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This is a list of utilities for creating a live USB . Only those listed on Wikipedia are included. | https://en.wikipedia.org/wiki/List_of_tools_to_create_bootable_USB |
This is a list of topics related to pi ( π ), the fundamental mathematical constant . | https://en.wikipedia.org/wiki/List_of_topics_related_to_π |
In mathematics , topology (from the Greek words τόπος , 'place, location', and λόγος , 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations , such as stretching , twisting , crumpling and bending, but not tearing or gluing .
A topological space is a set endowed with a structure, called a topology , which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity . Euclidean spaces , and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies . A property that is invariant under such deformations is a topological property . Basic examples of topological properties are: the dimension , which allows distinguishing between a line and a surface ; compactness , which allows distinguishing between a line and a circle; connectedness , which allows distinguishing a circle from two non-intersecting circles.
The ideas underlying topology go back to Gottfried Leibniz , who in the 17th century envisioned the geometria situs and analysis situs . Leonhard Euler 's Seven Bridges of Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed.
This is a list of topology topics. See also: | https://en.wikipedia.org/wiki/List_of_topology_topics |
This is a list of train-surfing injuries and deaths . | https://en.wikipedia.org/wiki/List_of_train-surfing_injuries_and_deaths |
This is a list of notable translation software .
List of PO file editors/translator (in no particular order): | https://en.wikipedia.org/wiki/List_of_translation_software |
This is a list of megaprojects within the transport sector. Take care in comparing the cost of projects from different times—even a few years apart—due to inflation ; comparing nominal costs without taking this into account can be highly misleading. Note that inflation-calculated values are current as of 2023 [update] .
According to the Oxford Handbook of Megaproject Management in 2017, "Megaprojects are large-scale, complex ventures that typically cost $1 billion or more, take many years to develop and build, involve multiple public and private stakeholders, are transformational, and impact millions of people." [ 1 ]
(initial segment)
(initial bore)
6.83 billion USD is for 2010 prices [ 62 ]
17 bridges connecting the islands of Honshū and Shikoku
2022 (Phase 2)
Nairobi Naivasha
2018 (New westbound span)
Core section opened May 24, 2022, full integration of routes and completion expected by May 2023. [ 114 ]
2022 (First part of orange line)
Expected
Unclear timeline for rest of lines/stations
2018 (First stretch)
2020 (Second stretch)
Expected
Unclear timeline for rest of lines/stations
Expected 2024 ( Andrijevica segment)
Expected 2027 [ 145 ]
Expected 2028
(NHDP: 53.2, 75.3 in 2023) [ 169 ]
(Bharatmala: 132.4) [ 170 ]
2026: Bharatmala Phase I [ 171 ]
Phase II was set to start in 2024, but now is uncertain [ 172 ]
(sections 1,2, & 4 are already complete)
(line 1)
2008 (Phase 2)
2017 (Phase 3)
2.6 (Phase 2)
3.54 (Phase 3)
3.6 (Phase 2)
4.3 (Phase 3)
2026 (Phase 1)
2030 (Full completion)
2026 (Phase 1)
2028 (Full completion) | https://en.wikipedia.org/wiki/List_of_transport_megaprojects |
The following is a list of widely known trees and shrubs. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] Taxonomic families for the following trees and shrubs are listed in alphabetical order, likewise the genera and closely related species. The list currently includes 1352 species. | https://en.wikipedia.org/wiki/List_of_trees_and_shrubs_by_taxonomic_family |
This list of triangle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or in triangular arrays such as Pascal's triangle or triangular matrices , or concretely in physical space. It does not include metaphors like love triangle in which the word has no reference to the geometric shape.
The (incomplete) Bell polynomials from a triangular array of polynomials (see also Polynomial sequence ). | https://en.wikipedia.org/wiki/List_of_triangle_topics |
This is a list of organizations involved in research in or advocacy of tribology , the scientific and engineering discipline related to friction , lubrication and wear . | https://en.wikipedia.org/wiki/List_of_tribology_organizations |
Trichloroethylene (TCE) is a common industrial solvent mostly used for metal degreasing. Due to its wide use in industries, there have been several incidences of waste TCE leaking into aquifers and contaminating groundwaters.
Due to their similar industrial uses, areas contaminated with mainly TCE may also be contaminated with tetrachloroethylene in smaller amounts.
The first known report of TCE in groundwater was given in 1949 by two English public chemists who described two separate instances of well contamination by industrial releases of TCE. [ 1 ]
Exposure to TCE occurs mainly through contaminated drinking water. With a specific gravity greater than 1 (denser than water), trichloroethylene can be present as a dense non-aqueous phase liquid (DNAPL) if sufficient quantities are introduced into the environment. Another significant source of vapor exposure in Superfund sites that has contaminated groundwater, such as at the Twin Cities Army Ammunition Plant , was by showering. TCE readily volatilizes out of hot water and into the air. Long, hot showers would then volatilize more TCE into the air. In a home closed tightly to conserve the cost of heating and cooling, these vapors would then recirculate. Based on available federal and state surveys, between 9% and 34% of the drinking water supply sources tested in the U.S. may have some TCE contamination, though EPA has reported that most water supplies are in compliance with the maximum contaminant level (MCL) of 5 ppb. [ 2 ]
In addition, a growing concern in recent years at sites with TCE contamination in soil or groundwater has been vapor intrusion in buildings, which has resulted in indoor air exposures, such is in a recent case in the McCook Field neighborhood of Dayton, Ohio , United States. [ 3 ] Trichloroethylene has been detected in 852 Superfund sites across the United States, [ 4 ] according to the Agency for Toxic Substances and Disease Registry (ATSDR). Under the Safe Drinking Water Act of 1974, and as amended [ 5 ] annual water quality testing is required for all public drinking water distributors. The EPA'S current guidelines for TCE are online. [ 6 ]
The EPA's table of "TCE Releases to Ground" is dated 1987 to 1993, thereby omitting one of the largest Superfund cleanup sites in the nation, the North IBW in Scottsdale, Arizona. Earlier, TCE was dumped here, and was subsequently detected in the municipal drinking water wells in 1982, prior to the study period. [ 7 ]
Marine Corps Base Camp Lejeune [ 8 ] in North Carolina may be the largest TCE contamination site in the United States. Legislation could force the EPA to establish a health advisory and a national public drinking water regulation to limit trichloroethylene. [ 9 ]
The 1998 film A Civil Action dramatizes the EPA lawsuit Anne Anderson, et al., v. Cryovac, Inc. concerning trichloroethylene contamination that occurred in Woburn, Massachusetts in the 1970s and 1980s.
Until recent years, the US Agency for Toxic Substances and Disease Registry (ATSDR) contended that trichloroethylene had little-to-no carcinogenic potential, and was probably a co-carcinogen —that is, it acted in concert with other substances to promote the formation of tumors.
In 2023, the United States EPA determined that trichloroethylene presents an unreasonable risk of injury to human health under 52 out of 54 conditions of use, including during manufacturing, processing, mixing, recycling , vapor degreasing, as a lubricant, adhesive, sealant , cleaning product, and spray. It is dangerous from both inhalation and dermal exposure and was most strongly associated with immunosuppressive effects for acute exposure, as well as autoimmune effects for chronic exposures. [ 33 ]
As of June 1, 2023, two U.S. states ( Minnesota and New York ) have acted on the EPA's findings and banned trichloroethylene in all cases but research and development. [ 34 ] [ 35 ]
In 2001, a draft report of the Environmental Protection Agency (EPA) laid the groundwork for tough new standards to limit public exposure to trichloroethylene. The assessment set off a fight between the EPA and the Department of Defense (DoD), the Department of Energy , and NASA , who appealed directly to the White House. They argued that the EPA had produced junk science , its assumptions were badly flawed, and that evidence exonerating the chemical was ignored. [ citation needed ]
The DoD has about 1,400 military properties nationwide that are contaminated with trichloroethylene. Many of these sites are detailed and updated by www.cpeo.org and include a former ammunition plant in the Twin Cities area. [ 36 ] Twenty three sites in the Energy Department's nuclear weapons complex—including Lawrence Livermore National Laboratory in the San Francisco Bay area, and NASA centers, including the Jet Propulsion Laboratory in La Cañada Flintridge are reported to have TCE contamination.
Political appointees in the EPA sided with the Pentagon and agreed to pull back the risk assessment. In 2004, the National Academy of Sciences was given a $680,000 contract to study the matter, releasing its report in the summer of 2006. The report has raised more concerns about the health effects of TCE.
In the European Union , the Scientific Committee on Occupational Exposure Limit Values (SCOEL) recommends an exposure limit for workers exposed to trichloroethylene of 10 ppm (54.7 mg/m 3 ) for 8-hour TWA and of 30 ppm (164.1 mg/m 3 ) for STEL (15 minutes). [ 37 ]
Existing EU legislation aimed at protection of workers against risks to their health (including Chemical Agents Directive 98/24/EC [ 38 ] and Carcinogens Directive 2004/37/EC [ 39 ] ) currently do not impose binding minimum requirements for controlling risks to workers health during the use phase or throughout the life cycle of trichloroethylene. However, in case the ongoing discussions under the Carcinogens Directive will result in setting of a binding Occupational Exposure Limit for trichloroethylene for protection of workers; this conclusion may be revisited.
The Solvents Emissions Directive 1999/13/EC [ 40 ] and Industrial Emissions Directive 2010/75/EC [ 41 ] impose binding minimum requirements for emissions of trichloroethylene to the environment for certain activities, including surface cleaning. However, the activities with solvent consumption below a specified threshold are not covered by these minimum requirements.
According to European regulation, the use of trichloroethylene is prohibited for individuals at a concentration greater than 0.1%. In industry, trichloroethylene should be substituted before April 21, 2016 (unless an exemption is requested before October 21, 2014) [ 42 ] by other products such as tetrachloroethylene (perchloroethylene), methylene chloride (dichloromethane), or other hydrocarbon derivatives ( ketones , alcohols , ...).
In recent times, [ when? ] there has been a substantial reduction in the production output of trichloroethylene; alternatives for use in metal degreasing abound, some chlorinated aliphatic hydrocarbons being phased out in a large majority of industries due to the potential for health effects and the legal liability that ensues as a result.
The U.S. military has virtually eliminated its use of the chemical, allegedly purchasing only 11 gallons in 2005. [ 43 ] : 4 About 100 tons of it was used annually in the U.S. as of 2006. [ 43 ] : 5 | https://en.wikipedia.org/wiki/List_of_trichloroethylene-related_incidents |
Numbers can be classified according to how they are represented or according to the properties that they have. | https://en.wikipedia.org/wiki/List_of_types_of_numbers |
A solar cell (also called photovoltaic cell or photoelectric cell) is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect , which is a physical and chemical phenomenon. It is a form of photoelectric cell, defined as a device whose electrical characteristics, such as current, voltage or resistance, vary when exposed to light.
The following are the different types of solar cells. | https://en.wikipedia.org/wiki/List_of_types_of_solar_cells |
This list of types of systems engineering gives an overview of the types of systems engineering . The reference section gives an overview of major publications in each field and the universities that offer these programs. Universities can be listed here under multiple specialism. A general list of universities that offer SE programs is given in the List of systems engineering at universities . | https://en.wikipedia.org/wiki/List_of_types_of_systems_engineering |
The following is a list of schools with industrial engineering or an equivalent degree program. | https://en.wikipedia.org/wiki/List_of_universities_with_industrial_engineering_programs |
CH 2 ) 4 COOH
CH=CH(CH 2 ) 3 COOH
CH=CHCH 2 CH=CH(CH 2 ) 2 COOH
CH=CH(CH 2 ) 3 COOH
CH=CH(CH 2 ) 5 COOH
The following fatty acids have one unsaturated bond.
Crotonic acid has 4 carbons, is included in croton oil , and is a trans -2-mono-unsaturated fatty acid. C 3 H 5 CO 2 H, IUPAC organization name ( E )-but-2-enoic acid, trans -but-2-enoic acid, numerical representation 4:1, n-1, molecular weight 86.09, melting point 72–74 °C, boiling point 180–181 °C, specific gravity 1.027. CAS registry number 107-93-7.
Myristoleic acid has 14 carbons, is found in whale blubber , and is a cis -9-monounsaturated fatty acid. C 13 H 25 CO 2 H, IUPAC organization name ( Z )-tetradec-9-enoic acid, numerical representation 14:1, n-5, molecular weight 226.36, melting point of −4.5 – −4 °C. CAS Registry Number 544-64-9.
Palmitoleic acid has 16 carbons, is found in cod liver oil , sardine oil , and herring oil , and is a cis -9-monounsaturated fatty acid. C 15 H 29 CO 2 H, IUPAC organization name ( Z )-hexadec-9-enoic acid, n-7, numerical representation of 16:1, molecular weight 254.41, melting point 5 °C, specific gravity 0.894. CAS Registry Number 373-49-9.
Sapienic acid has 16 carbons, is found in the skin, and is a cis -6-mono-unsaturated fatty acid. C 15 H 29 CO 2 H, IUPAC organization name ( Z )-6-Hexadecenoic acid, n-10, numerical expression 16:1, molecular weight 254.41. CAS Registry Number 17004-51-2.
Oleic acid has 18 carbons, is found in most animal fats and olive oil , and is a cis -9-monounsaturated fatty acid. C 17 H 33 CO 2 H, IUPAC organization name ( Z )-octadec-9-enoic acid, numerical representation 18:1 (9), n-9, molecular weight 282.46, melting point 13.4 °C, specific gravity 0.891. CAS Registry Number 112-80-1.
Elaidic acid has 18 carbons and is a trans -9-mono-unsaturated fatty acid. It is also a trans isomer of oleic acid. C 17 H 33 CO 2 H, IUPAC organization name ( E )-octadec-9-enoic acid, numerical representation 18:1 (9), n-9, molecular weight 282.46, melting point 43–45 °C. CAS Registry Number 112-79-8.
Vaccenic acid has 18 carbons, is found in beef tallow , mutton , and butter , and is a trans -11-mono-unsaturated fatty acid. C 17 H 33 CO 2 H, IUPAC organization name ( E )-octadec-11-enoic acid, numerical representation 18:1 (11) n-7, molecular weight 282.46. CAS Registry Number 506-17-2.
Gadoleic acid has 20 carbons, is found in cod liver oil and other marine animal oils, and is a cis -9-mono-unsaturated fatty acid. C 19 H 37 CO 2 H, IUPAC organization name ( Z )-icos-9-enoic acid, numerical representation 20:1 (9), n-11, molecular weight 310.51. CAS Registry Number 29204-02-2.
Eicosenoic acid has 20 carbons, is found in a wide variety of plant oils, and is a cis -11-mono-unsaturated fatty acid. C 19 H 37 CO 2 H, IUPAC organization name ( Z )-icos-11-enoic acid, numerical representation 20:1 (11), n-9, molecular weight 310.51. CAS Registry Number 5561-99-9.
Erucic acid has 22 carbons, is found in rapeseed oil and mustard oil , and is a cis -13-monounsaturated is a fatty acid. C 21 H 41 CO 2 H, IUPAC organization name ( Z )-docos-13-enoic acid, numerical representation 22:1, n-9, molecular weight 338.57, melting point 33–35 °C. CAS Registry Number 112-86-7.
Nervonic acid has 24 carbons, is found in brain glycolipids (Nervon) and sphingomyelin , and is a cis -15-mono-unsaturated fatty acid. C 23 H 45 CO 2 H, IUPAC organization name ( Z )-tetracos-15-enoic acid, numerical representation 24:1, n-9, molecular weight 366.62, melting point 42–43 °C. CAS Registry Number 506-37-6.
The following fatty acids have two unsaturated bonds.
Linoleic acid has 18 carbons, is contained in many vegetable oils, particularly semi-drying oils, and is a cis -9- cis -12-di-unsaturated fatty acid. C 17 H 31 CO 2 H, IUPAC organization name (9 Z , 12 Z )-octadeca-9,12-dienoic acid, numerical representation 18:2 (9,12), n-6, molecular weight 280.45, melting point −5 °C, specific gravity 0.902. CAS Registry Number 60-33-3. There are isomers of linoleic acid with double bonds separated by one single bond. They are named conjugated linoleic acids .
Eicosadienoic acid (eicosadienoic's) has 20 carbons and is a cis -11- cis -14-di-unsaturated fatty acid. C 19 H 35 CO 2 H, IUPAC organization name (11 Z , 14 Z )-icosa-11,14-dienoic acid, numerical representation 20:2 (11,14), n-6, molecular weight 308.50.
Docosadienoic acid (docosadienoic's) has 22 carbons and is a cis -13- cis -16-di-unsaturated fatty acid. C 21 H 39 CO 2 H, IUPAC organization name (13 Z , 16 Z )-docosa-13,16-dienoic acid, numerical representation 22:2 (13,16), n-6, molecular weight 336.55. CAS Registry Number 7370-49-2.
The following fatty acids have three unsaturated bonds.
α-Linolenic acid (alpha-linolenic's) has 18 carbons, is found in linseed oil and drying oil , and is a 9,12,15-tri-unsaturated fatty acid. C 17 H 29 CO 2 H, IUPAC organization name (9 Z , 12 Z , 15 Z )-octadeca-9,12,15-trienoic acid, numerical representation 18:3 (9,12,15), n-3, molecular weight 278.43, melting point −11 °C, specific gravity 0.914. CAS Registry Number 463-40-1.
γ-Linolenic acid (gamma-linolenic's) has 18 carbons, is the structural isomer of α-linolenic acid. IUPAC organization name (6 Z , 9 Z , 12 Z )-octadeca-6,9,12-trienoic acid, numerical representation 18:3 (6,9,12), n-6. CAS Registry Number 506-26-3.
Pinolenic acid (pinolenic's) has 18 carbons, is found in pine nuts, and is a 5,9,12-triunsaturated fatty acid. C 17 H 29 CO 2 H, IUPAC organization name (5 Z , 9 Z , 12 Z )-octadeca-5,9,12-trienoic acid, numerical representation 18:3 (5,9,12), n-6, molecular weight 278.43. CAS Registry Number 16833-54-8.
α-Eleostearic acid (alpha-eleostearic's) has 18 carbons, is found in Kiri drying oil, and is a 9,11,13-triunsaturated fatty acid. C 17 H 29 CO 2 H, IUPAC organization name (9 Z , 11 E , 13 E )-octadeca-9,11,13-trienoic acid, numerical representation 18:3 (9,11,13), n-5, molecular weight 278.43.
β-Eleostearic acid (beta-eleostearic's, beta-eleostearic acid) is a geometric isomer of α-eleostearic acid. IUPAC organization name (9 E , 11 E , 13 E )-octadeca-9,11,13-trienoic acid, numerical representation 18:3 (9,11,13), n-5.
α- and β-Eleostearic acids are cis–trans isomers. Other cis–trans isomers of eleostearic acid are:
Catalpic acid (9 E , 11 E , 13 Z ) Punicic acid (9 Z , 11 E , 13 Z ).
Mead acid (Mead's) has 20 carbons, is a 5,8,11-tri-unsaturated fatty acid. C 19 H 33 CO 2 H, IUPAC organization name (5 Z , 8 Z , 11 Z )-icosa-5,8,11-trienoic acid, numerical representation 20:3 (5,8,11), n-9, molecular weight 306.48. CAS Registry Number 20590-32-3.
Dihomo-γ-linolenic acid (dihomo-gamma-linolenic's, dihomo-gamma-linolenic acid, DGLA ) has 20 carbons, and is an 8,11,14-tri-unsaturated fatty acid. C 19 H 33 CO 2 H, IUPAC organization name (8 Z , 11 Z , 14 Z )-icosa-8,11,14-trienoic acid, numerical representation 20:3 (8,11,14), n-6, molecular weight 306.48. CAS Registry Number 1783-84-2.
Eicosatrienoic acid (eicosatrienoic's, eicosatrienoic acid) has 20 carbons and is an 11,14,17- tri unsaturated fatty acid. C 19 H 33 CO 2 H, IUPAC organization name (11 Z , 14 Z , 17 Z )-icosa-11,14,17-trienoic acid, numerical representation 20:3 (11,14,17), n-3, molecular weight 306.48.
The following fatty acids have four unsaturated bonds.
Stearidonic acid (stearidonic's) has 18 carbons, is found in sardine oil and herring oil, and is a 6,9,12,15-tetraunsaturated fatty acid. C 17 H 27 CO 2 H, IUPAC organization name (6 Z , 9 Z , 12 Z , 15 Z )-octadeca-6,9,12,15-tetraenoic acid, numerical representation 18:4 (6,9,12,15), n-3, molecular weight 276.41. CAS Registry Number 20290-75-9.
Arachidonic acid (arachidonic's) has 20 carbons, is present in animal visceral fat (brain, liver, kidney, lung, spleen), and is a 5,8,11,14-tetra-unsaturated fatty acid. C 19 H 31 CO 2 H, IUPAC organization name (5 Z , 8 Z , 11 Z , 14 Z )-icosa-5,8,11,14-tetraenoic acid, numerical representation 20:4 (5,8,11,14), n-6, molecular weight 304.47, boiling point 169–171 °C. CAS Registry Number 506-32-1.
In signal transduction , arachidonic acid is produced through decomposition of the phospholipid cell membrane . This gives rise to the arachidonic acid cascade , a metabolic pathway that yields lipid mediator compounds [ 19 ] such as prostaglandins , thromboxanes and leukotrienes . This pathway has attracted study for its key role in inflammatory diseases such as asthma . [ 20 ]
Eicosatetraenoic acid (eicosatetraenoic's) has 20 carbons and is an 8,11,14,17-tetraunsaturated fatty acid. C 19 H 31 CO 2 H, IUPAC organization name (8 Z , 11 Z , 14 Z , 17 Z )-icosa-8,11,14,17-tetraenoic acid, numerical representation 20:4 (8,11,14,17), n-3, molecular weight 304.47.
Adrenic acid (adrenic'sd) has 22 carbons and is a 7,10,13,16-tetra-unsaturated fatty acid. C 21 H 35 CO 2 H, IUPAC organization name (7 Z , 10 Z , 13 Z , 16 Z )-docosa-7,10,13,16-tetraenoic acid, numerical representation 22:4 (7,10,13,16), n-6, molecular weight 332.52. CAS Registry Number 28874-58-0.
The following fatty acids have five unsaturated bonds.
Bosseopentaenoic acid (Boseopentaen's), has 20 carbons and is a 5,8,10,12,14-pentaunsaturated fatty acid. C 17 H 25 CO 2 H, IUPAC organization name (5 Z , 8 Z , 10 E , 12 E , 14 Z )-eicosa-5,8,10,12,14-pentaenoic acid, numerical representation 20:5 (5,8,10,12,14), n-6, molecular weight 302.46 g·mol−1. [ 21 ]
Eicosapentaenoic acid ( EPA ) has 20 carbons, is found in fish oil, is a pentaunsaturated fatty acid. It is one of the essential fatty acids . The recommendation of ingesting fish oil supplements during pregnancy is said to help increase the cognitive ability at 6 months, but mercury concentration in fish products offsets the effect. In patients with hyperlipidemia and obstructive artery disease it can help lower triglycerides and also has an anti- platelet effect similar to other anti-platelet agents . It has also been shown to help in secondary prevention of ischemic heart disease as shown with the JELIS test .
C 19 H 29 CO 2 H, IUPAC organization name (5 Z , 8 Z , 11 Z , 14 Z , 17 Z )-icosa-5,8,11,14,17-pentaenoic acid, numerical representation of 20:5 (5,8,11,14,17), n-3, molecular weight 302.45, melting point −54 – −53 °C, specific gravity 0.943. CAS Registry Number 10417-94-4.
Ozubondo acid (Ozubondo's, Osbond acid), has 22 carbons, is a 4,7,10,13,16- pentaunsaturated fatty acid. C 21 H 33 CO 2 H, IUPAC organization name (4 Z , 7 Z , 10 Z , 13 Z , 16 Z )-docosa-4,7,10,13,16-pentaenoic acid, numerical representation 22:5 (4,7,10,13,16), n-6, molecular weight 330.50. CAS Registry Number 25182-74-5
Sardine acid ( clupanodonic acid ) has 22 carbons, is found in sardine oil and herring oil, is a 7,10,13,16,19- pentaunsaturated fatty acid. C 21 H 33 CO 2 H, IUPAC organization name (7 Z , 10 Z , 13 Z , 16 Z , 19 Z )-docosa-7,10,13,16,19-pentaenoic acid, numerical representation 22:5 (7,10,13,16,19), n-3, molecular weight 330.50.
Tetracosapentaenoic acid has 24 carbons, is a 9,12,15,18,21-penta unsaturated fatty acid. C 23 H 37 CO 2 H, IUPAC organization name (9 Z , 12 Z , 15 Z , 18 Z , 21 Z )-tetracosa-9,12,15,18,21-pentaenoic acid, numerical representation 24:5 (9,12,15,18,21), n-3, molecular weight 358.56.
The following fatty acids have six unsaturated bonds.
Cervonic acid (or docosahexaenoic acid ) has 22 carbons, is found in fish oil, is a 4,7,10,13,16,19-hexa unsaturated fatty acid. In the human body its generation depends on consumption of omega 3 essential fatty acids (e.g., ALA or EPA), but the conversion process is inefficient. [ 22 ] C 21 H 31 CO 2 H, IUPAC organization name (4 Z , 7 Z , 10 Z , 13 Z , 16 Z , 19 Z )-docosa-4,7,10,13,16,19-hexaenoic acid, numerical representation 22:6 (4,7,10,13,16,19), n-3, molecular weight 328.49, melting point −44 °C, specific gravity 0.950. CAS Registry Number 6217-54-5.
Herring acid (Herring's, Nisinic acid) is a 6,9,12,15,18,21-hexa unsaturated fatty acid with 24 carbon atoms. C 23 H 35 CO 2 H, IUPAC organization name (6 Z , 9 Z , 12 Z , 15 Z , 18 Z , 21 Z )-tetracosa-6,9,12,15,18,21-hexaenoic acid, numerical representation 24:6 (6,9,12,15,18,21), n-3, molecular weight 356.54. | https://en.wikipedia.org/wiki/List_of_unsaturated_fatty_acids |
This article is a list of notable unsolved problems in astronomy . Problems may be theoretical or experimental. Theoretical problems result from inability of current theories to explain observed phenomena or experimental results. Experimental problems result from inability to test or investigate a proposed theory. Other problems involve unique events or occurrences that have not repeated themselves with unclear causes. | https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_astronomy |
This is a list of unsolved problems in chemistry . Problems in chemistry are considered unsolved when an expert in the field considers it unsolved or when several experts in the field disagree about a solution to a problem. | https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_chemistry |
This is a list of notable computer users' groups categorized by interest. | https://en.wikipedia.org/wiki/List_of_users'_groups |
This is a list of excipients per vaccine, as published by the United States Centers for Disease Control . Vaccine ingredients and production in other nations are substantially the same. Also listed are substances used in the manufacturing process. [ 1 ]
The initial list is based on information from the Centers for Disease Control and Prevention (CDC) and the Food and Drug Administration (FDA) and thus limited to US-approved vaccines. | https://en.wikipedia.org/wiki/List_of_vaccine_excipients |
This is a list of vaccine -related topics .
A vaccine is a biological preparation that improves immunity to a particular disease . A vaccine typically contains an agent that resembles a disease-causing microorganism, and is often made from weakened or killed forms of the microbe or its toxins. The agent stimulates the body's immune system to recognize the agent as foreign, destroy it, and "remember" it, so that the immune system can more easily recognize and destroy any of these microorganisms that it later encounters. [ 1 ] | https://en.wikipedia.org/wiki/List_of_vaccine_topics |
Vaginal tumors are neoplasms (tumors) found in the vagina . They can be benign or malignant . [ 1 ] [ a ] A neoplasm is an abnormal growth of tissue that usually forms a tissue mass. [ 2 ] [ 3 ] [ 4 ] Vaginal neoplasms may be solid, cystic or of mixed type. [ 5 ]
Vaginal cancers arise from vaginal tissue, with vaginal sarcomas develop from bone , cartilage , fat , muscle , blood vessels or other connective or supportive tissue. [ 6 ] [ 7 ] Tumors in the vagina may also be metastases (malignant tissue that has spread to the vagina from other parts of the body). [ 8 ] [ 7 ] Cancer that has spread from the colon , bladder , and stomach is far more common than cancer that originates in the vagina itself. [ 9 ] Some benign tumors may later progress to become malignant tumors, such as vaginal cancers. [ 10 ] [ 11 ] Some neoplastic growths of the vagina are sufficiently rare as to be only described in case studies . [ 3 ]
Signs and symptoms may include a feeling of pressure, painful intercourse or bleeding. [ 12 ] Most vaginal tumors are located during a pelvic exam . Ultrasonography, CT and MRI imaging is used to establish the location and presence or absence of fluid in a tumor. [ 13 ] [ 14 ] Biopsy provides a more definitive diagnosis . [ 15 ]
melancytic nevus
metaplastic carcinoma
subtype of embryonal rhabdomyosarcoma
Verrucous, Warty
Vaginal tumors also can be found in domesticated animals: | https://en.wikipedia.org/wiki/List_of_vaginal_tumors |
The following are important identities involving derivatives and integrals in vector calculus .
For a function f ( x , y , z ) {\displaystyle f(x,y,z)} in three-dimensional Cartesian coordinate variables, the gradient is the vector field:
where i , j , k are the standard unit vectors for the x , y , z -axes. More generally, for a function of n variables ψ ( x 1 , … , x n ) {\displaystyle \psi (x_{1},\ldots ,x_{n})} , also called a scalar field, the gradient is the vector field : ∇ ψ = ( ∂ ∂ x 1 , … , ∂ ∂ x n ) ψ = ∂ ψ ∂ x 1 e 1 + ⋯ + ∂ ψ ∂ x n e n {\displaystyle \nabla \psi ={\begin{pmatrix}\displaystyle {\frac {\partial }{\partial x_{1}}},\ldots ,{\frac {\partial }{\partial x_{n}}}\end{pmatrix}}\psi ={\frac {\partial \psi }{\partial x_{1}}}\mathbf {e} _{1}+\dots +{\frac {\partial \psi }{\partial x_{n}}}\mathbf {e} _{n}} where e i ( i = 1 , 2 , . . . , n ) {\displaystyle \mathbf {e} _{i}\,(i=1,2,...,n)} are mutually orthogonal unit vectors.
As the name implies, the gradient is proportional to, and points in the direction of, the function's most rapid (positive) change.
For a vector field A = ( A 1 , … , A n ) {\displaystyle \mathbf {A} =\left(A_{1},\ldots ,A_{n}\right)} , also called a tensor field of order 1, the gradient or total derivative is the n × n Jacobian matrix : [ 1 ] J A = d A = ( ∇ A ) T = ( ∂ A i ∂ x j ) i j . {\displaystyle \mathbf {J} _{\mathbf {A} }=d\mathbf {A} =(\nabla \!\mathbf {A} )^{\textsf {T}}=\left({\frac {\partial A_{i}}{\partial x_{j}}}\right)_{\!ij}.}
For a tensor field T {\displaystyle \mathbf {T} } of any order k , the gradient grad ( T ) = d T = ( ∇ T ) T {\displaystyle \operatorname {grad} (\mathbf {T} )=d\mathbf {T} =(\nabla \mathbf {T} )^{\textsf {T}}} is a tensor field of order k + 1.
For a tensor field T {\displaystyle \mathbf {T} } of order k > 0, the tensor field ∇ T {\displaystyle \nabla \mathbf {T} } of order k + 1 is defined by the recursive relation ( ∇ T ) ⋅ C = ∇ ( T ⋅ C ) {\displaystyle (\nabla \mathbf {T} )\cdot \mathbf {C} =\nabla (\mathbf {T} \cdot \mathbf {C} )} where C {\displaystyle \mathbf {C} } is an arbitrary constant vector.
In Cartesian coordinates, the divergence of a continuously differentiable vector field F = F x i + F y j + F z k {\displaystyle \mathbf {F} =F_{x}\mathbf {i} +F_{y}\mathbf {j} +F_{z}\mathbf {k} } is the scalar-valued function: div F = ∇ ⋅ F = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) ⋅ ( F x , F y , F z ) = ∂ F x ∂ x + ∂ F y ∂ y + ∂ F z ∂ z . {\displaystyle \operatorname {div} \mathbf {F} =\nabla \cdot \mathbf {F} ={\begin{pmatrix}\displaystyle {\frac {\partial }{\partial x}},\ {\frac {\partial }{\partial y}},\ {\frac {\partial }{\partial z}}\end{pmatrix}}\cdot {\begin{pmatrix}F_{x},\ F_{y},\ F_{z}\end{pmatrix}}={\frac {\partial F_{x}}{\partial x}}+{\frac {\partial F_{y}}{\partial y}}+{\frac {\partial F_{z}}{\partial z}}.}
As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge.
The divergence of a tensor field T {\displaystyle \mathbf {T} } of non-zero order k is written as div ( T ) = ∇ ⋅ T {\displaystyle \operatorname {div} (\mathbf {T} )=\nabla \cdot \mathbf {T} } , a contraction of a tensor field of order k − 1. Specifically, the divergence of a vector is a scalar. The divergence of a higher-order tensor field may be found by decomposing the tensor field into a sum of outer products and using the identity, ∇ ⋅ ( A ⊗ T ) = T ( ∇ ⋅ A ) + ( A ⋅ ∇ ) T {\displaystyle \nabla \cdot \left(\mathbf {A} \otimes \mathbf {T} \right)=\mathbf {T} (\nabla \cdot \mathbf {A} )+(\mathbf {A} \cdot \nabla )\mathbf {T} } where A ⋅ ∇ {\displaystyle \mathbf {A} \cdot \nabla } is the directional derivative in the direction of A {\displaystyle \mathbf {A} } multiplied by its magnitude. Specifically, for the outer product of two vectors, [ 2 ] ∇ ⋅ ( A B T ) = B ( ∇ ⋅ A ) + ( A ⋅ ∇ ) B . {\displaystyle \nabla \cdot \left(\mathbf {A} \mathbf {B} ^{\textsf {T}}\right)=\mathbf {B} (\nabla \cdot \mathbf {A} )+(\mathbf {A} \cdot \nabla )\mathbf {B} .}
For a tensor field T {\displaystyle \mathbf {T} } of order k > 1, the tensor field ∇ ⋅ T {\displaystyle \nabla \cdot \mathbf {T} } of order k − 1 is defined by the recursive relation ( ∇ ⋅ T ) ⋅ C = ∇ ⋅ ( T ⋅ C ) {\displaystyle (\nabla \cdot \mathbf {T} )\cdot \mathbf {C} =\nabla \cdot (\mathbf {T} \cdot \mathbf {C} )} where C {\displaystyle \mathbf {C} } is an arbitrary constant vector.
In Cartesian coordinates, for F = F x i + F y j + F z k {\displaystyle \mathbf {F} =F_{x}\mathbf {i} +F_{y}\mathbf {j} +F_{z}\mathbf {k} } the curl is the vector field: curl F = ∇ × F = ( ∂ ∂ x , ∂ ∂ y , ∂ ∂ z ) × ( F x , F y , F z ) = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z F x F y F z | = ( ∂ F z ∂ y − ∂ F y ∂ z ) i + ( ∂ F x ∂ z − ∂ F z ∂ x ) j + ( ∂ F y ∂ x − ∂ F x ∂ y ) k {\displaystyle {\begin{aligned}\operatorname {curl} \mathbf {F} &=\nabla \times \mathbf {F} ={\begin{pmatrix}\displaystyle {\frac {\partial }{\partial x}},\ {\frac {\partial }{\partial y}},\ {\frac {\partial }{\partial z}}\end{pmatrix}}\times {\begin{pmatrix}F_{x},\ F_{y},\ F_{z}\end{pmatrix}}={\begin{vmatrix}\mathbf {i} &\mathbf {j} &\mathbf {k} \\{\frac {\partial }{\partial x}}&{\frac {\partial }{\partial y}}&{\frac {\partial }{\partial z}}\\F_{x}&F_{y}&F_{z}\end{vmatrix}}\\[1em]&=\left({\frac {\partial F_{z}}{\partial y}}-{\frac {\partial F_{y}}{\partial z}}\right)\mathbf {i} +\left({\frac {\partial F_{x}}{\partial z}}-{\frac {\partial F_{z}}{\partial x}}\right)\mathbf {j} +\left({\frac {\partial F_{y}}{\partial x}}-{\frac {\partial F_{x}}{\partial y}}\right)\mathbf {k} \end{aligned}}} where i , j , and k are the unit vectors for the x -, y -, and z -axes, respectively.
As the name implies the curl is a measure of how much nearby vectors tend in a circular direction.
In Einstein notation , the vector field F = ( F 1 , F 2 , F 3 ) {\displaystyle \mathbf {F} ={\begin{pmatrix}F_{1},\ F_{2},\ F_{3}\end{pmatrix}}} has curl given by: ∇ × F = ε i j k e i ∂ F k ∂ x j {\displaystyle \nabla \times \mathbf {F} =\varepsilon ^{ijk}\mathbf {e} _{i}{\frac {\partial F_{k}}{\partial x_{j}}}} where ε {\displaystyle \varepsilon } = ±1 or 0 is the Levi-Civita parity symbol .
For a tensor field T {\displaystyle \mathbf {T} } of order k > 1, the tensor field ∇ × T {\displaystyle \nabla \times \mathbf {T} } of order k is defined by the recursive relation ( ∇ × T ) ⋅ C = ∇ × ( T ⋅ C ) {\displaystyle (\nabla \times \mathbf {T} )\cdot \mathbf {C} =\nabla \times (\mathbf {T} \cdot \mathbf {C} )} where C {\displaystyle \mathbf {C} } is an arbitrary constant vector.
A tensor field of order greater than one may be decomposed into a sum of outer products , and then the following identity may be used: ∇ × ( A ⊗ T ) = ( ∇ × A ) ⊗ T − A × ( ∇ T ) . {\displaystyle \nabla \times \left(\mathbf {A} \otimes \mathbf {T} \right)=(\nabla \times \mathbf {A} )\otimes \mathbf {T} -\mathbf {A} \times (\nabla \mathbf {T} ).} Specifically, for the outer product of two vectors, [ 3 ] ∇ × ( A B T ) = ( ∇ × A ) B T − A × ( ∇ B ) . {\displaystyle \nabla \times \left(\mathbf {A} \mathbf {B} ^{\textsf {T}}\right)=(\nabla \times \mathbf {A} )\mathbf {B} ^{\textsf {T}}-\mathbf {A} \times (\nabla \mathbf {B} ).}
In Cartesian coordinates , the Laplacian of a function f ( x , y , z ) {\displaystyle f(x,y,z)} is Δ f = ∇ 2 f = ( ∇ ⋅ ∇ ) f = ∂ 2 f ∂ x 2 + ∂ 2 f ∂ y 2 + ∂ 2 f ∂ z 2 . {\displaystyle \Delta f=\nabla ^{2}\!f=(\nabla \cdot \nabla )f={\frac {\partial ^{2}\!f}{\partial x^{2}}}+{\frac {\partial ^{2}\!f}{\partial y^{2}}}+{\frac {\partial ^{2}\!f}{\partial z^{2}}}.}
The Laplacian is a measure of how much a function is changing over a small sphere centered at the point.
When the Laplacian is equal to 0, the function is called a harmonic function . That is, Δ f = 0. {\displaystyle \Delta f=0.}
For a tensor field , T {\displaystyle \mathbf {T} } , the Laplacian is generally written as: Δ T = ∇ 2 T = ( ∇ ⋅ ∇ ) T {\displaystyle \Delta \mathbf {T} =\nabla ^{2}\mathbf {T} =(\nabla \cdot \nabla )\mathbf {T} } and is a tensor field of the same order.
For a tensor field T {\displaystyle \mathbf {T} } of order k > 0, the tensor field ∇ 2 T {\displaystyle \nabla ^{2}\mathbf {T} } of order k is defined by the recursive relation ( ∇ 2 T ) ⋅ C = ∇ 2 ( T ⋅ C ) {\displaystyle \left(\nabla ^{2}\mathbf {T} \right)\cdot \mathbf {C} =\nabla ^{2}(\mathbf {T} \cdot \mathbf {C} )} where C {\displaystyle \mathbf {C} } is an arbitrary constant vector.
In Feynman subscript notation , ∇ B ( A ⋅ B ) = A × ( ∇ × B ) + ( A ⋅ ∇ ) B {\displaystyle \nabla _{\mathbf {B} }\!\left(\mathbf {A{\cdot }B} \right)=\mathbf {A} {\times }\!\left(\nabla {\times }\mathbf {B} \right)+\left(\mathbf {A} {\cdot }\nabla \right)\mathbf {B} } where the notation ∇ B means the subscripted gradient operates on only the factor B . [ 4 ] [ 5 ] [ 6 ]
More general but similar is the Hestenes overdot notation in geometric algebra . [ 7 ] [ 8 ] The above identity is then expressed as: ∇ ˙ ( A ⋅ B ˙ ) = A × ( ∇ × B ) + ( A ⋅ ∇ ) B {\displaystyle {\dot {\nabla }}\left(\mathbf {A} {\cdot }{\dot {\mathbf {B} }}\right)=\mathbf {A} {\times }\!\left(\nabla {\times }\mathbf {B} \right)+\left(\mathbf {A} {\cdot }\nabla \right)\mathbf {B} } where overdots define the scope of the vector derivative. The dotted vector, in this case B , is differentiated, while the (undotted) A is held constant.
The utility of the Feynman subscript notation lies in its use in the derivation of vector and tensor derivative identities, as in the following example which uses the algebraic identity C ⋅( A × B ) = ( C × A )⋅ B :
An alternative method is to use the Cartesian components of the del operator as follows (with implicit summation over the index i ):
Another method of deriving vector and tensor derivative identities is to replace all occurrences of a vector in an algebraic identity by the del operator, provided that no variable occurs both inside and outside the scope of an operator or both inside the scope of one operator in a term and outside the scope of another operator in the same term (i.e., the operators must be nested). The validity of this rule follows from the validity of the Feynman method, for one may always substitute a subscripted del and then immediately drop the subscript under the condition of the rule.
For example, from the identity A ⋅( B × C ) = ( A × B )⋅ C we may derive A ⋅(∇× C ) = ( A ×∇)⋅ C but not ∇⋅( B × C ) = (∇× B )⋅ C ,
nor from A ⋅( B × A ) = 0 may we derive A ⋅(∇× A ) = 0.
On the other hand, a subscripted del operates on all occurrences of the subscript in the term, so that A ⋅(∇ A × A ) = ∇ A ⋅( A × A ) = ∇⋅( A × A ) = 0.
Also, from A ×( A × C ) = A ( A ⋅ C ) − ( A ⋅ A ) C we may derive ∇×(∇× C ) = ∇(∇⋅ C ) − ∇ 2 C ,
but from ( A ψ )⋅( A φ ) = ( A ⋅ A )( ψφ ) we may not derive (∇ ψ )⋅(∇ φ ) = ∇ 2 ( ψφ ).
A subscript c on a quantity indicates that it is temporarily considered to be a constant. Since a constant is not a variable, when the substitution rule (see the preceding paragraph) is used it, unlike a variable, may be moved into or out of the scope of a del operator, as in the following example: [ 9 ]
Another way to indicate that a quantity is a constant is to affix it as a subscript to the scope of a del operator, as follows: [ 10 ] ∇ ( A ⋅ B ) A = A × ( ∇ × B ) + ( A ⋅ ∇ ) B {\displaystyle \nabla \left(\mathbf {A{\cdot }B} \right)_{\mathbf {A} }=\mathbf {A} {\times }\!\left(\nabla {\times }\mathbf {B} \right)+\left(\mathbf {A} {\cdot }\nabla \right)\mathbf {B} }
For the remainder of this article, Feynman subscript notation will be used where appropriate.
For scalar fields ψ {\displaystyle \psi } , ϕ {\displaystyle \phi } and vector fields A {\displaystyle \mathbf {A} } , B {\displaystyle \mathbf {B} } , we have the following derivative identities.
We have the following generalizations of the product rule in single-variable calculus .
Let f ( x ) {\displaystyle f(x)} be a one-variable function from scalars to scalars, r ( t ) = ( x 1 ( t ) , … , x n ( t ) ) {\displaystyle \mathbf {r} (t)=(x_{1}(t),\ldots ,x_{n}(t))} a parametrized curve, ϕ : R n → R {\displaystyle \phi \!:\mathbb {R} ^{n}\to \mathbb {R} } a function from vectors to scalars, and A : R n → R n {\displaystyle \mathbf {A} \!:\mathbb {R} ^{n}\to \mathbb {R} ^{n}} a vector field. We have the following special cases of the multi-variable chain rule .
For a vector transformation x : R n → R n {\displaystyle \mathbf {x} \!:\mathbb {R} ^{n}\to \mathbb {R} ^{n}} we have:
Here we take the trace of the dot product of two second-order tensors, which corresponds to the product of their matrices.
where J A = ( ∇ A ) T = ( ∂ A i / ∂ x j ) i j {\displaystyle \mathbf {J} _{\mathbf {A} }=(\nabla \!\mathbf {A} )^{\textsf {T}}=(\partial A_{i}/\partial x_{j})_{ij}} denotes the Jacobian matrix of the vector field A = ( A 1 , … , A n ) {\displaystyle \mathbf {A} =(A_{1},\ldots ,A_{n})} .
Alternatively, using Feynman subscript notation,
See these notes. [ 11 ]
As a special case, when A = B ,
The generalization of the dot product formula to Riemannian manifolds is a defining property of a Riemannian connection , which differentiates a vector field to give a vector-valued 1-form .
Note that the matrix J B − J B T {\displaystyle \mathbf {J} _{\mathbf {B} }\,-\,\mathbf {J} _{\mathbf {B} }^{\textsf {T}}} is antisymmetric.
The divergence of the curl of any continuously twice-differentiable vector field A is always zero: ∇ ⋅ ( ∇ × A ) = 0 {\displaystyle \nabla \cdot (\nabla \times \mathbf {A} )=0}
This is a special case of the vanishing of the square of the exterior derivative in the De Rham chain complex .
The Laplacian of a scalar field is the divergence of its gradient: Δ ψ = ∇ 2 ψ = ∇ ⋅ ( ∇ ψ ) {\displaystyle \Delta \psi =\nabla ^{2}\psi =\nabla \cdot (\nabla \psi )} The result is a scalar quantity.
The divergence of a vector field A is a scalar, and the divergence of a scalar quantity is undefined. Therefore, ∇ ⋅ ( ∇ ⋅ A ) is undefined. {\displaystyle \nabla \cdot (\nabla \cdot \mathbf {A} ){\text{ is undefined.}}}
The curl of the gradient of any continuously twice-differentiable scalar field φ {\displaystyle \varphi } (i.e., differentiability class C 2 {\displaystyle C^{2}} ) is always the zero vector : ∇ × ( ∇ φ ) = 0 . {\displaystyle \nabla \times (\nabla \varphi )=\mathbf {0} .}
It can be easily proved by expressing ∇ × ( ∇ φ ) {\displaystyle \nabla \times (\nabla \varphi )} in a Cartesian coordinate system with Schwarz's theorem (also called Clairaut's theorem on equality of mixed partials). This result is a special case of the vanishing of the square of the exterior derivative in the De Rham chain complex .
∇ × ( ∇ × A ) = ∇ ( ∇ ⋅ A ) − ∇ 2 A {\displaystyle \nabla \times \left(\nabla \times \mathbf {A} \right)\ =\ \nabla (\nabla {\cdot }\mathbf {A} )\,-\,\nabla ^{2\!}\mathbf {A} }
Here ∇ 2 is the vector Laplacian operating on the vector field A .
The divergence of a vector field A is a scalar, and the curl of a scalar quantity is undefined. Therefore, ∇ × ( ∇ ⋅ A ) is undefined. {\displaystyle \nabla \times (\nabla \cdot \mathbf {A} ){\text{ is undefined.}}}
The figure to the right is a mnemonic for some of these identities. The abbreviations used are:
Each arrow is labeled with the result of an identity, specifically, the result of applying the operator at the arrow's tail to the operator at its head. The blue circle in the middle means curl of curl exists, whereas the other two red circles (dashed) mean that DD and GG do not exist.
Below, the curly symbol ∂ means " boundary of " a surface or solid.
In the following surface–volume integral theorems, V denotes a three-dimensional volume with a corresponding two-dimensional boundary S = ∂ V (a closed surface ):
In the following curve–surface integral theorems, S denotes a 2d open surface with a corresponding 1d boundary C = ∂ S (a closed curve ):
Integration around a closed curve in the clockwise sense is the negative of the same line integral in the counterclockwise sense (analogous to interchanging the limits in a definite integral ):
In the following endpoint–curve integral theorems, P denotes a 1d open path with signed 0d boundary points q − p = ∂ P {\displaystyle \mathbf {q} -\mathbf {p} =\partial P} and integration along P is from p {\displaystyle \mathbf {p} } to q {\displaystyle \mathbf {q} } :
A tensor form of a vector integral theorem may be obtained by replacing the vector (or one of them) by a tensor, provided that the vector is first made to appear only as the right-most vector of each integrand. For example, Stokes' theorem becomes [ 18 ]
A scalar field may also be treated as a vector and replaced by a vector or tensor. For example, Green's first identity becomes
Similar rules apply to algebraic and differentiation formulas. For algebraic formulas one may alternatively use the left-most vector position. | https://en.wikipedia.org/wiki/List_of_vector_calculus_identities |
This is a list of vector spaces in abstract mathematics , by Wikipedia page. | https://en.wikipedia.org/wiki/List_of_vector_spaces_in_mathematics |
Listing of the diverse vegetation types of South Africa that have been sampled, classified, described, and mapped by the SANBI VEGMAP project. Vegetation types of Lesotho and Eswatini are included in the project. The vegetation map is useful for biodiversity assessment, research, conservation management and environmental planning, and includes a database. The project is ongoing as more data becomes available over time. The first map was published in 2006, and has been updated in 2009. 2012 and 2018. [ 1 ]
The classification system uses a hierarchy to organise the vegetation types within the nine defined biomes and a tenth azonal group. Bioregions are described within the biomes, and the vegetation types are at the more detailed level, and represent groups of communities with similar biotic and abiotic features. The vegetation types are plotted on the map in as much resolution as is available using a GIS system. [ 1 ]
Mapping of the distribution and extent of natural vegetation of South Africa started in 1918 when the Botanical Survey of the Union of South Africa was established. Maps by Pole-Evans (1936), Acocks (1953), and Low and Rebelo (1996) preceded the current system, which is the combined effort of participants from various centres in the country. [ 2 ]
Listed by biome:
88 Savanna vegetation types, code SV: [ 3 ]
73 Grassveld vegetation types, code G: [ 3 ]
81 Fynbos vegetation types, code FF: [ 3 ]
29 Renosterveld vegetation types, code FR: [ 3 ]
65 Succulent Karoo vegetation types, code SK: [ 3 ]
54 Albany thickets and Strandveld vegetation types, codes AT and FS: [ 3 ]
29 Nama Karoo and desert vegetation types, codes NK and D: [ 3 ]
35 Azonal vegetation types, code AZ: [ 3 ]
17 Forest and coastal belt vegetation types, codes FO and CB
8 Subantarctic vegetation types, code ST: [ 3 ] | https://en.wikipedia.org/wiki/List_of_vegetation_types_of_South_Africa |
This is a list of notable version control software systems .
The following have been discontinued or not released in more than a decade. | https://en.wikipedia.org/wiki/List_of_version-control_software |
This article lists veterinary pharmaceutical drugs alphabetically by name. Many veterinary drugs have more than one name and, therefore, the same drug may be listed more than once.
Abbreviations are used in the list as follows:
Azathioprine (Imuran, Azasan): This medication is an immune-suppressing drug used to treat various autoimmune diseases in dogs. | https://en.wikipedia.org/wiki/List_of_veterinary_drugs |
This is a list of physical RF and video connectors and related video signal standards.
Protocols:
( DE-9 )
Dual-link DVI-D male plug.
(X- px × Y-px ( i ) @ Z- Hz )
625 lines tv compatible
D-Terminal uses voltage levels to signal resolution .
(version 2.1) [ 11 ]
Digital | https://en.wikipedia.org/wiki/List_of_video_connectors |
This is a list of video games that use near field communication (NFC) technology .
Currently, games have leveraged NFC in unlocking additional features through payment. This takes the form of a direct transaction over NFC [ 1 ] or by purchasing a physical item, which signals to the platform that a certain set of features has been purchased (e.g. Skylanders ). This list catalogues gaming NFC platforms by device.
Here, games that leverage Apple's In-App Purchase framework use information stored in the NFC Secure Element to process the purchase through Apple Pay . While an NFC radio is not used here, the NFC protocol is used nonetheless.
While NFC bases are normally interoperable between all platforms, the Xbox 360 and Xbox One require specific bases that are compatible only with the respective platform. | https://en.wikipedia.org/wiki/List_of_video_games_using_NFC |
The following is a list of video transcoding software . | https://en.wikipedia.org/wiki/List_of_video_transcoding_software |
A virtual assistant ( VA ) is a software agent that can perform a range of tasks or services for a user based on user input such as commands or questions, including verbal ones. Such technologies often incorporate chatbot capabilities to streamline task execution. The interaction may be via text, graphical interface, or voice - as some virtual assistants are able to interpret human speech and respond via synthesized voices.
In many cases, users can ask their virtual assistants questions, control home automation devices and media playback, and manage other basic tasks such as email, to-do lists, and calendars - all with verbal commands. [ 1 ] In recent years, prominent virtual assistants for direct consumer use have included Apple 's Siri , Amazon Alexa , Google Assistant , and Samsung 's Bixby . [ 2 ] Also, companies in various industries often incorporate some kind of virtual assistant technology into their customer service or support. [ 3 ]
Into the 2020s, the emergence of artificial intelligence based chatbots , such as ChatGPT , has brought increased capability and interest to the field of virtual assistant products and services. [ 4 ] [ 5 ] [ 6 ]
Radio Rex was the first voice activated toy, patented in 1916 [ 7 ] and released in 1922. [ 8 ] It was a wooden toy in the shape of a dog that would come out of its house when its name is called.
In 1952, Bell Labs presented "Audrey", the Automatic Digit Recognition machine. It occupied a six-foot-high relay rack, consumed substantial power, had streams of cables and exhibited the myriad maintenance problems associated with complex vacuum-tube circuitry. It could recognize the fundamental units of speech, phonemes. It was limited to accurate recognition of digits spoken by designated talkers. It could therefore be used for voice dialing, but in most cases push-button dialing was cheaper and faster, rather than speaking the consecutive digits. [ 9 ]
Another early tool which was enabled to perform digital speech recognition was the IBM Shoebox voice-activated calculator, presented to the general public during the 1962 Seattle World's Fair after its initial market launch in 1961. This early computer, developed almost 20 years before the introduction of the first IBM Personal Computer in 1981, was able to recognize 16 spoken words and the digits 0 to 9.
The first natural language processing computer program or the chatbot ELIZA was developed by MIT professor Joseph Weizenbaum in the 1960s. It was created to "demonstrate that the communication between man and machine was superficial". [ 10 ] ELIZA used pattern matching and substitution methodology into scripted responses to simulate conversation, which gave an illusion of understanding on the part of the program.
Weizenbaum's own secretary reportedly asked Weizenbaum to leave the room so that she and ELIZA could have a real conversation. Weizenbaum was surprised by this, later writing: "I had not realized ... that extremely short exposures to a relatively simple computer program could induce powerful delusional thinking in quite normal people. [ 11 ]
This gave name to the ELIZA effect , the tendency to unconsciously assume computer behaviors are analogous to human behaviors; that is, anthropomorphisation, a phenomenon present in human interactions with virtual assistants.
The next milestone in the development of voice recognition technology was achieved in the 1970s at the Carnegie Mellon University in Pittsburgh , Pennsylvania with substantial support of the United States Department of Defense and its DARPA agency, funded five years of a Speech Understanding Research program, aiming to reach a minimum vocabulary of 1,000 words. Companies and academia including IBM, Carnegie Mellon University (CMU) and Stanford Research Institute took part in the program.
The result was "Harpy", it mastered about 1000 words, the vocabulary of a three-year-old and it could understand sentences. It could process speech that followed pre-programmed vocabulary, pronunciation, and grammar structures to determine which sequences of words made sense together, and thus reducing speech recognition errors.
In 1986, Tangora was an upgrade of the Shoebox, it was a voice recognizing typewriter. Named after the world's fastest typist at the time, it had a vocabulary of 20,000 words and used prediction to decide the most likely result based on what was said in the past. IBM's approach was based on a hidden Markov model , which adds statistics to digital signal processing techniques. The method makes it possible to predict the most likely phonemes to follow a given phoneme. Still each speaker had to individually train the typewriter to recognize his or her voice, and pause between each word.
In 1983, Gus Searcy invented the "Butler In A Box", an electronic voice home controller system. [ 12 ]
In the 1990s, digital speech recognition technology became a feature of the personal computer with IBM , Philips and Lernout & Hauspie fighting for customers. Much later the market launch of the first smartphone IBM Simon in 1994 laid the foundation for smart virtual assistants as we know them today. [ citation needed ]
In 1997, Dragon's Naturally Speaking software could recognize and transcribe natural human speech without pauses between each word into a document at a rate of 100 words per minute. A version of Naturally Speaking is still available for download and it is still used today, for instance, by many doctors in the US and the UK to document their medical records. [ citation needed ]
In 2001 Colloquis publicly launched SmarterChild , on platforms like AIM and MSN Messenger . While entirely text-based SmarterChild was able to play games, check the weather, look up facts, and converse with users to an extent. [ 13 ]
The first modern digital virtual assistant installed on a smartphone was Siri , which was introduced as a feature of the iPhone 4S on 4 October 2011. [ 14 ] Apple Inc. developed Siri following the 2010 acquisition of Siri Inc. , a spin-off of SRI International , which is a research institute financed by DARPA and the United States Department of Defense . [ 15 ] Its aim was to aid in tasks such as sending a text message, making phone calls, checking the weather or setting up an alarm. Over time, it has developed to provide restaurant recommendations, search the internet, and provide driving directions. [ citation needed ]
In November 2014, Amazon announced Alexa alongside the Echo. [ 16 ]
In April 2017 Amazon released a service for building conversational interfaces for any type of virtual assistant or interface.
In the 2020s, artificial intelligence (AI) systems like ChatGPT have gained popularity for their ability to generate human-like responses to text-based conversations. In February 2020, Microsoft introduced its Turing Natural Language Generation (T-NLG), which was then the "largest language model ever published at 17 billion parameters." [ 17 ] On November 30, 2022, ChatGPT was launched as a prototype and quickly garnered attention for its detailed responses and articulate answers across many domains of knowledge. The advent of ChatGPT and its introduction to the wider public increased interest and competition in the space. In February 2023, Google began introducing an experimental service called "Bard" which is based on its LaMDA program to generate text responses to questions asked based on information gathered from the web .
While ChatGPT and other generalized chatbots based on the latest generative AI are capable of performing various tasks associated with virtual assistants, there are also more specialized forms of such technology that are designed to target more specific situations or needs. [ 18 ] [ 4 ]
Virtual assistants work via:
Many virtual assistants are accessible via multiple methods, offering versatility in how users can interact with them, whether through chat, voice commands, or other integrated technologies.
Virtual assistants use natural language processing (NLP) to match user text or voice input to executable commands. Some continually learn using artificial intelligence techniques including machine learning and ambient intelligence .
To activate a virtual assistant using the voice, a wake word might be used. This is a word or groups of words such as "Hey Siri", "OK Google" or "Hey Google", "Alexa", and "Hey Microsoft". [ 21 ] As virtual assistants become more popular, there are increasing legal risks involved. [ 22 ] : 815
Virtual assistants may be integrated into many types of platforms or, like Amazon Alexa, across several of them:
Virtual assistants can provide a wide variety of services. These include: [ 30 ]
Conversational commerce is e-commerce via various means of messaging, including via voice assistants [ 33 ] but also live chat on e-commerce Web sites , live chat on messaging applications such as WeChat , Facebook Messenger and WhatsApp [ 34 ] and chatbots on messaging applications or Web sites.
A virtual assistant can work with customer support team of a business to provide 24x7 support to customers. It provides quick responses, which enhances a customer's experience.
Amazon enables Alexa "Skills" and Google "Actions", essentially applications that run on the assistant platforms.
Virtual assistants have a variety of privacy concerns associated with them. Features such as activation by voice pose a threat, as such features requires the device to always be listening. [ 35 ] Modes of privacy such as the virtual security button have been proposed to create a multilayer authentication for virtual assistants. [ 36 ]
The privacy policy of Google Assistant states that it does not store the audio data without the user's permission, but may store the conversation transcripts to personalise its experience. Personalisation can be turned off in settings. If a user wants Google Assistant to store audio data, they can go to Voice & Audio Activity (VAA) and turn on this feature. Audio files are sent to the cloud and used by Google to improve the performance of Google Assistant, but only if the VAA feature is turned on. [ 37 ]
The privacy policy of Amazon's virtual assistant, Alexa, states that it only listens to conversations when its wake word (like Alexa, Amazon, Echo) is used. It starts recording the conversation after the call of a wake word, and stops recording after 8 seconds of silence. It sends the recorded conversation to the cloud. It is possible to delete the recording from the cloud by visiting 'Alexa Privacy' in 'Alexa'. [ 38 ]
Apple states that it does not record audio to improve Siri. Instead, it claims to use transcripts. Transcript data is only sent if it is deemed important for analysis. Users can opt out anytime if they don't want Siri to send the transcripts in the cloud. [ 39 ]
Cortana is a voice-only virtual assistant with singular authentication. [ 40 ] [ 41 ] [ 42 ] This voice-activated device accesses user data to perform common tasks like checking weather or making calls, raising privacy concerns due to the lack of secondary authentication. [ 43 ] [ 44 ]
Added value of the virtual assistants can come among others from the following:
In 2019 Antonio A. Casilli , a French sociologist , criticized artificial intelligence and virtual assistants in particular in the following way:
At a first level the fact that the consumer provides free data for the training and improvement of the virtual assistant, often without knowing it, is ethically disturbing.
But at a second level, it might be even more ethically disturbing to know how these AIs are trained with this data.
This artificial intelligence is trained via neural networks , which require a huge amount of labelled data. However, this data needs to be labelled through a human process, which explains the rise of microwork in the last decade. That is, remotely using some people worldwide doing some repetitive and very simple tasks for a few cents, such as listening to virtual assistant speech data, and writing down what was said. Microwork has been criticized for the job insecurity it causes, and for the total lack of regulation: The average salary was 1,38 dollar/hour in 2010, [ 50 ] and it provides neither healthcare nor retirement benefits, sick pay , minimum wage . Hence, virtual assistants and their designers are controversial for spurring job insecurity, and the AIs they propose are still human in the way that they would be impossible without the microwork of millions of human workers. [ 49 ]
Privacy concerns are raised by the fact that voice commands are available to the providers of virtual assistants in unencrypted form, and can thus be shared with third parties and be processed in an unauthorized or unexpected manner. [ 51 ] Additionally to the linguistic content of recorded speech, a user's manner of expression and voice characteristics can implicitly contain information about his or her biometric identity, personality traits, body shape, physical and mental health condition, sex, gender, moods and emotions, socioeconomic status and geographical origin. [ 52 ]
Notable developer platforms for virtual assistants include:
In previous generations of text chat-based virtual assistants, the assistant was often represented by an avatar (a.k.a. interactive online character or automated character ) — this was known as an embodied agent .
Digital experiences enabled by virtual assistants are considered to be among the major recent technological advances and most promising consumer trends. Experts claim that digital experiences will achieve a status-weight comparable to 'real' experiences, if not become more sought-after and prized. [ 57 ] The trend is verified by a high number of frequent users and the substantial growth of worldwide user numbers of virtual digital assistants. In mid-2017, the number of frequent users of digital virtual assistants is estimated to be around 1 bn worldwide. [ 58 ] In addition, it can be observed that virtual digital assistant technology is no longer restricted to smartphone applications, but present across many industry sectors (incl. automotive , telecommunications, retail , healthcare and education). [ 59 ] In response to the significant R&D expenses of firms across all sectors and an increasing implementation of mobile devices, the market for speech recognition technology is predicted to grow at a CAGR of 34.9% globally over the period of 2016 to 2024 and thereby surpass a global market size of US$7.5 billion by 2024. [ 59 ] According to an Ovum study, the "native digital assistant installed base" is projected to exceed the world's population by 2021, with 7.5 billion active voice AI–capable devices. [ 60 ] According to Ovum, by that time "Google Assistant will dominate the voice AI–capable device market with 23.3% market share, followed by Samsung's Bixby (14.5%), Apple's Siri (13.1%), Amazon's Alexa (3.9%), and Microsoft's Cortana (2.3%)." [ 60 ]
Taking into consideration the regional distribution of market leaders, North American companies (e.g. Nuance Communications , IBM , eGain ) are expected to dominate the industry over the next years, due to the significant impact of BYOD ( Bring Your Own Device ) and enterprise mobility business models. Furthermore, the increasing demand for smartphone-assisted platforms are expected to further boost the North American intelligent virtual assistant (IVA) industry growth. Despite its smaller size in comparison to the North American market, the intelligent virtual assistant industry from the Asia-Pacific region, with its main players located in India and China is predicted to grow at an annual growth rate of 40% (above global average) over the 2016–2024 period. [ 59 ]
Virtual assistants should not be only seen as a gadget for individuals, as they could have a real economic utility for enterprises. As an example, a virtual assistant can take the role of an always available assistant with an encyclopedic knowledge. And which can organize meetings, check inventories, verify informations. Virtual assistants are all the more important that their integration in small and middle-sized enterprises often consists in an easy first step through the more global adaptation and use of Internet of Things (IoT) . Indeed, IoT technologies are first perceived by small and medium-sized enterprises as technologies of critical importance, but too complicated, risky or costly to be used. [ 61 ]
In May 2018, researchers from the University of California, Berkeley , published a paper that showed audio commands undetectable for the human ear could be directly embedded into music or spoken text, thereby manipulating virtual assistants into performing certain actions without the user taking note of it. [ 62 ] The researchers made small changes to audio files, which cancelled out the sound patterns that speech recognition systems are meant to detect. These were replaced with sounds that would be interpreted differently by the system and command it to dial phone numbers, open websites or even transfer money. [ 62 ] The possibility of this has been known since 2016, [ 62 ] and affects devices from Apple, Amazon and Google. [ 63 ]
In addition to unintentional actions and voice recording, another security and privacy risk associated with intelligent virtual assistants is malicious voice commands: An attacker who impersonates a user and issues malicious voice commands to, for example, unlock a smart door to gain unauthorized entry to a home or garage or order items online without the user's knowledge. Although some IVAs provide a voice-training feature to prevent such impersonation, it can be difficult for the system to distinguish between similar voices. Thus, a malicious person who is able to access an IVA-enabled device might be able to fool the system into thinking that they are the real owner and carry out criminal or mischievous acts. [ 64 ] | https://en.wikipedia.org/wiki/List_of_virtual_assistant_software |
The following is a list of Wikipedia articles relating to virtual printer software:
The following are distributed under free software licences:
The following are proprietary software but free of charge:
Virtual PDF printers for Microsoft Windows:
Virtual printers for Microsoft Windows: | https://en.wikipedia.org/wiki/List_of_virtual_printer_software |
There are two primary categories of virtual reality (VR) headsets :
Other categories include mobile headsets, which combine a smartphone with a mount , and hybrid solutions like the Oculus Quest with the Oculus Link feature that allows the standalone device to also serve as a tethered headset.
In addition, VR headsets are categorized by the degrees of freedom they provide:
( Constellation )
(pre-orders) [ 30 ]
(IMAX) [ 33 ] [ 34 ]
90 Hz [ 37 ]
(pre-orders) [ 42 ]
120º ("Small") [ 80 ]
120 Hz
HDR*
6DoF dual controllers
Adaptive triggers
Haptic feedback
Finger touch detection
Eye tracking*
Vibration on headset*
(*)Only supported on Playstation 5
$5000 (enterprise)
Gesture commands.
$540 (Standard)
(initially only in China)
60 Hz
Built-in speakers
90 Hz
72 Hz
60 Hz
(Discontinued)
$399 (128 GB)
$499 (256 GB)
90 Hz
90 Hz
€500 (256 GB)
90 Hz
96º Vertical [ 155 ]
90° Vertical
96° Vertical
105°(Vertical)
1 x 10 Gbps USB-C 3.1 Gen 2 or USB-C 3.2 Gen 2
Focal Edition：9,990 €/$
tracking, External display, LiDAR scanner, 3D camera
* Including price of VR touch peripherals.
The following tables compare general and technical information for a selection of popular retail head-mounted displays. See the individual display's articles for further information. Please note that the following table may be missing some information.
between emitters)
(facing camera)
for accessories/expansion
1 × 3.5 mm audio jack for headphones
2 × USB 2.0 (internal)
with 6DOF tracking
communication and calling.
communication | https://en.wikipedia.org/wiki/List_of_virtual_reality_headsets |
Dynamic viscosity is a material property which describes the resistance of a fluid to shearing flows. It corresponds roughly to the intuitive notion of a fluid's 'thickness'. For instance, honey has
a much higher viscosity than water . Viscosity is measured using a viscometer . Measured values span several orders
of magnitude. Of all fluids, gases have the lowest viscosities, and thick liquids have the highest.
The values listed in this article are representative estimates only, as they do not account for measurement uncertainties, variability in material definitions, or non-Newtonian behavior.
Kinematic viscosity is dynamic viscosity divided by fluid density. This page lists only dynamic viscosity.
For dynamic viscosity, the SI unit is Pascal-second. In engineering, the unit is usually Poise or centiPoise, with 1 Poise = 0.1 Pascal-second, and 1 centiPoise = 0.01 Poise.
For kinematic viscosity, the SI unit is m^2/s. In engineering, the unit is usually Stoke or centiStoke, with 1 Stoke = 0.0001 m^2/s, and 1 centiStoke = 0.01 Stoke.
For liquid, the dynamic viscosity is usually in the range of 0.001 to 1 Pascal-second, or 1 to 1000 centiPoise. The density is usually on the order of 1000 kg/m^3, i.e. that of water. Consequently, if a liquid has dynamic viscosity of n centiPoise, and its density is not too different from that of water, then its kinematic viscosity is around n centiStokes.
For gas, the dynamic viscosity is usually in the range of 10 to 20 microPascal-seconds, or 0.01 to 0.02 centiPoise. The density is usually on the order of 0.5 to 5 kg/m^3. Consequently, its kinematic viscosity is around 2 to 40 centiStokes.
Here "standard conditions" refers to temperatures of 25 °C and pressures of 1 atmosphere . Where data points are unavailable for 25 °C or 1 atmosphere, values are given at a nearby temperature/pressure.
The temperatures corresponding to each data point are stated explicitly. By contrast, pressure is omitted since gaseous viscosity depends only weakly on it.
The simple structure of noble gas molecules makes them amenable to accurate theoretical treatment. For this reason, measured viscosities of the noble gases serve as important tests of the kinetic-molecular theory of transport processes in gases (see Chapman–Enskog theory ). One of the key predictions of the theory is the following relationship between viscosity μ {\displaystyle \mu } , thermal conductivity k {\displaystyle k} , and specific heat c v {\displaystyle c_{v}} :
where f {\displaystyle f} is a constant which in general depends on the details of intermolecular interactions, but for spherically symmetric molecules is very close to 2.5 {\displaystyle 2.5} . [ 1 ]
This prediction is reasonably well-verified by experiments, as the following table shows. Indeed, the relation provides a viable means for obtaining thermal conductivities of gases since these are more difficult to measure directly than viscosity. [ 1 ] [ 2 ]
Substances composed of longer molecules tend to have larger viscosities due to the increased contact of molecules across layers of flow. [ 20 ] This effect can be observed for the n-alkanes and 1-chloroalkanes tabulated below. More dramatically, a long-chain hydrocarbon like squalene (C 30 H 62 ) has a viscosity an order of magnitude larger than the shorter n-alkanes (roughly 31 mPa·s at 25 °C). This is also the reason oils tend to be highly viscous, since they are usually composed of long-chain hydrocarbons.
The viscosity of an aqueous solution can either increase or decrease with concentration depending on the solute and the range of concentration. For instance, the table below shows that viscosity increases monotonically with concentration for sodium chloride and calcium chloride , but decreases for potassium iodide and cesium chloride (the latter up to 30% mass percentage, after which viscosity increases).
The increase in viscosity for sucrose solutions is particularly dramatic, and explains in part the common experience of sugar water being "sticky".
All values are given at 1 bar (approximately equal to atmospheric pressure ).
In the following table, the temperature is given in kelvins . | https://en.wikipedia.org/wiki/List_of_viscosities |
See List of fortifications for a list of notable fortified structures.
For city walls in particular, see List of cities with defensive walls . | https://en.wikipedia.org/wiki/List_of_walls |
This page consists of a list of wastewater treatment technologies : | https://en.wikipedia.org/wiki/List_of_wastewater_treatment_technologies |
The following compounds are liquid at room temperature and are completely miscible with water ; they are often used as solvents . Many of them are hygroscopic .
Category:Alcohol solvents | https://en.wikipedia.org/wiki/List_of_water-miscible_solvents |
This is a list of waves named after people (eponymous waves). | https://en.wikipedia.org/wiki/List_of_waves_named_after_people |
A variety of treaties and agreements have been enacted to regulate the use, development and possession of various types of weapons of mass destruction (WMD). Treaties may regulate weapons use under the customs of war ( Hague Conventions , Geneva Protocol ), ban specific types of weapons (Chemical Weapons Convention, Biological Weapons Convention), limit weapons research (Partial Test Ban Treaty, Comprehensive Nuclear-Test-Ban Treaty), limit allowable weapons stockpiles and delivery systems (START I, SORT) or regulate civilian use of weapon precursors (Chemical Weapons Convention, Biological Weapons Convention). The history of weapons control has also included treaties to limit effective defense against weapons of mass destruction in order to preserve the deterrent doctrine of mutual assured destruction (Anti-Ballistic Missile Treaty) as well as treaties to limit the spread of nuclear technologies geographically (African Nuclear Weapons Free Zone Treaty, Nuclear Non-Proliferation Treaty).
There is a separate list of states parties to several of the major weapons of mass destruction treaties .
* Year of entry into force in parentheses
(US withdrawal: 2002)
(expiration: 2 August 2019)
(USSR withdrawal: 14 June 2002)
(expiration: 5 February 2011)
(expiration: 7 January 1948) | https://en.wikipedia.org/wiki/List_of_weapons_of_mass_destruction_treaties |
This is a list of web analytics software used to collect and display data about visiting website users.
This is a comparison table of web analytics software released under a free software license .
This is a comparison table of web analytics proprietary software .
This is a comparison table of hosted web analytics software as a service . | https://en.wikipedia.org/wiki/List_of_web_analytics_software |
Web annotation can refer to online annotations of web resources such as web pages or parts of them, or a set of W3C standards developed for this purpose. The term can also refer to the creations of annotations on the World Wide Web and it has been used in this sense for the annotation tool INCEpTION, [ 1 ] formerly WebAnno. [ 2 ] This is a general feature of several tools for annotation in natural language processing or in the philologies .
With a web annotation system, a user can add, modify or remove information from a Web resource without modifying the resource itself. The annotations can be thought of as a layer on top of the existing resource, and this annotation layer is usually visible to other users who share the same annotation system. In such cases, the web annotation tool is a type of social software tool. For Web-based text annotation systems, see Text annotation .
Web annotation can be used for the following purposes:
Annotations can be considered an additional layer with respect to comments. Comments are published by the same publisher who hosts the original document. Annotations are added on top of that, but may eventually become comments which, in turn, may be integrated in a further version of the document itself. [ 3 ]
In the Web Annotation standard,
[a]n annotation is considered to be a set of connected resources, typically including a body and target, and conveys that the body is related to the target. The exact nature of this relationship changes according to the intention of the annotation, but the body is most frequently somehow "about" the target. (...) The (...) model supports additional functionality, enabling content to be embedded within the annotation, selecting arbitrary segments of resources, choosing the appropriate representation of a resource and providing styling hints to help clients render the annotation appropriately.
The basic data structures of Web Annotation (Fig. 1) are
The body can be a literal value or structured content (a URI). The target can be identified by an URI (e.g., fragment identifiers) and/or a selector that defines a domain-, resource- or application-specific access protocol, e.g., offset-based, XPath-based, etc.
Web Annotation was standardized on February 23, 2017 with the release of three official Recommendations by the W3C Web Annotation Working Group: [ 4 ] [ 5 ]
These recommendations were accompanied by additional working group notes that describe their application:
The Web Annotation data model is also provided in machine-readable form as the Web Annotation ontology. [ 11 ] Note that this ontology defines the Web Annotation namespace ( https://www.w3.org/ns/oa# ), and that this namespace is conventionally abbreviated as oa . This is the abbreviation for Open Annotation , a W3C Community Group whose specifications formed the basis for the Web Annotation standard. [ 12 ]
Web Annotation supersedes other standardization initiatives for annotations on the web within the W3C, e.g., the earlier Annotea project discontinued after 2003. [ 13 ] [ 14 ]
Web Annotation can be used in conjunction with (or as an alternative to) fragment identifiers that describe how to address elements within a web document by means of URIs . These include
Other, non-standardized fragment identifiers are in use, as well, e.g., within the NLP Interchange Format. [ 21 ]
Independently from Web Annotation, more specialized data models for representing annotations on the web have been developed, e.g., the NLP Interchange Format (NIF) [ 22 ] for applications in language technology. In early 2020, the W3C Community Group "Linked Data for Language Technology" launched an initiative to harmonize these vocabularies and to develop a consolidated RDF vocabulary for linguistic annotations on the web. [ 23 ]
Many of these systems require software to be installed to enable some or all of the features below. This fact is only noted in footnotes if the software that is required is additional software provided by a third party. | https://en.wikipedia.org/wiki/List_of_web_annotation_systems |
The following is a list of web browsers that are notable.
This is a table of personal computer web browsers by year of release of major version. The increased growth of the Internet in the 1990s and 2000s means that current browsers with small market shares have more total users than the entire market early on. For example, 90% market share in 1997 would be roughly 60 million users, but by the start of 2007 9% market share would equate to over 90 million users. [ 1 ]
Other software publishers have built browsers and other products around Microsoft's Trident engine. The following browsers are all based on that rendering engine:
Browsers that use both Trident and Gecko include:
Browsers that can use Trident , Gecko and Blink include:
Browsers created for enhancements of specific browsing activities.
Mosaic was the first widely used web browser. The National Center for Supercomputing Applications (NCSA) licensed the technology and many companies built their own web browser on Mosaic. The best known are the first versions of Internet Explorer and Netscape. | https://en.wikipedia.org/wiki/List_of_web_browsers |
The following is a list of web browsers for various Unix and Unix-like operating systems. Not all of these browsers are specific to these operating systems; some are available on non-Unix systems as well. Some, but not most, have a mobile version.
Colored items in this table are discontinued.
https://www.mozilla.org/en-US/firefox/android/ | https://en.wikipedia.org/wiki/List_of_web_browsers_for_Unix_and_Unix-like_operating_systems |
This article provides a list of widget toolkits (also known as GUI frameworks ), used to construct the graphical user interface (GUI) of programs, organized by their relationships with various operating systems .
Note that the X Window System was originally primarily for Unix-like operating systems, but it now runs on Microsoft Windows as well using, for example, Cygwin , so some or all of these toolkits can also be used under Windows.
General
RIAs
Full-stack framework
Resource-based
No longer developed
[ 22 ] ) [±] | https://en.wikipedia.org/wiki/List_of_widget_toolkits |
This is a list of wiki software programs. They are grouped by use case: standard wiki programs, personal wiki programs, hosted-only wikis, wiki-based content management software, and wiki-based project management software. They are further subdivided by the language of implementation: JavaScript, Java, PHP , Python, Perl , Ruby , and so on.
There are also wiki applications designed for personal use, [ 3 ] apps for mobile use, [ 4 ] and apps for use from USB flash drives . [ 5 ] They often include more features than traditional wikis, including:
A list of such software: | https://en.wikipedia.org/wiki/List_of_wiki_software |
A wide variety of different wireless data technologies exist, some in direct competition with one another, others designed for specific applications. Wireless technologies can be evaluated by a variety of different metrics of which some are described in this entry.
Standards can be grouped as follows in increasing range order:
Personal area network (PAN) systems are intended for short range communication between devices typically controlled by a single person. Some examples include wireless headsets for mobile phones or wireless heart rate sensors communicating with a wrist watch. Some of these technologies include standards such as ANT UWB , Bluetooth , Zigbee , and Wireless USB .
Wireless Sensor Networks (WSN / WSAN) are, generically, networks of low-power, low-cost devices that interconnect wirelessly to collect, exchange, and sometimes act-on data collected from their physical environments - "sensor networks". Nodes typically connect in a star or mesh topology. While most individual nodes in a WSAN are expected to have limited range ( Bluetooth , Zigbee, 6LoWPAN , etc.), particular nodes may be capable of more expansive communications ( Wi-Fi , Cellular networks , etc.) and any individual WSAN can span a wide geographical range. An example of a WSAN would be a collection of sensors arranged throughout an agricultural facility to monitor soil moisture levels, report the data back to a computer in the main office for analysis and trend modeling, and maybe turn on automatic watering spigots if the level is too low.
For wider area communications, wireless local area network (WLAN) is used. WLANs are often known by their commercial product name Wi-Fi . These systems are used to provide wireless access to other systems on the local network such as other computers, shared printers, and other such devices or even the internet. Typically a WLAN offers much better speeds and delays within the local network than an average consumer's Internet access . Older systems that provide WLAN functionality include DECT and HIPERLAN . These however are no longer in widespread use. One typical characteristic of WLANs is that they are mostly very local, without the capability of seamless movement from one network to another.
Cellular networks or WAN are designed for citywide/national/global coverage areas and seamless mobility from one access point (often defined as a base station ) to another allowing seamless coverage for very wide areas. Cellular network technologies are often split into 2nd generation 2G , 3G and 4G networks. Originally 2G networks were voice centric or even voice only digital cellular systems (as opposed to the analog 1G networks). Typical 2G standards include GSM and IS-95 with extensions via GPRS , EDGE and 1xRTT , providing Internet access to users of originally voice centric 2G networks. Both EDGE and 1xRTT are 3G standards, as defined by the ITU , but are usually marketed as 2.9G due to their comparatively low speeds and high delays when compared to true 3G technologies.
True 3G systems such as EV-DO , W-CDMA (including HSPA and HSPA+ ) provide combined circuit switched and packet switched data and voice services from the outset, usually at far better data rates than 2G networks with their extensions. All of these services can be used to provide combined mobile voice access and Internet access at remote locations.
4G networks provide even higher bitrates and many architectural improvements, which are not necessarily visible to the consumer. The current 4G systems that are deployed widely are WIMAX and LTE . The two are pure packet based networks without traditional voice circuit capabilities. These networks provide voice services via VoIP or VoLTE .
Some systems are designed for point-to-point line-of-sight communications, once two such nodes get too far apart they can no longer communicate. Other systems are designed to form a wireless mesh network using one of a variety of routing protocols . In a mesh network, when nodes get too far apart to communicate directly, they can still communicate indirectly through intermediate nodes.
The following standards are included in this comparison.
Antenna , RF front end enhancements and minor protocol timer tweaks have helped deploy long range P2P networks compromising on radial coverage, throughput and/or spectra efficiency ( 310 km & 382 km )
Notes: All speeds are theoretical maximums and will vary by a number of factors, including the use of external antennas, distance from the tower and the ground speed (e.g. communications on a train may be poorer than when standing still). Usually the bandwidth is shared between several terminals. The performance of each technology is determined by a number of constraints, including the spectral efficiency of the technology, the cell sizes used, and the amount of spectrum available.
For more comparison tables, see bit rate progress trends , comparison of mobile phone standards , spectral efficiency comparison table and OFDM system comparison table .
When discussing throughput, there is often a distinction between the peak data rate of the physical layer, the theoretical maximum data throughput and typical throughput.
The peak bit rate of the standard is the net bit rate provided by the physical layer in the fastest transmission mode (using the fastest modulation scheme and error code), excluding forward error correction coding and other physical layer overhead.
The theoretical maximum throughput for end user is clearly lower than the peak data rate due to higher layer overheads. Even this is never possible to achieve unless the test is done under perfect laboratory conditions.
The typical throughput is what users have experienced most of the time when well within the usable range to the base station. The typical throughput is hard to measure, and depends on many protocol issues such as transmission schemes (slower schemes are used at longer distance from the access point due to better redundancy), packet retransmissions and packet size. The typical throughput is often even lower because of other traffic sharing the same network or cell, interference or even the fixed line capacity from the base station onwards being limited.
Note that these figures cannot be used to predict the performance of any given standard in any given environment, but rather as benchmarks against which actual experience might be compared. | https://en.wikipedia.org/wiki/List_of_wireless_network_protocols |
Drugs or medicines may be withdrawn from commercial markets because of risks to patients, but also because of commercial reasons (e.g. lack of demand and relatively high production costs). When risks or harms are the cause, withdrawals will usually have been prompted by unexpected adverse effects that were not detected during the early, premaketing, clinical trials , i.e. they became apparent only from postmarketing surveillance data collected from the wider community during routine use over longer periods of time.
This list is not limited to drugs that were ever approved by the FDA. Some of them (lumiracoxib, rimonabant, tolrestat, ximelagatran, and zimeldine, for example) received marketing approval in Europe but had not yet been approved for marketing in the USA, when adverse effects became clear and their developers withdrew them from the market. Some drugs in this list (e.g. LSD) were never approved for marketing in the USA or Europe.
( Althesin )
( Cremophor EL ) [ 3 ] | https://en.wikipedia.org/wiki/List_of_withdrawn_drugs |
The following is a list of astronomers , astrophysicists and other notable women who have made contributions to the field of astronomy . | https://en.wikipedia.org/wiki/List_of_women_astronomers |
The following is a list of women who are the principal investigators (PIs), project scientists (PSs) or directors (Dirs) of astronomical instruments, missions or observatories.
Director of Science, European Space Agency (from 2023) | https://en.wikipedia.org/wiki/List_of_women_in_leadership_positions_on_astronomical_instrumentation_projects |
The following is a list of notable word processor programs . | https://en.wikipedia.org/wiki/List_of_word_processor_programs |
Many works of art are claimed to have been designed using the golden ratio .
However, many of these claims are disputed, or refuted by measurement. [ 1 ]
The golden ratio , an irrational number , is approximately 1.618; it is often denoted by the Greek letter φ ( phi ).
Various authors have claimed that early monuments have golden ratio proportions, often on conjectural interpretations, using approximate measurements, and only roughly corresponding to 1.618. [ 1 ] For example, claims have been made about golden ratio proportions in Egyptian, Sumerian and Greek vases, Chinese pottery, Olmec sculptures, and Cretan and Mycenaean products from the late Bronze Age. These predate by some 1,000 years the Greek mathematicians first known to have studied the golden ratio. [ 2 ] [ 3 ] However, the historical sources are obscure, and the analyses are difficult to compare because they employ differing methods. [ 2 ]
It is claimed, for instance, that Stonehenge (3100 BC – 2200 BC) has golden ratio proportions between its concentric circles. [ 2 ] [ 4 ] Kimberly Elam proposes this relation as early evidence of human cognitive preference for the golden ratio. [ 5 ] However, others point out that this interpretation of Stonehenge "may be doubtful" and that the geometric construction that generates it can only be surmised. [ 2 ] As another example, Carlos Chanfón Olmos states that the sculpture of King Gudea (c. 2350 BC) has golden proportions between all of its secondary elements repeated many times at its base. [ 3 ]
The Great Pyramid of Giza (constructed c. 2570 BC by Hemiunu ) exhibits the golden ratio according to various pyramidologists , including Charles Funck-Hellet. [ 3 ] [ 6 ] John F. Pile, interior design professor and historian, has claimed that Egyptian architects sought the golden proportions without mathematical techniques and that it is common to see the 1.618:1 ratio, along with many other simpler geometrical concepts, in their architectural details, art, and everyday objects found in tombs. In his opinion, "That the Egyptians knew of it and used it seems certain." [ 7 ]
From before the beginning of these theories, other historians and mathematicians have proposed alternative theories for the pyramid designs that are not related to any use of the golden ratio, and are instead based on purely rational slopes that only approximate the golden ratio. [ 8 ] The Egyptians of those times apparently did not know the Pythagorean theorem ; the only right triangle whose proportions they knew was the 3:4:5 triangle. [ 9 ]
The Acropolis of Athens (468–430 BC), including the Parthenon , according to some studies, has many proportions that approximate the golden ratio. [ 10 ] Other scholars question whether the golden ratio was known to or used by Greek artists and architects as a principle of aesthetic proportion. [ 11 ] Building the Acropolis is calculated to have been started around 600 BC, but the works said to exhibit the golden ratio proportions were created from 468 BC to 430 BC.
The Parthenon (447–432 BC), was a temple of the Greek goddess Athena . The Parthenon's facade as well as elements of its facade and elsewhere are claimed to be circumscribed by a progression of golden rectangles . [ 12 ] Some more recent studies dispute the view that the golden ratio was employed in the design. [ 1 ] [ 11 ] [ 13 ]
Hemenway claims that the Greek sculptor Phidias (c. 480–c. 430 BC) used the divine proportion in some of his sculptures. [ 14 ] He created Athena Parthenos in Athens and Statue of Zeus (one of the Seven Wonders of the Ancient World ) in the Temple of Zeus at Olympia . He is believed to have been in charge of other Parthenon sculptures, although they may have been executed by his disciple or peers. In the early 20th century, American mathematician Mark Barr proposed the Greek letter phi ( φ ), the first letter of Phidias's name, to denote the golden ratio. [ 15 ]
Lothar Haselberger claims that the Temple of Apollo in Didyma (c. 334 BC), designed by Daphnis of Mileto and Paionios of Ephesus, has golden proportions. [ 3 ]
It is claimed that the upper level of 21 rows and the lower level of 34 rows of the Ancient Theatre of Epidaurus form an approximation of the Golden number since 21 and 34 are successive Fibonacci numbers with their ratio at 34 / 21 ≈ 1.619 {\displaystyle 34/21\approx 1.619} and a careful examination of the theatre's center reveals two back-to-back triangles balanced by the Golden number. [ 16 ]
Between 1950 and 1960, Manuel Amabilis applied some of the analysis methods of Frederik Macody Lund and Jay Hambidge in several designs of prehispanic buildings, such as El Toloc and La Iglesia de Las Monjas (the Nuns Church), a notable complex of Terminal Classic buildings constructed in the Puuc architectural style at Chichen Itza . According to his studies, their proportions are concretized from a series of polygons, circles and pentagrams inscribed, as Lund found in his studies of Gothic churches. Manuel Amabilis published his studies along with several self-explanatory images of other pre-columbian buildings made with golden ratio proportions in La Arquitectura Precolombina de Mexico . [ 17 ] The work was awarded the gold medal and the title of Academico by the Real Academia de Bellas Artes de San Fernando (Spain) in the Fiesta de la Raza ( Columbus Day ) of 1929.
The Castle of Chichen Itza was built by the Maya civilization between the 11th and 13th centuries AD as a temple to the god Kukulcan . John Pile claims that its interior layout has golden ratio proportions. He says that the interior walls are placed so that the outer spaces are related to the central chamber by the golden ratio. [ 18 ]
The Great Mosque of Kairouan (built by Uqba ibn Nafi c. 670 C.E.) uses the golden ratio in the design including its plan, the prayer space, court, and minaret, [ 19 ] but the ratio does not appear in the original parts of the mosque. [ 20 ]
The Stupa of Borobudur in Java , Indonesia (built eighth to ninth century AD), the largest known Buddhist stupa, has the dimension of the square base related to the diameter of the largest circular terrace as 1.618:1, according to Pile. [ 21 ]
The Romanesque style of architecture prevailed in Europe between 900 and 1200, a period which ends with the transition to Gothic architecture . The contrast between Romanesque and Gothic concepts in religious buildings can be understood in the epistolary between St. Bernard , Cistercian , and the Abbot Suger of the order of Cluny , the initiator of Gothic art in St. Denis .
One of the most beautiful works of Romanesque Cistercian is the Sénanque Abbey in Provence. The Sénanque abbatial was founded in 1148 and consecrated in 1178. It was initiated in life of St Bernard of Clairvaux .
"La Lumière à Sénanque" (The Light in Sénanque), [ 22 ] a chapter of Cîteaux : commentarii cistercienses , a publication of the Cistercian Order . Its author, Kim Lloveras i Montserrat, made in 1992 a complete study of the abbatial, and argues that the abbatial church was designed using a system of measures founded in the golden ratio, and that the instruments used for its construction were the "Vescica" and the medieval squares used by the constructors, both designed with the golden ratio. The "Vescica" of Sénanque is located in the cloister of the monastery, in front of the Chapter, the site of the workshop.
In his 1919 book Ad Quadratum , Frederik Macody Lund , a historian who studied the geometry of several Gothic structures, claims that the Cathedral of Chartres (begun in the 12th century), the Notre-Dame of Laon (1157–1205), and the Notre-Dame de Paris (1160) are designed according to the golden ratio. [ 3 ] Other scholars argue that until Luca Pacioli's 1509 De Divina Proportione (see next section), the golden ratio was unknown to artists and architects, although this is not likely the case since the ratio was explicitly defined by Euclid. [ 11 ]
A 2003 conference on medieval architecture resulted in the book Ad Quadratum: The Application of Geometry to Medieval Architecture . According to a summary by one reviewer:
Most of the contributors consider that the setting out was done ad quadratum, using the sides of a square and its diagonal. This gave an incommensurate ratio of [square root of (2)] by striking a circular arc (which could easily be done with a rope rotating around a peg). Most also argued that setting out was done geometrically rather than arithmetically (with a measuring rod). Some considered that setting out also involved the use of equilateral or Pythagorean triangles, pentagons, and octagons. Two authors believe the Golden Section (or at least its approximation) was used, but its use in medieval times is not supported by most architectural historians. [ 23 ]
The Australian architectural historian John James made a detailed study of the Cathedral of Chartres. In his work The Master Masons of Chartres he says that Bronze, one of the master masons, used the golden ratio. It was the same relation as between the arms of their metal square:
Bronze by comparison was an innovator, in practical rather than in philosophic things. Amongst other things Bronze was one of the few masters to use the fascinating ratio of the golden mean. For the builder, the most important function Fi, as we write the golden mean, is that if the uses is consistently he will find that every subdivision, no matter how accidentally it may have been derived, will fit somewhere into the series. Is not too difficult a ratio to reproduce, and Bronze could have had the two arms of his metal square cut to represent it. All he would than have had to do was to place the square on the stone and, using the string draw between the corners, relate any two lengths by Phi. Nothing like making life easy. [ 24 ]
De divina proportione , written by Luca Pacioli in Milan in 1496–1498, published in Venice in 1509, [ 25 ] features 60 drawings by Leonardo da Vinci , some of which illustrate the appearance of the golden ratio in geometric figures. Starting with part of the work of Leonardo da Vinci, this architectural treatise was a major influence on generations of artists and architects.
Vitruvian Man , created by Leonardo da Vinci around the year 1492, [ 26 ] is based on the theories of the man after which the drawing takes its name, Vitruvius , who in De Architectura: The Planning of Temples (c. I BC) pointed that the planning of temples depends on symmetry, which must be based on the perfect proportions of the human body. Some authors feel there is no actual evidence that Da Vinci used the golden ratio in Vitruvian Man ; [ 27 ] however, Olmos [ 3 ] (1991) observes otherwise through geometrical analysis. He also proposes Leonardo da Vinci's self portrait , Michelangelo's David (1501–1504), Albrecht Dürer 's Melencolia I and the classic violin design by the masters of Cremona ( Guarneri , Stradivari and several members of the Amati family) as having similar regulator lines related to the golden ratio.
Da Vinci's Mona Lisa (c. 1503–1506) "has been the subject of so many volumes of contradicting scholarly and popular speculations that it virtually impossible to reach any unambiguous conclusions" with respect to the golden ratio, according to Livio. [ 11 ]
The Tempietto chapel at the Monastery of Saint Peter in Montorio , Rome, built by Bramante , has relations to the golden ratio in its elevation and interior lines. [ 28 ]
José Villagrán García has claimed [ 29 ] that the golden ratio is an important element in the design of the Mexico City Metropolitan Cathedral (circa 1667–1813). Olmos claims the same for the design of the cities of Coatepec (1579), Chicoaloapa (1579) and Huejutla (1580), as well as the Mérida Cathedral , the Acolman Temple, Christ Crucified by Diego Velázquez (1639) and The Immaculate Conception by Bartolomé Esteban Murillo . [ 3 ]
Matila Ghyka [ 30 ] and others [ 31 ] contend that Georges Seurat used golden ratio proportions in paintings like Parade de cirque , Le Pont de Courbevoie , and Bathers at Asnières . However, there is no direct evidence to support these claims. [ 27 ]
While the golden ratio appears to govern the geometric structure of Seurat's Parade de cirque (Circus Sideshow), [ 32 ] [ 33 ] modern consensus among art historians is that Seurat never used this "divine proportion" in his work. [ 34 ] [ 35 ] [ 36 ]
The final study of Parade , executed prior to the oil on canvas, is divided horizontally into fourths and vertically into sixths (4 : 6 ratio) corresponding to the dimensions of the canvas, which is one and one-half times wider than its vertical dimension. These axes do not correspond precisely to the golden section, 1 : 1.6, as might have been expected. Rather, they correspond to basic mathematical divisions (simple ratios that appear to approximate the golden section), as noted by Seurat with citations from the mathematician, inventor, esthetician Charles Henry . [ 34 ]
The idea of the Section d'Or (or Groupe de Puteaux) originated in the course of conversations between Albert Gleizes , Jean Metzinger and Jacques Villon . The group's title was suggested by Villon, after reading a 1910 translation of Leonardo da Vinci 's A Treatise on Painting by Joséphin Péladan . Péladan attached great mystical significance to the golden section ( French : nombre d'or ), and other similar geometric configurations. For Villon, this symbolized his belief in order and the significance of mathematical proportions, because it reflected patterns and relationships occurring in nature. Jean Metzinger and the Duchamp brothers were passionately interested in mathematics. Jean Metzinger, Juan Gris and possibly Marcel Duchamp at this time were associates of Maurice Princet , an amateur mathematician credited for introducing profound and rational scientific arguments into Cubist discussions. [ 37 ] The name 'Section d'Or' represented simultaneously a continuity with past traditions and current trends in related fields, while leaving open future developments in the arts. [ 38 ] [ 39 ]
The Sacrament of the Last Supper (1955): The canvas of this surrealist masterpiece by Salvador Dalí is a golden rectangle. A huge dodecahedron, with edges in golden ratio to one another, is suspended above and behind Jesus and dominates the composition. [ 11 ] [ 40 ]
Some works in the Dutch artistic movement called De Stijl , or neoplasticism, exhibit golden ratio proportions. Piet Mondrian used the golden section extensively in his neoplasticist, geometrical paintings, created circa 1918–38. [ 31 ] [ 41 ] Mondrian sought proportion in his paintings by observation, knowledge and intuition, rather than geometrical or mathematical methods. [ 42 ]
The Farnsworth House , designed by Ludwig Mies van der Rohe , has been described as "the proportions, within the glass walls, approach 1:2" [ 43 ] and "with a width to length ratio of 1:1.75 (nearly the golden section)" [ 44 ] and has been studied with his other works in relation to the golden ratio. [ 45 ]
The Swiss architect Le Corbusier , famous for his contributions to the modern international style , centered his design philosophy on systems of harmony and proportion. Le Corbusier's faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci number , which he described as "rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned." [ 46 ]
Le Corbusier explicitly used the golden ratio in his system for the scale of architectural proportion . He saw this system as a continuation of the long tradition of Vitruvius , Leonardo da Vinci's Vitruvian Man , the work of Leon Battista Alberti , and others who used the proportions of the human body to improve the appearance and function of architecture . In addition to the golden ratio, Le Corbusier based the system on human measurements , Fibonacci numbers, and the double unit. He took Leonardo's suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body's height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modulor system. [ 47 ]
In The Modulor: A Harmonious Measure to the Human Scale, Universally Applicable to Architecture and Mechanics Le Corbusier reveals he used his system in the Marseilles Unité d'habitation (in the general plan and section, the front elevation, plan and section of the apartment, in the woodwork, the wall, the roof and some prefabricated furniture), a small office in 35 rue de Sèvres, a factory in Saint-Die and the United Nations Headquarters building in New York City. [ 48 ] Many authors claim that the shape of the facade of the second is the result of three golden rectangles; [ 49 ] however, each of the three rectangles that can actually be appreciated have different heights.
Catalan architect Josep Lluis Sert , a disciple of Le Corbusier , applied the measures of the Modulor in all his particular works, including the Sert's House in Cambridge [ 50 ] and the Joan Miró Foundation in Barcelona. [ 51 ]
According to the official tourism page of Buenos Aires , Argentina , the ground floor of the Palacio Barolo (1923), designed by Italian architect Mario Palanti , is built according to the golden ratio. [ 52 ]
Another Swiss architect, Mario Botta , bases many of his designs on geometric figures. Several private houses he designed in Switzerland are composed of squares and circles, cubes and cylinders. In a house he designed in Origlio , the golden ratio is the proportion between the central section and the side sections of the house. [ 53 ]
Ernő Lendvai analyzes Béla Bartók 's works as being based on two opposing systems, that of the golden ratio and the acoustic scale , [ 54 ] though other music scholars reject that analysis. [ 11 ]
The musicologist Roy Howat has observed that the formal boundaries of Debussy's La mer correspond exactly to the golden section. [ 55 ] Trezise finds the intrinsic evidence "remarkable", but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions. [ 56 ]
Leonid Sabaneyev hypothesizes that the separate time intervals of the musical pieces connected by the "culmination event", as a rule, are in the ratio of the golden section. [ 57 ] However, the author attributes this incidence to the instinct of the musicians: "All such events are timed by author's instinct to such points of the whole length that they divide temporary durations into separate parts being in the ratio of the golden section."
Ron Knott [ 58 ] exposes how the golden ratio is unintentionally present in several pieces of classical music:
According to author Leon Harkleroad, "Some of the most misguided attempts to link music and mathematics have involved Fibonacci numbers and the related golden ratio." [ 61 ]
With few exceptions, numerators for the meter signatures (over 100) in Karlheinz Stockhausen 's Klavierstück IX are either Fibonacci or Lucas numbers. [ 62 ] | https://en.wikipedia.org/wiki/List_of_works_designed_with_the_golden_ratio |
This list of yttrium compounds shows compounds of yttrium. Inclusion criteria: those that have applications, academic significance, single crystal structures or have their own Wikipedia articles. | https://en.wikipedia.org/wiki/List_of_yttrium_compounds |
This is a list of common β-lactam antibiotics —both administered drugs and those not in clinical use—organized by structural class. Antibiotics are listed alphabetically within their class or subclass by their nonproprietary name. If an antibiotic is a combination drug , both ingredients will be listed.
cefuroxime, cefaclor, cefprozil
(With β-lactamase stability and enhanced activity against Gram-positive bacteria and Pseudomonas aeruginosa )
(activity against MRSA and variably VRE. *Not universally accepted nomenclature. NO Antipseudomonal activity, mostly ceftriaxone coverage with additional MRSA and some VRE)
(Broadest spectrum of β-lactam antibiotics) | https://en.wikipedia.org/wiki/List_of_β-lactam_antibiotics |
Lister's tubercle or dorsal tubercle of radius is a bony prominence located at the distal end of the radius . It is palpable on the dorsum of the wrist .
Lister's tubercle is found on the dorsal distal radius. [ 1 ] It varies in size and shape significantly. [ 2 ] [ 3 ] It can range from around 2 to 6 mm in height (averaging 3 mm), and around 6 to 26 mm in length (averaging 13 mm). [ 2 ] [ 3 ] Lister's tubercle consists of two peaks including radial peak and ulnar peak. [ 4 ]
Lister's tubercle serves as a pulley for the tendon of extensor pollicis longus , which wraps around the medial side and takes a 45° turn. [ 1 ] [ 2 ] [ 5 ]
Lister's tubercle is used as a useful landmark during wrist arthroscopy and other wrist surgery . [ 1 ] [ 6 ] It is palpable on the dorsum of the wrist. [ 1 ] It is often difficult to clearly distinguish with radiography . [ 1 ]
Hyperextension of the wrist can lead to fracture of Lister's tubercle, as pressure is increased from the extensor pollicis longus tendon. [ 7 ] An "island-shaped" fracture can also expose the tendon to a rough edge and lead to tendon rupture (usually long after the initial fracture). [ 8 ] | https://en.wikipedia.org/wiki/Lister's_tubercle |
In mathematics, a Listing number of a topological space is one of several topological invariants introduced by the 19th-century mathematician Johann Benedict Listing and later given this name by Charles Sanders Peirce . Unlike the later invariants given by Bernhard Riemann , the Listing numbers do not form a complete set of invariants: two different two-dimensional manifolds may have the same Listing numbers as each other. [ 1 ]
There are four Listing numbers associated with a space. [ 2 ] The smallest Listing number counts the number of connected components of a space, and is thus equivalent to the zeroth Betti number . [ 3 ]
This topology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Listing_number |
The UN numbers range from UN0001 to about UN3600 and are assigned by the United Nations Committee of Experts on the Transport of Dangerous Goods . | https://en.wikipedia.org/wiki/Lists_of_UN_numbers |
Animals are multicellular eukaryotic organisms in the biological kingdom Animalia . With few exceptions, animals consume organic material , breathe oxygen , are able to move , reproduce sexually , and grow from a hollow sphere of cells, the blastula , during embryonic development . Over 1.5 million living animal species have been described —of which around 1 million are insects —but it has been estimated there are over 7 million in total. Animals range in size from 8.5 millionths of a metre to 33.6 metres (110 ft) long and have complex interactions with each other and their environments, forming intricate food webs . The study of animals is called zoology .
Animals may be listed or indexed by many criteria, including taxonomy , status as endangered species , their geographical location, and their portrayal and/or naming in human culture.
List of extinct animals
The animal Kingdom contains some 35 extant phyla.
Basal animals are delineated according to the following cladogram :
Choanoflagellata
Porifera
Ctenophora
Placozoa
Cnidaria
Xenacoelomorpha
Nephrozoa
Animals : Porifera , Diploblasts
Diploblasts : Ctenophora , ParaHoxozoa
ParaHoxozoa : Placozoa , Cnidaria , Bilateria / Triploblast
Bilateria : Xenacoelomorpha , Nephrozoa
Nephrozoa : Protostomes , Deuterostomes | https://en.wikipedia.org/wiki/Lists_of_animals |
This is a list of lists, grouped by type of astronomical object . | https://en.wikipedia.org/wiki/Lists_of_astronomical_objects |
Lists of computers cover computers , or programmable machines, by period, type, vendor and region. | https://en.wikipedia.org/wiki/Lists_of_computers |
Types of engineer include:
Lists of individual engineers by discipline include: | https://en.wikipedia.org/wiki/Lists_of_engineers |
Integration is the basic operation in integral calculus . While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. This page lists some of the most common antiderivatives .
A compilation of a list of integrals (Integraltafeln) and techniques of integral calculus was published by the German mathematician Meier Hirsch [ de ] (also spelled Meyer Hirsch) in 1810. [ 1 ] These tables were republished in the United Kingdom in 1823. More extensive tables were compiled in 1858 by the Dutch mathematician David Bierens de Haan for his Tables d'intégrales définies , supplemented by Supplément aux tables d'intégrales définies in ca. 1864. A new edition was published in 1867 under the title Nouvelles tables d'intégrales définies .
These tables, which contain mainly integrals of elementary functions, remained in use until the middle of the 20th century. They were then replaced by the much more extensive tables of Gradshteyn and Ryzhik . In Gradshteyn and Ryzhik, integrals originating from the book by Bierens de Haan are denoted by BI.
Not all closed-form expressions have closed-form antiderivatives; this study forms the subject of differential Galois theory , which was initially developed by Joseph Liouville in the 1830s and 1840s, leading to Liouville's theorem which classifies which expressions have closed-form antiderivatives. A simple example of a function without a closed-form antiderivative is e − x 2 , whose antiderivative is (up to constants) the error function .
Since 1968 there is the Risch algorithm for determining indefinite integrals that can be expressed in term of elementary functions , typically using a computer algebra system . Integrals that cannot be expressed using elementary functions can be manipulated symbolically using general functions such as the Meijer G-function .
More detail may be found on the following pages for the lists of integrals :
Gradshteyn , Ryzhik , Geronimus , Tseytlin , Jeffrey, Zwillinger, and Moll 's (GR) Table of Integrals, Series, and Products contains a large collection of results. An even larger, multivolume table is the Integrals and Series by Prudnikov , Brychkov , and Marichev (with volumes 1–3 listing integrals and series of elementary and special functions , volume 4–5 are tables of Laplace transforms ). More compact collections can be found in e.g. Brychkov, Marichev, Prudnikov's Tables of Indefinite Integrals , or as chapters in Zwillinger's CRC Standard Mathematical Tables and Formulae or Bronshtein and Semendyayev 's Guide Book to Mathematics , Handbook of Mathematics or Users' Guide to Mathematics , and other mathematical handbooks.
Other useful resources include Abramowitz and Stegun and the Bateman Manuscript Project . Both works contain many identities concerning specific integrals, which are organized with the most relevant topic instead of being collected into a separate table. Two volumes of the Bateman Manuscript are specific to integral transforms.
There are several web sites which have tables of integrals and integrals on demand. Wolfram Alpha can show results, and for some simpler expressions, also the intermediate steps of the integration. Wolfram Research also operates another online service, the Mathematica Online Integrator.
C is used for an arbitrary constant of integration that can only be determined if something about the value of the integral at some point is known. Thus, each function has an infinite number of antiderivatives .
These formulas only state in another form the assertions in the table of derivatives .
When there is a singularity in the function being integrated such that the antiderivative becomes undefined at some point (the singularity), then C does not need to be the same on both sides of the singularity. The forms below normally assume the Cauchy principal value around a singularity in the value of C , but this is not necessary in general. For instance, in ∫ 1 x d x = ln | x | + C {\displaystyle \int {1 \over x}\,dx=\ln \left|x\right|+C} there is a singularity at 0 and the antiderivative becomes infinite there. If the integral above were to be used to compute a definite integral between −1 and 1, one would get the wrong answer 0. This however is the Cauchy principal value of the integral around the singularity. If the integration is done in the complex plane the result depends on the path around the origin, in this case the singularity contributes − i π when using a path above the origin and i π for a path below the origin. A function on the real line could use a completely different value of C on either side of the origin as in: [ 2 ] ∫ 1 x d x = ln | x | + { A if x > 0 ; B if x < 0. {\displaystyle \int {1 \over x}\,dx=\ln |x|+{\begin{cases}A&{\text{if }}x>0;\\B&{\text{if }}x<0.\end{cases}}}
The following function has a non-integrable singularity at 0 for n ≤ −1 :
Let f be a continuous function , that has at most one zero . If f has a zero, let g be the unique antiderivative of f that is zero at the root of f ; otherwise, let g be any antiderivative of f . Then ∫ | f ( x ) | d x = sgn ( f ( x ) ) g ( x ) + C , {\displaystyle \int \left|f(x)\right|\,dx=\operatorname {sgn}(f(x))g(x)+C,} where sgn( x ) is the sign function , which takes the values −1, 0, 1 when x is respectively negative, zero or positive.
This can be proved by computing the derivative of the right-hand side of the formula, taking into account that the condition on g is here for insuring the continuity of the integral.
This gives the following formulas (where a ≠ 0 ), which are valid over any interval where f is continuous (over larger intervals, the constant C must be replaced by a piecewise constant function):
If the function f does not have any continuous antiderivative which takes the value zero at the zeros of f (this is the case for the sine and the cosine functions), then sgn( f ( x )) ∫ f ( x ) dx is an antiderivative of f on every interval on which f is not zero, but may be discontinuous at the points where f ( x ) = 0 . For having a continuous antiderivative, one has thus to add a well chosen step function . If we also use the fact that the absolute values of sine and cosine are periodic with period π , then we get:
Ci , Si : Trigonometric integrals , Ei : Exponential integral , li : Logarithmic integral function , erf : Error function
There are some functions whose antiderivatives cannot be expressed in closed form . However, the values of the definite integrals of some of these functions over some common intervals can be calculated. A few useful integrals are given below.
If the function f has bounded variation on the interval [ a , b ] , then the method of exhaustion provides a formula for the integral: ∫ a b f ( x ) d x = ( b − a ) ∑ n = 1 ∞ ∑ m = 1 2 n − 1 ( − 1 ) m + 1 2 − n f ( a + m ( b − a ) 2 − n ) . {\displaystyle \int _{a}^{b}{f(x)\,dx}=(b-a)\sum \limits _{n=1}^{\infty }{\sum \limits _{m=1}^{2^{n}-1}{\left({-1}\right)^{m+1}}}2^{-n}f(a+m\left({b-a}\right)2^{-n}).}
The " sophomore's dream ": ∫ 0 1 x − x d x = ∑ n = 1 ∞ n − n ( = 1.29128 59970 6266 … ) ∫ 0 1 x x d x = − ∑ n = 1 ∞ ( − n ) − n ( = 0.78343 05107 1213 … ) {\displaystyle {\begin{aligned}\int _{0}^{1}x^{-x}\,dx&=\sum _{n=1}^{\infty }n^{-n}&&(=1.29128\,59970\,6266\dots )\\[6pt]\int _{0}^{1}x^{x}\,dx&=-\sum _{n=1}^{\infty }(-n)^{-n}&&(=0.78343\,05107\,1213\dots )\end{aligned}}} attributed to Johann Bernoulli . | https://en.wikipedia.org/wiki/Lists_of_integrals |
These are lists of investigational drugs : | https://en.wikipedia.org/wiki/Lists_of_investigational_drugs |
This is a List of Lists of mathematicians and covers notable mathematicians by nationality, ethnicity, religion, profession and other characteristics. Alphabetical lists are also available (see table to the right). | https://en.wikipedia.org/wiki/Lists_of_mathematicians |
Lists of mathematics topics cover a variety of topics related to mathematics . Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing.
Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference tables.
They also cover equations named after people, societies, mathematicians, journals, and meta-lists.
The purpose of this list is not similar to that of the Mathematics Subject Classification formulated by the American Mathematical Society . Many mathematics journals ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The subject codes so listed are used by the two major reviewing databases, Mathematical Reviews and Zentralblatt MATH . This list has some items that would not fit in such a classification, such as list of exponential topics and list of factorial and binomial topics , which may surprise the reader with the diversity of their coverage.
This branch is typically taught in secondary education or in the first year of university.
As a rough guide, this list is divided into pure and applied sections although in reality, these branches are overlapping and intertwined.
Algebra includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group .
Calculus studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change. Analysis evolved from calculus.
Geometry is initially the study of spatial figures like circles and cubes, though it has been generalized considerably. Topology developed from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension.
Combinatorics concerns the study of discrete (and usually finite ) objects. Aspects include "counting" the objects satisfying certain criteria ( enumerative combinatorics ), deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory ), finding "largest", "smallest", or "optimal" objects ( extremal combinatorics and combinatorial optimization ), and finding algebraic structures these objects may have ( algebraic combinatorics ).
Logic is the foundation that underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof.
The branch of mathematics deals with the properties and relationships of numbers, especially positive integers. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians.
A differential equation is an equation involving an unknown function and its derivatives.
In a dynamical system , a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.
Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". 1
The fields of mathematics and computing intersect both in computer science , the study of algorithms and data structures, and in scientific computing , the study of algorithmic methods for solving problems in mathematics, science, and engineering.
Information theory is a branch of applied mathematics and social science involving the quantification of information . Historically, information theory was developed to find fundamental limits on compressing and reliably communicating data.
Signal processing is the analysis, interpretation, and manipulation of signals . Signals of interest include sound , images , biological signals such as ECG , radar signals, and many others. Processing of such signals includes filtering , storage and reconstruction, separation of information from noise , compression , and feature extraction .
Probability theory is the formalization and study of the mathematics of uncertain events or knowledge. The related field of mathematical statistics develops statistical theory with mathematics. Statistics , the science concerned with collecting and analyzing data, is an autonomous discipline (and not a subdiscipline of applied mathematics ).
Game theory is a branch of mathematics that uses models to study interactions with formalized incentive structures ("games"). It has applications in a variety of fields, including economics , anthropology , political science , social psychology and military strategy .
Operations research is the study and use of mathematical models, statistics, and algorithms to aid in decision-making, typically with the goal of improving or optimizing the performance of real-world systems.
A mathematical statement amounts to a proposition or assertion of some mathematical fact, formula, or construction. Such statements include axioms and the theorems that may be proved from them, conjectures that may be unproven or even unprovable, and also algorithms for computing the answers to questions that can be expressed mathematically.
Among mathematical objects are numbers, functions, sets, a great variety of things called " spaces " of one kind or another, algebraic structures such as rings, groups, or fields, and many other things.
Mathematicians study and research in all the different areas of mathematics. The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical computer science and theoretical physics ).
In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. The following pages list the integrals of many different functions. | https://en.wikipedia.org/wiki/Lists_of_mathematics_topics |
This is a list of 194 sources that list elements classified as metalloids . The sources are listed in chronological order. Lists of metalloids differ since there is no rigorous widely accepted definition of metalloid (or its occasional alias, 'semi-metal'). Individual lists share common ground, with variations occurring at the margins. The elements most often regarded as metalloids are boron, silicon, germanium, arsenic, antimony and tellurium. [ n 1 ] Other sources may subtract from this list, add a varying number of other elements, or both.
Recognition status, as metalloids, of some elements in the p-block of the periodic table. Percentages are median appearance frequencies in the lists of metalloids . [ n 2 ] The staircase-shaped line is a typical example of the arbitrary metal–nonmetal dividing line found on some periodic tables.
This table shows which elements are included in each of 194 different lists of metalloids. A parenthesized symbol indicates an element whose inclusion in a particular metalloid list is qualified in some way by the author(s). The 'citations' rows show how many and what percentage of the authorities consider each element to be a metalloid, with qualified citations counted as one-half.
There is an average of 7.15 elements per metalloid list.
Elements cited in the listed sources (as of August 2011; n = 194) have appearance frequencies that occur in clusters of comparable values. The diamonds in the graph mark the mean appearance frequency of each cluster.
The resulting geometric trend line has the formula y = 199.47e −0.7423x and an R 2 value of 0.9962. [ n 3 ]
The elements commonly classified as metalloids are boron, silicon, germanium, arsenic, antimony and tellurium. [ n 4 ] The status of polonium and astatine is not settled. Most authors recognise one or the other, or both, as metalloids; Herman, Hoffmann and Ashcroft, on the basis of relativistic modelling, predict astatine will be a monatomic metal. [ n 5 ] One or more of carbon, aluminium, phosphorus, selenium, tin or bismuth, these being periodic table neighbours of the elements commonly classified as metalloids, are sometimes recognised as metalloids. [ n 6 ] Selenium, in particular, is commonly designated as a metalloid in environmental chemistry [ n 7 ] on account of similarities in its aquatic chemistry with that of arsenic and antimony. [ n 8 ] There are fewer references to beryllium, in spite of its periodic table position adjoining the dividing line between metals and nonmetals . Isolated references in the literature can also be found to the categorisation of other elements as metalloids. These elements include: hydrogen, nitrogen, [ n 9 ] sulfur, [ n 10 ] zinc, [ n 11 ] gallium, [ n 12 ] iodine, [ n 13 ] lead, [ n 14 ] and radon [ n 15 ] (citations are for references other than those listed above). | https://en.wikipedia.org/wiki/Lists_of_metalloids |
This is an index of lists of molecules (i.e. by year, number of atoms, etc.). Millions of molecules have existed in the universe since before the formation of Earth. Three of them, carbon dioxide , water and oxygen were necessary for the growth of life. Although humanity had always been surrounded by these substances, it has not always known what they were composed of.
The following is an index of list of molecules organized by time of discovery of their molecular formula or their specific molecule in case of isomers :
List of compounds | https://en.wikipedia.org/wiki/Lists_of_molecules |
This is a collection of lists of organisms by their population . While most of the numbers are estimates, they have been made by the experts in their fields. Species population is a science falling under the purview of population ecology and biogeography . Individuals are counted by census, as carried out for the piping plover ; [ 3 ] [ 4 ] using the transect method , as done for the mountain plover ; [ 5 ] and beginning in 2012 by satellite, with the emperor penguin being first subject counted in this manner. [ 6 ]
More than 99 percent of all species, amounting to over five billion species, [ 7 ] that ever lived on Earth are estimated to be extinct . [ 8 ] [ 9 ] Estimates on the number of Earth's current species range from 10 million to 14 million, [ 10 ] of which about 1.2 million have been documented and over 86 percent have not yet been described. [ 11 ] According to another study, the number of described species has been estimated at 1,899,587. [ 12 ] 2000–2009 saw approximately 17,000 species described per year. [ 12 ] The total number of undescribed organisms is unknown, but marine microbial species alone could number 20,000,000. [ 12 ] For this reason, the number of quantified species will always lag behind the number of described species, and species contained in these lists tend to be on the K side of the r/K selection continuum . More recently, in May 2016, scientists reported that 1 trillion species are estimated to be on Earth currently with only one-thousandth of one percent described. [ 13 ] The total number of related DNA base pairs on Earth is estimated at 5.0 x 10 37 and weighs 50 billion tonnes . [ 14 ] In comparison, the total mass of the biosphere has been estimated to be as much as 4 TtC (trillion [million million] tonnes of carbon ). [ 15 ] In July 2016, scientists reported identifying a set of 355 genes from the Last universal common ancestor (LUCA) of all organisms living on Earth. [ 16 ]
The domain of eukaryotes represent a small minority of the number of organisms; [ 17 ] however, due to their generally much larger size, their collective global biomass is estimated to be about equal to that of prokaryotes . [ 17 ] Prokaryotes number about 4–6 × 10 30 cells and 350–550 Pg of C. [ 18 ]
It is estimated that the most numerous bacteria are of a species of the Pelagibacterales (or SAR11) clade, perhaps Pelagibacter ubique , and the most numerous viruses are bacteriophages infecting these species. [ 19 ] It is estimated that the oceans contain about 2.4 × 10 28 (24 octillion) SAR11 cells. [ 20 ] The Deep Carbon Observatory has been exploring living forms in the interior of the Earth. "Life in deep Earth totals 15 to 23 billion tons of carbon". [ 21 ]
Recent figures indicate that there are more than 1.4 billion insects for each human on the planet, [ 27 ] or roughly 10 19 (10 quintillion) individual living insects on the earth at any given time. [ 28 ] An article in The New York Times claimed that the world holds 300 pounds of insects for every pound of humans. [ 28 ] Ants have colonised almost every landmass on Earth. Their population is estimated as between 10 16 –10 17 (10-100 quadrillion). [ 29 ] With an estimated 20 quadrillion ants their biomass comes to 12 megatons of dry carbon, which is more than all wild birds and non-human mammals combined. [ 30 ] [ 31 ] [ 32 ]
According to NASA in 2005, there were over 400 billion trees on our globe. [ 33 ] However, more recently, in 2015, using better methods, the global tree count has been estimated at 3 trillion. [ 34 ] Other studies show that the Amazonian forest alone yields approximately 430 billion trees. [ 35 ] Extrapolations from data compiled over a period of 10 years suggest that greater Amazonia, which includes the Amazon Basin and the Guiana Shield, harbors around 390 billion individual trees. [ 36 ] | https://en.wikipedia.org/wiki/Lists_of_organisms_by_population |
These are Wikipedia lists about the pharmaceutical industry . The pharmaceutical industry develops, produces, and markets drugs or pharmaceuticals licensed for use as medications . Pharmaceutical companies are allowed to deal in generic or brand medications and medical devices. They are subject to a variety of laws and regulations regarding the production, testing, and marketing of drugs . | https://en.wikipedia.org/wiki/Lists_of_pharmaceutical_industry_topics |
This is a list of notable awards for specific areas of science and technology . Typically these lists give the country of the sponsoring organization, the award name, sponsor name and a description of the award criteria. Some of the awards have broad scope, or cover the intersection of different disciplines, so an award may appear in more than one list. A list of general awards for science and technology is followed by the lists of more specific awards.
In July 2020 scientists reported that work honored by Nobel Prizes clusters in only a few scientific fields with only 36/71 having received at least one Nobel Prize of the 114/849 domains science could be divided into according to their DC2 and DC3 classification systems. Five of the 114 domains were shown to make up over half of the Nobel Prizes awarded 1995–2017 (particle physics [14%], cell biology [12.1%], atomic physics [10.9%], neuroscience [10.1%], molecular chemistry [5.3%]). [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Lists_of_science_and_technology_awards |
This article contains links to lists of scientists . | https://en.wikipedia.org/wiki/Lists_of_scientists |
There are several lists of sequenced genomes : | https://en.wikipedia.org/wiki/Lists_of_sequenced_genomes |
A space program is an organized effort by a government or a company with a goal related to outer space .
Lists of space programs include: | https://en.wikipedia.org/wiki/Lists_of_space_programs |
All stars but one can be associated with an IAU (International Astronomical Union) constellation. IAU constellations are areas of the sky. Although there are only 88 IAU constellations, the sky is actually divided into 89 irregularly shaped boxes as the constellation Serpens is split into two separate sections, Serpens Caput (the snake's head) to the west and Serpens Cauda (the snake's tail) to the east.
The only star that does not belong to a constellation is the Sun. The Sun travels through the 13 constellations along the ecliptic, the 12 of the Zodiac and Ophiuchus .
Among the remaining stars, the nearer ones exhibit proper motion , so it is only a matter of time before some of them cross a constellation boundary and switch constellations as a consequence. In 1992, Rho Aquilae became the first star to have its Bayer designation "invalidated" by moving to a neighbouring constellation—it is now a star of the constellation Delphinus . [ 1 ]
Stars are listed in the appropriate lists for the constellation, as follows:
Note that these lists are currently unfinished, and there may be stars missing that satisfy these conditions. If you come across one, please feel free to add it. | https://en.wikipedia.org/wiki/Lists_of_stars_by_constellation |
In geometry , many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror. Up to 3 face types exist centered on the fundamental triangle corners. Right triangle domains can have as few as 1 face type, making regular forms, while general triangles have at least 2 triangle types, leading at best to a quasiregular tiling.
There are different notations for expressing these uniform solutions, Wythoff symbol , Coxeter diagram , and Coxeter's t-notation.
Simple tiles are generated by Möbius triangles with whole numbers p,q,r, while Schwarz triangles allow rational numbers p,q,r and allow star polygon faces, and have overlapping elements.
The seven generator points with each set of p , q , r {\displaystyle p,q,r} (and a few special forms):
There are three special cases:
There are 4 symmetry classes of reflection on the sphere , and three in the Euclidean plane . A few of the infinitely many such patterns in the hyperbolic plane are also listed. (Increasing any of the numbers defining a hyperbolic or Euclidean tiling makes another hyperbolic tiling.)
Point groups:
Euclidean (affine) groups:
Hyperbolic groups:
The above symmetry groups only include the integer solutions on the sphere. The list of Schwarz triangles includes rational numbers, and determine the full set of solutions of nonconvex uniform polyhedra .
In the tilings above, each triangle is a fundamental domain, colored by even and odd reflections.
Selected tilings created by the Wythoff construction are given below.
Tilings are shown as polyhedra . Some of the forms are degenerate, given with brackets for vertex figures , with overlapping edges or vertices.
Spherical tilings with dihedral symmetry exist for all p = 2 , 3 , 4 , … {\displaystyle p=2,3,4,\dots } many with digon faces which become degenerate polyhedra. Two of the eight forms (Rectified and cantillated) are replications and are skipped in the table.
Some representative hyperbolic tilings are given, and shown as a Poincaré disk projection.
The Coxeter–Dynkin diagram is given in a linear form, although it is actually a triangle, with the trailing segment r connecting to the first node. | https://en.wikipedia.org/wiki/Lists_of_uniform_tilings_on_the_sphere,_plane,_and_hyperbolic_plane |
LiteBIRD ( Lite ( Light ) satellite for the studies of B-mode polarization and Inflation from cosmic background Radiation Detection ) is a planned small space observatory that aims to detect the footprint of the primordial gravitational wave on the cosmic microwave background (CMB) in a form of polarization pattern called B-mode .
LiteBIRD and OKEANOS were the two finalists for Japan's second Large-Class Mission. [ 5 ] [ 6 ] In May 2019, LiteBIRD was selected by the Japanese space agency . [ 7 ] LiteBIRD is planned to be launched in 2032 with an H3 launch vehicle for three years of observations at the Sun-Earth Lagrangian point L2. [ 2 ] [ 8 ]
Cosmological inflation is the leading theory of the first instant of the universe , called the Big Bang theory . Inflation postulates that the universe underwent a period of rapid expansion an instant after its formation, and it provides a convincing explanation for cosmological observations. [ 3 ] Inflation predicts that primordial gravitational waves were created during the inflationary era, about 10 −38 second after the beginning of the universe. [ 9 ] The primordial gravitational waves are expected to be imprinted in the CMB polarization map as special patterns, called the B-mode . [ 9 ] Measurements of polarization of the CMB radiation are considered as the best probe to detect the primordial gravitational waves, [ 10 ] that could bring a profound knowledge on how the Universe began, and may open a new era of testing theoretical predictions of quantum gravity , including those by the superstring theory . [ 9 ]
The science goal of LiteBIRD is to measure the CMB polarization over the entire sky with the sensitivity of δr <0.001, which allows testing the major single-field slow-roll inflation models experimentally. [ 1 ] [ 11 ] The design concept is being studied by an international team of scientists from Japan, U.S., Canada and Europe. [ 5 ] [ 12 ]
In order to separate CMB from the galactic emission, the measurements will cover 40 GHz to 400 GHz during a 3-year full sky survey using two telescopes on LiteBIRD . [ 3 ] [ 5 ] The Low Frequency Telescope (LFT) covers 40 GHz to 235 GHz, and the High Frequency Telescope (HFT) covers 280 GHz to 400 GHz. LFT has a 400 mm aperture
Crossed-Dragone telescope, and HFT has a 200 mm aperture on-axis refractor with two silicon lenses. [ 3 ] [ 5 ] [ 13 ] The baseline design considers an array of 2,622 superconducting polarimetric detectors. [ 3 ] [ 13 ] The entire optical system will be cooled down to approximately 5 K (−268.15 °C; −450.67 °F) to minimize the thermal emission, [ 14 ] and the focal plane is cooled to 100 mK with a two-stage sub-Kelvin cooler. [ 3 ] | https://en.wikipedia.org/wiki/LiteBIRD |
Huawei LiteOS is a discontinued lightweight real-time operating system (RTOS) developed by Huawei . [ 1 ] It is a POSIX compliant operating system for Internet of things (IoT) devices, and free and open-source software , released under a BSD 3-clause license . [ 2 ] Microcontrollers of different architectures such as ARM (M0/3/4/7, A7/17/53, ARM9/11), x86 , and RISC-V are supported by the project. Huawei's LiteOS is part of their '1+8+N' Internet of things system, and has been featured in several open source software development kits and industry offerings. [ 3 ]
Smartwatches by Huawei and its former Honor brand run LiteOS. [ 4 ] [ 5 ] LiteOS variants of kernels has since been incorporated into the IoT-oriented HarmonyOS with open source OpenHarmony .
On 20 May 2015 , at the Huawei Network Conference, Huawei proposed the '1+2+1' Internet of Things solution and release the IoT operating system named Huawei LiteOS. It has been reported development of the real-time operating system goes back as far as 2012. [ 2 ] [ 1 ] | https://en.wikipedia.org/wiki/LiteOS |
Litema, spelled as Ditema in South African Sesotho orthography (pronounced: /ditʼɪːma/; Singular: Tema , Sesotho for "text" or "ploughed land") is a form of Sesotho mural art composed of decorative and symbolic geometric patterns, commonly associated with Sesotho tradition today practised in Lesotho and neighbouring areas of South Africa. Basotho women generate litema on the outer walls and inside of homesteads by means of engraving, painting, relief mouldings and/or mosaic. Typically the geometric patterns are combed or scratched into the wet top layer of fresh clay and dung plaster of the wall, and later painted with earth ochers or, in contemporary times, manufactured paint. Patterns most often mimic ploughed fields through a combed texture, or the patterns refer to plant life, and more occasionally to other aspects of the natural world, such as referring to clan totem animal. Litema are transient; they may desiccate and crumble or be washed away by heavy rain. It is common for women of an entire village to apply litema on such special occasions as a wedding or a religious ceremony. [ 1 ]
As Gary van Wyk (1993:84) pointed out in his analysis of the etymology of the Sesotho noun denoting "Sesotho mural art," litema also refers to the associated concepts of "ploughed lands", [ 2 ] and the decorative tradition is symbolically linked to cultivation in many ways. It is derived from the verb stem -lema (in the infinitive , ho lema "to cultivate"), which is a reflex of the Proto-Bantu root *-dɪ̀m- "to cultivate (esp. with hoe)". [ 3 ] The orthographic ⟨l⟩ in li- ( Class 10 noun class prefix for Sesotho nouns ) is pronounced [d] in Sesotho since [d] is an allophone of /l/ occurring before the close vowels, /i/ and /u/. The orthographic ⟨e⟩ can have three possible values in Sesotho: /ɪ/, /ɛ/, and /e/. In ⟨litema⟩ is pronounced /ɪ/, as per the Proto-Bantu root.
The litema patterns are characterised by a multi-stage symmetry . Patterns are generally arranged in square cells. A wall to be shaped is divided into a grid to form the cells. Each cell is applied with the same pattern, which is usually rotated or mirrored from cell to cell. The symmetry of the overall pattern thus depends on the symmetries present in the basic pattern. There are designs with only one mirror axis in the basic patterns that result in an overall impression of flowing in one direction. Other basic patterns have several axes of symmetry or a rotational symmetry , and give the overall pattern a rather flat ornamental impression. The colour design is restrained, usually only two colours are used [ 1 ]
The tradition of mural art in Southern Africa is not of recent origins. While excavations at Sotho-Tswana archaeological sites have revealed hut floors that have survived the elements for as much as 1500 years, the earliest evidence of Sotho-Tswana mural painting stretches back about five centuries (Grant 1995:45; Van Wyk 1998:88). It long predates the tradition of Ndebele mural painting that has been globally popularized. Begun in the 19th century, the Ndzundza Ndebele mural art tradition called igwalo (more widely known as Ndebele house painting ), is said to be a synthesis of a Northern Sotho ditema tradition and the Nguni design traditions employed in beadwork, pottery and basket weaving. [ 4 ]
One of the earliest written accounts of Basotho mural art is by the missionary Rev. John Campbell. In his 1813 description of Batlhaping ( South Tswana ) art, Campbell stated the following:"Having heard of some paintings in Salakootoo's house, we went after breakfast to view them. We found them very rough representations of the camel-leopard, rhinoceros, elephant, lion, tiger, and stein-buck, which Salakootoo's wife had drawn on the clay wall, with white and black paint. However, they were as well done as we expected, and may lead to something better" (Grant 1995:43).
On his second journey in 1820, Campbell, gave an enthusiastic account of what he saw at the house of a certain chief "Sinosee" of the Hurutse lineage of the Sotho-Tswana. Campbell provided both illustrations as well as a verbal description of the chief's house: "The wall was painted yellow, and ornamented with figures of shields, elephants and camel-leopards, etc. It was also adorned with a neat cornice or border painting of a red colour...its walls (of Sinosee's bedroom) were decorated with delightful representations of elephants and giraffes… In some houses there were figures, pillars, etc moulded in hard clay and painted with different colours that would not have disgraced European workmen" (Van Wyk 1996:43; 1998:88). Campbell's accounts were compiled and published by historian George Stow, in his book The Native Races of South Africa (1905). [ 5 ] Stow also published the earliest known drawings of litema – reproductions of eight designs made by the " Bakuena " (the founding clan of the Basotho nation), which he likely drew himself, based on an unpublished letter by Stow in the South African Library in which he recounts visiting a ruined Bakoena kraal (Van Wyk 1998:89). Stow's drawings showed textured panels similar to litema engravings still made today as well as painted patterns of dots, stripes, triangles, and zigzags executed in limited colors.
In his 1861 book, the French missionary Eugene Casallis recalled the litema patterns he had experienced since settling among Basotho in the 1830s, calling the designs "ingenious", which suggests designs more intricate than the Bakoena examples Stow reproduced (Van Wyk 1998:89). Stow's documentation did not include any designs incorporating plant motifs like those seen in modern-day litema. Van Wyk (1994) suggests that the more modern and "intricate curvilinear designs have a distinctly Victorian or Edwardian flavor that was probably influenced by such turn-of-the-century European products as linoleum patterns, cast-iron moldings and lace".
Almost a century separates Stow's drawings from those done in 1976 by students of the Lesotho National Teachers Training College (Van Wyk 1989:89). Benedict Lira Mothibe, an art lecturer at the college at the time, instructed students to copy litema designs for the purposes of using these in classroom geometry lessons and as copies for potato prints. More importantly, it was an attempt by Mothibe to revive interest in what he considered a worthwhile Sesotho tradition. Gary van Wyk employed these drawings during his extensive field research in South Africa and Lesotho from 1991-1994, recording women's responses to the historical patterns, including the names and meanings they ascribed to them, and later republished several of the drawings. He found that although many of the specific vegetal patterns (e.g. "melons") that had been named in the 1970s had been forgotten by the 1990s and subsumed under a general descriptive category of "blomme", the Afrikaans word for "flowers," nonetheless this designation maintained the close symbolic association between women and vegetative fertility, linked to women's traditional roles as cultivators and foragers. Furthermore, a few patterns recorded by Mothibe were still identifiable and being produced in the early 1990s, such as one that refers to the board for marabaraba, a popular indigenous game like checkers (1998:90-91).
More recently (2003), Mothibe, in a further contribution towards the cause of preservation, compiled and donated a second edition on litema designs entitled Basotho Litema Patterns (With Modifications) to the School of Design Technology and Visual Art of the Central University of Technology , Free State , providing an updated record of designs and their interpretation. [ 6 ]
Research conducted by Van Wyk and Mathews in the late-1980s and mid-1990s, culminating in two photographically illustrated books titled African Painted Houses: Basotho Dwellings of Southern Africa (Van Wyk, 1998) and The African Mural (Chanquion & Matthews, 1989), suggests that the art of litema cannot be understood in purely aesthetic terms.
Source: [ 7 ]
In several works on this topic, Gary Van Wyk (1993, 1994, 1996, 1998) states that Sesotho murals are a form of religious art, appeals to the ancestors for the rain that delivers the fertility that nourishes the fields and thereby sustains the herds and the human community. Murals, he says, can be seen as prayers in paint. If the ancestors are satisfied, they provide rain that washes away the murals, and the cycle of life begins anew. It is fitting that murals are produced by women, who are symbolically linked to the house, which is a metaphor of the womb and of creation, and to the vegetal realm to which women are linked through their traditional roles as cultivators and foragers, and through several other vegetal symbols. The Basotho creation myth, for example, states that the nation emerged from a dark place deep in the earth through a bed of reeds; accordingly it was once customary upon the birth of child inside the earthen house, originally built in an igloo shape, and therefore womb-like, to place a reed in the doorway of the home until the child "crossed the reed" to emerge into the light of day (Van Wyk 1998: 103-107). Similarly, female initiates wear a reed mask, and during their initiation confinement they weave reed mats.
This symbolic link between the igloo-shaped house and the body later was transferred to modern rectangular homes with flat roofs, where the surrounds of doorways and windows were particularly ornamented, and the name for the litema patterns along the roofline was the "headband".
"The fecundity of fields and of women is celebrated in the creation of radiant blooms, unfurling fronds, spiralling tendrils and sprouts...Because agricultural labor was traditionally women's work, women who decorate houses can be viewed as picturing this work in the fields upon their walls. The murals are thus African landscapes, composed of the very landscape they represent" (Van Wyk 1994). This is most apparent in litema patterns that consist solely of uncolored combing into mud: these closely mimic the appearance of a plowed field. [ 8 ] Van Wyk found that red ocher, called letsoku , or "the blood of the earth", symbolized fertility and the blood of both menstruation and sacrifice, underscoring the key link between the ancestors and fertility and accounting for the fact that red ocher is invariably incorporated into every painting scheme. White symbolized the calm, purity and enlightenment that the ancestors promote and desire, while black represented the dark rain clouds that the ancestors deliver if all is calm and well, and these two colors are frequently combined in dense, alternating patterns applied to transitional zones of the architecture, such as the roofline and around doors and windows. Similarly, such patterns elements as triangles and zigzags likely also carried symbolic meanings that have become obscured in recent times. During the 1980s and early 1990s, Van Wyk also photographed murals that expressed political statements, using the colors of the banned African National Congress during the apartheid era, or incorporating specific political graphics or statements.
Tom Mathews in his writings (supported by photographs taken by his son Paul Chanquion) stated that flowers and dots were symbols of fertility. Furthermore, he states that chevron patterns represent water or uneven ground whilst triangles are symbols denoting male and female (Changuion & Matthews, 1989:9,19,55).
In the study conducted by the CUT , no persons knowledgeable in the art of litema (Bekker, Thabane and Mothibe) or practising litema artists had any knowledge of a deeper significance other than that of beautifying the home for aesthetic purposes. Some of the artists questioned did however share their opinions concerning the possibility of symbolic meaning. According to artists in the Free State, their mothers (many of whom originate from Lesotho), might have been aware of such meanings, but did not share this information with them during their teaching. [ 9 ] | https://en.wikipedia.org/wiki/Litema |
In mathematical logic , a literal is an atomic formula (also known as an atom or prime formula) or its negation . [ 1 ] [ 2 ] The definition mostly appears in proof theory (of classical logic ), e.g. in conjunctive normal form and the method of resolution .
Literals can be divided into two types: [ 2 ]
The polarity of a literal is positive or negative depending on whether it is a positive or negative literal.
In logics with double negation elimination (where ¬ ¬ x ≡ x {\displaystyle \lnot \lnot x\equiv x} ) the complementary literal or complement of a literal l {\displaystyle l} can be defined as the literal corresponding to the negation of l {\displaystyle l} . [ 3 ] We can write l ¯ {\displaystyle {\bar {l}}} to denote the complementary literal of l {\displaystyle l} . More precisely, if l ≡ x {\displaystyle l\equiv x} then l ¯ {\displaystyle {\bar {l}}} is ¬ x {\displaystyle \lnot x} and if l ≡ ¬ x {\displaystyle l\equiv \lnot x} then l ¯ {\displaystyle {\bar {l}}} is x {\displaystyle x} . Double negation elimination occurs in classical logics but not in intuitionistic logic .
In the context of a formula in the conjunctive normal form , a literal is pure if the literal's complement does not appear in the formula.
In Boolean functions , each separate occurrence of a variable, either in inverse or uncomplemented form, is a literal. For example, if A {\displaystyle A} , B {\displaystyle B} and C {\displaystyle C} are variables then the expression A ¯ B C {\displaystyle {\bar {A}}BC} contains three literals and the expression A ¯ C + B ¯ C ¯ {\displaystyle {\bar {A}}C+{\bar {B}}{\bar {C}}} contains four literals. However, the expression A ¯ C + B ¯ C {\displaystyle {\bar {A}}C+{\bar {B}}C} would also be said to contain four literals, because although two of the literals are identical ( C {\displaystyle C} appears twice) these qualify as two separate occurrences. [ 4 ]
In propositional calculus a literal is simply a propositional variable or its negation.
In predicate calculus a literal is an atomic formula or its negation, where an atomic formula is a predicate symbol applied to some terms , P ( t 1 , … , t n ) {\displaystyle P(t_{1},\ldots ,t_{n})} with the terms recursively defined starting from constant symbols, variable symbols, and function symbols. For example, ¬ Q ( f ( g ( x ) , y , 2 ) , x ) {\displaystyle \neg Q(f(g(x),y,2),x)} is a negative literal with the constant symbol 2, the variable symbols x , y , the function symbols f , g , and the predicate symbol Q . | https://en.wikipedia.org/wiki/Literal_(mathematical_logic) |
Lithia water is defined as a type of mineral water characterized by the presence of lithium salts (such as the carbonate , chloride , or citrate of lithium). [ 1 ] Natural lithia mineral spring waters are rare, and there are few commercially bottled lithia water products.
Between the 1880s and World War I, the consumption of bottled lithia mineral water was popular, [ 2 ] with all kinds of health claims attached to it starting with a misguided understanding of gout. [ 3 ] One of the first commercially sold lithia waters in the United States was bottled at Lithia Springs, Georgia , in 1888. [ 4 ] During this era, there was such a demand for lithia water that there was a proliferation of bottled lithia water products. However, only a few were natural lithia spring waters. Most of the bottled lithia water brands added lithium bicarbonate to spring water and called it lithia water. With the start of World War I and the formation of the new US government food safety agency, mineral water bottlers were under scrutiny. The new agency posted large fines against mineral water bottlers for mislabeled, misrepresented and adulterated products. [ 5 ] These government actions and their publicity, along with public works that made clean tap water readily accessible, caused the American public to lose confidence and interest in bottled mineral water. [ 5 ]
Lithia water contains various lithium salts, either natural or added. Mineral acid salts such as lithium bicarbonate do occur naturally; organic acid salts such as lithium citrate only occur after intentional addition because organic acids do not naturally occur in spring water .
The lithium health craze also affected soft drinks. An early version of Coca-Cola available in pharmacies' soda fountains called Lithia Coke was a mixture of Coca-Cola syrup and Bowden lithia spring water. [ 6 ] The soft drink 7 Up was named "7Up Lithiated Lemon Soda" when it was formulated in 1929 because it claimed to contain lithium citrate . The beverage was a patent medicine marketed as a cure for hangover . In 1936 the federal government forced the manufacturer to remove a number of health claims, and because "lithium was not an actual ingredient", the name was changed to just "7 Up" in 1937. [ 7 ] : §2 Many sources repeat an incorrect version of the 7 Up where the name is "Bib-Label Lithiated Lemon-Lime Soda" and the removal happened in 1948 due to a Food and Drug Administration ban. [ 6 ] [ 8 ] | https://en.wikipedia.org/wiki/Lithia_water |
Certain lithium compounds , also known as lithium salts , are used as psychiatric medication , [ 4 ] primarily for bipolar disorder and for major depressive disorder . [ 4 ] Lithium is taken orally (by mouth). [ 4 ]
Common side effects include increased urination , shakiness of the hands, and increased thirst. [ 4 ] Serious side effects include hypothyroidism , diabetes insipidus , and lithium toxicity . [ 4 ] Blood level monitoring is recommended to decrease the risk of potential toxicity. [ 4 ] If levels become too high, diarrhea, vomiting, poor coordination, sleepiness, and ringing in the ears may occur. [ 4 ] Lithium is teratogenic and can cause birth defects at high doses, especially during the first trimester of pregnancy. The use of lithium while breastfeeding is controversial; however, many international health authorities advise against it, and the long-term outcomes of perinatal lithium exposure have not been studied. [ 5 ] The American Academy of Pediatrics lists lithium as contraindicated for pregnancy and lactation. [ 6 ] The United States Food and Drug Administration categorizes lithium as having positive evidence of risk for pregnancy and possible hazardous risk for lactation. [ 6 ] [ 7 ]
Lithium salts are classified as mood stabilizers . [ 4 ] Lithium's mechanism of action is not known. [ 4 ]
In the nineteenth century, lithium was used in people who had gout , epilepsy , and cancer . [ 8 ] Its use in the treatment of mental disorders began with Carl Lange in Denmark [ 9 ] and William Alexander Hammond in New York City, [ 10 ] who used lithium to treat mania from the 1870s onwards, based on now-discredited theories involving its effect on uric acid. Use of lithium for mental disorders was re-established (on a different theoretical basis) in 1948 by John Cade in Australia. [ 8 ] Lithium carbonate is on the World Health Organization's List of Essential Medicines , [ 11 ] and is available as a generic medication . [ 4 ] In 2022, it was the 212th most commonly prescribed medication in the United States, with more than 1 million prescriptions. [ 12 ] [ 13 ] It appears to be underused in older people, [ 14 ] and in certain countries, for reasons including patients’ negative beliefs about lithium. [ 15 ]
In 1970, lithium was approved by the United States Food and Drug Administration (FDA) for the treatment of bipolar disorder, which remains its primary use in the US. [ 4 ] [ 16 ] It is sometimes used when other treatments are not effective in a number of other conditions, including major depression , [ 17 ] schizophrenia , disorders of impulse control, and some psychiatric disorders in children. [ 4 ] Because the FDA has not approved lithium for the treatment of other disorders, such use is off-label . [ 18 ] [ 17 ]
Lithium is primarily used as a maintenance drug in the treatment of bipolar disorder to stabilize mood and prevent manic episodes , but it may also be helpful in the acute treatment of manic episodes. [ 19 ] Although recommended by treatment guidelines for the treatment of depression in bipolar disorder, the evidence that lithium is superior to placebo for acute depression is low-quality; [ 20 ] [ 21 ] atypical antipsychotics are considered more effective for treating acute depressive episodes. [ 22 ] Lithium carbonate treatment was previously considered to be unsuitable for children; however, more recent studies show its effectiveness for treatment of early-onset bipolar disorder in children as young as eight. The required dosage is slightly less than the toxic level (representing a low therapeutic index ), requiring close monitoring of blood levels of lithium carbonate during treatment. [ 23 ] Within the therapeutic range there is a dose-response relationship. [ 24 ] A limited amount of evidence suggests lithium carbonate may contribute to the treatment of substance use disorders for some people with bipolar disorder. [ 25 ] [ 26 ] [ 27 ] Although it is believed that lithium prevents suicide in people with bipolar disorder, a 2022 systematic review found that "Evidence from randomised trials is inconclusive and does not support the idea that lithium prevents suicide or suicidal behaviour." [ 28 ]
Lithium is recommended for the treatment of schizophrenic disorders only after other antipsychotics have failed; it has limited effectiveness when used alone. [ 4 ] The results of different clinical studies of the efficacy of combining lithium with antipsychotic therapy for treating schizophrenic disorders have varied. [ 4 ]
Lithium is widely prescribed as an adjunct treatment for depression. [ 18 ]
If therapy with antidepressants (such as selective serotonin reuptake inhibitors [SSRIs]) does not fully treat and discontinue [ 29 ] the symptoms of major depressive disorder (MDD) (also known as refractory depression or treatment resistant depression [TRD]) [ 30 ] then a second augmentation agent is sometimes added to the therapy. [ 31 ] Lithium is one of the few augmentation agents for antidepressants to demonstrate efficacy in treating MDD in multiple randomized controlled trials and it has been prescribed ( off-label ) for this purpose since the 1980s. [ 17 ] A 2019 systematic review found some evidence of the clinical utility of adjunctive lithium, but the majority of supportive evidence is dated. [ 32 ]
While SSRIs have been mentioned above as a drug class in which lithium is used to augment, there are other classes in which lithium is added to increase effectiveness. Such classes are antipsychotics (used for bipolar disorder) as well as antiepileptic drugs (used for both psychiatric and epileptic cases). Lamotrigine and topiramate are two specific antiepileptic drugs in which lithium is used to augment. [ 33 ]
There are a few old studies indicating efficacy of lithium for acute depression with lithium having the same efficacy as tricyclic antidepressants . [ 34 ] A recent study concluded that lithium works best on chronic and recurrent depression when compared to modern antidepressant (i.e. citalopram) but not for patients with no history of depression. [ 35 ] A 2019 systemic review found no evidence to support the use of lithium for monotherapy. [ 32 ]
Lithium is widely believed to prevent suicide and is often used in clinical practice towards that end. However, meta-analyses, faced with evidence base limitations, have yielded differing results, and it therefore remains unclear whether or not lithium is efficacious in the prevention of suicide. [ 36 ] [ 37 ] [ 38 ] [ 39 ] [ 40 ] [ 41 ] However, some evidence suggests it is effective in significantly reducing the risk of self-harm and unintentional injury for bipolar disorder in comparison to no treatment and to anti-psychotics or valporate . [ 42 ] [ 43 ] According to meta-analyses, the increased presence of lithium in drinking water is correlated with lower overall suicide rates, especially among men. It is noted that further testing is needed to confirm this benefit. [ 44 ] [ 45 ]
Alzheimer's disease affects forty-five million people and is the fifth leading cause of death in the 65-plus population. [ 46 ] [ failed verification ] There is no complete cure for the disease, currently. However, lithium is being evaluated for its effectiveness as a potential therapeutic measure. One of the leading causes of Alzheimer's is the hyperphosphorylation of the tau protein by the enzyme GSK-3, which leads to the overproduction of amyloid peptides that cause cell death. [ 46 ] To combat this toxic amyloid aggregation, lithium upregulates the production of neuroprotectors and neurotrophic factors, as well as inhibiting the GSK-3 enzyme. [ 47 ] Lithium also stimulates neurogenesis within the hippocampus, making it thicker. [ 47 ] Yet another cause of Alzheimer's disease is the dysregulation of calcium ions within the brain. [ 48 ] Too much or too little calcium within the brain can lead to cell death. [ 48 ] Lithium can restore intracellular calcium homeostasis by inhibiting the wrongful influx of calcium upstream. [ 48 ] It also promotes the redirection of the influx of calcium ions into the lumen of the endoplasmic reticulum of the cells to reduce the oxidative stress within the mitochondria. [ 48 ]
In 2009, a study was performed by Hampel and colleagues [ 49 ] that asked patients with Alzheimer's to take a low dose of lithium daily for three months; it resulted in a significant slowing of cognitive decline, benefitting patients being in the prodromal stage the most. [ 47 ] Upon a secondary analysis, the brains of the Alzheimer's patients were studied and shown to have an increase in BDNF markers, meaning they had actually shown cognitive improvement. [ 47 ] Another study, a population study this time by Kessing et al., [ 50 ] showed a negative correlation between Alzheimer's disease deaths and the presence of lithium in drinking water. [ 47 ] Areas with increased lithium in their drinking water showed less dementia overall in their population. [ 47 ]
Those who use lithium should receive regular serum level tests and should monitor thyroid and kidney function for abnormalities, as it interferes with the regulation of sodium and water levels in the body, and can cause dehydration . Dehydration, which is compounded by heat, can result in increasing lithium levels. The dehydration is due to lithium inhibition of the action of antidiuretic hormone , which normally enables the kidney to reabsorb water from urine. This causes an inability to concentrate urine, leading to consequent loss of body water and thirst. [ 51 ]
Lithium concentrations in whole blood, plasma, serum, or urine may be measured using instrumental techniques as a guide to therapy, to confirm the diagnosis in potential poisoning victims, or to assist in the forensic investigation in a case of fatal overdosage. Serum lithium concentrations are usually in the range of 0.5–1.3 mmol/L (0.5–1.3 mEq/L ) in well-controlled people, but may increase to 1.8–2.5 mmol/L in those who accumulate the drug over time and to 3–10 mmol/L in acute overdose. [ 52 ] [ 53 ]
Lithium salts have a narrow therapeutic/toxic ratio, so should not be prescribed unless facilities for monitoring plasma concentrations are available. Doses are adjusted to achieve plasma concentrations of 0.4 [ a ] [ b ] to 1.2 mmol/L [ 54 ] on samples taken 12 hours after the preceding dose.
Given the rates of thyroid dysfunction, thyroid parameters should be checked before lithium is instituted and monitored after 3–6 months and then every 6–12 months. [ 55 ]
Given the risks of kidney malfunction, serum creatinine, and eGFR should be checked before lithium is instituted and monitored after 3–6 months at regular intervals. Patients who have a rise in creatinine on three or more occasions, even if their eGFR is > 60 ml/min/
1.73m2 require further evaluation, including a urinalysis for haematuria, and proteinuria, a review of their medical history with attention paid to cardiovascular, urological, and medication history, and blood pressure control and management. Overt proteinuria should be further quantified with a urine protein-to-creatinine ratio. [ 56 ]
For patients who have achieved long-term remission, it is recommended to discontinue lithium gradually and in a controlled fashion. [ 57 ] [ 34 ]
In patients stopping the medication, discontinuation symptoms including irritability or restlessness, and somatic symptoms like vertigo, dizziness, or lightheadedness may occur. Symptoms occur within the first week and are generally mild and self-limiting within weeks. [ 58 ]
Studies testing prophylactic use of lithium in cluster headaches (when compared to verapamil ), migraine attacks, and hypnic headache indicate good efficacy. [ 34 ]
The adverse effects of lithium include: [ 59 ] [ 60 ] [ 61 ] [ 62 ] [ 63 ] [ 64 ] [ 65 ]
In addition to tremors, lithium treatment appears to be a risk factor for development of parkinsonism -like symptoms, although the causal mechanism remains unknown. [ 72 ]
In the average bipolar patient, chronic lithium use is not associated with cognitive decline. [ 73 ] Depending on dosage and duration of use, lithium can be either pro-convulsant, or as its historical use suggests, anti-convulsant. [ 74 ]
Most side effects of lithium are dose-dependent. The lowest effective dose is used to limit the risk of side effects.
The rate of hypothyroidism is around six times higher in people who take lithium. Low thyroid hormone levels in turn increase the likelihood of developing depression. People taking lithium thus should routinely be assessed for hypothyroidism and treated with synthetic thyroxine if necessary. [ 70 ]
Because lithium competes with the antidiuretic hormone in the kidney, it increases water output into the urine, a condition called nephrogenic diabetes insipidus . Clearance of lithium by the kidneys is usually successful with certain diuretic medications, including amiloride and triamterene . [ 75 ] It increases the appetite and thirst ("polydypsia") and reduces the activity of thyroid hormone ( hypothyroidism ). [ 76 ] [ 77 ] The latter can be corrected by treatment with thyroxine and does not require the lithium dose to be adjusted. Lithium is also believed to cause renal dysfunction, although this does not appear to be common. [ 78 ]
Lambert et al. (2016), comparing the rate of hypothyroidism in patients with bipolar disorder treated with 9 different medications, found that lithium users do not have a particularly high rate of hypothyroidism (8.8%) among BD patients – only 1.39 times the rate in oxcarbazepine users (6.3%, the lowest group). Lithium and quetiapine are not statistically different in terms of hypothyroidism rates. However, lithium users are tested much more frequently for hypothyroidism than those using other drugs. The authors write that there may be an element of surveillance bias in understanding lithium's effects on the thyroid glands, as lithium users are tested 2.3–3.1 times as often. Furthermore, the authors argue that because hypothyroidism is common among BD patients regardless of lithium treatment, regular thyroid testing should be applied to all BD patients, not just those on lithium. [ 79 ] [ 68 ]
Lithium is a teratogen , which can cause birth defects in a small number of newborns. Case reports and several retrospective studies have demonstrated possible increases in the rate of a congenital heart defects (CHDs) including Ebstein's anomaly if taken during the first trimester of pregnancy. The risk is dose-dependent: in the 2017 AMX registry study, the risk of "any malformations" is increased by 11 +152 −47 % in those taking no more than 600 mg of lithium carbonate daily, by 60 +220 −93 % in those taking 601–900 mg daily, and by 222 +380 −75 % in those taking more than 900 mg daily. The first two numbers do not indicate a statistically significant association. [ 80 ] In a 2018 meta-analysis, there was a statistically significant 62 +71 −50 % increase in congenital malformations in general, but not for cardiac malformations specifically ( 54 +216 −90 % increase). [ 81 ] Exposure during any part of the pregnancy is associated with a slight but statistically significant increase in the risks of preterm birth and of a larger-than-usual baby at birth. [ 82 ]
Lithium is effective for preventing relapse during and after pregnancy. [ 81 ] As the risks of stopping Lithium can be significant, patients are sometimes recommended to stay on this medicine while pregnant. Careful weighing of the risks and benefits should be made in consultation with a psychiatric physician . [ 83 ] The relatively low teratogenic risk of lithium allows such a choice. [ 84 ] The decision should be made before the start of pregnancy, as there is no reason for stopping lithium once the pregnancy has started. [ 82 ]
For patients who are exposed to lithium, or plan to stay on the medication throughout their pregnancy, fetal echocardiography is routinely performed to monitor for cardiac anomalies. [ 85 ] Pregnancy is associated with a decrease in blood lithium levels (especially in the first and second trimesters), so more frequent monitoring with an increase in dose may be required to maintain control of symptoms. To prevent postpatrum psychosis, a higher blood lithium level may be desirable in the third trimester. [ 81 ]
While lithium is typically the most effective treatment, possible alternatives to Lithium include Lamotrigine and Second generation Antipsychotics for the treatment of acute bipolar depression or for the management of bipolar patients with normal mood during pregnancy. [ 84 ]
Initiating lithium immediately after delivery is also effective for preventing postpartum psychosis and postpartum bipolar relapse. This is an acceptable treatment option for women with a history of psychosis limited to the postpartum period. For women with diagnosed bipolar disorder, this provides less protection than maintaining lithium therapy during pregnancy. [ 81 ]
While only small amounts of Lithium are transmitted to the infant in breastmilk, there is limited data on the safety of Breastfeeding while on Lithium. Medical evaluation and monitoring of infants consuming breastmilk during maternal prescription may be indicated. [ 86 ] [ 87 ]
Lithium has been associated with several forms of kidney injury. [ 88 ] [ 89 ] It is estimated that impaired urinary concentrating ability is present in at least half of individuals on chronic lithium therapy, a condition called lithium-induced nephrogenic diabetes insipidus . [ 89 ] Continued use of lithium can lead to more serious kidney damage in an aggravated form of diabetes insipidus . [ 90 ] [ 91 ] In rare cases, some forms of lithium-caused kidney damage may be progressive and lead to end-stage kidney failure with a reported incidence of 0.2% to 0.7%. [ 92 ]
Some reports of kidney damage may be wrongly attributed to lithium, increasing the apparent rate of this adverse effect. [ 67 ] Nielsen et al. (2018), citing 6 large observational studies since 2010, argue that findings of decreased kidney function are partially inflated by surveillance bias. Furthermore, modern data does not show that lithium increases the risk of end-stage kidney disease. [ 68 ] Davis et al. (2018), using literature from a wider timespan (1977–2018), also found that lithium's association with chronic kidney disease is unproven with various contradicting results. They also find contradicting results regarding end-stage kidney disease. [ 93 ]
A 2015 nationwide study suggests that chronic kidney disease can be avoided by maintaining the serum lithium concentration at a level of 0.6–0.8 mmol/L and by monitoring serum creatinine every 3–6 months. [ 68 ]
Lithium-associated hyperparathyroidism is the leading cause of hypercalcemia in lithium-treated patients. Lithium may lead to exacerbation of pre-existing primary hyperparathyroidism or cause an increased set-point of calcium for parathyroid hormone suppression, leading to parathyroid hyperplasia .
Lithium plasma concentrations are known to be increased with concurrent use of diuretics —especially loop diuretics (such as furosemide) and thiazides —and non-steroidal anti-inflammatory drugs (NSAIDs) such as ibuprofen . [ 59 ] Lithium concentrations can also be increased with concurrent use of ACE inhibitors such as captopril , enalapril , and lisinopril . [ 94 ]
Lithium is primarily cleared from the body through glomerular filtration , but some is then reabsorbed together with sodium through the proximal tubule . Its levels are therefore sensitive to water and electrolyte balance. [ 95 ] Diuretics act by lowering water and sodium levels; this causes more reabsorption of lithium in the proximal tubules so that the removal of lithium from the body is less, leading to increased blood levels of lithium. [ 95 ] [ 96 ] ACE inhibitors have also been shown in a retrospective case-control study to increase lithium concentrations. This is likely due to constriction of the afferent arteriole of the glomerulus, resulting in decreased glomerular filtration rate and clearance. Another possible mechanism is that ACE inhibitors can lead to a decrease in sodium and water. This will increase lithium reabsorption and its concentrations in the body. [ 95 ]
Some drugs can increase the clearance of lithium from the body, which can result in decreased lithium levels in the blood. These drugs include theophylline , caffeine , and acetazolamide . Additionally, increasing dietary sodium intake may also reduce lithium levels by prompting the kidneys to excrete more lithium. [ 97 ]
Lithium is known to be a potential precipitant of serotonin syndrome in people concurrently on serotonergic medications such as antidepressants , buspirone and certain opioids such as pethidine (meperidine), tramadol , oxycodone , fentanyl and others. [ 59 ] [ 98 ] Lithium co-treatment is also a risk factor for neuroleptic malignant syndrome in people on antipsychotics and other antidopaminergic medications. [ 99 ]
High doses of haloperidol , fluphenazine , or flupenthixol may be hazardous when used with lithium; irreversible toxic encephalopathy has been reported. [ 100 ] Indeed, these and other antipsychotics have been associated with an increased risk of lithium neurotoxicity , even with low therapeutic lithium doses. [ 101 ] [ 102 ]
A high incidence of seizures has been reported with serotonergic psychedelics like psilocybin and LSD in people taking lithium. [ 103 ] [ 104 ] [ 105 ] [ 106 ] In an analysis of online reports, 47% of 62 accounts reported seizures when a psychedelic was taken while on lithium. [ 103 ] [ 104 ] [ 105 ] [ 106 ] Of these instances, 39% sought emergency medical treatment. [ 105 ] [ 106 ]
Lithium toxicity, which is also called lithium overdose and lithium poisoning, is the condition of having too much lithium in the blood. This condition also happens in persons who are taking lithium in which the lithium levels are affected by drug interactions in the body.
In acute toxicity, people have primarily gastrointestinal symptoms such as vomiting and diarrhea , which may result in volume depletion . During acute toxicity, lithium distributes later into the central nervous system resulting in mild neurological symptoms, such as dizziness. [ 55 ]
In chronic toxicity, people have primarily neurological symptoms which include nystagmus , tremor , hyperreflexia , ataxia , and change in mental status . During chronic toxicity, the gastrointestinal symptoms seen in acute toxicity are less prominent. The symptoms are often vague and nonspecific. [ 107 ]
If the lithium toxicity is mild or moderate, lithium dosage is reduced or stopped entirely. If the toxicity is severe, lithium may need to be removed from the body.
The specific biochemical mechanism of lithium action in stabilizing mood is unknown. [ 4 ]
Upon ingestion, lithium becomes widely distributed in the central nervous system and interacts with a number of neurotransmitters and receptors , decreasing norepinephrine release and increasing serotonin synthesis. [ 108 ]
Unlike many other psychoactive drugs , Li + typically produces no obvious psychotropic effects (such as euphoria ) in normal individuals at therapeutic concentrations. [ 108 ] Lithium may also increase the release of serotonin by neurons in the brain. [ 109 ] In vitro studies performed on serotonergic neurons from rat raphe nuclei have shown that when these neurons are treated with lithium, serotonin release is enhanced during a depolarization compared to no lithium treatment and the same depolarization. [ 110 ]
Lithium has a plethora of proposed molecular targets:
Lithium possesses neuroprotective properties by preventing apoptosis and increasing cell longevity. [ 122 ]
Although the search for a novel lithium-specific receptor is ongoing, the high concentration of lithium compounds required to elicit a significant pharmacological effect leads mainstream researchers to believe that the existence of such a receptor is unlikely. [ 123 ]
Evidence suggests that mitochondrial dysfunction is present in patients with bipolar disorder. [ 122 ] Oxidative stress and reduced levels of anti-oxidants (such as glutathione ) lead to cell death. Lithium may protect against oxidative stress by up-regulating complexes I and II of the mitochondrial electron transport chain . [ 122 ]
During mania, there is an increase in neurotransmission of dopamine that causes a secondary homeostatic down-regulation, resulting in decreased neurotransmission of dopamine, which can cause depression. [ 122 ] Additionally, the post-synaptic actions of dopamine are mediated through G-protein coupled receptors . Once dopamine is coupled to the G-protein receptors, it stimulates other secondary messenger systems that modulate neurotransmission. Studies found that in autopsies (which do not necessarily reflect living people), people with bipolar disorder had increased G-protein coupling compared to people without bipolar disorder. [ 122 ] Lithium treatment alters the function of certain subunits of the dopamine-associated G-protein, which may be part of its mechanism of action. [ 122 ]
Glutamate levels are observed to be elevated during mania . Lithium is thought to provide long-term mood stabilization and have anti- manic properties by modulating glutamate levels. [ 122 ] It is proposed that lithium competes with magnesium for binding to NMDA glutamate receptor , increasing the availability of glutamate in post-synaptic neurons , leading to a homeostatic increase in glutamate re-uptake which reduces glutamatergic transmission. [ 122 ] The NMDA receptor is also affected by other neurotransmitters such as serotonin and dopamine . Effects observed appear exclusive to lithium and have not been observed by other monovalent ions such as rubidium and cesium . [ 122 ]
GABA is an inhibitory neurotransmitter that plays an important role in regulating dopamine and glutamate neurotransmission . [ 122 ] It was found that patients with bipolar disorder had lower GABA levels, which results in excitotoxicity and can cause apoptosis (cell loss). Lithium has been shown to increase the level of GABA in plasma and cerebral spinal fluid. [ 124 ] Lithium counteracts these degrading processes by decreasing pro-apoptotic proteins and stimulating release of neuroprotective proteins. [ 122 ] Lithium's regulation of both excitatory dopaminergic and glutamatergic systems through GABA may play a role in its mood-stabilizing effects. [ 125 ]
Lithium's therapeutic effects are thought to be partially attributable to its interactions with several signal transduction mechanisms. [ 126 ] The cyclic AMP secondary messenger system is shown to be modulated by lithium. Lithium was found to increase the basal levels of cyclic AMP but impair receptor-coupled stimulation of cyclic AMP production. [ 122 ] It is hypothesized that the dual effects of lithium are due to the inhibition of G-proteins that mediate cyclic AMP production. [ 122 ] Over a long period of lithium treatment, cyclic AMP and adenylate cyclase levels are further changed by gene transcription factors . [ 122 ]
Lithium treatment has been found to inhibit the enzyme inositol monophosphatase , involved in degrading inositol monophosphate to inositol required in PIP 2 synthesis. This leads to lower levels of inositol triphosphate , created by decomposition of PIP 2 . [ 127 ] This effect has been suggested to be further enhanced with an inositol triphosphate reuptake inhibitor . Inositol disruptions have been linked to memory impairment and depression. It is known with good certainty that signals from the receptors coupled to the phosphoinositide signal transduction are affected by lithium. [ 128 ] myo-inositol is also regulated by the high affinity sodium mI transport system (SMIT). Lithium is hypothesized to inhibit mI entering the cells and mitigate the function of SMIT. [ 122 ] Reductions of cellular levels of myo-inositol results in the inhibition of the phosphoinositide cycle . [ 122 ]
Lithium's actions on Gsk3 result in activation of CREB, leading to higher expression of BDNF. (Valproate, another mood stabilizer, also increases the expression of BDNF.) As expected of increased BDNF expression, chronic lithium treatment leads to increased grey matter volume in brain areas implicated in emotional processing and cognitive control. [ 129 ] Bipolar patients treated with lithium also have higher white matter integrity compared to those taking other drugs. [ 130 ]
Lithium also increases the expression of mesencephalic astrocyte-derived neurotrophic factor (MANF), another neurotrophic factor , via the AP-1 transcription factor . MANF is able to regulate proteostasis by interacting with GRP78 , a protein involved in the unfolded protein response . [ 131 ]
Lithium was first used in the 19th century as a treatment for gout after scientists discovered that, at least in the laboratory, lithium could dissolve uric acid crystals isolated from the kidneys. The levels of lithium needed to dissolve urate in the body, however, were toxic. [ 132 ] Because of prevalent theories linking excess uric acid to a range of disorders, including depressive and manic disorders, Carl Lange in Denmark [ 9 ] and William Alexander Hammond in New York City [ 10 ] used lithium to treat mania from the 1870s onwards.
By the turn of the 20th century, as theory regarding mood disorders evolved and so-called "brain gout" disappeared as a medical entity, the use of lithium in psychiatry was largely abandoned; however, several lithium preparations were still produced for the control of renal calculi and uric acid diathesis . [ 18 ] As accumulating knowledge indicated a role for excess sodium intake in hypertension and heart disease , lithium salts were prescribed to patients for use as a replacement for dietary table salt ( sodium chloride ). This practice and the sale of lithium itself were both banned in the United States in February 1949, following the publication of reports detailing side effects and deaths. [ 133 ]
Also in 1949, the Australian psychiatrist John Cade and Australian biochemist Shirley Andrews rediscovered the usefulness of lithium salts in treating mania while working at the Royal Park Psychiatric Hospital in Victoria. [ 134 ] They were injecting rodents with urine extracts taken from manic patients in an attempt to isolate a metabolic compound which might be causing mental symptoms. Since uric acid in gout was known to be psychoactive, ( adenosine receptors on neurons are stimulated by it; caffeine blocks them), they needed soluble urate for a control. They used lithium urate, already known to be the most soluble urate compound, and observed that it caused the rodents to become tranquil. Cade and Andrews traced the effect to the lithium-ion itself, and after Cade ingested lithium himself to ensure its safety in humans, he proposed lithium salts as tranquilizers . He soon succeeded in controlling mania in chronically hospitalized patients with them. This was one of the first successful applications of a drug to treat mental illness, and it opened the door for the development of medicines for other mental problems in the next decades. [ 135 ]
The rest of the world was slow to adopt this treatment, largely because of deaths that resulted from even relatively minor overdosing, including those reported from the use of lithium chloride as a substitute for table salt. Largely through the research and other efforts of Denmark's Mogens Schou and Paul Baastrup in Europe, [ 132 ] and Samuel Gershon and Baron Shopsin in the U.S., this resistance was slowly overcome. Following the recommendation of the APA Lithium Task Force (William Bunney , Irvin Cohen (Chair), Jonathan Cole , Ronald R. Fieve , Samuel Gershon, Robert Prien, and Joseph Tupin [ 136 ] ), the application of lithium in manic illness was approved by the United States Food and Drug Administration in 1970, [ 137 ] becoming the 50th nation to do so. [ 18 ]
Lithium has now become a part of Western popular culture. Characters in Pi , Premonition , Stardust Memories , American Psycho , Garden State , and An Unmarried Woman all take lithium. It's the chief constituent of the calming drug in Ira Levin 's dystopian This Perfect Day . Sirius XM Satellite Radio in North America has a 1990s alternative rock station called Lithium, and several songs refer to the use of lithium as a mood stabilizer. These include: "Equilibrium met Lithium" by South African artist Koos Kombuis , " Lithium " by Evanescence , " Lithium " by Nirvana , "Lithium and a Lover" by Sirenia , "Lithium Sunset", from the album Mercury Falling by Sting , [ 138 ] and "Lithium" by Thin White Rope .
As with cocaine in Coca-Cola , lithium was widely marketed as one of several patent medicine products popular in the late 19th and early 20th centuries and was claimed to be included in many drinks including lithia water and 7 Up .
Charles Leiper Grigg , who launched his St. Louis-based company The Howdy Corporation, invented a formula for a lemon-lime soft drink in 1920. The product, at one point named "7Up Lithiated Lemon Soda", was launched two weeks before the Wall Street Crash of 1929 . [ 139 ] It claimed to contain the mood stabilizer lithium citrate , and was one of many patent medicine products popular in the late-19th and early-20th centuries. [ 140 ] All references to lithium were removed in 1937 after it became clear that 7Up contains no lithium. [ 141 ] : §2
Many sources written by scientists (instead of historians) incorrectly report that 7 Up was forced to remove lithium in 1948, with an FDA action that supposedly banned lithium from beverages. [ 142 ] Despite the supposed ban, in 1950, the Painesville Telegraph still carried an advertisement for a lithiated lemon beverage. [ 143 ]
Lithium carbonate ( Li 2 CO 3 ) is the most commonly used form of lithium salts , a carbonic acid involving the lithium element and a carbonate ion . Other lithium salts are also used as medication, such as lithium citrate ( Li 3 C 6 H 5 O 7 ), lithium sulfate , lithium chloride , and lithium orotate . [ 144 ] [ 145 ] Nanoparticles and microemulsions have also been invented as drug delivery mechanisms. As of 2020, there is a lack of evidence that alternate formulations or salts of lithium would reduce the need for monitoring serum lithium levels or lower systemic toxicity. [ 144 ]
As of 2017 lithium was marketed under many brand names worldwide, including Cade, Calith, Camcolit, Carbolim, Carbolit, Carbolith, Carbolithium, Carbolitium, Carbonato de Litio, Carboron, Ceglution, Contemnol, Efadermin (Lithium and Zinc Sulfate), Efalith (Lithium and Zinc Sulfate), Elcab, Eskalit, Eskalith, Frimania, Hypnorex, Kalitium, Karlit, Lalithium, Li-Liquid, Licarb, Licarbium, Lidin, Ligilin, Lilipin, Lilitin, Limas, Limed, Liskonum, Litarex, Lithane, Litheum, Lithicarb, Lithii carbonas, Lithii citras, Lithioderm, Lithiofor, Lithionit, Lithium, Lithium aceticum, Lithium asparagicum, Lithium Carbonate, Lithium Carbonicum, Lithium Citrate, Lithium DL-asparaginat-1-Wasser, Lithium gluconicum, Lithium-D-gluconat, Lithiumcarbonaat, Lithiumcarbonat, Lithiumcitrat, Lithiun, Lithobid, Lithocent, Lithotabs, Lithuril, Litiam, Liticarb, Litijum, Litio, Litiomal, Lito, Litocarb, Litocip, Maniprex, Milithin, Neurolepsin, Plenur, Priadel, Prianil, Prolix, Psicolit, Quilonium, Quilonorm, Quilonum, Téralithe, and Theralite. [ 1 ]
Tentative evidence in Alzheimer's disease showed that lithium may slow progression. [ 146 ] [ 147 ] It has been studied for its potential use in the treatment of amyotrophic lateral sclerosis (ALS), but a study showed lithium had no effect on ALS outcomes. [ 148 ] | https://en.wikipedia.org/wiki/Lithium_(medication) |
Lithium aluminium germanium phosphate , typically known with the acronyms LAGP or LAGPO , is an inorganic ceramic solid material whose general formula is Li 1+x Al x Ge 2-x (PO 4 ) 3 . [ 3 ] LAGP belongs to the NASICON (Sodium Super Ionic Conductors) family of solid conductors [ 3 ] and has been applied as a solid electrolyte in all-solid-state lithium-ion batteries . Typical values of ionic conductivity in LAGP at room temperature are in the range of 10 –5 - 10 –4 S/cm, [ 4 ] even if the actual value of conductivity is strongly affected by stoichiometry, microstructure, and synthesis conditions. [ 3 ] Compared to lithium aluminium titanium phosphate (LATP), which is another phosphate-based lithium solid conductor, the absence of titanium in LAGP improves its stability towards lithium metal . [ 4 ] In addition, phosphate-based solid electrolytes have superior stability against moisture and oxygen compared to sulfide-based electrolytes like Li 10 GeP 2 S 12 (LGPS) and can be handled safely in air, thus simplifying the manufacture process. [ 4 ] [ 5 ] Since the best performances are encountered when the stoichiometric value of x is 0.5, the acronym LAGP usually indicates the particular composition of Li 1.5 Al 0.5 Ge 1.5 (PO 4 ) 3 , which is also the typically used material in battery applications. [ 6 ]
Lithium-containing NASICON-type crystals are described by the general formula LiM 2 (PO 4 ) 3 , in which M stands for a metal or a metalloid ( Ti , Zr , Hf , Sn , Ge ), [ 6 ] and display a complex three-dimensional network of corner-sharing MO 6 octahedra and phosphate tetrahedra. [ 8 ] Lithium ions are hosted in voids in between, which can be subdivided into three kinds of sites: [ 3 ] [ 7 ]
In order to promote lithium conductivity at sufficiently high rates, Li(1) sites should be fully occupied and Li(2) sites should be fully empty. [ 6 ] Li(3) sites are located between Li(1) and Li(2) sites and are occupied only when large tetravalent cations are present in the structure, such as Zr , Hf , and Sn . [ 9 ] If some Ge 4+ cations in the LiGe 2 (PO 4 ) 3 (LGP) structure are partially replaced by Al 3+ cations, the LAGP material is obtained with the general formula Li 1+x Al x Ge 2-x (PO 4 ) 3 . [ 8 ] The single-phase NASICON structure is stable with x between 0.1 and 0.6; [ 6 ] when this limit is exceeded, a solid solution is no more possible and secondary phases tend to be formed. [ 3 ] Although Ge 4+ and Al 3+ cations have very similar ionic radii (0.53 Å for Ge 4+ vs. 0.535 Å for Al 3+ [ 6 ] ), cationic substitution leads to compositional disorder and promotes the incorporation of a larger amount of lithium ions to achieve electrical neutrality. [ 3 ] Additional lithium ions can be incorporated in either Li(2) or Li(3) empty sites. [ 9 ]
In the available scientific literature, there is not a unique description of the sites available for lithium ions and of their atomic coordination, as well as of the sites directly involved during the conduction mechanism. For example, only two available sites, namely Li(1) and Li(2), are mentioned in some cases, while the Li(3) site is neither occupied nor involved in the conduction process. [ 6 ] [ 8 ] This results in the lack of unambiguous description of LAGP local crystal structure, especially concerning the arrangement of lithium ions and site occupancy when germanium is partially replaced by aluminium. [ 3 ] [ 6 ] [ 8 ] [ 7 ] [ 10 ]
LAGP displays a rhombohedral unit cell with a space group R 3 c. [ 8 ]
LAGP crystals belong to the space group D 6 3d - R 3 c. [ 8 ] [ 11 ] The factor group analysis of NASICON-type materials with general formula M I M 2 IV PO 4 (where M I stands for a monovalent metal ion like Na + , Li + or K + , and M IV represents a tetravalent cation such as Ti 4+ , Ge 4+ , Sn 4+ , Zr 4+ or Hf 4+ ) is usually performed assuming the separation between internal vibrational modes (i.e. modes originating in PO 4 units) and external modes (i.e. modes arising from the translations of the M I and M IV cations, from PO 4 translations, and from PO 4 librations ). [ 11 ]
Focusing on internal modes only, the factor group analysis for R 3 c space group identifies 14 Raman-active modes for the PO 4 units: [ 8 ] [ 11 ] 6 of these modes correspond to stretching vibrations and 8 to bending vibrations. [ 8 ]
On the contrary, the analysis of external modes leads to many available vibrations: since the number of irreducible representations within the rhombohedral R 3 c space group is restricted, interactions among different modes could be expected and a clear assignment or discrimination becomes unfeasible. [ 12 ]
The vibrational properties of LAGP could be directly probed using Raman spectroscopy . LAGP shows the Raman features characteristic of all the NASICON -type materials, most of which caused by the vibrational motions of PO 4 units. [ 8 ] The main spectral regions in a Raman spectrum of NASICON-type materials are summarized in the following table.
or translation/libration motions of phosphate tetrahedra. [ 11 ]
The discrimination between symmetric and antisymmetric stretching vibration is usually not possible. [ 6 ] [ 8 ]
The Raman spectra of LAGP are usually characterized by broad peaks, even when the material is in its crystalline form. Indeed, both the presence of aluminium ions in place of germanium ions and the extra lithium ions introduce structural and compositional disorder in the sublattice, resulting in peak broadening. [ 8 ]
LAGP is a solid ionic conductor and features the two fundamental properties to be used as a solid-state electrolyte in lithium-ion batteries, namely a sufficiently high ionic conductivity and a negligible electronic conductivity. Indeed, during battery operations, LAGP should guarantee the easy and fast motion of lithium ions between cathode and anode , while preventing the transfer of electrons. [ 4 ]
As stated in the description of the crystal structure, three kinds of sites are available for hosting lithium ions in the LAGP NASICON structure, i.e. the Li(1) sites, the Li(2) sites and the Li(3) sites. Ionic conduction occurs because of hopping of lithium ions from Li(1) to Li(2) sites or across two Li(3) sites. The bottleneck to ionic motion is represented by a triangular window delimited by three oxygen atoms between Li(1) and Li(2) sites. [ 8 ] [ 7 ]
The ionic conductivity σ {\displaystyle \sigma } in LAGP follows the usual dependency on temperature expressed by an Arrhenius-type equation , which is typical of most of solid-state ionic conductors: [ 6 ]
σ = σ 0 T e − E a k B T {\displaystyle \sigma ={\frac {\sigma _{0}}{T}}e^{-{\frac {E_{a}}{k_{B}T}}}}
where
Typical values for the activation energies of bulk LAGP materials are in the range of 0.35 - 0.41 eV . [ 13 ] Similarly, the room-temperature ionic conductivity is closely related to the synthesis conditions and to the actual material microstructure, therefore the conductivity values reported in scientific literature span from 10 –5 S/cm up to 10 mS/cm, the highest value close to room temperature reported up to now. [ 3 ] [ 9 ] [ 14 ] Compared to LGP, the room-temperature ionic conductivity of LAGP is increased by 3-4 orders of magnitude upon partial substitution of Ge 4+ by Al 3+ . [ 8 ] Aluminium ions have a lower charge compared to Ge 4+ ions and additional lithium is incorporated in the NASICON structure to maintain charge balance, resulting in an enlarged number of charge carriers . The beneficial effect of aluminium is maximized for x around 0.4 - 0.5; [ 3 ] for larger Al content, the single-phase NASICON structure is not stable and secondary phases appear, mainly AlPO 4 , Li 4 P 2 O 7 , and GeO 2 . [ 15 ] Secondary phases are typically nonconductive; however, small and controlled amounts of AlPO 4 exert a densification effect which affects in a positive way the overall ionic conductivity of the material. [ 3 ]
The prefactor σ 0 in the Arrhenius equation can in turn be written as a function of fundamental constants and conduction parameters: [ 16 ]
σ 0 = 1 3 ( Z e ) 2 k B T n v 0 l 0 {\displaystyle \sigma _{0}={\frac {1}{3}}{\frac {(Ze)^{2}}{k_{B}T}}nv_{0}l_{0}}
where
The prefactor is directly proportional to the concentration of mobile lithium-ion carriers, which increases with the aluminium content in the material. As a result, since the dependency of the activation energy on aluminium content is negligible, the ionic conductivity is expected to increase with increasing Ge 4+ substitution by Al 3+ , until secondary phases are formed. [ 16 ] The introduction of aluminium also reduces the grain boundary resistivity of the material, [ 3 ] positively impacting on the total (bulk crystal + grain boundary) ionic conductivity of the LAGP material.
As expected for solid ionic conductors, the ionic conductivity of LAGP increases with increasing temperature. [ 16 ]
Regarding the electronic conductivity of LAGP, it should be as low as possible to prevent electrical short circuit between anode and cathode. As for ionic conductivity, the exact stoichiometry and microstructure, strongly connected to the synthesis method, have an influence on the electronic conductivity, even if the reported values are very low and close to (or lower than) 10 –9 S/cm. [ 17 ] [ 18 ]
The specific heat capacity of LAGP materials with general formula Li 1+x Al x Ge 2-x (PO 4 ) 3 fits into the Maier-Kelley polynomial law in the temperature range from room temperature to 700 °C: [ 16 ]
C p ( T ) = A + B ⋅ T + C ⋅ T − 2 {\displaystyle C_{p}(T)=A+B\cdot T+C\cdot T^{-2}}
where
Typical values are in the range of 0.75 - 1.5 J⋅g −1 ⋅K −1 in the temperature interval 25 - 100 °C. The A , B constants increase with the x value, i.e. with both the aluminium and the lithium content, while the constant C does not follow a precise trend. [ 16 ] As a result, the specific heat capacity of LAGP is expected to increase as the Al content grows and the Ge content decreases, which is consistent with data about the relative specific heats of aluminium and germanium compounds. [ 16 ]
In addition, the thermal diffusivity α {\displaystyle \alpha } of LAGP follows a decreasing trend with increasing temperature, irrespective of the aluminium content: [ 16 ]
α ∝ T − p {\displaystyle \alpha \propto T^{-p}}
The aluminium level affects the exponent p {\displaystyle p} , which varies from 0.08 (high Al content) to 0.11 (low Al content). [ 16 ] Such small values suggest the presence of a large number of point defects in the material, which is highly beneficial for solid ionic conductors. Finally, the expression for the thermal conductivity can be written: [ 16 ]
κ = 1 3 ⋅ C v ⋅ v p h ⋅ l p h = α ⋅ C p ⋅ ρ {\displaystyle \kappa ={\frac {1}{3}}\cdot C_{v}\cdot v_{ph}\cdot l_{ph}=\alpha \cdot C_{p}\cdot \rho }
where
Taking everything into account, as the aluminium content in LAGP increases, the ionic conductivity increases as well, while the thermal conductivity decreases, since a larger number of lithium ions enhances the phonon scattering, thus reducing the phonon mean free path and the thermal transport in the material. Therefore, thermal and ionic transports in LAGP ceramics are not correlated: the corresponding conductivities follow opposite trends as a function of the aluminium content and are affected in a different way by temperature variations (e.g., the ionic conductivity increases by one order of magnitude upon an increase from room temperature to 100 °C, while the thermal conductivity increases by only 6%). [ 16 ]
Detrimental secondary phases can also form because of thermal treatments or during the material production. Excessively high sintering /annealing temperatures or long dwelling times will result in the loss of volatile species (especially Li 2 O ) and in the decomposition of LAGP main phase into AlPO 4 and GeO 2 . [ 3 ] LAGP bulk samples and thin films are typically stable up to 700-750 °C; if this temperature is exceeded, volatile lithium is lost and the impurity phase GeO 2 forms. [ 6 ] [ 13 ] If the temperature is further increased beyond 950 °C, also AlPO 4 appears. [ 6 ]
Raman spectroscopy and in situ X-ray diffraction (XRD) are useful techniques that can be employed to recognise the phase purity of LAGP samples during and after the heat treatments. [ 6 ]
LAGP belongs to phosphate-based solid electrolytes and, in spite of showing a moderate ionic conductivity compared to other families of solid ionic conductors, it possesses some intrinsic advantages with respect to sulfides and oxides:
One of the main advantages of LAGP is its chemical stability in the presence of oxygen, water vapour, and carbon dioxide, which simplifies the manufacture process preventing the use of a glovebox or protected environments. Unlike sulfide-based solid electrolytes, which react with water releasing poisonous gaseous hydrogen sulfide , and garnet-type lithium lanthanum zirconium oxide (LLZO), which react with water and CO 2 to form passivating layers of LiOH and Li 2 CO 3 , [ 5 ] LAGP is practically inert in humid air. [ 6 ]
Another important advantage of LAGP is its wide electrochemical stability window , up to 6 V, which allows the use of such electrolyte in contact with high-voltage cathodes, thus enabling high energy densities. [ 19 ] However, the stability at very low voltages and against lithium metal is controversial: [ 20 ] even if LAGP is more stable than LATP because of the absence of titanium, some literature works report on the reduction of Ge 4+ by lithium as well, with formation of Ge 2+ and metallic germanium at the electrode-electrolyte interface and dramatic increase of interfacial resistance. [ 19 ]
The possible decomposition mechanism of LAGP in contact with metallic lithium is reported in the equation below: [ 10 ]
Several synthesis methods exist to produce LAGP in the form of bulk pellets or thin films, depending on the required performances and final applications. The synthesis path significantly affects the microstructure of the LAGP material, which plays a key role in determining its overall conductive properties. Indeed, a compact layer of crystalline LAGP with large and connected grains, and minimal amount of secondary, non-conductive phases ensures the highest conductivity values. On the contrary, an amorphous structure or the presence of small grains and pores tend to hinder the motion of lithium ions, [ 6 ] [ 13 ] with values of ionic conductivity in the range of 10 –8 - 10 –6 S/cm for glassy LAGP. [ 16 ]
In most cases, a post-process thermal treatment is performed to achieve the desired degree of crystallinity. [ 6 ]
Solid-state sintering is the most used synthesis process to produce solid-state electrolytes. Powders of LAGP precursors, including oxides like GeO 2 and Al 2 O 3 , are mixed, calcinated and densified at high temperature (700 - 1200 °C) and for long times (12 hours). Sintered LAGP is characterized by high crystalline quality, large grains, a compact microstructure, and high density, even if negative side effects such as loss of volatile lithium compounds and formation of secondary phases should be avoided while the material is kept at high temperature. [ 3 ]
The sintering parameters affects LAGP microstructure and purity and, ultimately, its ionic conductivity and conduction performances. [ 21 ]
LAGP glass-ceramics can be obtained starting from an amorphous glass with nominal composition of Li 1.5 Al 0.5 Ge 1.5 (PO 4 ) 3 , which is subsequently annealed to promote crystallization. Compared to solid-state sintering, ceramic melt-quenching followed by crystallization is a simpler and more flexible process which leads to a denser and more homogeneous microstructure. [ 6 ]
The starting point for glass crystallization is the synthesis of the glass through a melt-quenching process of precursors in suitable amount to achieve the desired stoichiometry. Different precursors can be used, especially to provide phosphorus to the material. [ 3 ] One possible route is the following:
The main steps are summarized in the following equation: [ 6 ]
The annealing temperature is selected to promote the full crystallization and avoiding the formation of detrimental secondary phases, pores, and cracks. Various temperatures are reported in different literature sources; however, crystallization does not usually start below 550-600 °C, while temperatures larger than 850 °C cause the extensive formation of impurity phases. [ 6 ]
The sol-gel technique enables the production of LAGP particles at lower processing temperatures compared to sintering or glass crystallization. [ 3 ] The typical precursor is a germanium organic compound, like germanium ethoxide Ge(OC 2 H 5 ) , which is dissolved in an aqueous solution with stoichiometric amounts of the sources of lithium, phosphorus, and aluminium. The mixture is then heated and stirred. The sol-gel process starts after the addition of a gelation agent and the final material is obtained after subsequent heating steps aimed at eliminating water and at promoting the pyrolysis reaction, followed by calcination . [ 15 ] [ 22 ]
The sol-gel process requires the use of germanium organic precursors, which are more expensive compared to GeO 2 . [ 7 ]
Sputtering (in particular radio-frequency magnetron sputtering) has been applied to the fabrication of LAGP thin-films starting from a LAGP target. Depending on the temperature of the substrate during the deposition, LAGP can be deposited in the cold sputtering or hot sputtering configuration. [ 13 ]
The film stoichiometry and microstructure can be tuned by controlling the deposition parameters, especially the power density, the chamber pressure, and the substrate temperature. Both amorphous and crystalline films are obtained, with a typical thickness around 1 μm. [ 13 ] [ 18 ] The room-temperature ionic conductivity and the activation energy of sputtered and annealed LAGP films are comparable with those of bulk pellets, i.e. 10 –4 S/cm and 0.31 eV. [ 13 ]
Pre-synthesized LAGP powders can be sprayed on a substrate to form a LAGP film by means of aerosol deposition. The powders are loaded into the aerosol deposition chamber and purified air is used as the carrier gas to drive the particles towards the substrate, where they impinge and coalesce to generate the film. Since the as-produced film is amorphous, an annealing treatment is usually performed to improve the film crystallinity and its conduction properties. [ 23 ]
Some other methods to produce LAGP materials have been reported in literature works, including liquid-based techniques, [ 7 ] spark plasma sintering , [ 1 ] and co-precipitation. [ 24 ]
In the following table, some ionic conductivity values are reported for LAGP materials produced with different synthesis routes, in the case of optimized production and annealing conditions.
LAGP is one of the most studied solid-state electrolytes for lithium-ion batteries. The use of a solid-state electrolyte improves the battery safety eliminating liquid-based electrolytes , which are flammable and usually unstable above 4.3 V. In addition, it physically separates the anode from the cathode, reducing the risk of short-circuit, and strongly inhibits lithium dendrite growth . Finally, solid-state electrolytes can operate in a wide range of temperatures, with minimum conductivity loss and decomposition issues. [ 4 ] Nevertheless, the ionic conductivity of solid-state electrolytes is some orders of magnitude lower than the one of conventional liquid-based electrolytes, therefore a thin electrolyte layer is preferred to reduce the overall internal impedance and to achieve a shorter diffusion path and larger energy densities . [ 4 ] Therefore, LAGP is a suitable candidate for all-solid-state thin-film lithium-ion batteries, in which the electrolyte thickness ranges from 1 to some hundreds of micrometres. [ 4 ] [ 13 ] The good mechanical strength of LAGP effectively suppress lithium dendrites during lithium stripping and plating, reducing the risk of internal short-circuit and battery failure. [ 19 ]
LAGP is applied as a solid-state electrolyte both as a pure material and as a component in organic-inorganic composite electrolytes. [ 3 ] For example, LAGP can be composited with polymeric materials, like polypropylene (PP) [ 25 ] or polyethylene oxide (PEO), [ 26 ] to improve the ionic conductivity and to tune the electrochemical stability. Moreover, since LAGP is not fully stable against metallic lithium because of the electrochemical reactivity of Ge 4+ cations, additional interlayers can be introduced between the lithium anode and the solid electrolyte to improve the interfacial stability. [ 3 ] The addition of a thin layer of metallic germanium inhibits the electrochemical reduction by lithium metal at very negative potentials and promotes the interfacial contact between the anode and the electrolyte, resulting in improved cycling performance and battery stability. [ 19 ] The use of polymer-ceramic composite interlayers or the excess of Li 2 O are alternative strategies to improve the electrochemical stability of LAGP at negative potentials. [ 3 ]
LAGP has been also tested not only as a solid electrolyte, but also as an anode material in lithium-ion battery, showing high electrochemical stability and good cycling performance. [ 17 ]
LAGP-based membranes have been applied as separators in lithium-sulfur batteries . [ 27 ] LAGP allows the transfer of lithium ions from anode to cathode but, at the same time, prevents the diffusion of polysulfides from the cathode, suppressing the polysulfide shuttle effect and enhancing the overall performance of the battery. [ 27 ] Typically, all-solid-state lithium-sulfur batteries are not fabricated because of high interfacial resistance; therefore, hybrid electrolytes are usually realized, in which LAGP acts as a barrier against polysulfide diffusion but it is combined with liquid or polymer electrolytes to promote fast lithium diffusion and to improve the interfacial contact with electrodes. [ 28 ] | https://en.wikipedia.org/wiki/Lithium_aluminium_germanium_phosphate |
Lithium aluminium hydride , commonly abbreviated to LAH , is an inorganic compound with the chemical formula Li [ Al H 4 ] or LiAlH 4 . It is a white solid, discovered by Finholt, Bond and Schlesinger in 1947. [ 4 ] This compound is used as a reducing agent in organic synthesis , especially for the reduction of esters , carboxylic acids , and amides . The solid is dangerously reactive toward water, releasing gaseous hydrogen (H 2 ). Some related derivatives have been discussed for hydrogen storage .
LAH is a colourless solid but commercial samples are usually gray due to contamination. [ 5 ] This material can be purified by recrystallization from diethyl ether . Large-scale purifications employ a Soxhlet extractor . Commonly, the impure gray material is used in synthesis, since the impurities are innocuous and can be easily separated from the organic products. The pure powdered material is pyrophoric , but not its large crystals. [ 6 ] Some commercial materials contain mineral oil to inhibit reactions with atmospheric moisture, but more commonly it is packed in moisture-proof plastic sacks. [ 7 ]
LAH violently reacts with water, including atmospheric moisture, to liberate hydrogen gas. The reaction proceeds according to the following idealized equation: [ 5 ]
This reaction provides a useful method to generate hydrogen in the laboratory. Aged, air-exposed samples often appear white because they have absorbed enough moisture to generate a mixture of the white compounds lithium hydroxide and aluminium hydroxide . [ 8 ]
LAH crystallizes in the monoclinic space group P 2 1 / c . The unit cell has the dimensions: a = 4.82, b = 7.81, and c = 7.92 Å, α = γ = 90° and β = 112°. In the structure, Li + cations are surrounded by five [AlH 4 ] − anions , which have tetrahedral molecular geometry . The Li + cations are bonded to one hydrogen atom from each of the surrounding tetrahedral [AlH 4 ] − anion creating a bipyramid arrangement. At high pressures (>2.2 GPa) a phase transition may occur to give β-LAH. [ 9 ]
Li[AlH 4 ] was first prepared from the reaction between lithium hydride (LiH) and aluminium chloride : [ 4 ] [ 5 ]
In addition to this method, the industrial synthesis entails the initial preparation of sodium aluminium hydride from the elements under high pressure and temperature: [ 10 ]
Li[AlH 4 ] is then prepared by a salt metathesis reaction according to:
which proceeds in a high yield. LiCl is removed by filtration from an ethereal solution of LAH, with subsequent precipitation of LAH to yield a product containing around 1% w / w LiCl. [ 10 ]
An alternative preparation starts from LiH, and metallic Al instead of AlCl 3 . Catalyzed by a small quantity of TiCl 3 (0.2%), the reaction proceeds well using dimethylether as solvent. This method avoids the cogeneration of salt. [ 11 ]
LAH is soluble in many ethereal solutions. However, it may spontaneously decompose due to the presence of catalytic impurities, though, it appears to be more stable in tetrahydrofuran (THF). Thus, THF is preferred over, e.g., diethyl ether , despite the lower solubility. [ 12 ]
LAH is metastable at room temperature. During prolonged storage it slowly decomposes to Li 3 [AlH 6 ] (lithium hexahydridoaluminate) and LiH . [ 13 ] This process can be accelerated by the presence of catalytic elements, such as titanium , iron or vanadium .
When heated LAH decomposes in a three-step reaction mechanism : [ 13 ] [ 14 ] [ 15 ]
R1 is usually initiated by the melting of LAH in the temperature range 150–170 °C, [ 16 ] [ 17 ] [ 18 ] immediately followed by decomposition into solid Li 3 [AlH 6 ] , although R1 is known to proceed below the melting point of Li[AlH 4 ] as well. [ 19 ] At about 200 °C, Li 3 [AlH 6 ] decomposes into LiH ( R2 ) [ 13 ] [ 15 ] [ 18 ] and Al which subsequently convert into LiAl above 400 °C ( R3 ). [ 15 ] Reaction R1 is effectively irreversible. R3 is reversible with an equilibrium pressure of about 0.25 bar at 500 °C. R1 and R2 can occur at room temperature with suitable catalysts. [ 20 ]
The table summarizes thermodynamic data for LAH and reactions involving LAH, [ 21 ] [ 22 ] in the form of standard enthalpy , entropy , and Gibbs free energy change, respectively.
Lithium aluminium hydride (LAH) is widely used in organic chemistry as a reducing agent . [ 5 ] It is more powerful than the related reagent sodium borohydride owing to the weaker Al-H bond compared to the B-H bond. [ 23 ] Often as a solution in diethyl ether and followed by an acid workup, it will convert esters , carboxylic acids , acyl chlorides , aldehydes , and ketones into the corresponding alcohols (see: carbonyl reduction ). Similarly, it converts amide , [ 24 ] [ 25 ] nitro , nitrile , imine , oxime , [ 26 ] and organic azides into the amines (see: amide reduction ). It reduces quaternary ammonium cations into the corresponding tertiary amines. Reactivity can be tuned by replacing hydride groups by alkoxy groups . Due to its pyrophoric nature, instability, toxicity, low shelf life and handling problems associated with its reactivity, it has been replaced in the last decade, both at the small-industrial scale and for large-scale reductions by the more convenient related reagent sodium bis (2-methoxyethoxy)aluminium hydride , which exhibits similar reactivity but with higher safety, easier handling and better economics. [ 27 ]
LAH is most commonly used for the reduction of esters [ 28 ] [ 29 ] and carboxylic acids [ 30 ] to primary alcohols; prior to the advent of LAH this was a difficult conversion involving sodium metal in boiling ethanol (the Bouveault-Blanc reduction ). Aldehydes and ketones [ 31 ] can also be reduced to alcohols by LAH, but this is usually done using milder reagents such as Na[BH 4 ] ; α, β-unsaturated ketones are reduced to allylic alcohols. [ 32 ] When epoxides are reduced using LAH, the reagent attacks the less hindered end of the epoxide, usually producing a secondary or tertiary alcohol. Epoxycyclohexanes are reduced to give axial alcohols preferentially. [ 33 ]
Partial reduction of acid chlorides to give the corresponding aldehyde product cannot proceed via LAH, since the latter reduces all the way to the primary alcohol. Instead, the milder lithium tri- tert -butoxyaluminum hydride , which reacts significantly faster with the acid chloride than with the aldehyde, must be used. For example, when isovaleric acid is treated with thionyl chloride to give isovaleroyl chloride, it can then be reduced via lithium tri- tert -butoxyaluminum hydride to give isovaleraldehyde in 65% yield. [ 34 ] [ 35 ]
Lithium aluminium hydride also reduces alkyl halides to alkanes . [ 36 ] [ 37 ] Alkyl iodides react the fastest, followed by alkyl bromides and then alkyl chlorides. Primary halides are the most reactive followed by secondary halides. Tertiary halides react only in certain cases. [ 38 ]
Lithium aluminium hydride does not reduce simple alkenes or arenes . Alkynes are reduced only if an alcohol group is nearby, [ 39 ] and alkenes are reduced in the presence of catalytic TiCl 4 . [ 40 ] It was observed that the LiAlH 4 reduces the double bond in the N -allylamides. [ 41 ]
LAH is widely used to prepare main group and transition metal hydrides from the corresponding metal halides .
LAH also reacts with many inorganic ligands to form coordinated alumina complexes associated with lithium ions. [ 21 ]
LiAlH 4 contains 10.6 wt% hydrogen, thereby making LAH a potential hydrogen storage medium for future fuel cell -powered vehicles . The high hydrogen content, as well as the discovery of reversible hydrogen storage in Ti-doped NaAlH 4 , [ 42 ] have sparked renewed research into LiAlH 4 during the last decade. A substantial research effort has been devoted to accelerating the decomposition kinetics by catalytic doping and by ball milling . [ 43 ] In order to take advantage of the total hydrogen capacity, the intermediate compound LiH must be dehydrogenated as well. Due to its high thermodynamic stability this requires temperatures in excess of 400 °C, which is not considered feasible for transportation purposes. Accepting LiH + Al as the final product, the hydrogen storage capacity is reduced to 7.96 wt%. Another problem related to hydrogen storage is the recycling back to LiAlH 4 which, owing to its relatively low stability, requires an extremely high hydrogen pressure in excess of 10000 bar. [ 43 ] Cycling only reaction R2 — that is, using Li 3 AlH 6 as starting material — would store 5.6 wt% hydrogen in a single step (vs. two steps for NaAlH 4 which stores about the same amount of hydrogen). However, attempts at this process have not been successful so far. [ citation needed ]
A variety of salts analogous to LAH are known. NaH can be used to efficiently produce sodium aluminium hydride (NaAlH 4 ) by metathesis in THF:
Potassium aluminium hydride (KAlH 4 ) can be produced similarly in diglyme as a solvent: [ 44 ]
The reverse, i.e., production of LAH from either sodium aluminium hydride or potassium aluminium hydride can be achieved by reaction with LiCl or lithium hydride in diethyl ether or THF : [ 44 ]
"Magnesium alanate" (Mg(AlH 4 ) 2 ) arises similarly using MgBr 2 : [ 45 ]
Red-Al (or SMEAH, NaAlH 2 (OC 2 H 4 OCH 3 ) 2 ) is synthesized by reacting sodium aluminum tetrahydride (NaAlH 4 ) and 2-methoxyethanol : [ 46 ] | https://en.wikipedia.org/wiki/Lithium_aluminium_hydride |
Lithium beryllide is a hypothetical intermetallic compound of lithium and beryllium that may have several possible compositions, including LiBe, LiBe 2 , Li 2 Be, LiBe 3 , Li 3 Be, Li 2 Be 3 , Li 3 Be 2 , LiBe 4 and Li 4 Be. [ 1 ] Computational methods indicate that some of these compositions may be superconductive under very high pressure and low temperature. [ 1 ] [ 2 ] [ 3 ]
This article about a hypothetical chemical compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Lithium_beryllide |
Lithium bis(trimethylsilyl)amide is a lithiated organosilicon compound with the formula LiN(Si(CH 3 ) 3 ) 2 . It is commonly abbreviated as LiHMDS or Li(HMDS) ( li thium h exa m ethyl d i s ilazide - a reference to its conjugate acid HMDS ) and is primarily used as a strong non-nucleophilic base and as a ligand . Like many lithium reagents, it has a tendency to aggregate and will form a cyclic trimer in the absence of coordinating species.
LiHMDS is commercially available, but it can also be prepared by the deprotonation of bis(trimethylsilyl)amine with n -butyllithium . [ 1 ] This reaction can be performed in situ . [ 2 ]
Once formed, the compound can be purified by sublimation or distillation .
LiHMDS is often used in organic chemistry as a strong non-nucleophilic base . [ 3 ] Its conjugate acid has a p K a of ~26, [ 4 ] making it is less basic than other lithium bases, such as LDA (p K a of conjugate acid ~36). It is relatively more sterically hindered and hence less nucleophilic than other lithium bases. It can be used to form various organolithium compounds, including acetylides [ 3 ] or lithium enolates . [ 2 ]
where Me = CH 3 . As such, it finds use in a range of coupling reactions, particularly carbon-carbon bond forming reactions such as the Fráter–Seebach alkylation and mixed Claisen condensations .
An alternative synthesis of tetrasulfur tetranitride entails the use of S(N(Si(CH 3 ) 3 ) 2 ) 2 as a precursor with pre-formed S–N bonds. S(N(Si(CH 3 ) 3 ) 2 ) 2 is prepared by the reaction of lithium bis(trimethylsilyl)amide and sulfur dichloride ( SCl 2 ).
The S(N(Si(CH 3 ) 3 ) 2 ) 2 reacts with the combination of SCl 2 and sulfuryl chloride ( SO 2 Cl 2 ) to form S 4 N 4 , trimethylsilyl chloride , and sulfur dioxide : [ 5 ]
Li(HMDS) can react with a wide range of metal halides , by a salt metathesis reaction , to give metal bis(trimethylsilyl)amides .
where X = Cl, Br, I and sometimes F
Metal bis(trimethylsilyl)amide complexes are lipophilic due to the ligand and hence are soluble in a range of nonpolar organic solvents , this often makes them more reactive than the corresponding metal halides, which can be difficult to solubilise. The steric bulk of the ligands causes their complexes to be discrete and monomeric; further increasing their reactivity. Having a built-in base, these compounds conveniently react with protic ligand precursors to give other metal complexes and hence are important precursors to more complex coordination compounds . [ 6 ]
LiHMDS is volatile and has been discussed for use for atomic layer deposition of lithium compounds. [ 7 ]
Like many organolithium reagents, lithium bis(trimethylsilyl)amide can form aggregates in solution. The extent of aggregation depends on the solvent. In coordinating solvents, such as ethers [ 8 ] and amines , [ 9 ] the monomer and dimer are prevalent. In the monomeric and dimeric state, one or two solvent molecules bind to lithium centers. With ammonia as donor base lithium bis(trimethylsilyl)amide forms a trisolvated monomer that is stabilized by intermolecular hydrogen bonds. [ 10 ] [ 11 ] In noncoordinating solvents, such as aromatics or pentane , the complex oligomers predominate, including the trimer. [ 9 ] In the solid state structure is trimeric. [ 12 ] | https://en.wikipedia.org/wiki/Lithium_bis(trimethylsilyl)amide |
Lithium borohydride (LiBH 4 ) is a borohydride and known in organic synthesis as a reducing agent for esters . Although less common than the related sodium borohydride , the lithium salt offers some advantages, being a stronger reducing agent and highly soluble in ethers, whilst remaining safer to handle than lithium aluminium hydride . [ 3 ]
Lithium borohydride may be prepared by the metathesis reaction , which occurs upon ball-milling the more commonly available sodium borohydride and lithium bromide : [ 4 ]
Alternatively, it may be synthesized by treating boron trifluoride with lithium hydride in diethyl ether : [ 5 ]
Lithium borohydride is useful as a source of hydride (H – ). It can react with a range of carbonyl substrates and other polarized carbon structures to form a hydrogen–carbon bond. It can also react with Brønsted–Lowry -acidic substances (sources of H + ) to form hydrogen gas.
As a hydride reducing agent, lithium borohydride is stronger than sodium borohydride [ 6 ] [ 7 ] but weaker than lithium aluminium hydride. [ 7 ] Unlike the sodium analog, it can reduce esters to alcohols, nitriles and primary amides to amines , and can open epoxides . The enhanced reactivity in many of these cases is attributed to the polarization of the carbonyl substrate by complexation to the lithium cation. [ 3 ] Unlike the aluminium analog, it does not react with nitro groups , carbamic acids , alkyl halides , or secondary and tertiary amides.
Lithium borohydride reacts with water to produce hydrogen. This reaction can be used for hydrogen generation. [ 8 ]
Although this reaction is usually spontaneous and violent, somewhat-stable aqueous solutions of lithium borohydride can be prepared at low temperature if degassed , distilled water is used and exposure to oxygen is carefully avoided. [ 9 ]
Lithium borohydride is renowned as one of the highest- energy-density chemical energy carriers . Although presently of no practical importance, the solid liberates 65 MJ / kg heat upon treatment with atmospheric oxygen. Since it has a density of 0.67 g/cm 3 , oxidation of liquid lithium borohydride gives 43 MJ/L . In comparison, gasoline gives 44 MJ/kg (or 35 MJ/L), while liquid hydrogen gives 120 MJ/kg (or 8.0 MJ/L). [ nb 1 ] The high specific energy density of lithium borohydride has made it an attractive candidate to propose for automobile and rocket fuel, but despite the research and advocacy, it has not been used widely. As with all chemical-hydride-based energy carriers, lithium borohydride is very complex to recycle (i.e. recharge) and therefore suffers from a low energy conversion efficiency . While batteries such as lithium-ion carry an energy density of up to 0.72 MJ/kg and 2.0 MJ/L, their DC -to-DC conversion efficiency can be as high as 90%. [ 10 ] In view of the complexity of recycling mechanisms for metal hydrides, [ 11 ] such high energy-conversion efficiencies are not practical with present technology. | https://en.wikipedia.org/wiki/Lithium_borohydride |
Lithium burning is a nucleosynthetic process in which lithium is depleted in a star . Lithium is generally present in brown dwarfs and not in older low-mass stars. Stars, which by definition must achieve the high temperature (2.5 × 10 6 K) necessary for fusing hydrogen , rapidly deplete their lithium.
Burning of the most abundant isotope of lithium , lithium-7, occurs by a collision of lithium-7 and a proton producing beryllium-8 , which promptly decays into two helium-4 nuclei. The temperature necessary for this reaction is just below the temperature necessary for hydrogen fusion . Convection in low-mass stars ensures that lithium in the whole volume of the star is depleted. [ 1 ] Therefore, the presence of the lithium line in a candidate brown dwarf's spectrum is a strong indicator that it is indeed substellar.
From a study of lithium abundances in 53 T Tauri stars , it has been found that lithium depletion varies strongly with size, suggesting that lithium burning by the P-P chain , during the last highly convective and unstable stages during the pre–main sequence later phase of the Hayashi contraction may be one of the main sources of energy for T Tauri stars. Rapid rotation tends to improve mixing and increase the transport of lithium into deeper layers where it is destroyed. T Tauri stars generally increase their rotation rates as they age, through contraction and spin-up, as they conserve angular momentum. This causes an increased rate of lithium loss with age. Lithium burning will also increase with higher temperatures and mass, and will last for at most a little over 100 million years.
The P-P chain for lithium burning is as follows
It will not occur in stars less than sixty times the mass of Jupiter. In this way, the rate of lithium depletion can be used to calculate the age of the star.
The use of lithium to distinguish candidate brown dwarfs from low-mass stars is commonly referred to as the lithium test . Heavier stars like the Sun can retain lithium in their outer atmospheres, which never get hot enough for lithium depletion, but those are distinguishable from brown dwarfs by their size. Brown dwarfs at the high end of their mass range (60–75 M J ) can be hot enough to deplete their lithium when they are young. Dwarfs of mass greater than 65 M J can burn off their lithium by the time they are half a billion years old; thus, this test is not perfect. [ 2 ] | https://en.wikipedia.org/wiki/Lithium_burning |
Lithium chlorate is the inorganic chemical compound with the formula LiClO 3 .
Like all chlorates , it is an oxidizer and may become unstable and possibly explosive if mixed with organic materials, reactive metal powders, or sulfur.
It can be manufactured by the reaction of hot, concentrated lithium hydroxide with chlorine:
Lithium chlorate has one of the highest solubilities in water for a chemical compound. It is also a six-electron oxidant. Its electrochemical reduction is facilitated by acid, electrocatalysts and redox mediators. These properties make lithium chlorate a useful oxidant for high energy density flow batteries . [ 5 ] Lithium chlorate has a very low melting point for an inorganic ionic salt. | https://en.wikipedia.org/wiki/Lithium_chlorate |
This page provides supplementary chemical data on Lithium chloride .
The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet ( MSDS ) for this chemical from a reliable source such as SIRI , and follow its directions. | https://en.wikipedia.org/wiki/Lithium_chloride_(data_page) |
Lithium diisopropylamide (commonly abbreviated LDA ) is a chemical compound with the molecular formula LiN(CH(CH 3 ) 2 ) 2 . It is used as a strong base and has been widely utilized due to its good solubility in non-polar organic solvents and non-nucleophilic nature. It is a colorless solid, but is usually generated and observed only in solution. It was first prepared by Hamell and Levine in 1950 along with several other hindered lithium diorganylamides to effect the deprotonation of esters at the α position without attack of the carbonyl group. [ 2 ]
LDA is commonly formed by treating a cooled (0 to −78 °C) mixture of tetrahydrofuran and diisopropylamine with n -butyllithium . [ 3 ]
When dissociated, the diisopropylamide anion can become protonated to form diisopropylamine. Diisopropylamine has a p K a value of 36. Therefore, its conjugate base is suitable for the deprotonation of compounds with greater acidity, importantly, such weakly acidic compounds (carbon acids) of the type HC(Z)R 2 , where Z = C(O)R', C(O)OR' or CN. Conventional protic functional groups such as alcohols and carboxylic acids are readily deprotonated.
Like most organolithium reagents , LDA is not a salt, but is highly polar. It forms aggregates in solution, with the extent of aggregation depending on the nature of the solvent. In THF its structure is primarily that of a solvated dimer . [ 4 ] [ 5 ] In nonpolar solvents such as toluene , it forms a temperature-dependent oligomer equilibrium. At room temperature trimers and tetramers are the most likely structures. With decreasing temperature the aggregation extends to pentameric and higher oligomeric structures. [ 6 ]
Solid LDA is pyrophoric , [ 7 ] but its solutions are generally not. As such it is commercially available as a solution in polar aprotic solvents such as THF and ether; however, for small scale use (less than 50 mmol), it is common and more cost effective to prepare LDA in situ .
The deprotonation of carbon acids can proceed with either kinetic or thermodynamic reaction control . Kinetic controlled deprotonation requires a base that is sterically hindered and strong enough to remove the proton irreversibly. For example, in the case of phenylacetone , deprotonation can produce two different enolates . LDA has been shown to deprotonate the methyl group, which is the kinetic course of the deprotonation. To ensure the production of the kinetic product, a slight excess (1.1 equiv) of lithium diisopropylamide is used, and the ketone is added to the base at –78 °C. Because the ketone is quickly and quantitatively converted to the enolate and base is present in excess at all times, the ketone is unable to act as a proton shuttle to catalyze the gradual formation of the thermodynamic product. A weaker base such as an alkoxide , which reversibly deprotonates the substrate, affords the more thermodynamically stable benzylic enolate. An alternative to the weaker base is to use a strong base which is present at a lower concentration than the ketone. For instance, with a slurry of sodium hydride in THF or dimethylformamide (DMF), the base only reacts at the solution–solid interface. A ketone molecule might be deprotonated at the kinetic site. This enolate may then encounter other ketones and the thermodynamic enolate will form through the exchange of protons, even in an aprotic solvent which does not contain hydronium ions.
LDA can, however, act as a nucleophile under certain conditions. | https://en.wikipedia.org/wiki/Lithium_diisopropylamide |
Lithium helide is a compound of helium and lithium with the formula LiHe . The substance is a cold low-density gas made of Van der Waals molecules , each composed of a helium atom and lithium atom bound by van der Waals force . [ 1 ] The preparation of LiHe opens up the possibility to prepare other helium dimers , and beyond that multi-atom clusters that could be used to investigate Efimov states and Casimir retardation effects . [ 2 ]
It was detected in 2013. Previously 7 Li 4 He was predicted to have a binding energy of 0.0039 cm −1 (7.7×10 −8 eV, 1.2×10 −26 J, or 6 mK [ 2 ] ), and a bond length of 28 Å. [ 1 ] Other van der Waals-bound helium molecules were previously known including Ag 3 He and He 2 . [ 1 ] Detection of LiHe was done via fluorescence. The lithium atom in the X 2 Σ state was excited to A 2 Π. The spectrum showed a pair of lines, each split into two with the hyperfine structure of 7 Li. The lines had wavenumbers of 14902.563, 14902.591, 14902.740, and 14902.768 cm −1 . The two pairs are separated by 0.177 cm −1 . This is explained by two different vibrational states of the LiHe molecule: 1/2 and 3/2. [ 1 ] The bonding between the atoms is so low that it cannot withstand any rotation or greater vibration without breaking apart. The lowest rotation states would have energies of 40 and 80 mK, greater than the binding energy around 6 mK. [ 2 ]
LiHe was formed by laser ablation of lithium metal into a cryogenic helium buffer gas at a temperature between 1 and 5 K. The proportion of LiHe molecules was proportional to the density of He, and declined as the temperature increased. [ 1 ]
LiHe is polar and paramagnetic . [ 2 ]
The average separation between the lithium and helium atoms depends on the isotope. For 6 LiHe the separation is 48.53 Å, but for 7 LiHe the distance is much smaller at 28.15 Å on average. [ 3 ]
If the helium atom of LiHe is excited so that the 1s electron is promoted to 2s, it decays by transferring energy to ionise lithium, and the molecule breaks up. This is called interatomic Coulombic decay . The energy of the Li + and He decay products is distributed in a curve that oscillates up and down about a dozen times. [ 3 ] | https://en.wikipedia.org/wiki/Lithium_helide |
Lithium hypochlorite is a chemical compound with the chemical formula of Li O Cl . It is the lithium salt of hypochlorous acid . It consists of lithium cations ( Li + ) and hypochlorite anions ( − OCl ). It is a colorless, crystalline compound. It has been used as a disinfectant for pools, and is also used as a reagent for some chemical reactions.
Doses of 500 mg/kg cause detrimental clinical signs and significant mortality in rats . [ 1 ] The use of chlorine -based disinfectants in domestic water , although widespread, has led to some controversy because of the formation of small quantities of harmful byproducts such as chloroform . Studies showed no uptake of lithium if pools with lithium hypochlorite have been used. [ 2 ]
Lithium hypochlorite has been used as a fast-acting disfinectant for vinyl swimming pools . However, due to the increasing demand for lithium in lithium-ion batteries , manufacturers have stopped producing lithium hypochlorite, making it much harder to find these days. [ 3 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Lithium_hypochlorite |
Lithium hypofluorite is an inorganic compound with the chemical formula of Li O F . It is a compound of lithium , fluorine , and oxygen . [ 1 ] [ 2 ] [ 3 ] This is a lithium salt of hypofluorous acid , [ 4 ] and contains lithium cations Li + and hypofluorite anions − OF . [ dubious – discuss ]
The salt theoretically results from the neutralization of hypofluorous acid (HOF) and lithium hydroxide (LiOH). It can be formed by the action of fluorine on lithium hydroxide:
The compound is quite unstable, since it contains oxygen in the oxidation state of 0. It, therefore, tends to decompose to lithium fluoride and oxygen gas:
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Lithium_hypofluorite |
Lithium iodide , or LiI, is a compound of lithium and iodine . When exposed to air , it becomes yellow in color, due to the oxidation of iodide to iodine. [ 2 ] It crystallizes in the NaCl motif . [ 3 ] It can participate in various hydrates . [ 4 ]
Lithium iodide is used as a solid-state electrolyte for high-temperature batteries. It is also the standard electrolyte in artificial pacemakers [ 6 ] due to the long cycle life it enables. [ 7 ] The solid is used as a phosphor for neutron detection. [ 8 ] It is also used, in a complex with Iodine , in the electrolyte of dye-sensitized solar cells .
In organic synthesis , LiI is useful for cleaving C-O bonds. For example, it can be used to convert methyl esters to carboxylic acids : [ 9 ]
Similar reactions apply to epoxides and aziridines .
Lithium iodide was used as a radiocontrast agent for CT scans . Its use was discontinued due to renal toxicity. Inorganic iodine solutions suffered from hyperosmolarity and high viscosities. Current iodinated contrast agents are organoiodine compounds . [ 10 ]
It is also useful in MALDI imaging mass spectrometry of lipids by adding lithium salts to the matrix solution. [ 11 ] | https://en.wikipedia.org/wiki/Lithium_iodide |
Lithium naphthalene is an organic salt with the chemical formula Li + [ C 10 H 8 ] − . In the research laboratory, it is used as a reductant in the synthesis of organic, organometallic , and inorganic chemistry. It is usually generated in situ. Lithium naphthalene crystallizes with ligands bound to Li + . [ 1 ] The anion is a well-known example of an organic radical .
The compound is prepared by stirring the metallic lithium with naphthalene in an ethereal solvent , usually as tetrahydrofuran or dimethoxyethane . The resulting salt is dark green. [ 2 ] The reaction of naphthalene with lithium can be accelerated by sonication. Methods for assaying lithium naphthalene have been developed as well. [ 3 ] As a radical, its solutions show a strong EPR signal near g = 2.0. [ 4 ] Its deep green color arises from absorptions at 463, 735 nm. [ 5 ]
Several solvates of lithium naphthalene have been characterized by X-ray crystallography . The effects are subtle, the outer pair of HC–CH bonds contract by 3 pm and the other nine C–C bonds elongate by 2–3 pm. Net: reduction weakens the bonding. [ 6 ]
With a reduction potential near −2.5 V versus the normal hydrogen electrode , the naphthalene radical anion is a strong reducing agent . [ 5 ]
The anion is strongly basic , and a typical degradation pathway involves reaction with water and related protic sources such as alcohols . These reactions afford dihydronaphthalene :
Alkali metal salts of the naphthalene radical anion are used to prepare complexes of naphthalene. [ 7 ]
Many related radical anions are known such as those derived from anthracene , with other alkali metals (especially sodium ), and with diverse ligands attached to the alkali metal cations . Dilithium naphthalene is also known in the form [Li + ( tmeda ) 2 ] 2 [C 10 H 8 ] 2− . [ 8 ] [ 1 ] | https://en.wikipedia.org/wiki/Lithium_naphthalene |
Lithium nitrate is an inorganic compound with the formula LiNO 3 . It is the lithium salt of nitric acid (an alkali metal nitrate ). The salt is deliquescent , absorbing water to form the hydrated form, lithium nitrate trihydrate. Its eutectics are of interest for heat transfer fluids. [ 2 ]
It is made by treating lithium carbonate or lithium hydroxide with nitric acid .
This deliquescent colourless salt is an oxidizing agent used in the manufacture of red-colored fireworks and flares .
The hydrated form, lithium nitrate trihydrate, has an extremely high specific heat of fusion , 287 ± 7 J/g , [ 3 ] and hence can be used for thermal energy storage at its melt temperature of 303.3 K. [ 4 ]
Lithium nitrate has been proposed as a medium to store heat collected from the sun for cooking. A Fresnel lens would be used to melt solid lithium nitrate, which would then function as a "solar battery", allowing heat to be redistributed later by convection. [ 5 ]
Lithium nitrate can be synthesized by reacting nitric acid and lithium carbonate.
Generally when forming LiNO 3 , a pH indicator is used to determine when all of the acid has been neutralized. However, this neutralization can also be recognized with the loss of carbon dioxide production. [ 6 ] In order to rid the final product of excess water, the sample is heated.
Lithium nitrate can be toxic to the body when ingested by targeting the central nervous system, thyroids, kidneys, and cardio-vascular system. [ 7 ] When exposed to the skin, eyes, and mucous membranes, lithium nitrate can cause irritation to these areas. [ 8 ] | https://en.wikipedia.org/wiki/Lithium_nitrate |
Lithium nitrite is the lithium salt of nitrous acid, with formula LiNO 2 . This compound is hygroscopic and very soluble in water. It is used as a corrosion inhibitor in mortar . [ 4 ] It is also used in the production of explosives , due to its ability to nitrosate ketones under certain conditions. [ 5 ]
Lithium nitrate (LiNO 3 ) will undergo thermal decomposition above 500 °C to yield the evolution of lithium nitrite and oxygen as in the following reaction: [ 6 ]
Lithium nitrite can also be prepared by the reaction of nitric oxide (NO) with lithium hydroxide (LiOH) as shown below: [ 6 ]
Lithium nitrite crystals can be obtained most efficiently by reacting lithium sulfate and barium nitrite in an aqueous solution. However, these crystals can also be prepared by mixing equal amounts of lithium sulfate and potassium nitrite in highly concentrated aqueous solution. This is followed by considerable evaporation and filtration, which removes the resulting precipitate of potassium sulfate and lithium potassium sulfate after further evaporation and extraction with absolute alcohol. [ 7 ]
Lithium nitrite is exceptionally soluble in absolute alcohol. However, potassium nitrite is not very soluble. This makes absolute alcohol a choice solvent for the crystallization of lithium nitrite because the crystals can be extracted in a substantially pure state. The alcoholic solution will leave a white residue of small crystals upon evaporation. The addition of a small amount of water to this residue will yield the larger needle-shaped crystals of lithium nitrite monohydrate (LiNO 2 ·H 2 O). [ 7 ]
The above methods will result in flat, needle-shaped crystals. These crystals are white and typically 1–2 cm. in length. Below 100 °C, these crystals will melt in their own water of crystallization and will tend to lose water slowly. Rapid dehydration will occur at temperatures above 160 °C as well as a minuscule loss of nitrogen oxide. This rapid dehydration leaves behind a residue which consists almost entirely of the anhydrous salt. [ 7 ] This anhydrous salt is extraordinarily soluble in water and will readily form a supersaturated solution. Monohydrate crystals will deposit from this supersaturated solution upon cooling or with the addition of ready formed salt crystals. [ 7 ]
Reinforcement bars, ready mixed concrete materials, and repair materials are often subject to corrosion. These resources will rapidly degrade due to chloride attack and carbonatation . This not only affects the service lives of such materials, but it also requires a considerable cost for the repair of such defects. Lithium nitrite and calcium nitrite are generally used in the construction industry as a means to protect reinforced concrete structures from corrosion. Unlike calcium nitrite inhibitors, lithium nitrite is particularly valued for corrosion inhibition and resistance of carbonation when an accelerated hardening process is not used and when a high concentration of 10% or more cement is added by weight. [ 4 ]
Generally speaking, studying the effectiveness of such inhibitors has been done using destructive methods. These studies require placing specimens to accelerated corrosion and measuring the degree of corrosion. "However, it is extremely difficult to measure the effect of corrosion inhibitors in actual structures using a destructive method."
Recently, sensors that can measure changes in electrical resistance due to the corrosion in iron and thus indicate the degree of corrosion of a material have been developed. These sensors provide a non-destructive way to evaluate the degree of corrosion in concrete materials. Therefore, the effect of lithium nitrite as a corrosion inhibitor has also been studied by non-destructive means. [ 4 ]
A study was conducted in Korea to experimentally determine the most effective dose and performance of lithium nitrite corrosion inhibitors. This experiment employed the molar ratio of nitrite ions to chloride ions (NO 2 − /Cl − ) as a test parameter. This study concluded that a lithium nitrite dosage of 0.6 in the nitrite-chloride ion molar ratio is a successful dosage for mortar containing chlorides. [ 4 ] | https://en.wikipedia.org/wiki/Lithium_nitrite |
Lithium oxalate is an organic compound with the chemical formula Li 2 C 2 O 4 . It is a salt of lithium metal and oxalic acid . [ 3 ] [ 4 ] It consists of lithium cations Li + and oxalate anions C 2 O 2− 4 . Lithium oxalate is soluble in water and converts to lithium oxide when heated. [ 5 ]
One of the methods of synthesis is the reaction of direct neutralization of oxalic acid with lithium hydroxide :
The compound crystallizes in the monoclinic system , cell parameters a = 3.400 Å , b = 5.156 Å, c = 9.055 Å, β = 95.60°, Z = 4. [ 3 ]
Lithium oxalate decomposes when heated at 410–500 °C (770–932 °F; 683–773 K):
In pyrotechnics , the compound is used to color the flame red . [ 6 ] | https://en.wikipedia.org/wiki/Lithium_oxalate |
Lithium perchlorate is the inorganic compound with the formula LiClO 4 . This white or colourless crystalline salt is noteworthy for its high solubility in many solvents. It exists both in anhydrous form and as a trihydrate .
Lithium perchlorate is used as a source of oxygen in some chemical oxygen generators . It decomposes at about 400 °C, yielding lithium chloride and oxygen : [ 5 ]
Over 60% of the mass of the lithium perchlorate is released as oxygen. [ 2 ] It has both the highest oxygen to weight and oxygen to volume ratio of all practical perchlorate salts, and higher oxygen to volume ratio than liquid oxygen . [ 6 ]
Lithium perchlorate is used as an oxidizer in some experimental solid rocket propellants , and to produce red colored flame in pyrotechnic compositions. [ 2 ] [ 7 ]
LiClO 4 is highly soluble in organic solvents, even diethyl ether. Such solutions are employed in Diels–Alder reactions , where it is proposed that the Lewis acidic Li + binds to Lewis basic sites on the dienophile, thereby accelerating the reaction. [ 8 ]
Lithium perchlorate is also used as a co-catalyst in the coupling of α,β-unsaturated carbonyls with aldehydes, also known as the Baylis–Hillman reaction . [ 9 ]
Solid lithium perchlorate is found to be a mild and efficient Lewis acid for promoting cyanosilylation of carbonyl compounds under neutral conditions. [ 10 ]
Lithium perchlorate is also used as an electrolyte salt in lithium-ion batteries . Lithium perchlorate is chosen over alternative salts such as lithium hexafluorophosphate or lithium tetrafluoroborate when its superior electrical impedance , conductivity , hygroscopicity , and anodic stability properties are of importance to the specific application. [ 11 ] However, these beneficial properties are often overshadowed by the electrolyte's strong oxidizing properties, making the electrolyte reactive toward its solvent at high temperatures and/or high current loads. Due to these hazards the battery is often considered unfit for industrial applications. [ 11 ]
Concentrated solutions of lithium perchlorate (4.5 mol/L) are used as a chaotropic agent to denature proteins .
Lithium perchlorate can be manufactured by reaction of sodium perchlorate with lithium chloride . It can be also prepared by electrolysis of lithium chlorate at 200 mA/cm 2 at temperatures above 20 °C. [ 12 ]
Perchlorates often give explosive mixtures with organic compounds, finely divided metals, sulfur, and other reducing agents. [ 12 ] [ 2 ] | https://en.wikipedia.org/wiki/Lithium_perchlorate |
Lithium peroxide is the inorganic compound with the formula Li 2 O 2 . Lithium peroxide is a white solid, and unlike most other alkali metal peroxides, it is nonhygroscopic . Because of its high oxygen:mass and oxygen:volume ratios, the solid has been used to remove CO 2 from and release O 2 to the atmosphere in spacecraft . [ 4 ]
It is prepared by the reaction of hydrogen peroxide and lithium hydroxide . This reaction initially produces lithium hydroperoxide : [ 4 ] [ 5 ]
This lithium hydroperoxide may exist as lithium peroxide monoperoxohydrate trihydrate (Li 2 O 2 ·H 2 O 2 ·3H 2 O).
Dehydration of this material gives the anhydrous peroxide salt:
Li 2 O 2 decomposes at about 450 °C to give lithium oxide :
The structure of solid Li 2 O 2 has been determined by X-ray crystallography and density functional theory . The solid features eclipsed "ethane-like" Li 6 O 2 subunits with an O-O distance of around 1.5 Å. [ 6 ]
It is used in air purifiers where weight is important, e.g., spacecraft or other sealed spaces and apparatuses to absorb carbon dioxide and release oxygen in the reaction: [ 4 ]
Li 2 O 2 + CO 2 → Li 2 CO 3 + 1 ⁄ 2 O 2
Similar to the reaction of lithium hydroxide with carbon dioxide to release 1 Li 2 CO 3 and 1 H 2 O, lithium peroxide has high absorption capacity and absorbs more CO 2 than does the same weight of lithium hydroxide and offers the bonus of releasing oxygen instead of water. [ 7 ]
Lithium peroxide can also act as a catalyst for polymerization of styrene to polystyrene. The polymerization of styrene to polystyrene typically involves the use of radical initiators via the free radical chain mechanism but lithium peroxide can also initiate radical polymerization reactions under certain conditions, although not as widely used.
The reversible lithium peroxide reaction is the basis for a prototype lithium–air battery . Using oxygen from the atmosphere allows the battery to eliminate storage of oxygen for its reaction, saving battery weight and size. [ 8 ] | https://en.wikipedia.org/wiki/Lithium_peroxide |
Lithium phosphate is a phosphate salt of lithium , with the molecular formula Li 3 PO 4 . [ 3 ] It is a white solid slightly soluble in water.
It is primarily used in the production of lithium iron phosphate (LiFePO₄) for making lithium-ion batteries . [ 3 ]
Trilithium phosphate can be produced by the neutralization of lithium carbonate using phosphoric acid : [ 1 ]
The low-temperature polymorph (β-Li 3 PO 4 ) crystallizes as an orthorhombic crystal with the space group Pmn 2 1 . If heated to above 500°C, it converts to another polymorph, γ-Li 3 PO 4 . [ 4 ]
Large doses of lithium phosphate may cause dizziness , and sometimes, kidney damage. According to some reports, dehydration , weight loss , and thyroid disturbances can occur due to high exposure of lithium ions. Nervous system defects, including slurred speech, blurred vision , sensory loss, and convulsions may also occur. [ 3 ] | https://en.wikipedia.org/wiki/Lithium_phosphate |
Spodumene is a pyroxene mineral consisting of lithium aluminium inosilicate , Li Al ( Si O 3 ) 2 , and is a commercially important source of lithium. It occurs as colorless to yellowish, purplish, or lilac kunzite (see below), or alternatively yellowish-green or emerald-green hiddenite ; it takes the form of prismatic crystals, often of great size. Single crystals of 14.3 m (47 ft) in size are reported from the Black Hills of South Dakota , United States. [ 6 ] [ 7 ]
The naturally occurring low-temperature form α-spodumene is in the monoclinic system, and the high-temperature β-spodumene crystallizes in the tetragonal system. α-Spodumene converts to β-spodumene at temperatures above 900 °C. [ 5 ] Typically crystals are heavily striated along the principal axis. Crystal faces are often etched and pitted with triangular markings. [ not verified in body ]
Spodumene was first described in 1800 for an occurrence in the type locality in Utö , Södermanland , Sweden . It was discovered by Brazilian naturalist Jose Bonifacio de Andrada e Silva . The name is derived from the Greek spodumenos (σποδούμενος), meaning "burnt to ashes", owing to the opaque ash-grey appearance of material refined for use in industry. [ 2 ]
Spodumene occurs in lithium-rich granite pegmatites and aplites . Associated minerals include quartz , albite , petalite , eucryptite , lepidolite , and beryl . [ 3 ]
Transparent material has long been used as a gemstone with varieties kunzite and hiddenite noted for their strong pleochroism . Source localities include the Democratic Republic of Congo (DRC), Afghanistan , Australia , Brazil , Madagascar (see mining ), Pakistan , Québec in Canada , and North Carolina and California in the U.S.
Since 2018, the DRC has been known to have the largest lithium spodumene hard-rock deposit in the world, with mining operations occurring in the central DRC territory of Manono , Tanganyika Province . [ 8 ] As of 2021, the Australian company AVZ Minerals [ 9 ] is developing the Manono Lithium and Tin project, and has a resource size of 400 million tonnes of high-grade low-impurity ore at 1.65% lithium oxide ( Li 2 O ) [ 10 ] spodumene hard-rock based on studies and drilling of Roche Dure, one of several pegmatites in the deposit.
Spodumene is an important source of lithium , for use in ceramics , mobile phones and batteries (including for automotive applications), medicine , Pyroceram , and as a fluxing agent. As of 2019, around half of lithium is extracted from mineral ores, which mainly consist of spodumene. Lithium is recovered from spodumene by dissolution in acid , or extraction with other reagents, after roasting to convert it to the more reactive β-spodumene. The advantage of spodumene as a lithium source compared to brine sources is the higher lithium concentration, but at a higher extraction cost. [ 11 ]
In 2016, the price of spodumene concentrate was forecast to be $500–600/ton for years to come. [ 12 ] However, price spiked above $800 in January 2018, and production increased more than consumption, resulting in the price declining to $400 by September 2020. [ 13 ] [ 14 ]
World production of lithium via spodumene was around 80,000 metric tonnes per annum in 2018, primarily from the Greenbushes pegmatite of Western Australia and from some Chinese and Chilean sources. The Talison Minerals mine in Greenbushes, Western Australia (involving Tianqi Lithium , Albemarle Corporation , and Global Advanced Metals ), is reported to be the world's second-largest and to have the highest grade of ore at 2.4% Li 2 O (2012 figures). [ 15 ]
In 2020, Australia expanded spodumene mining to become the leading lithium-producing country in the world. [ 16 ]
An important economic concentrate of spodumene, known as spodumene concentrate 6 or SC6 , is a high-purity lithium ore with around 6% lithium content being produced as a raw material for the subsequent production of lithium-ion batteries for electric vehicles. [ 17 ] [ 18 ]
Extraction of lithium from spodumene, often SC6, is challenging due to the tight binding of lithium in the crystal structure .
Traditional lithium refining in the 2010s involves acid leaching of lithium-containing ores, precipitation of impurities, concentration of the lithium solution, and then conversion to lithium carbonate or lithium hydroxide . These refining methods result in significant quantities of caustic waste effluent and tailings , which are usually either highly acidic or alkali. [ 11 ] Suitable extraction reagents include alkali metal sulfates, such as sodium sulfate , sodium carbonate , chlorine , or hydrofluoric acid . [ 19 ]
Another processing method relies on pyrometallurgical processing of SC6—roasting at high temperatures exceeding 800 °C (1,470 °F) to convert the spodumene from the tightly bound alpha structure to a more open beta structure from which the lithium is more easily extracted—then cooling and reacting with various reagents in a sequence of hydrometallurgical processing steps. Some offer the use of noncaustic reagents and result in reduced waste streams, potentially allowing the use of a closed-loop refining process. [ 20 ] Tesla has developed and, as of 2025, is operationalizing at scale, this process of lithium refinement that does not require strong acids to extract lithium from spodumene. Their method mixes sodium chloride with the open-beta-structure spodumene concentrate and water. Agitation at high temperatures produces a slurry rich in lithium that can be filtered and purified into lithium hydroxide . The sands and limestone waste products can be repurposed as construction materials. A $375 million Tesla refinery plant located on 1,200 acres in Robstown, Texas , is under construction using this process. It began partial operation in December 2024. The site was chosen for its proximity to the Port of Corpus Christi , where spodumene can easily be imported. [ 21 ]
A common form of more highly refined lithium from both of the above processes is lithium hydroxide, commonly used as an input in the battery industry to manufacture lithium-ion (Li-ion) battery cathode material.
Hiddenite is a pale, emerald-green gem variety first reported from Alexander County, North Carolina , U.S. [ 22 ] It was named in honor of William Earl Hidden (16 February 1853 – 12 June 1918), mining engineer, mineral collector, and mineral dealer. [ 23 ] [ additional citation(s) needed ]
This emerald-green variety of spodumene is colored by chromium, just as for emeralds . Some green spodumene is colored with substances other than chromium; such stones tend to have a lighter color; they are not true hiddenite.
Kunzite is a purple-colored gemstone , a variety of spodumene, with the color coming from minor to trace amounts of manganese . Exposure to sunlight can fade its color. [ 23 ]
Kunzite was discovered in 1902, and was named after George Frederick Kunz , Tiffany & Co 's chief jeweler at the time, and a noted mineralogist. [ 23 ] It has been found in Brazil, the U.S., Canada, CIS , Mexico , Sweden, Western Australia, Afghanistan, and Pakistan . [ 23 ] [ 24 ]
Triphane is the name used for yellowish varieties of spodumene. [ 25 ] | https://en.wikipedia.org/wiki/Lithium_refining |
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