment ). [ 39 ] Poincaré was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincaré as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In The Measure of Time (1898), Poincaré said, "A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention." He also argued that scientists have to set the constancy of the speed of light as a postulate to give physical theories the simplest form. [ 40 ] Based on these assumptions he discussed in 1900 Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronised by exchanging light signals assumed to travel with the same speed in both directions in a moving frame. [ 41 ]
In 1881 Poincaré described hyperbolic geometry in terms of the hyperboloid model , formulating transformations leaving invariant the Lorentz interval x 2 + y 2 − z 2 = − 1 {\displaystyle x^{2}+y^{2}-z^{2}=-1} , which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions. [ 42 ] [ 43 ] In addition, Poincaré's other models of hyperbolic geometry ( Poincaré disk model , Poincaré half-plane model ) as well as the Beltrami–Klein model can be related to the relativistic velocity space (see Gyrovector space ).
In 1892 Poincaré developed a mathematical theory of light including polarization . His vision of the action of polarizers and retarders, acting on a sphere representing polarized states, is called the Poincaré sphere . [ 44 ] It was shown that the Poincaré sphere possesses an underlying Lorentzian symmetry, by which it can be used as a geometrical representation of Lorentz transformations and velocity additions. [ 45 ]
He discussed the "principle of relative motion" in two papers in 1900 [ 41 ] [ 46 ] and named it the principle of relativity in 1904, according to which no physical experiment can discriminate between a state of uniform motion and a state of rest. [ 47 ] In 1905 Poincaré wrote to Lorentz about Lorentz's paper of 1904, which Poincaré described as a "paper of supreme importance". In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz. [ 48 ] In a second letter to Lorentz, Poincaré gave his own reason why Lorentz's time dilation factor was indeed correct after all—it was necessary to make the Lorentz transformation form a group—and he gave what is now known as the relativistic velocity-addition law. [ 49 ] Poincaré later delivered a paper at the meeting of the Academy of Sciences in Paris on 5 June 1905 in which these issues were addressed. In the published version of that he wrote: [ 50 ]
The essential point, established by Lorentz, is that the equations of the electromagnetic field are not altered by a certain transformation (which I will call by the name of Lorentz) of the form:
and showed that the arbitrary function ℓ ( ε ) {\displaystyle \ell \left(\varepsilon \right)} must be unity for all ε {\displaystyle \varepsilon } (Lorentz had set ℓ = 1 {\displaystyle \ell =1} by a different argument) to make the transformations form a group. In an enlarged version of the paper that appeared in 1906 Poincaré pointed out that the combination x 2 + y 2 + z 2 − c 2 t 2 {\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}} is invariant . He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing c t − 1 {\displaystyle ct{\sqrt {-1}}} as a fourth imaginary coordinate, and he used an early form of four-vectors . [ 51 ] Poincaré expressed a lack of interest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit. [ 52 ] So it was Hermann Minkowski who worked out the consequences of this notion in 1907. [ 52 ] [ 53 ]
Like others before, Poincaré (1900) discovered a relation between mass and electromagnetic energy . While studying the conflict between the action/reaction principle and Lorentz ether theory , he tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields are included. [ 41 ] He noticed that the action/reaction principle does not hold for matter alone, but that the electromagnetic field has its own momentum. Poincaré concluded that the electromagnetic field energy of an electromagnetic wave behaves like a fictitious fluid ( fluide fictif ) with a mass density of E / c 2 . If the center of mass frame is defined by both the mass of matter and the mass of the fictitious fluid, and if the fictitious fluid is indestructible— it's neither created or destroyed —then the motion of the center of mass frame remains uniform. But electromagnetic energy can be converted into other forms of energy. So Poincaré assumed that there exists a non-electric energy fluid at each point of space, into which electromagnetic energy can be transformed and which also carries a mass proportional to the energy. In this way, the motion of the center of mass remains uniform. Poincaré said that one should not be too surprised by these assumptions, since they are only mathematical fictions.
However, Poincaré's resolution led to a paradox when changing frames: if a Hertzian oscillator radiates in a certain direction, it will suffer a recoil from the inertia of the fictitious fluid. Poincaré performed a Lorentz boost (to order v / c ) to the frame of the moving source. He noted that energy conservation holds in both frames, but that the law of conservation of momentum is violated. This would allow perpetual motion , a notion which he abhorred. The laws of nature would have to be different in the frames of reference , and the relativity principle would not hold. Therefore, he argued that also in this case there has to be another compensating mechanism in the ether .
Poincaré himself came back to this topic in his St. Louis lecture (1904). [ 47 ] He rejected [ 54 ] the possibility that energy carries mass and criticized his own solution to compensate the above-mentioned problems:
The apparatus will recoil as if it were a cannon and the projected energy a ball, and that contradicts the principle of Newton, since our present projectile has no mass; it is not matter, it is energy. [..] Shall we say that the space which separates the oscillator from the receiver and which the disturbance must traverse in passing from one to the other, is not empty, but is filled not only with ether, but with air, or even in inter-planetary space with some subtile, yet ponderable fluid; that this matter receives the shock, as does the receiver, at the moment the energy reaches it, and recoils, when the disturbance leaves it? That would save Newton's principle, but it is not true. If the energy during its propagation remained always attached to some material substratum, this matter would carry the light along with it and Fizeau has shown, at least for the air, that there is nothing of the kind. Michelson and Morley have since confirmed this. We might also suppose that the motions of matter proper were exactly compensated by those of the ether; but that would lead us to the same considerations as those made a moment ago. The principle, if thus interpreted, could explain anything, since whatever the visible motions we could imagine hypothetical motions to compensate them. But if it can explain anything, it will allow us to foretell nothing; it will not allow us to choose between the various possible hypotheses, since it explains everything in advance. It therefore becomes useless.
In the above quote he refers to the Hertz assumption of total aether entrainment that was falsified by the Fizeau experiment but that experiment does indeed show that that light is partially "carried along" with a substance. Finally in 1908 [ 55 ] he revisits the problem and ends with abandoning the principle of reaction altogether in favor of supporting a solution based in the inertia of aether itself.
But we have seen above that Fizeau's experiment does not permit of our retaining the theory of Hertz; it is necessary therefore to adopt the theory of Lorentz, and consequently to renounce the principle of reaction.
He also discussed two other unexplained effects: (1) non-conservation of mass implied by Lorentz's variable mass γ m {\displaystyle \gamma m} , Abraham's theory of variable mass and Kaufmann 's experiments on the mass of fast moving electrons and (2) the non-conservation of energy in the radium experiments of Marie Curie .
It was Albert Einstein 's concept of mass–energy equivalence (1905) that a body losing energy as radiation or heat was losing mass of amount m = E / c 2 that resolved [ 56 ] Poincaré's paradox, without using any compensating mechanism within the ether. [ 57 ] The Hertzian oscillator loses mass in the emission process, and momentum is conserved in any frame. However, concerning Poincaré's solution of the Center of Gravity problem, Einstein noted that Poincaré's formulation and his own from 1906 were mathematically equivalent. [ 58 ]
In 1905 Poincaré first proposed gravitational waves ( ondes gravifiques ) emanating from a body and propagating at the speed of light. He wrote:
It has become important to examine this hypothesis more closely and in particular to ask in what ways it would require us to modify the laws of gravitation. That is what I have tried to determine; at first I was led to assume that the propagation of gravitation is not instantaneous, but happens with the speed of light. [ 59 ] [ 50 ]
Einstein's first paper on relativity was published three months after Poincaré's short paper, [ 50 ] but before Poincaré's longer version. [ 51 ] Einstein relied on the principle of relativity to derive the Lorentz transformations and used a similar clock synchronisation procedure ( Einstein synchronisation ) to the one that Poincaré (1900) had described, but Einstein's paper was remarkable in that it contained no references at all. Poincaré never acknowledged Einstein's work on special relativity . However, Einstein expressed sympathy with Poincaré's outlook obliquely in a letter to Hans Vaihinger on 3 May 1919, when Einstein considered Vaihinger's general outlook to be close to his own and Poincaré's to be close to Vaihinger's. [ 60 ] In public, Einstein acknowledged Poincaré posthumously in the text of a lecture in 1921 titled " Geometrie und Erfahrung (Geometry and Experience)" in connection with non-Euclidean geometry , but not in connection with special relativity. A few years before his death, Einstein commented on Poincaré as being one of the pioneers of relativity, saying "Lorentz had already recognized that the transformation named after him is essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further ....". [ 61 ]
Poincaré's work in the development of special relativity is well recognised, [ 56 ] though most historians stress that despite many similarities with Einstein's work, the two had very different research agendas and interpretations of the work. [ 62 ] Poincaré developed a similar physical interpretation of local time and noticed the connection to signal velocity, but contrary to Einstein he continued to use the ether-concept in his papers and argued that clocks at rest in the ether show the "true" time, and moving clocks show the local time. So Poincaré tried to keep the relativity principle in accordance with classical concepts, while Einstein developed a mathematically equivalent kinematics based on the new physical concepts of the relativity of space and time. [ 63 ] [ 64 ] [ 65 ] [ 66 ] [ 67 ]
While this is the view of most historians, a minority go much further, such as E. T. Whittaker , who held that Poincaré and Lorentz were the true discoverers of relativity. [ 68 ]
Poincaré introduced group theory to physics, and was the first to study the group of Lorentz transformations . [ 69 ] [ 70 ] He also made major contributions to the theory of discrete groups and their representations.
The subject is clearly defined by Felix Klein in his "Erlangen Program" (1872): the geometry invariants of arbitrary continuous transformation, a kind of geometry. The term "topology" was introduced, as suggested by Johann Benedict Listing , instead of previously used "Analysis situs". Some important concepts were introduced by Enrico Betti and Bernhard Riemann . But the foundation of this science, for a space of any dimension, was created by Poincaré. His first article on this topic appeared in 1894. [ 71 ]
His research in geometry led to the abstract topological definition of homotopy and homology . He also first introduced the basic concepts and invariants of combinatorial topology, such as Betti numbers and the fundamental group . Poincaré proved a formula relating the number of edges, vertices and faces of n -dimensional polyhedron (the Euler–Poincaré theorem ) and gave the first precise formulation of the intuitive notion of dimension. [ 72 ]
Poincaré published two now classical monographs, "New Methods of Celestial Mechanics" (1892–1899) and "Lectures on Celestial Mechanics" (1905–1910). In them, he successfully applied the results of their research to the problem of the motion of three bodies and studied in detail the behavior of solutions (frequency, stability, asymptotic, and so on). They introduced the small parameter method, fixed points, integral invariants, variational equations, the convergence of the asymptotic expansions. Generalizing a theory of Bruns (1887), Poincaré showed that the three-body problem is not integrable. In other words, the general solution of the three-body problem can not be expressed in terms of algebraic and transcendental functions through unambiguous coordinates and velocities of the bodies. His work in this area was the first major achievement in celestial mechanics since Isaac Newton . [ 73 ]
These monographs include an idea of Poincaré, which later became the basis for mathematical " chaos theory " (see, in particular, the Poincaré recurrence theorem ) and the general theory of dynamical systems .
Poincaré authored important works on astronomy for the equilibrium figures of a gravitating rotating fluid . He introduced the important concept of bifurcation points and proved the existence of equilibrium figures such as the non-ellipsoids, including ring-shaped and pear-shaped figures, and their stability. For this discovery, Poincaré received the Gold Medal of the Royal Astronomical Society (1900). [ 74 ]
After defending his doctoral thesis on the study of singular points of the system of differential equations , Poincaré wrote a series of memoirs under the title "On curves defined by differential equations" (1881–1882). [ 75 ] In these articles, he built a new branch of mathematics, called " qualitative theory of differential equations ". Poincaré showed that even if the differential equation can not be solved in terms of known functions, yet from the very form of the equation, a wealth of information about the properties and behavior of the solutions can be found. In particular, Poincaré investigated the nature of the trajectories of the integral curves in the plane, gave a classification of singular points ( saddle , focus , center , node ), introduced the concept of a limit cycle and the loop index , and showed that the number of limit cycles is always finite, except for some special cases. Poincaré also developed a general theory of integral invariants and solutions of the variational equations. For the finite-difference equations , he created a new direction – the asymptotic analysis of the solutions. He applied all these achievements to study practical problems of mathematical physics and celestial mechanics , and the methods used were the basis of its topological works. [ 76 ]
Poincaré's work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris . He linked his way of thinking to how he made several discoveries.
The mathematician Darboux claimed he was un intuitif (an intuitive ), arguing that this is demonstrated by the fact that he worked so often by visual representation. Jacques Hadamard wrote that Poincaré's research demonstrated marvelous clarity [ 77 ] and Poincaré himself wrote that he believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.
Poincaré's mental organisation was interesting not only to Poincaré himself but also to Édouard Toulouse , a psychologist of the Psychology Laboratory of the School of Higher Studies in Paris. Toulouse wrote a book entitled Henri Poincaré (1910). [ 78 ] [ 79 ] In it, he discussed Poincaré's regular schedule:
These abilities were offset to some extent by his shortcomings:
In addition, Toulouse stated that most mathematicians worked from principles already established while Poincaré started from basic principles each time (O'Connor et al., 2002).
His method of thinking is well summarised as:
Habitué à négliger les détails et à ne regarder que les cimes, il passait de l'une à l'autre avec une promptitude surprenante et les faits qu'il découvrait se groupant d'eux-mêmes autour de leur centre étaient instantanément et automatiquement classés dans sa mémoire (accustomed to neglecting details and to looking only at mountain tops, he went from one peak to another with surprising rapidity, and the facts he discovered, clustering around their center, were instantly and automatically pigeonholed in his memory).
Poincaré is credited with laying the foundations of special relativity , [ 11 ] [ 10 ] with some arguing that he should be credited with its creation. [ 80 ] He is said to have "dominated the mathematics and the theoretical physics of his time", and that "he was without a doubt the most admired mathematician while he was alive, and he remains today one of the world's most emblematic scientific figures." [ 81 ] Poincaré is regarded as a "universal specialist", as he refined celestial mechanics , he progressed nearly all parts of mathematics of his time, including creating new subjects, is a father of special relativity, participated in all the great debates of his time in physics, was a major actor in the great epistemological debates of his day in relation to philosophy of science , and Poincaré was the one who investigated the 1879 Magny shaft firedamp explosion as an engineer. [ 81 ] Due to the breadth of his research, Poincaré was the only member to be elected to every section of the French Academy of Sciences of the time, those being geometry, mechanics, physics, astronomy and navigation. [ 82 ]
Physicist Henri Becquerel nominated Poincaré for a Nobel Prize in 1904, as Becquerel took note that "Poincaré's mathematical and philosophical genius surveyed all of physics and was among those that contributed most to human progress by giving researchers a solid basis for their journeys into the unknown." [ 83 ] After his death, he was praised by many intellectual figures of his time, as the author Marie Bonaparte wrote to his widowed wife Louise that "He was – as you know better than anyone – not only the greatest thinker, the most powerful genius of our time – but also a deep and incomparable heart; and having been close to him remains the precious memory of a whole life." [ 84 ]
Mathematician E.T. Bell titled Poincaré as "The Last Universalist", and noted his prowess in many fields, stating that: [ 85 ]
Poincaré was the last man to take practically all mathematics, both pure and applied, as his province . . . few mathematicians have had the breadth of philosophical vision that Poincaré had and none is his superior in the gift of clear exposition.
When philosopher and mathematician Bertrand Russell was asked who was the greatest man that France had produced in modern times, he instantly replied "Poincaré". [ 85 ] Bell noted that if Poincaré had been as strong in practical science as he was in theoretical, he might have "made a fourth with the incomparable three, Archimedes , Newton , and Gauss ." [ 86 ]
Bell further noted his powerful memory, one that was even superior to Leonhard Euler 's, stating that: [ 86 ]
His principal diversion was reading, where his unusual talents first showed up. A book once read - at incredible speed - became a permanent possession, and he could always state the page and line where a particular thing occurred. He retained this powerful memory all his life. This rare faculty, which Poincaré shared with Euler who had it in a lesser degree, might be called visual or spatial memory. In temporal memory - the ability to recall with uncanny precision a sequence of events long passed — he was also unusually strong.
Bell notes the terrible eyesight of Poincaré, he almost completely remembered formulas and theorems by ear, and "unable to see the board distinctly when he became a student of advanced mathematics, he sat back and listened, following and remembering perfectly without taking notes - an easy feat for him, but one incomprehensible to most mathematicians." [ 86 ]
Awards
Named after him
Henri Poincaré did not receive the Nobel Prize in Physics , but he had influential advocates like Henri Becquerel or committee member Gösta Mittag-Leffler . [ 90 ] [ 91 ] The nomination archive reveals that Poincaré received a total of 51 nominations between 1904 and 1912, the year of his death. [ 92 ] Of the 58 nominations for the 1910 Nobel Prize, 34 named Poincaré. [ 92 ] Nominators included Nobel laureates Hendrik Lorentz and Pieter Zeeman (both of 1902), Marie Curie (of 1903), Albert Michelson (of 1907), Gabriel Lippmann (of 1908) and Guglielmo Marconi (of 1909). [ 92 ]
The fact that renowned theoretical physicists like Poincaré, Boltzmann or Gibbs were not awarded the Nobel Prize is seen as evidence that the Nobel committee had more regard for experimentation than theory. [ 93 ] [ 94 ] In Poincaré's case, several of those who nominated him pointed out that the greatest problem was to name a specific discovery, invention, or technique. [ 90 ]
Poincaré had philosophical views opposite to those of Bertrand Russell and Gottlob Frege , who believed that mathematics was a branch of logic . Poincaré strongly disagreed, claiming that intuition was the life of mathematics. Poincaré gives an interesting point of view in his 1902 book Science and Hypothesis :
For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistaken, this is only from their mistaking its rule.
Poincaré believed that arithmetic is synthetic . He argued that Peano's axioms cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is a priori synthetic and not analytic . Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were similar to those of Immanuel Kant (Kolak, 2001, Folina 1992). He strongly opposed Cantorian set theory , objecting to its use of impredicative definitions. [ 95 ]
However, Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of non-Euclidean space can be known analytically. Poincaré held that convention plays an important role in physics. His view (and some later, more extreme versions of it) came to be known as " conventionalism ". [ 96 ] Poincaré believed that Newton's first law was not empirical but is a conventional framework assumption for mechanics (Gargani, 2012). [ 97 ] He also believed that the geometry of physical space is conventional. He considered examples in which either the geometry of the physical fields or gradients of temperature can be changed, either describing a space as non-Euclidean measured by rigid rulers, or as a Euclidean space where the rulers are expanded or shrunk by a variable heat distribution. However, Poincaré thought that we were so accustomed to Euclidean geometry that we would prefer to change the physical laws to save Euclidean geometry rather than shift to non-Euclidean physical geometry. [ 98 ]
Poincaré's famous lectures before the Société de Psychologie in Paris (published as Science and Hypothesis , The Value of Science , and Science and Method ) were cited by Jacques Hadamard as the source for the idea that creativity and invention consist of two mental stages, first random combinations of possible solutions to a problem, followed by a critical evaluation . [ 99 ]
Although he most often spoke of a deterministic universe , Poincaré said that the subconscious generation of new possibilities involves chance .
It is certain that the combinations which present themselves to the mind in a kind of sudden illumination after a somewhat prolonged period of unconscious work are generally useful and fruitful combinations... all the combinations are formed as a result of the automatic action of the subliminal ego, but those only which are interesting find their way into the field of consciousness... A few only are harmonious, and consequently at once useful and beautiful, and they will be capable of affecting the geometrician's special sensibility I have been speaking of; which, once aroused, will direct our attention upon them, and will thus give them the opportunity of becoming conscious... In the subliminal ego, on the contrary, there reigns what I would call liberty, if one could give this name to the mere absence of discipline and to disorder born of chance. [ 100 ]
Poincaré's two stages—random combinations followed by selection—became the basis for Daniel Dennett 's two-stage model of free will . [ 101 ]
Popular writings on the philosophy of science :
On algebraic topology :
On celestial mechanics :
On the philosophy of mathematics :
Other:
Exhaustive bibliography of English translations:
Here is a list of theorems proved by Poincaré: | https://en.wikipedia.org/wiki/Henri_Poincaré |
Henrik Svensmark (born 1958) is a Danish physicist and professor in the Division of Solar System Physics at the Danish National Space Institute (DTU Space) in Copenhagen . [ 1 ] He is known for his work on the hypothesis that fewer cosmic rays are an indirect cause of global warming via cloud formation. [ 2 ] [ 3 ] [ 4 ]
Henrik Svensmark obtained a Master of Science in Engineering (Cand. Polyt) in 1985 and a Ph.D. in 1987 from the Physics Laboratory I at the Technical University of Denmark . [ 5 ]
Henrik Svensmark is director of the Center for Sun-Climate Research at the Danish Space Research Institute (DSRI), a part of the Danish National Space Center . He previously headed the sun-climate group at DSRI. He held postdoctoral positions in physics at three other organizations: University of California, Berkeley , Nordic Institute for Theoretical Physics , and the Niels Bohr Institute . [ 6 ]
In 1997, Svensmark and Eigil Friis-Christensen popularised a theory that linked galactic cosmic rays and global climate change mediated primarily by variations in the intensity of the solar wind , which they have termed cosmoclimatology . This theory had earlier been reviewed by Dickinson. [ 7 ] One of the small-scale processes related to this link was studied in a laboratory experiment performed at the Danish National Space Center (paper published in the Proceedings of the Royal Society A , February 8, 2007).
Svensmark's conclusions from his research downplay the significance of the effects of man-made increases in atmospheric CO 2 on recent and historical global warming , with him arguing that while the climate change role of greenhouse gases is considerable, solar variations play a larger role. [ citation needed ]
Svensmark detailed his theory of cosmoclimatology in a paper published in 2007. [ 8 ] The Center for Sun-Climate Research at the Danish National Space Institute "investigates the connection between solar activity and climatic changes on Earth". [ 9 ] [ 10 ] Its homepage lists several publications earlier works related to cosmoclimatology. [ 11 ] [ 12 ]
Svensmark and Nigel Calder published a book The Chilling Stars: A New Theory of Climate Change (2007) describing the Cosmoclimatology theory that cosmic rays "have more effect on the climate than manmade CO 2 ":
A documentary film on Svensmark's theory, The Cloud Mystery , was produced by Lars Oxfeldt Mortensen [ 14 ] [ 15 ] and premiered in January 2008 on Danish TV 2.
In April 2012, Svensmark published an expansion of his theory in the Monthly Notices of the Royal Astronomical Society [ 16 ]
In the new work he claims that the diversity of life on Earth over the last 500 million years might be explained by tectonics affecting the sea-level together with variations in the local supernova rate, and virtually nothing else. This suggests that the progress of evolution is affected by climate variation depending on the galactic cosmic ray flux.
The director of DTU Space, Prof. Eigil Friis-Christensen, commented: "When this enquiry into effects of cosmic rays from supernova remnants began 16 years ago, we never imagined that it would lead us so deep into time, or into so many aspects of the Earth's history. The connection to evolution is a culmination of this work."
Preliminary experimental tests have been conducted in the SKY Experiment at the Danish National Space Science Center. CERN , the European Organization for Nuclear Research in Geneva, is preparing comprehensive verification in the CLOUD Project.
Svensmark conducted proof of concept experiments in the SKY Experiment at the Danish National Space Institute. [ 17 ]
To investigate the role of cosmic rays in cloud formation low in the Earth's atmosphere, the SKY experiment used natural muons (heavy electrons) that can penetrate even to the basement of the National Space Institute in Copenhagen. The hypothesis, verified by the experiment, is that electrons released in the air by the passing muons promote the formation of molecular clusters that are building blocks for cloud condensation nuclei.
Critics of the hypothesis claimed that particle clusters produced measured just a few nanometres across, whereas aerosols typically need to have a diameter of at least 50 nm in order to serve as so-called cloud condensation nuclei. Further experiments by Svensmark and collaborators published in 2013 [ 18 ] showed that aerosols with diameter larger than 50 nm are produced by ultraviolet light (from trace amounts of ozone , sulfur dioxide , and water vapor), large enough to serve as cloud condensation nuclei.
Scientists are preparing detailed atmospheric physics experiments to test Svensmark's thesis, building on the Danish findings. CERN started a multi-phase project in 2006, including rerunning the Danish experiment. CERN plans to use an accelerator rather than rely on natural cosmic rays. CERN's multinational project will give scientists a permanent facility where they can study the effects of both cosmic rays and charged particles in the Earth's atmosphere. [ 19 ] CERN's project is named CLOUD (Cosmics Leaving OUtdoor Droplets). [ 20 ]
Dunne et al. (2016) have presented the main outcomes of 10 years of results obtained at the CLOUD experiment performed at CERN. They have studied in detail the physico-chemical mechanisms and the kinetics of aerosols formation. The nucleation process of water droplets/ice micro-crystals from water vapor reproduced in the CLOUD experiment and also directly observed in the Earth atmosphere do not only involve ions formation due to cosmic rays but also a range of complex chemical reactions with sulfuric acid , ammonia and organic compounds emitted in the air by human activities and by organisms living on land or in the oceans ( plankton ). [ 21 ] Although they observe that a fraction of cloud nuclei is effectively produced by ionisation due to the interaction of cosmic rays with the constituents of Earth atmosphere, this process is insufficient to attribute the present climate modifications to the fluctuations of the cosmic rays intensity modulated by changes in the solar activity and Earth magnetosphere.
Oceanographer Paul Farrar (2000) [ 22 ] argued that, based on the spatial distribution of the cloud variation during Svensmark's study period, the variation was due to an El Niño which was synchronized with the cosmic ray signal used by Svensmark during the data period of his study.
A (2003) critique by physicist Peter Laut of Svensmark's theory reanalyzed Svensmark's data and suggested that it does not support a correlation between cosmic rays and global temperature changes; it also disputes some of the theoretical bases for the theory. [ 23 ] Svensmark replied to the paper, stating that "...nowhere in Peter Laut’s (PL) paper has he been able to explain, where physical data have been handled incorrectly, how the character of my papers are misleading, or where my work does not live up to scientific standards" [ 24 ]
Mike Lockwood of the UK's Rutherford Appleton Laboratory and Claus Froehlich of the World Radiation Center in Switzerland published a paper in 2007 which concluded that the increase in mean global temperature observed since 1985 correlates so poorly with solar variability that no type of causal mechanism may be ascribed to it, although they accept that there is "considerable evidence" for solar influence on Earth's pre-industrial climate and to some degree also for climate changes in the first half of the 20th century. [ 25 ]
Svensmark's coauthor Calder responded to the study in an interview with LondonBookReview.com, where he put forth the counterclaim that global temperature has not risen since 1999. [ 26 ]
Later in 2007, Svensmark and Friis-Christensen brought out a Reply to Lockwood and Fröhlich which concludes that surface air temperature records used by Lockwood and Fröhlich apparently are a poor guide to Sun-driven physical processes, but tropospheric air temperature records do show an impressive negative correlation between cosmic-ray flux and air temperatures up to 2006 if a warming trend, oceanic oscillations and volcanism are removed from the temperature data. They also point out that Lockwood and Fröhlich present their data by using running means of around 10 years, which creates the illusion of a continued temperature rise, whereas all unsmoothed data point to a flattening of the temperature, coincident with the present maxing out of the magnetic activity of the Sun, and which the continued rapid increase in CO 2 concentrations seemingly has been unable to overrule.
In April 2008, Professor Terry Sloan of Lancaster University published a paper in the journal Environmental Research Letters titled "Testing the proposed causal link between cosmic rays and cloud cover", [ 27 ] which found no significant link between cloud cover and cosmic ray intensity in the last 20 years. Svensmark responded by saying "Terry Sloan has simply failed to understand how cosmic rays work on clouds". [ 28 ] Dr. Giles Harrison of Reading University , describes the work as important "as it provides an upper limit on the cosmic ray-cloud effect in global satellite cloud data". Harrison studied the effect of cosmic rays in the UK. [ 29 ] He states: "Although the statistically significant non-linear cosmic ray effect is small, it will have a considerably larger aggregate effect on longer timescale (e.g. century) climate variations when day-to-day variability averages out". Brian H. Brown (2008) of Sheffield University further found a statistically significant (p<0.05) short term 3% association between Galactic Cosmic Rays (GCR) and low level clouds over 22 years with a 15-hour delay. Long-term changes in cloud cover (> 3 months) and GCR gave correlations of p=0.06. [ 30 ]
More recently, Laken et al. (2012) [ 31 ] found that new high quality satellite data show that the El Niño Southern Oscillation is responsible for most changes in cloud cover at the global and regional levels. They also found that galactic cosmic rays, and total solar irradiance did not have any statistically significant influence on changes in cloud cover.
Lockwood (2012) [ 32 ] conducted a thorough review of the scientific literature on the "solar influence" on climate. It was found that when this influence is included appropriately into climate models causal climate change claims such as those made by Svensmark are shown to have been exaggerated. Lockwood's review also highlighted the strength of evidence in favor of the solar influence on regional climates.
Sloan and Wolfendale (2013) [ 33 ] demonstrated that while temperature models showed a small correlation every 22 years, less than 14 percent of global warming since the 1950s could be attributed to cosmic ray rate. The study concluded that the cosmic ray rate did not match the changes in temperature, indicating that it was not a causal relationship. Another 2013 study found, contrary to Svensmark's claims, "no statistically significant correlations between cosmic rays and global albedo or globally averaged cloud height." [ 34 ]
In 2013, a laboratory study by Svensmark, Pepke and Pedersen published in Physics Letters A showed that there is in fact a correlation between cosmic rays and the formation of aerosols of the type that seed clouds. Extrapolating from the laboratory to the actual atmosphere, the authors asserted that solar activity is responsible for approximately 50 percent of temperature variation. [ 35 ] [ 36 ]
In a detailed 2007 post on the scientists' blog RealClimate , Rasmus E. Benestad presented arguments for considering Svensmark's claims to be "wildly exaggerated". [ 37 ] ( Time magazine has characterized the main purpose of this blog as a "straightforward presentation of the physical evidence for global warming". [ 38 ] ) | https://en.wikipedia.org/wiki/Henrik_Svensmark |
In physical chemistry , Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional at equilibrium to its partial pressure above the liquid. The proportionality factor is called Henry's law constant . It was formulated by the English chemist William Henry , who studied the topic in the early 19th century.
In simple words, it states that the partial pressure of a gas in the vapour phase is directly proportional to the mole fraction of a gas in solution.
An example where Henry's law is at play is the depth-dependent dissolution of oxygen and nitrogen in the blood of underwater divers that changes during decompression , going to decompression sickness . An everyday example is carbonated soft drinks , which contain dissolved carbon dioxide. Before opening, the gas above the drink in its container is almost pure carbon dioxide , at a pressure higher than atmospheric pressure . After the bottle is opened, this gas escapes, moving the partial pressure of carbon dioxide above the liquid to be much lower, resulting in degassing as the dissolved carbon dioxide comes out of the solution.
In his 1803 publication about the quantity of gases absorbed by water, [ 1 ] William Henry described the results of his experiments:
… water takes up, of gas condensed by one, two, or more additional atmospheres, a quantity which, ordinarily compressed, would be equal to twice, thrice, &c. the volume absorbed under the common pressure of the atmosphere.
Charles Coulston Gillispie states that John Dalton "supposed that the separation of gas particles one from another in the vapor phase bears the ratio of a small whole number to their interatomic distance in solution. Henry's law follows as a consequence if this ratio is a constant for each gas at a given temperature." [ 2 ]
Under high pressure, solubility of CO 2 increases. On opening a container of a carbonated beverage under pressure, pressure decreases to atmospheric, so that solubility decreases and the carbon dioxide forms bubbles that are released from the liquid.
It is often noted that beer served by gravity (that is, directly from a tap in the cask) is less heavily carbonated than the same beer served via a hand-pump (or beer-engine). This is because beer is pressurised on its way to the point of service by the action of the beer engine, causing carbon dioxide to dissolve in the beer. This then comes out of solution once the beer has left the pump, causing a higher level of perceptible 'condition' in the beer.
Concentration of O 2 in the blood and tissues is so low that they feel weak and are unable to think properly, a condition called hypoxia .
In underwater diving , gas is breathed at the ambient pressure which increases with depth due to the hydrostatic pressure . Solubility of gases increases with greater depth (greater pressure) according to Henry's law, so the body tissues take on more gas over time in greater depths of water. When ascending the diver is decompressed and the solubility of the gases dissolved in the tissues decreases accordingly. If the supersaturation is too great, bubbles may form and grow, and the presence of these bubbles can cause blockages in capillaries, or distortion in the more solid tissues which can cause damage known as decompression sickness . To avoid this injury the diver must ascend slowly enough that the excess dissolved gas is carried away by the blood and released into the lung gas.
There are many ways to define the proportionality constant of Henry's law, which can be subdivided into two fundamental types: One possibility is to put the aqueous phase into the numerator and the gaseous phase into the denominator ("aq/gas"). This results in the Henry's law solubility constant H s {\displaystyle H_{\rm {s}}} . Its value increases with increased solubility. Alternatively, numerator and denominator can be switched ("gas/aq"), which results in the Henry's law volatility constant H v {\displaystyle H_{\rm {v}}} . The value of H v {\displaystyle H_{\rm {v}}} decreases with increased solubility. IUPAC describes several variants of both fundamental types. [ 3 ] This results from the multiplicity of quantities that can be chosen to describe the composition of the two phases. Typical choices for the aqueous phase are molar concentration ( c a {\displaystyle c_{\rm {a}}} ), molality ( b {\displaystyle b} ), and molar mixing ratio ( x {\displaystyle x} ). For the gas phase, molar concentration ( c g {\displaystyle c_{\rm {g}}} ) and partial pressure ( p {\displaystyle p} ) are often used. It is not possible to use the gas-phase mixing ratio ( y {\displaystyle y} ) because at a given gas-phase mixing ratio, the aqueous-phase concentration c a {\displaystyle c_{\rm {a}}} depends on the total pressure and thus the ratio y / c a {\displaystyle y/c_{\rm {a}}} is not a constant. [ 4 ] To specify the exact variant of the Henry's law constant, two superscripts are used. They refer to the numerator and the denominator of the definition. For example, H s c p {\displaystyle H_{\rm {s}}^{cp}} refers to the Henry solubility defined as c / p {\displaystyle c/p} .
Atmospheric chemists often define the Henry solubility as H s c p = c a p , {\displaystyle H_{\text{s}}^{cp}={\frac {c_{\text{a}}}{p}},} where c a {\displaystyle c_{\text{a}}} is the concentration of a species in the aqueous phase, and p {\displaystyle p} is the partial pressure of that species in the gas phase under equilibrium conditions.
The SI unit for H s c p {\displaystyle H_{\text{s}}^{cp}} is mol/(m 3 ·Pa); however, often the unit M / atm is used, since c a {\displaystyle c_{\text{a}}} is usually expressed in M (1 M = 1 mol/dm 3 ) and p {\displaystyle p} in atm (1 atm = 101325 Pa).
The Henry solubility can also be expressed as the dimensionless ratio between the aqueous-phase concentration c a {\displaystyle c_{\text{a}}} of a species and its gas-phase concentration c g {\displaystyle c_{\text{g}}} : H s c c = c a c g . {\displaystyle H_{\text{s}}^{cc}={\frac {c_{\text{a}}}{c_{\text{g}}}}.}
For an ideal gas, the conversion is H s c c = R T H s c p , {\displaystyle H_{\text{s}}^{cc}=RTH_{\text{s}}^{cp},} where R {\displaystyle R} is the gas constant , and T {\displaystyle T} is the temperature.
Sometimes, this dimensionless constant is called the water–air partitioning coefficient K WA {\displaystyle K_{\text{WA}}} . [ 5 ] It is closely related to the various, slightly different definitions of the Ostwald coefficient L {\displaystyle L} , as discussed by Battino (1984). [ 6 ]
Another Henry's law solubility constant is H s x p = x p , {\displaystyle H_{\text{s}}^{xp}={\frac {x}{p}},} where x {\displaystyle x} is the molar mixing ratio in the aqueous phase. For a dilute aqueous solution the conversion between x {\displaystyle x} and c a {\displaystyle c_{\text{a}}} is c a ≈ x ρ H 2 O M H 2 O , {\displaystyle c_{\text{a}}\approx x{\frac {\rho _{{\ce {H2O}}}}{M_{{\ce {H_2O}}}}},} where ρ H 2 O {\displaystyle \rho _{{\ce {H2O}}}} is the density of water, and M H 2 O {\displaystyle M_{{\ce {H2O}}}} is the molar mass of water. Thus H s x p ≈ M H 2 O ρ H 2 O H s c p . {\displaystyle H_{\text{s}}^{xp}\approx {\frac {M_{{\ce {H2O}}}}{\rho _{{\ce {H2O}}}}}H_{\text{s}}^{cp}.}
The SI unit for H s x p {\displaystyle H_{\text{s}}^{xp}} is Pa −1 , although atm −1 is still frequently used.
It can be advantageous to describe the aqueous phase in terms of molality instead of concentration. The molality of a solution does not change with T {\displaystyle T} , since it refers to the mass of the solvent. In contrast, the concentration c {\displaystyle c} does change with T {\displaystyle T} , since the density of a solution and thus its volume are temperature-dependent. Defining the aqueous-phase composition via molality has the advantage that any temperature dependence of the Henry's law constant is a true solubility phenomenon and not introduced indirectly via a density change of the solution. Using molality, the Henry solubility can be defined as H s b p = b p , {\displaystyle H_{\text{s}}^{bp}={\frac {b}{p}},} where b {\displaystyle b} is used as the symbol for molality (instead of m {\displaystyle m} ) to avoid confusion with the symbol m {\displaystyle m} for mass. The SI unit for H s b p {\displaystyle H_{\text{s}}^{bp}} is mol/(kg·Pa). There is no simple way to calculate H s c p {\displaystyle H_{\text{s}}^{cp}} from H s b p {\displaystyle H_{\text{s}}^{bp}} , since the conversion between concentration c a {\displaystyle c_{\text{a}}} and molality b {\displaystyle b} involves all solutes of a solution. For a solution with a total of n {\displaystyle n} solutes with indices i = 1 , … , n {\displaystyle i=1,\ldots ,n} , the conversion is c a = b ρ 1 + ∑ i = 1 n b i M i , {\displaystyle c_{\text{a}}={\frac {b\rho }{1+\sum \limits _{i=1}^{n}b_{i}M_{i}}},} where ρ {\displaystyle \rho } is the density of the solution, and M i {\displaystyle M_{i}} are the molar masses. Here b {\displaystyle b} is identical to one of the b i {\displaystyle b_{i}} in the denominator. If there is only one solute, the equation simplifies to c a = b ρ 1 + b M . {\displaystyle c_{\text{a}}={\frac {b\rho }{1+bM}}.}
Henry's law is only valid for dilute solutions where b M ≪ 1 {\displaystyle bM\ll 1} and ρ ≈ ρ H 2 O {\displaystyle \rho \approx \rho _{{\ce {H2O}}}} . In this case the conversion reduces further to c a ≈ b ρ H 2 O , {\displaystyle c_{\text{a}}\approx b\rho _{{\ce {H2O}}},} and thus H s b p ≈ H s c p ρ H 2 O . {\displaystyle H_{\text{s}}^{bp}\approx {\frac {H_{\text{s}}^{cp}}{\rho _{{\ce {H2O}}}}}.}
According to Sazonov and Shaw, [ 7 ] the dimensionless Bunsen coefficient α {\displaystyle \alpha } is defined as "the volume of saturating gas, V 1 , reduced to T ° = 273.15 K, p ° = 1 bar, which is absorbed by unit volume V 2 * of pure solvent at the temperature of measurement and partial pressure of 1 bar." If the gas is ideal, the pressure cancels out, and the conversion to H s c p {\displaystyle H_{\text{s}}^{cp}} is simply H s c p = α 1 R T STP , {\displaystyle H_{\text{s}}^{cp}=\alpha {\frac {1}{RT^{\text{STP}}}},} with T STP {\displaystyle T^{\text{STP}}} = 273.15 K. Note, that according to this definition, the conversion factor is not temperature-dependent. Independent of the temperature that the Bunsen coefficient refers to, 273.15 K is always used for the conversion. The Bunsen coefficient, which is named after Robert Bunsen , has been used mainly in the older literature, and IUPAC considers it to be obsolete. [ 3 ]
According to Sazonov and Shaw, [ 7 ] the Kuenen coefficient S {\displaystyle S} is defined as "the volume of saturating gas V (g), reduced to T ° = 273.15 K, p ° = bar, which is dissolved by unit mass of pure solvent at the temperature of measurement and partial pressure 1 bar." If the gas is ideal, the relation to H s c p {\displaystyle H_{\text{s}}^{cp}} is H s c p = S ρ R T STP , {\displaystyle H_{\text{s}}^{cp}=S{\frac {\rho }{RT^{\text{STP}}}},} where ρ {\displaystyle \rho } is the density of the solvent, and T STP {\displaystyle T^{\text{STP}}} = 273.15 K. The SI unit for S {\displaystyle S} is m 3 /kg. [ 7 ] The Kuenen coefficient, which is named after Johannes Kuenen , has been used mainly in the older literature, and IUPAC considers it to be obsolete. [ 3 ]
A common way to define a Henry volatility is dividing the partial pressure by the aqueous-phase concentration:
The SI unit for H v p c {\displaystyle H_{\rm {v}}^{pc}} is Pa·m 3 /mol.
Another Henry volatility is
The SI unit for H v p x {\displaystyle H_{\rm {v}}^{px}} is Pa. However, atm is still frequently used.
The Henry volatility can also be expressed as the dimensionless ratio between the gas-phase concentration c g {\displaystyle c_{\text{g}}} of a species and its aqueous-phase concentration c a {\displaystyle c_{\text{a}}} :
In chemical engineering and environmental chemistry , this dimensionless constant is often called the air–water partitioning coefficient K AW {\displaystyle K_{\text{AW}}} . [ 8 ] [ 9 ]
A large compilation of Henry's law constants has been published by Sander (2023). [ 10 ] A few selected values are shown in the table below:
When the temperature of a system changes, the Henry constant also changes. The temperature dependence of equilibrium constants can generally be described with the Van 't Hoff equation , which also applies to Henry's law constants:
where Δ sol H {\displaystyle \Delta _{\text{sol}}H} is the enthalpy of dissolution. Note that the letter H {\displaystyle H} in the symbol Δ sol H {\displaystyle \Delta _{\text{sol}}H} refers to enthalpy and is not related to the letter H {\displaystyle H} for Henry's law constants. This applies to the Henry's solubility ratio, H s {\displaystyle H_{s}} ; for Henry's volatility ratio, H v {\displaystyle H_{v}} , the sign of the right-hand side must be reversed.
Integrating the above equation and creating an expression based on H ∘ {\displaystyle H^{\circ }} at the reference temperature T ∘ {\displaystyle T^{\circ }} = 298.15 K yields:
The van 't Hoff equation in this form is only valid for a limited temperature range in which Δ sol H {\displaystyle \Delta _{\text{sol}}H} does not change much with temperature (around 20K of variations).
The following table lists some temperature dependencies:
Solubility of permanent gases usually decreases with increasing temperature at around room temperature. However, for aqueous solutions, the Henry's law solubility constant for many species goes through a minimum. For most permanent gases, the minimum is below 120 °C. Often, the smaller the gas molecule (and the lower the gas solubility in water), the lower the temperature of the maximum of the Henry's law constant. Thus, the maximum is at about 30 °C for helium, 92 to 93 °C for argon, nitrogen and oxygen, and 114 °C for xenon. [ 12 ]
The Henry's law constants mentioned so far do not consider any chemical equilibria in the aqueous phase. This type is called the intrinsic , or physical , Henry's law constant. For example, the intrinsic Henry's law solubility constant of formaldehyde can be defined as
In aqueous solution, formaldehyde is almost completely hydrated:
The total concentration of dissolved formaldehyde is
Taking this equilibrium into account, an effective Henry's law constant H s , e f f {\displaystyle H_{\rm {s,eff}}} can be defined as
For acids and bases, the effective Henry's law constant is not a useful quantity because it depends on the pH of the solution. [ 10 ] In order to obtain a pH-independent constant, the product of the intrinsic Henry's law constant H s cp {\displaystyle H_{\rm {s}}^{{\ce {cp}}}} and the acidity constant K A {\displaystyle K_{{\ce {A}}}} is often used for strong acids like hydrochloric acid (HCl):
Although H ′ {\displaystyle H'} is usually also called a Henry's law constant, it is a different quantity and it has different units than H s cp {\displaystyle H_{\rm {s}}^{{\ce {cp}}}} .
Values of Henry's law constants for aqueous solutions depend on the composition of the solution, i.e., on its ionic strength and on dissolved organics. In general, the solubility of a gas decreases with increasing salinity (" salting out "). However, a " salting in " effect has also been observed, for example for the effective Henry's law constant of glyoxal . The effect can be described with the Sechenov equation, named after the Russian physiologist Ivan Sechenov (sometimes the German transliteration "Setschenow" of the Cyrillic name Се́ченов is used). There are many alternative ways to define the Sechenov equation, depending on how the aqueous-phase composition is described (based on concentration, molality, or molar fraction) and which variant of the Henry's law constant is used. Describing the solution in terms of molality is preferred because molality is invariant to temperature and to the addition of dry salt to the solution. Thus, the Sechenov equation can be written as
where H s , 0 b p {\displaystyle H_{\rm {s,0}}^{bp}} is the Henry's law constant in pure water, H s b p {\displaystyle H_{\rm {s}}^{bp}} is the Henry's law constant in the salt solution, k s {\displaystyle k_{\rm {s}}} is the molality-based Sechenov constant, and b ( salt ) {\displaystyle b({\text{salt}})} is the molality of the salt.
Henry's law has been shown to apply to a wide range of solutes in the limit of infinite dilution ( x → 0), including non-volatile substances such as sucrose . In these cases, it is necessary to state the law in terms of chemical potentials . For a solute in an ideal dilute solution, the chemical potential depends only on the concentration. For non-ideal solutions, the activity coefficients of the components must be taken into account:
where γ c = H v p ∗ {\displaystyle \gamma _{c}={\frac {H_{\rm {v}}}{p^{*}}}} for a volatile solute; c ° = 1 mol/L.
For non-ideal solutions, the infinite dilution activity coefficient γ c depends on the concentration and must be determined at the concentration of interest. The activity coefficient can also be obtained for non-volatile solutes, where the vapor pressure of the pure substance is negligible, by using the Gibbs-Duhem relation :
By measuring the change in vapor pressure (and hence chemical potential) of the solvent, the chemical potential of the solute can be deduced.
The standard state for a dilute solution is also defined in terms of infinite-dilution behavior. Although the standard concentration c ° is taken to be 1 mol/L by convention, the standard state is a hypothetical solution of 1 mol/L in which the solute has its limiting infinite-dilution properties. This has the effect that all non-ideal behavior is described by the activity coefficient: the activity coefficient at 1 mol/L is not necessarily unity (and is frequently quite different from unity).
All the relations above can also be expressed in terms of molalities b rather than concentrations, e.g.:
where γ b = H v p b p ∗ {\displaystyle \gamma _{b}={\frac {H_{\rm {v}}^{pb}}{p^{*}}}} for a volatile solute; b ° = 1 mol/kg.
The standard chemical potential μ m °, the activity coefficient γ m and the Henry's law constant H v pb all have different numerical values when molalities are used in place of concentrations.
Henry's law solubility constant H s , 2 , M x p {\displaystyle H_{\rm {s,2,M}}^{xp}} for a gas 2 in a mixture M of two solvents 1 and 3 depends on the individual constants for each solvent, H s , 2 , 1 x p {\displaystyle H_{\rm {s,2,1}}^{xp}} and H s , 2 , 3 x p {\displaystyle H_{\rm {s,2,3}}^{xp}} according [ 13 ] to:
Where x 1 {\displaystyle x_{1}} , x 3 {\displaystyle x_{3}} are the molar ratios of each solvent in the mixture and a 13 is the interaction parameter of the solvents from Wohl expansion of the excess chemical potential of the ternary mixtures.
A similar relationship can be found for the volatility constant H v , 2 , M p x {\displaystyle H_{\rm {v,2,M}}^{px}} , by remembering that H v p x = 1 / H s x p {\displaystyle H_{\rm {v}}^{px}=1/H_{\rm {s}}^{xp}} and that, both being positive real numbers, ln H s x p = − ln ( 1 / H s x p ) = − ln H v p x {\displaystyle \ln H_{\rm {s}}^{xp}=-\ln(1/H_{\rm {s}}^{xp})=-\ln H_{\rm {v}}^{px}} , thus:
For a water-ethanol mixture, the interaction parameter a 13 has values around 0.1 ± 0.05 {\displaystyle 0.1\pm 0.05} for ethanol concentrations (volume/volume) between 5% and 25%. [ 14 ]
In geochemistry , a version of Henry's law applies to the solubility of a noble gas in contact with silicate melt. One equation used is
where
Henry's law is a limiting law that only applies for "sufficiently dilute" solutions, while Raoult's law is generally valid when the liquid phase is almost pure or for mixtures of similar substances. [ 15 ] The range of concentrations in which Henry's law applies becomes narrower the more the system diverges from ideal behavior. Roughly speaking, that is the more chemically "different" the solute is from the solvent.
For a dilute solution, the concentration of the solute is approximately proportional to its mole fraction x , and Henry's law can be written as
This can be compared with Raoult's law :
where p * is the vapor pressure of the pure component.
At first sight, Raoult's law appears to be a special case of Henry's law, where H v px = p *. This is true for pairs of closely related substances, such as benzene and toluene , which obey Raoult's law over the entire composition range: such mixtures are called ideal mixtures.
The general case is that both laws are limit laws , and they apply at opposite ends of the composition range. The vapor pressure of the component in large excess, such as the solvent for a dilute solution, is proportional to its mole fraction, and the constant of proportionality is the vapor pressure of the pure substance (Raoult's law). The vapor pressure of the solute is also proportional to the solute's mole fraction, but the constant of proportionality is different and must be determined experimentally (Henry's law). In mathematical terms:
Raoult's law can also be related to non-gas solutes. | https://en.wikipedia.org/wiki/Henry's_law |
The Henry Draper Medal is awarded every 4 years by the United States National Academy of Sciences "for investigations in astronomical physics ". [ 2 ] [ 3 ] Named after Henry Draper , the medal is awarded with a gift of USD $15,000. [ 4 ] The medal was established under the Draper Fund by his widow, Anna Draper, in honor of her husband, [ 5 ] and was first awarded in 1886 to Samuel Pierpont Langley "for numerous investigations of a high order of merit in solar physics, and especially in the domain of radiant energy". [ 1 ] It has since been awarded 45 times.
The medal has been awarded to multiple individuals in the same year: in 1977 it was awarded to Arno Allan Penzias and Robert Woodrow Wilson "for their discovery of the cosmic microwave radiation (a remnant of the very early universe), and their leading role in the discovery of interstellar molecules"; [ 6 ] [ 7 ] in 1989 to Riccardo Giovanelli and Martha P. Haynes "for the first three-dimensional view of some of the remarkable large-scale filamentary structures of our visible universe"; [ 2 ] in 1993 to Ralph Asher Alpher and Robert Herman "for their insight and skill in developing a physical model of the evolution of the universe and in predicting the existence of a microwave background radiation years before this radiation was serendipitously discovered" [ 8 ] and in 2001 to R. Paul Butler and Geoffrey Marcy "for their pioneering investigations of planets orbiting other stars via high-precision radial velocities". [ 9 ]
Source: National Academy of Sciences | https://en.wikipedia.org/wiki/Henry_Draper_Medal |
Henry Eyring (February 20, 1901 – December 26, 1981) was a Mexico -born United States theoretical chemist whose primary contribution was in the study of chemical reaction rates and intermediates.
Eyring developed the Absolute Rate Theory or Transition state theory of chemical reactions, connecting the fields of chemistry and physics through atomic theory, quantum theory, and statistical mechanics. [ 1 ]
Eyring, a third-generation member of the Church of Jesus Christ of Latter-day Saints (LDS Church), was reared on a cattle ranch in Colonia Juárez, Chihuahua , a Mormon colony , for the first 11 years of his life. His father, Edward Christian Eyring, practiced plural marriage ; Edward married Caroline Romney (1893) and her sister Emma Romney (1903), both daughters of Miles Park Romney , the great-grandfather of Mitt Romney . [ 2 ]
In July 1912, the Eyrings and about 4,200 other immigrants were driven out of Mexico by violent insurgents during the Mexican Revolution and moved to El Paso, Texas . After living in El Paso for approximately one year, the Eyrings relocated to Pima, Arizona , where he completed high school and showed a special aptitude for mathematics and science . [ 3 ] He also studied at Gila Academy in Thatcher, Arizona , now Eastern Arizona College . [ 4 ] One of the pillars at the front of the main building still bears his name, along with that of his sister Camilla's husband, Spencer W. Kimball , later president of the LDS Church. [ 5 ]
Eyring earned a BS in mining engineering at the University of Arizona by working in a copper mine. He then received a fellowship from the US Bureau of Mines fellowship and earned his M.Sc. in metallurgy. Having seen the high rates of accidents in the mines, and breathed sulfur fumes from blast furnaces at a smelter, he chose to do his Ph.D. in chemistry . He pursued and received his doctoral degree in chemistry from the University of California, Berkeley in 1927 [ 3 ] for a thesis on A Comparison of the Ionization by, and Stopping Power for, Alpha Particles of Elements and Compounds. [ 6 ]
Princeton University recruited Eyring as an instructor in 1931. He would continue his work at Princeton until 1946. In 1946 he was offered a position as dean of the graduate school at the University of Utah , with professorships in chemistry and metallurgy. [ 3 ] The chemistry building on the University of Utah campus is now named in his honor. [ 7 ]
A prolific writer, Eyring authored more than 600 scientific articles, ten scientific books, and a few books on the subject of science and religion. He received the Wolf Prize in Chemistry in 1980 and the National Medal of Science in 1966 for developing the Absolute Rate Theory or Transition state theory of chemical reactions, one of the most important developments of 20th-century chemistry. [ 1 ]
Several other chemists later received the Nobel Prize for work based on the Absolute Rate Theory, and his failure to receive the Nobel was a matter of surprise to many. [ 8 ] The Nobel Prize organization admitted that "Strangely, Eyring never received a Nobel Prize"; the Royal Swedish Academy of Sciences apparently did not understand Eyring's theory until it was too late to award him the Nobel. The academy awarded him the Berzelius Medal in 1977 as partial compensation. [ 9 ] Sterling M. McMurrin believed Eyring should have received the Nobel Prize but was not awarded it because of his religion. [ 10 ]
Eyring was elected president of the American Chemical Society in 1963 and the Association for the Advancement of Science in 1965. [ 11 ]
Eyring married Mildred Bennion. She was a native of Granger, Utah , who had a degree from the University of Utah and served as head of the physical education department there. She met Eyring while pursuing a doctorate at the University of Wisconsin . [ 12 ] They had three sons together. The oldest, Edward M. "Ted" Eyring was an emeritus professor of chemistry at the University of Utah. The second son, Henry B. Eyring is a general authority of the LDS Church, while the youngest son Harden B. Eyring is a higher education administrator for the State of Utah. His wife, Mildred, died June 25, 1969, in Salt Lake City, Utah. On August 13, 1971, he married Winifred Brennan in the LDS Church's Salt Lake Temple .
Eyring was a member of the LDS Church throughout his life. His views of science and religion were captured in this quote: "Is there any conflict between science and religion? There is no conflict in the mind of God, but often there is conflict in the minds of men." [ 13 ] Eyring also feared overeager defenders of faith would discard new scientific findings because of apparent contradictions. He encouraged parents and teachers to distinguish between "what they know to be true and what they think may be true," to avoid clumping them together and "throwing the baby out with the bath." [ 14 ] : 245–247
As a member of the LDS Church, Eyring served as a branch president , district president , and, for over twenty years, a member of the general board of the Deseret Sunday School Union . As of 2024, his son, Henry B. Eyring , is an apostle and member of the church's First Presidency .
Henry Eyring authored, co-authored, or edited the following books or journals: | https://en.wikipedia.org/wiki/Henry_Eyring_(chemist) |
Henry George Forder (27 September 1889 – 21 September 1981) was a New Zealand mathematician.
Born in Shotesham All Saints , near Norwich , he won a scholarships first to a Grammar school and then to University of Cambridge . After teaching mathematics at a number of schools, he was appointed to the chair of mathematics at Auckland University College in New Zealand in 1933. He was very critical of the state of the New Zealand curriculum and set about writing a series of well received textbooks .
His Foundations of Euclidean Geometry (1927) was reviewed by F.W. Owens, who noted that 40 pages are devoted to "concepts of classes, relations , linear order, non archimedean systems, ..." and that order axioms together with a continuity axiom and a Euclidean parallel axiom are the required foundation.
The object achieved is a "continuous and rigorous development of the [Euclidean] doctrine in the light of modern investigations." [ 1 ]
In 1929 Forder obtained drawings and notes of Robert William Genese on the exterior algebra of Grassmann . He relied on methods of H. F. Baker in Principles of Geometry to extend Genese's beginning into a complete development with applications throughout geometry. When The Calculus of Extension appeared in 1941 it was reviewed by Homer V. Craig: "The theorem density is exceptionally high and consequently despite the superior exposition it is not an easy book to work straight through – perhaps the key chapters suffer from a lack of recapitulation...
[It] provides the best exposition of the fundamental processes of the Ausdehnungslehre and the most inclusive treatment of the geometrical applications available at present." [ 2 ]
Henry Forder was elected Fellow of the Royal Society of New Zealand in 1947 and received an honorary DSc from the University of Auckland in 1959. [ 3 ]
The Forder Lectureship was established jointly by the London Mathematical Society and the New Zealand Mathematical Society in his honour in 1986. [ 4 ] | https://en.wikipedia.org/wiki/Henry_Forder |
The Henry George theorem states that under certain conditions, aggregate spending by government on public goods will increase aggregate rent based on land value ( land rent) more than that amount, with the benefit of the last marginal investment equaling its cost. The theory is named for 19th century U.S. political economist and activist Henry George .
This general relationship, first noted by the French physiocrats in the 18th century, is one basis for advocating the collection of a tax based on land rents to help defray the cost of public investment that helps create land values. Henry George popularized this method of raising public revenue in his works (especially in Progress and Poverty ), which launched the 'single tax' movement .
In 1977, Joseph Stiglitz showed that under certain conditions, beneficial investments in public goods will increase aggregate land rents by at least as much as the investments' cost. [ 1 ] This proposition was dubbed the "Henry George theorem", as it characterizes a situation where Henry George's ' single tax ' on land values, is not only efficient, it is also the only tax necessary to finance public expenditures. [ 2 ] Henry George had famously advocated for the replacement of all other taxes with a land value tax , arguing that as the location value of land was improved by public works, its economic rent was the most logical source of public revenue. [ 3 ]
Subsequent studies generalized the principle and found that the theorem holds even after relaxing assumptions. [ 4 ] Studies indicate that even existing land prices, which are depressed due to the existing burden of taxation on income and investment, are great enough to replace taxes at all levels of government. [ 5 ] [ 6 ] [ 7 ]
Economists later discussed whether the theorem provides a practical guide for determining optimal city and enterprise size. Mathematical treatments suggest that an entity obtains optimal population when the opposing marginal costs and marginal benefits of additional residents are balanced.
The status quo alternative is that the bulk of the value of public improvements is captured by the landowners , because the state has only (unfocused) income and capital taxes by which to do so. [ 8 ] [ 9 ]
The following derivation follows an economic model presented in Joseph Stiglitz’ 1977 theory of local public goods . [ 1 ]
The resource constraint for a small urban economy can be written as:
Y = f ( N ) = c N + G {\displaystyle Y=f(N)=cN+G}
Where Y is output, f(N) is a concave production function, N is the size of the workforce or population, c is the per capita consumption of private goods, and G is government expenditures on local public goods.
Land rents in this model are calculated using a ’Ricardian rent identity’ :
R = f ( N ) − f ′ ( N ) N {\displaystyle R=f(N)-f^{\prime }(N)N}
Where f ′ ( N ) = d Y / d N = {\displaystyle f^{\prime }(N)=dY/dN=} marginal product of laborers .
The community planner wishes to choose the size of N that maximizes the per capita consumption of private goods:
c = f ( N ) − G N {\displaystyle c={\frac {f(N)-G}{N}}}
Differentiating using the quotient rule yields:
d c d N = N f ′ ( N ) − f ( N ) + G N 2 = 0 {\displaystyle {\frac {dc}{dN}}={\frac {Nf^{\prime }(N)-f(N)+G}{N^{2}}}=0}
From which we derive first-order conditions:
c = f ′ ( N ) , {\textstyle c=f^{\prime }(N)\;,}
G = f ( N ) − f ′ ( N ) N , {\textstyle G=f(N)-f^{\prime }(N)N\;,}
N ∗ = f ( N ) − G f ′ ( N ) . {\textstyle N^{*}={\frac {f(N)\;-\;G}{f^{\prime }(N)}}\;.}
Comparison of the FOC for G and the Ricardian rent identity yields the equality:
R = G . {\displaystyle R=G\;.}
The following derivation follows an urban economic model presented in Richard Arnott and Joseph Stiglitz's paper titled Aggregate Land Rents, Expenditure on Public Goods, and Optimal City Size. [ 10 ]
Essential Assumptions
Let "A" stand for assumption.
Additional Assumptions
The Model
By (A.3), transport costs f {\displaystyle f} at distance t {\displaystyle t} are linear with respect to distance:
f ( t ) = f ′ ( t ) t {\displaystyle f(t)=f^{\prime }(t)t}
Since land is homogenous à la (A.4), the rent gradient is found by:
R ′ ( t ) = − f ′ ( t ) = − f ( t ) t {\displaystyle R^{\prime }(t)=-f^{\prime }(t)=-{\frac {f(t)}{t}}}
Because we are integrating over a circular region (A.5), we can use shell integration to calculate aggregate land rents:
A L R = ∫ 0 t ∗ R ( t ) 2 π t d t {\displaystyle ALR=\int _{0}^{t^{*}}R(t)2\pi t\;dt}
Where t ∗ {\displaystyle t^{*}} is the distance of the urban boundary from the urban center.
Integration by parts and substitution of R ′ ( t ) = − f ( t ) / t {\displaystyle R^{\prime }(t)=-f(t)/t} yields:
A L R = R ( t ∗ ) π t ∗ 2 − ∫ 0 t ∗ R ( t ) π t 2 d t = R ( t ∗ ) π t ∗ 2 + ∫ 0 t ∗ f ( t ) π t d t {\displaystyle {\begin{aligned}ALR&{}=R(t^{*})\pi t^{*2}-\int _{0}^{t^{*}}R(t)\pi t^{2}\,dt\\&{}=R(t^{*})\pi t^{*2}+\int _{0}^{t^{*}}f(t)\pi t\,dt\end{aligned}}}
R ( t ∗ ) π t ∗ 2 {\displaystyle R(t^{*})\pi t^{*2}} are land rents at the urban boundary times the area of the city. Therefore, the rest are differential land rents:
D L R = ∫ 0 t ∗ − R ′ ( t ) π t 2 d t = ∫ 0 t ∗ f ( t ) π t d t {\displaystyle DLR=\int _{0}^{t^{*}}-R^{\prime }(t)\pi t^{2}dt=\int _{0}^{t^{*}}f(t)\pi t\;dt}
Aggregate transportation costs are calculated as:
A T C = ∫ 0 t ∗ f ( t ) 2 π t d t {\displaystyle ATC=\int _{0}^{t^{*}}f(t)2\pi t\,dt}
Therefore, in the limiting case where transportation costs are linear, land is homogenous, and the shape of the city is circular, we obtain:
D L R = A T C 2 {\displaystyle DLR={\frac {ATC}{2}}}
Since transport costs are linear, we may write e = f ′ ( t ) = f ( t ) / t {\displaystyle e=f^{\prime }(t)=f(t)/t} as a constant. Bringing the constants outside ATCs integral and computing yields:
A T C = 2 e π ∫ 0 t ∗ t 2 d t = 2 e 3 π t ∗ 3 {\displaystyle ATC=2e\pi \int _{0}^{t^{*}}t^{2}\,dt={\frac {2e}{3}}\pi t^{*3}}
Because units characterizing the geometry of the city are given by (A.5) and (A.6), we can calculate the urban radius as:
t ∗ = ( N π ) 1 / 2 = N 1 / 2 π − 1 / 2 {\displaystyle t^{*}=\left({\frac {N}{\pi }}\right)^{1/2}=N^{1/2}\pi ^{-1/2}}
Substitution of t ∗ {\displaystyle t^{*}} into A T C {\displaystyle ATC} yields:
A T C = 2 e 3 π − 1 / 2 N 3 / 2 = k N 3 / 2 {\displaystyle ATC={\frac {2e}{3}}\pi ^{-1/2}N^{3/2}=kN^{3/2}}
Where k = 2 e 3 π − 1 / 2 {\displaystyle k={\frac {2e}{3}}\pi ^{-1/2}} is a composite constant since it's only made of constants.
The resource constraint for large urban economies can therefore be written as:
y N = c N + G + k N 3 / 2 {\displaystyle yN=cN+G+kN^{3/2}}
Where y {\displaystyle y} is treated as constant under (A.2).
(A.1) requires that the urban planner solves the following maximization problem:
max N c = y − G N − k N 1 / 2 {\displaystyle \max _{N}c=y-{\frac {G}{N}}-kN^{1/2}}
Take first-order conditions using the quotient and power rules:
d c d N = G N 2 − k 2 N − 1 / 2 = 0 {\displaystyle {\frac {dc}{dN}}={\frac {G}{N^{2}}}-{\frac {k}{2}}N^{-1/2}=0}
Or:
G = k 2 N 3 / 2 = A T C 2 {\displaystyle G={\frac {k}{2}}N^{3/2}={\frac {ATC}{2}}}
Therefore, comparing D L R {\displaystyle DLR} and the first-order condition for G {\displaystyle G} yields the Henry George theorem for large urban economies:
D L R = A T C 2 = G {\displaystyle DLR={\frac {ATC}{2}}=G}
A similar result can be obtained by employing a Lagrangian function . However, since the Henry George theorem is satisfied for any level of expenditure on pure local public goods G {\displaystyle G} , deriving the optimal level of G {\displaystyle G} that satisfies the Samuelson condition isn’t necessary. [ 11 ] | https://en.wikipedia.org/wiki/Henry_George_theorem |
Henry Johnston Scott Matthew FRCPE (22 March 1914 – 7 April 1997) was a Scottish physician and toxicologist in charge of the Regional Poisoning Treatment Centre from 1964 and Director of the Scottish Poisons Information Bureau from 1965. [ 1 ] Matthew changed his career path, concentrating on Toxicology in 1957 [ 2 ] and was known as the Father of Clinical Toxicology . [ 3 ]
Matthew was born in Edinburgh in 1914. He went to the University of Edinburgh to study Medicine after schooling at Edinburgh Academy . Matthew graduated from the University of Edinburgh in the top five of the final examinations of 1937. His career in surgery began at the Royal Infirmary of Edinburgh and Great Ormond Street Hospital , London ; however, this didn't last long because of the outbreak of World War II. During the war, he served with the Royal Army Medical Corps in the Middle East and Persia. Following the war, after a brief break, he returned to Scotland and went into general practice, joining the faculty of Medicine as a consultant physician specializing in Cardiology at Edinburgh Royal Infirmary in 1945. [ 2 ] [ 3 ] In 1951 he was elected a member of the Harveian Society of Edinburgh . [ 4 ]
Matthew had to convert his specialization because of the crucial decision made by the manager of the Royal Infirmary, designating the ward for incidental delirium (Ward 3) a Regional Poisoning Treatment Centre (RPTC) in response to a report issued by the Ministry of Health in England and the Scottish Home and Health Department . [ 2 ] [ 3 ] In 1964, He officially started his long-term research and clinical practice of Toxicology. Regarding the turning point of his motivation in concentrating on Toxicology, he noticed that patients were prescribed and overdosed on barbiturates as a remedy, with which he strongly disagreed. Matthew reassessed and improved the role of gastric lavage and aspiration in respect of barbiturates overdose , which was abandoned in Denmark in 1946; the research has become a recommended reference among the clinical staff widely. [ 3 ]
Matthew retired in 1975 and suffered from prostate cancer in his later life. [ 2 ] | https://en.wikipedia.org/wiki/Henry_Johnston_Scott_Matthew |
Henry Prevost Babbage (1824–1918) was a soldier in the Bengal Army of the East India Company . After retiring with the rank of major general , he continued the work of his father, Charles Babbage , whom he had assisted as a student. He organised and edited his father's papers and prototypes and arranged for their publication and completion. These works included Babbage's Calculating Engines (1889) and a working Analytical Engine Mill – a simplified portion of the full Analytical Engine design. [ 2 ]
He was brevetted as a colonel in the Bengal Staff Corps on 10 June 1874. [ 3 ]
This computing article is a stub . You can help Wikipedia by expanding it .
This biographical article related to the British Armed Forces or its predecessor forces is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Henry_Prevost_Babbage |
Henry Stephen Rzepa (born 1950) [ 3 ] is a chemist and Emeritus Professor of Computational Chemistry at Imperial College London . [ 4 ] [ citation needed ]
Rzepa was born in 1950 and was educated at Wandsworth Comprehensive School in London. He then entered the chemistry department at Imperial College London where he graduated in 1971. He stayed to do a Ph.D. on the physical organic chemistry of indoles supervised by Brian Challis. [ 5 ] [ 6 ]
After spending three years doing postdoctoral research at University of Texas at Austin , Texas with Michael Dewar [ 7 ] in the emerging field of computational chemistry , he returned to Imperial College and was eventually appointed as Professor of the college in 2003. As of 2017 [update] he is Emeritus Professor of Computational Chemistry. [ 8 ] [ 9 ] [ citation needed ]
His research interests [ 2 ] directed towards combining different types of chemical information tools for solving structural, mechanistic and stereochemical problems in organic , bioorganic , organometallic chemistry and catalysis , using techniques such as semiempirical molecular orbital methods (the MNDO family), Nuclear Magnetic Resonance (NMR) spectroscopy, X-ray crystallography and ab initio quantum theories. Aware of the complex semantic issues involved in converging different areas of chemistry to address modern multidisciplinary problems, he started investigating the use of the Internet as an information and integrating medium around 1987, focusing in 1994 on the World Wide Web as having the most potential. [ 10 ] Peter Murray-Rust and he first introduced Chemical Markup Language (CML) in 1995 as a rich carrier of semantic chemical information and data; and they coined the term Datument as a portmanteau word to better express the evolution from the documents produced by traditional academic publishing methods to the Semantic Web ideals expressed by Tim Berners-Lee . [ 11 ] [ 12 ] [ 13 ]
His contributions to chemistry [ 14 ] [ 15 ] [ 16 ] [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ] include exploration of Möbius aromaticity , highlighted by the theoretical discovery of relatively stable forms of cyclic conjugated molecules which exhibit two and higher half-twists in the topology rather than just the single twist associated with Mobius systems. He is responsible for unraveling the mechanistic origins of stereocontrol in a variety of catalytic polymerisation reactions, including that of lactide to polylactide, a new generation of bio-sustainable polymer not dependent on oil. He is also known for the integration of chemistry (in the form of CML) with emergent Internet technologies and trends such as RSS and podcasting , for the introduction of the Chemical MIME types in 1994, and for organizing the ECTOC online conferences in organic chemistry , which ran from 1995 to 1998. [ 23 ]
Rzepa was awarded the Herman Skolnik Award in 2012 by the American Chemical Society . [ 1 ] | https://en.wikipedia.org/wiki/Henry_Rzepa |
The Henry adsorption constant is the constant appearing in the linear adsorption isotherm , which formally resembles Henry's law ; therefore, it is also called Henry's adsorption isotherm . It is named after British chemist William Henry . This is the simplest adsorption isotherm in that the amount of the surface adsorbate is represented to be proportional to the partial pressure of the adsorptive gas: [ 1 ]
where:
For solutions, concentrations, or activities , are used instead of the partial pressures.
The linear isotherm can be used to describe the initial part of many practical isotherms. It is typically taken as valid for low surface coverages, and the adsorption energy being independent of the coverage (lack of inhomogeneities on the surface).
The Henry adsorption constant can be defined as: [ 2 ]
where:
Source: [ 2 ]
If a solid body is modeled by a constant field and the structure of the field is such that it has a penetrable core, then
Here x ′ {\displaystyle x'} is the position of the dividing surface, u = u ( x ) {\displaystyle u=u(x)} is the external force field, simulating a solid, u 0 {\displaystyle u_{0}} is the field value deep in the solid, β = 1 / k B T {\displaystyle \beta =1/k_{B}T} , k B {\displaystyle k_{B}} is the Boltzmann constant, and T {\displaystyle T} is the temperature.
Introducing "the surface of zero adsorption"
where
and
we get
and the problem of K H {\displaystyle K_{H}} determination is reduced to the calculation of x 0 {\displaystyle x_{0}} .
Taking into account that for Henry absorption constant we have
where ϱ ( z ′ ) {\displaystyle \varrho (z')} is the number density inside the solid, we arrive at the parametric dependence
where
Source: [ 2 ]
If a static membrane is modeled by a constant field and the structure of the field is such that it has a penetrable core and vanishes when x = ± ∞ {\displaystyle x=\pm \infty } , then
We see that in this case the K H {\displaystyle K_{H}} sign and value depend on the potential u {\displaystyle u} and temperature only.
Source: [ 3 ]
If a solid body is modeled by a constant hard-core field, then
or
where
Here
For the hard solid potential
where x s t e p {\displaystyle x_{step}} is the position of the potential discontinuity. So, in this case
Sources: [ 2 ] [ 3 ]
The choice of the dividing surface, strictly speaking, is arbitrary, however, it is very desirable to take into account the type of external potential u ( x ) {\displaystyle u(x)} . Otherwise, these expressions are at odds with the generally accepted concepts and common sense.
First, x ′ {\displaystyle x'} must lie close to the transition layer (i.e., the region where the number density varies), otherwise it would mean the attribution of the bulk properties of one of the phase to the surface.
Second. In the case of weak adsorption, for example, when the potential is close to the stepwise, it is logical to choose x ′ {\displaystyle x'} close to x 0 {\displaystyle x_{0}} . (In some cases, choosing x 0 ± R {\displaystyle x_{0}\pm R} , where R {\displaystyle R} is particle radius, excluding the "dead" volume.)
In the case of pronounced adsorption it is advisable to choose x ′ {\displaystyle x'} close to the right border of the transition region. In this case all particles from the transition layer will be attributed to the solid, and K H {\displaystyle K_{H}} is always positive. Trying to put x ′ = x 0 {\displaystyle x'=x_{0}} in this case will lead to a strong shift of x ′ {\displaystyle x'} to the solid body domain, which is clearly unphysical.
Conversely, if u 0 < 0 {\displaystyle u_{0}<0} (fluid on the left), it is advisable to choose x ′ {\displaystyle x'} lying on the left side of the transition layer. In this case the surface particles once again refer to the solid and K H {\displaystyle K_{H}} is back positive.
Thus, except in the case of static membrane, we can always avoid the "negative adsorption" for one-component systems. | https://en.wikipedia.org/wiki/Henry_adsorption_constant |
The Henry reaction is a classic carbon–carbon bond formation reaction in organic chemistry . Discovered in 1895 by the Belgian chemist Louis Henry (1834–1913), it is the combination of a nitroalkane and an aldehyde or ketone in the presence of a base to form β-nitro alcohols. [ 1 ] [ 2 ] [ 3 ] This type of reaction is also referred to as a nitroaldol reaction (nitroalkane, aldehyde, and alcohol). It is nearly analogous to the aldol reaction that had been discovered 23 years prior that couples two carbonyl compounds to form β-hydroxy carbonyl compounds known as "aldols" (aldehyde and alcohol). [ 2 ] [ 4 ] The Henry reaction is a useful technique in the area of organic chemistry due to the synthetic utility of its corresponding products, as they can be easily converted to other useful synthetic intermediates. These conversions include subsequent dehydration to yield nitroalkenes , oxidation of the secondary alcohol to yield α-nitro ketones, or reduction of the nitro group to yield β-amino alcohols.
Many of these uses have been exemplified in the syntheses of various pharmaceuticals including the β-blocker ( S )-propranolol , [ 5 ] [ 6 ] the HIV protease inhibitor Amprenavir (Vertex 478), and construction of the carbohydrate subunit of the anthracycline class of antibiotics, L-Acosamine . [ 6 ] The synthetic scheme of the L-Acosamine synthesis can be found in the Examples section of this article.
The Henry reaction begins with the deprotonation of the nitroalkane on the α-carbon position forming a nitronate . The pKa of most nitroalkanes is approximately 17. [ 7 ] [ 8 ] Although this structure is nucleophilic both at the deprotonated carbon and at the oxy-anions of the nitro group, [ 9 ] the observed result is of the carbon attacking the carbonyl compound. The resulting β-nitro alkoxide is protonated by the conjugate acid of the base that originally deprotonated the nitroalkyl structure, giving the respective β-nitro alcohol as product.
All steps of the Henry reaction are reversible. This is due to the lack of a committed step in the reaction to form product. It is for this reason that research has been geared towards modifications to drive the reaction to completion. [ 2 ] [ 3 ] More information about this can be found in the modification section of this article.
The figure below illustrates one of the commonly accepted models for stereoselection without any modification to the Henry reaction. In this model, stereoselectivity is governed by the size of the R groups in the model (such as a carbon chain), as well as by a transition state that minimizes dipole by orienting the nitro group and carbonyl oxygen anti each other (on opposite sides of the molecule). The R groups play a role in the transition state of the Henry reaction: the larger the R groups on each of the substrates, the more they will tend to orient themselves away from each other (commonly referred to as steric effects ). [ 3 ] [ 10 ]
Due to the reversibility of the reaction and the tendency for easy epimerization of the nitro-substituted carbon atom (among a number of factors), the Henry reaction will typically produce a mixture of enantiomers or diastereomers . It is for this reason that explanations for stereoselectivity remain scarce without some modification of the reaction. [ 3 ] In recent years, research focus has shifted toward modifications of the Henry reaction to overcome this synthetic challenge.
The first example of an enantioselective nitroaldol reaction was reported in 1992 using Shibasaki catalysts . [ 11 ] One of the most frequently employed methods for inducing enantio- or diastereoselectivity in the Henry reaction is the use of chiral metal catalysts, in which the nitro group and carbonyl oxygen coordinate to a metal that is bound to a chiral organic molecule. Some metals that have been used include zinc, cobalt, copper, magnesium, and chromium. [ 12 ] A depiction of this coordination is illustrated above.
One of the many features of the Henry reaction that makes it synthetically attractive is that it utilizes only a catalytic amount of base to drive the reaction. Additionally a variety of bases can be used including ionic bases such as alkali metal hydroxides, alkoxides, carbonates, and sources of fluoride anion (e.g. TBAF) or nonionic organic amine bases including TMG, DBU, DBN, and PAP. The base and solvent used do not have a large influence on the overall outcome of the reaction. [ 2 ]
One of the main drawbacks of the Henry reaction is the potential for side reactions throughout. Aside from the inherent reversibility of the reaction (or "retro–Henry") that can prevent the reaction from proceeding, the β-nitro alcohol also has the potential to undergo dehydration. For sterically hindered substrates, it is also possible for a base-catalyzed self-condensation ( Cannizzaro reaction ) to occur. A general scheme of the Cannizzaro reaction is depicted below. [ 2 ]
There have been a series of modifications made to the Henry reaction. Of these some of the most important include employing high-pressure and sometimes solvent free conditions to improve chemo- and regioselectivity [ 2 ] and chiral metal catalysts to induce enantio-or diastereoselectivity. [ 12 ] The aza-Henry reaction is also used to produce nitroamines and can be a reliable synthetic route for the synthesis of vicinal diamines. [ 13 ]
Perhaps one of the most synthetically useful modifications to the Henry reaction is the use of an organocatalyst . [ 2 ] [ 12 ] [ 14 ] The catalytic cycle is shown below.
Benjamin List described that while this is a broad explanation, his brief review illustrates that this is a plausible mechanistic explanation for almost all reactions that involve an organocatalyst. An example of this type of reaction is illustrated in the Examples section of this article.
In addition to the previously mentioned modifications to the Henry reaction there are a variety of others. This includes the conversion of unreactive alkyl nitro compounds to their corresponding dianions which will react faster with carbonyl substrates, reactions can be accelerated using PAP as base, utilization of the reactivity of aldehydes with α,α-doubly deprotonated nitroalkanes to give nitronate alkoxides that yield mainly syn-nitro alcohols once protonated, and finally generation of nitronate anions in which one oxygenatom on the nitro group is silyl-protected to yield anti-β-nitro alcohols in the presence of a fluoride anion source when reacted with an aldehyde. [ 2 ] [ 3 ] | https://en.wikipedia.org/wiki/Henry_reaction |
In mathematics , Hensel's lemma , also known as Hensel's lifting lemma , named after Kurt Hensel , is a result in modular arithmetic , stating that if a univariate polynomial has a simple root modulo a prime number p , then this root can be lifted to a unique root modulo any higher power of p . More generally, if a polynomial factors modulo p into two coprime polynomials , this factorization can be lifted to a factorization modulo any higher power of p (the case of roots corresponds to the case of degree 1 for one of the factors).
By passing to the "limit" (in fact this is an inverse limit ) when the power of p tends to infinity, it follows that a root or a factorization modulo p can be lifted to a root or a factorization over the p -adic integers .
These results have been widely generalized, under the same name, to the case of polynomials over an arbitrary commutative ring , where p is replaced by an ideal , and "coprime polynomials" means "polynomials that generate an ideal containing 1 ".
Hensel's lemma is fundamental in p -adic analysis , a branch of analytic number theory .
The proof of Hensel's lemma is constructive , and leads to an efficient algorithm for Hensel lifting , which is fundamental for factoring polynomials , and gives the most efficient known algorithm for exact linear algebra over the rational numbers .
Hensel's original lemma concerns the relation between polynomial factorization over the integers and over the integers modulo a prime number p and its powers. It can be straightforwardly extended to the case where the integers are replaced by any commutative ring , and p is replaced by any maximal ideal (indeed, the maximal ideals of Z {\displaystyle \mathbb {Z} } have the form p Z , {\displaystyle p\mathbb {Z} ,} where p is a prime number).
Making this precise requires a generalization of the usual modular arithmetic , and so it is useful to define accurately the terminology that is commonly used in this context.
Let R be a commutative ring, and I an ideal of R . Reduction modulo I refers to the replacement of every element of R by its image under the canonical map R → R / I . {\displaystyle R\to R/I.} For example, if f ∈ R [ X ] {\displaystyle f\in R[X]} is a polynomial with coefficients in R , its reduction modulo I , denoted f mod I , {\displaystyle f{\bmod {I}},} is the polynomial in ( R / I ) [ X ] = R [ X ] / I R [ X ] {\displaystyle (R/I)[X]=R[X]/IR[X]} obtained by replacing the coefficients of f by their image in R / I . {\displaystyle R/I.} Two polynomials f and g in R [ X ] {\displaystyle R[X]} are congruent modulo I , denoted f ≡ g ( mod I ) {\textstyle f\equiv g{\pmod {I}}} if they have the same coefficients modulo I , that is if f − g ∈ I R [ X ] . {\displaystyle f-g\in IR[X].} If h ∈ R [ X ] , {\displaystyle h\in R[X],} a factorization of h modulo I consists in two (or more) polynomials f, g in R [ X ] {\displaystyle R[X]} such that h ≡ f g ( mod I ) . {\textstyle h\equiv fg{\pmod {I}}.}
The lifting process is the inverse of reduction. That is, given objects depending on elements of R / I , {\displaystyle R/I,} the lifting process replaces these elements by elements of R {\displaystyle R} (or of R / I k {\displaystyle R/I^{k}} for some k > 1 ) that maps to them in a way that keeps the properties of the objects.
For example, given a polynomial h ∈ R [ X ] {\displaystyle h\in R[X]} and a factorization modulo I expressed as h ≡ f g ( mod I ) , {\textstyle h\equiv fg{\pmod {I}},} lifting this factorization modulo I k {\displaystyle I^{k}} consists of finding polynomials f ′ , g ′ ∈ R [ X ] {\displaystyle f',g'\in R[X]} such that f ′ ≡ f ( mod I ) , {\textstyle f'\equiv f{\pmod {I}},} g ′ ≡ g ( mod I ) , {\textstyle g'\equiv g{\pmod {I}},} and h ≡ f ′ g ′ ( mod I k ) . {\textstyle h\equiv f'g'{\pmod {I^{k}}}.} Hensel's lemma asserts that such a lifting is always possible under mild conditions; see next section.
Originally, Hensel's lemma was stated (and proved) for lifting a factorization modulo a prime number p of a polynomial over the integers to a factorization modulo any power of p and to a factorization over the p -adic integers . This can be generalized easily, with the same proof to the case where the integers are replaced by any commutative ring , the prime number is replaced by a maximal ideal , and the p -adic integers are replaced by the completion with respect to the maximal ideal. It is this generalization, which is also widely used, that is presented here.
Let m {\displaystyle {\mathfrak {m}}} be a maximal ideal of a commutative ring R , and
be a polynomial in R [ X ] {\displaystyle R[X]} with a leading coefficient α 0 {\displaystyle \alpha _{0}} not in m . {\displaystyle {\mathfrak {m}}.}
Since m {\displaystyle {\mathfrak {m}}} is a maximal ideal, the quotient ring R / m {\displaystyle R/{\mathfrak {m}}} is a field , and ( R / m ) [ X ] {\displaystyle (R/{\mathfrak {m}})[X]} is a principal ideal domain , and, in particular, a unique factorization domain , which means that every nonzero polynomial in ( R / m ) [ X ] {\displaystyle (R/{\mathfrak {m}})[X]} can be factorized in a unique way as the product of a nonzero element of ( R / m ) {\displaystyle (R/{\mathfrak {m}})} and irreducible polynomials that are monic (that is, their leading coefficients are 1).
Hensel's lemma asserts that every factorization of h modulo m {\displaystyle {\mathfrak {m}}} into coprime polynomials can be lifted in a unique way into a factorization modulo m k {\displaystyle {\mathfrak {m}}^{k}} for every k .
More precisely, with the above hypotheses, if h ≡ α 0 f g ( mod m ) , {\textstyle h\equiv \alpha _{0}fg{\pmod {\mathfrak {m}}},} where f and g are monic and coprime modulo m , {\displaystyle {\mathfrak {m}},} then, for every positive integer k there are monic polynomials f k {\displaystyle f_{k}} and g k {\displaystyle g_{k}} such that
and f k {\displaystyle f_{k}} and g k {\displaystyle g_{k}} are unique (with these properties) modulo m k . {\displaystyle {\mathfrak {m}}^{k}.}
An important special case is when f = X − r . {\displaystyle f=X-r.} In this case the coprimality hypothesis means that r is a simple root of h mod m . {\displaystyle h{\bmod {\mathfrak {m}}}.} This gives the following special case of Hensel's lemma, which is often also called Hensel's lemma.
With above hypotheses and notations, if r is a simple root of h mod m , {\displaystyle h{\bmod {\mathfrak {m}}},} then r can be lifted in a unique way to a simple root of h mod m n {\displaystyle h{\bmod {{\mathfrak {m}}^{n}}}} for every positive integer n . Explicitly, for every positive integer n , there is a unique r n ∈ R / m n {\displaystyle r_{n}\in R/{\mathfrak {m}}^{n}} such that r n ≡ r ( mod m ) {\textstyle r_{n}\equiv r{\pmod {\mathfrak {m}}}} and r n {\displaystyle r_{n}} is a simple root of h mod m n . {\displaystyle h{\bmod {\mathfrak {m}}}^{n}.}
The fact that one can lift to R / m n {\displaystyle R/{\mathfrak {m}}^{n}} for every positive integer n suggests to "pass to the limit" when n tends to the infinity. This was one of the main motivations for introducing p -adic integers .
Given a maximal ideal m {\displaystyle {\mathfrak {m}}} of a commutative ring R , the powers of m {\displaystyle {\mathfrak {m}}} form a basis of open neighborhoods for a topology on R , which is called the m {\displaystyle {\mathfrak {m}}} - adic topology . The completion of this topology can be identified with the completion of the local ring R m , {\displaystyle R_{\mathfrak {m}},} and with the inverse limit lim ← R / m n . {\displaystyle \lim _{\leftarrow }R/{\mathfrak {m}}^{n}.} This completion is a complete local ring , generally denoted R ^ m . {\displaystyle {\widehat {R}}_{\mathfrak {m}}.} When R is the ring of the integers, and m = p Z , {\displaystyle {\mathfrak {m}}=p\mathbb {Z} ,} where p is a prime number, this completion is the ring of p -adic integers Z p . {\displaystyle \mathbb {Z} _{p}.}
The definition of the completion as an inverse limit, and the above statement of Hensel's lemma imply that every factorization into pairwise coprime polynomials modulo m {\displaystyle {\mathfrak {m}}} of a polynomial h ∈ R [ X ] {\displaystyle h\in R[X]} can be uniquely lifted to a factorization of the image of h in R ^ m [ X ] . {\displaystyle {\widehat {R}}_{\mathfrak {m}}[X].} Similarly, every simple root of h modulo m {\displaystyle {\mathfrak {m}}} can be lifted to a simple root of the image of h in R ^ m [ X ] . {\displaystyle {\widehat {R}}_{\mathfrak {m}}[X].}
Hensel's lemma is generally proved incrementally by lifting a factorization over R / m n {\displaystyle R/{\mathfrak {m}}^{n}} to either a factorization over R / m n + 1 {\displaystyle R/{\mathfrak {m}}^{n+1}} ( Linear lifting ), or a factorization over R / m 2 n {\displaystyle R/{\mathfrak {m}}^{2n}} ( Quadratic lifting ).
The main ingredient of the proof is that coprime polynomials over a field satisfy Bézout's identity . That is, if f and g are coprime univariate polynomials over a field (here R / m {\displaystyle R/{\mathfrak {m}}} ), there are polynomials a and b such that deg a < deg g , {\displaystyle \deg a<\deg g,} deg b < deg f , {\displaystyle \deg b<\deg f,} and
Bézout's identity allows defining coprime polynomials and proving Hensel's lemma, even if the ideal m {\displaystyle {\mathfrak {m}}} is not maximal. Therefore, in the following proofs, one starts from a commutative ring R , an ideal I , a polynomial h ∈ R [ X ] {\displaystyle h\in R[X]} that has a leading coefficient that is invertible modulo I (that is its image in R / I {\displaystyle R/I} is a unit in R / I {\displaystyle R/I} ), and factorization of h modulo I or modulo a power of I , such that the factors satisfy a Bézout's identity modulo I . In these proofs, A ≡ B ( mod I ) {\textstyle A\equiv B{\pmod {I}}} means A − B ∈ I R [ X ] . {\displaystyle A-B\in IR[X].}
Let I be an ideal of a commutative ring R , and h ∈ R [ X ] {\displaystyle h\in R[X]} be a univariate polynomial with coefficients in R that has a leading coefficient α {\displaystyle \alpha } that is invertible modulo I (that is, the image of α {\displaystyle \alpha } in R / I {\displaystyle R/I} is a unit in R / I {\displaystyle R/I} ).
Suppose that for some positive integer k there is a factorization
such that f and g are monic polynomials that are coprime modulo I , in the sense that there exist a , b ∈ R [ X ] , {\displaystyle a,b\in R[X],} such that a f + b g ≡ 1 ( mod I ) . {\textstyle af+bg\equiv 1{\pmod {I}}.} Then, there are polynomials δ f , δ g ∈ I k R [ X ] , {\displaystyle \delta _{f},\delta _{g}\in I^{k}R[X],} such that deg δ f < deg f , {\displaystyle \deg \delta _{f}<\deg f,} deg δ g < deg g , {\displaystyle \deg \delta _{g}<\deg g,} and
Under these conditions, δ f {\displaystyle \delta _{f}} and δ g {\displaystyle \delta _{g}} are unique modulo I k + 1 R [ X ] . {\displaystyle I^{k+1}R[X].}
Moreover, f + δ f {\displaystyle f+\delta _{f}} and g + δ g {\displaystyle g+\delta _{g}} satisfy the same Bézout's identity as f and g , that is, a ( f + δ f ) + b ( g + δ g ) ≡ 1 ( mod I ) . {\displaystyle a(f+\delta _{f})+b(g+\delta _{g})\equiv 1{\pmod {I}}.} This follows immediately from the preceding assertions, but is needed to apply iteratively the result with increasing values of k .
The proof that follows is written for computing δ f {\displaystyle \delta _{f}} and δ g {\displaystyle \delta _{g}} by using only polynomials with coefficients in R / I {\displaystyle R/I} or I k / I k + 1 . {\displaystyle I^{k}/I^{k+1}.} When R = Z {\displaystyle R=\mathbb {Z} } and I = p Z , {\displaystyle I=p\mathbb {Z} ,} this allows manipulating only integers modulo p .
Proof: By hypothesis, α {\displaystyle \alpha } is invertible modulo I . This means that there exists β ∈ R {\displaystyle \beta \in R} and γ ∈ I R [ X ] {\displaystyle \gamma \in IR[X]} such that α β = 1 − γ . {\displaystyle \alpha \beta =1-\gamma .}
Let δ h ∈ I k R [ X ] , {\displaystyle \delta _{h}\in I^{k}R[X],} of degree less than deg h , {\displaystyle \deg h,} such that
(One may choose δ h = h − α f g , {\displaystyle \delta _{h}=h-\alpha fg,} but other choices may lead to simpler computations. For example, if R = Z {\displaystyle R=\mathbb {Z} } and I = p Z , {\displaystyle I=p\mathbb {Z} ,} it is possible and better to choose δ h = p k δ h ′ {\displaystyle \delta _{h}=p^{k}\delta '_{h}} where the coefficients of δ h ′ {\displaystyle \delta '_{h}} are integers in the interval [ 0 , p − 1 ] . {\displaystyle [0,p-1].} )
As g is monic, the Euclidean division of a δ h {\displaystyle a\delta _{h}} by g is defined, and provides q and c such that a δ h = q g + c , {\displaystyle a\delta _{h}=qg+c,} and deg c < deg g . {\displaystyle \deg c<\deg g.} Moreover, both q and c are in I k R [ X ] . {\displaystyle I^{k}R[X].} Similarly, let b δ h = q ′ f + d , {\displaystyle b\delta _{h}=q'f+d,} with deg d < deg f , {\displaystyle \deg d<\deg f,} and q ′ , d ∈ I k R [ X ] . {\displaystyle q',d\in I^{k}R[X].}
One has q + q ′ ∈ I k + 1 R [ X ] . {\displaystyle q+q'\in I^{k+1}R[X].} Indeed, one has
As f g {\displaystyle fg} is monic, the degree modulo I k + 1 {\displaystyle I^{k+1}} of f g ( q + q ′ ) {\displaystyle fg(q+q')} can be less than deg f g {\displaystyle \deg fg} only if q + q ′ ∈ I k + 1 R [ X ] . {\displaystyle q+q'\in I^{k+1}R[X].}
Thus, considering congruences modulo I k + 1 , {\displaystyle I^{k+1},} one has
So, the existence assertion is verified with
Let R , I , h and α {\displaystyle \alpha } as a in the preceding section. Let
be a factorization into coprime polynomials (in the above sense), such deg f 0 + deg g 0 = deg h . {\displaystyle \deg f_{0}+\deg g_{0}=\deg h.} The application of linear lifting for k = 1 , 2 , … , n − 1 … , {\displaystyle k=1,2,\ldots ,n-1\ldots ,} shows the existence of δ f {\displaystyle \delta _{f}} and δ g {\displaystyle \delta _{g}} such that deg δ f < deg f , {\displaystyle \deg \delta _{f}<\deg f,} deg δ g < deg g , {\displaystyle \deg \delta _{g}<\deg g,} and
The polynomials δ f {\displaystyle \delta _{f}} and δ g {\displaystyle \delta _{g}} are uniquely defined modulo I n . {\displaystyle I^{n}.} This means that, if another pair ( δ f ′ , δ g ′ ) {\displaystyle (\delta '_{f},\delta '_{g})} satisfies the same conditions, then one has
Proof : Since a congruence modulo I n {\displaystyle I^{n}} implies the same concruence modulo I n − 1 , {\displaystyle I^{n-1},} one can proceed by induction and suppose that the uniqueness has been proved for n − 1 , the case n = 0 being trivial. That is, one can suppose that
By hypothesis, has
and thus
By induction hypothesis, the second term of the latter sum belongs to I n , {\displaystyle I^{n},} and the same is thus true for the first term. As α {\displaystyle \alpha } is invertible modulo I , there exist β ∈ R {\displaystyle \beta \in R} and γ ∈ I {\displaystyle \gamma \in I} such that α β = 1 + γ . {\displaystyle \alpha \beta =1+\gamma .} Thus
using the induction hypothesis again.
The coprimality modulo I implies the existence of a , b ∈ R [ X ] {\displaystyle a,b\in R[X]} such that 1 ≡ a f + b g ( mod I ) . {\textstyle 1\equiv af+bg{\pmod {I}}.} Using the induction hypothesis once more, one gets
Thus one has a polynomial of degree less than deg g {\displaystyle \deg g} that is congruent modulo I n {\displaystyle I^{n}} to the product of the monic polynomial g and another polynomial w . This is possible only if w ∈ I n R [ X ] , {\displaystyle w\in I^{n}R[X],} and implies δ g − δ g ′ ∈ I n R [ X ] . {\displaystyle \delta _{g}-\delta '_{g}\in I^{n}R[X].} Similarly, δ f − δ f ′ {\displaystyle \delta _{f}-\delta '_{f}} is also in I n R [ X ] , {\displaystyle I^{n}R[X],} and this proves the uniqueness.
Linear lifting allows lifting a factorization modulo I n {\displaystyle I^{n}} to a factorization modulo I n + 1 . {\displaystyle I^{n+1}.} Quadratic lifting allows lifting directly to a factorization modulo I 2 n , {\displaystyle I^{2n},} at the cost of lifting also the Bézout's identity and of computing modulo I n {\displaystyle I^{n}} instead of modulo I (if one uses the above description of linear lifting).
For lifting up to modulo I N {\displaystyle I^{N}} for large N one can use either method. If, say, N = 2 k , {\displaystyle N=2^{k},} a factorization modulo I N {\displaystyle I^{N}} requires N − 1 steps of linear lifting or only k − 1 steps of quadratic lifting. However, in the latter case the size of the coefficients that have to be manipulated increase during the computation. This implies that the best lifting method depends on the context (value of N , nature of R , multiplication algorithm that is used, hardware specificities, etc.). [ citation needed ]
Quadratic lifting is based on the following property.
Suppose that for some positive integer k there is a factorization
such that f and g are monic polynomials that are coprime modulo I , in the sense that there exist a , b ∈ R [ X ] , {\displaystyle a,b\in R[X],} such that a f + b g ≡ 1 ( mod I k ) . {\textstyle af+bg\equiv 1{\pmod {I^{k}}}.} Then, there are polynomials δ f , δ g ∈ I k R [ X ] , {\displaystyle \delta _{f},\delta _{g}\in I^{k}R[X],} such that deg δ f < deg f , {\displaystyle \deg \delta _{f}<\deg f,} deg δ g < deg g , {\displaystyle \deg \delta _{g}<\deg g,} and
Moreover, f + δ f {\displaystyle f+\delta _{f}} and g + δ g {\displaystyle g+\delta _{g}} satisfy a Bézout's identity of the form
(This is required for allowing iterations of quadratic lifting.)
Proof : The first assertion is exactly that of linear lifting applied with k = 1 to the ideal I k {\displaystyle I^{k}} instead of I . {\displaystyle I.}
Let α = a f + b g − 1 ∈ I k R [ X ] . {\displaystyle \alpha =af+bg-1\in I^{k}R[X].} One has
where
Setting δ a = − a Δ {\displaystyle \delta _{a}=-a\Delta } and δ b = − b Δ , {\displaystyle \delta _{b}=-b\Delta ,} one gets
which proves the second assertion.
Let f ( X ) = X 6 − 2 ∈ Q [ X ] . {\displaystyle f(X)=X^{6}-2\in \mathbb {Q} [X].}
Modulo 2, Hensel's lemma cannot be applied since the reduction of f ( X ) {\displaystyle f(X)} modulo 2 is simply [ 1 ] pg 15-16
with 6 factors X {\displaystyle X} not being relatively prime to each other. By Eisenstein's criterion , however, one can conclude that the polynomial f ( X ) {\displaystyle f(X)} is irreducible in Q 2 [ X ] . {\displaystyle \mathbb {Q} _{2}[X].} Over k = F 7 {\displaystyle k=\mathbb {F} _{7}} , on the other hand, one has
where 4 {\displaystyle 4} is the square root of 2 in F 7 {\displaystyle \mathbb {F} _{7}} . As 4 is not a cube in F 7 , {\displaystyle \mathbb {F} _{7},} these two factors are irreducible over F 7 {\displaystyle \mathbb {F} _{7}} . Hence the complete factorization of X 6 − 2 {\displaystyle X^{6}-2} in Z 7 [ X ] {\displaystyle \mathbb {Z} _{7}[X]} and Q 7 [ X ] {\displaystyle \mathbb {Q} _{7}[X]} is
where α = … 450 454 7 {\displaystyle \alpha =\ldots 450\,454_{7}} is a square root of 2 in Z 7 {\displaystyle \mathbb {Z} _{7}} that can be obtained by lifting the above factorization. Finally, in F 727 [ X ] {\displaystyle \mathbb {F} _{727}[X]} the polynomial splits into
with all factors relatively prime to each other, so that in Z 727 [ X ] {\displaystyle \mathbb {Z} _{727}[X]} and Q 727 [ X ] {\displaystyle \mathbb {Q} _{727}[X]} there are 6 factors X − β {\displaystyle X-\beta } with the (non-rational) 727-adic integers
Let f ( x ) {\displaystyle f(x)} be a polynomial with integer (or p -adic integer) coefficients, and let m , k be positive integers such that m ≤ k . If r is an integer such that
then, for every m > 0 {\displaystyle m>0} there exists an integer s such that
Furthermore, this s is unique modulo p k + m , and can be computed explicitly as the integer such that
where a {\displaystyle a} is an integer satisfying
Note that f ( r ) ≡ 0 mod p k {\displaystyle f(r)\equiv 0{\bmod {p}}^{k}} so that the condition s ≡ r mod p k {\displaystyle s\equiv r{\bmod {p}}^{k}} is met. As an aside, if f ′ ( r ) ≡ 0 mod p {\displaystyle f'(r)\equiv 0{\bmod {p}}} , then 0, 1, or several s may exist (see Hensel Lifting below).
We use the Taylor expansion of f around r to write:
From r ≡ s mod p k , {\displaystyle r\equiv s{\bmod {p}}^{k},} we see that s − r = tp k for some integer t . Let
For m ⩽ k , {\displaystyle m\leqslant k,} we have:
The assumption that f ′ ( r ) {\displaystyle f'(r)} is not divisible by p ensures that f ′ ( r ) {\displaystyle f'(r)} has an inverse mod p m {\displaystyle p^{m}} which is necessarily unique. Hence a solution for t exists uniquely modulo p m , {\displaystyle p^{m},} and s exists uniquely modulo p k + m . {\displaystyle p^{k+m}.}
Using the above hypotheses, if we consider an irreducible polynomial
such that a 0 , a n ≠ 0 {\displaystyle a_{0},a_{n}\neq 0} , then
In particular, for f ( X ) = X 6 + 10 X − 1 {\displaystyle f(X)=X^{6}+10X-1} , we find in Q 2 [ X ] {\displaystyle \mathbb {Q} _{2}[X]}
but max { | a 0 | , | a n | } = 0 {\displaystyle \max\{|a_{0}|,|a_{n}|\}=0} , hence the polynomial cannot be irreducible. Whereas in Q 7 [ X ] {\displaystyle \mathbb {Q} _{7}[X]} we have both values agreeing, meaning the polynomial could be irreducible. In order to determine irreducibility, the Newton polygon must be employed. [ 2 ] : 144
Note that given an a ∈ F p {\displaystyle a\in \mathbb {F} _{p}} the Frobenius endomorphism y ↦ y p {\displaystyle y\mapsto y^{p}} gives a nonzero polynomial x p − a {\displaystyle x^{p}-a} that has zero derivative
hence the p th roots of a {\displaystyle a} do not exist in Z p {\displaystyle \mathbb {Z} _{p}} . For a = 1 {\displaystyle a=1} , this implies that Z p {\displaystyle \mathbb {Z} _{p}} cannot contain the root of unity μ p {\displaystyle \mu _{p}} .
Although the p th roots of unity are not contained in F p {\displaystyle \mathbb {F} _{p}} , there are solutions of x p − x = x ( x p − 1 − 1 ) {\displaystyle x^{p}-x=x(x^{p-1}-1)} . Note that
is never zero, so if there exists a solution, it necessarily lifts to Z p {\displaystyle \mathbb {Z} _{p}} . Because the Frobenius gives a p = a , {\displaystyle a^{p}=a,} all of the non-zero elements F p × {\displaystyle \mathbb {F} _{p}^{\times }} are solutions. In fact, these are the only roots of unity contained in Q p {\displaystyle \mathbb {Q} _{p}} . [ 3 ]
Using the lemma, one can "lift" a root r of the polynomial f modulo p k to a new root s modulo p k +1 such that r ≡ s mod p k (by taking m = 1 ; taking larger m follows by induction). In fact, a root modulo p k +1 is also a root modulo p k , so the roots modulo p k +1 are precisely the liftings of roots modulo p k . The new root s is congruent to r modulo p , so the new root also satisfies f ′ ( s ) ≡ f ′ ( r ) ≢ 0 mod p . {\displaystyle f'(s)\equiv f'(r)\not \equiv 0{\bmod {p}}.} So the lifting can be repeated, and starting from a solution r k of f ( x ) ≡ 0 mod p k {\displaystyle f(x)\equiv 0{\bmod {p}}^{k}} we can derive a sequence of solutions r k +1 , r k +2 , ... of the same congruence for successively higher powers of p , provided that f ′ ( r k ) ≢ 0 mod p {\displaystyle f'(r_{k})\not \equiv 0{\bmod {p}}} for the initial root r k . This also shows that f has the same number of roots mod p k as mod p k +1 , mod p k +2 , or any other higher power of p , provided that the roots of f mod p k are all simple.
What happens to this process if r is not a simple root mod p ? Suppose that
Then s ≡ r mod p k {\displaystyle s\equiv r{\bmod {p}}^{k}} implies f ( s ) ≡ f ( r ) mod p k + 1 . {\displaystyle f(s)\equiv f(r){\bmod {p}}^{k+1}.} That is, f ( r + t p k ) ≡ f ( r ) mod p k + 1 {\displaystyle f(r+tp^{k})\equiv f(r){\bmod {p}}^{k+1}} for all integers t . Therefore, we have two cases:
Example. To see both cases we examine two different polynomials with p = 2 :
f ( x ) = x 2 + 1 {\displaystyle f(x)=x^{2}+1} and r = 1 . Then f ( 1 ) ≡ 0 mod 2 {\displaystyle f(1)\equiv 0{\bmod {2}}} and f ′ ( 1 ) ≡ 0 mod 2 . {\displaystyle f'(1)\equiv 0{\bmod {2}}.} We have f ( 1 ) ≢ 0 mod 4 {\displaystyle f(1)\not \equiv 0{\bmod {4}}} which means that no lifting of 1 to modulus 4 is a root of f ( x ) modulo 4.
g ( x ) = x 2 − 17 {\displaystyle g(x)=x^{2}-17} and r = 1 . Then g ( 1 ) ≡ 0 mod 2 {\displaystyle g(1)\equiv 0{\bmod {2}}} and g ′ ( 1 ) ≡ 0 mod 2 . {\displaystyle g'(1)\equiv 0{\bmod {2}}.} However, since g ( 1 ) ≡ 0 mod 4 , {\displaystyle g(1)\equiv 0{\bmod {4}},} we can lift our solution to modulus 4 and both lifts (i.e. 1, 3) are solutions. The derivative is still 0 modulo 2, so a priori we don't know whether we can lift them to modulo 8, but in fact we can, since g (1) is 0 mod 8 and g (3) is 0 mod 8, giving solutions at 1, 3, 5, and 7 mod 8. Since of these only g (1) and g (7) are 0 mod 16 we can lift only 1 and 7 to modulo 16, giving 1, 7, 9, and 15 mod 16. Of these, only 7 and 9 give g ( x ) = 0 mod 32 , so these can be raised giving 7, 9, 23, and 25 mod 32. It turns out that for every integer k ≥ 3 , there are four liftings of 1 mod 2 to a root of g ( x ) mod 2 k .
In the p -adic numbers, where we can make sense of rational numbers modulo powers of p as long as the denominator is not a multiple of p , the recursion from r k (roots mod p k ) to r k +1 (roots mod p k +1 ) can be expressed in a much more intuitive way. Instead of choosing t to be an(y) integer which solves the congruence
let t be the rational number (the p k here is not really a denominator since f ( r k ) is divisible by p k ):
Then set
This fraction may not be an integer, but it is a p -adic integer, and the sequence of numbers r k converges in the p -adic integers to a root of f ( x ) = 0. Moreover, the displayed recursive formula for the (new) number r k +1 in terms of r k is precisely Newton's method for finding roots to equations in the real numbers.
By working directly in the p -adics and using the p -adic absolute value , there is a version of Hensel's lemma which can be applied even if we start with a solution of f ( a ) ≡ 0 mod p such that f ′ ( a ) ≡ 0 mod p . {\displaystyle f'(a)\equiv 0{\bmod {p}}.} We just need to make sure the number f ′ ( a ) {\displaystyle f'(a)} is not exactly 0. This more general version is as follows: if there is an integer a which satisfies:
then there is a unique p -adic integer b such f ( b ) = 0 and | b − a | p < | f ′ ( a ) | p . {\displaystyle |b-a|_{p}<|f'(a)|_{p}.} The construction of b amounts to showing that the recursion from Newton's method with initial value a converges in the p -adics and we let b be the limit. The uniqueness of b as a root fitting the condition | b − a | p < | f ′ ( a ) | p {\displaystyle |b-a|_{p}<|f'(a)|_{p}} needs additional work.
The statement of Hensel's lemma given above (taking m = 1 {\displaystyle m=1} ) is a special case of this more general version, since the conditions that f ( a ) ≡ 0 mod p and f ′ ( a ) ≢ 0 mod p {\displaystyle f'(a)\not \equiv 0{\bmod {p}}} say that | f ( a ) | p < 1 {\displaystyle |f(a)|_{p}<1} and | f ′ ( a ) | p = 1. {\displaystyle |f'(a)|_{p}=1.}
Suppose that p is an odd prime and a is a non-zero quadratic residue modulo p . Then Hensel's lemma implies that a has a square root in the ring of p -adic integers Z p . {\displaystyle \mathbb {Z} _{p}.} Indeed, let f ( x ) = x 2 − a . {\displaystyle f(x)=x^{2}-a.} If r is a square root of a modulo p then:
where the second condition is dependent on the fact that p is odd. The basic version of Hensel's lemma tells us that starting from r 1 = r we can recursively construct a sequence of integers { r k } {\displaystyle \{r_{k}\}} such that:
This sequence converges to some p -adic integer b which satisfies b 2 = a . In fact, b is the unique square root of a in Z p {\displaystyle \mathbb {Z} _{p}} congruent to r 1 modulo p . Conversely, if a is a perfect square in Z p {\displaystyle \mathbb {Z} _{p}} and it is not divisible by p then it is a nonzero quadratic residue mod p . Note that the quadratic reciprocity law allows one to easily test whether a is a nonzero quadratic residue mod p , thus we get a practical way to determine which p -adic numbers (for p odd) have a p -adic square root, and it can be extended to cover the case p = 2 using the more general version of Hensel's lemma (an example with 2-adic square roots of 17 is given later).
To make the discussion above more explicit, let us find a "square root of 2" (the solution to x 2 − 2 = 0 {\displaystyle x^{2}-2=0} ) in the 7-adic integers. Modulo 7 one solution is 3 (we could also take 4), so we set r 1 = 3 {\displaystyle r_{1}=3} . Hensel's lemma then allows us to find r 2 {\displaystyle r_{2}} as follows:
Based on which the expression
turns into:
which implies t = 1. {\displaystyle t=1.} Now:
And sure enough, 10 2 ≡ 2 mod 7 2 . {\displaystyle 10^{2}\equiv 2{\bmod {7}}^{2}.} (If we had used the Newton method recursion directly in the 7-adics, then r 2 = r 1 − f ( r 1 ) / f ′ ( r 1 ) = 3 − 7 / 6 = 11 / 6 , {\displaystyle r_{2}=r_{1}-f(r_{1})/f'(r_{1})=3-7/6=11/6,} and 11 / 6 ≡ 10 mod 7 2 . {\displaystyle 11/6\equiv 10{\bmod {7}}^{2}.} )
We can continue and find r 3 = 108 = 3 + 7 + 2 ⋅ 7 2 = 213 7 {\displaystyle r_{3}=108=3+7+2\cdot 7^{2}=213_{7}} . Each time we carry out the calculation (that is, for each successive value of k ), one more base 7 digit is added for the next higher power of 7. In the 7-adic integers this sequence converges, and the limit is a square root of 2 in Z 7 {\displaystyle \mathbb {Z} _{7}} which has initial 7-adic expansion
If we started with the initial choice r 1 = 4 {\displaystyle r_{1}=4} then Hensel's lemma would produce a square root of 2 in Z 7 {\displaystyle \mathbb {Z} _{7}} which is congruent to 4 (mod 7) instead of 3 (mod 7) and in fact this second square root would be the negative of the first square root (which is consistent with 4 = −3 mod 7).
As an example where the original version of Hensel's lemma is not valid but the more general one is, let f ( x ) = x 2 − 17 {\displaystyle f(x)=x^{2}-17} and a = 1. {\displaystyle a=1.} Then f ( a ) = − 16 {\displaystyle f(a)=-16} and f ′ ( a ) = 2 , {\displaystyle f'(a)=2,} so
which implies there is a unique 2-adic integer b satisfying
i.e., b ≡ 1 mod 4. There are two square roots of 17 in the 2-adic integers, differing by a sign, and although they are congruent mod 2 they are not congruent mod 4. This is consistent with the general version of Hensel's lemma only giving us a unique 2-adic square root of 17 that is congruent to 1 mod 4 rather than mod 2. If we had started with the initial approximate root a = 3 then we could apply the more general Hensel's lemma again to find a unique 2-adic square root of 17 which is congruent to 3 mod 4. This is the other 2-adic square root of 17.
In terms of lifting the roots of x 2 − 17 {\displaystyle x^{2}-17} from modulus 2 k to 2 k +1 , the lifts starting with the root 1 mod 2 are as follows:
For every k at least 3, there are four roots of x 2 − 17 mod 2 k , but if we look at their 2-adic expansions we can see that in pairs they are converging to just two 2-adic limits. For instance, the four roots mod 32 break up into two pairs of roots which each look the same mod 16:
The 2-adic square roots of 17 have expansions
Another example where we can use the more general version of Hensel's lemma but not the basic version is a proof that any 3-adic integer c ≡ 1 mod 9 is a cube in Z 3 . {\displaystyle \mathbb {Z} _{3}.} Let f ( x ) = x 3 − c {\displaystyle f(x)=x^{3}-c} and take initial approximation a = 1. The basic Hensel's lemma cannot be used to find roots of f ( x ) since f ′ ( r ) ≡ 0 mod 3 {\displaystyle f'(r)\equiv 0{\bmod {3}}} for every r . To apply the general version of Hensel's lemma we want | f ( 1 ) | 3 < | f ′ ( 1 ) | 3 2 , {\displaystyle |f(1)|_{3}<|f'(1)|_{3}^{2},} which means c ≡ 1 mod 2 7. {\displaystyle c\equiv 1{\bmod {2}}7.} That is, if c ≡ 1 mod 27 then the general Hensel's lemma tells us f ( x ) has a 3-adic root, so c is a 3-adic cube. However, we wanted to have this result under the weaker condition that c ≡ 1 mod 9. If c ≡ 1 mod 9 then c ≡ 1, 10, or 19 mod 27. We can apply the general Hensel's lemma three times depending on the value of c mod 27: if c ≡ 1 mod 27 then use a = 1, if c ≡ 10 mod 27 then use a = 4 (since 4 is a root of f ( x ) mod 27), and if c ≡ 19 mod 27 then use a = 7. (It is not true that every c ≡ 1 mod 3 is a 3-adic cube, e.g., 4 is not a 3-adic cube since it is not a cube mod 9.)
In a similar way, after some preliminary work, Hensel's lemma can be used to show that for any odd prime number p , any p -adic integer c congruent to 1 modulo p 2 is a p -th power in Z p . {\displaystyle \mathbb {Z} _{p}.} (This is false for p = 2.)
Suppose A is a commutative ring , complete with respect to an ideal m , {\displaystyle {\mathfrak {m}},} and let f ( x ) ∈ A [ x ] . {\displaystyle f(x)\in A[x].} a ∈ A is called an "approximate root" of f , if
If f has an approximate root then it has an exact root b ∈ A "close to" a ; that is,
Furthermore, if f ′ ( a ) {\displaystyle f'(a)} is not a zero-divisor then b is unique.
This result can be generalized to several variables as follows:
As a special case, if f i ( a ) ≡ 0 mod m {\displaystyle f_{i}(\mathbf {a} )\equiv 0{\bmod {\mathfrak {m}}}} for all i and det J f ( a ) {\displaystyle \det J_{\mathbf {f} }(\mathbf {a} )} is a unit in A then there is a solution to f ( b ) = 0 with b i ≡ a i mod m {\displaystyle b_{i}\equiv a_{i}{\bmod {\mathfrak {m}}}} for all i .
When n = 1, a = a is an element of A and J f ( a ) = J f ( a ) = f ′ ( a ) . {\displaystyle J_{\mathbf {f} }(\mathbf {a} )=J_{f}(a)=f'(a).} The hypotheses of this multivariable Hensel's lemma reduce to the ones which were stated in the one-variable Hensel's lemma.
Completeness of a ring is not a necessary condition for the ring to have the Henselian property: Goro Azumaya in 1950 defined a commutative local ring satisfying the Henselian property for the maximal ideal m to be a Henselian ring .
Masayoshi Nagata proved in the 1950s that for any commutative local ring A with maximal ideal m there always exists a smallest ring A h containing A such that A h is Henselian with respect to m A h . This A h is called the Henselization of A . If A is noetherian , A h will also be noetherian, and A h is manifestly algebraic as it is constructed as a limit of étale neighbourhoods . This means that A h is usually much smaller than the completion  while still retaining the Henselian property and remaining in the same category [ clarification needed ] . | https://en.wikipedia.org/wiki/Hensel's_lemma |
A bryophilous lichen is one that grows on a bryophyte – that is, on a moss or liverwort . [ 1 ] Those which grow on mosses are known as muscicolous lichens , [ 2 ] while those which grow on liverworts are called hepaticolous lichens . [ 3 ] Muscicolous derives from the Latin muscus meaning moss, [ 4 ] while the suffix colous means "living or growing in or on". [ 5 ] Lichens are slow-growing organisms, and so are far more likely to be overgrown by a bryophyte than to overgrow one. [ 6 ] [ 7 ] However, they are better able to compete if the bryophyte is sickly or decaying and they can be parasitic upon them. [ 1 ] [ 8 ] [ 9 ] Some, rather than overgrowing the bryophyte, instead live among its branches. [ 9 ] Bryophilous lichens are particularly common in heathland and arctic or alpine tundra . [ 9 ] Because many are small and inconspicuous, they are easy to overlook. [ 1 ]
This article about lichens or lichenology is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hepaticolous_lichen |
Hepatocyte nuclear factors ( HNFs ) are a group of phylogenetically unrelated transcription factors that regulate the transcription of a diverse group of genes into proteins . These proteins include blood clotting factors and in addition, enzymes and transporters involved with glucose , cholesterol , and fatty acid transport and metabolism . [ 1 ] [ 2 ]
As the name suggests, hepatocyte nuclear factors are expressed predominantly in the liver . However HNFs are also expressed and play important roles in a number of other tissues so that the name hepatocyte nuclear factor is somewhat misleading. Nevertheless, the liver is the only tissue in which a significant number of different HNFs are expressed at the same time. In addition, there are a number of genes which contain multiple promoter and enhancer regions each regulated by a different HNF. Furthermore, efficient expression of these genes require synergistic activation by multiple HNFs. Hence hepatocyte nuclear factors function to ensure liver specific expression of certain genes.
As is the case with many transcription factors, HNFs regulate the expression of a wide variety of target genes and therefore functions. These functions (and especially functions involving the liver) include development and metabolic homeostasis of the organism. For example, HNFs influence expression of the insulin gene as well as genes involved in glucose transport and metabolism. In embryo development, HNF4α is thought to have an important role in the development of the liver , kidney , and intestines .
Variants of the genes can cause several relatively rare forms of MODY , an inherited, early onset form of diabetes. Mutations in the HNF4α , HNF1α, or HNF1β genes are linked to MODY 1 , MODY 3 , and MODY 5 respectively. [ 3 ] Mutations in HNF genes are also associated with a number of others diseases including hepatic adenomas and renal cysts .
The following is a list of human hepatocyte nuclear factors (see also boxes to the right for additional information about these proteins):
Members of the HNF1 subfamily contain a POU-homeodomain and bind to DNA as homodimers.
The HNF3 subfamily members contain a winged helix DNA-binding domain and bind to DNA as monomers.
Members of the HNF4 subfamily are nuclear receptors and bind to DNA either as homodimers or RXR heterodimers.
The HNF6 subfamily members contain a cut-homeodomain ( ONECUT ) bind to DNA as monomers. | https://en.wikipedia.org/wiki/Hepatocyte_nuclear_factors |
Hepatopancreatic parvoviruses (HPV) are viruses with single-stranded DNA genomes that are in the family Parvoviridae , and which infect shrimp , prawn and other crustaceans . [ 1 ] HPV infects the epithelial cells of the host's hepatopancreas and midgut , [ 2 ] leading to stunted growth at the early life stage. For shrimp farms, especially in Asian countries such as China , India and Indonesia , HPV can lead to economic losses in aquaculture due to the reduced production. [ 3 ]
Hepatopancreatic parvoviruses (HPV) are icosahedral particles with an average 22 nm diameter , [ 4 ] whose genomes consist of negative single-stranded DNA molecules. [ 4 ] Four complete genome sequences of HPV are available to date: [ 1 ] Thailand ( Penaeus monodon densovirus (PmoDNV)), [ 5 ] Australia ( Penaeus merguiensis densovirus (PmeDNV)), [ 6 ] India ( Penaeus monodon densovirus (PmoDNV) [ 7 ] and South Korea ( F. chinensis hepatopancreatic densovirus (FcDNV)). [ 8 ]
Different strains of HPV show genetic variance , isolated by shrimp species and/or geographical regions. [ 1 ] For example, there is a 10% sequence variation between South Korean and Chinese stains, which can be explained by the hosts' adaption to different spatial conditions in the two countries. [ 1 ]
HPV is known to infect ten species of shrimp and freshwater prawns including Penaeus vannamei , Penaeus semisulcatus , Penaeus chinensis , Penaeus setosus , Penaeus monodon , Penaeus indicus , Penaeus cyaneus , and Penaeus japonicus . [ 9 ] [ 10 ] The virus infects shrimp at an early stage of growth. [ 11 ] It causes stunted growth, stopping growth when the shrimp reaches about 6 centimeters in length. [ 12 ] HPV infects the epithelial cells of the shrimp's hepatopancreas and midgut . [ 9 ] This results in hepatopancreatic atrophy , low growth rates, loss of appetite, reduced pre-hatching, and an increase in ectoparasites on the body surface and gills . [ 9 ] HPV can cause mortality in epizootics in P. merguiensis and P. semisulcatus after 4-8 weeks, with a mortality rate of 50-100%. [ 13 ]
Hepatopancreatic parvovirus (HPV) has been found to be widely distributed in wild, cultured and hatchery reared shrimps throughout the world including Australia , China , Korea , Taiwan , the Philippines , Indonesia , Malaysia , Singapore , Kenya , Israel , Kuwait , North and South America and India . [ 3 ]
The first case of HPV was reported in 1982 by a commercial farm in Singapore where reports of increased mortalities in early larval and post larval stages of the Banana Prawn, Penaeus merguiensis , and stunted growth in juveniles were found. [ 3 ] [ 14 ] Individual shrimp with the HPV infection displayed nonspecific signs during the juvenile stages, including poor growth rate, anorexia , reduced preening activity , increased surface fouling , and occasional opacity of tail musculature . [ 13 ] These signs were accompanied by mortalities, which reached up to 50-100% of an affected population of P. merguiensis within 4-8 weeks of disease onset. [ 1 ] [ 13 ]
Soon after, cultured populations of four shrimp species from four separate culture facilities in Asia were found to be adversely affected by a disease of presumed viral etiology . [ 13 ] In 1984, samples of P. esculentus from Moreton Bay and the Gulf of Carpentaria of Australia were reported to show similar signs of the virus. [ 1 ]
In 1987, the importation of live Asian shrimp for aquaculture subsequently spread the disease to wild shrimp in North and South America . [ 1 ] In 1995, a new strain of HPV (HPVchin) was reported to be found in P. chinensis in Korea which then was then introduced into Hawaii after the importation of infected shrimp. [ 1 ] [ 15 ] In 1992, HPV infection in the black tiger shrimp ( P. monodon ) was first reported from Thailand which then was reported in India by 2002. [ 1 ] Wild stocks of P. semisulcatus were reported with the infection in 2005 in India . [ 16 ] Additional strains of HPV have been documented in P. monodon from India , Madagascar , New Caledonia and Tanzania and in P. chinensis from South Korea and China . [ 1 ]
The natural host range of HPV includes a number of cultured and captured shrimp species from all around the world, including Penaeus merguiensis , Penaeus semisulcatus , Penaeus chinensis (=orientalis) , Penaeus esculentus , Penaeus monodon , Penaeus indicus , Penaeus penicillatus , Penaeus japonicus , Penaeus stylirostris and Penaeus vannamei . A HPV-like agent was found in Macrobrachium rosenbergii . To date, ten strains of HPV have been described. [ 1 ] HPV is observed to transmit vertically and horizontally . Feeding experiments show that P. monodon post-larvae can be infected by the HPV carried by Artemia , which implies the risk of rearing system contamination. [ 17 ] Parents-offspring transmissions are both reported by aquaculture farms in China and India, confirming the vertical transmission of HPV. [ 18 ] [ 19 ]
HPV first attaches to the microvilli of host cells and then enters them through pinocytosis . Parvovirus particles can infected by exposure to infected water or by cannibalism of tissues of infected hosts. [ 1 ] Cannibalism is ordinary among crustacean species and can intensify as the pressure increases in the communities, such as high density, low oxygen, and low food availability, which are commonly found in shrimp farms. [ 20 ]
Currently, there are no targeted antiviral therapies or vaccines for HPV, underscoring the continued importance of preventive measures in mitigating outbreaks of the disease. [ 1 ]
Therefore, prioritizing research into the prevention and management of HPV infections is crucial. [ 1 ] [ 10 ] Additionally, advancing studies on viral proteins and their functions in replication should serve as the cornerstone for future investigations in this field. Maintaining optimal water quality parameters, such as temperature , pH , and dissolved oxygen levels , to reduce stress on shrimp and support their immune system function. [ 1 ] [ 20 ]
HPV has been found to have greater genetic diversity than other shrimp viruses. The variation in HPV is a reflection of its wide geographic distribution, as it has been found in samples of penaeid shrimp collected from Africa , Australia , and Asia . [ 1 ]
The genetic variation among geographic isolates of HPV can be divided into 4 well-separated genotypes: Tanzania , Korea , Thailand , and Australia . [ 21 ] Isolates from Tanzania and Madagascar form one subclade , Thailand , Indonesia , and India form the second subclade , Australia and New Caledonia form the third, and Korea and China form the forth subclade . The viral etiology of HPV varies amongst shrimp. HPV has been linked to growth reduction of farmed P. monodon in Thailand ; however, in Madagascar , HPV infection appears to have no negative effect on shrimp growth. [ 21 ] It is speculated that the different effects may be related to differences among viral genotypes , host populations and/or farming practices. [ 21 ]
HPV poses environmental and economical challenges in the aquaculture industry. Aquaculture is one of the fastest growing food producing sectors in the world where the reported global production of food from aquaculture comprised 87.5 million tonnes of aquatic animals mostly for use as human food. [ 22 ] Shrimp farming has rapidly expanded in Asia and generated substantial income for farmers in many developing countries . [ 23 ] The increased occurrence of devastating viral diseases in shrimp culture systems threatens the sustainability of both the aquaculture industry and the commercial shrimp fishery.
HPV is associated with reduced growth rates of juvenile shrimp without showing any gross signs of disease and can lead to mass mortalities in shrimp populations. [ 21 ] Therefore, outbreaks can result in substantial losses for shrimp farmers due to decreased yields, increased mortality rates, and costly disease management measures such as quarantine protocols and treatment regimens. [ 9 ] [ 1 ] These impacts reverberate through the entire aquaculture supply chain , affecting livelihoods and food security in regions dependent on shrimp farming. [ 23 ] In India , the shrimp aquaculture industry started only during the mid-eighties, flourished well and proved lucrative initially until the sector was affected by diseases. Ecologically, infected shrimp may shed the virus into surrounding waters, potentially spreading the disease to wild crustacean populations. [ 18 ] [ 19 ] | https://en.wikipedia.org/wiki/Hepatopancreatic_parvovirus |
Drug-induced liver injury (DILI) Toxin-induced hepatitis Drug-induced hepatitis Drug-induced hepatic necrosis Drug-induced hepatic fibrosis Drug-induced hepatic granuloma Toxic liver disease with hepatitis Toxic liver disease with cholestasis Toxic hepatitis Toxic liver disease Toxin-induced liver disease Drug-induced liver disease Drug-induced liver damage Hepatogenous poisoning
Hepatotoxicity (from hepatic toxicity ) implies chemical-driven liver damage. Drug-induced liver injury (DILI) is a cause of acute and chronic liver disease caused specifically by medications and the most common reason for a drug to be withdrawn from the market after approval.
The liver plays a central role in transforming and clearing chemicals and is susceptible to the toxicity from these agents. Certain medicinal agents, when taken in overdoses (e.g. acetaminophen, paracetamol ) and sometimes even when introduced within therapeutic ranges (e.g. halothane ), may injure the organ. Other chemical agents, such as those used in laboratories and industries, natural chemicals (e.g., alpha-amanitin ), and herbal remedies (two prominent examples being kava , though the causal mechanism is unknown, and comfrey , through pyrrolizidine alkaloid content) can also induce hepatotoxicity. Chemicals that cause liver injury are called hepatotoxins .
More than 900 drugs have been implicated in causing liver injury [ 1 ] (see LiverTox, external link, below) and it is the most common reason for a drug to be withdrawn from the market. Hepatotoxicity and drug-induced liver injury also account for a substantial number of compound failures, highlighting the need for toxicity prediction models (e.g. DTI), [ 2 ] and drug screening assays, such as stem cell -derived hepatocyte-like cells, that are capable of detecting toxicity early in the drug development process. [ 3 ] Chemicals often cause subclinical injury to the liver, which manifests only as abnormal liver enzyme tests .
Drug-induced liver injury is responsible for 5% of all hospital admissions and 50% of all acute liver failures . [ 4 ] [ 5 ]
Adverse drug reactions are classified as type A (intrinsic or pharmacological) or type B (idiosyncratic). [ 6 ] Type A drug reaction accounts for 80% of all toxicities. [ 7 ]
Drugs or toxins that have a pharmacological (type A) hepatotoxicity are those that have predictable dose-response curves (higher concentrations cause more liver damage) and well characterized mechanisms of toxicity, such as directly damaging liver tissue or blocking a metabolic process. As in the case of paracetamol overdose, this type of injury occurs shortly after some threshold for toxicity is reached. Carbon tetrachloride is commonly used to induce acute type A liver injury in animal models.
Idiosyncratic (type B) injury occurs without warning, when agents cause non-predictable hepatotoxicity in susceptible individuals, which is not related to dose and has a variable latency period. [ 8 ] This type of injury does not have a clear dose-response nor temporal relationship, and most often does not have predictive models. Idiosyncratic hepatotoxicity has led to the withdrawal of several drugs from market even after rigorous clinical testing as part of the FDA approval process; Troglitazone (Rezulin) [ 2 ] [ 9 ] and trovafloxacin (Trovan) are two prime examples of idiosyncratic hepatotoxins pulled from market.
The herb kava has caused a number of cases of idiosyncratic liver injury, ranging everywhere from asymptomatic to fatal.
Oral use of the antifungal ketoconazole has been associated with hepatic toxicity, including some fatalities; [ 10 ] however, such effects appear to be limited to doses taken over a period longer than 7 days. [ 11 ]
Paracetamol also known as acetaminophen, and by the brand names of Tylenol and Panadol, is usually well-tolerated in prescribed dose, but overdose is the most common cause of drug-induced liver disease and acute liver failure worldwide. [ 12 ] Damage to the liver is not due to the drug itself but to a toxic metabolite ( N -acetyl- p -benzoquinone imine (NAPQI)) produced by cytochrome P-450 enzymes in the liver. [ 13 ] In normal circumstances, this metabolite is detoxified by conjugating with glutathione in phase 2 reaction. In an overdose, a large amount of NAPQI is generated, which overwhelms the detoxification process and leads to liver cell damage. Nitric oxide also plays a role in inducing toxicity. [ 14 ] The risk of liver injury is influenced by several factors including the dose ingested, concurrent alcohol or other drug intake, interval between ingestion and antidote, etc. The dose toxic to the liver is quite variable from person to person and is often thought to be lower in chronic alcoholics. [ 15 ] [ 16 ] Measurement of blood level is important in assessing prognosis, higher levels predicting a worse prognosis. Administration of Acetylcysteine , a precursor of glutathione, can limit the severity of the liver damage by capturing the toxic NAPQI. Those that develop acute liver failure can still recover spontaneously, but may require transplantation if poor prognostic signs such as encephalopathy or coagulopathy is present (see King's College Criteria ). [ 17 ]
Although individual analgesics rarely induce liver damage due to their widespread use, NSAIDs have emerged as a major group of drugs exhibiting hepatotoxicity. Both dose-dependent and idiosyncratic reactions have been documented. [ 18 ] Aspirin and phenylbutazone are associated with intrinsic hepatotoxicity; idiosyncratic reaction has been associated with ibuprofen, sulindac, phenylbutazone, piroxicam, diclofenac and indomethacin.
Glucocorticoids are so named due to their effect on the carbohydrate mechanism. They promote glycogen storage in the liver. An enlarged liver is a rare side-effect of long-term steroid use in children. [ 19 ] The classical effect of prolonged use both in adult and paediatric population is steatosis . [ 20 ]
Isoniazide (INH) is one of the most commonly used drugs for tuberculosis ; it is associated with mild elevation of liver enzymes in up to 20% of patients and severe hepatotoxicity in 1-2% of patients. [ 21 ]
There are also cases where other hydrazine derivative drugs, such as the MAOI antidepressant iproniazid , are associated with liver damage. [ 22 ] [ 23 ] Phenelzine has been associated with abnormal liver tests. [ 24 ] Toxic effects can develop from antibiotics, such as amoxicillin/clavulanic acid . [ 25 ] [ 26 ]
Examples include alpha-Amanitin containing mushrooms, kava, and aflatoxin producing molds. Pyrrolizidine alkaloids , which occur in some plants, can be toxic. [ 27 ] [ 28 ] Green tea extract is a growing cause of liver failure due to its inclusion in more products. [ 29 ] [ 30 ] [ 31 ]
Examples include: Ackee fruit , Bajiaolian , Camphor , Copaltra , Cycasin , Garcinia , [ 32 ] Kava leaves, pyrrolizidine alkaloids , Horse chestnut leaves, Valerian , Comfrey . [ 33 ] [ 34 ] Chinese herbal remedies: Jin Bu Huan , Ephedra , Shou Wu Pian , Bai Xian Pi . [ 35 ] [ 36 ]
Examples include arsenic , carbon tetrachloride , and vinyl chloride . [ 37 ]
Drugs continue to be taken off the market due to late discovery of hepatotoxicity. Due to its unique metabolism and close relationship with the gastrointestinal tract , the liver is susceptible to injury from drugs and other substances. 75% of blood coming to the liver arrives directly from gastrointestinal organs and the spleen via portal veins that bring drugs and xenobiotics in near-undiluted form. Several mechanisms are responsible for either inducing hepatic injury or worsening the damage process.
Many chemicals damage mitochondria , an intracellular organelle that produces energy. Its dysfunction releases excessive amount of oxidants that, in turn, injure hepatic cells. Activation of some enzymes in the cytochrome P-450 system such as CYP2E1 also lead to oxidative stress. [ 38 ] Injury to hepatocyte and bile duct cells lead to accumulation of bile acid inside the liver . This promotes further liver damage. [ 39 ] Non- parenchymal cells such as Kupffer cells , collagen-producing stellate cells , and leukocytes (i.e. neutrophil and monocyte ) also have a role in the mechanism.
The human body subjects most, but not all, compounds to various chemical processes (i.e. metabolism ) to make them suitable for elimination. This involves chemical transformations to (a) reduce fat solubility and (b) to change biological activity. Although almost all tissues in the body have some ability to metabolize chemicals, smooth endoplasmic reticulum in the liver is the principal "metabolic clearing house" for both endogenous chemicals (e.g., cholesterol , steroid hormones, fatty acids , proteins ) and exogenous substances (e.g., drugs, alcohol). [ 40 ] The central role played by liver in the clearance and transformation of chemicals makes it susceptible to drug-induced injury.
Drug metabolism is usually divided into two phases: phase 1 and phase 2 . Phase 1 reaction is generally speaking to prepare a drug for phase 2. However, many compounds can be metabolized by phase 2 directly or be excreted without any phase 2 reactions occurring. Phase 1 reaction involves oxidation , reduction , hydrolysis , hydration and many other rare chemical reactions. These processes tend to increase water solubility of the drug and can generate metabolites that are more chemically active and/or potentially toxic. Most of phase 2 reactions take place in cytosol and involve conjugation with endogenous compounds via transferase enzymes. Phase 1 are typically more suitable for elimination.
A group of enzymes located in the endoplasmic reticulum, known as cytochrome P-450 , is the most important family of metabolizing enzymes in the liver. Cytochrome P-450 is not a single enzyme, but rather consists of a closely related family of 50 isoforms ; six of them metabolize 90% of drugs. [ 41 ] [ 42 ] There is a tremendous diversity of individual P-450 gene products, and this heterogeneity allows the liver to perform oxidation on a vast array of chemicals (including most drugs) in phase 1. Three important characteristics of the P-450 system have roles in drug-induced toxicity:
Each of the P-450 proteins is unique and accounts (to some extent) for the variation in drug metabolism between individuals. Genetic variations ( polymorphism ) in P-450 metabolism should be considered when patients exhibit unusual sensitivity or resistance to drug effects at normal doses. Such polymorphism is also responsible for variable drug response among patients of differing ethnic backgrounds.
Many substances can influence the P-450 enzyme mechanism. Drugs interact with the enzyme family in several ways. [ 45 ] Drugs that modify cytochrome P-450 enzyme are referred to as either inhibitors or inducers. Enzyme inhibitors block the metabolic activity of one or several P-450 enzymes. This effect usually occurs immediately. On the other hand, inducers increase P-450 activity by increasing enzyme production, or, in the case of CYP2E1, preventing degradation in the proteasome . There is usually a delay before enzyme activity increases. [ 42 ]
Some drugs may share the same P-450 specificity and thus competitively block their biotransformation. This may lead to accumulation of drugs metabolized by the enzyme. This type of drug interaction may also reduce the rate of generation of toxic metabolites.
Chemicals produce a wide variety of clinical and pathological hepatic injury. Biochemical markers (e.g. alanine transferase , alkaline phosphatase and bilirubin ) are often used to indicate liver damage. Liver injury is defined as a rise in either (a) ALT level more than three times of upper limit of normal (ULN), (b) ALP level more than twice ULN, or (c) total bilirubin level more than twice ULN when associated with increased ALT or ALP. [ 46 ] [ 47 ] Liver damage is further characterized into hepatocellular (predominantly initial Alanine transferase elevation) and cholestatic (initial alkaline phosphatase rise) types. However they are not mutually exclusive and mixed types of injuries are often encountered.
Specific histo-pathological patterns of liver injury from drug-induced damage are discussed below.
This is the most common type of drug-induced liver cell necrosis where the injury is largely confined to a particular zone of the liver lobule . It may manifest as a very high level of ALT and severe disturbance of liver function leading to acute liver failure .
In this pattern, hepatocellular necrosis is associated with infiltration of inflammatory cells. There can be three types of drug-induced hepatitis. (A) viral hepatitis is the most common, where histological features are similar to acute viral hepatitis. (B) in focal or non-specific hepatitis, scattered foci of cell necrosis may accompany lymphocytic infiltration. (C) chronic hepatitis is very similar to autoimmune hepatitis clinically, serologically, and histologically.
Liver injury leads to impairment of bile flow and cases are predominated by itching and jaundice. Histology may show inflammation (cholestatic hepatitis) or it can be bland (without any parenchymal inflammation). On rare occasions, it can produce features similar to primary biliary cirrhosis due to progressive destruction of small bile ducts ( vanishing duct syndrome ).
Hepatotoxicity may manifest as triglyceride accumulation, which leads to either small-droplet (microvesicular) or large-droplet (macrovesicular) fatty liver. There is a separate type of steatosis by which phospholipid accumulation leads to a pattern similar to the diseases with inherited phospholipid metabolism defects (e.g., Tay–Sachs disease )
Drug-induced hepatic granulomas are usually associated with granulomas in other tissues and patients typically have features of systemic vasculitis and hypersensitivity. More than 50 drugs have been implicated.
These result from injury to the vascular endothelium.
Neoplasms have been described with prolonged exposure to some medications or toxins. Hepatocellular carcinoma, angiosarcoma, and liver adenomas are the ones usually reported.
This remains a challenge in clinical practice due to a lack of reliable markers. [ 48 ] Many other conditions lead to similar clinical as well as pathological pictures. To diagnose hepatotoxicity, a causal relationship between the use of the toxin or drug and subsequent liver damage has to be established, but might be difficult, especially when idiosyncratic reaction is suspected. [ 49 ] Simultaneous use of multiple drugs may add to the complexity. As in acetaminophen toxicity, well established, dose-dependent, pharmacological hepatotoxicity is easier to spot. Several clinical scales such as CIOMS /RUCAM scale and Maria and Victorino criteria have been proposed to establish causal relationship between offending drug and liver damage. CIOMS/RUCAM scale involves a scoring system that categorizes the suspicion into "definite or highly probable" (score > 8), "probable" (score 6–8), "possible" (score 3–5), "unlikely" (score 1–2) and "excluded" (score ≤ 0). In clinical practice, physicians put more emphasis on the presence or absence of similarity between the biochemical profile of the patient and known biochemical profile of the suspected toxicity (e.g., cholestatic damage in amoxycillin-clauvonic acid ). [ 48 ]
In most cases, liver function will return to normal if the offending drug is stopped early. Additionally, the patient may require supportive treatment. In acetaminophen toxicity , however, the initial insult can be fatal. Fulminant hepatic failure from drug-induced hepatotoxicity may require liver transplantation. In the past, glucocorticoids in allergic features and ursodeoxycholic acid in cholestatic cases had been used, but there is no good evidence to support their effectiveness. [ citation needed ]
An elevation in serum bilirubin level of more than 2 times ULN with associated transaminase rise is an ominous sign. This indicates severe hepatotoxicity and is likely to lead to mortality in 10% to 15% of patients, especially if the offending drug is not stopped ( Hy's Law ). [ 50 ] [ 51 ] This is because it requires significant damage to the liver to impair bilirubin excretion, hence minor impairment (in the absence of biliary obstruction or Gilbert syndrome ) would not lead to jaundice. Other poor predictors of outcome are old age, female sex, high AST . [ 52 ] [ 53 ]
The following therapeutic drugs were withdrawn from the market primarily because of hepatotoxicity: Troglitazone , bromfenac , trovafloxacin , ebrotidine , nimesulide , nefazodone , ximelagatran and pemoline . [ 48 ] [ 54 ] [ 55 ] | https://en.wikipedia.org/wiki/Hepatotoxicity |
Hepelivirales is an order of viruses . [ 1 ]
The order contains the following families: [ 2 ]
This virus -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hepelivirales |
Hepoxilins (Hx) are a set of epoxyalcohol metabolites of polyunsaturated fatty acids (PUFA), i.e. they possess both an epoxide and an alcohol (i.e. hydroxyl ) residue. HxA3 , HxB3 , and their non-enzymatically formed isomers are nonclassic eicosanoid derived from acid the (PUFA), arachidonic acid . A second group of less well studied hepoxilins, HxA4 , HxB4 , and their non-enzymatically formed isomers are nonclassical eicosanoids derived from the PUFA, eicosapentaenoic acid . Recently, 14,15-HxA3 and 14,15-HxB3 have been defined as arachidonic acid derivatives that are produced by a different metabolic pathway than HxA3, HxB3, HxA4, or HxB4 and differ from the aforementioned hepoxilins in the positions of their hydroxyl and epoxide residues. Finally, hepoxilin-like products of two other PUFAs, docosahexaenoic acid and linoleic acid , have been described. All of these epoxyalcohol metabolites are at least somewhat unstable and are readily enzymatically or non-enzymatically to their corresponding trihydroxy counterparts, the trioxilins (TrX). HxA3 and HxB3, in particular, are being rapidly metabolized to TrXA3 , TrXB3 , and TrXC3 . Hepoxilins have various biological activities in animal models and/or cultured mammalian (including human) tissues and cells. The TrX metabolites of HxA3 and HxB3 have less or no activity in most of the systems studied but in some systems retain the activity of their precursor hepoxilins. Based on these studies, it has been proposed that the hepoxilins and trioxilins function in human physiology and pathology by, for example, promoting inflammation responses and dilating arteries to regulate regional blood flow and blood pressure.
HxA3 and HxB3 were first identified, named, shown to have biological activity in stimulating insulin secretion in cultured rat pancreatic islets of Langerhans in Canada in 1984 by CR Pace-Asciak and JM Martin. [ 1 ] Shortly thereafter, Pace-Asciak identified, named, and showed to have insulin secretagogue activity HxA4 and HxB4. [ 2 ]
HxA3, HxB3, and their isomers are distinguished from most other eicosanoids (i.e. signaling molecules made by oxidation of 20-carbon fatty acids) in that they contain both epoxide and hydroxyl residues; they are structurally differentiated in particular from two other classes of arachidonic acid-derived eicosanoids, the leukotrienes and lipoxins , in that they lack conjugated double bonds . HxA4 and HxB4 are distinguished from HxA3 and HxB3 by possessing four rather than three double bonds . The 14,15-HxA3 and 14,15-HxB3 non-classical eicosanoids are distinguished from the aforementioned hepoxilins in that they are formed by a different metabolic pathway and differ in the positioning of their epoxide and hydroxyl residues. Two other classes of epoxyalcohol fatty acids, those derived from the 22-carbon polyunsaturated fatty acid, docosahexaenoic acid, and the 18-carbon fatty acid, linoleic acid, are distinguished from the aforementioned hepoxilins by their carbon chain length; they are termed hepoxilin-like rather than hepoxilins. [ 3 ] [ 4 ] A hepoxilin-like derivative of linoleic acid is formed on linoleic acid that is esterified to a sphingosine in a complex lipid termed esterified omega-hydroxylacyl-sphingosin (EOS). [ 4 ]
The full structural identities of the hepoxilins and hepoxilin-like compounds in most studies are unclear in two important respects. First, the R versus S chirality of their hydroxy residue in the initial and most studies thereafter is undefined and therefore given with, for example, HxB3 as 10 R/S -hydroxy or just 10-hydroxy. Second, the R , S versus S , R chirality of the epoxide residue in these earlier studies likewise goes undefined and given with, for example, HxB3 as 11,12-epoxide. While some later studies have defined the chirality of these residues for the products they isolated, [ 5 ] it is often not clear that the earlier studies dealt with products that had exactly the same or a different chirality at these residues.
Hepoxilins, such as HxA3 and HxB3, are metabolic intermediates derived from the polyunsaturated fatty acid (PUFA), arachidonic acid. They possess both an epoxide and a hydroxyl residue. As metabolic intermediates, hepoxilins play several roles in human physiology and pathology. They have various biological activities in animal models and/or cultured mammalian (including human) tissues and cells. For example, they have been implicated in promoting the neutrophil-based inflammatory response to various bacteria in the intestines and lungs of rodents.
Human HxA3 and HxB3 are formed in a two-step reaction. First, molecular oxygen (O 2 ) is added to carbon 12 of arachidonic acid (i.e. 5Z,8Z,11Z,14Z-eicosatetraenoic acid) and concurrently the 11 Z double bond in this arachidonate moves to the 10 E position to form the intermediate product, 12 S -hydroperoxy-5Z,8Z,10E,14Z-eicosatetraenoic acid (i.e. 12 S -hydroperoxyeicosatetraenoic acid or 12 S -HpETE). Second, 12 S -HpETE is converted to the hepoxilin products, HxA3 (i.e. 8 R/S -hydroxy-11,12-oxido-5 Z ,9 E ,14 Z -eicosatrienoic acid) and HxB3 (i.e. 10 R/S -hydroxy-11,12-oxido-5 Z ,8 Z ,14 Z -eicosatrienoic acid). [ 3 ] This two-step metabolic reaction is illustrated below:
The second step in this reaction, the conversion of 12( S )-HpETE to HxA3 and HxB3, may be catalyzed by ALOX12 as an intrinsic property of the enzyme. [ 6 ] Based on gene knockout studies, however, the epidermal lipoxygenase, ALOXE3 , or more correctly, its mouse ortholog Aloxe3, appears responsible for converting 12( S )-HpETE to HxB3 in mouse skin and spinal tissue. [ 4 ] [ 7 ] [ 8 ] It is suggested that ALOXE3 contributes in part or whole to the production of HxB3 and perhaps other hepoxilins by tissues where it is expressed such as the skin. [ 4 ] [ 9 ] Furthermore, hydroperoxide-containing unsaturated fatty acids can rearrange non-enzymatically to form a variety of epoxyalcohol isomers. [ 10 ] The 12( S )-HpETE formed in tissues, it is suggested, may similar rearrange non-enzymatically to form HxA3 and HXB3. [ 4 ] Unlike the products made by ALOX12 and ALOXE3, which are stereospecific in forming only HxA3 and HxB3, however, this non-enzymatic production of hepoxilins may form a variety of hepoxilin isomers and occur as an artifact of tissue processing. [ 4 ] Finally, cellular peroxidases readily and rapidly reduce 12( S )-HpETE to its hydroxyl analog, 12 S -hydroxy-5Z,8Z,10E,14Z-eicosatetraenoic acid (12 S -HETE; see 12-hydroxyeicosatetraenoic acid ; this reaction competes with the hepoxilin-forming reaction and in cells expressing very high peroxidase activity may be responsible for blocking the formation of the hepoxilins. [ 3 ]
ALOX15 is responsible for metabolizing arachidonic acid to 14,15-HxA3 and 14,15-HxB3 as indicated in the following two-step reaction which first forms 15( S )-hydroperoxy-5 Z ,8 Z ,11 Z ,13 E -eicosatetraenoic acid (15 S -HpETE) and then two specific isomers of 11 S/R -hydroxy-14 S ,15 S -epoxy-5 Z ,8 Z ,12 E -eicosatrienoic acid (i.e. 14,15-HxA3) and 13 S/ R)-hydroxy-14 S ,15 S -epoxy-5 Z ,8 Z ,11 Z -eicosatrienoic acid (i.e. 14,15-HxB3):
5Z,8Z,11Z,14Z-eicosatetraenoic acid + O 2 → 15( S )-hydroperoxy-5 Z ,8 Z ,11 Z ,13 E -eicosatetraenoic acid → 11 R -hydroxy-14 S ,15 S -epoxy-5 Z ,8 Z ,12 E -eicosatrienoic acid and 13 R -hydroxy-14 S ,15 S -epoxy-5 Z ,8 Z ,11 Z -eicosatrienoic acid
ALOX15 appears capable of conducting both steps in this reaction [ 11 ] although further studies may show that ALOXE3, non-enzymatic rearrangements, and the reduction of 15 S -HpETE to 15( S )-hydroxy-5 Z ,8 Z ,11 Z ,13 E -eicosatetraenoic acid (i.e. 15 S -HETE; see 15-hydroxyicosatetraenoic acid ) may be involved in the production of 14,15-HxA3 and 14,15-HxB3 as they are in that of HxA3 and HxB3.
Production of the hepoxilin-like metabolites of docosahexaenoic acid, 7 R/S -hydroxy-10,11-epoxy-4 Z ,7 E ,13 Z ,16 Z ,19 Z -docosapentaenoic acid (i.e. 7-hydroxy-bis-α-dihomo-HxA5) and 10-hydroxy-13,14-epoxy-4 Z ,7 EZ ,11 E ,16 Z ,19 Z -docosapentaenoic acid (i.e. 10-hydroxy-bis-α-dihomo-HxA5) was formed (or inferred to be formed based on the formation of their tihydroxy metabolites (see trioxilins, below) as a result of adding docosahexaenoic acid to the pineal gland or hippocampus isolated from rats; the pathway(s) making these products has not been described. [ 3 ] [ 12 ]
A hepoxilin-like metabolite of linoleic acid forms in the skin of humans and rodents. This hepoxilin is esterified to sphinganine in a lipid complex termed EOS i.e. esterified omega-hydroxyacyl-sphingosine (see Lipoxygenase § Human lipoxygenases ) that also contains a very long chain fatty acid . In this pathway, ALOX12B metabolizes the esterified linoleic acid to its 9 R -hydroperoxy derivative and then ALOXE3 metabolizes this intermediate to its 13 R -hydroxy-9 R ,10 R -epoxy product. The pathway functions to deliver very long chain fatty acids to the cornified lipid envelope of the skin surface. [ 9 ]
HxA3 is extremely unstable and HxB3 is moderately unstable, rapidly decomposing to their tri-hydroxy products, for example, during isolation procedures that use an even mildly acidic methods; they are also rapidly metabolized enzymatically in cells to these same tri-hydroxy products, termed trioxilins (TrX's) or trihydroxyeicoxatrienoic acids (THETA's); HxA3 is converted to 8,11,12-trihydroxy-5 Z ,9 E ,14 Z -eicosatrienoic acid (trioxilin A3 or TrXA3) while HxB3 is converted to 10,11,12-trihydroxy-5 Z ,8 Z ,14 Z -eicosatrienoic acid (trioxilin B3 or TrXB3). [ 3 ] [ 13 ] A third trihydroxy acid, 8,9,12-trihydroxy-5 Z ,10 E ,14 Z eicosatrienoic acid (trioxilin C3 or TrXC3), has been detected in rabbit and mouse aorta tissue incubated with arachidonic acid. [ 5 ] [ 14 ] The metabolism of HxA3 to TrXA3 and HXB3 to TrX is accomplished by soluble epoxide hydrolase in mouse liver; since it is widely distributed in various tissues of various mammalian species, including humans, soluble epoxide hydrolase may be the principal enzyme responsible for metabolizing these and perhaps other hepoxilin compounds. [ 3 ] [ 15 ] It seems possible, however, that other similarly acting epoxide hydrolases such as microsomal epoxide hydrolase or epoxide hydrolase 2 may prove to hepoxilin hydrolase activity. While the trihydroxy products of hepoxilin synthesis are generally considered to be inactive and the sEH pathway therefore considered as functioning to limiting the actions of the hepoxilins, [ 3 ] [ 16 ] some studies found that TrXA3, TrXB3, and TrXC3 were more powerful than HxA3 in relaxing pre-contracted mouse arteries [ 5 ] and that TrXC3 was a relatively potent relaxer of rabbit pre-contracted aorta. [ 14 ]
HxA3 was converted through a Michael addition catalyzed by glutathione transferase to its glutathione conjugate, HxA3-C, i.e., 11-glutathionyl-HxA3, in a cell-free system or in homogenates of rat brain hippocampus tissue; HxA3-C proved to be a potent stimulator of membrane hyperpolarization in rat hippocampal CA1 neurons. [ 17 ] This formation of hepoxilin A3-C appears analogous to the formation of leukotriene C4 by the conjugation of glutathione to leukotriene A4 . Glutathione conjugates of 14,15-HxA3 and 14,15-HxB3 have also been detected the human Hodgkin disease Reed–Sternberg cell line, L1236. [ 11 ]
HxB3 and TrX3 are found esterified into the sn -2 position of phospholipid in human psoriasis lesions and samples of human psoriatic skin acylate HxBw and TrX2 into these phospholipids in vitro . [ 3 ] [ 18 ]
Virtually all of the biological studies on hepoxilins have been conducted in animals or in vitro on animal and human tissues, However, these studies give species-specific different results which complicate their relevancy to humans. The useful translation of these studies to human physiology, pathology, and clinical medicine and therapies requires much further study.
HxA3 and HxB3 possess pro-inflammatory actions in, for example, stimulating human neutrophil chemotaxis and increasing the permeability of skin capillaries. [ 3 ] [ 19 ] Studies in humans have found that the amount of HxB3 is >16-fold higher in psoriatic lesions than normal epidermis. It is present in psoriatic scales at ~10 micromolar, a concentration which is able to exert biologic effects; HxB3 was not detected in these tissues although its present was strongly indicated by the presence of its metabolite, TrXB3, at relatively high levels in psoriatic scales but not normal epidermal tissue. [ 13 ] These results suggest that the pro-inflammatory effects of HxA3 and HxB3 may contribute to the inflammatory response that accompanies psoriasis and perhaps other inflammatory skin conditions. [ 3 ] [ 13 ] [ 20 ] [ 21 ] HxA3 has also been implicating in promoting the neutrophil-based inflammatory response to various bacteria in the intestines and lungs of rodents.; [ 22 ] [ 23 ] this allows that this hepoxilin may also promote the inflammatory response of humans in other tissues, particularly those with a mucosa surface, besides the skin. In addition, HxA3 and a synthetic analog of HxB3, PBT-3, induce human neutrophils to produce neutrophil extracellular traps , i.e. DNA -rich extracellular fibril matrixes able to kill extracellular pathogens while minimizing tissue; hence these hepoxilins may contribute to innate immunity by being responsible of the direct killing of pathogens. [ 24 ]
In addition to 12 S -HETE and 12 R -HETE (see 12-HETE § Blood pressure ), HxA3, TrXA3, and TrXC3 but neither HxB3 nor TrXB3 relax mouse mesentery arteries pre-contracted by thromboxane A2 (TXA2). Mechanistically, these metabolites form in the vascular endothelium , move to the underlining smooth muscle, and reverse the smooth muscle contraction caused by TXA2 by functioning as a receptor antagonist , i.e. they competitively inhibit the binding of TXA2 to its thromboxane receptor , α isoform . [ 5 ] In contrast, 15-lipoxygenase-derived epoxyalcohol and trihydroxy metabolites of arachidonic acid viz., 15-hydroxy-11,12-epoxyeicosatrienoic acid, 13-hydroxy-14,15-epoxy-eicosatrienoic acid (a 14,15-HxA4 isomer), and 11,12,15-trihydroxyeicosatrienoic acid dilate rabbit aorta by an endothelium-derived hyperpolarizing factor (EDHF) mechanism, i.e. they form in the vessels endothelium, move to underlying smooth muscles, and trigger a response of hyperpolarization -induced relaxation by binding to and thereby opening their apamin -sensitive small conductance (SK) calcium-activated potassium channels . [ 5 ] [ 25 ] [ 26 ] The cited metabolites may use one or the other of these two mechanisms in different vascular beds and in different animal species to contribute in regulating regional blood flow and blood pressure. While the role of these metabolites in the human vasculature has not been studied, 12 S -HETE, 12 R -HETE, HxA3, TrXA3, and TrXC3 do inhibit the binding of TXA2 to the human thromboxane receptor. [ 5 ] [ 27 ]
HXA3 and HXB3 appear responsible for hyperalgesia and tactile allodynia (pain caused by a normally non-painful stimulus) response of mice to skin inflammation. In this model, the hepoxilins are released in spinal cord and directly activate TRPV1 and TRPA1 receptors to augment the perception of pain. [ 3 ] [ 28 ] [ 29 ] TRPV1 (the transient receptor potential cation channel subfamily V member 1 (TrpV1), also termed the capsaicin receptor or vanilloid receptor) and TRPA1 (Transient receptor potential cation channel, member A1) are plasma membrane ion channels on cells; these channels are known to be involved in the perception of pain caused by exogenous and endogenous physical and chemical stimuli in a wide range of animal species including humans.
Cultured rat RINm5F pancreatic islet cells undergoing oxidative stress secrete HxB3; HxB3 (and HxA3) in turn upregulates peroxidase enzymes which act to decrease this stress; it is proposed that this HxB3-triggered induction of oxidases constitutes a general compensatory defense response used by a variety of cells to protect their vitality and functionality. [ 30 ] [ 31 ]
The insulin-secreting actions of HxA3 and HxB3 on isolate rat pancreatic islet cells involves their ability to increase or potentiate the insulin-secreting activity of glucose, requires very high concentrations (e.g. 2 micromolar) of the hepoxilins, and has not been extended to intact animals or humans. [ 3 ] [ 32 ]
Hepoxilins are also produced in the brain. [ 33 ] | https://en.wikipedia.org/wiki/Hepoxilin |
Heptachlor is an organochlorine compound that was used as an insecticide . Usually sold as a white or tan powder, heptachlor is one of the cyclodiene insecticides. In 1962, Rachel Carson 's Silent Spring questioned the safety of heptachlor and other chlorinated insecticides. Due to its highly stable structure, heptachlor can persist in the environment for decades. In the United States, the Environmental Protection Agency has limited the sale of heptachlor products to the specific application of fire ant control in underground transformers. The amount that can be present in different foods is regulated. [ 3 ]
Analogous to the synthesis of other cyclodienes, heptachlor is produced via the Diels-Alder reaction of hexachlorocyclopentadiene and cyclopentadiene . The resulting adduct is chlorinated followed by treatment with hydrogen chloride in nitromethane in the presence of aluminum trichloride or with iodine monochloride . [ 4 ]
Compared to chlordane , it is about 3–5 times more active as an insecticide, but more inert chemically, being resistant to water and caustic alkalies. [ 4 ]
Soil microorganisms transform heptachlor by epoxidation , hydrolysis , and reduction. When the compound was incubated with a mixed culture of organisms, chlordene (hexachlorocyclopentadine, its precursor) formed, which was further metabolized to chlordene epoxide. Other metabolites include 1-hydroxychlordene, 1-hydroxy-2,3-epoxychlordene, and heptachlor epoxide. Soil microorganisms hydrolyze heptachlor to give ketochlordene. Rats metabolize heptachlor to the epoxide 1-exo-1-hydroxyheptachlor epoxide and 1,2-dihydrooxydihydrochlordene. When heptachlor epoxide was incubated with microsomal preparations form liver of pigs and from houseflies , the products found were diol and 1-hydroxy-2,3-epoxychlordene. [ 4 ] The metabolic scheme in rats shows two pathways with the same metabolite. The first involves following scheme: heptachlor → heptachlor epoxide → dehydrogenated derivative of 1-exo-hydroxy-2,3-exo-epoxychlordene → 1,2-dihydrooxydihydrochlordene. The second involves: heptachlor → 1-exo-hydroxychlordene → 1-exo-hydroxy, 2,3-exo-epoxychlordene → 1,2-dihydrooxydihydrochlordene. [ 5 ]
Heptachlor is a persistent organic pollutant (POP). It has a half life of ~1.3-4.2 days (air), ~0.03-0.11 years (water), and ~0.11-0.34 years (soil). One study described its half life to be 2 years and claimed that its residues could be found in soil 14 years after its initial application. Like other POPs, heptachlor is lipophilic and poorly soluble in water (0.056 mg/L at 25 °C), thus it tends to accumulate in the body fat of humans and animals.
Heptachlor epoxide is more likely to be found in the environment than its parent compound. The epoxide also dissolves more easily in water than its parent compound and is more persistent. Heptachlor and its epoxide absorb to soil particles and evaporate. [ 6 ]
The range of oral rat LD 50 values are 40 mg/kg to 162 mg/kg. Daily oral doses of heptachlor at 50 and 100 mg/kg were found to be lethal to rats after 10 days. For heptachlor epoxide, the oral LD 50 values ranging from 46.5 to 60 mg/kg. With rat oral of LD 50 47mg/kg, heptachlor epoxide is more toxic. A product of hydrogenation of heptachlor, β-dihydroheptachlor, has high insecticidal activity and low mammalian toxicity, rat oral LD 50 >5,000mg/kg. [ 4 ]
Humans may be exposed to heptachlor through drinking water and foods, including breast milk . [ 6 ] Heptachlor epoxide is derived from a pesticide that was banned in the U.S. in the 1980s. It is still found in soil and water supplies and can turn up in food. [ citation needed ] It can be passed along in breast milk. [ citation needed ]
The International Agency for Research on Cancer and the EPA have classified the compound as a possible human carcinogen . Animals exposed to heptachlor epoxide during gestation and infancy are found to have changes in nervous system and immune function. Exposure to higher doses of heptachlor in newborn animals leads to decreased body weight and death. [ 5 ]
The U.S. EPA MCL for drinking water is 0.0004 mg/L for heptachlor and 0.0002 mg/L for heptachlor epoxide. The U.S. FDA limit on food crops is 0.01 ppm, in milk 0.1 ppm, and on edible seafoods 0.3 ppm. The Occupational Safety and Health Administration has limit of 0.5 mg/m 3 (cubic meter of workplace air) for 8-hour shifts and 40-hour work weeks. [ 6 ]
An ATSDR report in 1993 found no studies with respect to death in humans after oral exposure to heptachlor or heptachlor epoxide.
The octanol-water partition coefficient (K ow ) of heptachlor is ~10 5.27 . Henry's Law constant is 2.3 · 10 −3 atm-m 3 /mol and the vapor pressure is 3 · 10 −4 mmHg at 20 °C. [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/Heptachlor |
Heptanitrocubane / ˌ h ɛ p t ə ˌ n aɪ t r oʊ ˈ k j uː b eɪ n / is an experimental high explosive based on the cubic eight-carbon cubane molecule and closely related to octanitrocubane . Seven of the eight hydrogen atoms at the corners of the cubane molecule are replaced by nitro groups, giving the final molecular formula C 8 H(NO 2 ) 7 .
As with octanitrocubane, not enough heptanitrocubane has been synthesized to perform detailed tests on its stability and energy. It is hypothesized to have slightly better performance than explosives such as HMX , the current high-energy standard explosive, based on chemical energy analysis. While in theory not as energetic as octanitrocubane's theoretical maximum density, the heptanitrocubane that has been synthesized so far is a more effective explosive than any octanitrocubane that has been produced, due to more efficient crystal packing and hence higher density. [ 1 ]
Heptanitrocubane was first synthesized by the same team who synthesized octanitrocubane, Philip Eaton and Mao-Xi Zhang at the University of Chicago , in 1999. [ 2 ] | https://en.wikipedia.org/wiki/Heptanitrocubane |
The Botulism Antitoxin Heptavalent (A, B, C, D, E, F, G) - (Equine) (trade name BAT ), made by Emergent BioSolutions Canada Inc. (formerly Cangene Corporation ), [ 1 ] is a licensed, commercially available botulism anti-toxin that effectively neutralizes all seven known botulinum nerve toxin serotypes (types A, B, C, D, E, F and G). It is indicated for sporadic cases of life-threatening botulism and is also stockpiled for the eventuality of botulinum nerve toxins being used in a future bioterrorist attack. [ 2 ]
BAT was first approved in 2010 by the Centers for Disease Control for the indication of treating naturally occurring non-infant botulism on an investigational basis, replacing two earlier products. It was then licensed for commercial marketing by the United States FDA in 2013. [ 3 ]
BAT is the only FDA-approved product available for treating botulism in adults, and for botulism in infants caused by botulinum toxins other than types A and B. BAT has been used to treat a case of type F infant botulism and, on a case-by-case basis, may be used for future cases of non-type A and non-type B infant botulism. [ 4 ]
Early administration of BAT is considered critical as the antitoxin can neutralize only circulating toxin, not toxin that has become bound to nerve terminals. [ citation needed ]
One vial (20 mL) of BAT is administered to a patient as an intravenous infusion. It must be diluted with 0.9% sodium chloride in a 1:10 ratio before use. A volumetric infusion pump is used for slow administration (0.5 mL/min for the initial 30 minutes) to minimize the possibility of allergic reactions. If no reactions are noted, the rate is increased to 1 mL/min for another 30 minutes, and then if still no reaction is evident, to 2 mL/min for the remainder of the procedure. [ 5 ]
In CDC studies of BAT, headache, fever, chills, rash, itching, and nausea were the most observed adverse events. It can trigger allergic reactions and delayed hypersensitivity reactions in people sensitive to horse proteins. [ 6 ]
BAT is derived from "despeciated" equine IgG antibodies , which have had the Fc portion cleaved off, leaving the F(ab') 2 portions . Compared to whole antibodies, as found in trivalent botulinum antitoxin (TBAT) available from local health departments (via the CDC), F(ab') 2 is less efficacious at neutralizing toxin, [ 6 ] but should carry a reduced risk of anaphylaxis . [ 7 ]
Unlike TBAT, BAT is considered effective against all known strains of botulism (A, B, C, D, E, F, and G). All antitoxins neutralize only circulating toxin in patients with symptoms of botulism that are continuing to progress; they have no effect on toxin already bound to the nerve terminals. (This is not, however, considered a reason to withhold the product from any patient, even if treatment has been delayed.) [ 6 ]
A related product, Botulism AntiToxin, Heptavalent, Equine, Types A, B, C, D, E, F and G ( HE-BAT ), is also available to the U.S. military under IND (experimental) protocols. This "equine" antitoxin requires skin testing with escalating dose challenges before full dose administration to obviate serious sensitivity to horse serum, as it consists of the whole non-despeciated antibody. [ 8 ]
The US Department of Defence also stocks HFabBAT, the despeciated version of HE-BAT, similar to BAT. [ 8 ]
BAT (formerly known as HBAT) was developed from equine (horse) plasma at the U.S. Army Medical Research Institute of Infectious Diseases (USAMRIID). The main funding stream was the Biomedical Advanced Research and Development Authority (within the US Department of Health and Human Services ' Office of the Assistant Secretary for Preparedness and Response ). It was then available for many years on an IND (investigational) basis from the US Centers for Disease Control and Prevention (CDC). [ 9 ]
On June 1, 2006, the DHHS awarded a $363 million contract to Emergent BioSolutions, (then Cangene Corporation) for 200,000 doses of BAT over five years for delivery into the US Strategic National Stockpile (SNS). [ 10 ] The CDC began supplying doses to the SNS in 2007 under a now $427 million contract with the DHHS, according to a Cangene press release. In 2010, the CDC replaced the licensed bivalent botulinum antitoxin AB ( BAT-AB ) and the investigational monovalent botulinum antitoxin E ( BAT-E ) with BAT when the former two products indications expired. This action left BAT as the only botulinum antitoxin available in the US for naturally occurring non-infant botulism. [ 10 ]
On March 22, 2013, the US Food and Drug Administration (FDA) approved BAT as the first product to treat all serotypes of botulism. This was considered a significant step in the US armamentarium for emergency use against a bioterrorist attack. The CDC continues to distribute the stockpiled antitoxin. [ 9 ]
The FDA approved BAT for marketing based on its efficacy as established in animal studies (efficacy trials in humans not being considered feasible or ethical). The safety of the antitoxin, however, was established in a study of 40 healthy volunteers as well as in the experimental treatment of 228 patients in a CDC program. [ 11 ]
After the February 2014 acquisition of Cangene Corporation by Emergent BioSolutions, Emergent took control of Cangene's products and contracts, including BAT. [ 12 ] In March 2017, Emergent extended its contract with the Biomedical Advanced Research and Development Authority (BARDA), adding $53 million in value throughout 2022 for the production and bulk storage of BAT. Under the conditions of the extension, future transport of BAT to the SNS was approved. BAT remains the only recognized, licensed, and distributed botulism antitoxin within the FDA and the CDC. [ 10 ]
In 2012, Emergent signed a 10-year contract to provide BAT to the Canadian Department of National Defense and the Public Health Agency of Canada , as well as individual provincial health officials. In December 2016, Health Canada approved Emergent's New Drug Submission for BAT under the Extraordinary Use New Drug Regulations, which provide guidelines for consideration of drugs that do not have clinical information about impacts on humans due to the nature of the conditions that the drugs are used to treat. Pleased with Canada's decision to prepare for botulinum toxin events, one of the "more likely biological threat agents", Adam Havey, executive vice president and president of the biodefense division at Emergent BioSolutions, said, "Emergent is committed to helping allied governments fulfill their preparedness needs. We expect to expand upon our longstanding relationship with the Canadian government and develop similar relations outside of North America..." [ 13 ]
BAT was approved by the Health Sciences Authority in Singapore in July 2019. [ 14 ]
BAT has undergone extensive testing for effectiveness and safety. Emergent BioSolutions, in a 2017 document published to describe prescription information for BAT, said that the effectiveness of the antitoxin is based on efficacy studies that demonstrably prove increased chances of survival. In two clinical studies cited by the company, the safety profile of BAT was proven acceptable when one or two vials of the antitoxin were intravenously delivered to healthy subjects. [ 15 ]
Another clinical trial, the BT-011 study, known also as Pharmacokinetics of Botulism Antitoxin Heptavalent in Pediatric Patients, was initiated to test the success of BAT in children who had contracted botulism (or had been suspected of contracting botulism). In the study, a serum sample was collected from pediatric patients to analyze the pharmacokinetics of BAT to better adjust pediatric dosing recommendations. The details of the study from ClinicalTrials.gov, are as follows: [ 16 ] | https://en.wikipedia.org/wiki/Heptavalent_botulism_antitoxin |
Herb-induced liver injury (HILI) is a form of drug-induced liver injury caused by herbal medicines , typically herbal supplements or herb-based ethnomedicines .
Herbs are a common component of ethnomedicines and their potential hepatotoxicity is a concern for people taking such medicines or other herbal supplements. [ 1 ]
Use of such products is widespread within Ayurvedic medicine . [ 2 ] Although injury from ayurvedic medicines has commonly been blamed on improper adulteration of drugs, a number of preparations can be harmful though direct effects purely because of their herbal ingredients. [ 2 ] | https://en.wikipedia.org/wiki/Herb-induced_liver_injury |
Herbal distillates , also known as floral waters , hydrosols , hydrolates , herbal waters , and essential waters , [ 1 ] are aqueous products of hydrodistillation . They are colloidal suspensions of essential oils as well as water-soluble components obtained by steam distillation or hydrodistillation (a variant of steam distillation) from plants and herbs. These herbal distillates have uses as flavorings and cosmetics . Common herbal distillates for skincare include rose water , [ 2 ] orange flower water , [ 3 ] and witch hazel . [ 4 ] Rosemary , [ 5 ] oregano , [ 6 ] and thyme [ 7 ] are hydrosols that may be used in food manufacturing industries.
Herbal distillates are produced in the same or similar manner as essential oils. However, essential oils will float to the top of the distillate where it can be removed, leaving behind the watery distillate. For this reason, the term essential water is an apt description. In the past, these essential waters were often considered a byproduct of distillation, but are now considered an important co-product. [ 8 ] The produced herbal waters are essentially diluted essential oils at less than 1% concentration (typically 0.02% to 0.05%). [ 9 ] Several factors, such as temperature and a herb's growth cycle, impact the characteristics of a distillate, and therefore influence the timing of the distillation. Rosemary, for example, should be distilled in the peak of summer before it flowers. [ 10 ]
1. Food industry: Herbal distillates are often used in culinary applications to add subtle flavors to foods and beverages. Their mild nature makes them ideal for infusing delicate flavors into dishes without the overpowering intensity of essential oils. Commonly used distillates in this context include rose water, orange blossom water, and peppermint hydrosol. Herbal distillates are also used to preserve food, and have been shown to be effective in achieving desirable effects, like reducing the degree of oxidation of some meats. [ 11 ]
2. Cosmetics: In the cosmetic industry, herbal distillates are prized for their gentle, skin-friendly properties. They are used in a variety of products, including:
3. Herbal Treatments: Herbal distillates are also employed in traditional and holistic medicine for their therapeutic benefits. Due to their lower concentration compared to essential oils, they are often used for:
4. Agriculture: Herbal distillates are also used as insecticides, herbicides, and antibacterial and antifungal agents in agriculture. Additionally, herbal distillates may be used in allelopathy , with possible applications including the manipulation of the timing of sprouting (see vivipary ) and germination . [ 11 ]
5. Clothing: Herbal distillates can be added to water in a clothes iron to add a delicate scent into clothing. Since herbal distillates do not contain hard minerals such as plastic and metal , [ 13 ] it will also help keep clothing irons working properly for much longer. [ 12 ]
The science of distillation is based on the fact that different substances evaporate at different temperatures. Unlike other extraction techniques based on solubility of a compound in either water or oil , distillation will separate components regardless of their solubility. The distillate will contain compounds that vaporize at or below the temperature of distillation. The actual chemical components of these orange herbal distillates have not yet been fully identified, but plant distillates will usually contain essential oil compounds as well as organic acids and other water-soluble plant components. Compounds with a higher vaporization point will remain behind and will include many of the water-soluble plant pigments and flavonoids . [ 14 ]
Because hydrosols are produced at high temperatures and are somewhat acidic, they tend to inhibit bacterial growth but not fungal growth . They are not sterile , and should be kept refrigerated to preserve freshness. [ 15 ] Herbal distillates degrade over time and will degrade faster than essential oils, which are more stable. [ 16 ] Small-scale producers of hydrosols must be particularly aware of the risk of bacterial contamination and take steps to prevent it. Despite concerns that there may be significant amounts of heavy metals in popular herbal distillates, this has not shown to be the case. [ 13 ] | https://en.wikipedia.org/wiki/Herbal_distillate |
Herbal medicine (also called herbalism , phytomedicine or phytotherapy ) is the study of pharmacognosy and the use of medicinal plants , which are a basis of traditional medicine . [ 1 ] With worldwide research into pharmacology , some herbal medicines have been translated into modern remedies, [ 2 ] such as the anti-malarial group of drugs called artemisinin isolated from Artemisia annua , a herb that was known in Chinese medicine to treat fever. [ 3 ] [ 4 ] There is limited scientific evidence for the safety and efficacy of many plants used in 21st-century herbalism, which generally does not provide standards for purity or dosage. [ 1 ] [ 5 ] The scope of herbal medicine sometimes includes fungal and bee products, as well as minerals , shells and certain animal parts. [ 6 ]
Paraherbalism describes alternative and pseudoscientific practices of using unrefined plant or animal extracts as unproven medicines or health-promoting agents. [ 1 ] [ 5 ] [ 7 ] [ 8 ] Paraherbalism relies on the belief that preserving various substances from a given source with less processing is safer or more effective than manufactured products, a concept for which there is no evidence. [ 7 ]
Archaeological evidence indicates that the use of medicinal plants dates back to the Paleolithic age, approximately 60,000 years ago. Written evidence of herbal remedies dates back over 5,000 years to the Sumerians , who compiled lists of plants. Some ancient cultures wrote about plants and their medical uses in books called herbals . In ancient Egypt, herbs were mentioned in Egyptian medical papyri , depicted in tomb illustrations, or on rare occasions found in medical jars containing trace amounts of herbs. [ 9 ] In ancient Egypt, the Ebers papyrus dates from about 1550 BCE, and covers more than 700 compounds, mainly of plant origin. [ 10 ] The earliest known Greek herbals came from Theophrastus of Eresos who, in the 4th century BCE, wrote in Greek Historia Plantarum , from Diocles of Carystus who wrote during the 3rd century BCE, and from Krateuas who wrote in the 1st century BCE. Only a few fragments of these works have survived intact, but from what remains, scholars have noted overlap with the Egyptian herbals. [ 11 ]
Seeds likely used for herbalism were found in archaeological sites of Bronze Age China dating from the Shang dynasty [ 12 ] ( c. 1600 – c. 1046 BCE ). Over a hundred of the 224 compounds mentioned in the Huangdi Neijing , an early Chinese medical text, are herbs. [ 13 ] Herbs were also commonly used in the traditional medicine of ancient India, where the principal treatment for diseases was diet. [ 14 ] De Materia Medica , originally written in Greek by Pedanius Dioscorides ( c. 40 – c. 90 CE ) of Anazarbus , Cilicia , a physician and botanist, is one example of herbal writing used over centuries until the 1600s. [ 15 ]
The World Health Organization (WHO) estimates that 80 percent of the population of some Asian and African countries presently uses herbal medicine for some aspect of primary health care. [ 16 ]
Some prescription drugs have a basis as herbal remedies, [ 2 ] including artemisinin , [ 17 ] digitalis , quinine and taxanes .
In 2015, the Australian Government's Department of Health published the results of a review of alternative therapies that sought to determine if any were suitable for being covered by health insurance ; herbalism was one of 17 topics evaluated for which no clear evidence of effectiveness was found. [ 18 ] Establishing guidelines to assess the safety and efficacy of herbal products, the European Medicines Agency provided criteria in 2017 for evaluating and grading the quality of clinical research in preparing monographs about herbal products. [ 19 ] In the United States, the National Center for Complementary and Integrative Health of the National Institutes of Health funds clinical trials on herbal compounds, provides fact sheets evaluating the safety, potential effectiveness and side effects of many plant sources, [ 20 ] and maintains a registry of clinical research conducted on herbal products. [ 21 ]
According to Cancer Research UK as of 2015, "there is currently no strong evidence from studies in people that herbal remedies can treat, prevent or cure cancer". [ 6 ]
The use of herbal remedies is more prevalent in people with chronic diseases , such as cancer, diabetes , asthma , and end-stage kidney disease . [ 22 ] [ 23 ] [ 24 ] Multiple factors such as gender, age, ethnicity, education and social class are also shown to have associations with the prevalence of herbal remedy use. [ 25 ]
There are many forms in which herbs can be administered, the most common of which is a liquid consumed as a herbal tea or a (possibly diluted) plant extract. [ 26 ]
Herbal teas , or tisanes, are the resultant liquid of extracting herbs into water, though they are made in a few different ways. Infusions are hot water extracts of herbs, such as chamomile or mint , through steeping . Decoctions are the long-term boiled extracts, usually of harder substances like roots or bark. Maceration is the cold infusion of plants with high mucilage -content, such as sage or thyme . To make macerates, plants are chopped and added to cold water. They are then left to stand for 7 to 12 hours (depending on the herb used). For most macerates, 10 hours is used. [ 27 ]
Tinctures are alcoholic extracts of herbs, which are generally stronger than herbal teas. [ 28 ] Tinctures are usually obtained by combining pure ethanol (or a mixture of pure ethanol with water) with the herb. A completed tincture has an ethanol percentage of at least 25% (sometimes up to 90%). [ 27 ] Non-alcoholic tinctures can be made with glycerin but it is believed to be less absorbed by the body than alcohol based tinctures and has a shorter shelf life. [ 29 ] Herbal wine and elixirs are alcoholic extracts of herbs, usually with an ethanol percentage of 12–38%. [ 27 ] Extracts include liquid extracts, dry extracts, and nebulisates. Liquid extracts are liquids with a lower ethanol percentage than tinctures. They are usually made by vacuum distilling tinctures. Dry extracts are extracts of plant material that are evaporated into a dry mass. They can then be further refined to a capsule or tablet. [ 27 ]
The exact composition of a herbal product is influenced by the method of extraction. A tea will be rich in polar components because water is a polar solvent . Oil, on the other hand, is a non-polar solvent and it will absorb non-polar compounds. Alcohol lies somewhere in-between. [ 26 ]
Many herbs are applied topically to the skin in a variety of forms. Essential oil extracts can be applied to the skin, usually diluted in a carrier oil. Many essential oils can burn the skin or are simply too high dose used straight; diluting them in olive oil or another food grade oil such as almond oil can allow these to be used safely as a topical. Salves , oils, balms , creams, and lotions are other forms of topical delivery mechanisms. Most topical applications are oil extractions of herbs. Taking a food grade oil and soaking herbs in it for anywhere from weeks to months allows certain phytochemicals to be extracted into the oil. This oil can then be made into salves, creams, lotions, or simply used as an oil for topical application. Many massage oils, antibacterial salves, and wound healing compounds are made this way. [ 30 ]
Inhalation , as in aromatherapy , can be used as a treatment. [ 31 ] [ 32 ] [ 33 ]
It is a popular misconception that herbal medicines are safe and side-effect free. [ 35 ] Consumption of herbs may cause adverse effects . [ 36 ] Furthermore, "adulteration, inappropriate formulation, or lack of understanding of plant and drug interactions have led to adverse reactions that are sometimes life threatening or lethal." [ 37 ] Proper double-blind clinical trials are needed to determine the safety and efficacy of each plant before medical use. [ 38 ]
Although many consumers believe that herbal medicines are safe because they are natural, herbal medicines and synthetic drugs may interact, causing toxicity to the consumer. Herbal remedies can also be dangerously contaminated, and herbal medicines without established efficacy, may unknowingly be used to replace prescription medicines. [ 39 ]
Standardization of purity and dosage is not mandated in the United States, but even products made to the same specification may differ as a result of biochemical variations within a species of plant. [ 40 ] Plants have chemical defense mechanisms against predators that can have adverse or lethal effects on humans. Examples of highly toxic herbs include poison hemlock and nightshade. [ 41 ] They are not marketed to the public as herbs, because the risks are well known, partly due to a long and colorful history in Europe, associated with "sorcery", "magic" and intrigue. [ 42 ]
Although not frequent, adverse reactions have been reported for herbs in widespread use. [ 43 ] On occasion serious untoward outcomes have been linked to herb consumption. A case of major potassium depletion has been attributed to chronic licorice ingestion, [ 44 ] and consequently professional herbalists avoid the use of licorice where they recognize that this may be a risk. Black cohosh has been implicated in a case of liver failure. [ 45 ] Few studies are available on the safety of herbs for pregnant women, [ 46 ] and one study found that use of complementary and alternative medicines is associated with a 30% lower ongoing pregnancy and live birth rate during fertility treatment. [ 47 ]
Examples of herbal treatments with likely cause-effect relationships with adverse events include aconite (which is often a legally restricted herb), Ayurvedic remedies , broom , chaparral , Chinese herb mixtures, comfrey , herbs containing certain flavonoids, germander , guar gum , liquorice root , and pennyroyal . [ 48 ] Examples of herbs that may have long-term adverse effects include ginseng , the endangered herb goldenseal , milk thistle , senna , aloe vera juice , buckthorn bark and berry , cascara sagrada bark , saw palmetto , valerian , kava (which is banned in the European Union), St. John's wort , khat , betel nut , the restricted herb ephedra , and guarana . [ 37 ]
There is also concern with respect to the numerous well-established interactions of herbs and drugs. [ 37 ] [ 49 ] In consultation with a physician, usage of herbal remedies should be clarified, as some herbal remedies have the potential to cause adverse drug interactions when used in combination with various prescription and over-the-counter pharmaceuticals, just as a customer should inform a herbalist of their consumption of actual prescription and other medication. [ 50 ] [ 51 ]
For example, dangerously low blood pressure may result from the combination of a herbal remedy that lowers blood pressure together with prescription medicine that has the same effect. Some herbs may amplify the effects of anticoagulants. [ 52 ] Certain herbs as well as common fruit interfere with cytochrome P450, an enzyme critical to much drug metabolism. [ 53 ]
In a 2018 study, the FDA identified active pharmaceutical additives in over 700 analyzed dietary supplements sold as "herbal", "natural" or "traditional". [ 54 ] The undisclosed additives included "unapproved antidepressants and designer steroids", as well as prescription drugs , such as sildenafil or sibutramine .
Researchers at the University of Adelaide found in 2014 that almost 20 percent of herbal remedies surveyed were not registered with the Therapeutic Goods Administration , despite this being a condition for their sale. [ 55 ] They also found that nearly 60 percent of products surveyed had ingredients that did not match what was on the label. Out of 121 products, only 15 had ingredients that matched their TGA listing and packaging. [ 55 ]
In 2015, the New York Attorney General issued cease and desist letters to four major U.S. retailers ( GNC , Target , Walgreens , and Walmart ) who were accused of selling herbal supplements that were mislabeled and potentially dangerous. [ 56 ] [ 57 ] Twenty-four products were tested by DNA barcoding as part of the investigation, with all but five containing DNA that did not match the product labels.
In some countries, formalized training and minimum education standards exist for herbalists, although these are not necessarily uniform within or between countries. In Australia, for example, the self-regulated status of the profession (as of 2009) resulted in variable standards of training, and numerous loosely formed associations setting different educational standards. [ 58 ] One 2009 review concluded that regulation of herbalists in Australia was needed to reduce the risk of interaction of herbal medicines with prescription drugs , to implement clinical guidelines and prescription of herbal products, and to assure self-regulation for protection of public health and safety. [ 58 ] In the United Kingdom, the training of herbalists is done by state-funded universities offering Bachelor of Science degrees in herbal medicine. [ 59 ] In the United States, according to the American Herbalist Guild, "there is currently no licensing or certification for herbalists in any state that precludes the rights of anyone to use, dispense, or recommend herbs." [ 60 ] However, there are U.S. federal restrictions for marketing herbs as cures for medical conditions, or essentially practicing as an unlicensed physician.
Over the years 2017–2021, the U.S. Food and Drug Administration (FDA) issued warning letters to numerous herbalism companies for illegally marketing products under "conditions that cause them to be drugs under section 201(g)(1) of the Act [21 U.S.C. § 321(g)(1)], because they are intended for use in the diagnosis, cure, mitigation, treatment, or prevention of disease and/or intended to affect the structure or any function of the body" when no such evidence existed. [ 61 ] [ 62 ] [ 63 ] During the COVID-19 pandemic , the FDA and U.S. Federal Trade Commission issued warnings to several hundred American companies for promoting false claims that herbal products could prevent or treat COVID-19 disease . [ 63 ] [ 64 ]
The World Health Organization (WHO), the specialized agency of the United Nations (UN) that is concerned with international public health, published Quality control methods for medicinal plant materials in 1998 to support WHO Member States in establishing quality standards and specifications for herbal materials, within the overall context of quality assurance and control of herbal medicines. [ 65 ]
In the European Union (EU), herbal medicines are regulated under the Committee on Herbal Medicinal Products . [ 66 ]
In the United States, herbal remedies are regulated dietary supplements by the Food and Drug Administration (FDA) under current good manufacturing practice (cGMP) policy for dietary supplements. [ 67 ] Manufacturers of products falling into this category are not required to prove the safety or efficacy of their product so long as they do not make 'medical' claims or imply uses other than as a 'dietary supplement', though the FDA may withdraw a product from sale should it prove harmful. [ 68 ] [ 69 ]
Canadian regulations are described by the Natural and Non-prescription Health Products Directorate which requires an eight-digit Natural Product Number or Homeopathic Medicine Number on the label of licensed herbal medicines or dietary supplements. [ 70 ]
Some herbs, such as cannabis and coca , are outright banned in most countries though coca is legal in most of the South American countries where it is grown. The Cannabis plant is used as a herbal medicine , and as such is legal in some parts of the world. Since 2004, the sales of ephedra as a dietary supplement is prohibited in the United States by the FDA, [ 71 ] and subject to Schedule III restrictions in the United Kingdom.
Herbalism has been criticized as a potential " minefield " of unreliable product quality, safety hazards, and the potential for misleading health advice. [ 1 ] [ 8 ] Globally, there are no standards across various herbal products to authenticate their contents, safety or efficacy, [ 40 ] and there is generally an absence of high-quality scientific research on product composition or effectiveness for anti-disease activity. [ 8 ] [ 72 ] Presumed claims of therapeutic benefit from herbal products, without rigorous evidence of efficacy and safety, receive skeptical views by scientists. [ 1 ]
Unethical practices by some herbalists and manufacturers, which may include false advertising about health benefits on product labels or literature, [ 8 ] and contamination or use of fillers during product preparation, [ 40 ] [ 73 ] may erode consumer confidence about services and products. [ 74 ] [ 75 ]
Paraherbalism is the pseudoscientific use of extracts of plant or animal origin as supposed medicines or health-promoting agents. [ 1 ] [ 7 ] [ 8 ] Phytotherapy differs from plant-derived medicines in standard pharmacology because it does not isolate and standardize the compounds from a given plant believed to be biologically active. It relies on the false belief that preserving the complexity of substances from a given plant with less processing is safer and potentially more effective, for which there is no evidence either condition applies. [ 7 ]
Phytochemical researcher Varro Eugene Tyler described paraherbalism as "faulty or inferior herbalism based on pseudoscience", using scientific terminology but lacking scientific evidence for safety and efficacy. Tyler listed ten fallacies that distinguished herbalism from paraherbalism, including claims that there is a conspiracy to suppress safe and effective herbs, herbs cannot cause harm, whole herbs are more effective than molecules isolated from the plants, herbs are superior to drugs, the doctrine of signatures (the belief that the shape of the plant indicates its function) is valid, dilution of substances increases their potency (a doctrine of the pseudoscience of homeopathy ), astrological alignments are significant, animal testing is not appropriate to indicate human effects, anecdotal evidence is an effective means of proving a substance works and herbs were created by God to cure disease. Tyler suggests that none of these beliefs have any basis in fact. [ 7 ] [ 76 ]
Up to 80% of the population in Africa uses traditional medicine as primary health care. [ 77 ]
Native Americans used about 2,500 of the approximately 20,000 plant species that are native to North America. [ 78 ]
In Andean healing practices, the use of entheogens , in particular the San Pedro cactus ( Echinopsis pachanoi ) is still a vital component, and has been around for millennia. [ 79 ]
Some researchers trained in both Western and traditional Chinese medicine have attempted to deconstruct ancient medical texts in the light of modern science. In 1972, Tu Youyou , a pharmaceutical chemist and Nobel Prize winner , extracted the anti-malarial drug artemisinin from sweet wormwood , a traditional Chinese treatment for intermittent fevers. [ 80 ]
In India, Ayurvedic medicine has quite complex formulas with 30 or more ingredients, including a sizable number of ingredients that have undergone " alchemical processing ", chosen to balance dosha . [ 81 ] In Ladakh, Lahul-Spiti, and Tibet, the Tibetan Medical System is prevalent, also called the "Amichi Medical System". Over 337 species of medicinal plants have been documented by C.P. Kala . Those are used by Amchis, the practitioners of this medical system. [ 82 ] [ 83 ] The Indian book, Vedas, mentions treatment of diseases with plants. [ 84 ]
In Indonesia , especially among the Javanese , the jamu traditional herbal medicine may have originated in the Mataram Kingdom era, some 1300 years ago. [ 85 ] The bas-reliefs on Borobudur depict the image of people grinding herbs with stone mortar and pestle , a drink seller, a herbalist, and masseuse treating people. [ 86 ] The Madhawapura inscription from Majapahit period mentioned a specific profession of herb mixer and combiner (herbalist), called Acaraki . [ 86 ] The book from Mataram dated from circa 1700 contains 3,000 entries of jamu herbal recipes, while Javanese classical literature Serat Centhini (1814) describes some jamu herbal concoction recipes. [ 86 ]
Though possibly influenced by Indian Ayurveda systems, the Indonesia archipelago holds numerous indigenous plants not found in India, including plants similar to those in Australia beyond the Wallace Line . [ 87 ] Jamu practices may vary from region to region, and are often not recorded, especially in remote areas of the country. [ 88 ] Although primarily herbal, some Jamu materials are acquired from animals, such as honey , royal jelly , milk, and Ayam Kampung eggs .
Herbalists tend to use extracts from parts of plants, such as the roots or leaves, [ 89 ] believing that plants are subject to environmental pressures and therefore develop resistance to threats such as radiation, reactive oxygen species and microbial attack to survive, providing defensive phytochemicals of use in herbalism. [ 89 ] [ 90 ]
Indigenous healers often claim to have learned by observing that sick animals change their food preferences to nibble at bitter herbs they would normally reject. [ 91 ] Field biologists have provided corroborating evidence based on observation of diverse species, such as chickens, sheep, butterflies , and chimpanzees . The habit of changing diet has been shown to be a physical means of purging intestinal parasites. Sick animals tend to forage plants rich in secondary metabolites , such as tannins and alkaloids . [ 92 ] | https://en.wikipedia.org/wiki/Herbal_medicine |
Herbchronology is the analysis of annual growth rings (or simply annual rings) in the secondary root xylem of perennial herbaceous plants . While leaves and stems of perennial herbs die down at the end of the growing season the root often persists for many years or even the entire life. [ 1 ] Perennial herb species belonging to the dicotyledon group (also known as perennial forbs ) are characterized by secondary growth , which shows as a new growth ring added each year to persistent roots. About two thirds of all perennial dicotyledonous herb species with a persistent root that grow in the strongly seasonal zone of the northern hemisphere show at least fairly clear annual growth rings. [ 1 ]
Counting of annual growth rings can be used to determine the age of a perennial herb similarly as it is done in trees using dendrochronology . [ 2 ] This way it was found that some perennial herbs live up to 50 years and more. [ 3 ] [ 4 ]
The term herb-chronology is referring to dendrochronology because of the similarity of the structures investigated. The term was introduced in the late 1990s, [ 5 ] however, the existence of annual rings in perennial herbs was already observed in earlier times by several researchers. [ 6 ] [ 7 ] [ 8 ]
Like trees and woody plants, perennial herbs have a growth zone called vascular cambium between the root bark and the root xylem . The vascular cambium ring is active during growing season and produces a new layer of xylem tissue or growth ring every year. This addition of a new lateral layer each year is called secondary growth and is exactly the same as in woody plants. Each individual growth ring consists of earlywood tissue that is formed at the beginning of the growing season and latewood tissue formed in summer and fall. Earlywood tissue is characterized by wide vessels or denser arrangement of vessels, whereas latewood tissue shows narrower vessels and/or lower vessel density. [ 1 ] [ 2 ]
Annual growth rings in herbs are usually only visible by means of a microscope and a specific staining method. Ring-like patterns visible in root cross-sections by the naked eye may be "false rings". [ 9 ]
The width of an annual growth ring depends on conditions during its formation: in a favorable year, a ring is wider, and in a less favorable year it is narrower. [ 10 ]
Herbchronology is used in many fields of ecological and biological research, for instance in community ecology , population biology , plant ecology and invasion biology .
Herbchronology is used as a tool to estimate plant age. This may be relevant information to determine :
Herbchronology allows to assess long-term annual growth rates of a perennial herbaceous plant without having to monitor it. This may be relevant information to assess … | https://en.wikipedia.org/wiki/Herbchronology |
Herbert Wayne " Herb " Boyer (born July 10, 1936) is an American biotechnologist, researcher and entrepreneur in biotechnology. Along with Stanley N. Cohen and Paul Berg , he discovered recombinant DNA , a method to coax bacteria into producing foreign proteins, which aided in jump-starting the field of genetic engineering . By 1969, he had performed studies on a couple of restriction enzymes of E. coli with especially useful properties.
He is recipient of the 1990 National Medal of Science , co-recipient of the 1996 Lemelson–MIT Prize , and a co-founder of Genentech . He was professor at the University of California, San Francisco (UCSF) and later served as vice president of Genentech from 1976 until his retirement in 1991. [ 1 ]
Herbert Boyer was born in 1936 in Derry, Pennsylvania . He received his bachelor's degree in biology and chemistry from Saint Vincent College in Latrobe, Pennsylvania , in 1958. He married his wife Grace the following year. He received his PhD at the University of Pittsburgh in 1963 and participated as an activist in the civil rights movement.
Boyer spent three years in postdoctoral work at Yale University in the laboratories of Professors Edward Adelberg and Bruce Carlton, and then became an assistant professor at the University of California, San Francisco and a professor of biochemistry from 1976 to 1991, where he discovered that genes from bacteria could be combined with genes from eukaryotes . In 1977, Boyer's laboratory and collaborators Keiichi Itakura and Arthur Riggs at City of Hope National Medical Center described the first-ever synthesis and expression of a peptide-coding gene. [ 2 ] In August 1978, he produced synthetic insulin using his new transgenic genetically modified bacteria , followed in 1979 by a growth hormone .
In 1976, Boyer founded Genentech with venture capitalist Robert A. Swanson . Genentech's approach to the first synthesis of insulin won out over Walter Gilbert 's approach at Biogen which used whole genes from natural sources. Boyer built his gene from its individual nucleotides .
In 1990, Boyer and his wife Grace gave the single largest donation ($10,000,000) bestowed on the Yale School of Medicine by an individual. The Boyer Center for Molecular Medicine was named after the Boyer family in 1991. [ 3 ] [ 4 ]
At the Class of 2007 Commencement, St. Vincent College announced that they had renamed the School of Natural Science, Mathematics, and Computing the Herbert W. Boyer School. [ 5 ]
Among his professional activities, Boyer is on the board of directors of Scripps Research . [ 6 ] | https://en.wikipedia.org/wiki/Herbert_Boyer |
Herbert Charles Brown (May 22, 1912 – December 19, 2004) was an American chemist and recipient of the 1979 Nobel Prize in Chemistry for his work with organoboranes .
Brown was born Herbert Brovarnik in London , to Ukrainian Jewish immigrants from Zhitomir , Pearl ( née Gorinstein) and Charles Brovarnik, a hardware store manager and carpenter. [ 2 ] His family moved to Chicago in June 1914, when he was two years old. [ 3 ] [ 4 ] Brown attended Crane Junior College in Chicago, where he met Sarah Baylen, whom he would later marry. The college was under threat of closing, and Brown and Baylen transferred to Wright Junior College . [ 4 ] In 1935 he left Wright and that autumn entered the University of Chicago , completing two years of studies in three quarters to earn a B.S. in 1936. [ 3 ] That same year, he became a naturalized United States citizen , [ 5 ] and began graduate studies at Chicago. On February 6, 1937, Brown married Baylen, whom he would later credit with sparking an interest in hydrides of boron that would eventually lead to the work for which he, together with Georg Wittig , would be awarded the Nobel prize in Chemistry in 1979, [ 3 ] and the following year received his degree as Ph.D. .
Unable to find a position in industry, he decided to accept a postdoctoral position, beginning his academic career. He became an instructor at Chicago in 1939, and held the position for four years before moving to Wayne University in Detroit as an assistant professor . In 1946, he was promoted to associate professor , and the following year became a professor of inorganic chemistry at Purdue University in 1947 [ 6 ] and joined the Beta Nu chapter of Alpha Chi Sigma there in 1960. [ 7 ] He held the position of Professor Emeritus from 1978 until his death in 2004. [ 3 ] The Herbert C. Brown Laboratory of Chemistry was named after him on Purdue University's campus. He was an honorary member of the International Academy of Science, Munich.
During World War II , while working with Hermann Irving Schlesinger , Brown discovered a method for producing sodium borohydride (NaBH 4 ), which can be used to produce boranes , compounds of boron and hydrogen . His work led to the discovery of the first general method for producing asymmetric pure enantiomers . The elements found as initials of his name H , C and B were his working field.
In 1969, he was awarded the National Medal of Science . [ 8 ]
Brown was quick to credit his wife Sarah with supporting him and allowing him to focus on creative efforts by handling finances, maintaining the house and yard, etc. According to Brown, after receiving the Nobel prize in Stockholm , he carried the medal and she carried the US$100,000 award.
In 1971, he received the Golden Plate Award of the American Academy of Achievement . [ 9 ]
He was inducted into the Alpha Chi Sigma Hall of Fame in 2000. [ 10 ]
He died December 19, 2004, at a hospital in Lafayette, Indiana after a heart attack . [ 11 ] His wife died May 29, 2005, aged 89.
As a doctoral student at the University of Chicago , Herbert Brown studied the reactions of diborane , B 2 H 6 . Hermann Irving Schlesinger's laboratory at the University of Chicago was one of two laboratories that prepared diborane. It was a rare compound that was only prepared in small quantities. Schlesinger was researching the reactions of diborane to understand why the simplest hydrogen-boron compound is B 2 H 6 instead of BH 3 . [ 12 ]
When Brown started his own research, he observed the reactions of diborane with aldehydes , ketones , esters , and acid chlorides . He discovered that diborane reacts with aldehydes and ketones to produce dialkoxyboranes, which are hydrolyzed by water to produce alcohols . Until this point, organic chemists did not have an acceptable method of reducing carbonyls under mild conditions. Yet Brown's Ph.D. thesis published in 1939 received little interest. Diborane was too rare to be useful as a synthetic reagent. [ 12 ]
In 1939, Brown became the research assistant in Schlesinger's laboratory. In 1940, they began to research volatile, low molecular weight uranium compounds for the National Defense Research Committee . Brown and Schlesinger successfully synthesized volatile uranium(IV) borohydride, which had a molecular weight of 298. The laboratory was asked to provide a large amount of the product for testing, but diborane was in short supply. They discovered that it could be formed by reacting lithium hydride with boron trifluoride in ethyl ether , allowing them to produce the chemical in larger quantities. This success was met with several new problems. Lithium hydride was also in short supply, so Brown and Schlesinger needed to find a procedure that would allow them to use sodium hydride instead. They discovered that sodium hydride and methyl borate reacted to produce sodium trimethoxyborohydride , which was viable as a substitute for the lithium hydride. [ 12 ]
Soon they were informed that there was no longer a need for uranium borohydride, but it appeared that sodium borohydride could be useful in generating hydrogen . They began to look for a cheaper synthesis and discovered that adding methyl borate to sodium hydride at 250° produced sodium borohydride and sodium methoxide. When acetone was used in an attempt to separate the two products, it was discovered that sodium borohydride reduced the acetone. [ 12 ]
Sodium borohydride is a mild reducing agent that works well in reducing aldehydes, ketones, and acid chlorides. Lithium aluminum hydride is a much more powerful reducing agent that can reduce almost any functional group . When Brown moved to Purdue University in 1947, he worked to find stronger borohydrides and milder aluminum hydrides that would provide a spectrum of reducing agents. The team of researchers at Purdue discovered that changing the metal ion of the borohydride to lithium , magnesium , or aluminum increases the reducing ability. They also found that introducing alkoxy substituents to the aluminum hydride decreases the reducing ability. They successfully developed a full spectrum of reducing agents. [ 12 ]
While researching these reducing agents, Brown's coworker, Dr. B. C. Subba Rao, discovered an unusual reaction between sodium borohydride and ethyl oleate . The borohydride added hydrogen and boron to the carbon-carbon double bond in the ethyl oleate. The organoborane product could then be oxidized to form an alcohol. [ 12 ] This two-step reaction is now called hydroboration-oxidation and is a reaction that converts alkenes into anti-Markovnikov alcohols. Markovnikov's rule states that, in adding hydrogen and a halide or hydroxyl group to a carbon-carbon double bond, the hydrogen is added to the less-substituted carbon of the bond and the hydroxyl or halide group is added to the more-substituted carbon of the bond. In hydroboration-oxidation, the opposite addition occurs. [ 13 ] | https://en.wikipedia.org/wiki/Herbert_C._Brown |
Herbert Morawetz (October 16, 1915 – October 29, 2017) was a Czech - American chemical engineer. He was a professor of chemistry at Polytechnic Institute of Brooklyn ; now New York University. His work focused on polymer chemistry [ 1 ] and macromolecules . He published two books: Macromolecules in Solution and Polymers and The Origins and Growth of a Science, both by Wiley.
Herbert's wife Cathleen Synge Morawetz was a prolific mathematician at NYU. His sister Sonja Morawetz Sinclair revealed in 2017 she was a WW2 codebreaker after seven decades of secrecy by Bletchley Park Signals Intelligence . He helped organize the defection of Mikhail Barishnikov from the Soviet Union in 1974. [ 2 ] [ 3 ] His brother, Oskar Morawetz was a Canadian composer. His brother John Morawetz was a Canadian businessman. | https://en.wikipedia.org/wiki/Herbert_Morawetz |
Herbfields are plant communities dominated by herbaceous plants , especially forbs and grasses . They are found where climatic conditions do not allow large woody plants to grow, such as in subantarctic and alpine tundra environments. Herbfield is defined in New South Wales (Australia) government legislation as native vegetation that predominantly does not contain an over-storey or a mid-storey and where ground cover is dominated by non-grass species. [ 1 ] The New Zealand Department of Conservation has described herbfield vegetation as that in which the cover of herbs in the canopy is 20–100%, and in which herb cover is greater than that of any other growth form, or of bare ground. [ 2 ]
Various kinds of herbfield include:
This article about environmental habitats is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Herbfield |
Herbicidal warfare is the use of substances primarily designed to destroy the plant-based ecosystem of an area. Although herbicidal warfare use chemical substances , its main purpose is to disrupt agricultural food production and/or to destroy plants which provide cover or concealment to the enemy, not to asphyxiate or poison humans and/or destroy human-made structures. Herbicidal warfare has been forbidden by the Environmental Modification Convention since 1978, which bans "any technique for changing the composition or structure of the Earth's biota ". [ 1 ]
Modern day herbicidal warfare resulted from military research discoveries of plant growth regulators during World War II , and is therefore a technological advance on the scorched earth practices by armies throughout history to deprive the enemy of food and cover. Work on military herbicides began in England in 1940, and by 1944, the United States joined in the effort. Even though herbicides are chemicals, due to their mechanism of action (growth regulators), they are often considered a means of biological warfare . Over 1,000 substances were investigated by the war's end for phytotoxic properties, and the Allies envisioned using herbicides to destroy Axis crops. British planners did not believe herbicides were logistically feasible against Nazi Germany .
In May 1945, United States Army Air Force commander General Victor Betrandias advanced a proposal to his superior, General Henry H. Arnold , to use of ammonium thiocyanate to reduce Japanese rice crops part of Allied air raids on Japan . This was part of larger set of proposed measures to starve the Japanese in submission. The plan calculated that ammonium thiocyanate would not be seen as " gas warfare " because the substance was not particularly dangerous to humans. On the other hand, the same plan envisaged that if the U.S. were to engage in "gas warfare" against Japan, then mustard gas would be an even more effective rice crop killer. The Joint Target Group rejected the plan as tactically unsound, but expressed no moral reservations. [ 2 ]
During the Malayan Emergency , British Commonwealth forces deployed herbicides and defoliants in the Malaysian countryside in order to deprive Malayan National Liberation Army (MNLA) insurgents of cover, potential sources of food and to flush them out of the jungle. The herbicides and defoliants they used contained Trioxone , an ingredient which also formed part of the chemical composition of the Agent Orange herbicide used by the U.S. military during the Vietnam War . Deployment of herbicides and defoliants served the dual purpose of thinning jungle trails to prevent ambushes and destroying crop fields in regions where the MNLA was active to deprive them of potential sources of food. In the summer of 1952, 500 hectares were sprayed with 90,000 liters of Trioxone from fire engines ; British Commonwealth forces found it difficult to operate the machinery in jungle conditions while wearing full protective gear. Herbicides and defoliants were also sprayed from Royal Air Force aircraft. [ 3 ]
Historical records of DOW chemical show that "Super Agent Orange", also called DOW Herbicide M-3393, was Agent Orange that was mixed with picloram . Super Orange was known to have been tested by representatives from Fort Detrick and DOW chemical in Texas, Puerto Rico, and Hawaii and later in Malaysia in a cooperative project with the International Rubber Research Institute. [ 4 ] Discussions in the British government centered on avoiding the thorny issue of whether herbicidal warfare in Malaya was in violation of the spirit of the 1925 Geneva Protocol , which only prohibited chemical warfare among signatory states in international armed conflicts. The British were keen to avoid accusations like the allegations of biological warfare in the Korean War leveled against the United States. The British government found that the simplest solution was to deny that a conflict was going on in Malaya. They declared the insurgency to be an internal security matter; thus, the use of herbicidal agents was a matter of police action, much like the use of CS gas for riot control. [ 3 ]
Many Commonwealth personnel who handled herbicides and defoliants during, and in the decades after, the conflict suffered from serious exposure to dioxin, which also led to soil erosion in areas of Malaysia. Roughly 10,000 civilians and insurgents in Malaysia also suffered from the effects of the defoliant, though many historians argue the true number was higher given that herbicides and defoliants were used on a large scale in the Malayan Emergency; the British government manipulated data and kept its deployment of herbicidal warfare secret in fear of a diplomatic backlash. [ 5 ] [ 6 ] [ 7 ]
The United States used herbicides in Southeast Asia during the Vietnam War . Success with Project AGILE field tests with herbicides in South Vietnam in 1961 and inspiration by the British use of herbicides and defoliants during the Malayan Emergency led to the formal herbicidal program Operation Trail Dust (1961–1971). Operation Ranch Hand , a U.S. Air Force program to use C-123K aircraft to spray herbicides over large areas, was one of many programs under Trail Dust. The aircrews charged with spraying the defoliant used a sardonic motto-"Only you can prevent forests"-a shortening of the U.S. Forest Services famous warning to the general public "Only you can prevent forest fires". The United States and its allies officially claims that herbicidal and incendiary agents like napalm fall outside the definition of "chemical weapons" and that Britain set the precedent by using them during the Malayan Emergency.
Ranch Hand started as a limited program of defoliation of border areas, security perimeters, and crop destruction. As the conflict continued, the anti-crop mission took on more prominence, and (along with other agents) defoliants became used to compel civilians to leave Viet Cong -controlled territories for government-controlled areas. It was also used experimentally for large area forest burning operations that failed to produce the desired results. Defoliation was judged in 1963 as improving visibility in jungles by 30–75% horizontally, and 40–80% vertically. Improvements in delivery systems by 1968 increased this to 50–70% horizontally, and 60–90% vertically. Ranch Hand pilots were the first to make an accurate 1:125,000 scale map of the Ho Chi Minh trail south of Tchepone , Laos by defoliating swaths perpendicular to the trail every half mile or so.
Use of herbicides in Vietnam caused a shortage of commercial pesticides in mid-1966 when the Defense Department had to use powers under the Defense Production Act of 1950 to secure supplies. The concentration of herbicides sprayed in Operation Ranch Hand was more than an order of magnitude greater than that in domestic use. Approximately 10% of the land surface of South Vietnam was sprayed—about 17,000 square kilometers. About 85% of the spraying was for defoliation and about 15% was for crop destruction. [ 8 ]
The United States had technical military symbols for herbicides that have since been replaced by the more common color code names derived from the banding on shipping drums. The US further distinguished between tactical herbicides , which were to be used in combat operations and commercial herbicides, which used in and around military bases, etc. [ 9 ]
In 1966 the United States Defense Department claimed that herbicides used in Vietnam were not harmful to people or the environment. In 1972 it was advised that a known impurity precluded the use of these herbicides in Vietnam and all remaining stocks should be returned home. In 1977 the United States Air Force destroyed its stocks of Agent Orange 200 miles west of Johnston Island on the incinerator ship M/T Vulcanus . The impurity, 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) was a suspected carcinogen that may have affected the health of over 17,000 United States servicemen, 4,000 Australians , 1,700 New Zealanders , Koreans , countless Vietnamese soldiers and civilians, and with over 40,000 children of veterans possibly suffering birth defects from herbicidal warfare.
Decades later the lingering problem of herbicidal warfare remains as a dominant issue of United States-Vietnam relations . In 2003, a coalition of Vietnamese survivors and long-term victims of Agent Orange sued a number of American-based and multinational chemical corporations for damages related to the manufacture and use of the chemical. A federal judge rejected the suit, claiming that the plaintiff's claim of direct responsibility was invalid. | https://en.wikipedia.org/wiki/Herbicidal_warfare |
Herbicides ( US : / ˈ ɜːr b ɪ s aɪ d z / , UK : / ˈ h ɜːr -/ ), also commonly known as weed killers , are substances used to control undesired plants , also known as weeds . [ 1 ] Selective herbicides control specific weed species while leaving the desired crop relatively unharmed, while non-selective herbicides (sometimes called "total weed killers") kill plants indiscriminately. [ 2 ] The combined effects of herbicides, nitrogen fertilizer, and improved cultivars has increased yields (per acre) of major crops by three to six times from 1900 to 2000. [ 3 ]
In the United States in 2012, about 91% of all herbicide usage, determined by weight applied, was in agriculture. [ 4 ] : 12 In 2012, world pesticide expenditures totaled nearly US$24.7 billion ; herbicides were about 44% of those sales and constituted the biggest portion, followed by insecticides , fungicides , and fumigants . [ 4 ] : 5 Herbicide is also used in forestry, [ 5 ] where certain formulations have been found to suppress hardwood varieties in favor of conifers after clearcutting , [ 6 ] as well as pasture systems.
Prior to the widespread use of herbicides, cultural controls , such as altering soil pH , salinity, or fertility levels, were used to control weeds. [ 7 ] Mechanical control including tillage and flooding were also used to control weeds. In the late 19th and early 20th centuries, inorganic chemicals such as sulfuric acid , arsenic, copper salts, kerosene and sodium chlorate were used to control weeds, but these chemicals were either toxic, flammable or corrosive and were expensive and ineffective at controlling weeds. [ 8 ] [ 9 ]
The major breakthroughs occurred during the Second World War as the result of research conducted independently in the United Kingdom and the United States into the potential use of herbicides in war . [ 10 ] The compound 2,4-D was first synthesized by W. G. Templeman at Imperial Chemical Industries . In 1940, his work with indoleacetic acid and naphthaleneacetic acid indicated that "growth substances applied appropriately would kill certain broad-leaved weeds in cereals without harming the crops," [ 11 ] [ 12 ] though these substances were too expensive and too short-lived in soil due to degradation by microorganisms to be of practical agricultural use; by 1941, his team succeeded in synthesizing a wide range of chemicals to achieve the same effect at lower cost and better efficacy, including 2,4-D. [ 13 ] In the same year, R. Pokorny in the US achieved this as well. [ 14 ] Independently, a team under Juda Hirsch Quastel , working at the Rothamsted Experimental Station made the same discovery. Quastel was tasked by the Agricultural Research Council (ARC) to discover methods for improving crop yield. By analyzing soil as a dynamic system, rather than an inert substance, he was able to apply techniques such as perfusion . Quastel was able to quantify the influence of various plant hormones , inhibitors, and other chemicals on the activity of microorganisms in the soil and assess their direct impact on plant growth . While the full work of the unit remained secret, certain discoveries were developed for commercial use after the war, including the 2,4-D compound. [ 15 ]
When 2,4-D was commercially released in 1946, it became the first successful selective herbicide, triggering a worldwide revolution in agricultural output. It allowed for greatly enhanced weed control in wheat , maize (corn), rice , and similar cereal grass crops, because it kills dicots (broadleaf plants), but not most monocots (grasses). The low cost of 2,4-D has led to continued usage today, and it remains one of the most commonly used herbicides in the world. [ 16 ] Like other acid herbicides, current formulations use either an amine salt (often trimethylamine ) or one of many esters of the parent compound.
The triazine family of herbicides, which includes atrazine , was introduced in the 1950s; they have the current distinction of being the herbicide family of greatest concern regarding groundwater contamination . Atrazine does not break down readily (within a few weeks) after being applied to soils of above-neutral pH . Under alkaline soil conditions, atrazine may be carried into the soil profile as far as the water table by soil water following rainfall causing the aforementioned contamination. Atrazine is thus said to have "carryover", a generally undesirable property for herbicides.
Glyphosate had been first prepared in the 1950s but its herbicidal activity was only recognized in the 1960s. It was marketed as Roundup in 1971. [ 17 ] The development of glyphosate-resistant crop plants, it is now used very extensively for selective weed control in growing crops. The pairing of the herbicide with the resistant seed contributed to the consolidation of the seed and chemistry industry in the late 1990s.
Many modern herbicides used in agriculture and gardening are specifically formulated to degrade within a short period after application.
Herbicides can be classified/grouped in various ways; for example, according to their activity, the timing of application, method of application, mechanism of their action, and their chemical structures.
Chemical structure of the herbicide is of primary affecting efficacy. 2,4-D, mecoprop , and dicamba control many broadleaf weeds but remain ineffective against turf grasses. [ 18 ]
Chemical additives influence selectivity. Surfactants alter the physical properties of the spray solution and the overall phytotoxicity of the herbicide, increasing translocation. Herbicide safeners enhance the selectivity by boosting herbicide resistance by the crop but allowing the herbicide to damage the weed.
Selectivity is determined by the circumstances and technique of application. Climatic factors affect absorption including humidity , light, precipitation, and temperature. Foliage-applied herbicides will enter the leaf more readily at high humidity by lengthening the drying time of the spray droplet and increasing cuticle hydration. Light of high intensity may break down some herbicides and cause the leaf cuticle to thicken, which can interfere with absorption. Precipitation may wash away or remove some foliage-applied herbicides, but it will increase root absorption of soil-applied herbicides. Drought-stressed plants are less likely to translocate herbicides. As temperature increases, herbicides' performance may decrease. Absorption and translocation may be reduced in very cold weather.
Non-selective herbicides, generally known as defoliants , are used to clear industrial sites, waste grounds, railways, and railway embankments. Paraquat , glufosinate , and glyphosate are non-selective herbicides. [ 18 ]
An herbicide is described as having low residual activity if it is neutralized within a short time of application (within a few weeks or months) – typically this is due to rainfall, or reactions in the soil. A herbicide described as having high residual activity will remain potent for the long term in the soil. For some compounds, the residual activity can leave the ground almost permanently barren. [ citation needed ]
Herbicides interfere with the biochemical machinery that supports plant growth. Herbicides often mimic natural plant hormones , enzyme substrates, and cofactors . They interfere with the metabolism in the target plants. Herbicides are often classified according to their site of action because as a general rule, herbicides within the same site of action class produce similar symptoms on susceptible plants. Classification based on the site of action of the herbicide is preferable as herbicide resistance management can be handled more effectively. [ 18 ] Classification by mechanism of action (MOA) indicates the first enzyme, protein, or biochemical step affected in the plant following application:
Complementary to mechanism-based classifications, herbicides are often classified according to their chemical structures or motifs. Similar structural types work in similar ways. For example, aryloxphenoxypropionates herbicides ( diclofop chlorazifop , fluazifop ) appear to all act as ACCase inhibitors. [ 19 ] The so-called cyclohexanedione herbicides, which are used against grasses, include the following commercial products cycloxydim , clethodim , tralkoxydim , butroxydim , sethoxydim , profoxydim , and mesotrione . [ 26 ] Knowing about herbicide chemical family grouping serves as a short-term strategy for managing resistance to site of action. [ 27 ] The phenoxyacetic acid mimic the natural auxin indoleacetic acid (IAA). This family includes MCPA , 2,4-D , and 2,4,5-T , picloram , dicamba , clopyralid , and triclopyr .
Using the Weed Science Society of America (WSSA) and herbicide Resistance and World Grains (HRAC) systems , herbicides are classified by mode of action. [ 28 ] Eventually the Herbicide Resistance Action Committee (HRAC) [ 29 ] and the Weed Science Society of America (WSSA) [ 30 ] developed a classification system. [ 31 ] [ 32 ] Groups in the WSSA and the HRAC systems are designated by numbers and letters, inform users awareness of herbicide mode of action and provide more accurate recommendations for resistance management. [ 33 ]
Most herbicides are applied as water-based sprays using ground equipment. Ground equipment varies in design, but large areas can be sprayed using self-propelled sprayers equipped with long booms, of 60 to 120 feet (18 to 37 m) with spray nozzles spaced every 20–30 inches (510–760 mm) apart. Towed, handheld, and even horse-drawn sprayers are also used. On large areas, herbicides may also at times be applied aerially using helicopters or airplanes, or through irrigation systems (known as chemigation ).
Weed-wiping may also be used, where a wick wetted with herbicide is suspended from a boom and dragged or rolled across the tops of the taller weed plants. This allows treatment of taller grassland weeds by direct contact without affecting related but desirable shorter plants in the grassland sward beneath. The method has the benefit of avoiding spray drift. In Wales , a scheme offering free weed-wiper hire was launched in 2015 in an effort to reduce the levels of MCPA in water courses. [ 34 ]
There is little difference in forestry in the early growth stages, when the height similarities between growing trees and growing annual crops yields a similar problem with weed competition. Unlike with annuals however, application is mostly unnecessary thereafter and is thus mostly used to decrease the delay between productive economic cycles of lumber crops. [ 35 ]
Herbicide volatilisation or spray drift may result in herbicide affecting neighboring fields or plants, particularly in windy conditions. Sometimes, the wrong field or plants may be sprayed due to error.
Although herbicidal warfare uses chemical substances , its main purpose is to disrupt agricultural food production or to destroy plants which provide cover or concealment to the enemy. During the Malayan Emergency , British Commonwealth forces deployed herbicides and defoliants in the Malaysian countryside in order to deprive Malayan National Liberation Army (MNLA) insurgents of cover, potential sources of food and to flush them out of the jungle. Deployment of herbicides and defoliants served the dual purpose of thinning jungle trails to prevent ambushes and destroying crop fields in regions where the MNLA was active to deprive them of potential sources of food. As part of this process, herbicides and defoliants were also sprayed from Royal Air Force aircraft. [ 36 ]
The use of herbicides as a chemical weapon by the U.S. military during the Vietnam War has left tangible, long-term impacts upon the Vietnamese people and U.S soldiers that handled the chemicals. [ 37 ] [ 38 ] More than 20% of South Vietnam's forests and 3.2% of its cultivated land were sprayed at least once between during the war. [ 39 ] The government of Vietnam says that up to four million people in Vietnam were exposed to the defoliant, and as many as three million people have suffered illness because of Agent Orange, [ 40 ] while the Viet Nam Red Cross Society estimates that up to one million people were disabled or have health problems as a result of exposure to Agent Orange. [ 41 ] The United States government has described these figures as unreliable. [ 42 ]
Many questions exist about herbicides' health and environmental effects, because of the many kinds of herbicide and the myriad potential targets, mostly unintended. For example, a 1995 panel of 13 scientists reviewing studies on the carcinogenicity of 2,4-D had divided opinions on the likelihood 2,4-D causes cancer in humans. [ 43 ] As of 1992 [update] , studies on phenoxy herbicides were too few to accurately assess the risk of many types of cancer from these herbicides, even although evidence was stronger that exposure to these herbicides is associated with increased risk of soft tissue sarcoma and non-Hodgkin lymphoma . [ 44 ]
Toxicity
Herbicides have widely variable toxicity . Acute toxicity , short term exposure effects, and chronic toxicity , from long term environmental or occupational exposure. Much public suspicion of herbicides confuses valid statements of acute toxicity with equally valid statements of lack of chronic toxicity at the recommended levels of usage. For instance, while glyphosate formulations with tallowamine adjuvants are acutely toxic, their use was found to be uncorrelated with any health issues like cancer in a massive US Department of Health study on 90,000 members of farmer families for over a period of 23 years. [ 45 ] That is, the study shows lack of chronic toxicity, but cannot question the herbicide's acute toxicity.
Health effects
Some herbicides cause a range of health effects ranging from skin rashes to death. The pathway of attack can arise from intentional or unintentional direct consumption, improper application resulting in the herbicide coming into direct contact with people or wildlife, inhalation of aerial sprays, or food consumption prior to the labelled preharvest interval. Under some conditions, certain herbicides can be transported via leaching or surface runoff to contaminate groundwater or distant surface water sources. Generally, the conditions that promote herbicide transport include intense storm events (particularly shortly after application) and soils with limited capacity to adsorb or retain the herbicides. Herbicide properties that increase likelihood of transport include persistence (resistance to degradation) and high water solubility. [ 46 ]
Contamination
Cases have been reported where Phenoxy herbicides are contaminated with dioxins such as TCDD ; [ 47 ] [ citation needed ] research has suggested such contamination results in a small rise in cancer risk after occupational exposure to these herbicides. [ 48 ] Triazine exposure has been implicated in a likely relationship to increased risk of breast cancer , although a causal relationship remains unclear. [ 49 ]
False claims
Herbicide manufacturers have at times made false or misleading claims about the safety of their products. Chemical manufacturer Monsanto Company agreed to change its advertising after pressure from New York attorney general Dennis Vacco ; Vacco complained about misleading claims that its spray-on glyphosate-based herbicides, including Roundup, were safer than table salt and "practically non-toxic" to mammals, birds, and fish (though proof that this was ever said is hard to find). [ 50 ] Roundup is toxic and has resulted in death after being ingested in quantities ranging from 85 to 200 ml, although it has also been ingested in quantities as large as 500 ml with only mild or moderate symptoms. [ 51 ] The manufacturer of Tordon 101 ( Dow AgroSciences , owned by the Dow Chemical Company ) has claimed Tordon 101 has no effects on animals and insects, [ 52 ] in spite of evidence of strong carcinogenic activity of the active ingredient, [ 53 ] picloram , in studies on rats. [ 54 ]
Herbicide use generally has negative impacts on many aspects of the environment. Insects, non-targeted plants, animals, and aquatic systems subject to serious damage from herbicides. Impacts are highly variable.
Bioaccumulation is a concern, both in terrestrial [ 55 ] and aquatic environments, [ 56 ] and is heavily dependent on both the kind of herbicide and the conditions. For example, fish in dark aquariums bioaccumulated 14 times more trifluralin than fish kept in well lit aquariums in a 1977 study. [ 57 ]
Atrazine and 2,4-dichlorophenoxyacetic acid have often been blamed for affecting reproductive behavior of aquatic life. A review in 2008 found that the data do not support this assertion in regards to atrazine, [ 58 ] but later works find these herbicides as having a detrimental effect on aquatic plant, invertebrate, and vertebrate life, as well as disrupting microbial communities in soil. [ 56 ]
Bird populations are one of many indicators of herbicide damage. Most observed effects are due not to toxicity, [ 59 ] but to habitat changes and the decreases in abundance of species on which birds rely for food or shelter. Herbicide use in silviculture , used to favor certain types of growth following clearcutting , can cause significant drops in bird populations. Even when herbicides which have low toxicity to birds are used, they decrease the abundance of many types of vegetation on which the birds rely. [ 35 ] Herbicide use in agriculture in the UK has been linked to a decline in seed-eating bird species which rely on the weeds killed by the herbicides. [ 60 ] Heavy use of herbicides in neotropical agricultural areas has been one of many factors implicated in limiting the usefulness of such agricultural land for wintering migratory birds. [ 61 ]
One major complication to the use of herbicides for weed control is the ability of plants to evolve herbicide resistance , rendering the herbicides ineffective against target plants. Out of 31 known herbicide modes of action, weeds have evolved resistance to 21. 268 plant species are known to have evolved herbicide resistance at least once. [ 62 ] Herbicide resistance was first observed in 1957, and since has evolved repeatedly in weed species from 30 families across the globe. [ 63 ] Weed resistance to herbicides has become a major concern in crop production worldwide. [ 64 ]
Resistance to herbicides is often attributed to overuse as well as the strong evolutionary pressure on the affected weeds. [ 65 ] Three agricultural practices account for the evolutionary pressure upon weeds to evolve resistance: monoculture , neglecting non-herbicide weed control practices, and reliance on one herbicide for weed control. [ 66 ] To minimize resistance, rotational programs of herbicide application, where herbicides with multiple modes of action are used, have been widely promoted. [ 27 ] In particular, glyphosate resistance evolved rapidly in part because when glyphosate use first began, it was continuously and heavily relied upon for weed control. [ 67 ] This caused incredibly strong selective pressure upon weeds, encouraging mutations conferring glyphosate resistance to persist and spread. [ 68 ]
However, in 2015, an expansive study showed an increase in herbicide resistance as a result of rotation, and instead recommended mixing multiple herbicides for simultaneous application. As of 2023, the effectiveness of combining herbicides is also questioned, particularly in light of the rise of non-target site resistance. [ 69 ] [ 70 ] [ 71 ]
Plants developed resistance to atrazine and to ALS-inhibitors relatively early, but more recently, glyphosate resistance has dramatically risen. Marestail is one weed that has developed glyphosate resistance. [ 72 ] Glyphosate-resistant weeds are present in the vast majority of soybean, cotton and corn farms in some U.S. states. Weeds that can resist multiple other herbicides are spreading. Few new herbicides are near commercialization, and none with a molecular mode of action for which there is no resistance. Because most herbicides could not kill all weeds, farmers rotate crops and herbicides to stop the development of resistant weeds.
A 2008–2009 survey of 144 populations of waterhemp in 41 Missouri counties revealed glyphosate resistance in 69%. Weeds from some 500 sites throughout Iowa in 2011 and 2012 revealed glyphosate resistance in approximately 64% of waterhemp samples. As of 2023, 58 weed species have developed glyphosate resistance. [ 73 ] Weeds resistant to multiple herbicides with completely different biological action modes are on the rise. In Missouri, 43% of waterhemp samples were resistant to two different herbicides; 6% resisted three; and 0.5% resisted four. In Iowa 89% of waterhemp samples resist two or more herbicides, 25% resist three, and 10% resist five. [ 67 ]
As of 2023, Palmer amaranth with resistance to six different herbicide modes of action has emerged. [ 74 ] Annual bluegrass collected from a golf course in the U.S. state of Tennessee was found in 2020 to be resistant to seven herbicides at once. [ 75 ] Rigid ryegrass and annual bluegrass share the distinction of the species with confirmed resistance to the largest number of herbicide modes of action, both with confirmed resistance to 12 different modes of action; however, this number references how many forms of herbicide resistance are known to have emerged in the species at some point, not how many have been found simultaneously in a single plant. [ 68 ] [ 76 ]
In 2015, Monsanto released crop seed varieties resistant to both dicamba and glyphosate, allowing for use of a greater variety of herbicides on fields without harming the crops. By 2020, five years after the release of dicamba-resistant seed, the first example of dicamba-resistant Palmer amaranth was found in one location. [ 77 ]
When mutations occur in the genes responsible for the biological mechanisms that herbicides interfere with, these mutations may cause the herbicide mode of action to work less effectively. This is called target-site resistance. Specific mutations that have the most helpful effect for the plant have been shown to occur in separate instances and dominate throughout resistant weed populations. This is an example of convergent evolution . [ 63 ] Some mutations conferring herbicide resistance may have fitness costs, reducing the plant's ability to survive in other ways, but over time, the least costly mutations tend to dominate in weed populations. [ 63 ]
Recently, incidences of non-target site resistance have increasingly emerged, such as examples where plants are capable of producing enzymes that neutralize herbicides before they can enter the plant's cells – metabolic resistance . This form of resistance is particularly challenging, since plants can develop non-target-site resistance to herbicides their ancestors were never directly exposed to. [ 77 ]
Resistance to herbicides can be based on one of the following biochemical mechanisms: [ 78 ] [ 79 ] [ 80 ]
The following terms are also used to describe cases where plants are resistant to multiple herbicides at once:
Due to herbicide resistance – a major concern in agriculture – a number of products combine herbicides with different means of action. Integrated pest management may use herbicides alongside other pest control methods.
Integrated weed management (IWM) approach utilizes several tactics to combat weeds and forestall resistance. This approach relies less on herbicides and so selection pressure should be reduced. [ 82 ] By relying on diverse weed control methods, including non-herbicide methods of weed control, the selection pressure on weeds to evolve resistance can be lowered. Researchers warn that if herbicide resistance is combatted only with more herbicides, "evolution will most likely win." [ 66 ] In 2017, the USEPA issued a revised Pesticide Registration Notice (PRN 2017-1), which provides guidance to pesticide registrants on required pesticide resistance management labeling. This requirement applies to all conventional pesticides and is meant to provide end-users with guidance on managing pesticide resistance. [ 83 ] An example of a fully executed label compliant with the USEPA resistance management labeling guidance can be seen on the specimen label for the herbicide, cloransulam-methyl, updated in 2022. [ 84 ]
Optimising herbicide input to the economic threshold level should avoid the unnecessary use of herbicides and reduce selection pressure. Herbicides should be used to their greatest potential by ensuring that the timing, dose, application method, soil and climatic conditions are optimal for good activity. In the UK, partially resistant grass weeds such as Alopecurus myosuroides (blackgrass) and Avena genus (wild oat) can often be controlled adequately when herbicides are applied at the 2-3 leaf stage, whereas later applications at the 2-3 tiller stage can fail badly. Patch spraying, or applying herbicide to only the badly infested areas of fields, is another means of reducing total herbicide use. [ 82 ]
When resistance is first suspected or confirmed, the efficacy of alternatives is likely to be the first consideration. If there is resistance to a single group of herbicides, then the use of herbicides from other groups may provide a simple and effective solution, at least in the short term. For example, many triazine-resistant weeds have been readily controlled by the use of alternative herbicides such as dicamba or glyphosate. [ 82 ]
The use of two or more herbicides which have differing modes of action can reduce the selection for resistant genotypes. Ideally, each component in a mixture should:
No mixture is likely to have all these attributes, but the first two listed are the most important. There is a risk that mixtures will select for resistance to both components in the longer term. One practical advantage of sequences of two herbicides compared with mixtures is that a better appraisal of the efficacy of each herbicide component is possible, provided that sufficient time elapses between each application. A disadvantage with sequences is that two separate applications have to be made and it is possible that the later application will be less effective on weeds surviving the first application. If these are resistant, then the second herbicide in the sequence may increase selection for resistant individuals by killing the susceptible plants which were damaged but not killed by the first application, but allowing the larger, less affected, resistant plants to survive. This has been cited as one reason why ALS-resistant Stellaria media has evolved in Scotland recently (2000), despite the regular use of a sequence incorporating mecoprop , a herbicide with a different mode of action. [ 82 ]
The term organic herbicide has come to mean herbicides intended for organic farming . Few natural herbicides rival the effectiveness of synthetics. [ 85 ] Some plants also produce their own herbicides, such as the genus Juglans ( walnuts ), or the tree of heaven ; such actions of natural herbicides, and other related chemical interactions, is called allelopathy . The applicability of these agents is unclear.
Herbicide resistance became a critical problem in Australian agriculture after many Australian sheep farmers began to exclusively grow wheat in their pastures in the 1970s. Introduced varieties of ryegrass , while good for grazing sheep, compete intensely with wheat. Ryegrasses produce so many seeds that, if left unchecked, they can completely choke a field. Herbicides provided excellent control, reducing soil disruption because of less need to plough. Within little more than a decade, ryegrass and other weeds began to develop resistance. In response Australian farmers changed methods. [ 86 ] By 1983, patches of ryegrass had become immune to Hoegrass ( diclofop-methyl ), a family of herbicides that inhibit an enzyme called acetyl coenzyme A carboxylase . [ 86 ] [ 87 ]
Ryegrass populations were large and had substantial genetic diversity because farmers had planted many varieties. Ryegrass is cross-pollinated by wind, so genes shuffle frequently. To control its distribution, farmers sprayed inexpensive Hoegrass, creating selection pressure . In addition, farmers sometimes diluted the herbicide to save money, which allowed some plants to survive application. Farmers turned to a group of herbicides that block acetolactate synthase when resistance appeared. Once again, ryegrass in Australia evolved a kind of "cross-resistance" that allowed it to break down various herbicides rapidly. Four classes of herbicides become ineffective within a few years. In 2013, only two herbicide classes called Photosystem II and long-chain fatty acid inhibitors, were effective against ryegrass. [ 86 ] | https://en.wikipedia.org/wiki/Herbicide |
Herbol is one of the oldest German brands for professional coatings . It has its origins in the Lackfabrik Herbig-Haarhaus that was founded in Cologne in 1844. The product range contains façade paints , interior wall paints , lacquers and glazing , crack reinforcement as well as concrete and floor system. The coatings systems are used for renovation, maintenance and new constructions. Since 1999 the brand Herbol is part of the Akzo Nobel Deco GmbH, an affiliate of the Dutch concern AkzoNobel , the world's biggest coatings manufacturer.
In 1844 Robert Friedrich Haarhaus founded the company in Cologne . In 1871 his son-in-law joined the company. The coatings business extended. After Robert Friedrich Haarhaus died in 1874 the company was renamed in Deutsch-Englische Lackfabrik . In 1899 Arthur Herbig's sons, Arthur Herbig and Adolf Herbig junior joined the company.
In 1903 the company was relocated to a new, modern production location on the Vitalisstraße in Cologne - Bickendorf , that is still used as German main plaint. [ 1 ] In 1904 Herbolin Flüssiges Porzellan was registered as trademark and became one of the first big German white-varnish-trademarks as well as Kristallweiß (Glasurit), Eburit (Beck & Co.) and Alpinaweiß (Deutsche Amphibolin-Werke). [ 1 ] In 1910 the company employed 80 workers.
In 1910 Herbol produced outside of Cologne for the first time. In Vienna and Paris Herbol products were manufactured under licence. In 1912 Arthur Herbig assumed the leadership of the company. A new colour factory was opened in Cologne in 1923, where in 1930 already 180 employees produced around 330 different products.
In World War II the main factory was known as war-strategic company, because it produced protective mimicry on a large scale. After a couple of air attacks 80 percent of the factory in Cologne were destroyed. After the surrender of the German the branches in Vienna , Berlin and Milan were expropriated. In August 1945 the production already started again in Cologne .
In 1952 Herbol started to produce dispersion paints. From 1945 synthetic resin was produced in the new built resin factory. During the following ten years the production of Herbig-Haarhaus expanded. New branches in Würzburg and Switzerland were commissioned. In 1955 Hans Herbig died; for the first time no bearer of the traditional name Herbig was to be found. During the next three years Erich Zschocke informed the company. The collection of the passionate fancier of hand-painted porcelain and varnished objects, together with the collection of Kurt Herberts, later paved the way for the collection of the Museum für Lackkunst (Museum for Lacquer Art) in Münster . In 1957 the Herbol- logo was redesigned by the American designer Raymond Loewy ( Coca-Cola bottle, Lucky Strike ). It showed the Herbol lettering within a paintbrush.
In 1968 the Herbig family sold the company to BASF AG and Bayer AG . In 1969 the blue logo was introduced as second brand label besides the paintbrush. BASF completely took over the branches in Cologne and Würzburg in 1970. Under new management the renewal and expansion of the trademark Herbol continued. After an extensive reorganisation and an increasing international orientation of the coatings business Herbol became part of the new founded Deco GmbH in 1997.
In 1999 the European coatings business of BASF was taken over by AkzoNobel . The new founded Akzo Nobel Deco GmbH managed Herbol from Cologne , distributing the trademark in many European countries. In 2007, together with BASF , the façade paint Herbol-Symbiotec was introduced as „first real Nano-façade-paint“. [ 2 ] Since 2010 all of Herbol's coatings follow the VOC -regulations. [ 3 ]
Herbol belongs to AkzoNobel . The product range is distributed via free wholesale and specialised trade as well as the trademarks ’ own distributor, AkzoNobel Farbe & Heimtex. Herbol is a recognized trademark in many European countries, i.e. in Austria , Switzerland , France and Belgium . It was successfully introduced to Italy . In 2011 it was officially introduced to the Netherlands . | https://en.wikipedia.org/wiki/Herbol |
Herbrand's theorem is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930). [ 1 ] It essentially allows a certain kind of reduction of first-order logic to propositional logic . Herbrand's theorem is the logical foundation for most automatic theorem provers . Although Herbrand originally proved his theorem for arbitrary formulas of first-order logic, [ 2 ] the simpler version shown here, restricted to formulas in prenex form containing only existential quantifiers , became more popular.
Let
be a formula of first-order logic with F ( y 1 , … , y n ) {\displaystyle F(y_{1},\ldots ,y_{n})} quantifier-free,
though it may contain additional free variables.
This version of Herbrand's theorem states that the above formula is valid if and only if there exists a finite sequence of terms t i j {\displaystyle t_{ij}} ,
possibly in an expansion of the language , with
such that
is valid. If it is valid, it is called a Herbrand disjunction for
Informally: a formula A {\displaystyle A} in prenex form containing only existential quantifiers is provable (valid) in first-order logic if and only if a disjunction composed of substitution instances of the quantifier-free subformula of A {\displaystyle A} is a tautology (propositionally derivable).
The restriction to formulas in prenex form containing only existential quantifiers does not limit the generality of the theorem, because formulas can be converted to prenex form and their universal quantifiers can be removed by Herbrandization . Conversion to prenex form can be avoided, if structural Herbrandization is performed. Herbrandization can be avoided by imposing additional restrictions on the variable dependencies allowed in the Herbrand disjunction.
A proof of the non-trivial direction of the theorem can be constructed according to the following steps:
However, sequent calculus and cut-elimination were not known at the time of Herbrand's proof, and Herbrand had to prove his theorem in a more complicated way. | https://en.wikipedia.org/wiki/Herbrand's_theorem |
In mathematical logic , a Herbrand interpretation is an interpretation in which all constants and function symbols are assigned very simple meanings. [ 1 ] Specifically, every constant is interpreted as itself, and every function symbol is interpreted as the application function on terms . The interpretation also defines predicate symbols as denoting a subset of the relevant Herbrand base , effectively specifying which ground atoms are true in the interpretation. This allows the symbols in a set of clauses to be interpreted in a purely syntactic way, separated from any real instantiation.
The importance of Herbrand interpretations is that, if there exists an interpretation that satisfies a given set of clauses S then there is a Herbrand interpretation that satisfies the clauses. Moreover, Herbrand's theorem states that if S is unsatisfiable then there is a finite unsatisfiable set of ground instances from the Herbrand universe defined by S . Since this set is finite, its unsatisfiability can be verified in finite time. However, there may be an infinite number of such sets to check.
Herbrand interpretations are named after Jacques Herbrand .
This logic -related article is a stub . You can help Wikipedia by expanding it .
This mathematical logic -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Herbrand_interpretation |
In first-order logic , a Herbrand structure S {\displaystyle S} is a structure over a vocabulary σ {\displaystyle \sigma } (also sometimes called a signature ) that is defined solely by the syntactical properties of σ {\displaystyle \sigma } . The idea is to take the symbol strings of terms as their values, e.g. the denotation of a constant symbol c {\displaystyle c} is just " c {\displaystyle c} " (the symbol). It is named after Jacques Herbrand .
Herbrand structures play an important role in the foundations of logic programming . [ 1 ]
The Herbrand universe serves as the universe in a Herbrand structure .
Let L σ {\displaystyle L^{\sigma }} , be a first-order language with the vocabulary
then the Herbrand universe H {\displaystyle H} of L σ {\displaystyle L^{\sigma }} (or of σ {\displaystyle \sigma } ) is
H = { c , f ( c ) , g ( c ) , f ( f ( c ) ) , f ( g ( c ) ) , g ( f ( c ) ) , g ( g ( c ) ) , … } {\displaystyle H=\{c,f(c),g(c),f(f(c)),f(g(c)),g(f(c)),g(g(c)),\dots \}}
The relation symbols are not relevant for a Herbrand universe since formulas involving only relations do not correspond to elements of the universe. [ 2 ]
A Herbrand structure interprets terms on top of a Herbrand universe .
Let S {\displaystyle S} be a structure , with vocabulary σ {\displaystyle \sigma } and universe U {\displaystyle U} . Let W {\displaystyle W} be the set of all terms over σ {\displaystyle \sigma } and W 0 {\displaystyle W_{0}} be the subset of all variable-free terms. S {\displaystyle S} is said to be a Herbrand structure iff
For a constant symbol c {\displaystyle c} and a unary function symbol f ( ⋅ ) {\displaystyle f(\,\cdot \,)} we have the following interpretation:
In addition to the universe, defined in § Herbrand universe , and the term denotations, defined in § Herbrand structure , the Herbrand base completes the interpretation by denoting the relation symbols.
A Herbrand base B H {\displaystyle {\mathcal {B}}_{H}} for a Herbrand structure is the set of all atomic formulas whose argument terms are elements of the Herbrand universe.
For a binary relation symbol R {\displaystyle R} , we get with the terms from above: | https://en.wikipedia.org/wiki/Herbrand_structure |
The Hercules DFXE was an American diesel truck engine produced by the Hercules Engine Company .
Part of the Hercules DFX series, the DFXE is a naturally aspirated , direct injection , overhead valve , inline six-cylinder engine. [ 1 ] [ 2 ] The engine had a displacement of 855 cu in (14.011 L), with a bore of 5 + 5 ⁄ 8 in (143 mm), a stroke of 6 in (150 mm) and a compression ratio of 14.8:1. [ 3 ] [ 4 ] It developed 201 bhp (150 kW) at 1,600 rpm and a maximum 685 ft⋅lbf (929 N⋅m) of torque at 1150 rpm; 660 ft⋅lbf (890 N⋅m) at 1600 rpm. [ 5 ] [ 6 ]
The DFXE was designed to requirements of the British Purchasing Commission for use in the Diamond T Model 980 tank transporter. As the Diamond T Model 980 was later adopted by the US, the DFXE was one of the few diesel engines used by US tactical trucks during World War II. [ 7 ] [ 8 ]
The engine was used in upright or horizontal configurations. [ 9 ]
It was used in the Diamond T Models 980 and 981 trucks in World War Two, the Le Tourneau Model B29 Tournapull earthmover (introduced in 1945), [ 10 ] and the Oliver OC-18 crawler tractor (introduced in 1952), [ 11 ] among others. | https://en.wikipedia.org/wiki/Hercules_DFXE |
Herd immunity (also called herd effect , community immunity , population immunity , or mass immunity ) is a form of indirect protection that applies only to contagious diseases . It occurs when a sufficient percentage of a population has become immune to an infection, whether through previous infections or vaccination , [ 1 ] that the communicable pathogen cannot maintain itself in the population, its low incidence thereby reducing the likelihood of infection for individuals who lack immunity. [ 2 ] [ 3 ] [ 4 ]
Once the herd immunity has been reached, disease gradually disappears from a population and may result in eradication or permanent reduction of infections to zero if achieved worldwide. [ 5 ] [ 6 ] Herd immunity created via vaccination has contributed to the reduction of many diseases. [ 7 ]
Some individuals either cannot develop immunity after vaccination or for medical reasons cannot be vaccinated. [ 8 ] [ 9 ] [ 10 ] Newborn infants are too young to receive many vaccines, either for safety reasons or because passive immunity renders the vaccine ineffective. [ 11 ] Individuals who are immunodeficient due to HIV/AIDS , lymphoma , leukemia , bone marrow cancer, an impaired spleen , chemotherapy , or radiotherapy may have lost any immunity that they previously had and vaccines may not be of any use for them because of their immunodeficiency. [ 9 ] [ 10 ] [ 11 ] [ 12 ]
A portion of those vaccinated may not develop long-term immunity. [ 2 ] [ 13 ] [ 14 ] Vaccine contraindications may prevent certain individuals from being vaccinated. [ 10 ] In addition to not being immune, individuals in one of these groups may be at a greater risk of developing complications from infection because of their medical status, but they may still be protected if a large enough percentage of the population is immune. [ 9 ] [ 10 ] [ 14 ] [ 15 ]
High levels of immunity in one age group can create herd immunity for other age groups. [ 7 ] Vaccinating adults against pertussis reduces pertussis incidence in infants too young to be vaccinated, who are at the greatest risk of complications from the disease. [ 16 ] [ 17 ] This is especially important for close family members, who account for most of the transmissions to young infants. [ 7 ] [ 14 ] In the same manner, children receiving vaccines against pneumococcus reduces pneumococcal disease incidence among younger, unvaccinated siblings. [ 18 ] Vaccinating children against pneumococcus and rotavirus has had the effect of reducing pneumococcus - and rotavirus -attributable hospitalizations for older children and adults, who do not normally receive these vaccines. [ 18 ] [ 19 ] [ 20 ] Influenza (flu) is more severe in the elderly than in younger age groups, but influenza vaccines lack effectiveness in this demographic due to a waning of the immune system with age. [ 7 ] [ 21 ] The prioritization of school-age children for seasonal flu immunization, which is more effective than vaccinating the elderly, however, has been shown to create a certain degree of protection for the elderly. [ 7 ] [ 21 ]
For sexually transmitted infections (STIs), high levels of immunity in heterosexuals of one sex induces herd immunity for heterosexuals of both sexes. [ 22 ] [ 23 ] [ 24 ] Vaccines against STIs that are targeted at heterosexuals of one sex result in significant declines in STIs in heterosexuals of both sexes if vaccine uptake in the target sex is high. [ 23 ] [ 24 ] [ 25 ] Herd immunity from female vaccination does not, however, extend to males who have sex with males. [ 24 ] High-risk behaviors make eliminating STIs difficult because, even though most infections occur among individuals with moderate risk, the majority of transmissions occur because of individuals who engage in high-risk behaviors. [ 22 ] For this reason, in certain populations it may be necessary to immunize high-risk individuals regardless of sex. [ 22 ] [ 24 ]
Herd immunity itself acts as an evolutionary pressure on pathogens, influencing viral evolution by encouraging the production of novel strains, referred to as escape mutants, that are able to evade herd immunity and infect previously immune individuals. [ 26 ] [ 27 ] The evolution of new strains is known as serotype replacement, or serotype shifting, as the prevalence of a specific serotype declines due to high levels of immunity, allowing other serotypes to replace it. [ 28 ] [ 29 ]
At the molecular level, viruses escape from herd immunity through antigenic drift , which is when mutations accumulate in the portion of the viral genome that encodes for the virus's surface antigen , typically a protein of the virus capsid , producing a change in the viral epitope . [ 30 ] [ 31 ] Alternatively, the reassortment of separate viral genome segments, or antigenic shift , which is more common when there are more strains in circulation, can also produce new serotypes . [ 26 ] [ 32 ] When either of these occur, memory T cells no longer recognize the virus, so people are not immune to the dominant circulating strain. [ 31 ] [ 32 ] For both influenza and norovirus , epidemics temporarily induce herd immunity until a new dominant strain emerges, causing successive waves of epidemics. [ 30 ] [ 32 ] As this evolution poses a challenge to herd immunity, broadly neutralizing antibodies and "universal" vaccines that can provide protection beyond a specific serotype are in development. [ 27 ] [ 33 ] [ 34 ]
Initial vaccines against Streptococcus pneumoniae significantly reduced nasopharyngeal carriage of vaccine serotypes (VTs), including antibiotic-resistant types, [ 18 ] [ 35 ] only to be entirely offset by increased carriage of non-vaccine serotypes (NVTs). [ 18 ] [ 28 ] [ 29 ] This did not result in a proportionate increase in disease incidence though, since NVTs were less invasive than VTs. [ 28 ] Since then, pneumococcal vaccines that provide protection from the emerging serotypes have been introduced and have successfully countered their emergence. [ 18 ] The possibility of future shifting remains, so further strategies to deal with this include expansion of VT coverage and the development of vaccines that use either killed whole-cells , which have more surface antigens, or proteins present in multiple serotypes. [ 18 ] [ 36 ]
If herd immunity has been established and maintained in a population for a sufficient time, the disease is inevitably eliminated – no more endemic transmissions occur. [ 5 ] If elimination is achieved worldwide and the number of cases is permanently reduced to zero, then a disease can be declared eradicated. [ 6 ] Eradication can thus be considered the final effect or end-result of public health initiatives to control the spread of contagious disease. [ 6 ] [ 7 ] In cases in which herd immunity is compromised, on the contrary, disease outbreaks among the unvaccinated population are likely to occur. [ 37 ]
The benefits of eradication include ending all morbidity and mortality caused by the disease, financial savings for individuals, health care providers, and governments, and enabling resources used to control the disease to be used elsewhere. [ 6 ] To date, two diseases have been eradicated using herd immunity and vaccination: rinderpest and smallpox . [ 2 ] [ 7 ] [ 38 ] Eradication efforts that rely on herd immunity are currently underway for poliomyelitis , though civil unrest and distrust of modern medicine have made this difficult. [ 2 ] [ 39 ] Mandatory vaccination may be beneficial to eradication efforts if not enough people choose to get vaccinated. [ 40 ] [ 41 ] [ 42 ] [ 43 ]
Herd immunity is vulnerable to the free rider problem . [ 44 ] Individuals who lack immunity, including those who choose not to vaccinate, free ride off the herd immunity created by those who are immune. [ 44 ] As the number of free riders in a population increases, outbreaks of preventable diseases become more common and more severe due to loss of herd immunity. [ 45 ] [ 46 ] [ 47 ] [ 41 ] [ 43 ] Individuals may choose to free ride or be hesitant to vaccinate for a variety of reasons, including the belief that vaccines are ineffective, [ 48 ] or that the risks associated with vaccines are greater than those associated with infection, [ 2 ] [ 46 ] [ 47 ] [ 48 ] mistrust of vaccines or public health officials, [ 49 ] bandwagoning or groupthinking , [ 41 ] [ 50 ] social norms or peer pressure , [ 48 ] and religious beliefs. [ 46 ] Certain individuals are more likely to choose not to receive vaccines if vaccination rates are high enough to convince a person that he or she may not need to be vaccinated, since a sufficient percentage of others are already immune. [ 2 ] [ 43 ]
Individuals who are immune to a disease act as a barrier in the spread of disease, slowing or preventing the transmission of disease to others. [ 51 ] An individual's immunity can be acquired via a natural infection or through artificial means, such as vaccination. [ 51 ] When a critical proportion of the population becomes immune, called the herd immunity threshold (HIT) or herd immunity level (HIL), the disease may no longer persist in the population, ceasing to be endemic . [ 5 ] [ 26 ]
The theoretical basis for herd immunity generally assumes that vaccines induce solid immunity, that populations mix at random, that the pathogen does not evolve to evade the immune response, and that there is no non-human vector for the disease. [ 2 ]
The critical value, or threshold, in a given population, is the point where the disease reaches an endemic steady state , which means that the infection level is neither growing nor declining exponentially . This threshold can be calculated from the effective reproduction number R e , which is obtained by taking the product of the basic reproduction number R 0 , the average number of new infections caused by each case in an entirely susceptible population that is homogeneous, or well-mixed, meaning each individual is equally likely to come into contact with any other susceptible individual in the population, [ 22 ] [ 26 ] [ 40 ] and S , the proportion of the population who are susceptible to infection, and setting this product to be equal to 1:
S can be rewritten as (1 − p ), where p is the proportion of the population that is immune so that p + S equals one. Then, the equation can be rearranged to place p by itself as follows: [ citation needed ]
With p being by itself on the left side of the equation, it can be renamed as p c , representing the critical proportion of the population needed to be immune to stop the transmission of disease, which is the same as the "herd immunity threshold" HIT. [ 22 ] R 0 functions as a measure of contagiousness, so low R 0 values are associated with lower HITs, whereas higher R 0 s result in higher HITs. [ 26 ] [ 40 ] For example, the HIT for a disease with an R 0 of 2 is theoretically only 50%, whereas a disease with an R 0 of 10 the theoretical HIT is 90%. [ 26 ]
When the effective reproduction number R e of a contagious disease is reduced to and sustained below 1 new individual per infection, the number of cases occurring in the population gradually decreases until the disease has been eliminated. [ 22 ] [ 26 ] [ 52 ] If a population is immune to a disease in excess of that disease's HIT, the number of cases reduces at a faster rate, outbreaks are even less likely to happen, and outbreaks that occur are smaller than they would be otherwise. [ 2 ] [ 22 ] If the population immunity falls below the herd immunity threshold, where the effective reproduction number increases to above 1, the population is said to have an "immunity gap", [ 53 ] and then the disease is neither in a steady state nor decreasing in incidence , but is actively spreading through the population and infecting a larger number of people than usual. [ 41 ] [ 52 ]
An assumption in these calculations is that populations are homogeneous, or well-mixed, meaning that every individual is equally likely to come into contact with any other individual, when in reality populations are better described as social networks as individuals tend to cluster together, remaining in relatively close contact with a limited number of other individuals. In these networks, transmission only occurs between those who are geographically or physically close to one another. [ 2 ] [ 40 ] [ 41 ] The shape and size of a network is likely to alter a disease's HIT, making incidence either more or less common. [ 26 ] [ 40 ] Mathematical models can use contact matrices to estimate the likelihood of encounters and thus transmission. [ 54 ]
In heterogeneous populations, R 0 is considered to be a measure of the number of cases generated by a "typical" contagious person, which depends on how individuals within a network interact with each other. [ 2 ] Interactions within networks are more common than between networks, in which case the most highly connected networks transmit disease more easily, resulting in a higher R 0 and a higher HIT than would be required in a less connected network. [ 2 ] [ 41 ] In networks that either opt not to become immune or are not immunized sufficiently, diseases may persist despite not existing in better-immunized networks. [ 41 ]
The cumulative proportion of individuals who get infected during the course of a disease outbreak can exceed the HIT. This is because the HIT does not represent the point at which the disease stops spreading, but rather the point at which each infected person infects fewer than one additional person on average. When the HIT is reached, the number of additional infections does not immediately drop to zero. The excess of the cumulative proportion of infected individuals over the theoretical HIT is known as the overshoot . [ 77 ] [ 78 ] [ 79 ]
The primary way to boost levels of immunity in a population is through vaccination. [ 2 ] [ 80 ] Vaccination is originally based on the observation that milkmaids exposed to cowpox were immune to smallpox, so the practice of inoculating people with the cowpox virus began as a way to prevent smallpox. [ 39 ] Well-developed vaccines provide protection in a far safer way than natural infections, as vaccines generally do not cause the diseases they protect against and severe adverse effects are significantly less common than complications from natural infections. [ 81 ] [ 82 ]
The immune system does not distinguish between natural infections and vaccines, forming an active response to both, so immunity induced via vaccination is similar to what would have occurred from contracting and recovering from the disease. [ 83 ] To achieve herd immunity through vaccination, vaccine manufacturers aim to produce vaccines with low failure rates, and policy makers aim to encourage their use . [ 80 ] After the successful introduction and widespread use of a vaccine, sharp declines in the incidence of diseases it protects against can be observed, which decreases the number of hospitalizations and deaths caused by such diseases. [ 84 ] [ 85 ] [ 86 ]
Assuming a vaccine is 100% effective, then the equation used for calculating the herd immunity threshold can be used for calculating the vaccination level needed to eliminate a disease, written as V c . [ 2 ] Vaccines are usually imperfect however, so the effectiveness, E , of a vaccine must be accounted for:
From this equation, it can be observed that if E is less than (1 − 1/ R 0 ), then it is impossible to eliminate a disease, even if the entire population is vaccinated. [ 2 ] Similarly, waning vaccine-induced immunity, as occurs with acellular pertussis vaccines , requires higher levels of booster vaccination to sustain herd immunity. [ 2 ] [ 16 ] If a disease has ceased to be endemic to a population, then natural infections no longer contribute to a reduction in the fraction of the population that is susceptible. Only vaccination contributes to this reduction. [ 22 ] The relation between vaccine coverage and effectiveness and disease incidence can be shown by subtracting the product of the effectiveness of a vaccine and the proportion of the population that is vaccinated, p v , from the herd immunity threshold equation as follows:
It can be observed from this equation that, all other things being equal (" ceteris paribus "), any increase in either vaccine coverage or vaccine effectiveness, including any increase in excess of a disease's HIT, further reduces the number of cases of a disease. [ 22 ] The rate of decline in cases depends on a disease's R 0 , with diseases with lower R 0 values experiencing sharper declines. [ 22 ]
Vaccines usually have at least one contraindication for a specific population for medical reasons, but if both effectiveness and coverage are high enough then herd immunity can protect these individuals. [ 8 ] [ 12 ] [ 15 ] Vaccine effectiveness is often, but not always, adversely affected by passive immunity, [ 87 ] [ 88 ] so additional doses are recommended for some vaccines while others are not administered until after an individual has lost his or her passive immunity. [ 11 ] [ 15 ]
Individual immunity can also be gained passively, when antibodies to a pathogen are transferred from one individual to another. This can occur naturally, whereby maternal antibodies, primarily immunoglobulin G antibodies, are transferred across the placenta and in colostrum to fetuses and newborns. [ 89 ] [ 90 ] Passive immunity can also be gained artificially, when a susceptible person is injected with antibodies from the serum or plasma of an immune person. [ 83 ] [ 91 ]
Protection generated from passive immunity is immediate, but wanes over the course of weeks to months, so any contribution to herd immunity is temporary. [ 5 ] [ 83 ] [ 92 ] For diseases that are especially severe among fetuses and newborns, such as influenza and tetanus, pregnant women may be immunized in order to transfer antibodies to the child. [ 8 ] [ 93 ] [ 94 ] In the same way, high-risk groups that are either more likely to experience infection, or are more likely to develop complications from infection, may receive antibody preparations to prevent these infections or to reduce the severity of symptoms. [ 91 ]
Herd immunity is often accounted for when conducting cost–benefit analyses of vaccination programs. It is regarded as a positive externality of high levels of immunity, producing an additional benefit of disease reduction that would not occur had no herd immunity been generated in the population. [ 95 ] [ 96 ] Therefore, herd immunity's inclusion in cost–benefit analyses results both in more favorable cost-effectiveness or cost–benefit ratios, and an increase in the number of disease cases averted by vaccination. [ 96 ] Study designs done to estimate herd immunity's benefit include recording disease incidence in households with a vaccinated member, randomizing a population in a single geographic area to be vaccinated or not, and observing the incidence of disease before and after beginning a vaccination program. [ 97 ] From these, it can be observed that disease incidence may decrease to a level beyond what can be predicted from direct protection alone, indicating that herd immunity contributed to the reduction. [ 97 ] When serotype replacement is accounted for, it reduces the predicted benefits of vaccination. [ 96 ]
Herd immunity was recognized as a naturally occurring phenomenon in the 1930s when it was observed that after a significant number of children had become immune to measles , the number of new infections temporarily decreased. [ 98 ] Mass vaccination to induce herd immunity has since become common and proved successful in preventing the spread of many contagious diseases. [ 22 ] Opposition to vaccination has posed a challenge to herd immunity, allowing preventable diseases to persist in or return to populations with inadequate vaccination rates. [ 45 ] [ 46 ] [ 47 ]
The exact herd immunity threshold (HIT) varies depending on the basic reproduction number of the disease. An example of a disease with a high threshold was the measles, with a HIT exceeding 95%. [ 99 ]
The term "herd immunity" was first used in 1894 by American veterinary scientist and then Chief of the Bureau of Animal Industry of the US Department of Agriculture Daniel Elmer Salmon to describe the healthy vitality and resistance to disease of well-fed herds of hogs. In 1916 veterinary scientists inside the same Bureau of Animal Industry used the term to refer to the immunity arising following recovery in cattle infected with brucellosis, also known as "contagious abortion." By 1923 it was being used by British bacteriologists to describe experimental epidemics with mice, experiments undertaken as part of efforts to model human epidemic disease. By the end of the 1920s the concept was used extensively - particularly among British scientists - to describe the build up of immunity in populations to diseases such as diphtheria, scarlet fever, and influenza. [ 100 ] Herd immunity was recognized as a naturally occurring phenomenon in the 1930s when A. W. Hedrich published research on the epidemiology of measles in Baltimore , and took notice that after many children had become immune to measles, the number of new infections temporarily decreased, including among susceptible children. [ 101 ] [ 98 ] In spite of this knowledge, efforts to control and eliminate measles were unsuccessful until mass vaccination using the measles vaccine began in the 1960s. [ 98 ] Mass vaccination, discussions of disease eradication, and cost–benefit analyses of vaccination subsequently prompted more widespread use of the term herd immunity . [ 2 ] In the 1970s, the theorem used to calculate a disease's herd immunity threshold was developed. [ 2 ] During the smallpox eradication campaign in the 1960s and 1970s, the practice of ring vaccination , to which herd immunity is integral, began as a way to immunize every person in a "ring" around an infected individual to prevent outbreaks from spreading. [ 102 ]
Since the adoption of mass and ring vaccination, complexities and challenges to herd immunity have arisen. [ 2 ] [ 80 ] Modeling of the spread of contagious disease originally made a number of assumptions, namely that entire populations are susceptible and well-mixed, which is not the case in reality, so more precise equations have been developed. [ 2 ] In recent decades, it has been recognized that the dominant strain of a microorganism in circulation may change due to herd immunity, either because of herd immunity acting as an evolutionary pressure or because herd immunity against one strain allowed another already-existing strain to spread. [ 30 ] [ 29 ] Emerging or ongoing fears and controversies about vaccination have reduced or eliminated herd immunity in certain communities, allowing preventable diseases to persist in or return to these communities. [ 45 ] [ 46 ] [ 47 ] | https://en.wikipedia.org/wiki/Herd_immunity |
A hereditary carrier ( genetic carrier or just carrier ), is a person or other organism that has inherited a recessive allele for a genetic trait or mutation but usually does not display that trait or show symptoms of the disease . Carriers are, however, able to pass the allele onto their offspring, who may then express the genetic trait.
Autosomal dominant-recessive inheritance is made possible by the fact that the individuals of most species (including all higher animals and plants) have two alleles of most hereditary predispositions because the chromosomes in the cell nucleus are usually present in pairs ( diploid ). Carriers can be female or male as the autosomes are homologous independently from the sex.
In carriers the expression of a certain characteristic is recessive. The individual has both a genetic predisposition for the dominant trait and a genetic predisposition for the recessive trait, and the dominant expression prevails in the phenotype . In an individual which is heterozygous regarding a certain allele, it is not externally recognisable that it also has the recessive allele. But if the carrier has a child, the recessive trait appears in the phenotype, in case the descendant receives the recessive allele from both parents and therefore does not possess the dominant allele that would cover the recessive trait. According to Mendelian Law of Segregation of genes an average of 25% of the offspring become homozygous and express the recessive trait. Carriers can either pass on normal autosomal recessive hereditary traits or an autosomal recessive hereditary disease .
Gonosomal recessive genes are also passed on by carriers. The term is used in human genetics in cases of hereditary traits in which the observed trait lies on the female sex chromosome , the X chromosome . These are sex-linked genes. The carriers are always women . Women have two homologous sex chromosomes (XX). Men cannot be carriers because they only have one X chromosome. If a man has a certain recessive genetic disposition on his X chromosome, this is called hemizygous and it gets phenotypically expressed.
Although the Y chromosome is not a really homologous chromosome and carries relatively little genetic information compared to X chromosomes, a genetic component on the Y chromosome can come to expression because there is no homologous chromosome with an allele which could overlay it.
Examples of traits inherited via the X chromosome are color blindness and the most common hereditary form of haemophilia which therefore affect men much more often than women. [ 1 ] [ 2 ]
Queen Victoria , and her daughters Princesses Alice and Beatrix, were carriers of the hemophilia gene (an abnormal allele of a gene, necessary to produce one of the blood clotting factors). Both had children who continued to pass on the gene to succeeding generations of the royal houses of Spain and Russia , into which they married. [ 3 ] Since males only have one X chromosome, males who carried the altered gene had hemophilia B. Those female children who inherited the altered gene were asymptomatic carriers who also would have passed it to half of their children.
Gonosomal dominant inheritances are also known. There are no carriers since owners of a dominant hereditary disposition phenotypically express the trait in each case. | https://en.wikipedia.org/wiki/Hereditary_carrier |
In mathematics, a hereditary property is a property of an object that is inherited by all of its subobjects, where the meaning of subobject depends on the context. These properties are particularly considered in topology and graph theory , but also in set theory .
In topology , a topological property is said to be hereditary if whenever a topological space has that property, then so does every subspace of it. If the latter is true only for closed subspaces , then the property is called weakly hereditary or closed-hereditary .
For example, second countability and metrisability are hereditary properties. Sequentiality and Hausdorff compactness are weakly hereditary, but not hereditary. [ 1 ] Connectivity is not weakly hereditary.
If P is a property of a topological space X and every subspace also has property P , then X is said to be "hereditarily P ".
Hereditary properties occur throughout combinatorics and graph theory, although they are known by a variety of names. For example, in the context of permutation patterns , hereditary properties are typically called permutation classes .
In graph theory , a hereditary property usually means a property of a graph which also holds for (is "inherited" by) its induced subgraphs . [ 2 ] Equivalently, a hereditary property is preserved by the removal of vertices. A graph class G {\displaystyle {\mathcal {G}}} is called hereditary if it is closed under induced subgraphs. Examples of hereditary graph classes are independent graphs (graphs with no edges), which is a special case (with c = 1) of being c -colorable for some number c , being forests , planar , complete , complete multipartite etc.
Sometimes the term "hereditary" has been defined with reference to graph minors ; then it may be called a minor-hereditary property. The Robertson–Seymour theorem implies that a minor-hereditary property may be characterized in terms of a finite set of forbidden minors .
The term "hereditary" has been also used for graph properties that are closed with respect to taking subgraphs. [ 3 ] In such a case, properties that are closed with respect to taking induced subgraphs, are called induced-hereditary . The language of hereditary properties and induced-hereditary properties provides a powerful tool for study of structural properties of various types of generalized colourings . The most important result from this area is the unique factorization theorem. [ 4 ]
There is no consensus for the meaning of " monotone property " in graph theory. Examples of definitions are:
The complementary property of a property that is preserved by the removal of edges is preserved under the addition of edges. Hence some authors avoid this ambiguity by saying a property A is monotone if A or A C (the complement of A) is monotone. [ 8 ] Some authors choose to resolve this by using the term increasing monotone for properties preserved under the addition of some object, and decreasing monotone for those preserved under the removal of the same object.
In a matroid , every subset of an independent set is again independent. This is a hereditary property of sets.
A family of matroids may have a hereditary property. For instance, a family that is closed under taking matroid minors may be called "hereditary".
In planning and problem solving , or more formally one-person games , the search space is seen as a directed graph with states as nodes, and transitions as edges. States can have properties, and such a property P is hereditary if for each state S that has P, each state that can be reached from S also has P.
The subset of all states that have P plus the subset of all states that have ~P form a partition of the set of states called a hereditary partition . This notion can trivially be extended to more discriminating partitions by instead of properties, considering aspects of states and their domains. If states have an aspect A , with d i ⊂ D a partition of the domain D of A , then the subsets of states for which A ∈ d i form a hereditary partition of the total set of states iff ∀ i , from any state where A ∈ d i only other states where A ∈ d i can be reached.
If the current state and the goal state are in different elements of a hereditary partition, there is no path from the current state to the goal state — the problem has no solution.
Can a checkers board be covered with domino tiles, each of which covers exactly two adjacent fields? Yes. What if we remove the top left and the bottom right field? Then no covering is possible any more, because the difference between number of uncovered white fields and the number of uncovered black fields is 2, and adding a domino tile (which covers one white and one black field) keeps that number at 2. For a total covering the number is 0, so a total covering cannot be reached from the start position.
This notion was first introduced by Laurent Siklóssy and Roach. [ 9 ]
In model theory and universal algebra , a class K of structures of a given signature is said to have the hereditary property if every substructure of a structure in K is again in K . A variant of this definition is used in connection with Fraïssé's theorem : A class K of finitely generated structures has the hereditary property if every finitely generated substructure is again in K . See age .
Recursive definitions using the adjective "hereditary" are often encountered in set theory .
A set is said to be hereditary (or pure ) if all of its elements are hereditary sets. It is vacuously true that the empty set is a hereditary set, and thus the set { ∅ } {\displaystyle \{\varnothing \}} containing only the empty set ∅ {\displaystyle \varnothing } is a hereditary set, and recursively so is { ∅ , { ∅ } } {\displaystyle \{\varnothing ,\{\varnothing \}\}} , for example. In formulations of set theory that are intended to be interpreted in the von Neumann universe or to express the content of Zermelo–Fraenkel set theory , all sets are hereditary, because the only sort of object that is even a candidate to be an element of a set is another set. Thus the notion of hereditary set is interesting only in a context in which there may be urelements .
A couple of notions are defined analogously:
Based on the above, it follows that in ZFC a more general notion can be defined for any predicate Φ ( x ) {\displaystyle \Phi (x)} . A set x is said to have hereditarily the property Φ ( x ) {\displaystyle \Phi (x)} if x itself and all members of its transitive closure satisfy Φ ( y ) {\displaystyle \Phi (y)} , i.e. x ∪ t c ( x ) ⊆ { y : Φ ( y ) } {\displaystyle x\cup \mathop {\rm {tc}} (x)\subseteq \{y:\Phi (y)\}} . Equivalently, x hereditarily satisfies Φ ( x ) {\displaystyle \Phi (x)} iff it is a member of a transitive subset of { y : Φ ( y ) } . {\displaystyle \{y:\Phi (y)\}.} [ 10 ] [ 11 ] A property (of a set) is thus said to be hereditary if it is inherited by every subset. For example, being well-ordered is a hereditary property, and so it being finite. [ 12 ]
If we instantiate in the above schema Φ ( x ) {\displaystyle \Phi (x)} with " x has cardinality less than κ", we obtain the more general notion of a set being hereditarily of cardinality less than κ, usually denoted by H κ {\displaystyle H_{\kappa }} [ 13 ] or H ( κ ) {\displaystyle H(\kappa )} . We regain the two simple notions we introduced above as H ( ω ) {\displaystyle H(\omega )} being the set of hereditarily finite sets and H ( ω 1 ) {\displaystyle H(\omega _{1})} being the set of hereditarily countable sets. [ 14 ] ( ω 1 {\displaystyle \omega _{1}} is the first uncountable ordinal .) | https://en.wikipedia.org/wiki/Hereditary_property |
Heredity , also called inheritance or biological inheritance , is the passing on of traits from parents to their offspring; either through asexual reproduction or sexual reproduction , the offspring cells or organisms acquire the genetic information of their parents. Through heredity, variations between individuals can accumulate and cause species to evolve by natural selection . The study of heredity in biology is genetics .
In humans, eye color is an example of an inherited characteristic: an individual might inherit the "brown-eye trait" from one of the parents. [ 1 ] Inherited traits are controlled by genes and the complete set of genes within an organism's genome is called its genotype . [ 2 ]
The complete set of observable traits of the structure and behavior of an organism is called its phenotype . These traits arise from the interaction of the organism's genotype with the environment . [ 3 ] As a result, many aspects of an organism's phenotype are not inherited. For example, suntanned skin derives from the interaction between a person's genotype and sunlight; [ 4 ] thus, suntans are not passed on to people's children. However, some people tan more easily than others, due to differences in their genotype: [ 5 ] a striking example is people with the inherited trait of albinism , who do not tan at all and are very sensitive to sunburn . [ 6 ]
Heritable traits are known to be passed from one generation to the next via DNA , a molecule that encodes genetic information. [ 2 ] DNA is a long polymer that incorporates four types of bases , which are interchangeable. The Nucleic acid sequence (the sequence of bases along a particular DNA molecule) specifies the genetic information: this is comparable to a sequence of letters spelling out a passage of text. [ 7 ] Before a cell divides through mitosis , the DNA is copied, so that each of the resulting two cells will inherit the DNA sequence. A portion of a DNA molecule that specifies a single functional unit is called a gene ; different genes have different sequences of bases. Within cells , the long strands of DNA form condensed structures called chromosomes . Organisms inherit genetic material from their parents in the form of homologous chromosomes , containing a unique combination of DNA sequences that code for genes. The specific location of a DNA sequence within a chromosome is known as a locus . If the DNA sequence at a particular locus varies between individuals, the different forms of this sequence are called alleles . DNA sequences can change through mutations , producing new alleles. If a mutation occurs within a gene, the new allele may affect the trait that the gene controls, altering the phenotype of the organism. [ 8 ]
However, while this simple correspondence between an allele and a trait works in some cases, most traits are more complex and are controlled by multiple interacting genes within and among organisms. [ 9 ] [ 10 ] Developmental biologists suggest that complex interactions in genetic networks and communication among cells can lead to heritable variations that may underlie some of the mechanics in developmental plasticity and canalization . [ 11 ]
Recent findings have confirmed important examples of heritable changes that cannot be explained by direct agency of the DNA molecule. These phenomena are classed as epigenetic inheritance systems that are causally or independently evolving over genes. Research into modes and mechanisms of epigenetic inheritance is still in its scientific infancy, but this area of research has attracted much recent activity as it broadens the scope of heritability and evolutionary biology in general. [ 12 ] DNA methylation marking chromatin , self-sustaining metabolic loops , gene silencing by RNA interference , and the three dimensional conformation of proteins (such as prions ) are areas where epigenetic inheritance systems have been discovered at the organismic level. [ 13 ] [ 14 ] Heritability may also occur at even larger scales. For example, ecological inheritance through the process of niche construction is defined by the regular and repeated activities of organisms in their environment. This generates a legacy of effect that modifies and feeds back into the selection regime of subsequent generations. Descendants inherit genes plus environmental characteristics generated by the ecological actions of ancestors. [ 15 ] Other examples of heritability in evolution that are not under the direct control of genes include the inheritance of cultural traits , group heritability , and symbiogenesis . [ 16 ] [ 17 ] [ 18 ] These examples of heritability that operate above the gene are covered broadly under the title of multilevel or hierarchical selection , which has been a subject of intense debate in the history of evolutionary science. [ 17 ] [ 19 ]
When Charles Darwin proposed his theory of evolution in 1859, one of its major problems was the lack of an underlying mechanism for heredity. [ 20 ] Darwin believed in a mix of blending inheritance and the inheritance of acquired traits ( pangenesis ). Blending inheritance would lead to uniformity across populations in only a few generations and then would remove variation from a population on which natural selection could act. [ 21 ] This led to Darwin adopting some Lamarckian ideas in later editions of On the Origin of Species and his later biological works. [ 22 ] Darwin's primary approach to heredity was to outline how it appeared to work (noticing that traits that were not expressed explicitly in the parent at the time of reproduction could be inherited, that certain traits could be sex-linked , etc.) rather than suggesting mechanisms. [ citation needed ]
Darwin's initial model of heredity was adopted by, and then heavily modified by, his cousin Francis Galton , who laid the framework for the biometric school of heredity. [ 23 ] Galton found no evidence to support the aspects of Darwin's pangenesis model, which relied on acquired traits. [ 24 ]
The inheritance of acquired traits was shown to have little basis in the 1880s when August Weismann cut the tails off many generations of mice and found that their offspring continued to develop tails. [ 25 ]
Scientists in Antiquity had a variety of ideas about heredity: Theophrastus proposed that male flowers caused female flowers to ripen; [ 26 ] Hippocrates speculated that "seeds" were produced by various body parts and transmitted to offspring at the time of conception; [ 27 ] and Aristotle thought that male and female fluids mixed at conception. [ 28 ] Aeschylus , in 458 BC, proposed the male as the parent, with the female as a "nurse for the young life sown within her". [ 29 ]
Ancient understandings of heredity transitioned to two debated doctrines in the 18th century. The Doctrine of Epigenesis and the Doctrine of Preformation were two distinct views of the understanding of heredity. The Doctrine of Epigenesis, originated by Aristotle , claimed that an embryo continually develops. The modifications of the parent's traits are passed off to an embryo during its lifetime. The foundation of this doctrine was based on the theory of inheritance of acquired traits . In direct opposition, the Doctrine of Preformation claimed that "like generates like" where the germ would evolve to yield offspring similar to the parents. The Preformationist view believed procreation was an act of revealing what had been created long before. However, this was disputed by the creation of the cell theory in the 19th century, where the fundamental unit of life is the cell, and not some preformed parts of an organism. Various hereditary mechanisms, including blending inheritance were also envisaged without being properly tested or quantified, and were later disputed. Nevertheless, people were able to develop domestic breeds of animals as well as crops through artificial selection. The inheritance of acquired traits also formed a part of early Lamarckian ideas on evolution. [ citation needed ]
During the 18th century, Dutch microscopist Antonie van Leeuwenhoek (1632–1723) discovered "animalcules" in the sperm of humans and other animals. [ 30 ] Some scientists speculated they saw a "little man" ( homunculus ) inside each sperm . These scientists formed a school of thought known as the "spermists". They contended the only contributions of the female to the next generation were the womb in which the homunculus grew, and prenatal influences of the womb. [ 31 ] An opposing school of thought, the ovists, believed that the future human was in the egg, and that sperm merely stimulated the growth of the egg. Ovists thought women carried eggs containing boy and girl children, and that the gender of the offspring was determined well before conception. [ 32 ]
An early research initiative emerged in 1878 when Alpheus Hyatt led an investigation to study the laws of heredity through compiling data on family phenotypes (nose size, ear shape, etc.) and expression of pathological conditions and abnormal characteristics, particularly with respect to the age of appearance. One of the projects aims was to tabulate data to better understand why certain traits are consistently expressed while others are highly irregular. [ 33 ]
The idea of particulate inheritance of genes can be attributed to the Moravian [ 34 ] monk Gregor Mendel who published his work on pea plants in 1865. However, his work was not widely known and was rediscovered in 1901. It was initially assumed that Mendelian inheritance only accounted for large (qualitative) differences, such as those seen by Mendel in his pea plants – and the idea of additive effect of (quantitative) genes was not realised until R.A. Fisher 's (1918) paper, " The Correlation Between Relatives on the Supposition of Mendelian Inheritance " Mendel's overall contribution gave scientists a useful overview that traits were inheritable. His pea plant demonstration became the foundation of the study of Mendelian Traits. These traits can be traced on a single locus. [ 35 ]
In the 1930s, work by Fisher and others resulted in a combination of Mendelian and biometric schools into the modern evolutionary synthesis . The modern synthesis bridged the gap between experimental geneticists and naturalists; and between both and palaeontologists, stating that: [ 36 ] [ 37 ]
The idea that speciation occurs after populations are reproductively isolated has been much debated. [ 38 ] In plants, polyploidy must be included in any view of speciation. Formulations such as 'evolution consists primarily of changes in the frequencies of alleles between one generation and another' were proposed rather later. The traditional view is that developmental biology (' evo-devo ') played little part in the synthesis, but an account of Gavin de Beer 's work by Stephen Jay Gould suggests he may be an exception. [ 39 ]
Almost all aspects of the synthesis have been challenged at times, with varying degrees of success. There is no doubt, however, that the synthesis was a great landmark in evolutionary biology. [ 40 ] It cleared up many confusions, and was directly responsible for stimulating a great deal of research in the post- World War II era.
Trofim Lysenko however caused a backlash of what is now called Lysenkoism in the Soviet Union when he emphasised Lamarckian ideas on the inheritance of acquired traits . This movement affected agricultural research and led to food shortages in the 1960s and seriously affected the USSR. [ 41 ]
There is growing evidence that there is transgenerational inheritance of epigenetic changes in humans [ 42 ] and other animals. [ 43 ]
The description of a mode of biological inheritance consists of three main categories:
These three categories are part of every exact description of a mode of inheritance in the above order. In addition, more specifications may be added as follows:
Determination and description of a mode of inheritance is also achieved primarily through statistical analysis of pedigree data. In case the involved loci are known, methods of molecular genetics can also be employed.
An allele is said to be dominant if it is always expressed in the appearance of an organism (phenotype) provided that at least one copy of it is present. For example, in peas the allele for green pods, G , is dominant to that for yellow pods, g . Thus pea plants with the pair of alleles either GG (homozygote) or Gg (heterozygote) will have green pods. The allele for yellow pods is recessive. The effects of this allele are only seen when it is present in both chromosomes, gg (homozygote). This derives from Zygosity , the degree to which both copies of a chromosome or gene have the same genetic sequence, in other words, the degree of similarity of the alleles in an organism. | https://en.wikipedia.org/wiki/Heredity |
The Herero and Nama genocide or Namibian genocide , [ 5 ] formerly known also as the Herero and Namaqua genocide , was a campaign of ethnic extermination and collective punishment waged against the Herero (Ovaherero) and the Nama peoples in German South West Africa (now Namibia ) by the German Empire . It was the first genocide to begin in the 20th century, [ 6 ] [ 7 ] [ 8 ] occurring between 1904 and 1908. [ 1 ] In January 1904, the Herero people, who were led by Samuel Maharero , and the Nama people, who were led by Captain Hendrik Witbooi , rebelled against German colonial rule . On 12 January 1904, they killed more than 100 German settlers in the area of Okahandja . [ 9 ]
In August 1904, German General Lothar von Trotha defeated the Ovaherero in the Battle of Waterberg and drove them into the desert of Omaheke , where most of them died of dehydration . In October, the Nama people also rebelled against the Germans, only to suffer a similar fate. Between 24,000 and 100,000 Hereros and 10,000 Nama were killed in the genocide. [ 10 ] The first phase of the genocide was characterized by widespread death from starvation and dehydration, due to the prevention of the Herero from leaving the Namib desert by German forces. Once defeated, thousands of Hereros and Namas were imprisoned in concentration camps , where the majority died of diseases, abuse, and exhaustion. [ 11 ] [ 12 ]
In 1985, the United Nations ' Whitaker Report classified the aftermath as an attempt to exterminate the Herero and Nama peoples of South West Africa , and therefore one of the earliest attempts at genocide in the 20th century. In 2004, the German government recognised the events in what a German minister qualified as an "apology" but ruled out financial compensation for the victims' descendants. [ 13 ] In July 2015, the German government and the speaker of the Bundestag officially called the events a "genocide"; however, it refused to consider reparations at that time. [ 14 ] [ 15 ] Despite this, the last batch of skulls and other remains of slaughtered tribesmen which were taken to Germany to promote racial superiority were taken back to Namibia in 2018, with Petra Bosse-Huber [ de ] , a German Protestant bishop, describing the event as "the first genocide of the 20th century". [ 16 ] [ 17 ]
In May 2021, the German government issued an official statement in which it said that Germany
"apologizes and bows before the descendants of the victims. Today, more than 100 years later, Germany asks for forgiveness for the sins of their forefathers. It is not possible to undo what has been done. But the suffering, inhumanity and pain inflicted on the tens of thousands of innocent men, women and children by Germany during the war in what is today Namibia must not be forgotten. It must serve as a warning against racism and genocide." [ 18 ]
The same year, the German government agreed to pay €1.1 billion over 30 years to fund projects in communities that were impacted by the genocide. [ 1 ]
The original inhabitants of what is now Namibia were the San and the Khoekhoe .
Herero, who speak a Bantu language , were originally a group of cattle herders who migrated into what is now Namibia during the mid-18th century. The Herero seized vast swathes of the arable upper plateaus which were ideal for cattle grazing. Agricultural duties, which were minimal, were assigned to enslaved Khoisan and Bushmen . Over the rest of the 18th century, the Herero slowly drove the Khoisan into the dry, rugged hills to the south and east. [ 19 ]
The Hereros were a pastoral people whose entire way of life centred on their cattle. The Herero language , while limited in its vocabulary for most areas, contains more than a thousand words for the colours and markings of cattle. The Hereros were content to live in peace as long as their cattle were safe and well-pastured, but became formidable warriors when their cattle were threatened. [ 20 ]
According to Robert Gaudi, "The newcomers, much taller and more fiercely warlike than the indigenous Khoisan people, were possessed of the fierceness that comes from basing one's way of life on a single source: everything they valued, all wealth and personal happiness, had to do with cattle. Regarding the care and protection of their herds, the Herero showed themselves utterly merciless, and far more 'savage' than the Khoisan had ever been. Because of their dominant ways and elegant bearing, the few Europeans who encountered Herero tribesmen in the early days regarded them as the region's 'natural aristocrats. ' " [ 21 ]
By the time of the Scramble for Africa , the area which was occupied by the Herero was known as Damaraland . The Nama were pastorals and traders and lived to the south of the Herero. [ 22 ] : 22
In 1883, Adolf Lüderitz , a German merchant, purchased a stretch of coast near Lüderitz Bay (Angra Pequena) from the reigning chief. The terms of the purchase were fraudulent, but the German government nonetheless established a protectorate over it. [ 23 ] At that time, it was the only overseas German territory deemed suitable for European settlement. [ 24 ]
Chief of the neighbouring Herero, Maharero rose to power by uniting all the Herero. [ 23 ] : 61 Faced with repeated attacks by the Khowesin, a clan of the Khoekhoe under Hendrik Witbooi , he signed a protection treaty on 21 October 1885 with Imperial Germany 's colonial governor Heinrich Ernst Göring (father of Hermann Göring ) but did not cede the land of the Herero. This treaty was renounced in 1888 due to lack of German support against Witbooi but it was reinstated in 1890. [ 25 ]
The Herero leaders repeatedly complained about violation of this treaty, as Herero women and girls were raped by Germans , a crime that the German judges and prosecutors were reluctant to punish. [ 26 ]
In 1890 Maharero's son, Samuel , signed a great deal of land over to the Germans in return for helping him to ascend to the Ovaherero throne, and to subsequently be established as paramount chief. [ 25 ] [ 23 ] : 29 German involvement in ethnic fighting ended in tenuous peace in 1894. [ 27 ] : 48 In that year, Theodor Leutwein became governor of the territory, which underwent a period of rapid development, while the German government sent the Schutztruppe (imperial colonial troops) to pacify the region. [ 28 ]
Both German colonial authorities and European settlers envisioned a predominantly white "new African Germany," wherein the native populations would be put onto reservations and their land distributed among settlers and companies. [ 29 ] Under German colonial rule, colonists were encouraged to seize land and cattle from the native Herero and Nama peoples and to subjugate them as slave laborers. [ 27 ] : 19, 34, 50, 149 [ 30 ] [ 31 ] : 8, 22 [ 32 ] [ 33 ] [ 34 ] : 147–149, 185–186, 209
Resentment brewed among the native populations over their loss of status and property to German ranchers arriving in South West Africa, and the dismantling of traditional political hierarchies. Previously ruling tribes were reduced to the same status as the other tribes they had previously ruled over and enslaved. This resentment contributed to the Herero Wars that began in 1904. [ 27 ] : 57 [ 31 ] : 3ff.
Major Theodor Leutwein , the Governor of German South West Africa , was well aware of the effect of the German colonial rule on Hereros. He later wrote: "The Hereros from early years were a freedom-loving people, courageous and proud beyond measure. On the one hand, there was the progressive extension of German rule over them, and on the other their own sufferings increasing from year to year." [ 35 ]
In January 1903, a German trader named Dietrich was walking from his homestead to the nearby town of Omaruru to buy a new horse. Halfway to Dietrich's destination, a wagon carrying the son of a Herero chief, his wife, and their son stopped by. In a common courtesy in Hereroland, the chief's son offered Dietrich a ride. [ 36 ]
That night, however, Dietrich got very drunk and after everyone was asleep, he attempted to rape the wife of the chief's son. When she resisted, Dietrich shot her dead. When he was tried for murder in Windhoek , Dietrich denied attempting to rape his victim. He alleged that he awoke thinking the camp was under attack and fired blindly into the darkness. The killing of the Herero woman, he claimed, was an unfortunate accident. The court acquitted him, alleging that Dietrich was suffering from "tropical fever" and temporary insanity . [ 36 ]
According to Leutwein, the murder "aroused extraordinary interest in Hereroland, especially since the murdered woman had been the wife of the son of a Chief and the daughter of another. Everywhere the question was asked: Have White people the right to shoot native women?" [ 36 ]
Governor Leutwein intervened. He had the Public Prosecutor appeal Dietrich's acquittal, a second trial took place (before the colony's supreme court), and this time Dietrich was found guilty of manslaughter and imprisoned. [ 35 ] The move prompted violent objections of German settlers who considered Leutwein a " race traitor ". [ citation needed ]
In 1903, some of the Nama clans rose in revolt under the leadership of Hendrik Witbooi . [ 28 ] A number of factors led the Herero to join them in January 1904.
One of the major issues was land rights. In 1903 the Herero learned of a plan to divide their territory with a railway line and set up reservations where they would be concentrated. [ 37 ] The Herero had already ceded more than a quarter of their 130,000 km 2 (50,000 sq mi) territory to German colonists by 1903, [ 27 ] : 60 before the Otavi railway line running from the African coast to inland German settlements was completed. [ 38 ] : 230 Completion of this line would have made the German colonies much more accessible and would have ushered a new wave of Europeans into the area. [ 39 ] : 133
Historian Horst Drechsler states that there was discussion of the possibility of establishing and placing the Herero in native reserves and that this was further proof of the German colonists' sense of ownership over the land. Drechsler illustrates the gap between the rights of a European and an African; the Reichskolonialbund (German Colonial League) held that, in regards to legal matters, the testimony of seven Africans was equivalent to that of a colonist. [ 39 ] : 132, 133 According to Bridgman, there were racial tensions underlying these developments; the average German colonist viewed native Africans as a lowly source of cheap labour, and others welcomed their extermination. [ 27 ] : 60
A new policy on debt collection , enforced in November 1903, also played a role in the uprising. For many years, the Herero population had fallen in the habit of borrowing money from colonist moneylenders at extreme interest rates (see usury ). For a long time, much of this debt went uncollected and accumulated, as most Herero had no means to pay. To correct this growing problem, Governor Leutwein decreed with good intentions that all debts not paid within the next year would be voided. [ 27 ] : 59 In the absence of hard cash, traders often seized cattle, or whatever objects of value they could get their hands on, as collateral . This fostered a feeling of resentment towards the Germans on the part of the Herero people, which escalated to hopelessness when they saw that German officials were sympathetic to the moneylenders who were about to lose what they were owed. [ 27 ] : 60
Racial tension was also at play. The German settlers often referred to black Africans as "baboons" and treated them with contempt. [ 27 ] : 62 [ 40 ]
One missionary reported: "The real cause of the bitterness among the Hereros toward the Germans is without question the fact that the average German looks down upon the natives as being about on the same level as the higher primates ('baboon' being their favourite term for the natives) and treat them like animals. The settler holds that the native has a right to exist only in so far as he is useful to the white man. This sense of contempt led the settlers to commit violence against the Hereros." [ 40 ]
The contempt manifested itself particularly in the concubinage of native women. In a practice referred to in Südwesterdeutsch as Verkafferung , native women were taken by male European traders and ranchers both willingly and by force. [ 40 ]
In 1903, the Hereros saw an opportunity to revolt. At that time, there was a distant Khoisan tribe in the south called the Bondelzwarts , who resisted German demands to register their guns. The Bondelzwarts engaged in a firefight with the German authorities which led to three Germans killed and a fourth wounded. The situation deteriorated further, and the governor of the Herero colony, Major Theodor Leutwein, went south to take personal command, leaving almost no troops in the north. [ 41 ]
The Herero revolted in early 1904, killing between 123 and 150 German settlers, as well as seven Boers and three women, [ 27 ] : 74 in what Nils Ole Oermann calls a "desperate surprise attack". [ 42 ]
The timing of their attack was carefully planned. After successfully asking a large Herero clan to surrender their weapons, Governor Leutwein was convinced that they and the rest of the native population were essentially pacified and so withdrew half of the German troops stationed in the colony. [ 27 ] : 56 Led by Chief Samuel Maharero , the Herero surrounded Okahandja and cut railroad and telegraph links to Windhoek , the colonial capital. Maharero then issued a manifesto in which he forbade his troops to kill any Englishmen, Boers, uninvolved peoples, women and children in general, or German missionaries. [ 27 ] : 70 The Herero revolts catalysed a separate revolt and attack on Fort Namutoni in the north of the country a few weeks later by the Ondonga . [ 43 ] [ 44 ]
A Herero warrior interviewed by German authorities in 1895 had described his people's traditional way of dealing with suspected cattle rustlers , a treatment which, during the uprising, was regularly extended to German soldiers and civilians, "We came across a few Khoisan whom of course we killed. I myself helped to kill one of them. First we cut off his ears, saying, 'You will never hear Herero cattle lowing.' Then we cut off his nose, saying, 'Never again shall you smell Herero cattle.' And then we cut off his lips, saying, 'You shall never again taste Herero cattle.' And finally we cut his throat." [ 45 ]
According to Robert Gaudi, "Leutwein knew that the wrath of the German Empire was about to fall on them and hoped to soften the blow. He sent desperate messages to Chief Samuel Maherero in hopes of negotiating an end to the war. In this, Leutwein acted on his own, heedless of the prevailing mood in Germany, which called for bloody revenge." [ 46 ]
The Hereros, however, were emboldened by their success and had come to believe that, "the Germans were too cowardly to fight in the open," and rejected Leutwein's offers of peace. [ 47 ]
One missionary wrote, "The Germans are filled with fearful hate. I must really call it a blood thirst against the Hereros. One hears nothing but talk of 'cleaning up,' 'executing,' 'shooting down to the last man,' 'no pardon,' etc." [ 47 ]
According to Robert Gaudi, "The Germans suffered more than defeat in the early months of 1904; they suffered humiliation, their brilliant modern army unable to defeat a rabble of 'half-naked savages.' Cries in the Reichstag , and from the Kaiser himself, for total eradication of the Hereros grew strident. When a leading member of the Social Democratic Party pointed out that the Hereros were as human as any German and possessed immortal souls, he was howled down by the entire conservative side of the legislature." [ 47 ]
Leutwein was forced to request reinforcements and an experienced officer from the German government in Berlin . [ 48 ] : 604 Lieutenant-General Lothar von Trotha was appointed commander-in-chief ( German : Oberbefehlshaber ) of South West Africa, arriving with an expeditionary force of 10,000 troops on 11 June. [ 49 ] [ 50 ]
Meanwhile, Leutwein was subordinate to the civilian Colonial Department of the Prussian Foreign Office, which was supported by Chancellor Bernhard von Bülow , while General Trotha reported to the military German General Staff , which was supported by Emperor Wilhelm II . [ 27 ] : 85 [ 51 ]
Leutwein wanted to defeat the most determined Herero rebels and negotiate a surrender with the remainder to achieve a political settlement. [ 48 ] : 605 Trotha, however, planned to crush the native resistance through military force. He stated that:
My intimate knowledge of many central African nations (Bantu and others) has everywhere convinced me of the necessity that the Negro does not respect treaties but only brute force. [ 23 ] : 173
By late spring of 1904, German troops were pouring into the colony. In August 1904, the main Herero forces were surrounded and crushed at the Battle of Waterberg . [ 41 ] : 21
In 1900, Kaiser Wilhelm II had been enraged by the killing of Baron Clemens von Ketteler , the Imperial German minister plenipotentiary in Beijing , during the Boxer Rebellion . The Kaiser took it as a personal insult from a people he viewed as racially inferior, all the more because of his obsession with the " Yellow Peril ". On 27 July 1900, the Kaiser gave the infamous Hunnenrede (Hun speech) in Bremerhaven to German soldiers being sent to Imperial China , ordering them to show the Boxers no mercy and to behave like Attila 's Huns . [ 52 ] General von Trotha had served in China, and was chosen in 1904 to command the expedition to German South West Africa precisely because of his record in China. [ 53 ] In 1904, the Kaiser was infuriated by the latest revolt in his colonial empire by a people whom he also viewed as inferior, and took the Herero rebellion as a personal insult, just as he had viewed the Boxers' assassination of Baron von Ketteler. [ 54 ] The tactless and bloodthirsty language that Wilhelm II used about the Herero people in 1904 is strikingly similar to the language he had used about the Chinese Boxers in 1900. [ 55 ] However, the Kaiser denied, together with Chancellor von Bülow, von Trotha's request to quickly quell the rebellion. [ 56 ]
No written order by Wilhelm II ordering or authorising genocide has survived. [ 54 ] In February 1945 an Allied bombing raid destroyed the building housing all of the documents of the Prussian Army from the Imperial period. [ 57 ] Despite this fact, surviving documents indicate that Trotha used the same tactics in Namibia that he had used in China, only on a much vaster scale. It is also known that throughout the genocide Trotha sent regular reports to both the General Staff and to the Kaiser. [ 58 ] Historian Jeremy-Sarkin Hughes believes that regardless of whether or not a written order was given, the Kaiser must have given General von Trotha verbal orders. [ 59 ] According to Hughes, the fact that Trotha was decorated and not court-martialed after the genocide became public knowledge lends support to the thesis that he was acting under orders. [ 60 ]
General von Trotha commented: "I know the tribes of Africa…. They are all alike. They only respond to force. It was and is my policy to use force with terrorism and even brutality. I shall annihilate the African tribes with streams of blood and streams of gold." [ 61 ] General von Trotha stated his proposed solution to end the resistance of the Herero people in a letter, before the Battle of Waterberg : [ 62 ] : 11
I believe that the nation as such should be annihilated, or, if this was not possible by tactical measures, have to be expelled from the country ... This will be possible if the water-holes from Grootfontein to Gobabis are occupied. The constant movement of our troops will enable us to find the small groups of this nation who have moved backwards and destroy them gradually.
Trotha's troops defeated 3,000–5,000 Herero combatants at the Battle of Waterberg on 11–12 August 1904 but were unable to encircle and annihilate the retreating survivors. [ 48 ] : 605
The pursuing German forces prevented groups of Herero from breaking from the main body of the fleeing force and pushed them further into the desert. As exhausted Herero fell to the ground, unable to go on, German soldiers killed men, women, and children. [ 63 ] : 22 Jan Cloete, acting as a guide for the Germans, witnessed the atrocities committed by the German troops and deposed the following statement: [ 39 ] : 157
I was present when the Herero were defeated in a battle in the vicinity of Waterberg. After the battle all men, women, and children who fell into German hands, wounded or otherwise, were mercilessly put to death. Then the Germans set off in pursuit of the rest, and all those found by the wayside and in the sandveld were shot down and bayoneted to death. The mass of the Herero men were unarmed and thus unable to offer resistance. They were just trying to get away with their cattle.
A portion of the Herero escaped the Germans and went to the Omaheke Desert , hoping to reach British Bechuanaland ; fewer than 1,000 Herero managed to reach Bechuanaland, where they were granted asylum by the British authorities. [ 64 ] To prevent them from returning, Trotha ordered the desert to be sealed off. [ 65 ] German patrols later found skeletons around holes 13 m (43 ft) deep that had been dug in a vain attempt to find water. Some sources also state that the German colonial army systematically poisoned desert water wells. [ 63 ] : 22 [ 66 ] Maherero and 500–1,500 men crossed the Kalahari into Bechuanaland where he was accepted as a vassal of the Batswana chief Sekgoma . [ 67 ]
On 2 October, Trotha issued a warning to the Herero: [ DE 1 ]
I, the great general of the German soldiers, send this letter to the Herero. The Herero are German subjects no longer. They have killed, stolen, cut off the ears and other parts of the body of wounded soldiers, and now are too cowardly to want to fight any longer. I announce to the people that whoever hands me one of the chiefs shall receive 1,000 marks, and 5,000 marks for Samuel Maherero. The Herero nation must now leave the country. If it refuses, I shall compel it to do so with the 'long tube' [cannon]. Any Herero found inside the German frontier, with or without a gun or cattle, will be executed. I shall spare neither women nor children. I shall give the order to drive them away and fire on them. Such are my words to the Herero people. [ 70 ]
He further gave orders that:
This proclamation is to be read to the troops at roll-call, with the addition that the unit that catches a captain will also receive the appropriate reward, and that the shooting at women and children is to be understood as shooting above their heads, so as to force them to run [away]. I assume absolutely that this proclamation will result in taking no more male prisoners, but will not degenerate into atrocities against women and children. The latter will run away if one shoots at them a couple of times. The troops will remain conscious of the good reputation of the German soldier. [ 31 ] : 56
Trotha gave orders that captured Herero males were to be executed , while women and children were to be driven into the desert where their death from starvation and thirst was to be certain; Trotha argued that there was no need to make exceptions for Herero women and children, since these would "infect German troops with their diseases", the insurrection Trotha explained "is and remains the beginning of a racial struggle". [ 48 ] : 605 After the war, Trotha argued that his orders were necessary, writing in 1909 that "If I had made the small water holes accessible to the womenfolk, I would run the risk of an African catastrophe comparable to the Battle of Beresonia ." [ 63 ] : 22
The German general staff was aware of the atrocities that were taking place; its official publication, named Der Kampf , noted that:
This bold enterprise shows up in the most brilliant light the ruthless energy of the German command in pursuing their beaten enemy. No pains, no sacrifices were spared in eliminating the last remnants of enemy resistance. Like a wounded beast the enemy was tracked down from one water-hole to the next, until finally he became the victim of his own environment. The arid Omaheke [desert] was to complete what the German army had begun: the extermination of the Herero nation. [ 71 ] [ 72 ]
Alfred von Schlieffen (Chief of the Imperial German General Staff ) approved of Trotha's intentions in terms of a "racial struggle" and the need to "wipe out the entire nation or to drive them out of the country", but had doubts about his strategy, preferring their surrender. [ 73 ]
Governor Leutwein, later relieved of his duties, complained to Chancellor von Bülow about Trotha's actions, seeing the general's orders as intruding upon the civilian colonial jurisdiction and ruining any chance of a political settlement. [ 48 ] : 606 According to Professor Mahmood Mamdani from Columbia University , opposition to the policy of annihilation was largely the consequence of the fact that colonial officials looked at the Herero people as a potential source of labour, and thus economically important. [ 62 ] : 12 For instance, Governor Leutwein wrote that:
I do not concur with those fanatics who want to see the Herero destroyed altogether ... I would consider such a move a grave mistake from an economic point of view. We need the Herero as cattle breeders ... and especially as labourers. [ 23 ] : 169
Having no authority over the military, Chancellor Bülow could only advise Emperor Wilhelm II that Trotha's actions were "contrary to Christian and humanitarian principle, economically devastating and damaging to Germany's international reputation". [ 48 ] : 606
Upon the arrival of new orders at the end of 1904, prisoners were herded into labor camps , where they were given to private companies as slave labourers or exploited as human guinea pigs in medical experiments. [ 3 ] [ 74 ]
Survivors of the massacre, the majority of whom were women and children, were eventually put in places like Shark Island concentration camp , where the German authorities forced them to work as slave labour for German military and settlers. All prisoners were categorised into groups fit and unfit for work, and pre-printed death certificates indicating "death by exhaustion following privation" were issued. [ 77 ] The British government published their well-known account of the German genocide of the Nama and Herero peoples in 1918. [ 78 ]
Many Herero and Nama died of disease, exhaustion, starvation and malnutrition. [ 8 ] [ 79 ] [ 80 ] Estimates of the mortality rate at the camps are between 45% [ 81 ] [ 82 ] and 74%. [ 34 ] : 196–216 [ 81 ] [ 82 ]
Food in the camps was extremely scarce, consisting of rice with no additions. [ 83 ] : 92 As the prisoners lacked pots and the rice they received was uncooked, it was indigestible; horses and oxen that died in the camp were later distributed to the inmates as food. [ 31 ] : 75 Dysentery and lung diseases were common. [ 31 ] : 76 Despite those conditions, the prisoners were taken outside the camp every day for labour under harsh treatment by the German guards, while the sick were left without any medical assistance or nursing care. [ 31 ] : 76 Many Herero and Nama were worked to death. [ 8 ]
Shootings, hangings, beatings, and other harsh treatment of the forced labourers (including use of sjamboks ) were common. [ 31 ] : 76 [ 84 ] A 28 September 1905 article in the South African newspaper Cape Argus detailed some of the abuse with the heading: "In German S. W. Africa: Further Startling Allegations: Horrible Cruelty". In an interview with Percival Griffith, "an accountant of profession, who owing to hard times, took up on transport work at Angra Pequena , Lüderitz ", related his experiences:
There are hundreds of them, mostly women and children and a few old men ... when they fall they are sjamboked by the soldiers in charge of the gang, with full force, until they get up ... On one occasion I saw a woman carrying a child of under a year old slung at her back, and with a heavy sack of grain on her head ... she fell. The corporal sjamboked her for certainly more than four minutes and sjamboked the baby as well ... the woman struggled slowly to her feet, and went on with her load. She did not utter a sound the whole time, but the baby cried very hard. [ 85 ]
During the war, a number of people from the Cape (in modern-day South Africa ) sought employment as transport riders for German troops in Namibia. Upon their return to the Cape, some of these people recounted their stories, including those of the imprisonment and genocide of the Herero and Nama people. Fred Cornell , an aspiring British diamond prospector, was in Lüderitz when the Shark Island concentration camp was being used. Cornell wrote of the camp:
Cold – for the nights are often bitterly cold there – hunger, thirst, exposure, disease and madness claimed scores of victims every day, and cartloads of their bodies were every day carted over to the back beach, buried in a few inches of sand at low tide, and as the tide came in the bodies went out, food for the sharks. [ 85 ] [ 86 ]
Shark Island was the most brutal of the German South West African camps. [ 87 ] Lüderitz lies in southern Namibia, flanked by desert and ocean. In the harbour lies Shark Island , which then was connected to the mainland only by a small causeway. The island is now, as it was then, barren and characterised by solid rock carved into surreal formations by the hard ocean winds. The camp was placed on the far end of the relatively small island, where the prisoners would have suffered complete exposure to the strong winds that sweep Lüderitz for most of the year. [ 85 ]
German Commander Ludwig von Estorff wrote in a report that approximately 1,700 prisoners (including 1,203 Nama) had died by April 1907. In December 1906, four months after their arrival, 291 Nama died (a rate of more than nine people per day). Missionary reports put the death rate at 12–18 per day; as many as 80% of the prisoners sent to Shark Island eventually died there. [ 85 ]
There are accusations of Herero women being coerced into sex slavery as a means of survival. [ 62 ] : 12 [ 88 ]
Trotha was opposed to contact between natives and settlers, believing that the insurrection was "the beginning of a racial struggle" and fearing that the colonists would be infected by native diseases. [ 48 ] : 606
Benjamin Madley argues that although Shark Island is referred to as a concentration camp, it functioned as an extermination camp or death camp. [ 89 ] [ 90 ] [ 91 ]
Prisoners were used for medical experiments and their illnesses or their recoveries from them were used for research. [ 92 ]
Experiments on live prisoners were performed by Dr. Bofinger, who injected Herero who were suffering from scurvy with various substances including arsenic and opium ; afterwards he researched the effects of these substances via autopsy. [ 22 ] : 225
Experimentation with the dead body parts of the prisoners was rife. Zoologist Leonhard Schultze [ de ] (1872–1955) noted taking "body parts from fresh native corpses" which according to him was a "welcome addition", and he also noted that he could use prisoners for that purpose. [ 93 ]
An estimated 300 skulls [ 94 ] were sent to Germany for experimentation, in part from concentration camp prisoners. [ 95 ] In October 2011, after three years of talks, the first 20 of an estimated 300 skulls stored in the museum of the Charité were returned to Namibia for burial. [ 96 ] [ 97 ] In 2014, 14 additional skulls were repatriated by the University of Freiburg . [ 98 ]
A census conducted in 1905 revealed that 25,000 Herero remained in German South West Africa . [ 38 ]
According to the Whitaker Report, the population of 80,000 Herero was reduced to 15,000 "starving refugees" between 1904 and 1907. [ 99 ] In Colonial Genocide and Reparations Claims in the 21st Century : The Socio-Legal Context of Claims under International Law by the Herero against Germany for Genocide in Namibia by Jeremy Sarkin-Hughes, a number of 100,000 victims is given. Up to 80% of the indigenous populations were killed. [ 100 ] [ 101 ]
Newspapers reported 65,000 victims when announcing that Germany recognized the genocide in 2004. [ 102 ] [ 103 ]
With the closure of concentration camps, all surviving Herero were distributed as labourers for settlers in the German colony. From that time on, all Herero over the age of seven were forced to wear a metal disc with their labour registration number, [ 62 ] : 12 and banned from owning land or cattle, a necessity for pastoral society. [ 83 ] : 89
About 19,000 German troops were engaged in the conflict, of which 3,000 saw combat. The rest were used for upkeep and administration. The German losses were 676 soldiers killed in combat, 76 missing, and 689 dead from disease. [ 31 ] : 88 The Reiterdenkmal (English: Equestrian Monument ) in Windhoek was erected in 1912 to celebrate the victory and to remember the fallen German soldiers and civilians. Until after Independence, no monument was built to the killed indigenous population. It remains a bone of contention in independent Namibia. [ 104 ]
The campaign cost Germany 600 million marks . The normal annual subsidy to the colony was 14.5 million marks. [ 31 ] : 88 [ 105 ] In 1908, diamonds were discovered in the territory, and this did much to boost its prosperity, though it was short-lived. [ 38 ] : 230
In 1915, during World War I , the German colony was taken over and occupied by the Union of South Africa , which was victorious in the South West Africa campaign . [ 106 ] South Africa received a League of Nations mandate over South West Africa on 17 December 1920. [ 107 ] [ 108 ]
The Herero genocide has commanded the attention of historians who study complex issues of continuity between the Herero genocide and the Holocaust . [ 109 ] It is argued that the Herero genocide set a precedent in Imperial Germany that would later be followed by Nazi Germany 's establishment of death camps . [ 110 ] [ 111 ]
According to Benjamin Madley, the German experience in South West Africa was a crucial precursor to Nazi colonialism and genocide. He argues that personal connections, literature, and public debates served as conduits for communicating colonialist and genocidal ideas and methods from the colony to Germany. [ 112 ] Tony Barta, an honorary research associate at La Trobe University , argues that the Herero genocide was an inspiration for Hitler in his war against the Jews , Slavs , Romani , and others whom he described as "non- Aryans ". [ 113 ]
According to Clarence Lusane , Eugen Fischer 's medical experiments can be seen as a testing ground for medical procedures which were later followed during the Nazi Holocaust . [ 81 ] Fischer later became chancellor of the University of Berlin , where he taught medicine to Nazi physicians. Otmar Freiherr von Verschuer was a student of Fischer, Verschuer himself had a prominent pupil, Josef Mengele . [ 114 ] [ 115 ] Franz Ritter von Epp , who was later responsible for the liquidation of virtually all Bavarian Jews and Roma as governor of Bavaria , took part in the Herero and Nama genocide as well. [ 116 ] Historians Robert Gerwarth and Stephan Malinowski have criticized this claim, asserting that Von Epp exercised no influence in Nazi extermination policies. [ 117 ]
Mahmood Mamdani argues that the links between the Herero genocide and the Holocaust are beyond the execution of an annihilation policy and the establishment of concentration camps and there are also ideological similarities in the conduct of both genocides. Focusing on a written statement by General Trotha which is translated as:
I destroy the African tribes with streams of blood ... Only following this cleansing can something new emerge, which will remain. [ 23 ] : 174
Mamdani takes note of the similarity between the aims of the General and the Nazis. According to Mamdani, in both cases there was a Social Darwinist notion of "cleansing", after which "something new" would "emerge". [ 62 ] : 12
Robert Gerwarth and Stephan Malinowski have questioned the supposed link with the Holocaust, finding it to be lacking in empirical evidence, and argue that Nazi policy represented a distinct turn away from typical European colonial practice. Additionally, they write that studies supporting the link completely ignore the influences of World War I, the German Revolution , and the activities of the Freikorps in the inurement of extreme violence as a method in the German political consciousness. [ 118 ]
Patrick Bernhard writes that the Nazis, including Heinrich Himmler , explicitly rejected the colonial experience of the German Empire as an "appallingly outdated" model; when they did draw inspiration from colonialism for Generalplan Ost , it was from the contemporary work of Italian fascists such as Giuseppe Tassinari in Libya , which they viewed as a shining example of fascist modernity . [ 119 ]
In 1985, the United Nations' Whitaker Report classified the massacres as an attempt to exterminate the Herero and Nama peoples of South West Africa , and therefore one of the earliest cases of genocide in the 20th century. [ 120 ]
In 1998, German President Roman Herzog visited Namibia and met Herero leaders. Chief Munjuku Nguvauva demanded a public apology and compensation. Herzog expressed regret but stopped short of an apology. He pointed out that international law requiring reparation did not exist in 1907, but he undertook to take the Herero petition back to the German government. [ 121 ]
On 16 August 2004, at the 100th anniversary of the start of the genocide, a member of the German government, Heidemarie Wieczorek-Zeul , Germany's Federal Minister for Economic Development and Cooperation , officially apologised and expressed grief about the genocide, declaring in a speech that:
We Germans accept our historical and moral responsibility and the guilt incurred by Germans at that time. [ 122 ]
She ruled out paying special compensations, but promised continued economic aid for Namibia which in 2004 amounted to $14M a year. [ 13 ] This number has been significantly increased since then, with the budget for the years 2016–17 allocating a sum total of €138M in monetary support payments. [ 123 ]
The Trotha family travelled to Omaruru in October 2007 by invitation of the royal Herero chiefs and publicly apologised for the actions of their relative. Wolf-Thilo von Trotha said:
We, the von Trotha family, are deeply ashamed of the terrible events that took place 100 years ago. Human rights were grossly abused that time. [ 124 ]
The Herero filed a lawsuit in the United States in 2001 demanding reparations from the German government and Deutsche Bank , which financed the German government and companies in Southern Africa. [ 125 ] [ 126 ] With a complaint filed with the United States District Court for the Southern District of New York in January 2017, descendants of the Herero and Nama people sued Germany for damages in the United States. The plaintiffs sued under the Alien Tort Statute , a 1789 U.S. law often invoked in human rights cases. Their proposed class-action lawsuit sought unspecified sums for thousands of descendants of the victims, for the "incalculable damages" that were caused. [ 127 ] [ 128 ] Germany seeks to rely on its state immunity as implemented in US law as the Foreign Sovereign Immunities Act , arguing that, as a sovereign nation, it cannot be sued in US courts in relation to its acts outside the United States. [ 129 ] In March 2019, the judge dismissed the claims due to the exceptions to sovereign immunity being too narrow for the case. [ 130 ]
In September 2020, the Second Circuit stated that the claimants did not prove that money used to buy property in New York could be traced back to wealth resulting from the seized property and therefore the lawsuit could not overcome Germany's immunity. In June 2021, the Supreme Court declined to hear a petition to revive the case. [ 131 ]
Germany, while admitting brutality in Namibia, at first refused to call it a "genocide", claiming that the term only became international law in 1945. However, in July 2015, then foreign minister Frank-Walter Steinmeier issued a political guideline stating that the massacre should be referred to as a "war crime and a genocide". Bundestag president Norbert Lammert wrote an article in Die Zeit that same month referring to the events as a genocide. These events paved the way for negotiations with Namibia. [ 132 ] [ 133 ] [ 134 ]
In 2015, the German government began negotiations with Namibia over a possible apology, and by 2016, Germany committed itself to apologizing for the genocide, as well as to refer to the event as a genocide; but the actual declaration was postponed while negotiations stalled over questions of compensation. [ 134 ] [ 135 ] [ 136 ]
On 11 August 2020, following negotiations over a potential compensation agreement between Germany and Namibia, President Hage Geingob of Namibia stated that the German government's offer was "not acceptable", while German envoy Ruprecht Polenz said he was "still optimistic that a solution can be found." [ 137 ]
On 28 May 2021, the German government announced that it was formally recognizing the atrocities committed as a genocide, following five years of negotiations. The declaration was made by foreign minister Heiko Maas , who also stated that Germany was asking Namibia and the descendants of the genocide victims for forgiveness. In addition to recognizing the events as a genocide, Germany agreed to give as a "gesture of recognition of the immeasurable suffering" €1.1 billion in aid to the communities impacted by the genocide. [ 138 ] [ 101 ]
Following the announcement, the agreement needs to be ratified by both countries' parliaments, after which Germany would send its president, Frank-Walter Steinmeier , to officially apologize for the genocide. The nations agreed not to use the term "reparation" to describe the financial aid package. [ 138 ] [ 101 ]
The agreement was criticized by the chairman of the Namibian Genocide Association, Laidlaw Peringanda, who insisted that Germany should purchase their ancestral lands back from the descendants of the German settlers and return it to the Herero and Nama people. The agreement was also criticized because negotiations were held solely between the German and Namibian governments, and did not include representatives of the Herero and Nama people. [ 138 ] [ 101 ]
Further criticism of the agreement came in 2024 with the filing of the South Africa v. Israel case at the International Court of Justice . After President Geingob criticized Germany's decision to back Israel in the case, Nandi Mazeingo of the Ovaherero Genocide Foundation called on Namibia to go further, saying "What South Africa did for Palestine is what Namibia must do for us as Hereros and Namas. They must go to that ICJ also, for us." [ 139 ]
Peter Katjavivi , a former Namibian ambassador to Germany, demanded in August 2008 that the skulls of Herero and Nama prisoners of the 1904–1908 uprising, which were taken to Germany for scientific research to claim the superiority of white Europeans over Africans, be returned to Namibia. Katjavivi was reacting to a German television documentary which reported that its investigators had found more than 40 of these skulls at two German universities, among them probably the skull of a Nama chief who had died on Shark Island near Lüderitz . [ 140 ] In September 2011, the skulls were returned to Namibia. [ 141 ] In August 2018, Germany returned all of the remaining skulls and other human remains which were examined in Germany to scientifically promote white supremacy. [ 16 ] [ 17 ] This was the third such transfer, and shortly before it occurred, German Protestant bishop Petra Bosse-Huber stated "Today, we want to do what should have been done many years ago – to give back to their descendents the remains of people who became victims of the first genocide of the 20th century." [ 16 ] [ 17 ]
On 17 May 2019, as a part of the repatriation process, the German government announced that it would return a stone symbol which it took from Namibia in the 1900s. [ 142 ]
[ 146 ]
"Dieser Erlaß ist bei den Appells den Truppen mitzuteilen mit dem Hinzufügen, daß auch der Truppe, die einen der Kapitäne fängt, die entsprechende Belohnung zu teil wird und daß das Schießen auf Weiber und Kinder so zu verstehen ist, daß über sie hinweggeschossen wird, um sie zum Laufen zu zwingen. Ich nehme mit Bestimmtheit an, daß dieser Erlaß dazu führen wird, keine männlichen Gefangenen mehr zu machen, aber nicht zu Grausamkeiten gegen Weiber und Kinder ausartet. Diese werden schon fortlaufen, wenn zweimal über sie hinweggeschossen wird. Die Truppe wird sich des guten Rufes der deutschen Soldaten bewußt bleiben." [ 68 ] [ 69 ] | https://en.wikipedia.org/wiki/Herero_and_Nama_genocide |
Heresthetic is a theoretical approach within political science that examines how political actors strategically manipulate the structure of political situations, decision-making processes, and agenda-setting to achieve favorable outcomes even when they lack majority support. [ 1 ] The term was coined by political scientist William H. Riker in the 1980s, combining the Greek words "hairesis" (choosing) and "rhetoric" to describe tactics beyond mere persuasion. [ 2 ]
Heresthetic belongs to the tradition of positive political theory , incorporating elements from game theory , public choice theory , rational choice theory , and social choice theory to analyze strategic political behavior. [ 3 ] While rhetoric focuses on persuading others to change their preferences, heresthetic involves restructuring the political environment to achieve victory using opponents' existing preferences. Common heresthetic strategies include dimension manipulation, strategic voting , agenda control , and the introduction of new alternatives to split opposing coalitions. [ 4 ] The concept has been influential in understanding political maneuvering in legislative politics , electoral systems , and constitutional design .
Riker argues that herestheticians win because they compel or persuade others to join them in voting or political coalitions. [ 5 ] Heresthetic focuses both on the use of rhetoric and political strategy. Riker argues that there are three vital components to heresthetic. [ 6 ]
These components allow herestheticians to manipulate political outcomes by structuring debate, rhetorically or structurally, to be more advantageous to their preferred position. [ 6 ]
The British Parliament is scheduling upcoming referendum votes to determine Scottish independence from the United Kingdom and if the UK should remain a member of the European Union . A member of parliament who has influence on how the votes will be structured, has a preference that Scotland will remain in union with the UK and that the UK will leave the EU. Scottish independence and the UK remaining a member of the EU is an undesirable outcome for the MP. While polling indicates that a majority of Scottish voters do not support independence, voters are more likely to support independence if the UK leaves the EU. [ 18 ] In order to receive his preferred outcome, the MP seeks for the referendum votes to be held in a sequence in which Scottish independence is determined first, and then UK withdrawal from the EU. This voting sequence demonstrates how herestheticians can manipulate the decision-making process so they can win. | https://en.wikipedia.org/wiki/Heresthetic |
In mathematics and physics, Herglotz's variational principle , named after German mathematician and physicist Gustav Herglotz , is an extension of the Hamilton's principle , where the Lagrangian L explicitly involves the action S {\displaystyle S} as an independent variable, and S {\displaystyle S} itself is represented as the solution of an ordinary differential equation (ODE) whose right hand side is the Lagrangian L {\displaystyle L} , instead of an integration of L {\displaystyle L} . [ 1 ] [ 2 ] Herglotz's variational principle is known as the variational principle for nonconservative Lagrange equations and Hamilton equations .
Suppose there is a Lagrangian L = L ( t , q , u , S ) {\displaystyle L=L(t,{\boldsymbol {q}},{\boldsymbol {u}},S)} of 2 n + 2 {\displaystyle 2n+2} variables, where q = ( q 1 , q 2 , … , q n ) {\displaystyle {\boldsymbol {q}}=(q_{1},q_{2},\dots ,q_{n})} and u = ( u 1 , u 2 , … , u n ) {\displaystyle {\boldsymbol {u}}=(u_{1},u_{2},\dots ,u_{n})} are n {\displaystyle n} dimensional vectors, and t , S {\displaystyle t,S} are scalar values. A time interval [ t 0 , t 1 ] {\displaystyle [t_{0},t_{1}]} is fixed. Given a time-parameterized curve q = q ( t ) {\displaystyle {\boldsymbol {q}}={\boldsymbol {q}}(t)} , consider the ODE { S ˙ ( t ) = L ( t , q ( t ) , q ˙ ( t ) , S ( t ) ) , t ∈ [ t 0 , t 1 ] S ( t 0 ) = S 0 {\displaystyle {\begin{cases}{\dot {S}}(t)=L(t,{\boldsymbol {q}}(t),{\boldsymbol {\dot {q}}}(t),S(t)),&t\in [t_{0},t_{1}]\\S(t_{0})=S_{0}\end{cases}}} When L ( t , q , u , S ) , q ( t ) , u ( t ) {\displaystyle L(t,{\boldsymbol {q}},{\boldsymbol {u}},S),{\boldsymbol {q}}(t),{\boldsymbol {u}}(t)} are all well-behaved functions, this equation allows a unique solution, and thus S 1 := S ( t 1 ) {\displaystyle S_{1}:=S(t_{1})} is a well defined number which is determined by the curve q ( t ) {\displaystyle {\boldsymbol {q}}(t)} . Herglotz's variation problem aims to minimize S 1 {\displaystyle S_{1}} over the family of curves q ( t ) {\displaystyle {\boldsymbol {q}}(t)} with fixed value q 0 {\displaystyle {\boldsymbol {q}}_{0}} at t = t 0 {\displaystyle t=t_{0}} and fixed value q 1 {\displaystyle {\boldsymbol {q}}_{1}} at t = t 1 {\displaystyle t=t_{1}} , i.e. the problem arg min q : q ( t 0 ) = q 0 , q ( t 1 ) = q 1 S 1 [ q ] {\displaystyle {\underset {{\boldsymbol {q}}:{\boldsymbol {q}}(t_{0})={\boldsymbol {q}}_{0},{\boldsymbol {q}}(t_{1})={\boldsymbol {q}}_{1}}{\arg \min }}S_{1}[{\boldsymbol {q}}]} Note that, when L {\displaystyle L} does not explicitly depend on S {\displaystyle S} , i.e. L = L ( t , q , u ) {\displaystyle L=L(t,{\boldsymbol {q}},{\boldsymbol {u}})} , the above ODE system gives exactly S ( t ) = ∫ t 0 t L ( t , q ( τ ) , q ( τ ) ) d τ {\textstyle S(t)=\int _{t_{0}}^{t}L(t,{\boldsymbol {q}}(\tau ),{\boldsymbol {q}}(\tau )){\rm {d}}\tau } , and thus S 1 = S ( t 1 ) = ∫ t 0 t 1 L ( t , q ( t ) , q ( t ) ) d t {\textstyle S_{1}=S(t_{1})=\int _{t_{0}}^{t_{1}}L(t,{\boldsymbol {q}}(t),{\boldsymbol {q}}(t)){\rm {d}}t} , which degenerates to the classical Hamiltonian action. The resulting Euler-Lagrange-Herglotz equation is d d t ( ∂ L ∂ q ˙ ) − ∂ L ∂ q = ∂ L ∂ S ∂ L ∂ q ˙ {\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left({\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\right)-{\frac {\partial L}{\partial {\boldsymbol {q}}}}={\frac {\partial L}{\partial S}}{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}} which involves an extra term ∂ L ∂ S ∂ L ∂ q ˙ {\textstyle {\frac {\partial L}{\partial S}}{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}} that can describes the dissipation of the system.
In order to solve this minimization problem, we impose a variation δ q {\displaystyle \delta {\boldsymbol {q}}} on q {\displaystyle {\boldsymbol {q}}} , and suppose S ( t ) {\displaystyle S(t)} undergoes a variation δ S ( t ) {\displaystyle \delta S(t)} correspondingly, then δ S ˙ ( t ) = L ( t , q ( t ) + δ q ( t ) , q ˙ ( t ) + δ q ˙ ( t ) , S ( t ) + δ S ( t ) ) − L ( t , q ( t ) , q ˙ ( t ) , S ( t ) ) = ∂ L ∂ q δ q ( t ) + ∂ L ∂ q ˙ δ q ˙ ( t ) + ∂ L ∂ S δ S ( t ) {\displaystyle {\begin{aligned}\delta {\dot {S}}(t)&=L(t,{\boldsymbol {q}}(t)+\delta {\boldsymbol {q}}(t),{\dot {\boldsymbol {q}}}(t)+\delta {\dot {\boldsymbol {q}}}(t),S(t)+\delta S(t))-L(t,{\boldsymbol {q}}(t),{\dot {\boldsymbol {q}}}(t),S(t))\\&={\frac {\partial L}{\partial {\boldsymbol {q}}}}\delta {\boldsymbol {q}}(t)+{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\delta {\dot {\boldsymbol {q}}}(t)+{\frac {\partial L}{\partial S}}\delta S(t)\end{aligned}}} and since the initial condition is not changed, δ S 0 = 0 {\displaystyle \delta S_{0}=0} . The above equation a linear ODE for the function δ S ( t ) {\displaystyle \delta S(t)} , and it can be solved by introducing an integrating factor μ ( t ) = e ∫ t 0 t ∂ L ∂ S d t {\displaystyle \mu (t)=\mathrm {e} ^{\int _{t_{0}}^{t}{\frac {\partial L}{\partial S}}\mathrm {d} t}} , which is uniquely determined by the ODE μ ˙ ( t ) = − μ ( t ) ∂ L ∂ S , u ( t 0 ) = 1. {\displaystyle {\dot {\mu }}(t)=-\mu (t){\frac {\partial L}{\partial S}},\quad u(t_{0})=1.} By multiplying μ ( t ) {\displaystyle \mu (t)} on both sides of the equation of δ S ˙ {\displaystyle \delta {\dot {S}}} and moving the term μ ( t ) ∂ L ∂ S δ S ( t ) {\textstyle \mu (t){\frac {\partial L}{\partial S}}\delta S(t)} to the left hand side, we get μ ( t ) δ S ˙ ( t ) − μ ( t ) ∂ L ∂ S δ S ( t ) = μ ( t ) ( ∂ L ∂ q δ q ( t ) + ∂ L ∂ q ˙ δ q ˙ ( t ) ) . {\displaystyle \mu (t)\delta {\dot {S}}(t)-\mu (t){\frac {\partial L}{\partial S}}\delta S(t)=\mu (t)\left({\frac {\partial L}{\partial {\boldsymbol {q}}}}\delta {\boldsymbol {q}}(t)+{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\delta {\dot {\boldsymbol {q}}}(t)\right).} Note that, since μ ˙ ( t ) = − μ ( t ) ∂ L ∂ S {\textstyle {\dot {\mu }}(t)=-\mu (t){\frac {\partial L}{\partial S}}} , the left hand side equals to μ ( t ) δ S ˙ ( t ) + μ ˙ ( t ) δ S ( t ) = d ( μ ( t ) δ S ( t ) ) d t {\displaystyle \mu (t)\delta {\dot {S}}(t)+{\dot {\mu }}(t)\delta S(t)={\frac {\mathrm {d} (\mu (t)\delta S(t))}{\mathrm {d} t}}} and therefore we can do an integration of the equation above from t = t 0 {\displaystyle t=t_{0}} to t = t 1 {\displaystyle t=t_{1}} , yielding μ ( t 1 ) δ S 1 − μ ( t 0 ) δ S 0 = ∫ t 0 t 1 μ ( t ) ( ∂ L ∂ q δ q ( t ) + ∂ L ∂ q ˙ δ q ˙ ( t ) ) d t {\displaystyle \mu (t_{1})\delta S_{1}-\mu (t_{0})\delta S_{0}=\int _{t_{0}}^{t_{1}}\mu (t)\left({\frac {\partial L}{\partial {\boldsymbol {q}}}}\delta {\boldsymbol {q}}(t)+{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\delta {\dot {\boldsymbol {q}}}(t)\right)\mathrm {d} t} where the δ S 0 = 0 {\displaystyle \delta S_{0}=0} so the left hand side actually only contains one term μ ( t 1 ) δ S 1 {\displaystyle \mu (t_{1})\delta S_{1}} , and for the right hand side, we can perform the integration-by-part on the ∂ L ∂ q ˙ δ q ˙ ( t ) {\textstyle {\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\delta {\dot {\boldsymbol {q}}}(t)} term to remove the time derivative on δ q {\textstyle \delta {\boldsymbol {q}}} : ∫ t 0 t 1 μ ( t ) ( ∂ L ∂ q δ q ( t ) + ∂ L ∂ q ˙ δ q ˙ ( t ) ) d t = ∫ t 0 t 1 μ ( t ) ∂ L ∂ q δ q ( t ) d t + ∫ t 0 t 1 μ ( t ) ∂ L ∂ q ˙ δ q ˙ ( t ) d t = ∫ t 0 t 1 μ ( t ) ∂ L ∂ q δ q ( t ) d t + μ ( t 1 ) ∂ L ∂ q ˙ δ q ( t 1 ) ⏟ = 0 − μ ( t 0 ) ∂ L ∂ q ˙ δ q ( t 0 ) ⏟ = 0 − ∫ t 0 t 1 d d t ( μ ( t ) ∂ L ∂ q ˙ ) δ q ( t ) d t = ∫ t 0 t 1 μ ( t ) ∂ L ∂ q δ q ( t ) d t − ∫ t 0 t 1 d d t ( μ ( t ) ∂ L ∂ q ˙ ) δ q ( t ) d t = ∫ t 0 t 1 μ ( t ) ∂ L ∂ q δ q ( t ) d t − ∫ t 0 t 1 ( μ ˙ ( t ) ∂ L ∂ q ˙ + μ ( t ) d d t ∂ L ∂ q ˙ ) δ q ( t ) d t = ∫ t 0 t 1 μ ( t ) ∂ L ∂ q δ q ( t ) d t − ∫ t 0 t 1 ( − μ ( t ) ∂ L ∂ S ∂ L ∂ q ˙ + μ ( t ) d d t ∂ L ∂ q ˙ ) δ q ( t ) d t = ∫ t 0 t 1 μ ( t ) ( ∂ L ∂ q + ∂ L ∂ S ∂ L ∂ q ˙ − d d t ∂ L ∂ q ˙ ) _ δ q ( t ) d t , {\displaystyle {\begin{aligned}&\int _{t_{0}}^{t_{1}}\mu (t)\left({\frac {\partial L}{\partial {\boldsymbol {q}}}}\delta {\boldsymbol {q}}(t)+{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\delta {\dot {\boldsymbol {q}}}(t)\right)\mathrm {d} t\\=&\int _{t_{0}}^{t_{1}}\mu (t){\frac {\partial L}{\partial {\boldsymbol {q}}}}\delta {\boldsymbol {q}}(t)\mathrm {d} t+\int _{t_{0}}^{t_{1}}\mu (t){\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\delta {\dot {\boldsymbol {q}}}(t)\mathrm {d} t\\=&\int _{t_{0}}^{t_{1}}\mu (t){\frac {\partial L}{\partial {\boldsymbol {q}}}}\delta {\boldsymbol {q}}(t)\mathrm {d} t+\mu (t_{1}){\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\underbrace {\delta {\boldsymbol {q}}(t_{1})} _{=0}-\mu (t_{0}){\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\underbrace {\delta {\boldsymbol {q}}(t_{0})} _{=0}-\int _{t_{0}}^{t_{1}}{\frac {\mathrm {d} }{\mathrm {d} t}}\left(\mu (t){\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\right)\delta {\boldsymbol {q}}(t)\mathrm {d} t\\=&\int _{t_{0}}^{t_{1}}\mu (t){\frac {\partial L}{\partial {\boldsymbol {q}}}}\delta {\boldsymbol {q}}(t)\mathrm {d} t-\int _{t_{0}}^{t_{1}}{\frac {\mathrm {d} }{\mathrm {d} t}}\left(\mu (t){\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\right)\delta {\boldsymbol {q}}(t)\mathrm {d} t\\=&\int _{t_{0}}^{t_{1}}\mu (t){\frac {\partial L}{\partial {\boldsymbol {q}}}}\delta {\boldsymbol {q}}(t)\mathrm {d} t-\int _{t_{0}}^{t_{1}}\left({\dot {\mu }}(t){\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}+\mu (t){\frac {\mathrm {d} }{\mathrm {d} t}}{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\right)\delta {\boldsymbol {q}}(t)\mathrm {d} t\\=&\int _{t_{0}}^{t_{1}}\mu (t){\frac {\partial L}{\partial {\boldsymbol {q}}}}\delta {\boldsymbol {q}}(t)\mathrm {d} t-\int _{t_{0}}^{t_{1}}\left(-\mu (t){\frac {\partial L}{\partial S}}{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}+\mu (t){\frac {\mathrm {d} }{\mathrm {d} t}}{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\right)\delta {\boldsymbol {q}}(t)\mathrm {d} t\\=&\int _{t_{0}}^{t_{1}}\mu (t){\underline {\left({\frac {\partial L}{\partial {\boldsymbol {q}}}}+{\frac {\partial L}{\partial S}}{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}-{\frac {\mathrm {d} }{\mathrm {d} t}}{\frac {\partial L}{\partial {\dot {\boldsymbol {q}}}}}\right)}}\delta {\boldsymbol {q}}(t)\mathrm {d} t,\end{aligned}}} and when S 1 {\displaystyle S_{1}} is minimized, δ S 1 = 0 {\displaystyle \delta S_{1}=0} for all δ q {\displaystyle \delta {\boldsymbol {q}}} , which indicates that the underlined term in the last line of the equation above has to be zero on the entire interval [ t 0 , t 1 ] {\displaystyle [t_{0},t_{1}]} , this gives rise to the Euler-Lagrange-Herglotz equation.
One simple one-dimensional ( n = 1 {\displaystyle n=1} ) example [ 3 ] is given by the Lagrangian L ( t , x , x ˙ , S ) = 1 2 m x ˙ 2 − V ( x ) − γ S {\displaystyle L(t,x,{\dot {x}},S)={\frac {1}{2}}m{\dot {x}}^{2}-V(x)-\gamma S} The corresponding Euler-Lagrange-Herglotz equation is given as d d t ( m x ˙ ) + V ′ ( x ) = − γ x ˙ , {\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}(m{\dot {x}})+V'(x)=-\gamma {\dot {x}},} which simplifies into m x ¨ = − V ′ ( x ) − γ x ˙ . {\displaystyle m{\ddot {x}}=-V'(x)-\gamma {\dot {x}}.} This equation describes the damping motion of a particle in a potential field V {\displaystyle V} , where γ {\displaystyle \gamma } is the damping coefficient. | https://en.wikipedia.org/wiki/Herglotz's_variational_principle |
Heritage Operations Processing System , Heritage Ops , short named HOPS , is a web-based tool for the day-to-day running and management of preserved and heritage railways. The system was developed, from a concept drawn up by Danny Scroggins and Luke Cartey. [ 1 ]
The HOPS Project began early in August 2009 in the rostering office of the signalling department at the Gloucestershire Warwickshire Railway – who embraced the use of the technology. Beta testing began in January 2010 with a small group of volunteers, the group being enlarged later that year. After this period, the system was made available to other UK heritage railways in January 2011. [ 2 ]
The purpose of the system is to provide administration tools associated with operating functions on heritage railways, such as staff rostering, timetabling, competence management and document control, etc. The system is used to assist railways in meeting the requirements of government legislation such as the Railways and Other Guided Transport Systems (Safety) Regulations 2006 (ROGS), which were introduced in Great Britain to put the 2004 European Railway Safety Directive into practice. [ 3 ] The system assists with competency management (as a requirement of the Safety Management System ). [ 4 ] [ 5 ]
The ethos of the development of the system has been that in the majority of cases, producing large-scale data-handling and storage facilities, with the appropriate level of security, access, backups, etc., would not be economical for an individual railway. A single program, in use by many railway companies, however, would make the investment economical. [ citation needed ]
The system has grown significantly in the five years it has been in development, mainly in response to feedback from users and demands of the industry,. | https://en.wikipedia.org/wiki/Heritage_Operations_Processing_System |
A heritage railway or heritage railroad (U.S. usage) is a railway operated as living history to re-create or preserve railway scenes of the past. Heritage railways are often old railway lines preserved in a state depicting a period (or periods) in the history of rail transport .
The British Office of Rail and Road defines heritage railways as follows: [ 1 ]
...'lines of local interest', museum railways or tourist railways that have retained or assumed the character and appearance and operating practices of railways of former times. Several lines that operate in isolation provide genuine transport facilities, providing community links. Most lines constitute tourist or educational attractions in their own right. Much of the rolling stock and other equipment used on these systems is original and is of historic value in its own right. Many systems aim to replicate both the look and operating practices of historic former railways companies.
Heritage railway lines have historic rail infrastructure which has been substituted (or made obsolete) in modern rail systems. Historical installations, such as hand-operated points , water cranes , and rails fastened with hand-hammered rail spikes , are characteristic features of heritage lines. Unlike tourist railways, which primarily carry tourists and have modern installations and vehicles, heritage-line infrastructure creates views and soundscapes of the past in operation.
Due to a lack of modern technology or the desire for historical accuracy, railway operations can be handled with traditional practices such as the use of tokens . Heritage infrastructure and operations often require the assignment of roles, based on historical occupations, to the railway staff. Some, or all, staff and volunteers, including Station masters and signalmen , sometimes wearing period-appropriate attire, can be seen on some heritage railways. Most heritage railways use heritage rolling stock, although modern rail vehicles can be used to showcase railway scenes with historical-line infrastructure.
While some heritage railways are profitable tourist attractions , many are not-for-profit entities; some of the latter depend on enthusiastic volunteers for upkeep and operations to supplement revenue from traffic and visitors. Still other heritage railways offer a viable public-transit option, and can maintain operations with revenue from regular riders or government subsidies.
Children's railways are extracurricular educational institutions where children and teenagers learn about railway work; they are often functional, passenger-carrying narrow-gauge rail lines. The railways developed in the USSR during the Soviet era . Many were called "Pioneer railways", after the youth organisation of that name . The first children's railway opened in Moscow [ 2 ] in 1932 and, at the breakup of the USSR, 52 children's railways existed in the country. [ 3 ] Although the fall of communist governments has led to the closure of some, preserved children's railways are still functioning in post-Soviet states and Eastern European countries .
Many children's railways were built on parkland in urban areas. Unlike many industrial areas typically served by a narrow-gauge railway, parks were free of redevelopment. Child volunteers and socialist fiscal policy enabled the existence of many of these railways. Children's railways which still carry traffic have often retained their original infrastructure and rolling stock, including vintage steam locomotives; [ 4 ] [ 5 ] some have acquired heritage vehicles from other railways.
Examples of children's railways with steam locomotives include the Dresden Park Railway in Germany; the Gyermekvasút in Budapest ; the Park Railway Maltanka in Poznań ; the Košice Children's Railway in Slovakia, and the 7 + 1 ⁄ 4 in ( 184 mm ) gauge steam railway on the grounds of St Nicholas' School in Merstham , Surrey , which the children help operate with assistance from the East Surrey 16mm Group and other volunteers. [ 6 ] [ 7 ]
Creating passages for trains up steep hills and through mountain regions offers many obstacles which call for technical solutions. Steep grade railway technologies and extensive tunneling may be employed. The use of narrow gauge allows tighter curves in the track, and offers a smaller structure gauge and tunnel size. At high altitudes, construction and logistical difficulties, limited urban development and demand for transport and special rolling-stock requirements have left many mountain railways unmodernized. The engineering feats of past railway builders and views of pristine mountain scenes have made many railways in mountainous areas profitable tourist attractions.
Pit railways have been in operation in underground mines all over the world. Small rail vehicles transport ore, waste rock, and workers through narrow tunnels. Sometimes trains were the sole mode of transport in the passages between the work sites and the mine entrance. The railway's loading gauge often dictated the cross-section of passages to be dug. At many mining sites, pit railways have been abandoned due to mine closure or adoption of new transportation equipment. Some show mines have a vintage pit railway and offer mantrip rides into the mine.
The Metro 1 (officially the Millennium Underground Railway or M1), built from 1894 to 1896, is the oldest line of the Budapest Metro system and the second-oldest underground railway in the world. [ 8 ] The M1 underwent major reconstruction during the 1980s and 1990s, and Line 1 now serves eight original stations whose original appearance has been preserved. In 2002, the line was listed as a UNESCO World Heritage Site . [ 9 ] In the Deák Ferenc Square concourse's Millennium Underground Museum, many other artifacts of the metro's early history may be seen.
The first heritage railway to be rescued and run entirely by volunteers was the Talyllyn Railway in Wales . This narrow-gauge line, taken over by a group of enthusiasts in 1950, was the beginning of the preservation movement worldwide.
La Trochita (officially Viejo Expreso Patagónico, the Old Patagonian Express) was declared a National Historic Monument by the Government of Argentina in 1999. [ 10 ] Trains on the Patagonian 750 mm ( 2 ft 5 + 1 ⁄ 2 in ) narrow-gauge railway use steam locomotives. The 402-kilometre-long (250 mi) railway runs through the foothills of the Andes between Esquel and El Maitén in Chubut Province and Ingeniero Jacobacci in Río Negro Province .
In southern Argentina, the Train of the End of the World to the Tierra del Fuego National Park is considered the world's southernmost functioning railway. Heritage railway operations started in 1994, after restoration of the old 500 mm ( 19 + 3 ⁄ 4 in ) (narrow-gauge) steam railway .
In Salta Province in northeastern Argentina, the Tren a las Nubes (Train to the Clouds) runs along 220 km (140 mi) of 1,000 mm ( 3 ft 3 + 3 ⁄ 8 in ) metre gauge track in what is one of the highest railways in the world . The line has 29 bridges, 21 tunnels, 13 viaducts, two spirals and two zigzags , and its highest point is 4,220 metres (13,850 ft) above sea level.
In the Misiones Province , more precisely in the Iguazú National Park, is the Ecological Train of the Forest. With a speed below 20 km per hour to avoid interfering with wildlife and the formations are propelled to liquefied petroleum gas (LPG), a non-polluting fuel. [ 11 ]
The Villa Elisa Historic Train (operated by Ferroclub Central Entrerriano) runs steam trains between the cities of Villa Elisa and Caseros in Entre Ríos Province , covering 36 km (22 mi) [ 12 ] in 120 minutes. [ 13 ]
The world's second preserved railway, and the first outside the United Kingdom, was Australia's Puffing Billy Railway . This railway operates on 15 miles (24 km) of track, with much of its original rolling stock built as early as 1898. Just about over half of Australia's heritage lines are operated by narrow gauge tank engines, much like the narrow gauge lines of the United Kingdom.
The Höllental Railway is a 4.9-kilometre-long (3.0 mi), 760 mm ( 2 ft 5 + 15 ⁄ 16 in ) narrow-gauge ( Bosnian gauge ) railway, operating in Lower Austria . It runs on summer weekends, connecting Reichenau an der Rax to the nearby Höllental .
Flanders , Belgium's northern Dutch-speaking region, has the Dendermonde–Puurs Steam Railway ; whereas Wallonia , with its strong history of 19th century heavy industries, has the Chemin de fer à vapeur des Trois Vallées and PFT operates the Chemin de Fer du Bocq .
Heritage streetcar lines:
Museums with operational heritage streetcar lines:
On the Finnish state-owned rail network , the section between Olli and Porvoo is a dedicated museum line. In southern Finland , it is the only line with many structural details abandoned by the rest of the network which regularly carries passenger traffic. Wooden sleepers , gravel ballast and low rail weight with no overhead catenary make it uniquely historical. [ 16 ] Along the line, the Hinthaara railway station and the Porvoo railway station area are included in the National Board of Antiquities' inventory of cultural environments of national significance in Finland. Also on the list is scenery in the Porvoonjoki Valley, through which the line passes. [ 17 ]
The Jokioinen Museum Railway is a stretch of preserved narrow-gauge railway between Humppila and Jokioinen . Nykarleby Järnväg is a stretch of rebuilt narrow-gauge railway on the bank of the old Kovjoki– Nykarleby line. [ 18 ]
The Buckower Kleinbahn [ de ] is a 4.9-kilometre (3.0 mi) spur line of the Prussian Eastern Railway , located in the Märkische Schweiz Nature Park in Brandenburg . It was originally constructed in 1897 as a narrow-gauge railway , with a gauge of 750 mm ( 2 ft 5 + 1 ⁄ 2 in ), connecting Buckow to the Müncheberg (Mark) station . This line was electrified and changed to standard gauge in 1930. It has operated as a heritage railway since 2002.
The Mountain railways of India are the railway lines that were built in the mountainous regions of India . The term mainly includes the narrow-gauge and metre-gauge railways in these regions but may also include some broad-gauge railways.
Of the Mountain railways of India, the Darjeeling Himalayan , Nilgiri Mountain and Kalka–Shimla Railways have been collectively designated as a UNESCO World Heritage Site . [ 19 ] [ 20 ] [ 21 ] To meet World Heritage criteria, the sites must retain some of their traditional infrastructure and culture.
The Nilgiri Mountain Railway is also the only rack and pinion railway in India. The Matheran Hill Railway , along with the Kangra Valley Railway are preserved narrow gauge railways under consideration for UNESCO status. Some scenic routes have been preserved as heritage railways. Here normal services have stopped, only tourist heritage trains are operated. Examples of these are the Patalpani–Kalakund Heritage Train and the Rajasthan Valley Queen Heritage train [ 22 ] which runs from Marwar Junction to Khamlighat .
In Indonesia there are several historic train lines and steam trains that are still operated today, including Ambarawa Railway Museum , Sawahlunto Railway Museum , Cepu Forest Railway , Jaladara excursion train in Surakarta , and several narrow gauge lines in the Sugar Factory area. [ 23 ]
In Italy the heritage railway institute is recognized and protected by law no. 128 of 9 August 2017, which has as its objective the protection and valorisation of disused, suspended or abolished railway lines, of particular cultural, landscape and tourist value, including both railway routes and stations and the related works of art and appurtenances, on which, upon proposal of the regions to which they belong, tourism-type traffic management is applied (art. 2, paragraph 1). [ 24 ] At the same time, the law identified a first list of 18 tourist railways, considered to be of particular value (art. 2, paragraph 2). [ 24 ]
The list is periodically updated by decree of the Ministry of Infrastructure and Transport , in agreement with the Ministry of Economy and Finance and the Ministry of Culture , also taking into account the reports in the State-Regions Conference, a list which in 2022 reached 26 railway lines. [ 25 ] According to article 1, law 128/2017 has as its purpose: "the protection and valorisation of railway sections of particular cultural, landscape and tourist value, which include railway routes, stations and related works of art and appurtenances, and of the historic and tourist rolling stock authorized to travel along them, as well as the regulation of the use of ferrocycles". [ 24 ]
Below is the list of railway lines recognized as tourist railways by Italian legislation.
b) pursuant to the Ministerial Decree of 30 March 2022: [ 25 ]
The Bernina railway line is a single-track 1,000 mm ( 3 ft 3 + 3 ⁄ 8 in ) metre gauge railway line forming part of the Rhaetian Railway (RhB). It links the spa resort of St. Moritz , in the canton of Graubünden , Switzerland , with the town of Tirano , in the Province of Sondrio , Italy , via the Bernina Pass . Reaching a height of 2,253 metres (7,392 ft) above sea level, it is the third highest railway crossing in Europe . It also ranks as the highest adhesion railway of the continent, and – with inclines of up to 7% – as one of the steepest adhesion railways in the world. The elevation difference on the section between the Bernina Pass and Tirano is 1,824 m (5,984 ft), allowing passengers to view glaciers along the line. On 7 July 2008, the Bernina line and the Albula railway line , which also forms part of the RhB, were recorded in the list of UNESCO World Heritage Sites , under the name Rhaetian Railway in the Albula / Bernina Landscapes . The whole site is a cross-border joint Swiss-Italian heritage area. Trains operating on the Bernina line include the Bernina Express .
In July 2023, Ferrovie dello Stato established a new company, the "FS Treni Turistici Italiani" (English: FS Italian Tourist Trains), with the mission "to propose an offer of railway services expressly designed and calibrated for quality, sustainable tourism and attentive to rediscovering the riches of the Italian territory. Tourism that can experience the train journey as an integral moment of the holiday, an element of quality in the overall tourist experience". [ 32 ] There are three service areas proposed:
Rail transport played a major role in the history of New Zealand and several rail enthusiast societies and heritage railways have been formed to preserve New Zealand's rich rail history.
The Čierny Hron Railway is a narrow-gauge railway in central Slovakia , established in the first decade of the 20th century and operating primarily as a freight railway for the local logging industry. From the late 1920s to the early 1960s, it also offered passenger transport between the villages of Hronec and Čierny Balog. The railway became Czechoslovakia 's most extensive forest railway network. After its closure in 1982, it received heritage status and was restored during the following decade. Since 1992, it has been one of Slovakia's official heritage railways and is a key regional tourist attraction. The Historical Logging Switchback Railway in Vychylovka is a heritage railway in north-central Slovakia, originally built to serve the logging industry in the Orava and Kysuce regions. Despite a closure and dissasembly of most of its original network during the early 1970s, its surviving lines and branches have been (or are being) restored. The railway is owned and operated by the Museum of Kysuce, with a 3.8-kilometre (2.4 mi) line open to tourists for sightseeing.
Switzerland has a very dense rail network , both standard and narrow gauge. The overwhelming majority of railways, built between the mid-19th and early 20th century , are still in regular operation today and electrified, a major exception being the Furka Steam Railway , the longest unelectrified line in the country and one of the highest rail crossings in Europe . Many railway companies, especially mountain railways , provide services with well-preserved historic trains for tourists, for instance the Rigi Railways , the oldest rack railway in Europe, and the Pilatus Railway , the steepest in the world. Two railways, the Albula Railway and the Bernina Railway , have been designated as a World Heritage Site , although they are essentially operated with modern rolling stock. Due to the availability of hydroelectric resources in the Alps, the Swiss network was electrified earlier than in the rest of Europe. [ 33 ] Some of the most emblematic pre-World War II electric locomotives and trains are the Crocodile , notably used on the Gotthard Railway , [ 34 ] and the Red Arrow . Both are occasionally operated by SBB Historic . Switzerland also comprehends a large number of funiculars, several still working with the original carriages, such as the Giessbachbahn .
In Britain, heritage railways are often railway lines which were run as commercial railways but were no longer needed (or closed down) and were taken over or re-opened by volunteers or non-profit organisations. The large number of heritage railways in the UK is due in part to the closure of many minor lines during the 1960s' Beeching cuts , and they were relatively easy to revive. There are between 100 and 150 heritage railways in the United Kingdom.
A typical British heritage railway will use steam locomotives and original rolling stock to create a period atmosphere, although some are concentrating on diesel and electric traction to re-create the post-steam era. Many run seasonally on partial routes, unconnected to a larger network (or railway), and charge high fares in comparison with transit services; as a result, they focus on the tourist and leisure markets. During the 1990s and 2000s, however, some heritage railways aimed to provide local transportation and extend their running seasons to carry commercial passenger traffic.
The first standard-gauge line to be preserved (not a victim of Beeching) was the Middleton Railway ; the second, and the first to carry passengers, was the Bluebell Railway .
Not-for-profit heritage railways differ in their quantity of service and some lines see traffic only on summer weekends. The more successful, such as the Severn Valley Railway and the North Yorkshire Moors Railway , may have up to five or six steam locomotives and operate a four-train service daily; smaller railways may run daily throughout the summer with only one steam locomotive. The Great Central Railway , the only preserved British main line with a double track, can operate over 50 trains on a busy timetable day.
After the privatisation of main-line railways, the line between not-for-profit heritage railways and for-profit branch lines may be blurred. The Romney, Hythe and Dymchurch Railway is an example of a commercial line run as a heritage operation and to provide local transportation, and the Severn Valley Railway has operated a few goods trains commercially. A number of heritage railway lines are regularly used by commercial freight operators.
Since the Bluebell Railway reopened to traffic in 1960, the definition of private standard gauge railways in the United Kingdom as preserved railways has evolved as the number of projects and their length, operating days and function have changed. The situation is further muddied by large variations in ownership-company structure, rolling stock and other assets. Unlike community railways , tourist railways in the UK are vertically integrated (although those operating mainly as charities separate their charitable and non-charitable activities for accounting purposes).
Heritage railways are known in the United States as tourist, historic, or scenic railroads. Most are remnants of original railroads, and some are reconstructed after having been scrapped. Some heritage railways preserve entire railroads in their original state using original structures, track, and motive power.
Examples of heritage railroads in the US by preservation type:
Other operations, such as the Valley Railroad or Hocking Valley Scenic Railway operate on historic track and utilize historic equipment, but are not reflective of the operations carried out by the original railroad they operate on. Hence, they do not fit into the Heritage Railway category, but rather Tourist Railway/Amusement.
Heritage streetcar lines are operating in over 20 U.S. cities, and are in planning or construction stages in others. Several new heritage streetcar lines have been opened since the 1970s; some are stand-alone lines while others make use of a section of a modern light rail system.
Heritage streetcar systems operating in Little Rock, Arkansas ; Memphis, Tennessee ; Dallas, Texas ; New Orleans, Louisiana ; Boston, Massachusetts ( MBTA Mattapan Trolley ) Philadelphia, Pennsylvania ( SEPTA route 15 ); and Tampa, Florida , are among the larger examples. A heritage line operates in Charlotte, North Carolina , and will become a part of the city's new transit system. Another such line, called The Silver Line , operates in San Diego .
The San Francisco Municipal Railway , or Muni, runs exclusively historic trolleys on its heavily used F Market & Wharves line. The line serves Market Street and the tourist areas along the Embarcadero, including Fisherman's Wharf .
Boston's Massachusetts Bay Transportation Authority runs exclusively PCC streetcars on its Mattapan Line , part of that authority's Red Line . The historic rolling stock is retained because doing so cost less than would a full rebuild of the line to accommodate either a heavy rail line (like the rest of the Red Line or the Blue or Orange Lines) or a modern light rail line (like the Green Line ). It is also unique in that it used almost exclusively by commuters and is not particularly popular with tourists (and thus may not really be a true heritage system, despite the historic rolling stock).
Dallas has the M-Line Trolley . Denver has the Platte Valley Trolley , a heritage line recalling the open-sided streetcars of the early 20th century. Old Pueblo Trolley is a volunteer-run heritage line in Tucson, Arizona ; its popularity inspired, in large part, a modern streetcar system for Tucson currently in the final planning stages, which would incorporate the heritage line. The VTA in San Jose, California , also maintains a heritage trolley fleet, for occasional use on the downtown portion of a new light rail system opened in 1988. Other cities with heritage streetcar lines include Galveston, Texas ; Kenosha, Wisconsin ; and San Pedro, California (home of the port of Los Angeles ). The National Park Service operates a system in Lowell, Massachusetts .
Most heritage streetcar lines use overhead trolley wires to power the cars, as was the case with the vast majority of original streetcar lines. However, on the Galveston Island Trolley heritage line, which opened in 1988, using modern-day replicas of vintage trolleys, the cars were powered by an on-board diesel engine, as local authorities were concerned that overhead wires would be too susceptible to damage from hurricanes. [ 35 ] In spite of that precaution, damage in 2008 from Hurricane Ike was heavy enough to put the line out of service indefinitely, and as of 2021 it has yet to reopen, but three streetcars are being repaired and reopening is planned. [ 36 ]
Another heritage line lacking trolley wires was Savannah's River Street Streetcar line, which opened in February 2009 and operated until around 2015. It was the first line to use a diesel/electric streetcar whose built-in electricity generator is powered by biodiesel . In El Reno, Oklahoma , the Heritage Express Trolley connects Heritage Park with downtown, [ 37 ] using a single streetcar that has been equipped with a propane-powered on-board generator. The car formerly operated on SEPTA's Norristown High Speed Line , where third-rail current collection is used. The El Reno line is single-track and 0.9 miles (1.4 km) long. [ 38 ]
In Portland, Oregon , replica-vintage cars provided a heritage streetcar service, named Portland Vintage Trolley , along a section of that city's 1986-operated light rail line from 1991 to 2014. [ 39 ] Elsewhere in Portland, the Willamette Shore Trolley is a seasonal, volunteer-operated excursion service on a former freight railroad line, to Lake Oswego, Oregon . This operation uses a diesel-powered generator on a trailer towed or pushed by the streetcar, as the line lacks trolley wires. Similarly, the Astoria Riverfront Trolley in Astoria, Oregon, is a seasonal heritage-trolley service along a section of former freight railroad and using a diesel-powered generator on a trailer to provide electricity to the streetcar.
Other seasonal or weekends-only heritage streetcar lines operate in Yakima, Washington ( Yakima Electric Railway Museum ); Fort Collins, Colorado ; and Fort Smith, Arkansas . The Fort Collins and Fort Smith lines are both operated by an original (as opposed to replica) Birney -type streetcar, and in both cases the individual car in use is listed on the National Register of Historic Places . [ 40 ] [ 41 ] In Philadelphia, the Penn's Landing Trolley operated seasonal and weekend service as a volunteer operation with former P&W equipment between September 1982 and December 17, 1995, on the Philadelphia Belt Line track on Columbus Boulevard in the historic Penn's Landing district.
Over 50 years later, the revival of extended streetcar operations in New Orleans is credited by many to the worldwide fame gained by its streetcars built by the Perley A. Thomas Car Works in 1922–23. These cars were operating on the system's Desire route made famous by Tennessee Williams ' A Streetcar Named Desire . Some Perley Thomas cars were maintained in continuous service on the St. Charles Streetcar Line until Hurricane Katrina caused major damage to the right-of-way in 2005. The historic streetcars suffered only minor damage and several were transferred to serve on the, then recently rebuilt, Canal Street line while the St. Charles line was being repaired. By June 22, 2008, service was restored to the entire length of the St. Charles Streetcar line. The New Orleans' St. Charles streetcar line is a National Historic Landmark . Pre-Katrina, New Orleans had plans to reconstruct the Desire line along its original route down St. Claude Avenue. Instead, the Loyola-UPT line was extended by building a spur down North Rampart Street to Elysian Fields Avenue .
In San Francisco , parts of the cable car and Muni streetcar system (specifically the above-mentioned F Market & Wharves line) are heritage lines, although they are also functioning parts of the city's transit system. The cable cars are a National Historic Landmark and are rare examples of vehicles with this distinction. Located east of San Francisco is one of several museums in the U.S. that restore and operate vintage streetcars and interurbans , the Western Railway Museum .
The preservation of the Talyllyn Railway was the inspiration for the 1953 Ealing Studios comedy The Titfield Thunderbolt . The film is centred on the preservation of a fictional Somerset branch line from Titfield to Mallingford. Filmed on the Camerton branch in the summer of 1952, the branch was lifted after production had finished.
Many preserved railways also served as a filming location for several production companies; for example, the Keighley and Worth Valley Railway served as a filming location for the 1970 adaptation of The Railway Children .
Series three of Survivors uses heritage railways to help reestablish transportation, communication and trade in post-apocalyptic England. [ citation needed ] | https://en.wikipedia.org/wiki/Heritage_railway |
The Herman Skolnik Award is awarded annually by the Division of Chemical Information of the American Chemical Society , "to recognize outstanding contributions to and achievements in the theory and practice of chemical information science". As of 2024 [update] the award is of 3,000 US dollars. [ 1 ]
It is named for Herman Skolnik (1914-1994), who was a co-founder of the then ACS Division of Chemical Literature in 1948 and a key figure in the Division. [ 2 ] The first award was made to him.
Source: [ 1 ] | https://en.wikipedia.org/wiki/Herman_Skolnik_Award |
Herman Thompson Briscoe (November 6, 1893 – October 8, 1960) was an American chemist and professor of chemistry. The Herman T. Briscoe Professorship in Chemistry at Indiana University was established in 1961, [ 1 ] and the Herman T. Briscoe Quadrangle Dormitory was dedicated in 1966. [ 2 ]
Herman T. Briscoe was born on November 6, 1893, in Shoals, Indiana . [ 3 ] Briscoe received his teaching certificate in 1912 from Indiana University in Bloomington, Indiana and began teaching at his home high school in Shoals for three academic years before becoming principal of Shoals high school and later superintendent of Shoals school district. He returned to Indiana University, earning his A.B. degree in chemistry with high distinction in 1917. Briscoe would then enlist in the U.S. army as a private in May 1918, transferring to the Hercules Powder Company as a research chemist until his discharge in 1919. [ 1 ] Between 1919 and 1922, Briscoe held successful teaching positions at Stark’s Military Academy, as an Austin Teaching Fellow at Harvard University , and at Colby College . [ 3 ] Returning to Indiana University for a third time, Herman T. Briscoe received his A.M. and Ph.D. degrees in chemistry in 1924 under the guidance of Professor Frank C. Mathers . [ 1 ]
Briscoe married Orah Elberta Briscoe (née Cole) in 1928. Orah, born in Liberty Center, IN in 1907, received her B.A. in Latin in 1929 and her M.A. in English in 1934. In 1929, their first child Catherine was born. They would have a total of 4 children. [ 4 ]
After receiving his Ph.D., Herman T. Briscoe was appointed assistant professor of chemistry at Indiana University, working his way to professor of chemistry in 1928. [ 3 ] Throughout his career, Briscoe authored or coauthored 23 publications on conductivity, physical properties, and the reactions of organic and inorganic molecules, supervised the graduate studies of 25 students, and published several general chemistry textbooks. [ 1 ]
In 1938, President of Indiana University Herman B. Wells appointed Briscoe as the secretary of the newly established self-survey committee, which sought the feedback of faculty and proposed administrative changes accordingly. In the same year, Briscoe was appointed Chairman of the Department of Chemistry of Indiana University following the recommendation of retiring Chairman Robert E. Lyons. Herman Briscoe would continue on to become Indiana University's first Dean of Faculties in 1939 and Vice President of Indiana University in 1940. [ 1 ] Briscoe gave up his appointment as Chairman of the Department of Chemistry in order to focus on his administrative roles as Vice President and Dean of Faculties, in which he served until his retirement in 1959. [ 3 ] | https://en.wikipedia.org/wiki/Herman_T._Briscoe |
Herman van Bekkum (26 September 1932 – 30 November 2020) was a Dutch organic chemist. He was professor of Catalysis in Organic Chemistry between 1971 and 1998 at Delft University of Technology . He served as rector magnificus of the university between 1975 and 1976. He was an expert in the field of carbohydrate chemistry and zeolites .
Van Bekkum was born on 26 September 1932 in Rotterdam . [ 1 ] [ 2 ] He studied technological chemistry at Delft University of Technology and graduated in 1959. He subsequently worked two years for Royal Dutch Shell before returning to Delft University to work as lecturer. In 1971 he was named professor of Catalysis in Organic Chemistry. From 1975 to 1976 he served as rector magnificus of the university. [ 3 ] As professor van Bekkum specialized in carbohydrate chemistry and the study of zeolites . [ 2 ] [ 4 ] In 1995 van Bekkum was appointed as the first president of the newly-founded Federation of the European Zeolite Association. [ 5 ]
In 1998 he officially retired, however, by 2013 he was still working at the university. [ 3 ] In his period at Delft University van Bekkum was doctoral advisor to 75 students. [ 3 ]
Van Bekkum was elected member of the Royal Netherlands Academy of Arts and Sciences in 1995. [ 6 ] He became an honorary member of the Royal Netherlands Chemical Society in 1998. [ 7 ]
Apart from his career in chemistry van Bekkum was a competitive chess player. [ 2 ]
He died on 30 November 2020 in Rotterdam, at age 88. [ 8 ] [ 9 ] | https://en.wikipedia.org/wiki/Herman_van_Bekkum |
Hermann Joseph Muller (December 21, 1890 – April 5, 1967) was an American geneticist who was awarded the 1946 Nobel Prize in Physiology or Medicine , "for the discovery that mutations can be induced by X-rays". [ 2 ] Muller warned of long-term dangers of radioactive fallout from nuclear war and nuclear testing , which resulted in greater public scrutiny of these practices.
Muller was born in New York City , the son of Frances (Lyons) and Hermann Joseph Muller Sr., an artisan who worked with metals. Muller was a third-generation American whose father's ancestors were originally Catholic and came to the United States from Koblenz . [ 3 ] His mother's family was of mixed Jewish (descended from Spanish and Portuguese Jews ) and Anglican background, and had come from Britain. [ 3 ] [ 4 ] Among his first cousins was Alfred Kroeber (Kroeber was Ursula Le Guin 's father) and first cousins once removed was Herbert J. Muller . [ 3 ] As an adolescent, Muller attended a Unitarian church and considered himself a pantheist ; in high school, he became an atheist . [ 5 ] He excelled in the public schools. At 16, he entered Columbia College . From his first semester, he was interested in biology; he became an early convert of the Mendelian - chromosome theory of heredity—and the concept of genetic mutations and natural selection as the basis for evolution . He formed a biology club and also became a proponent of eugenics ; the connections between biology and society would be his perennial concern. Muller earned a Bachelor of Arts degree in 1910. [ 6 ]
Muller remained at Columbia (the pre-eminent American zoology program at the time, due to E. B. Wilson and his students) for graduate school. He became interested in the Drosophila genetics work of Thomas Hunt Morgan 's fly lab after undergraduate bottle washers Alfred Sturtevant and Calvin Bridges joined his biology club. In 1911–1912, he studied metabolism at Cornell University , but remained involved with Columbia. He followed the drosophilists as the first genetic maps emerged from Morgan's experiments, and joined Morgan's group in 1912 (after two years of informal participation). [ 7 ]
In the fly group, Muller's contributions were primarily theoretical—explanations for experimental results and ideas and predictions for new experiments. In the emerging collaborative culture of the drosophilists, however, credit was assigned based on results rather than ideas; Muller felt cheated when he was left out of major publications. [ 8 ]
In 1914, Julian Huxley offered Muller a position at the recently founded William Marsh Rice Institute, now Rice University ; he hurried to complete his Doctor of philosophy degree and moved to Houston for the beginning of the 1915–1916 academic year (his degree was issued in 1916). At Rice, Muller taught biology and continued Drosophila lab work. In 1918, he proposed an explanation for the dramatic discontinuous alterations in Oenothera lamarckiana that were the basis of Hugo de Vries 's
theory of mutationism : "balanced lethals" allowed the accumulation of recessive mutations, and rare crossing over events resulted in the sudden expression of these hidden traits. In other words, de Vries's experiments were explainable by the Mendelian-chromosome theory. Muller's work was increasingly focused on mutation rate and lethal mutations . In 1918, Morgan, short-handed because many of his students and assistants were drafted for the U.S. entry into World War I , convinced Muller to return to Columbia to teach and to expand his experimental program. [ 9 ]
At Columbia, Muller and his collaborator and longtime friend Edgar Altenburg continued the investigation of lethal mutations. The primary method for detecting such mutations was to measure the sex ratios of the offspring of female flies. They predicted the ratio would vary from 1:1 due to recessive mutations on the X chromosome, which would be expressed only in males (which lacked the functional allele on a second X chromosome). Muller found a strong temperature dependence in mutation rate, leading him to believe that spontaneous mutation was the dominant mode (and to initially discount the role of external factors such as ionizing radiation or chemical agents). In 1920, Muller and Altenburg coauthored a seminal paper in Genetics on "modifier genes" that determine the size of mutant Drosophila wings. In 1919, Muller made the important discovery of a mutant (later found to be a chromosomal inversion ) that appeared to suppress crossing over, which opened up new avenues in mutation-rate studies. However, his appointment at Columbia was not continued; he accepted an offer from the University of Texas and left Columbia after the summer of 1920. [ 10 ]
Muller taught at the University of Texas from 1920 until 1932. Soon after returning to Texas, he married mathematics professor Jessie Marie Jacobs , whom he had courted previously. In his early years at Texas, Muller's Drosophila work was slow going; the data from his mutation rate studies were difficult to interpret. In 1923, he began using radium and X-rays , [ 11 ] but the relationship between radiation and mutation was difficult to measure because such radiation also sterilized the flies. In this period, he also became involved with eugenics and human genetics. He carried out a study of twins separated at birth that seemed to indicate a strong hereditary component of I.Q. Muller was critical of the new directions of the eugenics movement (such as anti-immigration), but was hopeful about the prospects for positive eugenics. [ 12 ] [ 13 ] In 1932, at the Third International Eugenics Congress , Muller gave a speech and stated, "eugenics might yet perfect the human race, but only in a society consciously organized for the common good". [ 14 ]
In 1926, a series of major breakthroughs began. In November, Muller carried out two experiments with varied doses of X-rays, the second of which used the crossing over suppressor stock ("ClB") he had found in 1919. A clear, quantitative connection between radiation and lethal mutations quickly emerged. Muller's discovery created a media sensation after he delivered a paper entitled "The Problem of Genetic Modification" at the Fifth International Congress of Genetics in Berlin ; it would make him one of the better-known public intellectuals of the early 20th century. By 1928, others had replicated his dramatic results, expanding them to other model organisms , such as wasps and maize . In the following years, he began publicizing the likely dangers of radiation exposure in humans (such as physicians who frequently operate X-ray equipment or shoe sellers who radiated their customers' feet). [ 15 ]
His lab grew quickly, but it shrank again following the onset of the Great Depression . Especially after the stock market crash, Muller was increasingly pessimistic about the prospects of capitalism . Some of his visiting lab members were from the USSR , and he helped edit and distribute an illegal leftist student newspaper, The Spark . It was a difficult period for Muller both scientifically and personally; his marriage was falling apart, and he was increasingly dissatisfied with his life in Texas. Meanwhile, the waning of the eugenics movement, ironically hastened by his own work pointing to the previously ignored connections between environment and genetics, meant that his ideas on the future of human evolution had reduced impact in the public sphere. [ 16 ] Muller's speech before the Third International Eugenics Conference in New York has been credited with marking the end of Galtonism , and perhaps even eugenics itself, as a popular movement in the sciences. H. Bentley Glass , a contemporary observer and Ph.D. student of Muller's, would say Muller's speech "just about finished the activity of the Eugenics Society". [ 17 ] Muller told the assembled that eugenic ideals could no longer be achieved, because the capitalistic system produces the wrong motives of individual action, and he disdained the natures of the dominant class, and the type of society they were creating. [ 18 ]
In September 1932, Muller moved to Berlin to work with the Russian expatriate geneticist Nikolay Timofeeff-Ressovsky ; a trip intended as a limited sabbatical stretched into an eight-year, five-country journey. In Berlin, he met two physicists who would later be significant to the biology community: Niels Bohr and Max Delbrück . The Nazi movement was precipitating the rapid emigration of scientific talent from Germany, and Muller was particularly opposed to the politics of National Socialism. The FBI was investigating Muller because of his involvement with The Spark , so he chose instead to go to the Soviet Union (an environment better suited to his political beliefs). In 1933, Muller and his wife reconciled, and their son David E. Muller and she moved with Hermann to Leningrad . There, at the Institute of Genetics, he imported the basic equipment for a Drosophila lab—including the flies—and set up shop. The institute was moved to Moscow in 1934, and Muller and his wife were divorced in 1935. [ 19 ]
In the USSR, Muller supervised a large and productive lab, and organized work on medical genetics. Most of his work involved further explorations of genetics and radiation. There he completed his eugenics book, Out of the Night , the main ideas of which dated to 1910. [ 20 ] By 1936, however, Joseph Stalin 's repressive policies and the rise of Lysenkoism was making the USSR an increasingly problematic place to live and work. Muller and many of the Russian genetics community did what they could to oppose Trofim Lysenko and his Larmarckian evolutionary theory, but Muller was soon forced to leave the Soviet Union after Stalin read a translation of his eugenics book and was "displeased by it, and...ordered an attack prepared against it." [ 21 ] By this time, Muller had already asked for a leave of absence. News of the Lysenko trials had reached the United States, and his son David was being raised there, after his divorce. [ 22 ] In the official declaration by the Institute, biological determinism was rejected: "The development of society is subject not to biological laws but to higher social laws. Attempts to spread to humanity the laws of the animal kingdom are an attempt to lower the human being to the level of beasts." [ 23 ]
Muller, with about 250 strains of Drosophila , moved to University of Edinburgh in September 1937, after brief stays in Madrid and Paris . In 1938, with war on the horizon, he began looking for a permanent position back in the United States. He also began courting Dorothea "Thea" Kantorowicz, a German refugee; they were married in May 1939. The Seventh International Congress on Genetics was held in Edinburgh later that year; Muller wrote a "Geneticists' Manifesto" [ 24 ] in response to the question: "How could the world's population be improved most effectively genetically?" He also engaged in a debate with the perennial genetics gadfly Richard Goldschmidt over the existence of the gene, for which little direct physical evidence existed at the time. [ 25 ]
When Muller returned to the United States in 1940, he took an untenured research position at Amherst College , in the department of Otto C. Glaser . After the U.S. entry into World War II , his position was extended indefinitely and expanded to include teaching. His Drosophila work in this period focused on measuring the rate of spontaneous (as opposed to radiation-induced) mutations. Muller's publication rate decreased greatly in this period, from a combination of lack of lab workers and experimentally challenging projects. However, he also worked as an adviser in the Manhattan Project (though he did not know that was what it was), as well as a study of the mutational effects of radar . Muller's appointment was ended after the 1944–1945 academic year, and despite difficulties stemming from his socialist political activities, he found a position as professor of zoology at Indiana University . [ 26 ] Here, he lived in a Dutch Colonial Revival house in Bloomington 's Vinegar Hill neighborhood. [ 27 ]
In 1946, Muller was awarded the Nobel Prize in Physiology or Medicine , "for the discovery that mutations can be induced by X-rays". Genetics, and especially the physical and physiological nature of the gene, was becoming a central topic in biology, and X-ray mutagenesis was a key to many recent advances, among them George Beadle and Edward Tatum 's work on Neurospora that established in 1941 the one gene-one enzyme hypothesis . [ 28 ] In Muller's Nobel Prize lecture, he argued that no threshold dose of radiation existed that did not produce mutagenesis , which led to the adoption of the linear no-threshold model of radiation on cancer risks. [ 29 ]
The Nobel Prize, in the wake of the atomic bombings of Hiroshima and Nagasaki , focused public attention on a subject Muller had been publicizing for two decades - the dangers of radiation. In 1952, nuclear fallout became a public issue; since Operation Crossroads , more and more evidence had been leaking out about radiation sickness and death caused by nuclear testing . Muller and many other scientists pursued an array of political activities to defuse the threat of nuclear war . With the Castle Bravo fallout controversy in 1954, the issue became even more urgent. [ citation needed ] In 1955, Muller was one of 11 prominent intellectuals to sign the Russell–Einstein Manifesto , the upshot of which was the first 1957 Pugwash Conference on Science and World Affairs , which addressed the control of nuclear weapons. [ 30 ] [ 31 ] He was a signatory (with many other scientists) of the 1958 petition to the United Nations, calling for an end to nuclear weapons testing, which was initiated by the Nobel Prize-winning chemist Linus Pauling . [ 30 ]
Muller's opinions on the effect of radiation on mutagenesis were used by Rachel Carson in her book Silent Spring , [ 32 ] however, his opinions have been criticized by some scientists; geneticist James F. Crow called Muller's view "alarmist" and wrote that it created in the public "an irrational fear of low-level radiation relative to other risks". [ 33 ] [ 34 ] It has been argued that Muller's opinion was not supported by studies on the survivors of the atomic bombings , or by research on mice, [ 35 ] and that he ignored another study that contradicted the linear no-threshold model he supported, thereby affecting the formulation of policy that favored this model. [ 29 ] He was also accused of suppressing opposing views and of being part of a US National Academy of Sciences Committee that misrepresented the research record to secure continued funding and strengthen his influence on US health policy. [ 36 ]
Muller was elected to the American Academy of Arts and Sciences in 1942 and the American Philosophical Society in 1947 [ 37 ] [ 38 ] Muller was awarded the Linnean Society of London 's Darwin-Wallace Medal in 1958 and the Kimber Genetics Award of the U.S. National Academy of Sciences, of which he was a member, in 1955. [ 39 ] [ 40 ] He served as president of the American Humanist Association from 1956 to 1958. [ 41 ] The American Mathematical Society selected him as its Gibbs Lecturer for 1958. [ 42 ] He retired in 1964. [ 43 ] The Drosophila basic units of inheritance, their chromosomal arms , are named " Muller elements " in Muller's honor. [ 44 ] he died in 1967.
H. J. Muller and science fiction writer Ursula K. Le Guin were first cousins once removed ; his father (Hermann J. Muller Sr.) and her father's mother (Johanna Muller Kroeber) were siblings, the children of Nicholas Müller, who immigrated to the United States in 1848, and at that time dropped the umlaut from his name. Another cousin was Herbert J. Muller , whose grandfather Otto was another son of Nicholas and a sibling of Hermann Sr. and Johanna. [ 45 ]
In a recent retrospective article about Muller's contribution, James Haber [ 46 ] wrote as follows:
Drosophila geneticist, Hermann Muller, envisioned the fundamental principles that such a molecule must have: to be auto-assembling and to be mutable but then again stable. He followed his prescient review of these properties with a remarkable prediction: learning about the hereditary material and its properties would not come from studying Drosophila, but from studying bacteria and their bacteriophages.
He was one of the signatories of the agreement to convene a convention for drafting a world constitution . [ 47 ] [ 48 ] As a result, for the first time in human history, a World Constituent Assembly convened to draft and adopt a Constitution for the Federation of Earth . [ 49 ]
Muller had a daughter, Helen J. Muller, now a professor emerita at the University of New Mexico , who has a daughter, Mala Htun , also a professor at the University of New Mexico. His son, David E. Muller , professor emeritus of mathematics and computer science at the University of Illinois and at New Mexico State University , died in 2008 in Las Cruces, New Mexico . David's mother was Jessie Jacobs Muller Offermann (1890–1954), Hermann's first wife. Helen's mother was Dorothea Kantorowicz Muller (1909–1986), Hermann's second wife, who came to the U.S. in 1940 as a German Jewish refugee. [ 3 ] He had a brief affair with Milly Bennett . [ 50 ] | https://en.wikipedia.org/wiki/Hermann_Joseph_Muller |
Hermann Schmalzried (born 21 January 1932 in Koblenz ) is a German chemist known for his work in physical chemistry, especially on the thermodynamics and kinetics of solid state chemistry.
Schmalzried received his diploma (with a diploma thesis on the fluorescence of benzopyrene ) from Theodor Förster at the University of Stuttgart and received his doctorate in 1958 at the Roentgen Institute of the University of Stuttgart with Richard Glocker (1890-1978) and was a postdoc with Carl Wagner at the Max Planck Institute for Biophysical Chemistry in Göttingen, a pioneer in solid state chemistry . He habilitated in 1966 at the Leibniz University Hannover on the topic of disorder in ternary ionic crystals. In 1966, he became a full professor at the Technical University of Clausthal and in 1975 at the Leibniz University Hannover. He was Courtesy Professor at Cornell University and Schottky Professor at Stanford University . [ 1 ] [ 2 ]
He wrote two textbooks on chemical reactions in solids, which were internationally standard works. He also dealt with thermodynamics of solids and electrochemistry . His group worked closely with Alan Lidiard 's group in England . [ 3 ] [ 4 ]
Schmalzried received the Wilhelm Jost Memorial Medal in 1994 and the Bunsen Medal in 2013. He is "External Scientific Member" of the Max Planck Institute for Biophysical Chemistry in Göttingen, member of the Göttingen Academy of Sciences , [ 5 ] the Leopoldina, corresponding member of the Austrian Academy of Sciences and member of the Academia Europaea (1989). [ 2 ] He was awarded an honorary doctor at the University of Stuttgart in 2003. [ 1 ] | https://en.wikipedia.org/wiki/Hermann_Schmalzried |
In geometry , Hermann–Mauguin notation is used to represent the symmetry elements in point groups , plane groups and space groups . It is named after the German crystallographer Carl Hermann (who introduced it in 1928) and the French mineralogist Charles-Victor Mauguin (who modified it in 1931). This notation is sometimes called international notation , because it was adopted as standard by the International Tables For Crystallography since their first edition in 1935.
The Hermann–Mauguin notation, compared with the Schoenflies notation , is preferred in crystallography because it can easily be used to include translational symmetry elements, and it specifies the directions of the symmetry axes. [ 1 ] [ 2 ]
Rotation axes are denoted by a number n – 1, 2, 3, 4, 5, 6, 7, 8, ... (angle of rotation φ = 360° / n ). For improper rotations , Hermann–Mauguin symbols show rotoinversion axes, unlike Schoenflies and Shubnikov notations, that shows rotation-reflection axes. The rotoinversion axes are represented by the corresponding number with a macron , n – 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , ... . 2 is equivalent to a mirror plane and usually notated as m. The direction of the mirror plane is defined as the direction perpendicular to it (the direction of the 2 axis).
Hermann–Mauguin symbols show non-equivalent axes and planes in a symmetrical fashion. The direction of a symmetry element corresponds to its position in the Hermann–Mauguin symbol. If a rotation axis n and a mirror plane m have the same direction, then they are denoted as a fraction n / m or n /m.
If two or more axes have the same direction, the axis with higher symmetry is shown. Higher symmetry means that the axis generates a pattern with more points. For example, rotation axes 3, 4, 5, 6, 7, 8 generate 3-, 4-, 5-, 6-, 7-, 8-point patterns, respectively. Improper rotation axes 3 , 4 , 5 , 6 , 7 , 8 generate 6-, 4-, 10-, 6-, 14-, 8-point patterns, respectively. If a rotation and a rotoinversion axis generate the same number of points, the rotation axis should be chosen. For example, the 3 / m combination is equivalent to 6 . Since 6 generates 6 points, and 3 generates only 3, 6 should be written instead of 3 / m (not 6 / m , because 6 already contains the mirror plane m). Analogously, in the case when both 3 and 3 axes are present, 3 should be written. However we write 4 / m , not 4 / m , because both 4 and 4 generate four points. In the case of the 6 / m combination, where 2, 3, 6, 3 , and 6 axes are present, axes 3 , 6 , and 6 all generate 6-point patterns, as we can see on the figure in the right, but the latter should be used because it is a rotation axis – the symbol will be 6 / m .
Finally, the Hermann–Mauguin symbol depends on the type [ clarification needed ] of the group .
These groups may contain only two-fold axes, mirror planes, and/or an inversion center. These are the crystallographic point groups 1 and 1 ( triclinic crystal system ), 2, m, and 2 / m ( monoclinic ), and 222, 2 / m 2 / m 2 / m , and mm2 ( orthorhombic ). (The short form of 2 / m 2 / m 2 / m is mmm.) If the symbol contains three positions, then they denote symmetry elements in the x , y , z direction, respectively.
These are the crystallographic groups 3, 32, 3m, 3 , and 3 2 / m ( trigonal crystal system ), 4, 422, 4mm, 4 , 4 2m, 4 / m , and 4 / m 2 / m 2 / m ( tetragonal ), and 6, 622, 6mm, 6 , 6 m2, 6 / m , and 6 / m 2 / m 2 / m ( hexagonal ). Analogously, symbols of non-crystallographic groups (with axes of order 5, 7, 8, 9, ...) can be constructed. These groups can be arranged in the following table
It can be noticed that in groups with odd-order axes n and n the third position in symbol is always absent, because all n directions, perpendicular to higher-order axis, are symmetrically equivalent. For example, in the picture of a triangle all three mirror planes ( S 0 , S 1 , S 2 ) are equivalent – all of them pass through one vertex and the center of the opposite side.
For even-order axes n and n there are n / 2 secondary directions and n / 2 tertiary directions. For example, in the picture of a regular hexagon one can distinguish two sets of mirror planes – three planes go through two opposite vertexes, and three other planes go through the centers of opposite sides. In this case any of two sets can be chosen as secondary directions, the rest set will be tertiary directions. Hence groups 4 2m, 6 2m, 8 2m, ... can be written as 4 m2, 6 m2, 8 m2, ... . For symbols of point groups this order usually doesn't matter; however, it will be important for Hermann–Mauguin symbols of corresponding space groups, where secondary directions are directions of symmetry elements along unit cell translations b and c , while the tertiary directions correspond to the direction between unit cell translations b and c . For example, symbols P 6 m2 and P 6 2m denote two different space groups. This also applies to symbols of space groups with odd-order axes 3 and 3 . The perpendicular symmetry elements can go along unit cell translations b and c or between them. Space groups P321 and P312 are examples of the former and the latter cases, respectively.
The symbol of point group 3 2 / m may be confusing; the corresponding Schoenflies symbol is D 3 d , which means that the group consists of 3-fold axis, three perpendicular 2-fold axes, and 3 vertical diagonal planes passing between these 2-fold axes, so it seems that the group can be denoted as 32m or 3m2. However, one should remember that, unlike Schoenflies notation, the direction of a plane in a Hermann–Mauguin symbol is defined as the direction perpendicular to the plane, and in the D 3 d group all mirror planes are perpendicular to 2-fold axes, so they should be written in the same position as 2 / m . Second, these 2 / m complexes generate an inversion center, which combining with the 3-fold rotation axis generates a 3 rotoinversion axis.
Groups with n = ∞ are called limit groups or Curie groups .
These are the crystallographic groups of a cubic crystal system : 23, 432, 2 / m 3 , 4 3m, and 4 / m 3 2 / m . All of them contain four diagonal 3-fold axes. These axes are arranged as 3-fold axes in a cube, directed along its four space diagonals (the cube has 4 / m 3 2 / m symmetry). These symbols are constructed the following way:
All Hermann–Mauguin symbols presented above are called full symbols . For many groups they can be simplified by omitting n -fold rotation axes in n / m positions. This can be done if the rotation axis can be unambiguously obtained from the combination of symmetry elements presented in the symbol. For example, the short symbol for 2 / m 2 / m 2 / m is mmm, for 4 / m 2 / m 2 / m is 4 / m mm, and for 4 / m 3 2 / m is m 3 m. In groups containing one higher-order axis, this higher-order axis cannot be omitted. For example, symbols 4 / m 2 / m 2 / m and 6 / m 2 / m 2 / m can be simplified to 4/mmm (or 4 / m mm) and 6/mmm (or 6 / m mm), but not to mmm; the short symbol for 3 2 / m is 3 m. The full and short symbols for all 32 crystallographic point groups are given in crystallographic point groups page.
Besides five cubic groups, there are two more non-crystallographic icosahedral groups ( I and I h in Schoenflies notation ) and two limit groups ( K and K h in Schoenflies notation ). The Hermann–Mauguin symbols were not designed for non-crystallographic groups, so their symbols are rather nominal and based on similarity to symbols of the crystallographic groups of a cubic crystal system. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] Group I can be denoted as 235, 25, 532, 53. The possible short symbols for I h are m 35 , m 5 , m 5 m, 53 m. The possible symbols for limit group K are ∞∞ or 2∞, and for K h are ∞ / m ∞ or m ∞ or ∞∞m.
Plane groups can be depicted using the Hermann–Mauguin system. The first letter is either lowercase p or c to represent primitive or centered unit cells . The next number is the rotational symmetry, as given above. The presence of mirror planes are denoted m , while glide reflections are only denoted g . Screw axes do not exist in two-dimensional spaces.
The symbol of a space group is defined by combining the uppercase letter describing the lattice type with symbols specifying the symmetry elements. The symmetry elements are ordered the same way as in the symbol of corresponding point group (the group that is obtained if one removes all translational components from the space group). The symbols for symmetry elements are more diverse, because in addition to rotations axes and mirror planes, space group may contain more complex symmetry elements – screw axes (combination of rotation and translation) and glide planes (combination of mirror reflection and translation). As a result, many different space groups can correspond to the same point group. For example, choosing different lattice types and glide planes one can generate 28 different space groups from point group mmm, e.g. Pmmm, Pnnn, Pccm, Pban, Cmcm, Ibam, Fmmm, Fddd, and so on. In some cases, a space group is generated when translations are simply added to a point group. [ 8 ] In other cases there is no point around which the point group applies. The notation is somewhat ambiguous, without a table giving more information. For example, space groups I23 and I2 1 3 (nos. 197 and 199) both contain two-fold rotational axes as well as two-fold screw axes. In the first, the two-fold axes intersect the three-fold axes, whereas in the second they do not. [ 9 ]
These are the Bravais lattice types in three dimensions:
The screw axis is noted by a number, n , where the angle of rotation is 360° / n . The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. For example, 2 1 is a 180° (twofold) rotation followed by a translation of 1 / 2 of the lattice vector. 3 1 is a 120° (threefold) rotation followed by a translation of 1 / 3 of the lattice vector.
The possible screw axes are: 2 1 , 3 1 , 3 2 , 4 1 , 4 2 , 4 3 , 6 1 , 6 2 , 6 3 , 6 4 , and 6 5 .
There are 4 enantiomorphic pairs of axes: (3 1 – 3 2 ), (4 1 – 4 3 ), (6 1 – 6 5 ), and (6 2 – 6 4 ). This enantiomorphism results in 11 pairs of enantiomorphic space groups, namely
The orientation of a glide plane is given by the position of the symbol in the Hermann–Mauguin designation, just as with mirror planes.
They are noted by a , b , or c depending on which axis (direction) the glide is along. There is also the n glide, which is a glide along the half of a diagonal of a face, and the d glide, which is along a quarter of either a face or space diagonal of the unit cell. The d glide is often called the diamond glide plane as it features in the diamond structure. In cases where there are two possibilities among a , b , and c (such as a or b ), the letter e is used. (In these cases, centering entails that both glides occur.) To summarize: | https://en.wikipedia.org/wiki/Hermann–Mauguin_notation |
In mathematics , Hermite's cotangent identity is a trigonometric identity discovered by Charles Hermite . [ 1 ] Suppose a 1 , ..., a n are complex numbers , no two of which differ by an integer multiple of π . Let
(in particular, A 1,1 , being an empty product , is 1). Then
The simplest non-trivial example is the case n = 2: | https://en.wikipedia.org/wiki/Hermite's_cotangent_identity |
In mathematics , Hermite's identity , named after Charles Hermite , gives the value of a summation involving the floor function . It states that for every real number x and for every positive integer n the following identity holds: [ 1 ] [ 2 ]
Split x {\displaystyle x} into its integer part and fractional part , x = ⌊ x ⌋ + { x } {\displaystyle x=\lfloor x\rfloor +\{x\}} . There is exactly one k ′ ∈ { 1 , … , n } {\displaystyle k'\in \{1,\ldots ,n\}} with
By subtracting the same integer ⌊ x ⌋ {\displaystyle \lfloor x\rfloor } from inside the floor operations on the left and right sides of this inequality, it may be rewritten as
Therefore,
and multiplying both sides by n {\displaystyle n} gives
Now if the summation from Hermite's identity is split into two parts at index k ′ {\displaystyle k'} , it becomes
Consider the function
Then the identity is clearly equivalent to the statement f ( x ) = 0 {\displaystyle f(x)=0} for all real x {\displaystyle x} . But then we find,
Where in the last equality we use the fact that ⌊ x + p ⌋ = ⌊ x ⌋ + p {\displaystyle \lfloor x+p\rfloor =\lfloor x\rfloor +p} for all integers p {\displaystyle p} . But then f {\displaystyle f} has period 1 / n {\displaystyle 1/n} . It then suffices to prove that f ( x ) = 0 {\displaystyle f(x)=0} for all x ∈ [ 0 , 1 / n ) {\displaystyle x\in [0,1/n)} . But in this case, the integral part of each summand in f {\displaystyle f} is equal to 0. We deduce that the function is indeed 0 for all real inputs x {\displaystyle x} . | https://en.wikipedia.org/wiki/Hermite's_identity |
In mathematics , the Hermite polynomials are a classical orthogonal polynomial sequence .
The polynomials arise in:
Hermite polynomials were defined by Pierre-Simon Laplace in 1810, [ 1 ] [ 2 ] though in scarcely recognizable form, and studied in detail by Pafnuty Chebyshev in 1859. [ 3 ] Chebyshev's work was overlooked, and they were named later after Charles Hermite , who wrote on the polynomials in 1864, describing them as new. [ 4 ] They were consequently not new, although Hermite was the first to define the multidimensional polynomials.
Like the other classical orthogonal polynomials , the Hermite polynomials can be defined from several different starting points. Noting from the outset that there are two different standardizations in common use, one convenient method is as follows:
These equations have the form of a Rodrigues' formula and can also be written as, He n ( x ) = ( x − d d x ) n ⋅ 1 , H n ( x ) = ( 2 x − d d x ) n ⋅ 1. {\displaystyle \operatorname {He} _{n}(x)=\left(x-{\frac {d}{dx}}\right)^{n}\cdot 1,\quad H_{n}(x)=\left(2x-{\frac {d}{dx}}\right)^{n}\cdot 1.}
The two definitions are not exactly identical; each is a rescaling of the other: H n ( x ) = 2 n 2 He n ( 2 x ) , He n ( x ) = 2 − n 2 H n ( x 2 ) . {\displaystyle H_{n}(x)=2^{\frac {n}{2}}\operatorname {He} _{n}\left({\sqrt {2}}\,x\right),\quad \operatorname {He} _{n}(x)=2^{-{\frac {n}{2}}}H_{n}\left({\frac {x}{\sqrt {2}}}\right).}
These are Hermite polynomial sequences of different variances; see the material on variances below.
The notation He and H is that used in the standard references. [ 5 ] The polynomials He n are sometimes denoted by H n , especially in probability theory, because 1 2 π e − x 2 2 {\displaystyle {\frac {1}{\sqrt {2\pi }}}e^{-{\frac {x^{2}}{2}}}} is the probability density function for the normal distribution with expected value 0 and standard deviation 1.
The n th-order Hermite polynomial is a polynomial of degree n . The probabilist's version He n has leading coefficient 1, while the physicist's version H n has leading coefficient 2 n .
From the Rodrigues formulae given above, we can see that H n ( x ) and He n ( x ) are even or odd functions depending on n : H n ( − x ) = ( − 1 ) n H n ( x ) , He n ( − x ) = ( − 1 ) n He n ( x ) . {\displaystyle H_{n}(-x)=(-1)^{n}H_{n}(x),\quad \operatorname {He} _{n}(-x)=(-1)^{n}\operatorname {He} _{n}(x).}
H n ( x ) and He n ( x ) are n th-degree polynomials for n = 0, 1, 2, 3,... . These polynomials are orthogonal with respect to the weight function ( measure ) w ( x ) = e − x 2 2 ( for He ) {\displaystyle w(x)=e^{-{\frac {x^{2}}{2}}}\quad ({\text{for }}\operatorname {He} )} or w ( x ) = e − x 2 ( for H ) , {\displaystyle w(x)=e^{-x^{2}}\quad ({\text{for }}H),} i.e., we have ∫ − ∞ ∞ H m ( x ) H n ( x ) w ( x ) d x = 0 for all m ≠ n . {\displaystyle \int _{-\infty }^{\infty }H_{m}(x)H_{n}(x)\,w(x)\,dx=0\quad {\text{for all }}m\neq n.}
Furthermore, ∫ − ∞ ∞ H m ( x ) H n ( x ) e − x 2 d x = π 2 n n ! δ n m , {\displaystyle \int _{-\infty }^{\infty }H_{m}(x)H_{n}(x)\,e^{-x^{2}}\,dx={\sqrt {\pi }}\,2^{n}n!\,\delta _{nm},} and ∫ − ∞ ∞ He m ( x ) He n ( x ) e − x 2 2 d x = 2 π n ! δ n m , {\displaystyle \int _{-\infty }^{\infty }\operatorname {He} _{m}(x)\operatorname {He} _{n}(x)\,e^{-{\frac {x^{2}}{2}}}\,dx={\sqrt {2\pi }}\,n!\,\delta _{nm},} where δ n m {\displaystyle \delta _{nm}} is the Kronecker delta .
The probabilist polynomials are thus orthogonal with respect to the standard normal probability density function.
The Hermite polynomials (probabilist's or physicist's) form an orthogonal basis of the Hilbert space of functions satisfying ∫ − ∞ ∞ | f ( x ) | 2 w ( x ) d x < ∞ , {\displaystyle \int _{-\infty }^{\infty }{\bigl |}f(x){\bigr |}^{2}\,w(x)\,dx<\infty ,} in which the inner product is given by the integral ⟨ f , g ⟩ = ∫ − ∞ ∞ f ( x ) g ( x ) ¯ w ( x ) d x {\displaystyle \langle f,g\rangle =\int _{-\infty }^{\infty }f(x){\overline {g(x)}}\,w(x)\,dx} including the Gaussian weight function w ( x ) defined in the preceding section.
An orthogonal basis for L 2 ( R , w ( x ) dx ) is a complete orthogonal system . For an orthogonal system, completeness is equivalent to the fact that the 0 function is the only function f ∈ L 2 ( R , w ( x ) dx ) orthogonal to all functions in the system.
Since the linear span of Hermite polynomials is the space of all polynomials, one has to show (in physicist case) that if f satisfies ∫ − ∞ ∞ f ( x ) x n e − x 2 d x = 0 {\displaystyle \int _{-\infty }^{\infty }f(x)x^{n}e^{-x^{2}}\,dx=0} for every n ≥ 0 , then f = 0 .
One possible way to do this is to appreciate that the entire function F ( z ) = ∫ − ∞ ∞ f ( x ) e z x − x 2 d x = ∑ n = 0 ∞ z n n ! ∫ f ( x ) x n e − x 2 d x = 0 {\displaystyle F(z)=\int _{-\infty }^{\infty }f(x)e^{zx-x^{2}}\,dx=\sum _{n=0}^{\infty }{\frac {z^{n}}{n!}}\int f(x)x^{n}e^{-x^{2}}\,dx=0} vanishes identically. The fact then that F ( it ) = 0 for every real t means that the Fourier transform of f ( x ) e − x 2 is 0, hence f is 0 almost everywhere . Variants of the above completeness proof apply to other weights with exponential decay .
In the Hermite case, it is also possible to prove an explicit identity that implies completeness (see section on the Completeness relation below).
An equivalent formulation of the fact that Hermite polynomials are an orthogonal basis for L 2 ( R , w ( x ) dx ) consists in introducing Hermite functions (see below), and in saying that the Hermite functions are an orthonormal basis for L 2 ( R ) .
The probabilist's Hermite polynomials are solutions of the differential equation ( e − 1 2 x 2 u ′ ) ′ + λ e − 1 2 x 2 u = 0 , {\displaystyle \left(e^{-{\frac {1}{2}}x^{2}}u'\right)'+\lambda e^{-{\frac {1}{2}}x^{2}}u=0,} where λ is a constant. Imposing the boundary condition that u should be polynomially bounded at infinity, the equation has solutions only if λ is a non-negative integer, and the solution is uniquely given by u ( x ) = C 1 He λ ( x ) {\displaystyle u(x)=C_{1}\operatorname {He} _{\lambda }(x)} , where C 1 {\displaystyle C_{1}} denotes a constant.
Rewriting the differential equation as an eigenvalue problem L [ u ] = u ″ − x u ′ = − λ u , {\displaystyle L[u]=u''-xu'=-\lambda u,} the Hermite polynomials He λ ( x ) {\displaystyle \operatorname {He} _{\lambda }(x)} may be understood as eigenfunctions of the differential operator L [ u ] {\displaystyle L[u]} . This eigenvalue problem is called the Hermite equation , although the term is also used for the closely related equation u ″ − 2 x u ′ = − 2 λ u . {\displaystyle u''-2xu'=-2\lambda u.} whose solution is uniquely given in terms of physicist's Hermite polynomials in the form u ( x ) = C 1 H λ ( x ) {\displaystyle u(x)=C_{1}H_{\lambda }(x)} , where C 1 {\displaystyle C_{1}} denotes a constant, after imposing the boundary condition that u should be polynomially bounded at infinity.
The general solutions to the above second-order differential equations are in fact linear combinations of both Hermite polynomials and confluent hypergeometric functions of the first kind. For example, for the physicist's Hermite equation u ″ − 2 x u ′ + 2 λ u = 0 , {\displaystyle u''-2xu'+2\lambda u=0,} the general solution takes the form u ( x ) = C 1 H λ ( x ) + C 2 h λ ( x ) , {\displaystyle u(x)=C_{1}H_{\lambda }(x)+C_{2}h_{\lambda }(x),} where C 1 {\displaystyle C_{1}} and C 2 {\displaystyle C_{2}} are constants, H λ ( x ) {\displaystyle H_{\lambda }(x)} are physicist's Hermite polynomials (of the first kind), and h λ ( x ) {\displaystyle h_{\lambda }(x)} are physicist's Hermite functions (of the second kind). The latter functions are compactly represented as h λ ( x ) = 1 F 1 ( − λ 2 ; 1 2 ; x 2 ) {\displaystyle h_{\lambda }(x)={}_{1}F_{1}(-{\tfrac {\lambda }{2}};{\tfrac {1}{2}};x^{2})} where 1 F 1 ( a ; b ; z ) {\displaystyle {}_{1}F_{1}(a;b;z)} are Confluent hypergeometric functions of the first kind . The conventional Hermite polynomials may also be expressed in terms of confluent hypergeometric functions, see below.
With more general boundary conditions , the Hermite polynomials can be generalized to obtain more general analytic functions for complex-valued λ . An explicit formula of Hermite polynomials in terms of contour integrals ( Courant & Hilbert 1989 ) is also possible.
The sequence of probabilist's Hermite polynomials also satisfies the recurrence relation He n + 1 ( x ) = x He n ( x ) − He n ′ ( x ) . {\displaystyle \operatorname {He} _{n+1}(x)=x\operatorname {He} _{n}(x)-\operatorname {He} _{n}'(x).} Individual coefficients are related by the following recursion formula: a n + 1 , k = { − ( k + 1 ) a n , k + 1 k = 0 , a n , k − 1 − ( k + 1 ) a n , k + 1 k > 0 , {\displaystyle a_{n+1,k}={\begin{cases}-(k+1)a_{n,k+1}&k=0,\\a_{n,k-1}-(k+1)a_{n,k+1}&k>0,\end{cases}}} and a 0,0 = 1 , a 1,0 = 0 , a 1,1 = 1 .
For the physicist's polynomials, assuming H n ( x ) = ∑ k = 0 n a n , k x k , {\displaystyle H_{n}(x)=\sum _{k=0}^{n}a_{n,k}x^{k},} we have H n + 1 ( x ) = 2 x H n ( x ) − H n ′ ( x ) . {\displaystyle H_{n+1}(x)=2xH_{n}(x)-H_{n}'(x).} Individual coefficients are related by the following recursion formula: a n + 1 , k = { − a n , k + 1 k = 0 , 2 a n , k − 1 − ( k + 1 ) a n , k + 1 k > 0 , {\displaystyle a_{n+1,k}={\begin{cases}-a_{n,k+1}&k=0,\\2a_{n,k-1}-(k+1)a_{n,k+1}&k>0,\end{cases}}} and a 0,0 = 1 , a 1,0 = 0 , a 1,1 = 2 .
The Hermite polynomials constitute an Appell sequence , i.e., they are a polynomial sequence satisfying the identity He n ′ ( x ) = n He n − 1 ( x ) , H n ′ ( x ) = 2 n H n − 1 ( x ) . {\displaystyle {\begin{aligned}\operatorname {He} _{n}'(x)&=n\operatorname {He} _{n-1}(x),\\H_{n}'(x)&=2nH_{n-1}(x).\end{aligned}}}
An integral recurrence that is deduced and demonstrated in [ 6 ] is as follows: He n + 1 ( x ) = ( n + 1 ) ∫ 0 x He n ( t ) d t − H e n ′ ( 0 ) , {\displaystyle \operatorname {He} _{n+1}(x)=(n+1)\int _{0}^{x}\operatorname {He} _{n}(t)dt-He'_{n}(0),}
H n + 1 ( x ) = 2 ( n + 1 ) ∫ 0 x H n ( t ) d t − H n ′ ( 0 ) . {\displaystyle H_{n+1}(x)=2(n+1)\int _{0}^{x}H_{n}(t)dt-H'_{n}(0).}
Equivalently, by Taylor-expanding , He n ( x + y ) = ∑ k = 0 n ( n k ) x n − k He k ( y ) = 2 − n 2 ∑ k = 0 n ( n k ) He n − k ( x 2 ) He k ( y 2 ) , H n ( x + y ) = ∑ k = 0 n ( n k ) H k ( x ) ( 2 y ) n − k = 2 − n 2 ⋅ ∑ k = 0 n ( n k ) H n − k ( x 2 ) H k ( y 2 ) . {\displaystyle {\begin{aligned}\operatorname {He} _{n}(x+y)&=\sum _{k=0}^{n}{\binom {n}{k}}x^{n-k}\operatorname {He} _{k}(y)&&=2^{-{\frac {n}{2}}}\sum _{k=0}^{n}{\binom {n}{k}}\operatorname {He} _{n-k}\left(x{\sqrt {2}}\right)\operatorname {He} _{k}\left(y{\sqrt {2}}\right),\\H_{n}(x+y)&=\sum _{k=0}^{n}{\binom {n}{k}}H_{k}(x)(2y)^{n-k}&&=2^{-{\frac {n}{2}}}\cdot \sum _{k=0}^{n}{\binom {n}{k}}H_{n-k}\left(x{\sqrt {2}}\right)H_{k}\left(y{\sqrt {2}}\right).\end{aligned}}} These umbral identities are self-evident and included in the differential operator representation detailed below, He n ( x ) = e − D 2 2 x n , H n ( x ) = 2 n e − D 2 4 x n . {\displaystyle {\begin{aligned}\operatorname {He} _{n}(x)&=e^{-{\frac {D^{2}}{2}}}x^{n},\\H_{n}(x)&=2^{n}e^{-{\frac {D^{2}}{4}}}x^{n}.\end{aligned}}}
In consequence, for the m th derivatives the following relations hold: He n ( m ) ( x ) = n ! ( n − m ) ! He n − m ( x ) = m ! ( n m ) He n − m ( x ) , H n ( m ) ( x ) = 2 m n ! ( n − m ) ! H n − m ( x ) = 2 m m ! ( n m ) H n − m ( x ) . {\displaystyle {\begin{aligned}\operatorname {He} _{n}^{(m)}(x)&={\frac {n!}{(n-m)!}}\operatorname {He} _{n-m}(x)&&=m!{\binom {n}{m}}\operatorname {He} _{n-m}(x),\\H_{n}^{(m)}(x)&=2^{m}{\frac {n!}{(n-m)!}}H_{n-m}(x)&&=2^{m}m!{\binom {n}{m}}H_{n-m}(x).\end{aligned}}}
It follows that the Hermite polynomials also satisfy the recurrence relation He n + 1 ( x ) = x He n ( x ) − n He n − 1 ( x ) , H n + 1 ( x ) = 2 x H n ( x ) − 2 n H n − 1 ( x ) . {\displaystyle {\begin{aligned}\operatorname {He} _{n+1}(x)&=x\operatorname {He} _{n}(x)-n\operatorname {He} _{n-1}(x),\\H_{n+1}(x)&=2xH_{n}(x)-2nH_{n-1}(x).\end{aligned}}}
These last relations, together with the initial polynomials H 0 ( x ) and H 1 ( x ) , can be used in practice to compute the polynomials quickly.
Turán's inequalities are H n ( x ) 2 − H n − 1 ( x ) H n + 1 ( x ) = ( n − 1 ) ! ∑ i = 0 n − 1 2 n − i i ! H i ( x ) 2 > 0. {\displaystyle {\mathit {H}}_{n}(x)^{2}-{\mathit {H}}_{n-1}(x){\mathit {H}}_{n+1}(x)=(n-1)!\sum _{i=0}^{n-1}{\frac {2^{n-i}}{i!}}{\mathit {H}}_{i}(x)^{2}>0.}
Moreover, the following multiplication theorem holds: H n ( γ x ) = ∑ i = 0 ⌊ n 2 ⌋ γ n − 2 i ( γ 2 − 1 ) i ( n 2 i ) ( 2 i ) ! i ! H n − 2 i ( x ) , He n ( γ x ) = ∑ i = 0 ⌊ n 2 ⌋ γ n − 2 i ( γ 2 − 1 ) i ( n 2 i ) ( 2 i ) ! i ! 2 − i He n − 2 i ( x ) . {\displaystyle {\begin{aligned}H_{n}(\gamma x)&=\sum _{i=0}^{\left\lfloor {\tfrac {n}{2}}\right\rfloor }\gamma ^{n-2i}(\gamma ^{2}-1)^{i}{\binom {n}{2i}}{\frac {(2i)!}{i!}}H_{n-2i}(x),\\\operatorname {He} _{n}(\gamma x)&=\sum _{i=0}^{\left\lfloor {\tfrac {n}{2}}\right\rfloor }\gamma ^{n-2i}(\gamma ^{2}-1)^{i}{\binom {n}{2i}}{\frac {(2i)!}{i!}}2^{-i}\operatorname {He} _{n-2i}(x).\end{aligned}}}
The physicist's Hermite polynomials can be written explicitly as H n ( x ) = { n ! ∑ l = 0 n 2 ( − 1 ) n 2 − l ( 2 l ) ! ( n 2 − l ) ! ( 2 x ) 2 l for even n , n ! ∑ l = 0 n − 1 2 ( − 1 ) n − 1 2 − l ( 2 l + 1 ) ! ( n − 1 2 − l ) ! ( 2 x ) 2 l + 1 for odd n . {\displaystyle H_{n}(x)={\begin{cases}\displaystyle n!\sum _{l=0}^{\frac {n}{2}}{\frac {(-1)^{{\tfrac {n}{2}}-l}}{(2l)!\left({\tfrac {n}{2}}-l\right)!}}(2x)^{2l}&{\text{for even }}n,\\\displaystyle n!\sum _{l=0}^{\frac {n-1}{2}}{\frac {(-1)^{{\frac {n-1}{2}}-l}}{(2l+1)!\left({\frac {n-1}{2}}-l\right)!}}(2x)^{2l+1}&{\text{for odd }}n.\end{cases}}}
These two equations may be combined into one using the floor function : H n ( x ) = n ! ∑ m = 0 ⌊ n 2 ⌋ ( − 1 ) m m ! ( n − 2 m ) ! ( 2 x ) n − 2 m . {\displaystyle H_{n}(x)=n!\sum _{m=0}^{\left\lfloor {\tfrac {n}{2}}\right\rfloor }{\frac {(-1)^{m}}{m!(n-2m)!}}(2x)^{n-2m}.}
The probabilist's Hermite polynomials He have similar formulas, which may be obtained from these by replacing the power of 2 x with the corresponding power of √ 2 x and multiplying the entire sum by 2 − n / 2 : He n ( x ) = n ! ∑ m = 0 ⌊ n 2 ⌋ ( − 1 ) m m ! ( n − 2 m ) ! x n − 2 m 2 m . {\displaystyle \operatorname {He} _{n}(x)=n!\sum _{m=0}^{\left\lfloor {\tfrac {n}{2}}\right\rfloor }{\frac {(-1)^{m}}{m!(n-2m)!}}{\frac {x^{n-2m}}{2^{m}}}.}
The inverse of the above explicit expressions, that is, those for monomials in terms of probabilist's Hermite polynomials He are x n = n ! ∑ m = 0 ⌊ n 2 ⌋ 1 2 m m ! ( n − 2 m ) ! He n − 2 m ( x ) . {\displaystyle x^{n}=n!\sum _{m=0}^{\left\lfloor {\tfrac {n}{2}}\right\rfloor }{\frac {1}{2^{m}m!(n-2m)!}}\operatorname {He} _{n-2m}(x).}
The corresponding expressions for the physicist's Hermite polynomials H follow directly by properly scaling this: [ 7 ] x n = n ! 2 n ∑ m = 0 ⌊ n 2 ⌋ 1 m ! ( n − 2 m ) ! H n − 2 m ( x ) . {\displaystyle x^{n}={\frac {n!}{2^{n}}}\sum _{m=0}^{\left\lfloor {\tfrac {n}{2}}\right\rfloor }{\frac {1}{m!(n-2m)!}}H_{n-2m}(x).}
The Hermite polynomials are given by the exponential generating function e x t − 1 2 t 2 = ∑ n = 0 ∞ He n ( x ) t n n ! , e 2 x t − t 2 = ∑ n = 0 ∞ H n ( x ) t n n ! . {\displaystyle {\begin{aligned}e^{xt-{\frac {1}{2}}t^{2}}&=\sum _{n=0}^{\infty }\operatorname {He} _{n}(x){\frac {t^{n}}{n!}},\\e^{2xt-t^{2}}&=\sum _{n=0}^{\infty }H_{n}(x){\frac {t^{n}}{n!}}.\end{aligned}}}
This equality is valid for all complex values of x and t , and can be obtained by writing the Taylor expansion at x of the entire function z → e − z 2 (in the physicist's case). One can also derive the (physicist's) generating function by using Cauchy's integral formula to write the Hermite polynomials as H n ( x ) = ( − 1 ) n e x 2 d n d x n e − x 2 = ( − 1 ) n e x 2 n ! 2 π i ∮ γ e − z 2 ( z − x ) n + 1 d z . {\displaystyle H_{n}(x)=(-1)^{n}e^{x^{2}}{\frac {d^{n}}{dx^{n}}}e^{-x^{2}}=(-1)^{n}e^{x^{2}}{\frac {n!}{2\pi i}}\oint _{\gamma }{\frac {e^{-z^{2}}}{(z-x)^{n+1}}}\,dz.}
Using this in the sum ∑ n = 0 ∞ H n ( x ) t n n ! , {\displaystyle \sum _{n=0}^{\infty }H_{n}(x){\frac {t^{n}}{n!}},} one can evaluate the remaining integral using the calculus of residues and arrive at the desired generating function.
A slight generalization states [ 8 ] e 2 x t − t 2 H k ( x − t ) = ∑ n = 0 ∞ H n + k ( x ) t n n ! {\displaystyle e^{2xt-t^{2}}H_{k}(x-t)=\sum _{n=0}^{\infty }{\frac {H_{n+k}(x)t^{n}}{n!}}}
If X is a random variable with a normal distribution with standard deviation 1 and expected value μ , then E [ He n ( X ) ] = μ n . {\displaystyle \operatorname {\mathbb {E} } \left[\operatorname {He} _{n}(X)\right]=\mu ^{n}.}
The moments of the standard normal (with expected value zero) may be read off directly from the relation for even indices: E [ X 2 n ] = ( − 1 ) n He 2 n ( 0 ) = ( 2 n − 1 ) ! ! , {\displaystyle \operatorname {\mathbb {E} } \left[X^{2n}\right]=(-1)^{n}\operatorname {He} _{2n}(0)=(2n-1)!!,} where (2 n − 1)!! is the double factorial . Note that the above expression is a special case of the representation of the probabilist's Hermite polynomials as moments: He n ( x ) = 1 2 π ∫ − ∞ ∞ ( x + i y ) n e − y 2 2 d y . {\displaystyle \operatorname {He} _{n}(x)={\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{\infty }(x+iy)^{n}e^{-{\frac {y^{2}}{2}}}\,dy.}
From the generating-function representation above, we see that the Hermite polynomials have a representation in terms of a contour integral , as He n ( x ) = n ! 2 π i ∮ C e t x − t 2 2 t n + 1 d t , H n ( x ) = n ! 2 π i ∮ C e 2 t x − t 2 t n + 1 d t , {\displaystyle {\begin{aligned}\operatorname {He} _{n}(x)&={\frac {n!}{2\pi i}}\oint _{C}{\frac {e^{tx-{\frac {t^{2}}{2}}}}{t^{n+1}}}\,dt,\\H_{n}(x)&={\frac {n!}{2\pi i}}\oint _{C}{\frac {e^{2tx-t^{2}}}{t^{n+1}}}\,dt,\end{aligned}}} with the contour encircling the origin.
Using the Fourier transform of the gaussian e − x 2 = 1 π ∫ e − t 2 + 2 i x t d t {\displaystyle e^{-x^{2}}={\frac {1}{\sqrt {\pi }}}\int e^{-t^{2}+2ixt}dt} , we have H n ( x ) = ( − 1 ) n e x 2 d n d x n e − x 2 = ( − 2 i ) n e x 2 π ∫ t n e − t 2 + 2 i x t d t He n ( x ) = ( − i ) n e x 2 / 2 2 π ∫ t n e − t 2 / 2 + i x t d t . {\displaystyle {\begin{aligned}H_{n}(x)&=(-1)^{n}e^{x^{2}}{\frac {d^{n}}{dx^{n}}}e^{-x^{2}}={\frac {(-2i)^{n}e^{x^{2}}}{\sqrt {\pi }}}\int t^{n}e^{-t^{2}+2ixt}dt\\\operatorname {He} _{n}(x)&={\frac {(-i)^{n}e^{x^{2}/2}}{\sqrt {2\pi }}}\int t^{n}\,e^{-t^{2}/2+ixt}\,dt.\end{aligned}}}
The addition theorem, or the summation theorem, states that [ 9 ] [ 10 ] : 8.958 ( ∑ k = 1 r a k 2 ) n 2 n ! H n ( ∑ k = 1 r a k x k ∑ k = 1 r a k 2 ) = ∑ m 1 + m 2 + … + m r = n , m i ≥ 0 ∏ k = 1 r { a k m k m k ! H m k ( x k ) } {\displaystyle {\frac {\left(\sum _{k=1}^{r}a_{k}^{2}\right)^{\frac {n}{2}}}{n!}}H_{n}\left({\frac {\sum _{k=1}^{r}a_{k}x_{k}}{\sqrt {\sum _{k=1}^{r}a_{k}^{2}}}}\right)=\sum _{m_{1}+m_{2}+\ldots +m_{r}=n,m_{i}\geq 0}\prod _{k=1}^{r}\left\{{\frac {a_{k}^{m_{k}}}{m_{k}!}}H_{m_{k}}\left(x_{k}\right)\right\}} for any nonzero vector a 1 : r {\displaystyle a_{1:r}} .
The multiplication theorem states that [ 9 ] H n ( λ x ) = λ n ∑ ℓ = 0 ⌊ n / 2 ⌋ ( − n ) 2 ℓ ℓ ! ( 1 − λ − 2 ) ℓ H n − 2 ℓ ( x ) {\displaystyle H_{n}\left(\lambda x\right)=\lambda ^{n}\sum _{\ell =0}^{\left\lfloor n/2\right\rfloor }{\frac {\left(-n\right)_{2\ell }}{\ell !}}(1-\lambda ^{-2})^{\ell }H_{n-2\ell }\left(x\right)} for any nonzero λ {\displaystyle \lambda } .
Feldheim formula [ 11 ] : Eq 46 1 a π ∫ − ∞ + ∞ e − x 2 a H m ( x + y λ ) H n ( x + z μ ) d x = ( 1 − a λ 2 ) m 2 ( 1 − a μ 2 ) n 2 ∑ r = 0 min ( m , n ) r ! ( m r ) ( n r ) ( 2 a ( λ 2 − a ) ( μ 2 − a ) ) r H m − r ( y λ 2 − a ) H n − r ( z μ 2 − a ) {\displaystyle {\begin{aligned}{\frac {1}{\sqrt {a\pi }}}&\int _{-\infty }^{+\infty }e^{-{\frac {x^{2}}{a}}}H_{m}\left({\frac {x+y}{\lambda }}\right)H_{n}\left({\frac {x+z}{\mu }}\right)dx\\&=\left(1-{\frac {a}{\lambda ^{2}}}\right)^{\frac {m}{2}}\left(1-{\frac {a}{\mu ^{2}}}\right)^{\frac {n}{2}}\sum _{r=0}^{\min(m,n)}r!{\binom {m}{r}}{\binom {n}{r}}\left({\frac {2a}{\sqrt {\left(\lambda ^{2}-a\right)\left(\mu ^{2}-a\right)}}}\right)^{r}H_{m-r}\left({\frac {y}{\sqrt {\lambda ^{2}-a}}}\right)H_{n-r}\left({\frac {z}{\sqrt {\mu ^{2}-a}}}\right)\end{aligned}}} where a ∈ C {\displaystyle a\in \mathbb {C} } has a positive real part. As a special case, [ 11 ] : Eq 52 1 π ∫ − ∞ + ∞ e − t 2 H m ( t sin θ + v cos θ ) H n ( t cos θ − v sin θ ) d t = ( − 1 ) n cos m θ sin n θ H m + n ( v ) {\displaystyle {\frac {1}{\sqrt {\pi }}}\int _{-\infty }^{+\infty }e^{-t^{2}}H_{m}(t\sin \theta +v\cos \theta )H_{n}(t\cos \theta -v\sin \theta )dt=(-1)^{n}\cos ^{m}\theta \sin ^{n}\theta H_{m+n}(v)}
Asymptotically, as n → ∞ , the expansion [ 12 ] e − x 2 2 ⋅ H n ( x ) ∼ 2 n π Γ ( n + 1 2 ) cos ( x 2 n − n π 2 ) {\displaystyle e^{-{\frac {x^{2}}{2}}}\cdot H_{n}(x)\sim {\frac {2^{n}}{\sqrt {\pi }}}\Gamma \left({\frac {n+1}{2}}\right)\cos \left(x{\sqrt {2n}}-{\frac {n\pi }{2}}\right)} holds true. For certain cases concerning a wider range of evaluation, it is necessary to include a factor for changing amplitude: e − x 2 2 ⋅ H n ( x ) ∼ 2 n π Γ ( n + 1 2 ) cos ( x 2 n − n π 2 ) ( 1 − x 2 2 n + 1 ) − 1 4 = Γ ( n ) Γ ( n 2 ) cos ( x 2 n − n π 2 ) ( 1 − x 2 2 n + 1 ) − 1 4 , {\displaystyle e^{-{\frac {x^{2}}{2}}}\cdot H_{n}(x)\sim {\frac {2^{n}}{\sqrt {\pi }}}\Gamma \left({\frac {n+1}{2}}\right)\cos \left(x{\sqrt {2n}}-{\frac {n\pi }{2}}\right)\left(1-{\frac {x^{2}}{2n+1}}\right)^{-{\frac {1}{4}}}={\frac {\Gamma (n)}{\Gamma \left({\frac {n}{2}}\right)}}\cos \left(x{\sqrt {2n}}-{\frac {n\pi }{2}}\right)\left(1-{\frac {x^{2}}{2n+1}}\right)^{-{\frac {1}{4}}},} which, using Stirling's approximation , can be further simplified, in the limit, to e − x 2 2 ⋅ H n ( x ) ∼ ( 2 n e ) n 2 2 cos ( x 2 n − n π 2 ) ( 1 − x 2 2 n + 1 ) − 1 4 . {\displaystyle e^{-{\frac {x^{2}}{2}}}\cdot H_{n}(x)\sim \left({\frac {2n}{e}}\right)^{\frac {n}{2}}{\sqrt {2}}\cos \left(x{\sqrt {2n}}-{\frac {n\pi }{2}}\right)\left(1-{\frac {x^{2}}{2n+1}}\right)^{-{\frac {1}{4}}}.}
This expansion is needed to resolve the wavefunction of a quantum harmonic oscillator such that it agrees with the classical approximation in the limit of the correspondence principle .
A better approximation, which accounts for the variation in frequency, is given by e − x 2 2 ⋅ H n ( x ) ∼ ( 2 n e ) n 2 2 cos ( x 2 n + 1 − x 2 3 − n π 2 ) ( 1 − x 2 2 n + 1 ) − 1 4 . {\displaystyle e^{-{\frac {x^{2}}{2}}}\cdot H_{n}(x)\sim \left({\frac {2n}{e}}\right)^{\frac {n}{2}}{\sqrt {2}}\cos \left(x{\sqrt {2n+1-{\frac {x^{2}}{3}}}}-{\frac {n\pi }{2}}\right)\left(1-{\frac {x^{2}}{2n+1}}\right)^{-{\frac {1}{4}}}.}
A finer approximation, [ 13 ] which takes into account the uneven spacing of the zeros near the edges, makes use of the substitution x = 2 n + 1 cos ( φ ) , 0 < ε ≤ φ ≤ π − ε , {\displaystyle x={\sqrt {2n+1}}\cos(\varphi ),\quad 0<\varepsilon \leq \varphi \leq \pi -\varepsilon ,} with which one has the uniform approximation e − x 2 2 ⋅ H n ( x ) = 2 n 2 + 1 4 n ! ( π n ) − 1 4 ( sin φ ) − 1 2 ⋅ ( sin ( 3 π 4 + ( n 2 + 1 4 ) ( sin 2 φ − 2 φ ) ) + O ( n − 1 ) ) . {\displaystyle e^{-{\frac {x^{2}}{2}}}\cdot H_{n}(x)=2^{{\frac {n}{2}}+{\frac {1}{4}}}{\sqrt {n!}}(\pi n)^{-{\frac {1}{4}}}(\sin \varphi )^{-{\frac {1}{2}}}\cdot \left(\sin \left({\frac {3\pi }{4}}+\left({\frac {n}{2}}+{\frac {1}{4}}\right)\left(\sin 2\varphi -2\varphi \right)\right)+O\left(n^{-1}\right)\right).}
Similar approximations hold for the monotonic and transition regions. Specifically, if x = 2 n + 1 cosh ( φ ) , 0 < ε ≤ φ ≤ ω < ∞ , {\displaystyle x={\sqrt {2n+1}}\cosh(\varphi ),\quad 0<\varepsilon \leq \varphi \leq \omega <\infty ,} then e − x 2 2 ⋅ H n ( x ) = 2 n 2 − 3 4 n ! ( π n ) − 1 4 ( sinh φ ) − 1 2 ⋅ e ( n 2 + 1 4 ) ( 2 φ − sinh 2 φ ) ( 1 + O ( n − 1 ) ) , {\displaystyle e^{-{\frac {x^{2}}{2}}}\cdot H_{n}(x)=2^{{\frac {n}{2}}-{\frac {3}{4}}}{\sqrt {n!}}(\pi n)^{-{\frac {1}{4}}}(\sinh \varphi )^{-{\frac {1}{2}}}\cdot e^{\left({\frac {n}{2}}+{\frac {1}{4}}\right)\left(2\varphi -\sinh 2\varphi \right)}\left(1+O\left(n^{-1}\right)\right),} while for x = 2 n + 1 + t {\displaystyle x={\sqrt {2n+1}}+t} with t complex and bounded, the approximation is e − x 2 2 ⋅ H n ( x ) = π 1 4 2 n 2 + 1 4 n ! n − 1 12 ( Ai ( 2 1 2 n 1 6 t ) + O ( n − 2 3 ) ) , {\displaystyle e^{-{\frac {x^{2}}{2}}}\cdot H_{n}(x)=\pi ^{\frac {1}{4}}2^{{\frac {n}{2}}+{\frac {1}{4}}}{\sqrt {n!}}\,n^{-{\frac {1}{12}}}\left(\operatorname {Ai} \left(2^{\frac {1}{2}}n^{\frac {1}{6}}t\right)+O\left(n^{-{\frac {2}{3}}}\right)\right),} where Ai is the Airy function of the first kind.
The physicist's Hermite polynomials evaluated at zero argument H n (0) are called Hermite numbers .
H n ( 0 ) = { 0 for odd n , ( − 2 ) n 2 ( n − 1 ) ! ! for even n , {\displaystyle H_{n}(0)={\begin{cases}0&{\text{for odd }}n,\\(-2)^{\frac {n}{2}}(n-1)!!&{\text{for even }}n,\end{cases}}} which satisfy the recursion relation H n (0) = −2( n − 1) H n − 2 (0) . Equivalently, H 2 n ( 0 ) = ( − 2 ) n ( 2 n − 1 ) ! ! {\displaystyle H_{2n}(0)=(-2)^{n}(2n-1)!!} .
In terms of the probabilist's polynomials this translates to He n ( 0 ) = { 0 for odd n , ( − 1 ) n 2 ( n − 1 ) ! ! for even n . {\displaystyle \operatorname {He} _{n}(0)={\begin{cases}0&{\text{for odd }}n,\\(-1)^{\frac {n}{2}}(n-1)!!&{\text{for even }}n.\end{cases}}}
Let M {\textstyle M} be a real n × n {\textstyle n\times n} symmetric matrix, then the Kibble–Slepian formula states that det ( I + M ) − 1 2 e x T M ( I + M ) − 1 x = ∑ K [ ∏ 1 ≤ i ≤ j ≤ n ( M i j / 2 ) k i j k i j ! ] 2 − t r ( K ) H k 1 ( x 1 ) ⋯ H k n ( x n ) {\displaystyle \det(I+M)^{-{\frac {1}{2}}}e^{x^{T}M(I+M)^{-1}x}=\sum _{K}\left[\prod _{1\leq i\leq j\leq n}{\frac {(M_{ij}/2)^{k_{ij}}}{k_{ij}!}}\right]2^{-tr(K)}H_{k_{1}}(x_{1})\cdots H_{k_{n}}(x_{n})} where ∑ K {\textstyle \sum _{K}} is the n ( n + 1 ) 2 {\displaystyle {\frac {n(n+1)}{2}}} -fold summation over all n × n {\textstyle n\times n} symmetric matrices with non-negative integer entries, t r ( K ) {\displaystyle tr(K)} is the trace of K {\displaystyle K} , and k i {\textstyle k_{i}} is defined as k i i + ∑ j = 1 n k i j {\textstyle k_{ii}+\sum _{j=1}^{n}k_{ij}} . This gives Mehler's formula when M = [ 0 u u 0 ] {\displaystyle M={\begin{bmatrix}0&u\\u&0\end{bmatrix}}} .
Equivalently stated, if T {\textstyle T} is a positive semidefinite matrix , then set M = − T ( I + T ) − 1 {\textstyle M=-T(I+T)^{-1}} , we have M ( I + M ) − 1 = − T {\textstyle M(I+M)^{-1}=-T} , so e − x T T x = det ( I + T ) − 1 2 ∑ K [ ∏ 1 ≤ i ≤ j ≤ n ( M i j / 2 ) k i j k i j ! ] 2 − t r ( K ) H k 1 ( x 1 ) … H k n ( x n ) {\displaystyle e^{-x^{T}Tx}=\det(I+T)^{-{\frac {1}{2}}}\sum _{K}\left[\prod _{1\leq i\leq j\leq n}{\frac {(M_{ij}/2)^{k_{ij}}}{k_{ij}!}}\right]2^{-tr(K)}H_{k_{1}}(x_{1})\dots H_{k_{n}}(x_{n})} Equivalently stated in a form closer to the boson quantum mechanics of the harmonic oscillator : [ 14 ] π − n / 4 det ( I + M ) − 1 2 e − 1 2 x T ( I − M ) ( I + M ) − 1 x = ∑ K [ ∏ 1 ≤ i ≤ j ≤ n M i j k i j / k i j ! ] [ ∏ 1 ≤ i ≤ n k i ! ] 1 / 2 2 − tr K ψ k 1 ( x 1 ) ⋯ ψ k n ( x n ) . {\displaystyle \pi ^{-n/4}\det(I+M)^{-{\frac {1}{2}}}e^{-{\frac {1}{2}}x^{T}(I-M)(I+M)^{-1}x}=\sum _{K}\left[\prod _{1\leq i\leq j\leq n}M_{ij}^{k_{ij}}/k_{ij}!\right]\left[\prod _{1\leq i\leq n}k_{i}!\right]^{1/2}2^{-\operatorname {tr} K}\psi _{k_{1}}\left(x_{1}\right)\cdots \psi _{k_{n}}\left(x_{n}\right).} where each ψ n ( x ) {\textstyle \psi _{n}(x)} is the n {\textstyle n} -th eigenfunction of the harmonic oscillator, defined as ψ n ( x ) := 1 2 n n ! ( 1 π ) 1 4 e − 1 2 x 2 H n ( x ) {\displaystyle \psi _{n}(x):={\frac {1}{\sqrt {2^{n}n!}}}\left({\frac {1}{\pi }}\right)^{\frac {1}{4}}e^{-{\frac {1}{2}}x^{2}}H_{n}(x)} The Kibble–Slepian formula was proposed by Kibble in 1945 [ 15 ] and proven by Slepian in 1972 using Fourier analysis. [ 16 ] Foata gave a combinatorial proof [ 17 ] while Louck gave a proof via boson quantum mechanics. [ 14 ] It has a generalization for complex-argument Hermite polynomials. [ 18 ] [ 19 ]
The Hermite polynomials can be expressed as a special case of the Laguerre polynomials : H 2 n ( x ) = ( − 4 ) n n ! L n ( − 1 2 ) ( x 2 ) = 4 n n ! ∑ k = 0 n ( − 1 ) n − k ( n − 1 2 n − k ) x 2 k k ! , H 2 n + 1 ( x ) = 2 ( − 4 ) n n ! x L n ( 1 2 ) ( x 2 ) = 2 ⋅ 4 n n ! ∑ k = 0 n ( − 1 ) n − k ( n + 1 2 n − k ) x 2 k + 1 k ! . {\displaystyle {\begin{aligned}H_{2n}(x)&=(-4)^{n}n!L_{n}^{\left(-{\frac {1}{2}}\right)}(x^{2})&&=4^{n}n!\sum _{k=0}^{n}(-1)^{n-k}{\binom {n-{\frac {1}{2}}}{n-k}}{\frac {x^{2k}}{k!}},\\H_{2n+1}(x)&=2(-4)^{n}n!xL_{n}^{\left({\frac {1}{2}}\right)}(x^{2})&&=2\cdot 4^{n}n!\sum _{k=0}^{n}(-1)^{n-k}{\binom {n+{\frac {1}{2}}}{n-k}}{\frac {x^{2k+1}}{k!}}.\end{aligned}}}
The physicist's Hermite polynomials can be expressed as a special case of the parabolic cylinder functions : H n ( x ) = 2 n U ( − 1 2 n , 1 2 , x 2 ) {\displaystyle H_{n}(x)=2^{n}U\left(-{\tfrac {1}{2}}n,{\tfrac {1}{2}},x^{2}\right)} in the right half-plane , where U ( a , b , z ) is Tricomi's confluent hypergeometric function . Similarly, H 2 n ( x ) = ( − 1 ) n ( 2 n ) ! n ! 1 F 1 ( − n , 1 2 ; x 2 ) , H 2 n + 1 ( x ) = ( − 1 ) n ( 2 n + 1 ) ! n ! 2 x 1 F 1 ( − n , 3 2 ; x 2 ) , {\displaystyle {\begin{aligned}H_{2n}(x)&=(-1)^{n}{\frac {(2n)!}{n!}}\,_{1}F_{1}{\big (}-n,{\tfrac {1}{2}};x^{2}{\big )},\\H_{2n+1}(x)&=(-1)^{n}{\frac {(2n+1)!}{n!}}\,2x\,_{1}F_{1}{\big (}-n,{\tfrac {3}{2}};x^{2}{\big )},\end{aligned}}} where 1 F 1 ( a , b ; z ) = M ( a , b ; z ) is Kummer's confluent hypergeometric function .
There is also [ 20 ] H n ( x ) = ( 2 x ) n 2 F 0 ( − 1 2 n , − 1 2 n + 1 2 − ; − 1 x 2 ) . {\displaystyle H_{n}\left(x\right)=(2x)^{n}{{}_{2}F_{0}}\left({-{\tfrac {1}{2}}n,-{\tfrac {1}{2}}n+{\tfrac {1}{2}} \atop -};-{\frac {1}{x^{2}}}\right).}
The Hermite polynomials can be obtained as the limit of various other polynomials. [ 21 ]
As a limit of Jacobi polynomials: lim α → ∞ α − 1 2 n P n ( α , α ) ( α − 1 2 x ) = H n ( x ) 2 n n ! . {\displaystyle \lim _{\alpha \to \infty }\alpha ^{-{\frac {1}{2}}n}P_{n}^{(\alpha ,\alpha )}\left(\alpha ^{-{\frac {1}{2}}}x\right)={\frac {H_{n}\left(x\right)}{2^{n}n!}}.} As a limit of ultraspherical polynomials: lim λ → ∞ λ − 1 2 n C n ( λ ) ( λ − 1 2 x ) = H n ( x ) n ! . {\displaystyle \lim _{\lambda \to \infty }\lambda ^{-{\frac {1}{2}}n}C_{n}^{(\lambda )}\left(\lambda ^{-{\frac {1}{2}}}x\right)={\frac {H_{n}\left(x\right)}{n!}}.} As a limit of associated Laguerre polynomials: lim α → ∞ ( 2 α ) 1 2 n L n ( α ) ( ( 2 α ) 1 2 x + α ) = ( − 1 ) n n ! H n ( x ) . {\displaystyle \lim _{\alpha \to \infty }\left({\frac {2}{\alpha }}\right)^{{\frac {1}{2}}n}L_{n}^{(\alpha )}\left((2\alpha )^{\frac {1}{2}}x+\alpha \right)={\frac {(-1)^{n}}{n!}}H_{n}\left(x\right).}
Similar to Taylor expansion, some functions are expressible as an infinite sum of Hermite polynomials. Specifically, if ∫ e − x 2 f ( x ) 2 d x < ∞ {\displaystyle \int e^{-x^{2}}f(x)^{2}dx<\infty } , then it has an expansion in the physicist's Hermite polynomials. [ 22 ]
Given such f {\displaystyle f} , the partial sums of the Hermite expansion of f {\displaystyle f} converges to in the L p {\displaystyle L^{p}} norm if and only if 4 / 3 < p < 4 {\displaystyle 4/3<p<4} . [ 23 ] x n = n ! 2 n ∑ k = 0 ⌊ n / 2 ⌋ 1 k ! ( n − 2 k ) ! H n − 2 k ( x ) = n ! ∑ k = 0 ⌊ n / 2 ⌋ 1 k ! 2 k ( n − 2 k ) ! He n − 2 k ( x ) , n ∈ Z + . {\displaystyle x^{n}={\frac {n!}{2^{n}}}\,\sum _{k=0}^{\left\lfloor n/2\right\rfloor }{\frac {1}{k!\,(n-2k)!}}\,H_{n-2k}(x)=n!\sum _{k=0}^{\left\lfloor n/2\right\rfloor }{\frac {1}{k!\,2^{k}\,(n-2k)!}}\,\operatorname {He} _{n-2k}(x),\qquad n\in \mathbb {Z} _{+}.} e a x = e a 2 / 4 ∑ n ≥ 0 a n n ! 2 n H n ( x ) , a ∈ C , x ∈ R . {\displaystyle e^{ax}=e^{a^{2}/4}\sum _{n\geq 0}{\frac {a^{n}}{n!\,2^{n}}}\,H_{n}(x),\qquad a\in \mathbb {C} ,\quad x\in \mathbb {R} .} e − a 2 x 2 = ∑ n ≥ 0 ( − 1 ) n a 2 n n ! ( 1 + a 2 ) n + 1 / 2 2 2 n H 2 n ( x ) . {\displaystyle e^{-a^{2}x^{2}}=\sum _{n\geq 0}{\frac {(-1)^{n}a^{2n}}{n!\left(1+a^{2}\right)^{n+1/2}2^{2n}}}\,H_{2n}(x).} erf ( x ) = 2 π ∫ 0 x e − t 2 d t = 1 2 π ∑ k ≥ 0 ( − 1 ) k k ! ( 2 k + 1 ) 2 3 k H 2 k ( x ) . {\displaystyle \operatorname {erf} (x)={\frac {2}{\sqrt {\pi }}}\int _{0}^{x}e^{-t^{2}}~dt={\frac {1}{\sqrt {2\pi }}}\sum _{k\geq 0}{\frac {(-1)^{k}}{k!(2k+1)2^{3k}}}H_{2k}(x).} cosh ( 2 x ) = e ∑ k ≥ 0 1 ( 2 k ) ! H 2 k ( x ) , sinh ( 2 x ) = e ∑ k ≥ 0 1 ( 2 k + 1 ) ! H 2 k + 1 ( x ) . {\displaystyle \cosh(2x)=e\sum _{k\geq 0}{\frac {1}{(2k)!}}\,H_{2k}(x),\qquad \sinh(2x)=e\sum _{k\geq 0}{\frac {1}{(2k+1)!}}\,H_{2k+1}(x).} cos ( x ) = e − 1 / 4 ∑ k ≥ 0 ( − 1 ) k 2 2 k ( 2 k ) ! H 2 k ( x ) sin ( x ) = e − 1 / 4 ∑ k ≥ 0 ( − 1 ) k 2 2 k + 1 ( 2 k + 1 ) ! H 2 k + 1 ( x ) {\displaystyle \cos(x)=e^{-1/4}\,\sum _{k\geq 0}{\frac {(-1)^{k}}{2^{2k}\,(2k)!}}\,H_{2k}(x)\quad \sin(x)=e^{-1/4}\,\sum _{k\geq 0}{\frac {(-1)^{k}}{2^{2k+1}\,(2k+1)!}}\,H_{2k+1}(x)}
The probabilist's Hermite polynomials satisfy the identity [ 24 ] He n ( x ) = e − D 2 2 x n , {\displaystyle \operatorname {He} _{n}(x)=e^{-{\frac {D^{2}}{2}}}x^{n},} where D represents differentiation with respect to x , and the exponential is interpreted by expanding it as a power series . There are no delicate questions of convergence of this series when it operates on polynomials, since all but finitely many terms vanish.
Since the power-series coefficients of the exponential are well known, and higher-order derivatives of the monomial x n can be written down explicitly, this differential-operator representation gives rise to a concrete formula for the coefficients of H n that can be used to quickly compute these polynomials.
Since the formal expression for the Weierstrass transform W is e D 2 , we see that the Weierstrass transform of ( √ 2 ) n He n ( x / √ 2 ) is x n . Essentially the Weierstrass transform thus turns a series of Hermite polynomials into a corresponding Maclaurin series .
The existence of some formal power series g ( D ) with nonzero constant coefficient, such that He n ( x ) = g ( D ) x n , is another equivalent to the statement that these polynomials form an Appell sequence . Since they are an Appell sequence, they are a fortiori a Sheffer sequence .
The probabilist's Hermite polynomials defined above are orthogonal with respect to the standard normal probability distribution, whose density function is 1 2 π e − x 2 2 , {\displaystyle {\frac {1}{\sqrt {2\pi }}}e^{-{\frac {x^{2}}{2}}},} which has expected value 0 and variance 1.
Scaling, one may analogously speak of generalized Hermite polynomials [ 25 ] He n [ α ] ( x ) {\displaystyle \operatorname {He} _{n}^{[\alpha ]}(x)} of variance α , where α is any positive number. These are then orthogonal with respect to the normal probability distribution whose density function is 1 2 π α e − x 2 2 α . {\displaystyle {\frac {1}{\sqrt {2\pi \alpha }}}e^{-{\frac {x^{2}}{2\alpha }}}.} They are given by He n [ α ] ( x ) = α n 2 He n ( x α ) = ( α 2 ) n 2 H n ( x 2 α ) = e − α D 2 2 ( x n ) . {\displaystyle \operatorname {He} _{n}^{[\alpha ]}(x)=\alpha ^{\frac {n}{2}}\operatorname {He} _{n}\left({\frac {x}{\sqrt {\alpha }}}\right)=\left({\frac {\alpha }{2}}\right)^{\frac {n}{2}}H_{n}\left({\frac {x}{\sqrt {2\alpha }}}\right)=e^{-{\frac {\alpha D^{2}}{2}}}\left(x^{n}\right).}
Now, if He n [ α ] ( x ) = ∑ k = 0 n h n , k [ α ] x k , {\displaystyle \operatorname {He} _{n}^{[\alpha ]}(x)=\sum _{k=0}^{n}h_{n,k}^{[\alpha ]}x^{k},} then the polynomial sequence whose n th term is ( He n [ α ] ∘ He [ β ] ) ( x ) ≡ ∑ k = 0 n h n , k [ α ] He k [ β ] ( x ) {\displaystyle \left(\operatorname {He} _{n}^{[\alpha ]}\circ \operatorname {He} ^{[\beta ]}\right)(x)\equiv \sum _{k=0}^{n}h_{n,k}^{[\alpha ]}\,\operatorname {He} _{k}^{[\beta ]}(x)} is called the umbral composition of the two polynomial sequences. It can be shown to satisfy the identities ( He n [ α ] ∘ He [ β ] ) ( x ) = He n [ α + β ] ( x ) {\displaystyle \left(\operatorname {He} _{n}^{[\alpha ]}\circ \operatorname {He} ^{[\beta ]}\right)(x)=\operatorname {He} _{n}^{[\alpha +\beta ]}(x)} and He n [ α + β ] ( x + y ) = ∑ k = 0 n ( n k ) He k [ α ] ( x ) He n − k [ β ] ( y ) . {\displaystyle \operatorname {He} _{n}^{[\alpha +\beta ]}(x+y)=\sum _{k=0}^{n}{\binom {n}{k}}\operatorname {He} _{k}^{[\alpha ]}(x)\operatorname {He} _{n-k}^{[\beta ]}(y).} The last identity is expressed by saying that this parameterized family of polynomial sequences is known as a cross-sequence. (See the above section on Appell sequences and on the differential-operator representation , which leads to a ready derivation of it. This binomial type identity, for α = β = 1 / 2 , has already been encountered in the above section on #Recursion relations .)
Since polynomial sequences form a group under the operation of umbral composition , one may denote by He n [ − α ] ( x ) {\displaystyle \operatorname {He} _{n}^{[-\alpha ]}(x)} the sequence that is inverse to the one similarly denoted, but without the minus sign, and thus speak of Hermite polynomials of negative variance. For α > 0 , the coefficients of He n [ − α ] ( x ) {\displaystyle \operatorname {He} _{n}^{[-\alpha ]}(x)} are just the absolute values of the corresponding coefficients of He n [ α ] ( x ) {\displaystyle \operatorname {He} _{n}^{[\alpha ]}(x)} .
These arise as moments of normal probability distributions: The n th moment of the normal distribution with expected value μ and variance σ 2 is E [ X n ] = He n [ − σ 2 ] ( μ ) , {\displaystyle E[X^{n}]=\operatorname {He} _{n}^{[-\sigma ^{2}]}(\mu ),} where X is a random variable with the specified normal distribution. A special case of the cross-sequence identity then says that ∑ k = 0 n ( n k ) He k [ α ] ( x ) He n − k [ − α ] ( y ) = He n [ 0 ] ( x + y ) = ( x + y ) n . {\displaystyle \sum _{k=0}^{n}{\binom {n}{k}}\operatorname {He} _{k}^{[\alpha ]}(x)\operatorname {He} _{n-k}^{[-\alpha ]}(y)=\operatorname {He} _{n}^{[0]}(x+y)=(x+y)^{n}.}
One can define the Hermite functions (often called Hermite-Gaussian functions) from the physicist's polynomials: ψ n ( x ) = ( 2 n n ! π ) − 1 2 e − x 2 2 H n ( x ) = ( − 1 ) n ( 2 n n ! π ) − 1 2 e x 2 2 d n d x n e − x 2 . {\displaystyle \psi _{n}(x)=\left(2^{n}n!{\sqrt {\pi }}\right)^{-{\frac {1}{2}}}e^{-{\frac {x^{2}}{2}}}H_{n}(x)=(-1)^{n}\left(2^{n}n!{\sqrt {\pi }}\right)^{-{\frac {1}{2}}}e^{\frac {x^{2}}{2}}{\frac {d^{n}}{dx^{n}}}e^{-x^{2}}.} Thus, 2 ( n + 1 ) ψ n + 1 ( x ) = ( x − d d x ) ψ n ( x ) . {\displaystyle {\sqrt {2(n+1)}}~~\psi _{n+1}(x)=\left(x-{d \over dx}\right)\psi _{n}(x).}
Since these functions contain the square root of the weight function and have been scaled appropriately, they are orthonormal : ∫ − ∞ ∞ ψ n ( x ) ψ m ( x ) d x = δ n m , {\displaystyle \int _{-\infty }^{\infty }\psi _{n}(x)\psi _{m}(x)\,dx=\delta _{nm},} and they form an orthonormal basis of L 2 ( R ) . This fact is equivalent to the corresponding statement for Hermite polynomials (see above).
The Hermite functions are closely related to the Whittaker function ( Whittaker & Watson 1996 ) D n ( z ) : D n ( z ) = ( n ! π ) 1 2 ψ n ( z 2 ) = ( − 1 ) n e z 2 4 d n d z n e − z 2 2 {\displaystyle D_{n}(z)=\left(n!{\sqrt {\pi }}\right)^{\frac {1}{2}}\psi _{n}\left({\frac {z}{\sqrt {2}}}\right)=(-1)^{n}e^{\frac {z^{2}}{4}}{\frac {d^{n}}{dz^{n}}}e^{\frac {-z^{2}}{2}}} and thereby to other parabolic cylinder functions .
The Hermite functions satisfy the differential equation ψ n ″ ( x ) + ( 2 n + 1 − x 2 ) ψ n ( x ) = 0. {\displaystyle \psi _{n}''(x)+\left(2n+1-x^{2}\right)\psi _{n}(x)=0.} This equation is equivalent to the Schrödinger equation for a harmonic oscillator in quantum mechanics, so these functions are the eigenfunctions .
ψ 0 ( x ) = π − 1 4 e − 1 2 x 2 , ψ 1 ( x ) = 2 π − 1 4 x e − 1 2 x 2 , ψ 2 ( x ) = ( 2 π 1 4 ) − 1 ( 2 x 2 − 1 ) e − 1 2 x 2 , ψ 3 ( x ) = ( 3 π 1 4 ) − 1 ( 2 x 3 − 3 x ) e − 1 2 x 2 , ψ 4 ( x ) = ( 2 6 π 1 4 ) − 1 ( 4 x 4 − 12 x 2 + 3 ) e − 1 2 x 2 , ψ 5 ( x ) = ( 2 15 π 1 4 ) − 1 ( 4 x 5 − 20 x 3 + 15 x ) e − 1 2 x 2 . {\displaystyle {\begin{aligned}\psi _{0}(x)&=\pi ^{-{\frac {1}{4}}}\,e^{-{\frac {1}{2}}x^{2}},\\\psi _{1}(x)&={\sqrt {2}}\,\pi ^{-{\frac {1}{4}}}\,x\,e^{-{\frac {1}{2}}x^{2}},\\\psi _{2}(x)&=\left({\sqrt {2}}\,\pi ^{\frac {1}{4}}\right)^{-1}\,\left(2x^{2}-1\right)\,e^{-{\frac {1}{2}}x^{2}},\\\psi _{3}(x)&=\left({\sqrt {3}}\,\pi ^{\frac {1}{4}}\right)^{-1}\,\left(2x^{3}-3x\right)\,e^{-{\frac {1}{2}}x^{2}},\\\psi _{4}(x)&=\left(2{\sqrt {6}}\,\pi ^{\frac {1}{4}}\right)^{-1}\,\left(4x^{4}-12x^{2}+3\right)\,e^{-{\frac {1}{2}}x^{2}},\\\psi _{5}(x)&=\left(2{\sqrt {15}}\,\pi ^{\frac {1}{4}}\right)^{-1}\,\left(4x^{5}-20x^{3}+15x\right)\,e^{-{\frac {1}{2}}x^{2}}.\end{aligned}}}
Following recursion relations of Hermite polynomials, the Hermite functions obey ψ n ′ ( x ) = n 2 ψ n − 1 ( x ) − n + 1 2 ψ n + 1 ( x ) {\displaystyle \psi _{n}'(x)={\sqrt {\frac {n}{2}}}\,\psi _{n-1}(x)-{\sqrt {\frac {n+1}{2}}}\psi _{n+1}(x)} and x ψ n ( x ) = n 2 ψ n − 1 ( x ) + n + 1 2 ψ n + 1 ( x ) . {\displaystyle x\psi _{n}(x)={\sqrt {\frac {n}{2}}}\,\psi _{n-1}(x)+{\sqrt {\frac {n+1}{2}}}\psi _{n+1}(x).}
Extending the first relation to the arbitrary m th derivatives for any positive integer m leads to ψ n ( m ) ( x ) = ∑ k = 0 m ( m k ) ( − 1 ) k 2 m − k 2 n ! ( n − m + k ) ! ψ n − m + k ( x ) He k ( x ) . {\displaystyle \psi _{n}^{(m)}(x)=\sum _{k=0}^{m}{\binom {m}{k}}(-1)^{k}2^{\frac {m-k}{2}}{\sqrt {\frac {n!}{(n-m+k)!}}}\psi _{n-m+k}(x)\operatorname {He} _{k}(x).}
This formula can be used in connection with the recurrence relations for He n and ψ n to calculate any derivative of the Hermite functions efficiently.
For real x , the Hermite functions satisfy the following bound due to Harald Cramér [ 26 ] [ 27 ] and Jack Indritz: [ 28 ] | ψ n ( x ) | ≤ π − 1 4 . {\displaystyle {\bigl |}\psi _{n}(x){\bigr |}\leq \pi ^{-{\frac {1}{4}}}.}
The Hermite functions ψ n ( x ) are a set of eigenfunctions of the continuous Fourier transform F . To see this, take the physicist's version of the generating function and multiply by e − 1 / 2 x 2 . This gives e − 1 2 x 2 + 2 x t − t 2 = ∑ n = 0 ∞ e − 1 2 x 2 H n ( x ) t n n ! . {\displaystyle e^{-{\frac {1}{2}}x^{2}+2xt-t^{2}}=\sum _{n=0}^{\infty }e^{-{\frac {1}{2}}x^{2}}H_{n}(x){\frac {t^{n}}{n!}}.}
The Fourier transform of the left side is given by F { e − 1 2 x 2 + 2 x t − t 2 } ( k ) = 1 2 π ∫ − ∞ ∞ e − i x k e − 1 2 x 2 + 2 x t − t 2 d x = e − 1 2 k 2 − 2 k i t + t 2 = ∑ n = 0 ∞ e − 1 2 k 2 H n ( k ) ( − i t ) n n ! . {\displaystyle {\begin{aligned}{\mathcal {F}}\left\{e^{-{\frac {1}{2}}x^{2}+2xt-t^{2}}\right\}(k)&={\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{\infty }e^{-ixk}e^{-{\frac {1}{2}}x^{2}+2xt-t^{2}}\,dx\\&=e^{-{\frac {1}{2}}k^{2}-2kit+t^{2}}\\&=\sum _{n=0}^{\infty }e^{-{\frac {1}{2}}k^{2}}H_{n}(k){\frac {(-it)^{n}}{n!}}.\end{aligned}}}
The Fourier transform of the right side is given by F { ∑ n = 0 ∞ e − 1 2 x 2 H n ( x ) t n n ! } = ∑ n = 0 ∞ F { e − 1 2 x 2 H n ( x ) } t n n ! . {\displaystyle {\mathcal {F}}\left\{\sum _{n=0}^{\infty }e^{-{\frac {1}{2}}x^{2}}H_{n}(x){\frac {t^{n}}{n!}}\right\}=\sum _{n=0}^{\infty }{\mathcal {F}}\left\{e^{-{\frac {1}{2}}x^{2}}H_{n}(x)\right\}{\frac {t^{n}}{n!}}.}
Equating like powers of t in the transformed versions of the left and right sides finally yields F { e − 1 2 x 2 H n ( x ) } = ( − i ) n e − 1 2 k 2 H n ( k ) . {\displaystyle {\mathcal {F}}\left\{e^{-{\frac {1}{2}}x^{2}}H_{n}(x)\right\}=(-i)^{n}e^{-{\frac {1}{2}}k^{2}}H_{n}(k).}
The Hermite functions ψ n ( x ) are thus an orthonormal basis of L 2 ( R ) , which diagonalizes the Fourier transform operator . [ 29 ] In short, we have: 1 2 π ∫ e − i k x ψ n ( x ) d x = ( − i ) n ψ n ( k ) , 1 2 π ∫ e + i k x ψ n ( k ) d k = i n ψ n ( x ) {\displaystyle {\frac {1}{\sqrt {2\pi }}}\int e^{-ikx}\psi _{n}(x)dx=(-i)^{n}\psi _{n}(k),\quad {\frac {1}{\sqrt {2\pi }}}\int e^{+ikx}\psi _{n}(k)dk=i^{n}\psi _{n}(x)}
The Wigner distribution function of the n th-order Hermite function is related to the n th-order Laguerre polynomial . The Laguerre polynomials are L n ( x ) := ∑ k = 0 n ( n k ) ( − 1 ) k k ! x k , {\displaystyle L_{n}(x):=\sum _{k=0}^{n}{\binom {n}{k}}{\frac {(-1)^{k}}{k!}}x^{k},} leading to the oscillator Laguerre functions l n ( x ) := e − x 2 L n ( x ) . {\displaystyle l_{n}(x):=e^{-{\frac {x}{2}}}L_{n}(x).} For all natural integers n , it is straightforward to see [ 30 ] that W ψ n ( t , f ) = ( − 1 ) n l n ( 4 π ( t 2 + f 2 ) ) , {\displaystyle W_{\psi _{n}}(t,f)=(-1)^{n}l_{n}{\big (}4\pi (t^{2}+f^{2}){\big )},} where the Wigner distribution of a function x ∈ L 2 ( R , C ) is defined as W x ( t , f ) = ∫ − ∞ ∞ x ( t + τ 2 ) x ( t − τ 2 ) ∗ e − 2 π i τ f d τ . {\displaystyle W_{x}(t,f)=\int _{-\infty }^{\infty }x\left(t+{\frac {\tau }{2}}\right)\,x\left(t-{\frac {\tau }{2}}\right)^{*}\,e^{-2\pi i\tau f}\,d\tau .} This is a fundamental result for the quantum harmonic oscillator discovered by Hip Groenewold in 1946 in his PhD thesis. [ 31 ] It is the standard paradigm of quantum mechanics in phase space .
There are further relations between the two families of polynomials.
It can be shown [ 32 ] [ 33 ] that the overlap between two different Hermite functions ( k ≠ ℓ {\displaystyle k\neq \ell } ) over a given interval has the exact result: ∫ x 1 x 2 ψ k ( x ) ψ ℓ ( x ) d x = 1 2 ( ℓ − k ) ( ψ k ′ ( x 2 ) ψ ℓ ( x 2 ) − ψ ℓ ′ ( x 2 ) ψ k ( x 2 ) − ψ k ′ ( x 1 ) ψ ℓ ( x 1 ) + ψ ℓ ′ ( x 1 ) ψ k ( x 1 ) ) . {\displaystyle \int _{x_{1}}^{x_{2}}\psi _{k}(x)\psi _{\ell }(x)\,dx={\frac {1}{2(\ell -k)}}\left(\psi _{k}'(x_{2})\psi _{\ell }(x_{2})-\psi _{\ell }'(x_{2})\psi _{k}(x_{2})-\psi _{k}'(x_{1})\psi _{\ell }(x_{1})+\psi _{\ell }'(x_{1})\psi _{k}(x_{1})\right).}
In the Hermite polynomial He n ( x ) of variance 1, the absolute value of the coefficient of x k is the number of (unordered) partitions of an n -element set into k singletons and n − k / 2 (unordered) pairs. Equivalently, it is the number of involutions of an n -element set with precisely k fixed points, or in other words, the number of matchings in the complete graph on n vertices that leave k vertices uncovered (indeed, the Hermite polynomials are the matching polynomials of these graphs). The sum of the absolute values of the coefficients gives the total number of partitions into singletons and pairs, the so-called telephone numbers
This combinatorial interpretation can be related to complete exponential Bell polynomials as He n ( x ) = B n ( x , − 1 , 0 , … , 0 ) , {\displaystyle \operatorname {He} _{n}(x)=B_{n}(x,-1,0,\ldots ,0),} where x i = 0 for all i > 2 .
These numbers may also be expressed as a special value of the Hermite polynomials: [ 34 ] T ( n ) = He n ( i ) i n . {\displaystyle T(n)={\frac {\operatorname {He} _{n}(i)}{i^{n}}}.}
The Christoffel–Darboux formula for Hermite polynomials reads ∑ k = 0 n H k ( x ) H k ( y ) k ! 2 k = 1 n ! 2 n + 1 H n ( y ) H n + 1 ( x ) − H n ( x ) H n + 1 ( y ) x − y . {\displaystyle \sum _{k=0}^{n}{\frac {H_{k}(x)H_{k}(y)}{k!2^{k}}}={\frac {1}{n!2^{n+1}}}\,{\frac {H_{n}(y)H_{n+1}(x)-H_{n}(x)H_{n+1}(y)}{x-y}}.}
Moreover, the following completeness identity for the above Hermite functions holds in the sense of distributions : ∑ n = 0 ∞ ψ n ( x ) ψ n ( y ) = δ ( x − y ) , {\displaystyle \sum _{n=0}^{\infty }\psi _{n}(x)\psi _{n}(y)=\delta (x-y),} where δ is the Dirac delta function , ψ n the Hermite functions, and δ ( x − y ) represents the Lebesgue measure on the line y = x in R 2 , normalized so that its projection on the horizontal axis is the usual Lebesgue measure.
This distributional identity follows Wiener (1958) by taking u → 1 in Mehler's formula , valid when −1 < u < 1 : E ( x , y ; u ) := ∑ n = 0 ∞ u n ψ n ( x ) ψ n ( y ) = 1 π ( 1 − u 2 ) exp ( − 1 − u 1 + u ( x + y ) 2 4 − 1 + u 1 − u ( x − y ) 2 4 ) , {\displaystyle E(x,y;u):=\sum _{n=0}^{\infty }u^{n}\,\psi _{n}(x)\,\psi _{n}(y)={\frac {1}{\sqrt {\pi (1-u^{2})}}}\,\exp \left(-{\frac {1-u}{1+u}}\,{\frac {(x+y)^{2}}{4}}-{\frac {1+u}{1-u}}\,{\frac {(x-y)^{2}}{4}}\right),} which is often stated equivalently as a separable kernel, [ 35 ] [ 36 ] ∑ n = 0 ∞ H n ( x ) H n ( y ) n ! ( u 2 ) n = 1 1 − u 2 e 2 u 1 + u x y − u 2 1 − u 2 ( x − y ) 2 . {\displaystyle \sum _{n=0}^{\infty }{\frac {H_{n}(x)H_{n}(y)}{n!}}\left({\frac {u}{2}}\right)^{n}={\frac {1}{\sqrt {1-u^{2}}}}e^{{\frac {2u}{1+u}}xy-{\frac {u^{2}}{1-u^{2}}}(x-y)^{2}}.}
The function ( x , y ) → E ( x , y ; u ) is the bivariate Gaussian probability density on R 2 , which is, when u is close to 1, very concentrated around the line y = x , and very spread out on that line. It follows that ∑ n = 0 ∞ u n ⟨ f , ψ n ⟩ ⟨ ψ n , g ⟩ = ∬ E ( x , y ; u ) f ( x ) g ( y ) ¯ d x d y → ∫ f ( x ) g ( x ) ¯ d x = ⟨ f , g ⟩ {\displaystyle \sum _{n=0}^{\infty }u^{n}\langle f,\psi _{n}\rangle \langle \psi _{n},g\rangle =\iint E(x,y;u)f(x){\overline {g(y)}}\,dx\,dy\to \int f(x){\overline {g(x)}}\,dx=\langle f,g\rangle } when f and g are continuous and compactly supported.
This yields that f can be expressed in Hermite functions as the sum of a series of vectors in L 2 ( R ) , namely, f = ∑ n = 0 ∞ ⟨ f , ψ n ⟩ ψ n . {\displaystyle f=\sum _{n=0}^{\infty }\langle f,\psi _{n}\rangle \psi _{n}.}
In order to prove the above equality for E ( x , y ; u ) , the Fourier transform of Gaussian functions is used repeatedly: ρ π e − ρ 2 x 2 4 = ∫ e i s x − s 2 ρ 2 d s for ρ > 0. {\displaystyle \rho {\sqrt {\pi }}e^{-{\frac {\rho ^{2}x^{2}}{4}}}=\int e^{isx-{\frac {s^{2}}{\rho ^{2}}}}\,ds\quad {\text{for }}\rho >0.}
The Hermite polynomial is then represented as H n ( x ) = ( − 1 ) n e x 2 d n d x n ( 1 2 π ∫ e i s x − s 2 4 d s ) = ( − 1 ) n e x 2 1 2 π ∫ ( i s ) n e i s x − s 2 4 d s . {\displaystyle H_{n}(x)=(-1)^{n}e^{x^{2}}{\frac {d^{n}}{dx^{n}}}\left({\frac {1}{2{\sqrt {\pi }}}}\int e^{isx-{\frac {s^{2}}{4}}}\,ds\right)=(-1)^{n}e^{x^{2}}{\frac {1}{2{\sqrt {\pi }}}}\int (is)^{n}e^{isx-{\frac {s^{2}}{4}}}\,ds.}
With this representation for H n ( x ) and H n ( y ) , it is evident that E ( x , y ; u ) = ∑ n = 0 ∞ u n 2 n n ! π H n ( x ) H n ( y ) e − x 2 + y 2 2 = e x 2 + y 2 2 4 π π ∬ ( ∑ n = 0 ∞ 1 2 n n ! ( − u s t ) n ) e i s x + i t y − s 2 4 − t 2 4 d s d t = e x 2 + y 2 2 4 π π ∬ e − u s t 2 e i s x + i t y − s 2 4 − t 2 4 d s d t , {\displaystyle {\begin{aligned}E(x,y;u)&=\sum _{n=0}^{\infty }{\frac {u^{n}}{2^{n}n!{\sqrt {\pi }}}}\,H_{n}(x)H_{n}(y)e^{-{\frac {x^{2}+y^{2}}{2}}}\\&={\frac {e^{\frac {x^{2}+y^{2}}{2}}}{4\pi {\sqrt {\pi }}}}\iint \left(\sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}(-ust)^{n}\right)e^{isx+ity-{\frac {s^{2}}{4}}-{\frac {t^{2}}{4}}}\,ds\,dt\\&={\frac {e^{\frac {x^{2}+y^{2}}{2}}}{4\pi {\sqrt {\pi }}}}\iint e^{-{\frac {ust}{2}}}\,e^{isx+ity-{\frac {s^{2}}{4}}-{\frac {t^{2}}{4}}}\,ds\,dt,\end{aligned}}} and this yields the desired resolution of the identity result, using again the Fourier transform of Gaussian kernels under the substitution s = σ + τ 2 , t = σ − τ 2 . {\displaystyle s={\frac {\sigma +\tau }{\sqrt {2}}},\quad t={\frac {\sigma -\tau }{\sqrt {2}}}.} | https://en.wikipedia.org/wiki/Hermite_polynomials |
In algebra , the term Hermite ring (after Charles Hermite ) has been applied to three different objects.
According to Kaplansky (1949) (p. 465), a ring is right Hermite if, for every two elements a and b of the ring, there is an element d of the ring and an invertible 2×2 matrix M over the ring such that ( a b ) M = ( d 0), and the term left Hermite is defined similarly. Matrices over such a ring can be put in Hermite normal form by right multiplication by a square invertible matrix ( Kaplansky (1949) , p. 468.) Lam (2006) (appendix to §I.4) calls this property K-Hermite , using Hermite instead in the sense given below.
According to Lam (1978) (§I.4, p. 26), a ring is right Hermite if any finitely generated stably free right module over the ring is free . This is equivalent to requiring that any row vector ( b 1 ,..., b n ) of elements of the ring which generate it as a right module (i.e., b 1 R + ... + b n R = R ) can be completed to a (not necessarily square [ clarification needed ] ) invertible matrix by adding some number of rows. The criterion of being left Hermite can be defined similarly. Lissner (1965) (p. 528) earlier called a commutative ring with this property an H-ring .
According to Cohn (2006) (§0.4), a ring is Hermite if, in addition to every stably free (left) module being free, it has invariant basis number .
All commutative rings which are Hermite in the sense of Kaplansky are also Hermite in the sense of Lam, but the converse is not necessarily true. All Bézout domains are Hermite in the sense of Kaplansky, and a commutative ring which is Hermite in the sense of Kaplansky is also a Bézout ring ( Lam (2006) , pp. 39-40.)
The Hermite ring conjecture , introduced by Lam (1978) (p. xi), states that if R is a commutative Hermite ring, then the polynomial ring R [ x ] is also a Hermite ring.
This algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hermite_ring |
In mathematics , the Hermite–Hadamard inequality , named after Charles Hermite and Jacques Hadamard and sometimes also called Hadamard's inequality , states that if a function f : [ a , b ] → R is convex , then the following chain of inequalities hold:
The inequality has been generalized to higher dimensions: if Ω ⊂ R n {\displaystyle \Omega \subset \mathbb {R} ^{n}} is a bounded, convex domain and f : Ω → R {\displaystyle f:\Omega \rightarrow \mathbb {R} } is a positive convex function, then
where c n {\displaystyle c_{n}} is a constant depending only on the dimension. | https://en.wikipedia.org/wiki/Hermite–Hadamard_inequality |
In mathematical analysis , a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign :
(where the ∗ {\displaystyle ^{*}} indicates the complex conjugate) for all x {\displaystyle x} in the domain of f {\displaystyle f} . In physics , this property is referred to as PT symmetry .
This definition extends also to functions of two or more variables, e.g., in the case that f {\displaystyle f} is a function of two variables it is Hermitian if
for all pairs ( x 1 , x 2 ) {\displaystyle (x_{1},x_{2})} in the domain of f {\displaystyle f} .
From this definition it follows immediately that: f {\displaystyle f} is a Hermitian function if and only if
Hermitian functions appear frequently in mathematics, physics, and signal processing . For example, the following two statements follow from basic properties of the Fourier transform: [ citation needed ]
Since the Fourier transform of a real signal is guaranteed to be Hermitian, it can be compressed using the Hermitian even/odd symmetry. This, for example, allows the discrete Fourier transform of a signal (which is in general complex) to be stored in the same space as the original real signal.
Where the ⋆ {\displaystyle \star } is cross-correlation , and ∗ {\displaystyle *} is convolution .
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Hermitian_function |
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