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Signs Of LIfe Detector ( SOLID ) is an analytical instrument under development to detect extraterrestrial life in the form of organic biosignatures obtained from a core drill during planetary exploration.
The instrument is based on fluorescent immunoassays and it is being developed by the Spanish Astrobiology Center (CAB) in collaboration with the NASA Astrobiology Institute . SOLID is currently undergoing testing for use in astrobiology space missions that search for common biomolecules that may indicate the presence of extraterrestrial life, past or present. The system was validated in field tests and engineers are looking into ways to refine the method and miniaturize the instrument further.
Modern astrobiology inquiry has emphasized the search for water on Mars , chemical biosignatures in the permafrost , soil and rocks at the planet's surface, and even biomarker gases in the atmosphere that may give away the presence of past or present life. [ 2 ] [ 3 ] The detection of preserved organic molecules of unambiguous biological origin is fundamental for the confirmation of present or past life, [ 4 ] but the 1976 Viking lander biological experiments failed to detect organics on Mars, and it is suspected it was because of the combined effects of heat applied during analysis and the unexpected presence of oxidants such as perchlorates in the Martian soil. [ 5 ] [ 6 ] The recent discovery of near surface ground ice on Mars supports arguments for the long-term preservation of biomolecules on Mars. [ 7 ]
SOLID demonstrated that antibodies are unaffected by acidity, heat and oxidants such as perchlorates, and it has emerged as a viable choice for an astrobiology mission directly searching for biosignatures. [ 1 ]
For a time, the ExoMars' Rosalind Franklin rover was planned to carry a similar instrument called Life Marker Chip. [ 8 ] [ 9 ]
SOLID was designed for automatic in situ detection and identification of substances from liquid and crushed samples under the conditions of outer space. [ 1 ] [ 10 ] The system uses hundreds of carefully selected antibodies to detect lipids, proteins , polysaccharides , and nucleic acids . These are complex biological polymers that could only be synthesized by life forms, and are therefore strong indicators — biosignatures — of past or present life.
SOLID consists of two separate functional units: a Sample Preparation Unit (SPU) for extractions by ultrasonication , and a Sample Analysis Unit (SAU), for fluorescent immunoassays . [ 10 ] The antibody microarrays are separated in hundreds of small compartments inside a biochip only a few square centimeters in size. [ 1 ]
SOLID instrument is able to perform both "sandwich" and competitive immunoassays using hundreds of well characterized and highly specific antibodies. [ 4 ] The technique called "sandwich immunoassay" is a non-competitive immunoassay in which the analyte (compound of interest in the unknown sample) is captured by an immobilized antibody, then a labeled antibody is bound to the analyte to reveal its presence. [ 1 ] In other words, the "sandwich" quantify antigens (i.e. biomolecules ) between two layers of antibodies (i.e. capture and detection antibody). For the competitive assay technique, unlabeled analyte displaces bound labelled analyte, which is then detected or measured.
An optical system is set up so that a laser beam excites the fluorochrome label and a CCD detector captures an image of the microarray that can be measured. [ 11 ]
The instrument is able to detect a broad range of molecular size compounds, from the amino acid size, peptides , proteins , to whole cells and spores , with sensitivities at 1–2 ppb (ng/mL) for biomolecules and 104 to 103 spores per milliliter. [ 1 ] [ 10 ] Some compartments in the microarray are reserved for samples of known nature and concentrations, that are used as controls for reference and comparison. SOLID instrument concept avoids the high-temperature treatments of other techniques that may destroy organic matter in the presence of Martian oxidants such as perchlorates . [ 1 ]
A field prototype of SOLID was first tested in 2005 in a simulated Mars drilling expedition called MARTE (Mars Analog Rio Tinto Experiment) [ 10 ] [ 11 ] [ 12 ] where the researchers tested a drill 10 m (33 ft) in depth, sample-handling systems, and immunoassays relevant to the search for life in the Martian subsurface. MARTE was funded by the NASA Astrobiology Science and Technology for Exploring Planets (ASTEP) program. [ 7 ] Using the sample cores, SOLID successfully detected several biological polymers in extreme environments in different parts of the world, including a deep South African mine, Antarctica's McMurdo Dry Valleys , Yellowstone , Iceland , Atacama Desert in Chile, and in the acid water of Rio Tinto . [ 10 ] [ 13 ]
Extracts obtained from Mars analogue sites on Earth were added to various perchlorate concentrations at −20 °C for 45 days and then the samples were analyzed with SOLID. [ 1 ] The results showed no interference from acidity or from the presence of 50 mM perchlorate which is 20 times higher than that found at the Phoenix landing site. [ 1 ] SOLID demonstrated that the chosen antibodies are unaffected by acidity, heat and oxidants such as perchlorates, and it has emerged as a viable choice for an astrobiology mission directly searching for biosignatures. [ 1 ]
In 2018, another field test took place at the Atacama Desert with a rover called ARADS (Atacama Rover Astrobiology Drilling Studies) that carried a core drill, SOLID instrument, and another life detection system called Microfluidic Life Analyzer (MILA). [ 14 ] MILA processes minuscule volumes of fluid samples to isolate amino acids , which are building blocks of proteins . The rover tested different strategies for searching for potential evidence of life in the soil, and established that roving, drilling and life detection can take place in concert. [ 14 ]
These tests validated the system for planetary exploration. [ 13 ] Some improvements to be addressed in the future are instrument miniaturization, extraction protocols, and antibody stability under outer space conditions. [ 4 ] [ 11 ] SOLID would be one of the payloads of the proposed Icebreaker Life to Mars, [ 15 ] [ 16 ] [ 17 ] or a lander to Europa . [ 18 ] | https://en.wikipedia.org/wiki/Signs_Of_LIfe_Detector |
Sigrid Doris Peyerimhoff (born 12 January 1937, in Rottweil ) is a theoretical chemist and Emeritus Professor at the Institute of Physical and Theoretical Chemistry, University of Bonn , Germany .
1988 Gottfried Wilhelm Leibniz-Prize
1994 Cross of Merit of the Federal Republic of Germany
2007 Cothenius-Medaille of the Academy of Sciences Leopoldina
2008 Grand Cross of Merit of the Federal Republic of Germany
University of Chicago , University of Washington , Princeton University , University of Mainz ,
After completing her abitur , Peyerimhoff studied physics at the University of Gießen , completing her degree in 1961 and receiving her doctorate under supervision of Bernhard Kockel in 1963. [ 1 ] After researching at the University of Chicago , the University of Washington , and Princeton University , she returned to Germany and gained her habilitation at the University of Gießen in 1967. She became professor for theoretical chemistry at the University of Mainz in 1970, and at the University of Bonn in 1972.
Her contributions have been to the development of ab initio quantum chemical methods, in particular, multireference configuration interaction , and to their application in many fields of physics and chemistry. Particular emphasis has been given to electronically excited states , molecular spectra and photochemistry . Many studies are on atmospheric molecules and ions, their lifetimes in excited states and decomposition due to radiative and non-radiative processes, and on stability and spectra of clusters.
Some of her students became well known for their contribution to quantum chemistry, including Bernd Engels , Stefan Grimme , Bernd A. Hess , Christel Marian , Matthias Ernzerhoff and Bernd M. Nestmann .
During her career, she received several awards and memberships:
She is also a member of the International Academy of Quantum Molecular Science
She is the author of over 400 original articles in various international journals [ 5 ] and coauthor of Umweltstandards: Fakten und Bewertungsprobleme am Beispiel des Strahlenrisikos . Her history of computational chemistry in Germany is of particular note. [ 6 ] She edited Interactions in Molecules . [ 7 ] | https://en.wikipedia.org/wiki/Sigrid_D._Peyerimhoff |
Sybren Otto (Groningen, 3 August 1971) is Professor of Systems chemistry at the Stratingh Institute for Chemistry , University of Groningen .
Otto studied chemistry at the University of Groningen and in 1994, he received his Master's degree , focusing on physical organic chemistry and biochemistry , with the distinction cum laude . In 1998, he obtained his PhD , again with the distinction cum laude, from his supervisor Prof. Jan B.F.N. Engberts for his thesis entitled Catalysis of Diels-Alder reactions in water.
After his subsequent research in both the United States (in 1998, with Prof. Steven L. Regen) at Lehigh University and in the United Kingdom (first with Prof. Jeremy K.M. Sanders and then, from 2001 onwards, as a Royal Society University Research Fellow , both at the University of Cambridge ), he was appointed assistant professor at the University of Groningen in 2009. In 2011, he was promoted to associate professor and in 2016, to full professor . [ 1 ] From 2014 to 2019, he coordinated the master's degree programme in chemistry.
Alongside his work at the university, Otto is also one of the six principal investigators of the Dutch national gravity programme for functional molecular systems (FMS; €26 million, over 10 years, 2013–2023). [ 2 ] The ambition of this programme is to gain control over molecular self-assembly . With this technology, nanomotors could be made, for example, or biomaterials to repair damaged bodily tissues .
Otto was the lead applicant and chair of the European Cooperation in Science & Technology (COST) Action CM1304 (Emergence and Evolution of Complex Chemical Systems), which united more than 95 European research groups. [ 3 ] He is the chair of the Gordon Research Conference on Systems Chemistry 2020 [ 4 ] and is editor-in-chief of the Journal of Systems Chemistry . [ 5 ]
Otto is a member of the Royal Dutch Chemical Society (KNCV), fellow of the Royal Society of Chemistry and member of the American Chemical Society . He is member of the steering committee of the Origins Center. [ 6 ] The Origins Center is a Dutch research platform for scientists who are involved in the key questions of the Dutch Research Agenda on the origin, evolution and future of life on Earth and in the universe. [ 7 ] Otto is active on several fronts in both the Netherlands and abroad. [ 8 ] Otto was elected a member of the Royal Netherlands Academy of Arts and Sciences in 2020. [ 9 ]
The research conducted by Otto and his research group is focused on various fields, varying from the origin of life ( self-replicating systems and the Darwinian evolution thereof ), to materials chemistry (self- synthesizing fibres , hydrogels and nanoparticle surfaces). [ 10 ]
Specific interests include self-replicating molecules , foldamers , catalysis , molecular recognition of biomolecules and self-synthesizing materials (materials of which their self-assembly drives the synthesis of the molecules that assemble). The complex chemical mixtures that are designed, made and researched often display new properties that are relevant to understanding how new traits are able to arise in nature. The final goal of all of this research is the de novo synthesis of new forms of life via the integration of self-replicating systems with metabolism and compartmentalization . [ 11 ] [ 12 ] His 114 publications have been cited a total of 8,873 times by other scientists. His h-index is 51. [ 13 ] | https://en.wikipedia.org/wiki/Sijbren_Otto |
Sikta Irrigation Project is one of the National Pride Projects of Nepal. [ 1 ] The intake is in the Rapti river in western Nepal . There are two canals with the capacity of 50 m3/s each. The length of canal is 45.25 kilometres in the western section and 53 kilometres in the eastern section. The canals are constituted into 3 phases. [ 2 ] As of 2019, 60% of the project has been completed.
The feasibility study of the project was done by Lahmeyer International GmbH from Germany in 1980. In 1983, the Department of Hydrology and Metrology revised the study. In 2004, the Irrigation Development Programme under the European Union concluded that the project is feasible which led the government to start the project by its own resources.
The initial project cost in 2005-06 was NPR 12.8 billion and estimated to be completed by 2014–15. The project is still under construction and is estimated to be complete by 2020. The project is expected to rise to NPR 25.02 billion. [ 3 ] In 2019, the project completion was 60%. [ 4 ]
The contractor for construction is CTC Kalika Joint Venture Pvt Ltd. The project targets to irrigate 42,000 hectares of land in Banke District .
The national Commission for Investigation of Abuse of Authority (CIAA) has lodged a corruption case of over NPR 2 billion in this project. The case was filed against former minister and chief of Kalika Construction Bikram Pandey over the construction of a canal and 20 other staffs. CIAA has made claims of Rs 2.13 billion from Bikram Pandey, NPR 1.56 billion from Dilip Bahadur Karki and NPR 593.45 million from Saroj Chandra Pandit. It also claims Rs 24.05 million from Uddhav Raj Chaulagai, the managing director of the consulting company (ERMC). [ 8 ] [ 9 ] | https://en.wikipedia.org/wiki/Sikta_Irrigation_Project |
Silane ( Silicane ) is an inorganic compound with chemical formula SiH 4 . It is a colorless, pyrophoric gas with a sharp, repulsive, pungent smell, somewhat similar to that of acetic acid . [ 6 ] Silane is of practical interest as a precursor to elemental silicon . Silanes with alkyl groups are effective water repellents for mineral surfaces such as concrete and masonry. Silanes with both organic and inorganic attachments are used as coupling agents. They are commonly used to apply coatings to surfaces or as an adhesion promoter. [ 7 ]
Silane can be produced by several routes. [ 8 ] Typically, it arises from the reaction of hydrogen chloride with magnesium silicide :
It is also prepared from metallurgical-grade silicon in a two-step process. First, silicon is treated with hydrogen chloride at about 300 °C to produce trichlorosilane , HSiCl3, along with hydrogen gas, according to the chemical equation
The trichlorosilane is then converted to a mixture of silane and silicon tetrachloride :
This redistribution reaction requires a catalyst.
The most commonly used catalysts for this process are metal halides , particularly aluminium chloride . This is referred to as a redistribution reaction, which is a double displacement involving the same central element. It may also be thought of as a disproportionation reaction, even though there is no change in the oxidation number for silicon (Si has a nominal oxidation number IV in all three species). However, the utility of the oxidation number concept for a covalent molecule [ vague ] , even a polar covalent molecule, is ambiguous. [ citation needed ] The silicon atom could be rationalized as having the highest formal oxidation state and partial positive charge in SiCl 4 and the lowest formal oxidation state in SiH 4 , since Cl is far more electronegative than is H. [ citation needed ]
An alternative industrial process for the preparation of very high-purity silane, suitable for use in the production of semiconductor-grade silicon, starts with metallurgical-grade silicon, hydrogen, and silicon tetrachloride and involves a complex series of redistribution reactions (producing byproducts that are recycled in the process) and distillations. The reactions are summarized below:
The silane produced by this route can be thermally decomposed to produce high-purity silicon and hydrogen in a single pass.
Still other industrial routes to silane involve reduction of silicon tetrafluoride ( SiF 4 ) with sodium hydride (NaH) or reduction of SiCl 4 with lithium aluminium hydride ( LiAlH 4 ).
Another commercial production of silane involves reduction of silicon dioxide ( SiO 2 ) under Al and H 2 gas in a mixture of NaCl and aluminum chloride ( AlCl 3 ) at high pressures: [ 9 ]
In 1857, the German chemists Heinrich Buff and Friedrich Woehler discovered silane among the products formed by the action of hydrochloric acid on aluminum silicide, which they had previously prepared. They called the compound siliciuretted hydrogen . [ 10 ]
For classroom demonstrations, silane can be produced by heating sand with magnesium powder to produce magnesium silicide ( Mg 2 Si ), then pouring the mixture into hydrochloric acid. The magnesium silicide reacts with the acid to produce silane gas, which burns on contact with air and produces tiny explosions. [ 11 ] This may be classified as a heterogeneous [ clarification needed ] acid–base chemical reaction, since the isolated Si 4− ion in the Mg 2 Si antifluorite structure can serve as a Brønsted–Lowry base capable of accepting four protons. It can be written as
In general, the alkaline-earth metals form silicides with the following stoichiometries : M II 2 Si , M II Si , and M II Si 2 . In all cases, these substances react with Brønsted–Lowry acids to produce some type of hydride of silicon that is dependent on the Si anion connectivity in the silicide. The possible products include SiH 4 and/or higher molecules in the homologous series Si n H 2 n +2 , a polymeric silicon hydride, or a silicic acid . Hence, M II Si with their zigzag chains of Si 2− anions (containing two lone pairs of electrons on each Si anion that can accept protons) yield the polymeric hydride (SiH 2 ) x .
Yet another small-scale route for the production of silane is from the action of sodium amalgam on dichlorosilane , SiH 2 Cl 2 , to yield monosilane along with some yellow polymerized silicon hydride (SiH) x . [ 12 ]
Silane is the silicon analogue of methane . All four Si−H bonds are equal and their length is 147.98 pm . [ 13 ] Because of the greater electronegativity of hydrogen in comparison to silicon, this Si–H bond polarity is the opposite of that in the C–H bonds of methane. One consequence of this reversed polarity is the greater tendency of silane to form complexes with transition metals. A second consequence is that silane is pyrophoric — it undergoes spontaneous combustion in air, without the need for external ignition. [ 14 ] However, the difficulties in explaining the available (often contradictory) combustion data are ascribed to the fact that silane itself is stable and that the natural formation of larger silanes during production, as well as the sensitivity of combustion to impurities such as moisture and to the catalytic effects of container surfaces causes its pyrophoricity. [ 15 ] [ 16 ] Above 420 °C (788 °F), silane decomposes into silicon and hydrogen ; it can therefore be used in the chemical vapor deposition of silicon.
The Si–H bond strength is around 384 kJ/mol, which is about 20% weaker than the H–H bond in H 2 . Consequently, compounds containing Si–H bonds are much more reactive than is H 2 . The strength of the Si–H bond is modestly affected by other substituents: the Si–H bond strengths are: SiHF 3 419 kJ/mol, SiHCl 3 382 kJ/mol, and SiHMe 3 398 kJ/mol. [ 17 ] [ 18 ]
While diverse applications exist for organosilanes , silane itself has one dominant application, as a precursor to elemental silicon, particularly in the semiconductor industry. The higher silanes, such as di- and trisilane, are only of academic interest. About 300 metric tons per year of silane were consumed in the late 1990s. [ needs update ] [ 16 ] Low-cost solar photovoltaic module manufacturing has led to substantial consumption of silane for depositing hydrogenated amorphous silicon (a-Si:H) on glass and other substrates like metal and plastic. The plasma-enhanced chemical vapor deposition (PECVD) process is relatively inefficient at materials utilization with approximately 85% of the silane being wasted. To reduce the waste and ecological footprint of a-Si:H-based solar cells further, several recycling efforts have been developed. [ 19 ] [ 20 ]
A number of fatal industrial accidents produced by combustion and detonation of leaked silane in air have been reported. [ 21 ] [ 22 ] [ 23 ]
Silane is a pyrophoric gas (capable of autoignition at temperatures below 54 °C or 129 °F). [ 24 ]
For lean mixtures a two-stage reaction process has been proposed, which consists of a silane consumption process and a hydrogen oxidation process. The heat of SiO 2 (s) condensation increases the burning velocity due to thermal feedback. [ 25 ]
Diluted silane mixtures with inert gases such as nitrogen or argon are even more likely to ignite when leaked into open air, compared to pure silane: even a 1% mixture of silane in pure nitrogen easily ignites when exposed to air. [ 26 ]
In Japan, in order to reduce the danger of silane for amorphous silicon solar cell manufacturing, several companies began to dilute silane with hydrogen gas. This resulted in a symbiotic benefit of making more stable solar photovoltaic cells as it reduced the Staebler–Wronski effect . [ citation needed ]
Unlike methane, silane is slightly toxic: the lethal concentration in air for rats ( LC 50 ) is 0.96% (9,600 ppm) over a 4-hour exposure. In addition, contact with eyes may form silicic acid with resultant irritation. [ 27 ]
In regards to occupational exposure of silane to workers, the US National Institute for Occupational Safety and Health has set a recommended exposure limit of 5 ppm (7 mg/m 3 ) over an eight-hour time-weighted average. [ 28 ] | https://en.wikipedia.org/wiki/Silane |
Silanization of silicon and mica is the coating of these materials with a thin layer of self assembling units.
Nanoscale analysis of proteins using atomic force microscopy (AFM) requires surfaces with well-defined topologies and chemistries for many experimental techniques. Biomolecules, particularly proteins, can be immobilized simply on an unmodified substrate surface through hydrophobic or electrostatic interactions. [ 1 ] However, several problems are associated with physical adsorption of proteins on surfaces. With metal surfaces, protein denaturation, unstable and reversible binding, nonspecific and random immobilization of protein have been reported. [ 2 ]
One alternative involves the interaction of chemically modified surfaces with proteins under non-denaturing circumstances. [ 2 ] Chemical modification of surfaces provides the potential to precisely control the chemistry of the surface, and with the correct chemical modifications, there are several advantages to this approach. First, the proteins adsorbed on the surface are more stable over a wide range of conditions. The proteins also adopt a more uniform orientation on the surface. Additionally, the higher density of protein deposition with greater reproducibility is possible.
Chemical modification of surfaces has been successfully applied in several instances to immobilize biomolecules in order to obtain valuable information. For instance, atomic force microscopy imaging of DNA has been performed using mica coated with 3-aminopropyltriethoxysilane ( APTES ). The negatively charged DNA backbone bound strongly to the positive charges on the amine functionality, leading to stable structures that could be imaged both in air and in buffer. [ 3 ] In a recent study by Behrens et al., amine-terminated silicon surfaces were successfully used to immobilize bone morphogenetic protein 2 (BMP2) for medical purposes (cf. hydrogen-terminated silicon surface ). [ 4 ] Molecules with amine groups (especially APTES) are important for biological applications, because they allow for simple electrostatic interactions with biomolecules. [ 5 ]
Self-assembled monolayers (SAM) are an extremely versatile approach that allows for precise control of surface characteristics. It was introduced in 1946 by Bigelow et al., [ 6 ] but it was not until 1983 that it attracted widespread interest, when the formation of SAMs of alkanethiolates on gold was reported by Allara et al. [ 7 ] Self-assembly of monolayers can be achieved using several systems. The basis for self-assembly is the formation of a covalent bond between the surface and the molecule forming the layer; and this requirement can be fulfilled using a variety of chemical groups such as organosilanes at hydroxylated materials (glass, silicon, aluminium oxide, mica) and organosulfur-based compounds species at noble metals . [ 7 ] [ 8 ] [ 9 ] While the latter system has been well characterized, much less is known about the behavior of organosilane layers on surfaces and the underlying mechanisms that control monolayer organization and structure.
Although silanization of silicate surfaces was introduced more than 40 years ago, the process of formation of smooth layers on surfaces is still poorly understood. Probably the most important reason for this situation is that a number of studies that have involved silanization as part of the procedure have not been concerned with thoroughly characterizing the silane layer formed. The one result that unifies recent studies on the characterization of silane layers is centered on the extreme sensitivity of the reactions that lead to the formation of silane layers. [ 9 ] Indeed, self-assembled layers of silanes on silicate surfaces have been reported to be dependent on various parameters such as humidity, temperature, impurities in the silane reagent and the type of silicate surface. In order to consistently and reproducibly make diverse functionalized surfaces with layers that are molecularly smooth, it is critical to understand the chemistry of the silicate surfaces and the ways in which various parameters affect the nature of the self-assembled layers.
Oxidized silicon has been extensively studied as a substrate for the deposition of biomolecules. Piranha solution can be used to increase the surface density of reactive hydroxyl groups on the surface of silicon. The –OH groups can hydrolyze and subsequently form siloxane linkages (Si-O-Si) with organic silane molecules. Preparation of silicon surfaces for silanization involves the removal of surface contaminants. This can be achieved by using UV-ozone and piranha solution . Piranha solution in particular constitutes quite a harsh treatment that can potentially damage the integrity of the silicon surface. Finlayson-Pitts et al. investigated the effect of certain treatments on silicon and concluded that both the roughness (3-5 Å) and the presence of scattered large particles were preserved after 1 cycle of plasma-treatment. [ 10 ] However, the silicon surface was significantly damaged after 30 cycles of treatment with piranha solution or plasma. In both cases, treatment introduced irregularities and large aggregates on the surface (aggregate size > 80 nm), with the effect being more pronounced when piranha was used. In either case, multiple treatments rendered the surface inadequate for deposition of small biomolecules.
Mica is another silicate that is widely used as substrate for the deposition of biomolecules. Mica bears a noticeable advantage over silicon because it is molecularly smooth and hence better suited for studies of small, flat molecules. [ 11 ] It has a crystalline structure with generic formula K[Si3Al]O10Al2(OH)2 and contains sheets of octahedral hydroxyl-aluminum sandwiched between two silicon tetrahedral layers. [ 12 ] In the silicon layer, one in four silicon atoms is replaced by an aluminum atom, generating a difference in charge that is offset by unbound K+ present in the region between neighboring silicon layers. [ 12 ] Muscovite mica is most susceptible to cleavage along the plane located in the potassium layer. When a freshly cleaved mica surface is placed in contact with water, hydrated potassium ions can desorb from the mica surface, leading to a negative charge at the surface.
Similar to silicon, the surface of mica does not contain an appreciable density of silanol groups for covalent attachment by silanes. [ 11 ] A recent study reported that freshly cleaved mica carries 11% silanol groups (i.e., approximately 1 in 10 silicon atoms bears a hydroxyl group). [ 12 ] Although it is possible that silanization may be carried out using untreated mica, the increased density of surface silanol groups on activated mica can significantly improve covalent attachment of silane molecules to the surface. Mica can be activated by treatment with argon/water plasma, leading to a silanol surface density of 30%. [ 12 ] [ 13 ] Working with activated surfaces introduces another consideration about the stability of the silanol groups on the activated surfaces. Giasson et al. reported that the silanol groups on freshly cleaved mica that was not subjected to any treatment were found to be more stable under high vacuum compared to the plasma-activated mica: after 64 hrs, surface coverage of the silanol groups for freshly cleaved mica plasma was roughly the same, while surface coverage for activated mica decreased 3-fold to 10%. [ 12 ]
Adsorption describes the process by which molecules or particles bind to surfaces and is distinguishable from absorption , whereby the particles spread in the bulk of the absorbing material. The adsorbed material is called the adsorbate, while the surface is called the adsorbent. It is common to distinguish between two types of adsorption, namely physical adsorption (which consists of intermolecular forces holding the adsorbed material to the surface) and chemical adsorption (which consists of covalent bonds tethering the adsorbed material to the surface). The nature of the layer of adsorbate formed depends on the interactions between the adsorbed material and the adsorbent. [ 14 ] More specifically, the mechanisms involved in adsorption include ion exchange (replacement of counter ions adsorbed from the solution by similarly charged ions), ion pairing (adsorption of ions from solution phase onto sites on the substrates that carry the opposite charge), hydrophobic bonding (non-polar attraction between groups on the substrate surface and molecules in solution), polarization of p-electrons polar interactions between partially charged sites on the substrate surface and molecules carrying opposite partial charges in solution, and covalent bonds. [ 9 ] [ 15 ] The variety of ways for adsorption to occur provides an indication of the complexities associated with controlling the type of layer that is adsorbed.
The type of silane used can further compound the problem, as in the case of APTES. APTES is the classical molecule used for the immobilization of biomolecules and has historically been the most widely studied molecule in the field by far. Since APTES contains three ethoxy groups per molecule, it can polymerize in the presence of water, leading to lateral polymerization between APTES molecules in horizontal and vertical directions and the formation of oligomers and polymers which can attach to the surface.
Self-assembly can be approached using solution-phase reactions or vapor-phase reactions. In solution-phase experiments, the silane is dissolved in an anhydrous solvent and placed in contact with the surface; in vapor-phase experiments, only the vapor of the silane reaches the substrate surface. [ 9 ]
Solution-phase reaction has historically been the method that has been most studied, and a general consensus that has evolved with regards to the conditions required for the formation of smooth aminosilane films includes the following: (1) an anhydrous solvent such as toluene is required, with a rigidly controlled trace amount of water to regulate the degree of polymerization of aminosilanes at the surface and in solution; (2) formation of oligomers and polymers is favored at higher silane concentrations (>10%); (3) moderate temperatures (60–90 °C) can disrupt non-covalent interactions such as hydrogen bonds, leading to fewer silane molecules that are weakly tethered to the surface. Additionally, condition (3) favors desorption of water from the substrate into the toluene phase20; (4) Rinsing with solvents such as toluene, ethanol and water following the silanization reaction favors the removal of weakly bonded silane molecules and the hydrolysis of residual alkoxy linkages in the layer; (5) drying and curing at high temperature (110 °C) favors the formation of siloxane linkages and also converts ammonium ions to the neutral amine, which is more reactive. [ 9 ]
Vapor-phase silanization has been approached as a way to circumvent the complexities of trace water in solution and silane purity. [ 9 ] Since oligomers and polymers of silanes have negligible vapor pressure at the reaction temperatures commonly used, they do not reach the surface of the silicate during deposition. Since there is no solvent in the system, it is easier to control the amount of water in the reaction. Smooth monolayers have been reported for vapor-phase silanizations of several types of silanes, including aminosilanes, octadecyltrimethoxysilane and fluoalkyl silanes. However, the nature of the attachment of the silane molecules to the substrate is uncertain, although siloxane bond formation can be favored by soaking the substrate in water following deposition.
In a recent study by Chen et al., APTES monolayers were obtained consistently at different temperatures and deposition times. The thicknesses of the layers obtained were 5 Å and 6 Å at 70 °C and 90 °C respectively, which corresponds to the approximate length of an APTES molecule and indicates that monolayers formed on the substrates in each case. [ 9 ] | https://en.wikipedia.org/wiki/Silanization_of_silicon_and_mica |
Silence compression is an audio processing technique used to effectively encode silent intervals, reducing the amount of storage or bandwidth needed to transmit audio recordings.
Silence can be defined as audio segments with negligible sound. Examples of silence are pauses between words or sentences in speech and pauses between notes in music. By compressing the silent intervals, the audio files become smaller and easier to handle, store, and send while still retaining the original sound quality. While techniques vary, silence compression is generally achieved through two crucial steps: detection of the silent intervals and the subsequent compression of those intervals. Applications of silence compression include telecommunications , audio streaming, voice recognition, audio archiving, and media production. [ 1 ]
Trimming is a method of silence compression in which the silent intervals are removed altogether. This is done by identifying audio intervals below a certain amplitude threshold, indicating silence, and removing that interval from the audio. A drawback of trimming is that it permanently changes the original audio and can cause noticeable artifacts when the audio is played back. [ 1 ]
Amplitude threshold trimming removes silence through the setting of an amplitude threshold in which any audio segments that fall below this threshold are considered silent and are truncated or completely removed. Some common amplitude threshold trimming algorithms are: [ citation needed ]
Energy -based trimming works through the analysis of an audio signal's energy levels. The energy level of an audio signal is the magnitude of the signal over a short time interval. A common formula to calculate the audio's energy is E = ∑ k = 1 N ( x ( k ) ) 2 {\displaystyle E=\sum _{k=1}^{N}(x(k))^{2}} , where E {\displaystyle E} is the energy of the signal, N {\displaystyle N} is the samples within the audio signal, and x ( k ) {\displaystyle x(k)} is the k {\displaystyle k} th sample's signal amplitude. Once the energy levels are calculated, a threshold is set in which all energy levels that fall below the threshold are considered to be silent and removed. Energy-based trimming can detect silence more accurately than amplitude-based trimming as it considers the overall power output of the audio as opposed to just the amplitude of the sound wave. Energy-based trimming is often used for voice/speech files due to the need to only store and transmit the relevant portions that contain sound. Some popular energy-based trimming algorithms include the Short-Time Energy (STE) and Zero Crossing Rate (ZCR) methods. [ 2 ] Similarly, those algorithms are also used in voice activity detection (VAD) to detect speech activity. [ 1 ] [ 3 ]
Silence suppression is a technique used within the context of Voice over IP (VoIP) and audio streaming to optimize the rate of data transfer. Through the temporary reduction of data in silent intervals, Audio can be broadcast over the internet in real-time more efficiently. [ 1 ] [ 3 ]
DTX works to optimize bandwidth usage during real-time telecommunications by detecting silent intervals and suspending the transmission of those intervals. Through continuously monitoring the audio signal, DTX algorithms can detect silence based on predefined criteria. When silence is detected, a signal is sent to the receiver which stops the transmission of audio data. When speech/sound is resumed, audio transmission is reactivated. This technique allows for uninterrupted communication while being highly efficient in the use of network resources. [ 1 ] [ 3 ]
Silence Encoding is essential for the efficient representation of silent intervals without the removal of silence altogether. This allows for the minimization of data needed to encode and transmit silence while upholding the audio signal's integrity. [ 4 ] [ 5 ] [ 6 ] There are several encoding methods used for this purpose:
RLE works to detect repeating identical samples in the audio and encodes those samples in a way that is more space-efficient. Rather than storing each identical sample individually, RLE stores a single sample and keeps count of how many times it repeats. RLE works well in encoding silence as silent intervals often consist of repeated sequences of identical samples. The reduction of identical samples stored subsequently reduces the size of the audio signal. [ 4 ] [ 5 ]
Huffman coding is an entropy encoding method and variable-length code algorithm that assigns more common values with shorter binary codes that require fewer bits to store. Huffman coding works in the context of silence compression by assigning frequently occurring silence patterns with shorter binary codes, reducing data size. [ 5 ] [ 6 ]
Differential encoding makes use of the similarity between consecutive audio samples during silent intervals by storing only the difference between samples. Differential encoding is used to efficiently encode the transitions between sound and silence and is useful for audio samples where silence is interspersed with active sound. [ 7 ] [ 8 ] [ 9 ] Some differential encoding algorithms include:
Delta modulation quantizes and encodes differences between consecutive audio samples by encoding the derivative of the audio sample's amplitude. By storing how the audio signal changes over time rather than the samples itself, the transition from silence to sound can be captured efficiently. Delta modulation typically uses a one-bit quantization mechanism, where 1 indicates an increase in the sample size and 0 indicates a decrease. While this allows for efficient use of bandwidth or storage, it is unable to provide high-fidelity encoding of low-amplitude signals. [ 8 ]
Delta-Sigma modulation is a more advanced variant of Delta modulation which allows for high-fidelity encodings for low-amplitude signals. This is done through quantizing at a high oversampling rate, allowing for a precise encoding of slight changes in the audio signal. Delta-sigma modulation is used in situations where maintaining a high audio fidelity is prioritized. [ 9 ]
The reduction of audio size from silence compression has uses in numerous applications: | https://en.wikipedia.org/wiki/Silence_compression |
In genetics , a silencer is a DNA sequence capable of binding transcription regulation factors , called repressors . DNA contains genes and provides the template to produce messenger RNA (mRNA). That mRNA is then translated into proteins. When a repressor protein binds to the silencer region of DNA, RNA polymerase is prevented from transcribing the DNA sequence into RNA. With transcription blocked, the translation of RNA into proteins is impossible. Thus, silencers prevent genes from being expressed as proteins. [ 1 ]
RNA polymerase, a DNA-dependent enzyme, transcribes the DNA sequences, called nucleotides , in the 3' to 5' direction while the complementary RNA is synthesized in the 5' to 3' direction. RNA is similar to DNA, except that RNA contains uracil, instead of thymine, which forms a base pair with adenine. An important region for the activity of gene repression and expression found in RNA is the 3' untranslated region . This is a region on the 3' terminus of RNA that will not be translated to protein but includes many regulatory regions.
Not much is yet known about silencers but scientists continue to study in hopes to classify more types, locations in the genome, and diseases associated with silencers. [ 2 ] [ 3 ]
A silencer is a sequence-specific element that induces a negative effect on the transcription of its particular gene. There are many positions in which a silencer element can be located in DNA. The most common position is found upstream of the target gene where it can help repress the transcription of the gene. [ 4 ] This distance can vary greatly between approximately -20 bp to -2000 bp upstream of a gene. Certain silencers can be found downstream of a promoter located within the intron or exon of the gene itself. Silencers have also been found within the 3 prime untranslated region (3' UTR) of mRNA. [ 5 ]
Currently, there are two main types of silencers in DNA, which are the classical silencer element and the non-classical negative regulatory element (NRE). In classical silencers, the gene is actively repressed by the silencer element, mostly by interfering with general transcription factor (GTF) assembly. [ 5 ] NREs passively repress the gene, usually by inhibiting other elements that are upstream of the gene. Of the NREs, there are certain silencers that are orientation-dependent meaning that the binding factor binds in a particular direction relative to other sequences. Promoter-dependent silencers are understood to be silencer elements because they are position and orientation-dependent but must also use a promoter-specific factor. [ 5 ] There has been a recent discovery of Polycomb-group Response Elements (PREs), which can allow and inhibit repression depending on the protein bound to it, and the presence of non-coding transcription. [ 4 ]
For classical silencers, the signaling pathway is relatively simple. Since repression is active, silencer elements target the assembly of GTFs, necessary for transcription of the gene. These silencer elements are mostly located upstream of the gene and can vary between short and long distances. For long-range silencers, it has been observed that the DNA will form a loop in order to bring the silencer closer to the promoter and loop out the interfering DNA. [ 4 ] Silencers also target helicase sites in the DNA that are rich in adenine and thymine (AT) and prone to unwinding the DNA, allowing room to initiate transcription. The inhibited helicase activity leads to the inhibition of transcription. This is commonly seen in the human thyrotropin-β gene promoter. NREs can induce a bend in the promoter region to block interactions, as seen when an NRE binds to Yin-Yang 1 ( YY1 ), [ 5 ] and flank regulatory signals or promoter regions as well. When the silencer region is located within an intron, there can be two types of repressions. First, there can be a physical blockage of a splice site. Second, there can be a bend in the DNA that will inhibit RNA processing. [ 5 ]
When located in the exon or the untranslated region, the silencer will mainly be classical or position-dependent. However, these silencers can carry out their activity prior to transcription. [ 5 ] Most silencers are constitutively expressed in organisms, only allowing activation of a gene by either inhibiting the silencer or by activating an enhancer region. The best example of this is the Neuronal-Restrictive Silencer Factor (NRSF) that is produced by the REST gene. The REST gene produces NRSF in order to repress the transcription of neuronal genes that are essential for localization of neuronal tissue. When a silencer represses REST , NRSF is also inhibited, allowing for the transcription of neuronal genes. [ 5 ]
Another regulatory element located upstream of the gene is an enhancer . Enhancers function as a "turn on" switch in gene expression and will activate the promoter region of a particular gene while silencers act as the "turn off" switch. Though these two regulatory elements work against each other, both sequence types affect the promoter region in very similar ways. [ 4 ] Because silencers have not been thoroughly identified and analyzed, the extensive research on enhancers has aided biologists in understanding the mechanics of the silencer. Enhancers can be found in many of the same areas that silencers are found, such as upstream of the promoter by many kilobase pairs, or even downstream within the intron of the gene. [ 4 ] DNA looping is also a model function used by enhancers in order to shorten the proximity of the promoter to the enhancer. Enhancers also function with transcription factors in order to initiate expression, much like silencers can with repressors. [ 4 ]
There are several differences in the regulation of metabolic control in eukaryotes and in prokaryotes. Prokaryotes vary the numbers of specific enzymes made in their cells in order to regulate gene expression, which is slow metabolic control, and also regulate enzymatic pathways through mechanisms such as feedback inhibition and allosteric regulation , which is rapid metabolic control. [ 6 ] The genes of prokaryotes are grouped together based on similar functions into units called operons which consist of a promoter and an operator . The operator is the binding site for the repressor and thus has a function equivalent to the silencer region in Eukaryotic DNA. When a repressor protein is bound to the operator, RNA polymerase cannot bind to the promoter to initiate the transcription of the operon.
The lac operon in the prokaryote E. coli consists of genes that produce enzymes to break down lactose. Its operon is an example of a prokaryotic silencer. The three functional genes in this operon are lacZ, lacY, and lacA. [ 6 ] The repressor gene, lacI, will produce the repressor protein LacI which is under allosteric regulation. These genes are activated by the presence of lactose in the cell which acts as an effector molecule that binds to LacI. When the repressor is bound to lactose, it will not bind to the operator, which allows RNA polymerase to bind to the promoter to initiate transcription of the operon. When the repressor's allosteric site is not bound to lactose, its active site will bind to the operator to prevent RNA polymerase from transcribing the genes of the lac operon.
Eukaryotes have a much larger genome and thus have different methods of gene regulation than in prokaryotes. All cells in a eukaryotic organism have the same DNA but are specified through differential gene expression, a phenomenon known as genetic totipotency . [ 7 ] However, in order for a cell to express the genes for proper functioning, the genes must be closely regulated to express the correct properties. Genes in eukaryotes are controlled on the transcriptional , post-transcriptional , translational , and post-translational levels. [ 8 ] On the transcriptional level, gene expression is regulated by altering transcription rates. Genes that encode proteins include exons which will encode the polypeptides, introns that are removed from mRNA before the translation of proteins, a transcriptional start site in which RNA polymerase binds, and a promoter. [ 9 ]
Eukaryotic genes contain an upstream promoter and a core promoter also referred to as a basal promoter. A common basal promoter is the TATAAAAAA sequence known as the TATA box . The TATA box is a complex with several different proteins including transcription factor II D (TFIID) which includes the TATA-binding protein (TBP) that binds to the TATA box along with 13 other proteins that bind to TBP. The TATA box binding proteins also include the transcription factor II B (TFIIB) which binds to both DNA and RNA polymerases. [ 9 ]
Silencers in eukaryotes control gene expression on a transcriptional level in which the mRNA is not transcribed. These DNA sequences may act as either silencers or enhancers based on the transcription factor that binds to the sequence and binding of this sequence will prevent promoters such as the TATA box from binding to RNA polymerase. [ 7 ] A repressor protein may have regions that bind to the DNA sequence as well as regions that bind to the transcription factors assembled at the promoter of the gene which would create a chromosome looping mechanism. [ 9 ] Looping brings silencers in close proximity to the promoters to ensure that groups of proteins needed for optimal gene expression will work together.
Genetic mutations occur when nucleotide sequences in an organism are altered. These mutations lead to not only observable phenotypic influences in an individual, but also alterations that are undetectable phenotypically. The sources for these mutations can be errors during replication, spontaneous mutations, and chemical and physical mutagens ( UV and ionizing radiation , heat). [ 10 ] Silencers, being encoded in the genome, are susceptible to such alterations which, in many cases, can lead to severe phenotypical and functional abnormalities. In general terms, mutations in silencer elements or regions could lead to either the inhibition of the silencer's action or to the persisting repression of a necessary gene. This can then lead to the expression or suppression of an undesired phenotype which may affect the normal functionality of certain systems in the organism. Among the many silencer elements and proteins, REST/NSRF is an important silencer factor that has a variety of impacts, not only in neural aspects of development. In fact, in many cases, REST/NSRF acts in conjunction with RE-1/NRSE to repress and influence non-neuronal cells. [ 11 ] Its effects range from frogs ( Xenopus laevis ) to humans, with innumerous effects in phenotype and also in development. In Xenopus laevis , REST/NRSF malfunction or damage has been associated to abnormal ectodermal patterning during development and significant consequences in neural tube, cranial ganglia, and eye development. [ 12 ] In humans, a deficiency in the REST/NSRF silencer element has been correlated to Huntington's disease due to the decrease in the transcription of BDNF .
Furthermore, ongoing studies indicate that NRSE is involved in the regulation of the ANP gene, which when over expressed, can lead to ventricular hypertrophy . [ 13 ] Mutations in the Polycomb-group (PcG) complexes also presented significant modifications in physiological systems of organisms. Hence, modification in silencer elements and sequences can result in either devastating or unnoticeable changes.
The effects and influences of RE1/NRSE and REST/NRSF are significant in non-neuronal cells that require the repression or silencing of neuronal genes. These silencer elements also regulate the expression of genes that do not induce neuron-specific proteins and studies have shown the extensive impact these factors have in cellular processes. In Xenopus laevis, RE1/NRSE and REST/NRSF dysfunction or mutation demonstrated significant impact on neural tube , cranial ganglia , and eye development. [ 12 ] All of these alterations can be traced to an improper patterning of the ectoderm during Xenopus development. Thus, a mutation or alteration in either the silencing region RE1/NRSE or silencer REST/NRSF factor can disrupt the proper differentiation and specification of the neuroepithelial domain and also hinder the formation of skin or ectoderm. [ 12 ] The lack of these factors result in a decreased production of bone morphogenetic protein (BMP), which translates into a deficient development of the neural crest . [ 12 ] Hence, the effects of NRSE and NRSF are of fundamental importance for neurogenesis of the developing embryo, and also in the early stages of ectodermal patterning. Ultimately, inadequate functioning of these factors can result in aberrant neural tube, cranial ganglia, and eye development in Xenopus .
Huntington's disease (HD) is an inherited neurodegenerative disorder, with symptoms emerging during an individual's mid-adulthood. The most noticeable symptoms of this progressive disease are cognitive and motor impairments, as well as behavioral alterations. [ 14 ] These impairments can develop into dementia , chorea , and eventually death. At the molecular level, HD results from a mutation in the huntingtin protein (Htt). More specifically, there is an abnormal repetition of a CAG sequence towards the 5’-end of the gene, which then leads to the development of a toxic polyglutamine (polyQ) stretch in the protein. The mutated Htt protein affects an individual's proper neural functions by inhibiting the action of REST/NRSF.
REST/NRSF is an important silencer element that binds to regulatory regions to control the expression of certain proteins involved in neural functions. The mechanistic actions of huntingtin are still not fully understood, but a correlation between Htt and REST/NRSF exists in HD development. By attaching to the REST/NRSF, the mutated huntingtin protein inhibits the action of the silencer element, and retains it in the cytosol. Thus, REST/NRSF cannot enter the nucleus and bind to the 21 base-pair RE-1/NRSE regulatory element. An adequate repression of specific target genes are of fundamental importance, as many are involved in the proper development of neuronal receptors, neurotransmitters , synaptic vesicle proteins, and channel proteins. A deficiency in the proper development of these proteins can cause the neural dysfunctions seen in Huntington's disease. In addition to the lack of repression due to the inactive REST/NRSF, mutated huntingtin protein can also decrease the transcription of the brain-derived neurotropic factor (BDNF) gene. BDNF influences the survival and development of neurons in the central nervous system as well as the peripheral nervous system. This abnormal repression occurs when the RE1/NRSE region within the BDNF promoter region is activated by the binding of REST/NRSF, which leads to the lack of transcription of the BDNF gene. [ 15 ] Hence, the anomalous repression of the BDNF protein suggests a significant impact in Huntington's disease.
REST/NRSF in conjunction with RE1/NRSE also acts outside the nervous system as regulators and repressors. Current research has linked RE1/NRSE activity with the regulation of the expression of the atrial natriuretic peptide ( ANP ) gene. [ 13 ] An NRSE regulatory region is present in the 3’ untranslated region of the ANP gene and acts as a mediator for its appropriate expression. The protein encoded by the ANP gene is important during embryonic development for the maturation and development of cardiac myocytes . However, during early childhood and throughout adulthood, ANP expression is suppressed or kept to a minimum in the ventricle. Thus, an abnormal induction of the ANP gene can lead to ventricular hypertrophy and severe cardiac consequences. In order to maintain the repression of the gene, NRSF (neuron-restrictive silencer factor) or REST binds to the NRSE region in the 3’untranslated region of the ANP gene. Furthermore, the NRSF-NRSE complex recruits a transcriptional corepressor known as mSin3. [ 13 ] This leads to the activity of histone deacetylase in the region and the repression of the gene. Therefore, studies have revealed the correlation between REST/NRSF and RE1/NRSE in regulating the ANP gene expression in ventricular myocytes. A mutation in either the NRSF or NRSE can lead to an undesirable development of ventricular myocytes, due to lack of repression, which can then cause ventricular hypertrophy. Left ventricular hypertrophy, for example, increases an individual's chance of sudden death due to a ventricular arrhythmia resulting from the increased ventricular mass. [ 16 ] In addition to the influence on the ANP gene, the NRSE sequence regulates other cardiac embryonic genes, such as brain natriuretic peptide BNP, skeletal α-actin, and Na, K – ATPase α3 subunit. [ 13 ] Hence, the regulatory activity of both NRSE and NRSF in mammals prevents not only neural dysfunctions but also physiological and phenotypical abnormalities in other non-neuronal regions of the body.
The Polycomb-group (PcG) regulatory complexes are known for their influence in the epigenetic regulation of stem cells,
especially in hematopoietic stem cells. The Polycomb Repressive Complex 1 (PRC 1) is directly involved in the process of hematopoiesis, and functions together with, for example, the PcG gene “ Bmi1 ”. Studies in mice indicate that organisms with mutated “Bmi1” demonstrate deficient mitochondrial functioning, and also hindered the ability of hematopoietic cells to self-renew. Likewise, mutations in PRC2 genes were related to hematological conditions such as acute lymphoblastic leukemia (ALL), which is a form of leukemia. Hence, Polycomb-group genes and proteins are involved in the proper maintenance of hematopoiesis in the body. [ 17 ] | https://en.wikipedia.org/wiki/Silencer_(genetics) |
Silent mode is a setting available on mobile phones and pagers that, when activated, disables the ringtones and, in some cases, also the vibrating alerts or alarm . Unlike the airplane mode , the silent mode still allows the device to receive and send calls and messages. This quiet option may be useful in meetings, speeches , libraries , museums , or places of worship . In some places it is mandatory to use the silent mode or to switch off the device. [ 1 ]
As mobile technology has evolved, so has the functionality of silent mode. Modern smartphones now allow users to customize silent mode with more granularity, such as enabling vibration alerts for specific contacts or allowing certain types of notifications (e.g., alarms [ 2 ] or emergency alerts) to bypass the silent setting. Additionally, some devices integrate automated silent mode features, activating it based on location, time of day, or during calendar events. This automation helps users maintain phone etiquette in social or professional environments without manual input.
Silent mode also plays a significant role in accessibility, particularly for individuals with hearing impairments. By utilizing vibration or visual notifications (such as flashing lights), devices in silent mode can still alert users to incoming calls or messages without relying on sound. Additionally, many devices allow integration with accessibility features, ensuring that users can customize notifications in ways that best suit their needs. This ensures that silent mode remains functional and inclusive for a wider range of users.
Modern smartphones allow users to customize silent mode settings. For example, users can allow specific notifications, such as alarms or calls from priority contacts, while silencing all other alerts. Many devices also offer automated features, where silent mode activates based on location or calendar events. This enhances convenience, ensuring silent mode is applied automatically during meetings or at specific times.
Airplane mode | Mobile phone features
Silent mode has accessibility features that benefit users with hearing impairments. By relying on vibration or visual notifications, such as flashing lights, users can still be alerted without sound. Devices also offer integration with broader accessibility settings, ensuring customization for individual needs.
Accessibility features
This mobile technology related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silent_mode |
The Silesia corpus is a collection of files intended for use as a benchmark for testing lossless data compression algorithms. It was created in 2003 as an alternative for the Canterbury corpus and Calgary corpus , based on concerns about how well these represented modern files. It contains various data types, including large text documents, executable files, and databases. [ 1 ]
The corpus consists of 12 files, totaling 211MB. The files were chosen to represent what the author considered to be data types likely to grow rapidly in size over time, such as computer programs and databases, along with more traditional compression benchmarks, such as large text files. [ 1 ]
Because it has a broader and more modern selection of datatypes, it is considered a better source of test data for compression algorithms when compared to the Calgary corpus . [ 2 ]
This computer science article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silesia_corpus |
Silicalite is an inorganic compound with the formula SiO 2 . It is one of several forms ( polymorphs ) of silicon dioxide . It is a white solid. It consists of tetrahedral silicon centers and two-coordinate oxides. It is prepared by hydrothermal reaction using tetrapropylammonium hydroxide followed by calcining to remove residual ammonium salts. The compound is notable in being ca. 33% porous. It is useful because the material contains (SiO) 10 rings that allow sorption of hydrophobic molecules of diameter 0.6 nm . [ 1 ]
A commercially important modification of silicalite is titanium silicalite. With the formula Si 1−x Ti x O 2 , it consists of silicalite with Ti doped into some Si sites. Unlike conventional polymorphs of titanium dioxide , the Ti centers in titanium silicalite have tetrahedral coordination geometry. The material is a useful catalyst for the reaction of hydrogen peroxide with propylene to give propylene oxide . [ 2 ]
This article about materials science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silicalite |
Silicate mineral paints or mineral colors are paint coats with mineral binding agents. Two relevant mineral binders play a role in the field of colors: Lime , and silicate .
Under the influence of carbon dioxide, lime-based binders carbonate and water silicate-based binders solidify. Together they form calcium silicate hydrates. [ 1 ]
Lime paints (aside from Fresco-technique) are only moderately weather resistant, so people apply them primarily in monument preservation . Mineral colors are commonly understood to be silicate paints. These paints use potassium water glass as binder. They are also called water glass paints or Keimfarben (after the inventor).
Mineral silicate paint coats are considered durable and weather resistant. Lifetimes exceeding a hundred years are possible. The city hall in Schwyz and "Gasthaus Weißer Adler" in Stein am Rhein (both in Switzerland) received their coats of mineral paint in 1891, and facades in Oslo from 1895 or in Traunstein , Germany from 1891.
Alchemists in their pursuit of the philosopher's stone (to manufacture gold) found glassy shimmering pearls in fireplaces. Sand mixed with potash and heat coalesced into pearls of water glass. Small round panes of water glass were first industrially manufactured for used as windows in the 19th century by Van Baerle in Gernsheim and Johann Gottfried Dingler in Augsburg . Johann Nepomuk von Fuchs made the first attempts to create paints with water glass.
Around 1850, the painters Kaulbach and Schlotthauer applied facade paints of the Pinakothek in Munich . Due to use of earth pigments, which cannot be silicated, the paintings washed out of the water glass.
In 1878, the craftsman and researcher Adolf Wilhelm Keim patented mineral paints . Since then, they have been manufactured by the successor company Keimfarben in Diedorf near Augsburg .
Keim depended on V. van Baerle as the source of water glass. Keim also attempted to manufacture silicate paints himself. His experiments took years to mature, but he finally achieved good results. The Silinwerk van Baerle in Gernsheim near the Rhine river and Keimfarben in Diedorf near Augsburg are well-known manufacturers. [ 2 ]
The impetus for Keim's intense research originated from King Ludwig I. of Bavaria . The art-minded monarch was so impressed by the colorful lime frescoes in northern Italy that he desired to experience such artwork in his own kingdom Bavaria . But the weather north of the alps - known to be significantly more harsh - destroyed the artful paintings within short time. Therefore, he issued an order to Bavarian science to develop paint with the appearance of lime but greater durability.
Mineral paint contains inorganic colorants , and potassium-based , alkali silicate ( water glass ), also known as potassium silicate , liquid potassium silicate , or LIQVOR SILICIVM . A coat with mineral colors does not form a layer but instead permanently bonds to the substrate material ( silicification ).
The result is a highly durable connection between paint coat and substrate. The water glass binding agent is highly resistant to UV light. While dispersions based on acrylate or silicone resin over the years tend to grow brittle, chalky, and crack under UV, the inorganic binder water glass remains stable. The chemical fusion with the substrate and the UV stability of the binder are the fundamental reasons for the extraordinarily high lifetime of silicate paints.
Silicate paints require siliceous substrate for setting. For this reason they are highly suitable for mineral substrates such as mineral plasters and concrete , thus they are of only limited use for application on wood and metal. The permeability to water vapor of silicate paints is equivalent to that of the substrate, so silicate paints do not inhibit the diffusion of water vapor. Moisture contained in parts of a structure or in the plaster may diffuse outward without resistance: this keeps walls dry and prevents structural damage. This addition helps avoid condensation of water on the surface of building materials, reducing the risk of infestation by algae and fungi. The high alkalinity of the water glass binding agent adds to the inhibitory effect against infestation by microorganisms and eliminates the need for additional preservatives.
As mineral paint coats are not prone to static charging and thermo-plasticity (stickiness developing under heat), which is common for surfaces coated with dispersion or silicone resin, soiling happens less, so fewer dirt particles cling to the surface and are easier to wash off. [ 3 ] Silicate paints are incombustible and free of organic additives or solvents (DIN 18363 Painting and coating work Section 2.4.1).
Silicate paints are highly color-tone stable. As they are solely colored with mineral pigments that do not fade with exposure to UV radiation, the silicate paint coats remain constant in color for decades.
Silicate paints are based upon mineral raw materials. They are environmentally compatible in manufacture and effect. Their high durability helps to preserve resources, and their contaminant-free composition preserves health and environment. For this reason, silicate paints have gained popularity, especially in sustainable construction.
Commonly three types of silicate paints are distinguished: Pure silicate paint consisting of two components, a color powder in dry or water-paste form and the liquid binder water glass. (DIN 18363 Painting and coating work Section 2.4.1). The processing of pure silicate paints require great experience and know-how but is now of historic interest.
Around the middle of the 20th century the first single-component silicate paint was developed. The addition of up to five mass percent of organic additives (e.g. acrylate dispersion, hydrophobisers, thickeners or similar) makes ready-to-use paint in containers possible. These are also called "dispersion silicate paints" ( DIN 18363 Painting and coating work Section 2.4.1). The range of application for such silicate paints is significantly higher than for pure silicate paints as the dispersion allows coats for less solid substrates and/or organic composition. Above that handling and processing is simpler than pure silicate paint.
A third category of silicate paints was introduced in 2002: sol-silicate paint. The binder is a combination of silica sol and water glass. The organic fraction is limited to 5 mass percent similar to dispersion silicate paint allowing for chemical setting and retaining of the silicate specific advantages. The sol silicate paint allows use on non-mineral plaster. [ 4 ] For these the bonding occurs chemically and physically. The sol-silicate paint has revolutionized the field of application of silicate paints. These paints can be applied easily and safely to nearly all common substrates. | https://en.wikipedia.org/wiki/Silicate_mineral_paint |
In geology, silicification is a process in which silica -rich fluids seep into the voids of Earth materials , e.g., rocks, wood, bones, shells, and replace the original materials with silica (SiO 2 ). Silica is a naturally existing and abundant compound found in organic and inorganic materials, including Earth's crust and mantle . There are a variety of silicification mechanisms. In silicification of wood, silica permeates into and occupies cracks and voids in wood such as vessels and cell walls. [ 1 ] The original organic matter is retained throughout the process and will gradually decay through time. [ 2 ] In the silicification of carbonates , silica replaces carbonates by the same volume. [ 3 ] Replacement is accomplished through the dissolution of original rock minerals and the precipitation of silica. This leads to a removal of original materials out of the system. [ 3 ] [ 4 ] Depending on the structures and composition of the original rock, silica might replace only specific mineral components of the rock. Silicic acid (H 4 SiO 4 ) in the silica-enriched fluids forms lenticular, nodular, fibrous, or aggregated quartz , opal , or chalcedony that grows within the rock. [ 5 ] Silicification happens when rocks or organic materials are in contact with silica-rich surface water, buried under sediments and susceptible to groundwater flow, or buried under volcanic ashes. Silicification is often associated with hydrothermal processes. [ 1 ] Temperature for silicification ranges in various conditions: in burial or surface water conditions, temperature for silicification can be around 25°−50°; whereas temperatures for siliceous fluid inclusions can be up to 150°−190°. [ 6 ] [ 7 ] Silicification could occur during a syn- depositional or a post-depositional stage, commonly along layers marking changes in sedimentation such as unconformities or bedding planes . [ 5 ] [ 8 ]
The sources of silica can be divided into two categories: silica in organic and inorganic materials. The former category is also known as biogenic silica , which is a ubiquitous material in animals and plants. The latter category is the second most abundant element in Earth's crust. [ 9 ] Silicate minerals are the major components of 95% of presently identified rocks. [ 10 ]
Biogenic silica is the major source of silica for diagenesis. One of the prominent examples is the presence of silica in phytoliths in the leaves of plants, i.e. grasses, and Equisetaceae . Some suggested that silica present in phytoliths can serve as a defense mechanism against the herbivores, where the presence of silica in leaves increases the difficulty in digestion, harming the fitness of herbivores. [ 11 ] However, evidence on the effects of silica on the wellbeing of animals and plants is still insufficient.
Besides, sponges are another biogenic source of naturally occurring silica in animals. They belong to the phylum Porifera in the classification system. Silicious sponges are commonly found with silicified sedimentary layers , for example in the Yanjiahe Formation in South China. [ 12 ] Some of them occur as sponge spicules and are associated with microcrystalline quartz or other carbonates after silicification. [ 12 ] It could also be the main source of precipitative beds such as cherts beds or cherts in petrified woods. [ 12 ]
Diatoms , an important group of microalgae living in marine environments, contribute significantly to the source of diagenetic silica. They have cell walls made of silica, also known as diatom frustules . [ 13 ] In some silicified sedimentary rocks, fossils of diatoms are unearthed. This suggests that diatoms frustules were sources of silica for silicification. [ 13 ] Some examples are silicified limestones of Miocene Astoria Formation in Washington, silicified ignimbrite in El Tatio Geyser Field in Chile, and Tertiary siliceous sedimentary rocks in western pacific deep sea drills. [ 13 ] [ 14 ] [ 15 ] The presence of biogenic silica in various species creates a large-scale marine silica cycle that circulates silica through the ocean. Silica content is therefore high in active silica upwelling areas in the deep-marine sediments. Besides, carbonate shells that deposited in shallow marine environments enrich silica contents at continental shelf areas. [ 16 ]
The major component of the Earth's upper mantle is silica (SiO 2 ), which makes it the primary source of silica in hydrothermal fluids. SiO 2 is a stable component. It often appears as quartz in volcanic rocks . Some quartz that is derived from pre-existing rocks, appear in the form of sand and detrital quartz that interact with seawater to produce siliceous fluids. [ 12 ] In some cases, silica in siliceous rocks are subjected to hydrothermal alteration and react with seawater at certain temperatures, forming an acidic solution for silicification of nearby materials. In the rock cycle , the chemical weathering of rocks also releases silica in the form of silicic acid as by-products . [ 12 ] Silica from weathered rocks is washed into waters and deposit into shallow-marine environments. [ 17 ]
The presence of hydrothermal fluids is essential as a medium for geochemical reactions during silicification. In the silicification of different materials, different mechanisms are involved. In the silicification of rock materials like carbonates, replacement of minerals through hydrothermal alteration is common; while the silicification of organic materials such as woods is solely a process of permeation. [ 17 ] [ 1 ]
The replacement of silica involves two processes:
1) Dissolution of rock minerals [ 1 ]
2) Precipitation of silica [ 1 ]
It could be explained through the carbonate-silica replacement. Hydrothermal fluids are undersaturated with carbonates and supersaturated with silica. When carbonate rocks get in contact with hydrothermal fluids, due to the difference in gradient, carbonates from the original rock dissolve into the fluid whereas silica precipitate out of it. [ 1 ] The carbonate that dissolved is therefore pulled out from the system while the silica precipitated recrystallizes into various silicate minerals, depending on the silica phase. [ 17 ] The solubility of silica strongly depends on the temperature and pH value of the environment [ 3 ] where pH9 is the controlling value. [ 1 ] Under a condition of pH lower than 9, silica precipitates out of the fluid; when the pH value is above 9, silica becomes highly soluble. [ 3 ]
In the silicification of woods, silica dissolves in hydrothermal fluid and seeps into lignin in cell walls. Precipitation of silica out of the fluids produces silica deposition within the voids, especially in the cell walls. [ 1 ] [ 18 ] Cell materials are broken down by the fluids, yet the structure remains stable due to the development of minerals. Cell structures are slowly replaced by silica. Continuous penetration of siliceous fluids results in different stages of silicification i.e. primary and secondary. The loss of fluids over time leads to the cementation of silicified woods through late silica addition. [ 20 ]
The rate of silicification depends on a few factors:
1) Rate of breakage of original cells [ 20 ]
2) Availability of silica sources and silica content in the fluid [ 1 ] [ 3 ]
3) Temperature and pH of silicification environment [ 1 ] [ 3 ]
4) Interference of other diagenetic processes [ 3 ] [ 21 ]
These factors affect the silicification process in many ways. The rate of breakage of original cells controls the development of the mineral framework, hence the replacement of silica. [ 20 ] Availability of silica directly determines the silica content in fluids. The higher the silica content, the faster silicification could take place. [ 1 ] The same concept applies to the availability of hydrothermal fluids. The temperature and pH of the environment determine the condition for silicification to occur. [ 3 ] [ 21 ] This is closely connected to the burial depth or association with volcanic events. Interference of other diagenetic processes could sometimes create disturbance to silicification. The relative time of silicification to other geological processes could serve as a reference for further geological interpretations. [ 1 ] [ 18 ] [ 20 ] [ 21 ]
In the Conception Bay in Newfoundland, Southeastern coast of Canada, a series of Pre-Cambrian to Cambrian-linked volcanic rocks were silicified. The rocks mainly consist of rhyolitic and basaltic flows, with crystal tuffs and breccia interbedded. Regional silicification was taken place as a preliminary alteration process before other geochemical processes occurred. [ 22 ] The source of silica near the area was from hot siliceous fluids from rhyolitic flow under a static condition. [ 22 ] A significant portion of silica appeared in the form of white chalcedonic quartz, quartz veins as well as granular quartz crystal. [ 22 ] Due to the difference in rock structures, silica replaces different materials in rocks of close locations. The following table shows the replacement of silica at different localities: [ 22 ]
In the Semail Nappe of Oman in the United Arb Emirates, silicified serpentinite was found. The occurrence of such geological features is rather unusual. It is a pseudomorphic alteration where the protolith of serpentinite was already silicified. [ 23 ] Due to tectonic events, basal serpentinite was fractured and groundwater permeated along the faults, forming a large-scale circulation of groundwater within the strata. [ 23 ] Through hydrothermal dissolution, silica precipitated and crystallized around the voids of serpentinite. [ 24 ] Therefore, silicification can only be seen along groundwater paths. [ 24 ] The silicification of serpentinite was formed under the condition where groundwater flow and carbon dioxide concentration are low. [ 23 ] [ 24 ]
Silicified carbonates can appear as silicified carbonate rock layers, [ 3 ] or in the form of silicified karsts. The Paleogene Madrid Basin in Central Spain is a foreland basin resulted from the Alpine uplift, an example of silicified carbonates in rock layers. The lithology consists of carbonate and detritus units that were formed in a lacustrine environment. The rock units are silicified where cherts, quartz, and opaline minerals are found in the layers. [ 25 ] It is conformable with the underlying evaporitic beds, also dated from similar ages. It is found that there were two stages of silicification within the rock strata. [ 25 ] The earlier stage of silicification provided a better condition and site for the precipitation of silica. The source of silica is still uncertain. [ 25 ] There are no biogenic silica detected from the carbonates. However, microbial films in carbonates are found, which could suggest the presence of diatoms. [ 25 ]
Karsts are carbonate caves formed from a dissolution of carbonate rocks such as limestones and dolomites . They are usually susceptible to groundwater and are dissolved in these drainage. Silicified karsts and cave deposits are formed when siliceous fluids enter karsts through faults and cracks. [ 17 ] The Mid-Proterozoic Mescal Limestone from the Apache Group in central Arizona is classic examples of silicified karsts. A portion of the carbonates are replaced by cherts in early diagenesis and the remaining portion is completely silicified in later stages. [ 17 ] The source of silica in carbonates are usually associated with the presence of biogenetic silica; however, the source of silica in Mescal Limestone is from weathering of overlying basalts , which are extrusive igneous rocks that have high silica content. [ 17 ]
Silicification of woods usually occur in terrestrial conditions, but sometimes it could be done in aquatic environments. [ 18 ] Surface water silicification can be done through the precipitation of silica in silica-enriched hot springs. On the northern coast of central Japan, the Tateyama hot spring has a high silica content that contributes to the silicification of nearby fallen woods and organic materials. Silica precipitates rapidly out of the fluids and opal is the main form of silica. [ 1 ] With a temperature of around 70 °C and a pH value of around 3, the opal deposited is composed of silica spheres of different sizes arranged randomly. [ 1 ]
Mafic magma dominated the seafloor at around 3.9 Ga during the Hadean - Archean transition. [ 26 ] Due to rapid silicification, the felsic continental crust began to form. [ 27 ] In the Archean, the continental crust was composed of tonalite–trondhjemite–granodiorite (TTG) as well as granite– monzonite – syenite suites. [ 27 ]
The Mount Goldsworthy in the Pilbara Craton located in Western Australia holds one of the earliest silicification example with an Archean clastic meta-sedimentary rock sequence, revealing the surface environment of the Earth in the early times with evidence from silicification and hydrothermal alteration. The unearthed rocks are found to be SiO2 dominant in terms of mineral composition. [ 8 ] The succession was subjected to a high degree of silicification due to hydrothermal interaction with seawater at low temperatures. [ 8 ] Lithic fragments were replaced with microcrystalline quartz and protoliths were altered during silicification. [ 8 ] The condition of silicification and the elements that were present suggested that the surface temperature and carbon dioxide contents were high during either or both syn-deposition and post-deposition. [ 8 ]
The Barberton Greenstone Belt in South Africa, specifically the Eswatini Supergroup of around 3.5–3.2 Ga, is a suite of well-preserved silicified volcanic-sedimentary rocks. With the composition ranging from ultramafic to felsic, the silicified volcanic rocks are directly beneath the bedded chert layer. Rocks are more silicified near the bedded chert contact, suggesting a relationship between chert deposition and silicification. [ 28 ] The silica altered zones reveal that hydrothermal activities, as in seawater circulation, actively circulate the rock layers through fractures and fault during the deposition of bedded chert. [ 29 ] The seawater was heated up and therefore picked up silicious materials from underneath volcanic origin. The silica enriched fluids bring about silicification of rocks through seeping into porous materials in the syn-depositional stage at a low-temperature condition. [ 29 ] [ 30 ] | https://en.wikipedia.org/wiki/Silicification |
The silicon-vacancy center (Si-V) is an optically active defect in diamond (referred to as a color center) that is receiving an increasing amount of interest in the diamond research community. This interest is driven primarily by the coherent optical properties of the Si-V, especially compared to the well-known and extensively-studied nitrogen-vacancy center (N-V). While the negative Si-V − center has received the majority of the silicon-vacancy center research, interest is growing in the neutral Si-V 0 center as well.
The Si-V center is formed by replacing two neighboring carbon atoms in the diamond lattice with one silicon atom, which places itself between the two vacant lattice sites. This configuration has a D 3d point group symmetry. [ 2 ]
The Si-V − center is a single- hole (spin-1/2) system with ground and excited electronic states located within the diamond bandgap. The ground and excited electronic states have two orbital states split by spin–orbit coupling . Each of these spin–orbit states is doubly degenerate by spin, and this splitting can be affected by lattice strain. Phonons in the diamond lattice drive transitions between these orbital states, causing rapid equilibration of the orbital population at temperatures above ca. 1 K. [ 3 ]
All four transitions between the two ground and two excited orbital states are dipole allowed with a sharp zero-phonon line (ZPL) at 738 nm (1.68 eV) [ 4 ] and minimal phononic sideband in a roughly 20 nm window around 766 nm. [ 5 ] The Si-V center emits much more of its emission into its ZPL, approximately 70% ( Debye–Waller factor of 0.7), than most other optical centers in diamond, such as the nitrogen-vacancy center (Debye–Waller factor ~ 0.04). [ 6 ] The Si-V − center also has higher excited states that relax quickly to the lowest excited states, allowing off-resonant excitation.
The Si-V center has an inversion symmetry, and no static electric dipole moment (to the first order); it is therefore insensitive to the Stark shift that could result from inhomogeneous electric fields within the diamond lattice. This property, together with the weak electron-phonon coupling, results in a narrow ZPL in the Si-V center, which is mostly limited by its intrinsic lifetime. [ 7 ] Bright photoluminescence , narrow optical lines, and ease of finding optically indistinguishable Si-V centers favor them for applications in solid-state quantum optics .
Although the optical transitions of the Si-V − center preserve the electron spin , the rapid phonon-induced mixing between the Si-V − orbital states causes spin decoherence. At very low temperatures below 100 millikelvin , spin coherence for the Si-V − center improves significantly. [ 8 ] It is possible to use the 29 Si nuclear spin and the electron spin of the Si-V as qubits for quantum information applications. [ 9 ] [ 10 ] [ 11 ]
The N-V center is a similar defect in diamond with more historical significance. Research on the N-V center dates to the 1950s, [ 12 ] but the negative Si-V − center was discovered in 1980 [ 13 ] and the neutral Si-V 0 center was first seen in 2011. [ 14 ] The two defects have different advantages and drawbacks. At room temperature, the N-V center has much better spin coherence, a wider ZPL, and wider phonon sideband. [ 2 ] The sharpness of the Si-V center's ZPL, it's large Debye–Waller factor , as well as its ability to remain stable in nanophotonic structures are the main properties that have drawn research to it instead of using the more studied N-V center.
The Si-V 0 center has one fewer electron than the Si-V − , giving it a neutral charge and different properties. The newer Si-V 0 center has a spin-1 system [ 15 ] with electron spin resonance [ 14 ] that gives it a spin coherence superior to the Si-V − center. [ 16 ] At room temperature, its ZPL lies in the infrared spectrum at 946 nm with an excellent Debye-Waller factor of 0.9, [ 15 ] as compared to the red ZPL peak of the Si-V − at 738 nm. However, stabilizing SiV 0 is more of a challenge, with high precision (1-3 ppm) needed in controlling its boron concentration. [ 16 ]
Ion implantation has been used to synthesize Si-V centers in nanodiamonds. [ 17 ] [ 18 ] [ 19 ] Si ions are implanted into the NDs at specific depths and implantation energies before being annealed. [ 17 ] [ 18 ] After the ion implantation, additional thermal treatments may be applied to repair structural defects and activate impurities. Unlike the ion implantation used to produce N-V centers, Si-V complexes can withstand higher temperature thermal treatments without dissociation risk. [ 20 ] In practice, Si-V centers have been synthesized using multiple systems, with differing optical properties such as the widths of resultant ZPLs . [ 17 ] [ 18 ]
Chemical vapor deposition (CVD) is used to synthesize Si-V centers via a similar process to that used to produce N-V centers [ 20 ] .. In the case of Si-V centers, there are two main types of CVD used. First, when a solid containing Silicon is etched with hydrogen, and SiH x radicals dope the diamond lattice. [ 21 ] Second, a silicon containing plasma is created containing SiH 3 which functions as the dopant. [ 22 ] Si-V centers have been synthesized via tetramethylsilane (TMS) gas as a doping source, [ 23 ] [ 22 ] and in the hydrogen plasma example chemicals such as H2/CH4/CO2 and H2/CH4/N2 have been used to grow the diamonds on Si substrates. [ 24 ]
Si-V centers' special properties make them preferred to N-V centers in some specific applications. [ 20 ] Si-V centers can be used in temperature sensing, [ 19 ] [ 25 ] photoelectric detectors, [ 26 ] and biochemical visualization [ 27 ] [ 28 ] amongst others.
Because Si-V centers have such a sharp ZPL, they are used in temperature probes that measure the change in ZPL peaks. These temperature probes have achieved sub-Kelvin precision in less than a second, and do not need individual calibration. Due to the non-invasive nature of these luminescent thermometers, they lend themselves well to biological applications. [ 25 ] For example, Si-V nano-scale thermometers have been used for thermosensing within live cells. [ 28 ]
Though there is little research favoring Si-V centers over N-V centers in photoelectric detectors, Si-V centers still exhibit a greater response and faster cutoff time compared to undoped detectors. This technology is expected to have applications in many fields including quantum information processing and bio-marking. [ 26 ]
Confocal microscopes utilizing Si-V centers have been used to visualize cells in a non-invasive way. [ 28 ] Additionally, nano diamond vacancy centers like Si-V centers can detect chemical reactions within cells and function as long-term biological markers . [ 27 ]
Si-V − centers in dilution refrigeration systems below 100 millikelvin can be used in quantum network applications, with spin memory long enough for entanglement up to 500 kilometers. [ 8 ] This is because Si-V − centers can be integrated in nanophotonic structures to improve their interaction with photons for quantum communication. Nuclear spins, such as the 29 Si nuclear spin of the center itself [ 11 ] or 13 C nuclear spins naturally present in the diamond around the Si-V [ 8 ] can also be used as nuclear memory qubits. Research interest in the neutral Si-V 0 center is also growing, since it has better spin coherence than the negative Si-V − center at higher temperature. Spin coherence of 1 second has been achieved for Si-V 0 , [ 16 ] giving it potential as a material to be used in quantum networks. | https://en.wikipedia.org/wiki/Silicon-vacancy_center_in_diamond |
The Silicon Disk System was the first commercially available RAM disk for microcomputers . [ 1 ]
It was written by Jerry Karlin in 1979/80. Karlin was joined by Peter Cheesewright, and their company Microcosm Research Ltd. marketed the product for a number of years. The product was available as a standalone and also bundled with a number of different microcomputers and RAM-board products. Later, the Silicon Disk System was sold by Microcosm Ltd . Initially, it was available for the CP/M operating system. Versions for the MP/M , CP/M-86 , and MP/M-86 operating systems followed. Following the launch of the IBM PC, a version for the MS-DOS and PC DOS operating systems was produced.
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silicon_Disk_System |
Silicon Milkroundabout is a series of job fairs held in London, England [ 1 ] and Edinburgh, Scotland [ 2 ] for the UK tech start-up community. [ 3 ] The event's name is a portmanteau of Silicon Roundabout and the Milk round university recruiting events.
The company was founded by Cristiana Camisotti, Ian Hogarth , and Pete Smith [ 4 ] [ 5 ] [ 6 ] - the latter two are also the founders of Songkick - in 2011. Its inaugural event took place in a pub with 40 start-up companies. [ 5 ] The initiative was supported by David Cameron 's initiative Tech City . [ 7 ]
The event was expanded into Scotland in 2015 as Silicon Milkroundabout Scotland 1.0. [ 8 ] This event was held in Edinburgh with 40 companies and 450 attendees.
The intention of the business was to attract computer science talent to the startup community, in response to a high number of vacancies in the tech start-up sector. [ 3 ] [ 9 ] [ 10 ]
Events are held biannually in London and Edinburgh, [ citation needed ] and attendees are required to go through an application process to attend. [ 11 ] Events are free for job seekers with a ticket to attend. [ 12 ]
The event taking place in April 2020 was postponed due to the COVID-19 pandemic . [ 13 ]
Due to the small space in which it took place in 2022, the number of people inside the London event had to be limited, and this led to some goers complaining about not having enough time there. [ 14 ] | https://en.wikipedia.org/wiki/Silicon_Milkroundabout |
Silicon carbide color centers are point defects in the crystal lattice of silicon carbide , which are known as color centers. These color centers have multiple uses, some of which are in photonics, semiconductors, and quantum applications like metrology and quantum communication . Defects in materials have a plethora of applications, but the reason defects, or color centers in silicon carbide are significant is due to many important properties of these color centers. Silicon carbide as a material has second-order nonlinearity, as well as optical transparency and low two-photon absorption. This makes silicon carbide viable to be an alternate platform for many things, including but not limited to nanofabrication, integrated quantum photonics, and quantum systems in large-scale wafers. [ 1 ]
There are mainly three methods for fabricating silicon carbide color centers. [ 2 ] The three methods are electronic irradiation, ion injection, and femtosecond laser writing.
This technique works by exposing the material to an electron beam that is highly ionizing. This knocks off electrons in the material itself, which generates color centers (or defects). [ 3 ] This process however, requires a large amount of energy, having 9MeV normally being the lower limit of energy in most materials. [ 3 ]
Ion injection is normally used to dope semiconductors, but it can also be used to create color centers. An ion is first accelerated to a certain energy, normally in the MeV range. This ion is then accelerated into the material, which then implants the ion into the material, changing the material composition, which can create a color center. [ 4 ]
Utilizing a nonlinear laser writing process, along with the appropriate aberration correction, defects can be generated at any depth in the crystal. This process preserves spin and optical coherence properties. [ 5 ] [ 6 ] The way it works is from multiphoton ionization from the femtosecond laser process. This method of fabricating defects does not only work for silicon carbide, but can also work for other materials. [ 7 ]
Other types of fabrication for defects are neutron irradiation , proton irradiation, and focused Si beams. [ 1 ]
Currently [ when? ] , new methods of fabrication are also being experimented with to try and reduce the energy used, or the complication of the process. One of the new methods is a new method of utilizing a laser writing method with a nanosecond laser. [ 2 ]
There are multiple types of defects in silicon carbide, some of which are listed below: [ clarification needed ]
Transition metal color centers:
Studies have been done on TV1 as a qubit , which provided a better spin-photon interface than TV2. [ 8 ] [ 9 ] Recently however, the role of V si (-) as a qubit has been full identified. [ 10 ]
Recently [ when? ] , these color centers in silicon carbide have shown promise in becoming one of the best single-photon emitters for non-classical light sources. [ 11 ] Traditionally, attenuated lasers have been the substitute for single-photon sources . This works for quantum cryptography , but they are a partial substitute, and in the end this was not a substitute for single-photon sources as they do not produce single photons. [ 11 ] Normally, there are two main methods of generating single photons: spontaneous parametric down-conversion and epitaxial quantum dots . [ citation needed ]
In spontaneous parametric down-conversion, single photons can be produced up to a rate of 10 6 photons per second. [ 12 ] [ 13 ] [ 14 ] [ 11 ] The drawback to this approach is that there is no way to generate single photons on demand. This makes this type of generation hard to use practically. [ citation needed ]
Epitaxial quantum dots are shown to generate single photons exceptionally when put under electrical pumping. This however works under very low temperatures, which also makes these applications harder to do practically in experiments. [ 11 ] [ 15 ] [ 16 ] [ 17 ]
Color centers in silicon carbide, diamonds, and other related materials would be more practical that the two other traditional approaches due to the higher temperature that they can operate at when under optical and electrical pumping. [ 11 ]
Silicon carbide is currently being used in the semiconductor industry already, due to the fact that it belongs to a family of materials called complementary metal–oxide–semiconductor compatible materials, as well as its reliability in fabrication of high-quality single crystal wafers. [ 1 ] Since semiconductors by definition already have point defects, some may be used for purposes like single-photon sources. [ citation needed ]
When studied at the single defect level, single emitters could be isolated. As a result of this, silicon carbide color centers can be used for applications in quantum cryptography protocols. [ 1 ] One example of this was a study on nitrogen-vacancy centers in diamonds in 2014, which are similar to color centers in silicon carbide, that showcased novel results on how in diamonds, the nitrogen-vacancy were color centers, which also are fluorescent impurities that have many applications [ 18 ]
Quantum entanglement between the electron spin state and the single photon quantum state occurs when two conditions are met:
This quantum entanglement allows the creation of quantum networks, which leads to quantum communications, quantum memory , and metrology. [ 1 ]
When the color centers are first brought to an excited state, a photon can be emitted from the decay from the excited state to the ground states . This photon can then interact with other sources of static and variable magnetic fields. As a result of this, the spin transition frequency and the coherence time are altered, which then this effect is used in quantum sensing . [ 1 ]
Much of the color center research was originally performed using diamond instead of silicon carbide. For comparison, the nitrogen-vacancy in diamond has similar quantum properties to the divacancy in silicon carbide. Diamond's vacancy potentially has better quantum properties than silicon carbide's, but one of the major benefits of silicon carbide and its color centers is increased scalability and greater ease of manufacture when compared to diamond. Additionally, silicon carbide does not suffer from complications in production such as graphitization during irradiation which is possible during diamond color center manufacture. [ citation needed ] | https://en.wikipedia.org/wiki/Silicon_carbide_color_centers |
A silicon compiler is an electronic design automation software tool that is used for high-level synthesis of integrated circuits. Such a tool takes a user's specification of an IC design as input and automatically generates an integrated circuit (IC) design files as output for further fabrication by the semiconductor fabrication plant or manually from discrete components. The process is sometimes referred to as hardware compilation . The silicon compiler may use the vendor's Process Design Kit for production.
Silicon compilation takes place in three major steps:
Silicon compilation was first described in 1979 by David L. Johannsen, under the guidance of his thesis adviser, Carver Mead . [ 1 ]
Johannsen, Mead, and Edmund K. Cheng subsequently founded Silicon Compilers Inc. (SCI) in 1981.
Edmund Cheng designed an Ethernet Data Link Controller chip [ 2 ] in 1981–82 using structured design methodology, in order to drive the software and circuit-library development at SCI. The project went from concept to chip specification in 3 months, and from chip specification to tape-out in 5 months. Fabricated using a 3- micron NMOS process, the chip measured 50,600 square mils in die area, and was being marketed and manufactured in volume-production by 1983 under license from SCI.
John Wawrzynek at Caltech used some of the earliest silicon compilers in 1982 as part of the "Yet Another Processor Project" (YAPP), akin to YACC . [ 3 ]
In 1983–84, the SCI team designed and implemented the data-path chip used in the MicroVAX in seven months.
MicroVAX's data-path chip contains the entire 32-bit processor, except its microcode store and control-store sequencer, and contains 37,000 transistors.
At the time, chips with similar levels of complexity required about 3 years to design and implement.
Including those seven months, Digital Equipment Corporation completed the design and implementation of the MicroVAX within one year. [ 4 ] | https://en.wikipedia.org/wiki/Silicon_compiler |
Silicon isotope biogeochemistry is the study of environmental processes using the relative abundance of Si isotopes . As the relative abundance of Si stable isotopes varies among different natural materials, [ 2 ] the differences in abundance can be used to trace the source of Si, and to study biological, geological, and chemical processes. [ 1 ] The study of stable isotope biogeochemistry of Si aims to quantify the different Si fluxes in the global biogeochemical silicon cycle, to understand the role of biogenic silica within the global Si cycle, and to investigate the applications and limitations of the sedimentary Si record as an environmental and palaeoceanographic proxy . [ 1 ]
Silicon in nature is typically bonded to oxygen, in a tetravalent oxidation state. The major forms of solid Si are silicate minerals and amorphous silica, whereas in aqueous solutions the dominant forms are orthosilicic acid and its dissociated species. [ 3 ] There are three stable isotopes of Si , associated with the following mean natural abundances: 28 Si– 92.23%, 29 Si– 4.67%, and 30 Si– 3.10%. [ 2 ] The isotopic composition of Si is often formulated by the delta notation, as the following:
The reference material (standard) for defining the δ 30 Si of a sample is the National Bureau of Standards (NBS) 28 Sand Quartz, which has been certified and distributed by the National Institute of Standards and Technology (NIST) , and is also named NIST RM 8546. [ 3 ] Currently, there are four main analytical methods for the measurement of Si isotopes: Gas Source Isotope-Ratio Mass Spectrometry (GC-IRMS), Secondary Ion Mass Spectrometry (SIMS), Multi-Collector Inductively Coupled Plasma Mass Spectrometry (MC–IPC–MS), and Laser Ablation MC–ICP–MS. [ 3 ]
Primary minerals are the minerals that crystalize during the formation of Earth's crust , and their typical δ 30 Si isotopic value is in the range of −0.9‰ – +1.4‰. [ 1 ] Earth's crust is constantly undergoing weathering processes, which dissolve Si and produce secondary Si minerals simultaneously. The formation of secondary Si discriminates against the heavy Si isotope ( 30 Si), creating minerals with relatively low δ 30 Si isotopic values (−3‰ – +2.5‰, mean: −1.1‰). [ 4 ] It has been suggested that this isotopic fractionation is controlled by the kinetic isotope effect of Si adsorption to Aluminum hydroxides , which takes place in early stages of weathering. [ 5 ] As a result of incorporation of lighter Si isotopes into secondary minerals, the remaining dissolved Si will be relative enriched in the heavy Si isotope ( 30 Si), and associated with relatively high δ 30 Si isotopic values (−1‰ – +2‰, mean: +0.8‰). [ 4 ] The dissolved Si is often transported by rivers to the oceans.
Silicon uptake by plants typically discriminates against the light Si isotope, forming 30 Si-enriched plants (δ 30 Si of 0–6‰). [ 1 ] The reason for this relatively large isotopic fractionation remains unclear, mainly because the mechanisms of Si uptake by plants are yet to be understood. Silicon in plants can be found in the xylem , which is associated with exceptionally high δ 30 Si values. [ 6 ] Phytoliths , microscopic structures of silica in plant tissues, have relatively lower δ 30 Si values. [ 6 ] For example, it was reported that the mean δ 30 Si of phytoliths in various wheat organs were -1.4–2.1‰, [ 7 ] which is lower than the typical range for vegetation (δ 30 Si of 0–6‰). Phytoliths are relatively soluble, and as plants decay they contribute to the terrestrial dissolved Si budget. [ 1 ]
In aquatic environments (rivers, lakes and ocean), dissolved Si is utilized by diatoms , dictyochales , radiolarians and sponges to produce solid bSiO 2 structures. The biomineralized silica has an amorphous structure and therefore its properties may vary among the different organisms. [ 8 ] Biomineralization by diatoms induces the largest Si flux within the ocean, and thus it has a crucial role in the global Si cycle. [ 9 ] During Si uptake by diatoms, there is an isotopic discrimination against the heavy isotope, forming 30 Si-depleted biogenic silica minerals. [ 10 ] As a result, the remaining dissolved Si in the surrounding water is 30 Si-enriched. Since diatoms rely on sunlight for photosynthesis , they inhabit in surface waters, and thus the surface water of the ocean are typically 30 Si-enriched. [ 1 ] Although there is less available data on the isotopic fractionation during biomineralization by radiolarians , it has been suggested that radiolarians also discriminate against the heavy isotope ( 30 Si), and that the magnitude of isotopic fractionation is of a similar range as biomineralization by diatoms. [ 11 ] Sponges also show an isotopic preference for 28 Si over 30 Si, but the magnitude of their isotopic fractionation is often larger [ 1 ] (For quantitative comparation, see Figure 2).
Hydrothermal vents contribute dissolved Si to the ocean Si reservoir. Currently, it is challenging to determine the magnitude of hydrothermal Si fluxes, due to lack of data on the δ 30 Si values associated with this flux. [ 1 ] There are only two published data points of the δ 30 Si value of hydrothermal vents (−0.4‰ and −0.2‰). [ 12 ]
The δ 30 Si value of sediment porewater may be affected by post-depositional ( diagenetic ) precipitation or dissolution of Si. It is important to understand the extent and isotopic fractionations of these processes, as they alter the δ 30 Si values of the originally deposited sediments, and determine the δ 30 Si preserved in the rock record. [ 1 ] Generally, precipitation of Si prefers the light isotope ( 28 Si) and leads to 30 Si-enriched dissolved Si in the hosting solution. [ 13 ] The isotopic effect of Si dissolution in porewater is yet to be clear, as some studies report a preference for 28 Si during dissolution, [ 14 ] while other studies document that isotopic fractionation was not expressed during dissolution of sediments. [ 15 ]
The silicic acid leakage hypothesis (SALH) is a suggested mechanism that aims to explain the atmospheric CO 2 variations between glacial and interglacial periods. [ 16 ] This hypothesis proposes that during glacial periods, as a result of enhanced dust deposition in the southern ocean , diatoms consume less Si relative to nitrogen. The decrease in the Si:N uptake ratios leads to Si excess in the southern ocean, which leaks to lower latitudes of the ocean that are dominated by coccolithophores . As the Si concentrations rise, the diatom population may outcompete the coccolithophores , reducing the CaCO 3 precipitation and altering ocean alkalinity and the carbonate pump . [ 17 ] These changes would induce a new ocean-atmosphere steady state with lower atmospheric CO 2 concentrations, consistent with the draw down of CO 2 observed in the last glacial period. [ 16 ] The δ 30 Si and δ 15 N isotopic values archived in the southern ocean diatom sediments has been used to examine this hypothesis, [ 18 ] as the dynamics of Si and N supply and utilization during the last deglaciation could be interpreted from this record. In alignment with the silicic acid leakage hypothesis, these isotopic archives suggest that Si utilization in the southern ocean increased during the deglaciation. [ 18 ]
There have been attempts to reconstruct ocean paleotemperatures by chert Si isotopic record, which proposed that the Archean seawater temperatures were significantly higher than modern (~70 °C). [ 19 ] However, subsequent studies question this palaeothermometry method and offer alternative explanation for the δ 30 Si values of Archean rocks. [ 3 ] These signals could result from diagenetic alteration processes that overprint the original δ 30 Si values, [ 20 ] or reflect that Archean cherts were composed of different Si sources. It is plausible that in during the Archean the dominant sources of Si sediments were weathering, erosion, silicification of clastic sediments or hydrothermal activity, [ 21 ] in contrast to the vast SiO 2 biomineralization in the modern ocean.
According to empirical calibrations, the difference in δ 30 Si (denoted as Δ 30 Si) between sponges and their hosting water is correlated with the Si concentration of the hosting solution. [ 22 ] Therefore, it has been suggested that the Si concentrations in bottom waters of ancient oceans can be interpreted from the δ 30 Si of coexisting sponge spicules , which are preserved in the rock record. [ 22 ] It has been proposed that this relation is determined by the growth rate and the Si uptake kinetics of sponges, [ 22 ] but the current understanding of sponge biomineralization pathways is limited. [ 1 ] Although the mechanism behind this relation is yet to be clear, it appears consistent among various laboratory experiments, modern environments, and core top sediments. [ 1 ] However, there is also evidence that the δ 30 Si of carnivorous sponges may differ significantly from the expected correlation. [ 23 ] | https://en.wikipedia.org/wiki/Silicon_isotope_biogeochemistry |
Silicon nanowires , also referred to as SiNWs , are a type of semiconductor nanowire most often formed from a silicon precursor by etching of a solid or through catalyzed growth from a vapor or liquid phase. Such nanowires have promising applications in lithium-ion batteries, thermoelectrics and sensors . Initial synthesis of SiNWs is often accompanied by thermal oxidation steps to yield structures of accurately tailored size and morphology. [ 1 ]
SiNWs have unique properties that are not seen in bulk (three-dimensional) silicon materials. These properties arise from an unusual quasi one-dimensional electronic structure and are the subject of research across numerous disciplines and applications. The reason that SiNWs are considered one of the most important one-dimensional materials is they could have a function as building blocks for nanoscale electronics assembled without the need for complex and costly fabrication facilities. [ 2 ] SiNWs are frequently studied towards applications including photovoltaics , nanowire batteries , thermoelectrics and non-volatile memory. [ 3 ]
Owing to their unique physical and chemical properties, silicon nanowires are a promising candidate for a wide range of applications that draw on their unique physico-chemical characteristics, which differ from those of bulk silicon material. [ 1 ]
SiNWs exhibit charge trapping behavior which renders such systems of value in applications necessitating electron hole separation such as photovoltaics, and photocatalysts. [ 4 ] Recent experiment on nanowire solar cells has led to a remarkable improvement of the power conversion efficiency of SiNW solar cells from <1% to >17% in the last few years. [ 5 ]
The ability for lithium ions to intercalate into silicon structures renders various Si nanostructures of interest towards applications as anodes in Li-ion batteries (LiBs) . SiNWs are of particular merit as such anodes as they exhibit the ability to undergo significant lithiation while maintaining structural integrity and electrical connectivity. [ 6 ]
Silicon nanowires are efficient thermoelectric generators because they combine a high electrical conductivity, owing to the bulk properties of doped Si, with low thermal conductivity due to the small cross section. [ 7 ]
Charge trapping behavior and tunable surface governed transport properties of SiNWs render this category of nanostructures of interest towards use as metal insulator semiconductors and field effect transistors , [ 8 ] where the silicon nanowire is the main channel of the FET which connect the source to the drain terminal, facilitating electron transfer between the two terminals with further applications as nano-electronic storage devices, [ 9 ] in flash memory , logic devices as well as chemical, gas and biological sensors. [ 3 ] [ 10 ] [ 11 ]
Since SiNWFET was first reported in 2001, [ 12 ] it has caused wide concern in the sensor area, because of their superior physical properties such as high carrier mobility, [ 13 ] high current switch ratio, and close to ideal subthreshold slope. Furthermore, it is cost-efficient and could be manufactured on large scale, since it is combined with CMOS fabricating technology. Specifically, in bioresearch, SiNWFET has high sensitivity and specificity to biological targets and could offer label-free detection after being modified with small biological molecules to match the target object. What’s more, SiNWFET could be fabricated in arrays and be selectively functionalized, which enables the simultaneous detection and analysis of multiple targets. [ 14 ] Multiplexed detection could greatly improve throughput and efficiency of biodetection.
Several synthesis methods are known for SiNWs and these can be broadly divided into methods which start with bulk silicon and remove material to yield nanowires, also known as top-down synthesis, and methods which use a chemical or vapor precursor to build nanowires in a process generally considered to be bottom-up synthesis. [ 3 ]
These methods use material removal techniques to produce nanostructures from a bulk precursor
Subsequent to physical or chemical processing, either top-down or bottom-up, to obtain initial silicon nanostructures, thermal oxidation steps are often applied in order to obtain materials with desired size and aspect ratio . Silicon nanowires exhibit a distinct and useful self-limiting oxidation behaviour whereby oxidation effectively ceases due to diffusion limitations, which can be modeled. [ 1 ] This phenomenon allows accurate control of dimensions and aspect ratios in SiNWs and has been used to obtain high aspect ratio SiNWs with diameters below 5 nm. [ 19 ] The self-limiting oxidation of SiNWs is of value towards lithium-ion battery materials.
There is significant interest in SiNWs for their unique properties and the ability to control size and aspect ratio with great accuracy. As yet, limitations in large-scale fabrication impede the uptake of this material in the full range of investigated applications. Combined studies of synthesis methods, oxidation kinetics and properties of SiNW systems aim to overcome the present limitations and facilitate the implementation of SiNW systems, for example, high quality vapor-liquid-solid–grown SiNWs with smooth surfaces can be reversibly stretched with 10% or more elastic strain, approaching the theoretical elastic limit of silicon, which could open the doors for the emerging “elastic strain engineering” and flexible bio-/nano-electronics. [ 20 ] | https://en.wikipedia.org/wiki/Silicon_nanowire |
In semiconductor manufacturing , silicon on insulator ( SOI ) technology is fabrication of silicon semiconductor devices in a layered silicon–insulator–silicon substrate , to reduce parasitic capacitance within the device, thereby improving performance. [ 1 ] SOI-based devices differ from conventional silicon-built devices in that the silicon junction is above an electrical insulator , typically silicon dioxide or sapphire (these types of devices are called silicon on sapphire , or SOS). The choice of insulator depends largely on intended application, with sapphire being used for high-performance radio frequency (RF) and radiation-sensitive applications, and silicon dioxide for diminished short-channel effects in other microelectronics devices. [ 2 ] The insulating layer and topmost silicon layer also vary widely with application. [ 3 ]
SOI technology is one of several manufacturing strategies to allow the continued miniaturization of microelectronic devices, colloquially referred to as "extending Moore's Law " (or "More Moore", abbreviated "MM"). Reported benefits of SOI relative to conventional silicon ( bulk CMOS ) processing include: [ 4 ]
From a manufacturing perspective, SOI substrates are compatible with most conventional fabrication processes. In general, an SOI-based process may be implemented without special equipment or significant retooling of an existing factory. Among challenges unique to SOI are novel metrology requirements to account for the buried oxide layer and concerns about differential stress in the topmost silicon layer. The threshold voltage of the transistor depends on the history of operation and applied voltage to it, thus making modeling harder.
The primary barrier to SOI implementation is the drastic increase in substrate cost, which contributes an estimated 10–15% increase to total manufacturing costs. [ 6 ] [ additional citation(s) needed ] FD-SOI (Fully Depleted Silicon On Insulator) has been seen as a potential low cost alternative to FinFETs. [ 7 ]
An SOI MOSFET is a metal–oxide–semiconductor field-effect transistor (MOSFET) device in which a semiconductor layer such as silicon or germanium is formed on an insulator layer which may be a buried oxide (BOX) layer formed in a semiconductor substrate. [ 8 ] [ 9 ] [ 10 ] SOI MOSFET devices are adapted for use by the computer industry. [ citation needed ] The buried oxide layer can be used in SRAM designs. [ 11 ] There are two types of SOI devices: PDSOI (partially depleted SOI) and FDSOI (fully depleted SOI) MOSFETs. For an n-type PDSOI MOSFET the sandwiched n-type film between the gate oxide (GOX) and buried oxide (BOX) is large, so the depletion region can't cover the whole n region. So to some extent PDSOI behaves like bulk MOSFET . Obviously there are some advantages over the bulk MOSFETs. The film is very thin in FDSOI devices so that the depletion region covers the whole channel region. In FDSOI the front gate (GOX) supports fewer depletion charges than the bulk so an increase in inversion charges occurs resulting in higher switching speeds. The limitation of the depletion charge by the BOX induces a suppression of the depletion capacitance and therefore a substantial reduction of the subthreshold swing allowing FD SOI MOSFETs to work at lower gate bias resulting in lower power operation. The subthreshold swing can reach the minimum theoretical value for MOSFET at 300K, which is 60mV/decade. This ideal value was first demonstrated using numerical simulation. [ 12 ] [ 13 ] Other drawbacks in bulk MOSFETs, like threshold voltage roll off, etc. are reduced in FDSOI since the source and drain electric fields can't interfere due to the BOX. The main problem in PDSOI is the " floating body effect (FBE)" since the film is not connected to any of the supplies. [ citation needed ]
SiO 2 -based SOI wafers can be produced by several methods:
An exhaustive review of these various manufacturing processes may be found in reference [ 1 ]
IBM began to use SOI in the high-end RS64-IV "Istar" PowerPC-AS microprocessor in 2000. Other examples of microprocessors built on SOI technology include AMD 's 130 nm, 90 nm, 65 nm, 45 nm and 32 nm single, dual, quad, six and eight core processors since 2001. [ 21 ] Freescale adopted SOI in their PowerPC 7455 CPU in late 2001, currently [ when? ] Freescale is shipping SOI products in 180 nm, 130 nm, 90 nm and 45 nm lines. [ 22 ] The 90 nm PowerPC - and Power ISA -based processors used in the Xbox 360 , PlayStation 3 , and Wii use SOI technology as well. Competitive offerings from Intel however continue [ when? ] to use conventional bulk CMOS technology for each process node, instead focusing on other venues such as HKMG and tri-gate transistors to improve transistor performance. In January 2005, Intel researchers reported on an experimental single-chip silicon rib waveguide Raman laser built using SOI. [ 23 ]
As for the traditional foundries, in July 2006 TSMC claimed no customer wanted SOI, [ 24 ] but Chartered Semiconductor devoted a whole fab to SOI. [ 25 ]
In 1990, Peregrine Semiconductor began development of an SOI process technology utilizing a standard 0.5 μm CMOS node and an enhanced sapphire substrate. Its patented silicon on sapphire (SOS) process is widely used in high-performance RF applications. The intrinsic benefits of the insulating sapphire substrate allow for high isolation, high linearity and electro-static discharge (ESD) tolerance. Multiple other companies have also applied SOI technology to successful RF applications in smartphones and cellular radios. [ 26 ] [ additional citation(s) needed ]
SOI wafers are widely used in silicon photonics . [ 27 ] The crystalline silicon layer on insulator can be used to fabricate optical waveguides and other optical devices, either passive or active (e.g. through suitable implantations). The buried insulator enables propagation of infrared light in the silicon layer on the basis of total internal reflection. The top surface of the waveguides can be either left uncovered and exposed to air (e.g. for sensing applications), or covered with a cladding, typically made of silica [ 28 ]
The major disadvantage of SOI technology when compared to conventional semiconductor industry is increased cost of manufacturing. [ 29 ] As of 2012 only IBM and AMD used SOI as basis for high-performance processors and the other manufacturers (Intel, TSMC, Global Foundries etc.) used conventional silicon wafers to build their CMOS chips. [ 29 ]
As of 2020 the market utilizing the SOI process was projected to grow up by ~15% for the next 5 years according to Market Research Future group. [ 30 ] | https://en.wikipedia.org/wiki/Silicon_on_insulator |
Silicone hydrophobic powder, generally abbreviated as SHP, is a versatile chemical additive known for its remarkable water-repellent properties. It is a fine, white powder composed of silicone polymer, a synthetic polymer known for its unique combination of flexibility, stability, and resistance to various environmental factors. [ 1 ]
The water-repelling liquid is applied:
In addition, the treated surface does not change its appearance, maintains air permeability - material is not sweated and retains the ability to output pairs.
The water-repelling liquid is applied:
In addition, the treated surface does not change its appearance, maintains air permeability - material is not sweated and retains the ability to output pairs.
The positive effects of the application of methyl hydride siloxane:
Water emulsion of organo silicon the methyl hydride siloxane with additives of emulsifier, biocides and stabilizers
Solids content in the emulsion SE 50-94M is 50%. The color is from white to light gray.
Application:
The emulsion oligo methyl hydride siloxane has properties and characteristics similar with the methyl hydride siloxane. The emulsion is also used to provide various materials with water repellency properties.
However, as oligo methyl hydride siloxane is the water emulsion, it can be applied as an additive in the production of solutions and mixtures that is by the volumetric method.
Liquid is a mixture of tetra ethoxy silane and polyethoxy siloxanes.
Application
Commercially available siliconates include potassium methyl siliconate (CAS 31795-24-1, CH 5 KO 3 Si) and sodium methyl siliconate (CAS 16589-43-8, CH 5 NaO 3 Si). These are supplied as a concentrate in water with an active content of between 30 and 40% by weight. This solution is further diluted in water prior to their application by spraying, dipping or rolling to a mineral building material, such as brickwork, to make the surface water repellent. [ 2 ] The dilution is clear, stable with a high pH of 13 to 14. When applied to a surface the siliconate reacts with carbon dioxide in the air to form an insoluble water resistant treatment within 24 hours.
The methyl group has now attached itself to the substrata.
The salts formed by this reaction are often the cause of white efflorescence when too much of the solution is applied to the surface. | https://en.wikipedia.org/wiki/Silicon_organic_water_repellent |
Silicon tetraazide is a thermally unstable binary compound of silicon and nitrogen with a nitrogen content of 85.7% (by molar mass ). This high-energy compound combusts spontaneously and can only be studied in a solution. [ 1 ] [ 2 ] [ 3 ] A further coordination to a six-fold coordinated structure such as a hexaazidosilicate ion [Si(N 3 ) 6 ] 2− [ 4 ] or as an adduct with bidentate ligands Si(N 3 ) 4 ·L 2 [ 2 ] will result in relatively stable, crystalline solids that can be handled at room temperature.
Silicon tetraazide is synthesized by conversion of silicon tetrachloride with sodium azide in benzene . [ 1 ] [ 3 ]
The reaction of silicon tetrachloride with an excess of sodium azide at room temperature in acetonitrile will result in the formation of sodium hexaazidosilicate ( Na 2 [Si(N 3 ) 6 ] ) which by adding ligands such as 2,2′-bipyridine and 1,10-phenanthroline will result in stable silicon tetraazide adducts. [ 2 ] Other bases such as pyridine and tetramethylethylenediamine will not react with the hexaazidosilicate ion. [ 2 ]
Another preparation of a bis(triphenylphosphine)iminium hexaazidosilicate salt [(Ph 3 P) 2 N] 2 [Si(N 3 ) 6 ] is possible by conversion of bis(triphenylphosphine)iminium azide [(Ph 3 P) 2 N]N 3 with silicon tetrachloride in acetonitrile, where Ph is phenyl . [ 4 ]
Silicon tetraazide is a white crystalline compound that will detonate at even 0 °C. [ 1 ] The pure compound, and also silicon chloride triazide SiCl(N 3 ) 3 and silicon dichloride diazide SiCl 2 (N 3 ) 2 contaminated samples, can detonate spontaneously without clear cause. [ 5 ] The compound is susceptible to hydrolysis . [ 3 ] It is soluble in diethylether and benzene . [ 1 ]
The addition compound with 2,2′-bipyridine is much more stable. A melting point of 212 °C with a melting enthalpy of 110 J/g is recorded. The DSC measurement shows at 265 °C a sharp exothermic reaction with an enthalpy of −2400 J/g. Similar results are found for the addition compound with 1,10-phenanthroline. As the hemiacetonitrile solvatated isolated compound expels solvent at 100 °C, and shows then in the DSC measurement from 240 °C onwards a strong exothermic reaction with a generated heat of 2300 J/g. [ 2 ] The enthalpies are higher than that of sodium azide with −800 J/g, [ 6 ] but still lower than the values encountered with classic explosives such as RDX with −4500 J/g. [ 2 ] The addition compounds are stable in solution. It can be concluded from IR-spectroscopy and proton NMR data that no dissociation occurs in silicon tetraazide and 2,2'-bipyridine or for example 1,10-phenanthroline. [ 2 ] The bis(triphenylphosphino)iminium hexaazidosilicate salt [(Ph 3 P) 2 N] 2 [Si(N 3 ) 6 ] on the other hand is relatively stable. The compound melts at 214 °C and shows in the DSC measurement at 250 °C a reaction. [ 4 ] One mass spectrometry coupled thermogravimetric analysis investigation indicated as reaction products nitrogen , silicon tetraazide and hydrazoic acid . [ 4 ]
A practical application of free silicon tetraazide is unlikely due to the high instability. In solution the compound has potential uses as raw material for nitrogen-rich materials. [ 2 ] One application as reagent in the manufacture of polyolefins has been patented. [ 7 ] The stabilized adducts can serve as energetic compounds as a replacement for lead azide . [ 2 ] | https://en.wikipedia.org/wiki/Silicon_tetraazide |
This page provides supplementary chemical data on silicon tetrachloride .
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, it this case, noting that one should "avoid all contact! In all cases consult a doctor! ... inhalation causes sore throat and Burning sensation". [ 1 ] | https://en.wikipedia.org/wiki/Silicon_tetrachloride_(data_page) |
Silicone foam is a synthetic rubber product used in gasketing , sheets and firestops . It is available in solid, cured form as well as in individual liquid components for field installations. [ 1 ]
When the constituent components of silicone foam are mixed together, they evolve hydrogen gas, which causes bubbles to form within the rubber, as it changes from liquid to solid. This results in an outward pressure. Temperature and humidity can influence the rate of expansion.
This chemical process -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silicone_foam |
Silicone quaternary amine is a polymeric chemical antimicrobial agent [ 1 ] used in some odor-repellent socks , including Burlington Bioguard Socks. [ 2 ]
This article about polymer science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silicone_quaternary_amine |
A silicon–oxygen bond ( Si−O bond ) is a chemical bond between silicon and oxygen atoms that can be found in many inorganic and organic compounds . [ 1 ] In a silicon–oxygen bond, electrons are shared unequally between the two atoms , with oxygen taking the larger share due to its greater electronegativity . This polarisation means Si–O bonds show characteristics of both covalent and ionic bonds . [ 2 ] Compounds containing silicon–oxygen bonds include materials of major geological and industrial significance such as silica , silicate minerals and silicone polymers like polydimethylsiloxane . [ 1 ] [ 3 ]
On the Pauling electronegativity scale , silicon has an electronegativity of 1.90 and oxygen 3.44. The electronegativity difference between the elements is therefore 1.54. Because of this moderately large difference in electronegativities, the Si−O bond is polar but not fully ionic . Carbon has an electronegativity of 2.55 so carbon–oxygen bonds have an electronegativity difference of 0.89 and are less polar than silicon–oxygen bonds. Silicon–oxygen bonds are therefore covalent and polar , with a partial positive charge on silicon and a partial negative charge on oxygen: Si δ+ —O δ− . [ 2 ]
Silicon–oxygen single bonds are longer (1.6 vs 1.4 Å ) but stronger (452 vs. about 360 kJ mol −1 ) than carbon–oxygen single bonds. [ 1 ] However, silicon–oxygen double bonds are weaker than carbon–oxygen double bonds (590 vs. 715 kJ mol −1 ) due to a better overlap of p orbitals forming a stronger pi bond in the latter. This is an example of the double bond rule . For these reasons, carbon dioxide is a molecular gas containing two C=O double bonds per carbon atom whereas silicon dioxide is a polymeric solid containing four Si–O single bonds per silicon atom; molecular SiO 2 containing two Si=O double bonds would polymerise. [ 4 ] Other compounds containing Si=O double bonds are normally very reactive and unstable with respect to polymerisation or oligomerization . Silanones oligomerise to siloxanes unless they are stabilised, [ 5 ] for example by coordination to a metal centre, [ 6 ] coordination to Lewis acids or bases , [ 7 ] or by steric shielding . [ 8 ]
Disiloxane groups, Si–O–Si, tend to have larger bond angles than their carbon counterparts, C–O–C. The Si–O–Si angle ranges from about 130–180°, whereas the C–O–C angle in ethers is typically 107–113°. Si–O–C groups are intermediate, tending to have bond angles smaller than Si–O–Si but larger than C–O–C. The main reasons are hyperconjugation (donation from an oxygen p orbital to an Si–R σ* sigma antibonding molecular orbital , for example) and ionic effects (such as electrostatic repulsion between the two neighbouring partially positive silicon atoms). Recent calculations suggest π backbonding from an oxygen 2p orbital to a silicon 3d orbital makes only a minor contribution to bonding as the Si 3d orbital is too high in energy. [ 2 ]
The Si–O–Si angle is 144° in α-quartz , 155° in β-quartz , 147° in α-cristobalite and (153±20)° in vitreous silica . It is 180° in coesite (another polymorph of SiO 2 ), in Ph 3 Si–O–SiPh 3 , [ 17 ] and in the [O 3 Si–O–SiO 3 ] 6− ion in thortveitite , Sc 2 Si 2 O 7 . It increases progressively from 133° to 180° in Ln 2 Si 2 O 7 as the size and coordination number of the lanthanide decreases from neodymium to lutetium. It is 150° in hemimorphite and 134° in lithium metasilicate and sodium metasilicate . [ 1 ]
In silicate minerals, silicon often forms single bonds to four oxygen atoms in a tetrahedral molecular geometry , forming a silicon–oxygen tetrahedron . At high pressures, silicon can increase its coordination number to six, as in stishovite . [ 1 ] | https://en.wikipedia.org/wiki/Silicon–oxygen_bond |
Silicothermic reactions are thermic chemical reactions using silicon as the reducing agent at high temperature (800-1400°C).
They were initially commercialized for the production of low-carbon ferromanganese before and during World War I ( F. M. Becket played a significant role) and are still used today. They were also historically used for the production of low-carbon ferrochrome, but were displaced by electric methods.
The most prominent example is the Pidgeon process (developed commercially in Canada during the Second World War [ 1 ] by Lloyd Montgomery Pidgeon ) for reducing magnesium metal from ores . Other processes include the Bolzano process and the magnetherm process . All three are commercially used for magnesium production.
This chemical reaction article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silicothermic_reaction |
Silk surfacing was a surface finishing of cotton to obtain an appearance similar to silk.
In contrast to other imitative finishes such as mercerizing , In Silk surfacing, real silk was used in this treatment. Cotton was treated with acid and then silk waste (mixed) solution cotton to provide a lustrous appearance. [ 1 ] [ 2 ] [ 3 ]
The steps are as follows:
The cotton is encased with silk. Although the finish was less durable, was adapted for selected products only that were less likely to wash. [ 4 ] [ 1 ] [ 2 ] [ 3 ]
This textile arts article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silk_surfacing |
A sill plate or sole plate in construction and architecture is the bottom horizontal member of a wall or building to which vertical members are attached. The word "plate" is typically omitted in America and carpenters speak simply of the "sill". Other names are rat sill , ground plate , ground sill , groundsel , night plate , and midnight sill . [ 1 ] [ 2 ] [ 3 ]
Sill plates are usually composed of lumber but can be any material. The timber at the top of a wall is often called a top plate, pole plate, mudsill, wall plate or simply "the plate".
In historic buildings the sills were almost always large, solid timbers framed together at the corners, carry the bents , and are set on the stone or brick foundation walls, piers , or piles (wood posts driven or set into the ground). The sill typically carries the wall framing (posts and studs) and floor joists .
There are rare examples of historic buildings in the U.S. where the floor joists land on the foundation and a plank sill or timber sill sit on top of the joists. [ 4 ] Another rare, historic building technique is for the posts of a timber-frame building to land directly on a foundation or in the ground and the sills fit between the posts and are called interrupted sills .
In modern wood construction, sills usually come in sizes of 2×4, 2×6, 2×8, and 2×10. In stick framing , the sill is made of treated lumber , and is anchored to the foundation wall, often with J-bolts , to keep the building from coming off the foundation during a severe storm or earthquake. Building codes require that the bottom of the sill plate be kept 6 to 8 inches above the finished grade, to hinder termites, and to prevent the sill plate from rotting.
In automobiles , the sill plate is located underneath the door and sometimes displays the make or model of the vehicle.
In naval architecture , sill also refers to the lower horizontal plate (frame) height, above which doors and access opening are fixed. | https://en.wikipedia.org/wiki/Sill_plate |
Silly Putty is a toy containing silicone polymers that have unusual physical properties. It can flow like a liquid, bounce and can be stretched or broken depending on the amount of physical stress to which it is subjected. It contains viscoelastic liquid silicones, a type of non-Newtonian fluid , which makes it act as a viscous liquid over a long period of time but as an elastic solid over a short time period. It was originally created during research into a potential rubber substitute for use by the United States in World War II . [ 1 ] [ 2 ] [ 3 ]
The name Silly Putty is a trademark of Crayola LLC. [ 4 ] Other names are used to market similar substances from other manufacturers.
As a bouncing putty , Silly Putty is noted for its unusual characteristics. It bounces when dropped from a height, but breaks when struck or stretched sharply; it can also float in a liquid and will form a puddle given enough time. Silly Putty and most other retail putty products have viscoelastic agents added to reduce the flow and enable the putty to hold its shape. [ 5 ]
The original coral-colored Silly Putty is composed of 65% dimethylsiloxane ( hydroxy -terminated polymers with boric acid ), 17% silica (crystalline quartz), 9% Thixatrol ST ( castor oil derivative), 4% polydimethylsiloxane , 1% decamethyl cyclopentasiloxane , 1% glycerine , and 1% titanium dioxide . [ 6 ]
Silly Putty's unusual flow characteristics are due to the ingredient polydimethylsiloxane (PDMS), a viscoelastic substance. Viscoelasticity is a type of non-Newtonian flow , characterizing a material that acts as a viscous liquid over a long time period but as an elastic solid over a short time period. [ 7 ] Because its apparent viscosity increases directly with respect to the amount of force applied, Silly Putty can be characterized as a dilatant fluid. [ 5 ]
Silly Putty is also a fairly good adhesive . When newspaper ink was petroleum based, Silly Putty could be used to transfer newspaper images to other surfaces, providing amusement by distorting the transferred image afterwards. Newer papers with soy-based inks are more resistant to this process. [ 8 ]
Generally, Silly Putty is difficult to remove from textured items such as dirt and clothing. Hand sanitizers containing alcohol are often helpful. Silly Putty will dissolve when in contact with an alcohol; after the alcohol evaporates, the material will not exhibit its original properties. [ 9 ]
If Silly Putty is submerged in warm or hot water, it will become softer and thus "melt" much faster. It also becomes harder to remove small amounts of it from surfaces. After a long period of time, it will return to its original viscosity. [ 6 ]
Silly Putty is sold as a 13 g (0.46 oz) piece of clay inside an egg-shaped plastic container. The Silly Putty brand is owned by Crayola LLC (formerly the Binney & Smith company). As of July 2009 [update] , twenty thousand eggs of Silly Putty are sold daily. Since 1950, more than 300 million eggs of Silly Putty (approximately 4,500 short tons or 4,100 tonnes) have been sold. [ 10 ] It is available in various colors, including glow-in-the-dark and metallic. Other brands offer similar materials, sometimes in larger-sized containers, and in a similarly wide variety of colors or with different properties, such as magnetism and iridescence . [ citation needed ]
During World War II, Japan invaded rubber-producing countries as it expanded its sphere of influence in the Pacific Rim . Rubber was vital for the production of rafts , tires , vehicle and aircraft parts, gas masks , and boots . In the US, all rubber products were rationed; citizens were encouraged to make their rubber products last until the end of the war and to donate spare tires, boots, and coats. Meanwhile, the government funded research into synthetic rubber compounds to attempt to solve this shortage. [ 11 ]
Credit for the invention of Silly Putty is disputed [ 12 ] and has been attributed variously to Earl Warrick [ 3 ] of the then newly formed Dow Corning ; Harvey Chin; and James Wright , a Scottish -born inventor working for General Electric in New Haven , Connecticut . [ 13 ] Throughout his life, Warrick insisted that he and his colleague, Rob Roy McGregor, received the patent for Silly Putty before Wright did; [ 14 ] but Crayola's history of Silly Putty states that Wright first invented it in 1943. [ 11 ] [ 15 ] [ 16 ] Both researchers independently discovered that reacting boric acid with silicone oil would produce a gooey, bouncy material with several unique properties. The non-toxic putty would bounce when dropped, could stretch farther than regular rubber, would not go moldy, and had a very high melting temperature. However, the substance did not have all the properties needed to replace rubber. [ 1 ]
In 1949, toy store owner Ruth Fallgatter came across the putty. She contacted marketing consultant Peter C. L. Hodgson (1912–1976). [ 17 ] The two decided to market the bouncing putty by selling it in a clear case. Although it sold well, Fallgatter did not pursue it further. However, Hodgson saw its potential. [ 1 ] [ 5 ]
Already US$12,000 in debt, Hodgson borrowed $147 to buy a batch of the putty to pack 1 oz (28 g) portions into plastic eggs for $1, calling it Silly Putty. Initial sales were poor, but after a New Yorker article mentioned it, Hodgson sold over 250,000 eggs of silly putty in three days. [ 5 ] However, Hodgson was almost put out of business in 1951 by the Korean War . Silicone, the main ingredient in silly putty, was put on ration, harming his business. A year later, the restriction on silicone was lifted and the production of Silly Putty resumed. [ 10 ] [ 18 ] Initially, it was primarily targeted towards adults. However, by 1955, the majority of its customers were aged six to twelve. In 1957, Hodgson produced the first televised commercial for Silly Putty, which aired during the Howdy Doody Show . [ 19 ]
In 1961, Silly Putty went worldwide, becoming a hit in the Soviet Union and Europe. In 1968, it was taken into lunar orbit by the Apollo 8 astronauts. [ 18 ]
Peter Hodgson died in 1976. A year later, Binney & Smith, the makers of Crayola products, acquired the rights to Silly Putty. As of 2005 [update] , annual Silly Putty sales exceeded six million eggs. [ 20 ]
Silly Putty was inducted into the National Toy Hall of Fame on May 28, 2001. [ 21 ]
In addition to its success as a toy, other uses for the putty have been found. In the home, it can be used to remove substances such as dirt, lint, pet hair, or ink from various surfaces. The material's unique properties have found niche use in medical and scientific applications. Occupational therapists use it for rehabilitative therapy of hand injuries. [ 22 ] A number of other brands (such as Power Putty and TheraPutty ) alter the material's properties, offering different levels of resistance. The material is also used as a tool to help reduce stress, and exists in various viscosities based on the user's preference. [ citation needed ]
Because of its adhesive characteristics, it was used by Apollo astronauts to secure their tools in zero gravity. [ 23 ] Scale model building hobbyists use the putty as a masking medium when spray-painting model assemblies. [ 24 ] [ 25 ] The Steward Observatory uses a Silly-Putty backed lap to polish astronomical telescope mirrors. [ 26 ] [ 27 ]
Researchers from Trinity College Dublin School of Physics (Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN) and Advanced Materials and Bioengineering Research (AMBER) Research Centers) have discovered nano composite mixtures of graphene and Silly Putty behave as sensitive pressure sensors, claiming the ability to measure the footsteps of a spider crawling on it. [ 28 ] | https://en.wikipedia.org/wiki/Silly_Putty |
Silopi Asphaltite Mine is an asphaltite mine located in Şırnak Province in Turkey [ 1 ] which supplies fuel for Şırnak Silopi power station . [ 2 ] | https://en.wikipedia.org/wiki/Silopi_asphaltite_mine |
The Silsbee effect or Silsbee current refers to the effect by which, if the electric current through a superconductor exceeds a critical level, the superconducting state will be destroyed. [ 1 ] The size of the critical current (which can be as large as 100 amperes in a 1-mm wire) depends on the nature and geometry of the specimen and is related to whether the magnetic field produced by the current exceeds the critical field at the surface of the superconductor. [ 2 ]
The effect is named after Francis B. Silsbee who studied conductivity at low temperatures. [ 3 ] | https://en.wikipedia.org/wiki/Silsbee_effect |
The silt density index is a measure for the fouling capacity of water in reverse osmosis systems. The test measures the rate at which a 0.45- micrometre filter is plugged when subjected to a constant water pressure of 206.8 kPa (30 psi). The SDI gives the percent drop per minute in the flow rate of the water through the filter, averaged over a period of time such as 15 minutes. [ citation needed ] [ 1 ]
Typically, spiral-wound reverse osmosis systems will need an SDI less than 5, and hollow fiber reverse osmosis systems will need an SDI less than 3. In these kinds of systems, deep-well waters (with a typical SDI of 3) could be used straight from the source. If fed from surface waters (with a typical SDI greater than 6), the water will need to be filtered before use. [ citation needed ] Seawater desalination plants utilising reverse osmosis systems also need very efficient filtering due to the typically high but variable SDI of seawater. [ 2 ]
This hydrology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silt_density_index |
A silt fence , sometimes (misleadingly) called a filter fence , [ 1 ] is a temporary sediment control device used on construction sites to protect water quality in nearby streams, rivers, lakes and seas from sediment (loose soil ) in stormwater runoff . Silt fences are widely used on construction sites in North America and elsewhere, due to their low cost and simple design. [ 2 ] However, their effectiveness in controlling sediment can be limited, due to problems with poor installation, proper placement, and/or inadequate maintenance. [ 3 ]
Silt fences are often installed as perimeter controls. They are typically used in combination with sediment basins and sediment traps , as well as with erosion controls , which are designed to retain sediment in place where soil is being disturbed by construction processes (i.e., land grading and other earthworks ). [ 4 ]
A typical fence consists of a piece of synthetic filter fabric (also called a geotextile ) stretched between a series of wooden or metal fence stakes along a horizontal contour level. The stakes are installed on the downhill side of the fence, and the bottom edge of the fabric can be trenched into the soil and backfilled on the uphill side, although it is quite difficult to move the trenched "spoil" from the downside to the upside of the trench. The design/placement of the silt fence should create a pooling of runoff, which then allows sedimentation to occur. Water can seep through the silt fence fabric, but the fabric often becomes "blocked off" with fine soil particles (all sediment-retention devices have this challenge, and none of them "filter" storm water for very long). [ citation needed ] A few hours after a storm event, the fabric can be "disturbed" in order to dislodge the fines, and allow clean water to flow through. Depending on the protected watershed and erosion, larger soil particles will settle out, ultimately filling the silt fence to the top of the structure; requiring another silt fence above or below it (creating a new ponding area), or for the silt fence to be removed, the sediment removed or spread out, and a new fence installed. The fence is not designed to concentrate or channel stormwater. The fence is installed on a site before soil disturbance begins, and is placed down-slope from the disturbance area. [ 5 ] [ 6 ]
Sediment is captured by silt fences most often through ponding of water and settling, rather than filtration by the fabric. Sand and silt tends to clog the fabric, and then the sediments settle in the temporary pond. [ 7 ] : p.6–9 [ 8 ] : p.7–46
Some government jurisdictions in the United States recommend or require the use of a reinforced fence, sometimes called a "super" silt fence or an enhanced silt fence, on some construction sites. [ 9 ] This design uses filter fabric reinforced by a wire mesh or chain link fence . The metal backing gives the fence increased strength to resist the weight of soil and water which may be trapped by the fence in a large drainage area, and discourages construction site operators from driving vehicles over the fence. [ 10 ] However, an improper installation of a super silt fence can create an inadvertent sediment basin when the filter fabric becomes clogged. This typically causes flooding and increased downstream pollution . Most super silt fence specifications are outdated, requiring the trenching installation method, which has been shown to be highly susceptible to "washing out" under the fabric due to improper back-filling and inadequate compaction. [ citation needed ]
Some state agencies recommend an installation technique called "static slicing" as an improved method for ensuring effectiveness and longevity of a silt fence system on a construction site. The technique involves inserting a narrow blade into the soil with a wedge-type point on its tip to slightly disrupt the soil upward, while simultaneously inserting the silt fence fabric into the slot with a moving pivot, while the machine is moving forward. This step is followed by mechanical soil compaction , setting of fence posts, and attaching the fabric. [ 6 ] [ 11 ]
Silt fence fabrics (geotextiles) tested in laboratory settings have shown to be effective at trapping sediment particles. [ 13 ] : 45–47 Although there have been few field tests of silt fences installed at construction sites, these tests have shown generally poor results. [ 13 ] : 27–31, 53–55 (Effectiveness testing involved measurements for both total suspended solids and turbidity .) Other studies and articles about silt fence usage and practice document problems with installation and maintenance, implying poor performance. [ 1 ]
Since 1998, static slicing the material into the ground has proven to be the most efficient and most effective installation method because slicing maintains the soil on both sides of the fence, and is conducive to proper compaction—which is critical to performance, as well. [ citation needed ] In 2000 the U.S. Environmental Protection Agency (EPA) co-sponsored silt fence efficacy field research through its Environmental Technology Verification Program, and in general, the report found the static slicing method to be highly effective, and efficient. [ 14 ] Silt fence effectiveness is best determined by how many hundreds of pounds of sediment are contained behind a given silt fence after a storm event, and not turbidity, etc. as sediment-retention is the end goal, and not a water-quality measurement used in erosion control, for instance. [ citation needed ]
Silt fences may perform poorly for a variety of reasons, including improper location (e.g. placing fence where it will not pond runoff water), improper installation (e.g. failure to adequately embed and backfill the lower edge of fabric in the soil) and lack of maintenance—fabric falling off of the posts, or posts knocked down. A silt fence top-full of sediment may need maintenance/replacement, but it is a huge success. [ 7 ] : p.6–10 The fabric may become damaged with holes and tears if construction materials are stored next to or on top of the fence. During various phases of construction at a site, a silt fence may be removed relocated and reinstalled multiple times. [ 13 ] : 30–31 It may be difficult to maintain effectiveness of a silt fence under such operating conditions. Location of fences in areas with high flows may lead to fence failures when the installation is not adequately back-filled and properly compacted, and/or the post-spacing is inadequate. [ 8 ] : p.7–46 | https://en.wikipedia.org/wiki/Silt_fence |
Siltation is water pollution caused by particulate terrestrial clastic material, with a particle size dominated by silt or clay . It refers both to the increased concentration of suspended sediments and to the increased accumulation (temporary or permanent) of fine sediments on bottoms where they are undesirable. Siltation is most often caused by soil erosion or sediment spill.
It is sometimes referred to by the ambiguous term " sediment pollution ", which can also refer to a chemical contamination of sediments accumulated on the bottom, or to pollutants bound to sediment particles. Although "siltation" is not perfectly stringent, since it also includes particle sizes other than silt, it is preferred for its lack of ambiguity.
The origin of the increased sediment transport into an area may be erosion on land or activities in the water.
In rural areas, the erosion source is typically soil degradation by intensive or inadequate agricultural practices, leading to soil erosion , especially in fine-grained soils such as loess . The result will be an increased amount of silt and clay in the water bodies that drain the area. In urban areas, the erosion source is typically construction activities, which involve clearing the original land-covering vegetation and temporarily creating something akin to an urban desert from which fines are easily washed out during rainstorms.
In water, the main pollution source is sediment spill from dredging , the transportation of dredged material on barges, and the deposition of dredged material in or near water. Such deposition may be made to get rid of unwanted material, such as the offshore dumping of material dredged from harbours and navigation channels. The deposition may also be to build up the coastline, for artificial islands , or for beach replenishment .
Climate change also affects siltation rates. [ 1 ]
Another important cause of siltation is the septage and other sewage sludges that are discharged from households or business establishments with no septic tanks or wastewater treatment facilities to bodies of water.
While the sediment in transport is in suspension , it acts as a pollutant for those who require clean water, such as for cooling or in industrial processes, and it includes aquatic life that are sensitive to suspended material in the water. While nekton have been found to avoid spill plumes in the water (e.g. the environmental monitoring project during the building of the Øresund Bridge ), filtering benthic organisms have no way of escape. Among the most sensitive organisms are coral polyps. Generally speaking, hard bottom communities and mussel banks (including oysters) are more sensitive to siltation than sand and mud bottoms. Unlike in the sea, in a stream, the plume will cover the entire channel, except possibly for backwaters, and so fish will also be directly affected in most cases.
Siltation can also affect navigation channels or irrigation channels. It refers to the undesired accumulation of sediments in channels intended for vessels or for distributing water.
One may distinguish between measurements at the source, during transport, and within the affected area. Source measurements of erosion may be very difficult since the lost material may be a fraction of a millimeter per year. Therefore, the approach taken is typically to measure the sediment in transport in the stream, by measuring the sediment concentration and multiplying that with the discharge ; for example, 50 mg/L (1.8 × 10 −6 lb/cu in) times 30 m 3 /s (1,100 cu ft/s) gives 1.5 kg/s (200 lb/min).
Also, sediment spill is better measured in transport than at the source. The sediment transport in open water is estimated by measuring the turbidity , correlating turbidity to sediment concentration (using a regression developed from water samples that are filtered, dried, and weighed), multiplying the concentration with the discharge as above, and integrating over the entire plume. To distinguish the spill contribution, the background turbidity is subtracted from the spill plume turbidity. Since the spill plume in open water varies in space and time, an integration over the entire plume is required, and repeated many times to get acceptably low uncertainty in the results. The measurements are made close to the source, in the order of a few hundred meters.
Anything beyond a work area buffer zone for sediment spill is considered the potential impact area. In the open sea, the impact of concern is almost exclusively with the sessile bottom communities since empirical data show that fish effectively avoid the impacted area. The siltation affects the bottom community in two main ways. The suspended sediment may interfere with the food gathering of filtering organisms, and the sediment accumulation on the bottom may bury organisms to the point that they starve or even die. It is only if the concentration is extreme that it decreases the light level sufficiently for impacting primary productivity. An accumulation of as little as 1 mm (0.039 in) may kill coral polyps.
While the effect of the siltation on the biota (once the harm is already done) can be studied by repeated inspection of selected test plots, the magnitude of the siltation process in the impact area may be measured directly by monitoring in real time. Parameters to measure are sediment accumulation, turbidity at the level of the filtering biota, and optionally incident light. [ 2 ]
Siltation of the magnitude that it affects shipping can also be monitored by repeated bathymetric surveys.
In rural areas, the first line of defense is to maintain land cover and prevent soil erosion in the first place. The second line of defense is to trap the material before it reaches the stream network (known as sediment control ). In urban areas, the defenses are to keep land uncovered for as short a time as possible during construction and to use silt screens to prevent the sediment from getting released in water bodies.
During dredging, the spill can be minimized but not eliminated completely by the way the dredger is designed and operated. If the material is deposited on land, efficient sedimentation basins can be constructed. If it is dumped into relatively deep water, there will be a significant spill during dumping but not thereafter, and the spill that arises has minimal impact if there are only fine-sediment bottoms nearby.
One of the most difficult conflicts of interest to resolve, as regards siltation mitigation, is perhaps beach nourishment . When sediments are placed on or near beaches in order to replenish an eroding beach, any fines in the material will continue to be washed out for as long as the sand is being reworked. Since all replenished beaches are eroding or they would not need replenishment, they will contribute to nearshore siltation almost for as long as it takes to erode away what was added, albeit with somewhat decreasing intensity over time. Since the leakage is detrimental to coral reefs, the practice leads to a direct conflict between the public interest of saving beaches, and preserving any nearshore coral reefs. To minimize the conflict, beach replenishment should not be done with sand containing any silt or clay fractions. In practice the sand is often taken from offshore areas, and since the proportion of fines in sediments typically increases in the offshore direction, the deposited sand will inevitably contain a significant percentage of siltation-contributing fines.
It is desirable to minimize the siltation of irrigation channels by hydrologic design, the objective being not to create zones with falling sediment transport capacity, as that is conducive to sedimentation. Once sedimentation has occurred, in irrigation or navigation channels, dredging is often the only remedy. | https://en.wikipedia.org/wiki/Siltation |
The Silurian hypothesis is a thought experiment , [ 1 ] which assesses modern science's ability to detect evidence of a prior advanced civilization, perhaps several million years ago. The most probable clues for such a civilization could be carbon , radioactive elements or temperature variation. The name "Silurian" derives from the eponymous sapient species from the BBC science fiction series Doctor Who , who in the series established an advanced civilization prior to humanity , though not from the eponymous geological period .
Astrophysicists Adam Frank and Gavin Schmidt proposed the "Silurian Hypothesis" in a 2018 paper, [ 2 ] exploring the possibility of detecting an advanced civilization before humans in the geological record. They argued that there has been sufficient fossil carbon to fuel an industrial civilization since the Carboniferous Period (~350 million years ago); however, finding direct evidence, such as technological artifacts, is unlikely due to the rarity of fossilization and Earth's exposed surface . Instead, researchers might find indirect evidence, such as climate changes, anomalies in sediment, or traces of nuclear waste . The hypothesis also speculates that artifacts from past civilizations could be found on the Moon and Mars , where erosion and tectonic activity are less likely to erase evidence. The concept of pre-human civilizations has been explored in popular culture, including novels, television shows, short stories, and video games.
The idea was presented in a 2018 paper by Adam Frank , an astrophysicist at the University of Rochester , and Gavin Schmidt , director of the Goddard Institute for Space Studies . Frank and Schmidt imagined an advanced civilization before humans and pondered whether it would "be possible to detect an industrial civilization in the geological record". [ 2 ] They argue as early as the Carboniferous period (~350 million years ago) "there has been sufficient fossil carbon to fuel an industrial civilization comparable with our own". However, they also wrote: "While we strongly doubt that any previous industrial civilization existed before our own, asking the question in a formal way that articulates explicitly what evidence for such a civilization might look like raises its own useful questions related both to astrobiology and to Anthropocene studies." [ 2 ] The term "Silurian hypothesis" was inspired by the fictional species called the Silurians from the British television series Doctor Who . [ 1 ]
According to Frank and Schmidt, since fossilization is relatively rare and little of Earth's exposed surface is from before the Quaternary time period (~2.5 million years ago), there is low probability of finding direct evidence of such a civilization, such as technological artifacts. After a great time span, the researchers concluded, contemporary humans would be more likely to find indirect evidence such as rapid changes in temperature or climate (as occurred during the Paleocene–Eocene Thermal Maximum ~55 million years ago); evidence of tapping geothermal power sources; or anomalies in sediment such as their chemical composition (e.g., evidence of artificial fertilizers ) or isotope ratios (e.g., there is no naturally occurring plutonium-244 outside a supernova , so evidence of this isotope could indicate a technologically advanced civilization). [ 2 ] [ 3 ] Objects that could indicate possible evidence of past civilizations include plastics and nuclear waste residues buried deep underground or on the ocean floor. [ 2 ] The paper also mentions the natural fission reactors at Oklo, Gabon, which were active some two billion years BP —while none of the transuranic elements it produced are still present (they have since decayed to longer-lived or stable daughter nuclides), the depletion of 235 U and the characteristic isotope ratios of fission products were used to confirm that fission had indeed occurred.
Frank and Schmidt speculate such a civilization could have gone to space and left artifacts on other celestial bodies, such as the Moon and Mars . Evidence for artifacts on these two worlds would be easier to find than on Earth, where erosion and tectonic activity would erase much of it. [ 4 ] Frank first approached Schmidt to discuss how to detect alien civilizations via their potential impact upon climate through the study of ice cores and tree rings. They both realized that the hypothesis could be expanded and applied to Earth and humanity due to the fact that humans have been in their current form for the past 300,000 years and have had sophisticated technology for only the last few centuries. [ 5 ]
The eponymous Silurians on Doctor Who are a race of reptilian humanoids from Earth's past, making their first appearance in the show in 1970. Frank and Schmidt cite Inherit the Stars , a 1977 novel by J. P. Hogan as containing a similar hypothesis, but also say they were surprised by how rarely the concept was explored in science fiction . [ 2 ] In Larry Niven 's 1980 short story "The Green Marauder", [ 6 ] an alien over 700 million years old (due to relativistic travel ) tells a human about the last time it visited Earth, and the hopeless plea from Earth's anaerobic civilization for help against the growing environmental threat of chlorophyll. Published in 1987, "Toolmaker Koan" by John McLoughlin examines humans meeting dinosaurs. The Star Trek Voyager 1997 episode " Distant Origin " has the crew encounter the Voth, a spacefaring race that appear to have evolved on Earth from dinosaurs. When discussing this theory with a Voth scientist, Chakotay speculates that their ancestors evolved on an isolated continent that was destroyed by cataclysm, with all traces buried under oceans or kilometers of rock. | https://en.wikipedia.org/wiki/Silurian_hypothesis |
Silvana Konermann (born May 18, 1988) is a Swiss-American bioengineer and neuroscientist whose research focuses on CRISPR , genome engineering , transcription and epigenetics , and Alzheimer's disease . She is an assistant professor of biochemistry at Stanford University and co-founder and executive director of Arc Institute .
Konermann's research laboratory aims to understand the molecular pathways that drive the development of Alzheimer’s disease using next-generation functional genomics , with the long-term goal of developing rationally targeted therapeutics for neurodegenerative disorders. [ 1 ]
Konermann attended Sächsisches Landesgymnasium Sankt Afra zu Meißen in Saxony , Germany. [ 2 ] The minor planet 21546 Konermann was named in honor of her 2006 second-place finish at the Intel International Science and Engineering Fair . [ 3 ] She received her Bachelor's degree in neurobiology from ETH Zurich in 2009. [ 4 ]
In 2010, Konermann entered the Brain and Cognitive Sciences PhD program at the Massachusetts Institute of Technology . She joined Feng Zhang 's lab at the Broad Institute and McGovern Institute for Brain Research as one of Zhang's first graduate students. During her PhD, Konermann contributed to the development of pioneering genetic perturbation technologies, including one of the first systems for genome-scale CRISPR activation . [ 5 ] She completed her PhD in neuroscience in 2016, receiving the Harold M. Weintraub Graduate Student Award for "outstanding achievement during graduate studies in the biological sciences." [ 6 ]
As a postdoctoral fellow at the Salk Institute , Konermann was part of the team that discovered Cas13d , a new subclass of compact RNA-targeting CRISPR effectors. [ 7 ] She was named an HHMI Hanna H. Gray Fellow in 2017 and a CZ Biohub investigator in 2019. In October 2019, Konermann joined Stanford as an assistant professor of biochemistry. [ 8 ]
Along with UC Berkeley professor Patrick Hsu and Stripe CEO Patrick Collison , Konermann is a co-founder of nonprofit research organization Arc Institute , where she currently serves as executive director and maintains her research laboratory as a core investigator. [ 9 ] [ 10 ]
In June 2022, Konermann married Irish tech billionaire Patrick Collison , the co-founder and CEO of Stripe . [ 9 ] Konermann met Collison at the 2004 EU Young Scientist competition . [ 9 ] [ 11 ] [ 12 ] | https://en.wikipedia.org/wiki/Silvana_Konermann |
The Silver Branch or Silver Bough ( Irish : An Craobh Airgid ) is a symbol found in Irish mythology and literature.
Featured in the Irish poem The Voyage of Bran and the narrative Cormac's Adventure in the Land of Promise , it represents entry into the Celtic Otherworld or Tír na nÓg .
In Imram Brain ("Voyage of Bran"), the silver apple branch with white apple blossoms was brought to Bran mac Febail by a mysterious woman, who disclosed that the branch of white silver ( Irish : findargat ) was from Emain (or Emne), presumably the land where she hailed from. After singing verses describing her land as the place of delight (with poetic names such as the "Plain of White Silver"); thereafter she slipped away, and the branch sprang back to her, with Bran having no power to keep it in his grasp. [ 1 ] Bran then mounted on a voyage and reached the Land of Women (Tír inna m-Ban), [ 2 ] which is Emain, at least according to some commentators. [ 3 ] [ a ] Some other commentators venture the silver branch Bran saw originated in Emain Ablach , [ 6 ] even though that extended form does not appear in the text of the Imram Brain . [ b ]
The land of the branch turned out to be some sort of "Otherworld", for even though Bran and his crew believed they tarried at the Land of Women for a year, it turned out to be many years, even centuries, so that when they approached Ireland, they learned that they had become ancient history, and a member who tried to set foot on land turned into ashes. [ 8 ] [ 9 ]
Eleanor Hull wrote a paper drawing parallel between this silver branch and the golden bough of Roman legend which was required for entry into the Underworld (Pluto). [ 10 ] In like manner, the branch (silver or otherwise) is an object given to a human invited by a denizen of the Otherworld to visit his/her realm, offering "a clue binding the desired one to enter". [ 11 ] One of the paralleling examples was the branch seen by Bran. [ 12 ]
Though not a genuine Celticist , to quote W. H. Evans-Wentz , "the silver branch of the sacred apple-tree bearing blossoms.. borne by the Fairy Woman is a passport to Tír n-aill (the Celtic Otherworld )". [ 13 ]
A magical silver branch with three golden apples belonged to the sea deity Manannán mac Lir and was given to the high king Cormac mac Airt in the narrative Echtra Cormaic or "Cormac's Adventure in the Land of Promise". The sea god initially visited Cormac's ramparts (at Tara ) as an unidentified warrior from a land "wherein there is nought save truth, and there is neither age nor decay nor gloom", etc., later identified as the Land of Promise ( Tír Tairngire ). The branch created magical soporific music that assuaged those afflicted with injury or illness to sleep, including "women in child-bed". [ c ] [ 14 ]
In a variant text under the title "How Cormac mac Airt Got his Branch", [ d ] the same object is not described as a silver branch, but rather a "glittering fairy branch with nine apples of red gold ". [ 16 ] [ e ] [ f ]
Here, the branch possessed the additional ability make people forget their woes. [ 20 ] Cormac bargained his wife and children away to obtain the branch, and when the wife and daughter learn of this to their utter disheartening, Cormac jiggles the branch to cause their sorrows to depart. [ 16 ] This ability is reminiscent of the grief-soothing lapdog Petit Crû and its jingling bell in Tristan and Isolde , as pointed out by Gertrude Schoepperle . [ 21 ]
Also, in Immacallam in dá Thuarad , or The Dialogue of the Two Sages , the mystic symbol used by gods , fairies , magicians , and by all initiates who know the mystery of life and death, is thus described as a Druid symbol:–'Neidhe' (a young bard who aspired to succeed his father as chief poet of Ulster ), "made his journey with a silver branch over him. [ g ] [ 22 ] [ 23 ] The Anradhs , or poets of the second order, carried a silver branch, but the Ollamhs , or chief poets, carried a branch of gold; all other poets bore a branch of bronze." [ 24 ] [ 25 ] | https://en.wikipedia.org/wiki/Silver_Branch |
The Silver Medal of the Zoological Society of London is "Awarded to a Fellow of the Society or any other person for contributions to the understanding and appreciation of zoology, including such activities as public education in natural history, and wildlife conservation." [ 1 ] It was first awarded in 1847. [ 2 ]
In 1964, the criteria for the Silver Medal were changed, split into 2 categories. Category 1 is awarded to individuals for Curation or distinguished service to the Society, whilst Category 2 is awarded to fellows who have provided a significant contribution to the field of zoology, including in both wildlife conservation and public education of natural history. [ 3 ]
Seirian Sumner | https://en.wikipedia.org/wiki/Silver_Medal_(Zoological_Society_of_London) |
The Silver Sparrow computer virus is malware that runs on x86 - and Apple M1 -based Macintosh computers. [ 1 ] [ 2 ] Engineers at the cyber security firm Red Canary have detected two versions of the malware in January and February 2021. [ 3 ]
Two versions of the malware were reported. The first version (described as the "non-M1" version) is compiled for Intel x86-64 . It was first detected in January 2021. [ 3 ] The second version contains code that runs natively on Apple's proprietary M1 processor, and was probably released in December 2020 and discovered in February 2021. [ 4 ] [ 3 ] The virus connects to a server hosted on Amazon Web Services . [ 5 ] The software includes a self-destruct mechanism . [ 1 ]
As of 23 February 2021, information about how the malware is spread and what system may be compromised is sparse. It is uncertain whether Silver Sparrow is embedded inside malicious advertisements, pirated software, or bogus Adobe Flash Player updaters. Red Canary has theorized that systems could have been infected through malicious search engine results that might have directed them to download the code. [ 3 ] The ultimate object of the malware's release is also still unknown. [ 3 ]
Silver Sparrow is the second malware virus observed to include M1-native code. [ 6 ]
As of 23 February 2021, Internet security company Malwarebytes has discovered over 29,000 Macs worldwide running their anti-malware software to be infected with Silver Sparrow. [ 7 ] Silver Sparrow infected Macs have been found in 153 countries as of February 17, with higher concentrations reported in the US, UK, Canada, France, and Germany, according to data from Malwarebytes . [ 1 ] Over 39,000 Macs were affected in the beginning of March 2021. [ 8 ]
On 23 February 2021, a spokesperson of Apple Inc. stated that "there is no evidence to suggest the malware they identified has delivered a malicious payload to infected users." Apple also revoked the certificates of the developer accounts used to sign the packages, thereby preventing any additional Macs from becoming infected. [ 9 ]
This malware -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silver_Sparrow_(malware) |
Silver Spring Networks , headquartered in San Jose, California , was a provider of smart grid products, with offices in Australia, Singapore, Brazil, and the United Kingdom. In January 2018, the company was acquired by Itron for $830 million and was renamed Itron Networked Solutions. [ 2 ] [ 3 ] [ 4 ]
Besides communications devices, Silver Spring Networks developed software for utilities and customers to improve energy efficiency . [ 5 ]
Silver Spring Networks was founded in July 2002 as Real Time Techomm in Butler, Wisconsin , near Milwaukee . [ 6 ] [ 7 ] Original founders included Eric Dresselhuys who had worked on related technology since 1995, and Keith Burge.
In 2002, funding came from Denver angel investor Jack Thompson.
The company adopted the name of the street in Milwaukee of its original office and was relocated to San Mateo, California in 2003. At this time, Foundation Capital invested $8 million in the company and Raj Vaswani joined the founding team. Ray Bell became interim CEO and chief technology officer, but left to found Grid Net in 2005. [ 8 ]
Other investors included Northgate Capital, Kleiner Perkins Caufield & Byers and Google . [ 9 ] The company moved its headquarters to San Jose in 2016. [ 10 ]
The first large pilot deployment was started in 2007 with Florida Power & Light (FPL) in southern Florida.
In 2008, Pacific Gas and Electric Company (PG&E) signed an agreement to provide the company's smart meters, and remained the largest customer for at least several years.
On July 7, 2011, Silver Spring Networks filed with the U.S. Securities and Exchange Commission (SEC) to raise up to $150 million in an initial public offering . [ 11 ]
On March 13, 2013, Silver Spring Networks became a public company via an initial public offering on New York Stock Exchange , raising $81 million. [ 12 ] [ 13 ]
Silver Spring Networks developed equipment that creates wireless mesh networks and transmits energy consumption data between meters, consumers and utilities in real time. The software indicates how much money is spent on electricity and indicates how much can be saved if one switches to energy-efficient models. [ 14 ]
The meters in the PG&E deployment include two radios: one in the unlicensed ISM band of 902 to 928 MHz for communication back to the utility provider, and another intended for future communication to a home network . [ 15 ] The technology has low bit rate requirements, but also needs to be very low cost. [ 16 ]
Silver Spring was a partner with more than 40 companies and provides additional applications to utilities and customers on the Smart Energy Platform like smart thermostats , in-home displays, and electric vehicle (EV) charging technology. [ 17 ] [ 18 ]
Silver Spring began its technology offering with a smart grid network based on Internet Protocol (IP) technology, which was advocated for the smart grid by the U.S. Federal Communications Commission (FCC) and other smart grid experts. [ 19 ] Silver Spring expanded on the network to smart grid application software that includes demand response (DR), demand management [ 5 ] and other services for utilities and their customers. [ 17 ]
In October 2009 Silver Spring acquired Greenbox Technology, and developed its web-based software into a product called CustomerIQ. [ 11 ]
In an Oklahoma Gas & Electric pilot program involving 2,500 homes in the summer of 2010 on Silver Spring’s Smart Energy Platform, participants saw an average energy use drop of up to 33 percent during the highest price periods. The pilot consisted of several groups using Silver Spring’s web-based energy management solution as well as smart thermostats and in-home energy displays on various dynamic pricing schemes. [ 20 ] | https://en.wikipedia.org/wiki/Silver_Spring_Networks |
Silver acetylide is an inorganic chemical compound with the formula Ag 2 C 2 , a metal acetylide . The compound can be regarded as a silver salt of the weak acid , acetylene . The salt's anion consists of two carbon atoms linked by a triple bond , thus, its structure is [Ag + ] 2 [ − C≡C − ] . The alternate name "silver carbide" is rarely used, although the analogous calcium compound CaC 2 is called calcium carbide . Silver acetylide is a primary explosive .
Silver acetylide can be produced by passing acetylene gas through a solution of silver nitrate : [ 3 ]
The reaction product is a greyish to white precipitate. This is the same synthesis from Berthelot in which he first found silver acetylide in 1866. [ 4 ]
The double salt is formed in acidic or neutral silver nitrate solutions. Performing the synthesis in basic ammonia solution does not allow the double salt to form, producing pure silver acetylide. To properly form the double salt, acetylene gas is passed through dilute silver nitrate and nitric acid solution. Instead of the conventional synthesis of passing acetylene gas through silver nitrate solution, a purer and whiter precipitate can be formed by passing acetylene gas through acetone and adding the acetylene solution drop-wise to a dilute silver nitrate and nitric acid solution. The reaction was performed at ambient room temperature.
Silver acetylide can be formed on the surface of silver or high-silver alloys, e.g. in pipes used for transport of acetylene, if silver brazing was used in their joints.
Pure silver acetylide is a heat- and shock-sensitive primary explosive . Silver acetylide decomposes through the reaction:
The detonation velocity of the silver acetylide-silver nitrate double salt is 1980 m/s, while that of pure silver acetylide is 1200 m/s. [ 5 ]
Silver acetylide is not soluble in water and is not appreciably soluble in any other solvent. | https://en.wikipedia.org/wiki/Silver_acetylide |
Silver azide is the chemical compound with the formula AgN 3 . It is a silver (I) salt of hydrazoic acid . It forms a colorless crystals. Like most azides, it is a primary explosive .
Silver azide can be prepared by treating an aqueous solution of silver nitrate with sodium azide . [ 2 ] The silver azide precipitates as a white solid, leaving sodium nitrate in solution.
X-ray crystallography shows that AgN 3 is a coordination polymer with square planar Ag + coordinated by four azide ligands . Correspondingly, each end of each azide ligand is connected to a pair of Ag + centers. The structure consists of two-dimensional AgN 3 layers stacked one on top of the other, with weaker Ag–N bonds between layers. The coordination of Ag + can alternatively be described as highly distorted 4 + 2 octahedral, the two more distant nitrogen atoms being part of the layers above and below. [ 3 ]
In its most characteristic reaction, the solid decomposes explosively, releasing nitrogen gas:
The first step in this decomposition is the production of free electrons and azide radicals; thus the reaction rate is increased by the addition of semiconducting oxides. [ 4 ] Pure silver azide explodes at 340 °C , but the presence of impurities lowers this down to 270 °C. [ 5 ] This reaction has a lower activation energy and initial delay than the corresponding decomposition of lead azide . [ 6 ]
AgN 3 , like most heavy metal azides , is a dangerous primary explosive . Decomposition can be triggered by exposure to ultraviolet light or by impact. [ 2 ] Ceric ammonium nitrate [NH 4 ] 2 [Ce(NO 3 ) 6 ] is used as an oxidising agent to destroy AgN 3 in spills. [ 5 ] | https://en.wikipedia.org/wiki/Silver_azide |
Silver bromate is an inorganic compound with the molecular formula AgBrO 3 . It is a white powder that is toxic and is both light and heat-sensitive. [ 2 ]
Silver bromate can be used as an oxidant for the transformation of tetrahydropyranyl ethers to carbonyl compounds . [ 3 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silver_bromate |
Silver bromide (AgBr), a soft, pale-yellow, water-insoluble salt well known (along with other silver halides) for its unusual sensitivity to light . This property has allowed silver halides to become the basis of modern photographic materials. [ 2 ] AgBr is widely used in photographic films and is believed by some to have been used for faking the Shroud of Turin . [ 3 ] The salt can be found naturally as the mineral bromargyrite (bromyrite).
Although the compound can be found in mineral form, AgBr is typically prepared by the reaction of silver nitrate with an alkali bromide, typically potassium bromide : [ 2 ]
Although less convenient, the salt can also be prepared directly from its elements.
Modern preparation of a simple, light-sensitive surface involves forming an emulsion of silver halide crystals in a gelatine, which is then coated onto a film or other support. The crystals are formed by precipitation in a controlled environment to produce small, uniform crystals (typically < 1 μm in diameter and containing ~10 12 Ag atoms) called grains. [ 2 ]
Silver bromide reacts readily with liquid ammonia to generate a variety of ammine complexes, like Ag(NH 3 ) 2 Br and Ag(NH 3 ) 2 Br − 2 . In general: [ 4 ]
Silver bromide reacts with triphenylphosphine to give a tris(triphenylphosphine) product: [ 5 ]
AgF, AgCl, and AgBr all have face-centered cubic (fcc) rock-salt (NaCl) lattice structure with the following lattice parameters: [ 6 ]
The larger halide ions are arranged in a cubic close-packing, while the smaller silver ions fill the octahedral gaps between them, giving a 6-coordinate structure where a silver ion Ag + is surrounded by 6 Br − ions, and vice versa. The coordination geometry for AgBr in the NaCl structure is unexpected for Ag(I) which typically forms linear, trigonal (3-coordinated Ag) or tetrahedral (4-coordinated Ag) complexes.
Unlike the other silver halides, iodargyrite (AgI) contains a hexagonal zincite lattice structure.
The silver halides have a wide range of solubilities. The solubility of AgF is about 6 × 10 7 times that of AgI. These differences are attributed to the relative solvation enthalpies of the halide ions; the enthalpy of solvation of fluoride is anomalously large. [ 7 ]
Although photographic processes have been in development since the mid-1800s, there were no suitable theoretical explanations until 1938 with the publication of a paper by R.W. Gurney and N.F. Mott. [ 8 ] This paper triggered a large amount of research in fields of solid-state chemistry and physics, as well more specifically in silver halide photosensitivity phenomena. [ 2 ]
Further research into this mechanism revealed that the photographic properties of silver halides (in particular AgBr) were a result of deviations from an ideal crystal structure. Factors such as crystal growth, impurities, and surface defects all affect concentrations of point ionic defects and electronic traps, which affect the sensitivity to light and allow for the formation of a latent image . [ 3 ]
The major defect in silver halides is the Frenkel defect , where silver ions are located interstitially (Ag i + ) in high concentration with their corresponding negatively charged silver-ion vacancies (Ag v − ). What is unique about AgBr Frenkel pairs is that the interstitial Ag i + are exceptionally mobile, and that its concentration in the layer below the grain surface (called the space-charge layer) far exceeds that of the intrinsic bulk. [ 3 ] [ 9 ] The formation energy of the Frenkel pair is low at 1.16 eV , and the migration activation energy is unusually low at 0.05 eV (compare to NaCl: 2.18 eV for the formation of a Schottky pair and 0.75 eV for cationic migration). These low energies result in large defect concentrations, which can reach near 1% near the melting point. [ 9 ]
The low activation energy in silver bromide can be attributed the silver ions' high quadrupolar polarizability; that is, it can easily deform from a sphere into an ellipsoid. This property, a result of the d 9 electronic configuration of the silver ion, facilitates migration in both the silver ion and in silver-ion vacancies, thus giving the unusually low migration energy (for Ag v − : 0.29–0.33 eV, compared to 0.65 eV for NaCl). [ 9 ]
Studies have demonstrated that the defect concentrations are strongly affected (up to several powers of 10) by crystal size. Most defects, such as interstitial silver ion concentration and surface kinks, are inversely proportional to crystal size, although vacancy defects are directly proportional. This phenomenon is attributed to changes in the surface chemistry equilibrium, and thus affects each defect concentration differently. [ 3 ]
Impurity concentrations can be controlled by crystal growth or direct addition of impurities to the crystal solutions. Although impurities in the silver bromide lattice are necessary to encourage Frenkel defect formation, studies by Hamilton have shown that above a specific concentration of impurities, the numbers of defects of interstitial silver ions and positive kinks reduce sharply by several orders of magnitude. After this point, only silver-ion vacancy defects, which actually increase by several orders of magnitude, are prominent. [ 3 ]
When light is incident on the silver halide grain surface, a photoelectron is generated when a halide loses its electron to the conduction band: [ 2 ] [ 3 ] [ 10 ]
After the electron is released, it will combine with an interstitial Ag i + to create a silver metal atom Ag i 0 : [ 2 ] [ 3 ] [ 10 ]
Through the defects in the crystal, the electron is able to reduce its energy and become trapped in the atom. [ 2 ] The extent of grain boundaries and defects in the crystal affect the lifetime of the photoelectron, where crystals with a large concentration of defects will trap an electron much faster than a purer crystal. [ 10 ]
When a photoelectron is mobilized, a photohole h• is also formed, which also needs to be neutralized. The lifetime of a photohole, however, does not correlate with that of a photoelectron. This detail suggests a different trapping mechanism; Malinowski suggests that the hole traps may be related to defects as a result of impurities. [ 10 ] Once trapped, the holes attract mobile, negatively charged defects in the lattice: the interstitial silver vacancy Ag v − : [ 10 ]
The formation of the h.Ag v lowers its energy sufficiently to stabilize the complex and reduce the probability of ejection of the hole back into the valance band (the equilibrium constant for hole-complex in the interior of the crystal is estimated at 10 −4 . [ 10 ]
Additional investigations on electron- and hole-trapping demonstrated that impurities also can be a significant trapping system. Consequently, interstitial silver ions may not be reduced. Therefore, these traps are actually loss mechanisms, and are considered trapping inefficiencies. For example, atmospheric oxygen can interact with photoelectrons to form an O 2 − species, which can interact with a hole to reverse the complex and undergo recombination. Metal ion impurities such as copper(I), iron(II), and cadmium(II) have demonstrated hole-trapping in silver bromide. [ 3 ]
Once the hole-complexes are formed, they diffuse to the surface of the grain as a result of the formed concentration gradient. Studies demonstrated that the lifetimes of holes near the surface of the grain are much longer than those in the bulk, and that these holes are in equilibrium with adsorbed bromine. The net effect is an equilibrium push at the surface to form more holes. Therefore, as the hole-complexes reach the surface, they disassociate: [ 10 ]
By this reaction equilibrium, the hole-complexes are constantly consumed at the surface, which acts as a sink, until removed from the crystal. This mechanism provides the counterpart to the reduction of the interstitial Ag i + to Ag i 0 , giving an overall equation of: [ 10 ]
Now that some of the theory has been presented, the actual mechanism of the photographic process can be discussed. To summarize, as a photographic film is subjected to an image, photons incident on the grain produce electrons which interact to yield silver metal. More photons hitting a particular grain will produce a larger concentration of silver atoms, containing between 5 and 50 silver atoms (out of ~10 12 atoms), depending on the sensitivity of the emulsion. The film now has a concentration gradient of silver atom specks based upon varying intensity light across its area, producing an invisible " latent image ". [ 2 ] [ 10 ]
While this process is occurring, bromine atoms are being produced at the surface of the crystal. To collect the bromine, a layer on top of the emulsion, called a sensitizer, acts as a bromine acceptor. [ 10 ]
During film development the latent image is intensified by addition of a chemical, typically hydroquinone , that selectivity reduces those grains which contain atoms of silver. The process, which is sensitive to temperature and concentration, will completely reduce grains to silver metal, intensifying the latent image on the order of 10 10 to 10 11 . This step demonstrates the advantage and superiority of silver halides over other systems: the latent image, which takes only milliseconds to form and is invisible, is sufficient to produce a full image from it. [ 2 ]
After development, the film is "fixed", during which the remaining silver salts are removed to prevent further reduction, leaving the "negative" image on the film. The agent used is sodium thiosulfate , and reacts according to the following equation: [ 2 ]
An indefinite number of positive prints can be generated from the negative by passing light through it and undertaking the same steps outlined above. [ 2 ]
As silver bromide is heated within 100 °C of its melting point, an Arrhenius plot of the ionic conductivity shows the value increasing and "upward-turning". Other physical properties such as elastic moduli, specific heat, and the electronic energy gap also increase, suggesting the crystal is approaching instability. [ 9 ] This behavior, typical of a semi-conductor, is attributed to a temperature-dependence of Frenkel defect formation, and, when normalized against the concentration of Frenkel defects, the Arrhenius plot linearizes. [ 9 ] | https://en.wikipedia.org/wiki/Silver_bromide |
Silver chlorate is an inorganic compound with molecular formula AgClO 3 . It forms white tetragonal crystals. [ 1 ] [ 2 ] Like all chlorates, it is water-soluble and an oxidizing agent. As a simple metal salt, it is a common chemical in basic inorganic chemistry experiments. It is light-sensitive, so it must be stored in tightly closed dark-coloured containers.
The substance exhibits blasting properties, therefore it is sometimes used as a primary explosive.
Silver(I) means silver is in its normal +1 oxidation state .
Silver chlorate is produced by the reaction of silver nitrate with sodium chlorate to produce both silver chlorate and sodium nitrate .
Alternatively, it may be produced by the transmission of chlorine through a suspension of silver oxide .
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silver_chlorate |
Silver chromate is an inorganic compound with formula Ag 2 CrO 4 which appears as distinctively coloured brown-red crystals. The compound is insoluble and its precipitation is indicative of the reaction between soluble chromate and silver precursor salts (commonly potassium / sodium chromate with silver nitrate ). [ 5 ] [ 7 ] [ 8 ] This reaction is important for two uses in the laboratory: in analytical chemistry it constitutes the basis for the Mohr method of argentometry , [ 9 ] whereas in neuroscience it is used in the Golgi method of staining neurons for microscopy. [ 10 ]
In addition to the above, the compound has been tested as a photocatalyst for wastewater treatment . [ 7 ] The most important practical and commercial application for silver chromate, however, is its use in Li-Ag 2 CrO 4 batteries, a type of lithium battery mainly found in artificial pacemaker devices. [ 11 ]
As for all chromates , which are chromium(VI) species, the compound poses a hazard of toxicity, carcinogenicity and genotoxicity , as well as great environmental harm.
Silver chromate is usually produced by the salt metathesis reaction of potassium chromate (K 2 CrO 4 ) and silver nitrate (AgNO 3 ) in purified water – the silver chromate will precipitate out of the aqueous reaction mixture: [ 7 ] [ 5 ] [ 8 ]
This occurs as the solubility of silver chromate is very low ( K sp = 1.12×10 −12 or 6.5×10 −5 mol/L). [ 2 ]
The formation of insoluble Ag 2 CrO 4 nanostructures via the above reaction with good control over particle size and shape has been achieved through sonochemistry , template-assisted synthesis or hydrothermal methods. [ 7 ]
The compound is polymorphic and can exhibit two crystal structures depending on temperature: hexagonal at higher and orthorhombic at lower temperatures. [ 7 ] The hexagonal phase transforms to the orthorhombic upon cooling below the crystal structure transition temperature T =482 °C.
The orthorhombic polymorph is the commonly encountered one and it crystallizes in the space group Pnma , with two distinct coordination environments for the silver ions (one tetragonal bipyramidal and the other distorted tetrahedral). [ 5 ]
The characteristic brick-red / acajou colour (absorption λ max =450 nm) of silver chromate is rather unlike other chromates which are typically yellow to yellowish orange in appearance. This difference in absorption has been hypothesised to be due to the charge-transfer transition between the silver 4 d orbital and chromate e * orbitals, although this seems not to be the case based on careful analysis of UV/Vis spectroscopic data. [ 8 ] Instead, the shift in λ max is more likely attributed to the Davydov splitting effect. [ 8 ]
The precipitation of the strongly coloured silver chromate is used to indicate the endpoint in the titration of chloride with silver nitrate in the Mohr method of argentometry .
The reactivity of the chromate anion with silver is lower than with halides ( e.g. chlorides) so that in a mixture of both ions, only silver chloride precipitate will form: [ 9 ]
Only when no chloride (or any halogen) is left will silver chromate form and precipitate out.
Prior to the endpoint the solution has a milky lemon-yellow appearance, due to the suspension of the AgCl precipitate already formed and the yellow colour of the chromate ion in solution. Approaching the endpoint, additions of AgNO 3 lead to steadily more slowly disappearing red colouration. When the red-brownish colour persists (with some greyish spots of silver chloride in it) the endpoint of titration is reached.
This method is only suitable for near neutral pH: in very low (acidic) pH, the silver chromate is soluble (due to the formation of H 2 CrO 4 ), and in alkaline pH, the silver precipitates as the hydroxide . [ 9 ]
The titration was introduced by Mohr in the mid 19th century and despite limitations in pH conditions it has not completely fallen out of use since. [ 9 ] An example of a practical application of Mohr's method is in determining the chloride level of salt water pools. [ citation needed ]
A very different application of the same reaction is for the staining of neurons so that their morphology becomes visible under a microscope. [ 10 ] The technique involves first impregnating aldehyde-fixed brain tissue with a 2% aqueous potassium dichromate solution. This is followed by drying and immersion in a 2% aqueous silver nitrate solution.
By the same reaction as above, silver chromate forms and by a mechanism not entirely understood the precipitation occurs inside some of the neurons, allowing detailed observation of morphological details too fine for common staining techniques. [ 10 ]
Several variations on the method exist to increase contrast or selectivity in the type of neuron stained, and include additional impregnation in mercuric chloride solution (Golgi-Cox) or post-treatment with osmium tetroxide (Cajal or rapid Golgi). [ 10 ]
The previously infeasible observations enabled by the silver chromate staining technique led to the eventual award of the 1906 Nobel Prize in Physiology or Medicine to discoverer Golgi and pioneer of its use and improvement Ramón y Cajal . [ 10 ]
Silver chromate has been investigated for possible use as a catalyst for the photocatalytic degradation of organic pollutants in wastewater . Although Ag 2 CrO 4 nanoparticles are somehow effective for this purpose, the high toxicity of chromium(VI) to humans and the environment requires additional complex procedures for the containment of any chromium from the catalyst, which must be prevented from leaching into the treated wastewater. [ 7 ]
Li-Ag 2 CrO 4 batteries are a type of Li-metal batteries developed in the early 1970s by Saft , in which silver chromate serves as the cathode, metallic lithium as the anode, and a lithium perchlorate solution as the electrolyte . [ 11 ]
The battery was intended for biomedical applications and had characteristics like high reliability and shelf life quality for the time of discovery. Lithium-silver chromate batteries have therefore found wide application in implanted pacemaker devices. [ 11 ] | https://en.wikipedia.org/wiki/Silver_chromate |
Silver dichromate is a chemical compound with the formula Ag 2 Cr 2 O 7 . It is insoluble in water and decomposes when treated with hot water. Its anion has a charge of -2.
Related complexes are used as oxidants in organic chemistry . [ 1 ] For instance, tetrakis(pyridine)silver dichromate, [Ag 2 (py) 4 ] 2+ [Cr 2 O 7 ] 2− , is used to convert benzylic and allylic alcohols to corresponding carbonyl compounds . [ 2 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silver_dichromate |
Silver economy is the system of production , distribution and consumption of goods and services aimed at using the purchasing potential of older and ageing people and satisfying their consumption, living and health needs. The silver economy is analyzed in the field of social gerontology not as an existing economic system but as an instrument of ageing policy and the political idea of forming a potential, needs-oriented economic system for the aging population . [ 1 ] [ 2 ] Its main element is gerontechnology as a new scientific, research and implementation paradigm. [ 3 ]
The phrase "silver economy" is sometimes used interchangeably with the term "silver market" (the “ageing marketplace” or the “mature market”), which is a narrower concept. The wording "silver market" was created in the 1970s in Japan in the context of increasing of the availability of facilities for seniors. Silver market includes, among others, good, values and services for affluent older people; special solutions in trade between operators, allowing adjustments to aging workforce; ideas of universal design and transgenerational design that aim is to adapt goods and services to people of different ages ("age-friendly"), physical condition and cognitive abilities, which may result in improved social integration . [ 4 ]
The silver economy is not a single sector, but rather a collection of products and services from many existing economic sectors , including information technology , telecommunications , financial sector , housing , transport , energy , tourism , culture , infrastructure and local services , and long-term care . [ 5 ] Currently, silver economy is growing at a very good pace because its public is increasingly numerous and in this sense, we can distinguish the two needs it covers: the pleasure associated with active ageing and understood as "wanting" (will, motivation and interests) which is more typical of young older people (third age); and that of products and services aimed at social and health care, adapted technology or the improvement of infrastructures such as the home, understood as "needing" and characteristic of older people of the fourth age (over 80 years of age). The opportunities are very varied, although the characteristics of this heterogeneous population group need to be fully understood. [ 6 ] | https://en.wikipedia.org/wiki/Silver_economy |
Silver iodate (AgIO 3 ) is a light-sensitive, white crystal composed of silver , iodine and oxygen . Unlike most metal iodates, it is practically insoluble in water.
Silver iodate can be obtained by reacting silver nitrate (AgNO 3 ) with sodium iodate or potassium iodate. The by-product of the reaction is sodium nitrate . [ 2 ]
Alternatively, it can be created by the action of iodine in a solution of silver oxide .
Silver iodate is used to detect traces of chlorides in blood. [ citation needed ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silver_iodate |
Silver iodide is an inorganic compound with the formula Ag I . The compound is a bright yellow solid, but samples almost always contain impurities of metallic silver that give a grey colouration. The silver contamination arises because some samples of AgI can be highly photosensitive . This property is exploited in silver-based photography . Silver iodide is also used as an antiseptic and in cloud seeding .
The structure adopted by silver iodide is temperature dependent: [ 8 ]
Silver iodide is prepared by reaction of an iodide solution (e.g., potassium iodide ) with a solution of silver ions (e.g., silver nitrate ). A yellowish solid quickly precipitates . The solid is a mixture of the two principal phases. Dissolution of the AgI in hydroiodic acid , followed by dilution with water, precipitates β-AgI. Alternatively, dissolution of AgI in a solution of concentrated silver nitrate followed by dilution affords α-AgI. [ 10 ] Unless the preparation is conducted in dark conditions, the solid darkens rapidly, the light causing the reduction of ionic silver to metallic. The photosensitivity varies with sample purity.
The crystalline structure of β-AgI is similar to that of ice , allowing it to induce freezing by the process known as heterogeneous nucleation . Approximately 50,000 kg are used for cloud seeding annually, each seeding experiment consuming 10–50 grams. [ 11 ] (see also Project Stormfury , Operation Popeye ). [ citation needed ]
Extreme exposure can lead to argyria , characterized by localized discolouration of body tissue. [ 12 ] | https://en.wikipedia.org/wiki/Silver_iodide |
Silver nitrate is an inorganic compound with chemical formula AgNO 3 . It is a versatile precursor to many other silver compounds, such as those used in photography . It is far less sensitive to light than the halides . [ citation needed ] It was once called lunar caustic because silver was called luna by ancient alchemists who associated silver with the moon . [ 7 ] In solid silver nitrate , the silver ions are three- coordinated in a trigonal planar arrangement. [ 4 ]
Albertus Magnus , in the 13th century, documented the ability of nitric acid to separate gold and silver by dissolving the silver. [ 8 ] Indeed silver nitrate can be prepared by dissolving silver in nitric acid followed by evaporation of the solution. The stoichiometry of the reaction depends upon the concentration of nitric acid used.
The structure of silver nitrate has been examined by X-ray crystallography several times. In the common orthorhombic form stable at ordinary temperature and pressure, the silver atoms form pairs with Ag---Ag contacts of 3.227 Å. Each Ag + center is bonded to six oxygen centers of both uni- and bidentate nitrate ligands. The Ag-O distances range from 2.384 to 2.702 Å. [ 4 ]
A typical reaction with silver nitrate is to suspend a rod of copper in a solution of silver nitrate and leave it for a few hours. The silver nitrate reacts with copper to form hairlike crystals of silver metal and a blue solution of copper nitrate :
Silver nitrate decomposes when heated:
Qualitatively, decomposition is negligible below the melting point, but becomes appreciable around 250 °C and fully decomposes at 440 °C. [ 9 ]
Most metal nitrates thermally decompose to the respective oxides , but silver oxide decomposes at a lower temperature than silver nitrate, so the decomposition of silver nitrate yields elemental silver instead.
Silver nitrate is the least expensive salt of silver; it offers several other advantages as well. It is non- hygroscopic , in contrast to silver fluoroborate and silver perchlorate . In addition, it is relatively stable to light, and it dissolves in numerous solvents, including water. The nitrate can be easily replaced by other ligands , rendering AgNO 3 versatile. Treatment with solutions of halide ions gives a precipitate of AgX (X = Cl, Br, I). When making photographic film , silver nitrate is treated with halide salts of sodium or potassium to form insoluble silver halide in situ in photographic gelatin , which is then applied to strips of tri- acetate or polyester . Similarly, silver nitrate is used to prepare some silver-based explosives, such as the fulminate , azide , or acetylide , through a precipitation reaction .
Treatment of silver nitrate with base gives dark grey silver oxide : [ 10 ]
The silver cation, Ag + , reacts quickly with halide sources to produce the insoluble silver halide, which is a cream precipitate if Br − is used, a white precipitate if Cl − is used and a yellow precipitate if I − is used. This reaction is commonly used in inorganic chemistry to abstract halides:
where X − = Cl − , Br − , or I − .
Other silver salts with non-coordinating anions , namely silver tetrafluoroborate and silver hexafluorophosphate are used for more demanding applications.
Similarly, this reaction is used in analytical chemistry to confirm the presence of chloride , bromide , or iodide ions . Samples are typically acidified with dilute nitric acid to remove interfering ions, e.g. carbonate ions and sulfide ions. This step avoids confusion of silver sulfide or silver carbonate precipitates with that of silver halides. The color of precipitate varies with the halide: white ( silver chloride ), pale yellow/cream ( silver bromide ), yellow ( silver iodide ). AgBr and especially AgI photo-decompose to the metal, as evidenced by a grayish color on exposed samples.
The same reaction was used on steamships in order to determine whether or not boiler feedwater had been contaminated with seawater . It is still used to determine if moisture on formerly dry cargo is a result of condensation from humid air, or from seawater leaking through the hull. [ 11 ]
Silver nitrate is used in many ways in organic synthesis , e.g. for deprotection and oxidations. Ag + binds alkenes reversibly, and silver nitrate has been used to separate mixtures of alkenes by selective absorption. The resulting adduct can be decomposed with ammonia to release the free alkene. [ 12 ] Silver nitrate is highly soluble in water but is poorly soluble in most organic solvents, except acetonitrile (111.8 g/100 g, 25 °C). [ 13 ]
In histology , silver nitrate is used for silver staining , for demonstrating reticular fibers, proteins and nucleic acids . For this reason it is also used to demonstrate proteins in PAGE gels. It can be used as a stain in scanning electron microscopy . [ 14 ]
Cut flower stems can be placed in a silver nitrate solution, which prevents the production of ethylene. This delays ageing of the flower. [ 15 ]
Silver nitrate produces long-lasting stain when applied to skin and is one of indelible ink’s ingredients. An electoral stain makes use of this to mark a finger of people who have voted in an election, allowing easy identification to prevent double-voting. [ 16 ] [ 17 ]
In addition to staining skin, silver nitrate has a history of use in stained glass. In the 14th century, artists began using a "silver stain" (also known as a yellow stain) made from silver nitrate to create a yellow effect on clear glass. The stain would produce a stable color that could range from pale lemon to deep orange or gold. Silver stain was often used with glass paint, and was applied to the opposite side of the glass as the paint. It was also used to create a mosaic effect by reducing the number of pieces of glass in a window. Despite the age of the technique, this process of creating stained glass remains almost entirely unchanged. [ 18 ]
Silver salts have antiseptic properties. In 1881 Credé introduced a method known as Credé's prophylaxis , which used of dilute (2%) solutions of silver nitrate in newborn babies ' eyes at birth to prevent contraction of gonorrhea from the mother, which could cause blindness via ophthalmia neonatorum . (Modern antibiotics are now used instead). [ 19 ] [ 20 ] [ 21 ] [ 22 ]
Fused silver nitrate, shaped into sticks, was traditionally called "lunar caustic". It is used as a cauterizing agent, for example to remove granulation tissue around a stoma . General Sir James Abbott noted in his journals that in India in 1827 it was infused by a British surgeon into wounds in his arm resulting from the bite of a mad dog to cauterize the wounds and prevent the onset of rabies. [ 23 ]
Silver nitrate is used to cauterize superficial blood vessels in the nose to help prevent nosebleeds .
Dentists sometimes use silver nitrate-infused swabs to heal oral ulcers . Silver nitrate is used by some podiatrists to kill cells located in the nail bed.
The Canadian physician C. A. Douglas Ringrose researched the use of silver nitrate for sterilization procedures , believing that silver nitrate could be used to block and corrode the fallopian tubes. [ 24 ] The technique was ineffective. [ 25 ]
Much research has been done in evaluating the ability of the silver ion at inactivating Escherichia coli , a microorganism commonly used as an indicator for fecal contamination and as a surrogate for pathogens in drinking water treatment. Concentrations of silver nitrate evaluated in inactivation experiments range from 10–200 micrograms per liter as Ag + .
Silver's antimicrobial activity saw many applications prior to the discovery of modern antibiotics, when it fell into near disuse. Its association with argyria made consumers wary and led them to turn away from it when given an alternative. [ citation needed ]
Repeated daily application of silver nitrate can induce adequate destruction of cutaneous warts , but occasionally pigmented scars may develop. In a placebo-controlled study of 70 patients, silver nitrate given over nine days resulted in clearance of all warts in 43% and improvement in warts in 26% one month after treatment compared to 11% and 14%, respectively, in the placebo group. [ 26 ]
As an oxidant, silver nitrate should be properly stored away from organic compounds. It reacts explosively with ethanol. [ 27 ] Despite its common usage in extremely low concentrations to prevent gonorrhea and control nosebleeds, silver nitrate is still very toxic and corrosive. [ 28 ] Brief exposure will not produce any immediate side effects other than the purple, brown or black stains on the skin, but upon constant exposure to high concentrations, side effects will be noticeable, which include burns. Long-term exposure may cause eye damage. Silver nitrate is known to be a skin and eye irritant. Silver nitrate has not been thoroughly investigated for potential carcinogenic effect . [ 29 ]
Silver nitrate is currently unregulated in water sources by the United States Environmental Protection Agency. However, if more than 1 gram of silver is accumulated in the body, a condition called argyria may develop. Argyria is a permanent cosmetic condition in which the skin and internal organs turn a blue-gray color. The United States Environmental Protection Agency used to have a maximum contaminant limit for silver in water until 1990, when it was determined that argyria did not impact the function of any affected organs despite the discolouration. [ 30 ] Argyria is more often associated with the consumption of colloidal silver solutions rather than with silver nitrate, since it is only used at extremely low concentrations to disinfect the water. However, it is still important to be wary before ingesting any sort of silver-ion solution.
https://www.cofesilver.com/en/silver_bar :silver bar explanation. pricing investing | https://en.wikipedia.org/wiki/Silver_nitrate |
Silver nitride is an explosive chemical compound with symbol Ag 3 N. It is a black, metallic-looking [ 3 ] solid which is formed when silver oxide or silver nitrate [ 4 ] is dissolved in concentrated solutions of ammonia , causing formation of the diammine silver complex which subsequently breaks down to Ag 3 N. The standard free energy of the compound is about +315 kJ/mol, making it an endothermic compound which decomposes explosively to metallic silver and nitrogen gas.
Silver nitride was formerly referred to as fulminating silver , but this can cause confusion with silver fulminate or silver azide , other compounds which have also been referred to by this name. The fulminate and azide compounds do not form from ammoniacal solutions of Ag 2 O. [ 2 ] Fulminating silver was first prepared in 1788 by the French chemist Claude Louis Berthollet . [ 5 ] 70 years earlier, in 1716 Johann Kunckel von Löwenstern had already described the preparation. [ 6 ]
Silver nitride is poorly soluble in water, but decomposes in mineral acids; decomposition is explosive in concentrated acids. It also slowly decomposes in air at room temperature and explodes upon heating to 165 °C. [ 7 ]
Silver nitride is often produced inadvertently during experiments involving silver compounds and ammonia, leading to surprise detonations. Whether silver nitride is formed depends on the concentration of ammonia in the solution. Silver oxide in 1.52 M ammonia solution readily converts to the nitride, while silver oxide in 0.76 M solution does not form nitride. [ 2 ] Silver oxide can also react with dry ammonia to form Ag 3 N. Silver nitride is more dangerous when dry; dry silver nitride is a contact explosive which may detonate from the slightest touch, even a falling water droplet. [ 2 ] It is also explosive when wet, although less so, and explosions do not propagate well in wet deposits of the compound. Because of its long-term instability, undetonated deposits of Ag 3 N will lose their sensitivity over time.
Silver nitride may appear as black crystals, grains, crusts, or mirrorlike deposits on container walls. Suspected deposits may be dissolved by adding dilute ammonia or concentrated ammonium carbonate solution, removing the explosion hazard. [ 3 ] [ 8 ]
The name "silver nitride" is sometimes also used to describe a reflective coating consisting of alternating thin layers of silver metal and silicon nitride . This material is not explosive, and is not a true silver nitride. It is used to coat mirrors and shotguns . [ 9 ] [ 10 ] | https://en.wikipedia.org/wiki/Silver_nitride |
Silver overlay is an electroplated coating of silver on a non-conductive surface such as porcelain or glass . Most techniques used to create silver overlay involve the use of special flux which contains silver and turpentine oil . This is then painted on the glass ornament as a design. After the painting is complete, the entire ornament is fired under relatively low heat, it is then cleaned after being quenched and cooled, then it is placed in a solution of silver. A low-voltage current is run through the solution and the silver binds in the design, creating a permanent fusion of the silver with the glass. [ 1 ] [ 2 ]
A much older technique of overlay, which was commonly used in the Indian subcontinent since ancient times, involves the use of a silver sheet wrapped around the ornament and then the design beaten onto the sheet or it may be burnished. This technique renders the design silhouetted against a dark backdrop and was commonly called the Aftabi design technique. This technique of overlay predates the technique that is common today, but without the use of electroplating, it was a time-consuming and tedious process, which could only be accomplished by skilled artisans. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ]
The history of who first devised the process is unknown. What is known is that from 1870 onwards, a number of patents were filed for the process. Although all patents appear after 1870, it has been suggested that the process may have been discovered earlier, and the patents claimed a short time afterward. The most well known patent holders are Frederick Shirley from the United States of America, whose patent dates to 1879, Erard and Round who were under the auspices of Stevens & Williams Ltd. whose patent is from 1889, John Sharling also of the USA, whose patent is from 1893 and Friedrich Deusch , the German inventor whose name is most associated with silver overlay today, whose patented the process in 1895 and displayed his work in 1907 at an exhibition in Bordeaux . [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ]
Deusch returned to Schwäbisch Gmünd in southern Germany where, in 1912, he founded his firm Deusch & Co. Deusch continued exhibiting his wares and gained the Gold Medal at the 1913 World Exposition in Ghent , Belgium .
With his presence, Schwäbisch Gmünd became the center of German silver overlay production. Schwäbisch Gmünd (about 20,000 inhabitants at that time) had a long tradition since the 16th century in the art of artists working with gold and silver. A school for applied arts existed there from an early date, which became a school for the precious metal industry in 1907.
In the 1920s almost 190 firms were involved in the precious metals industry. [ 13 ] The presence of materials, artisans, and component suppliers in on place created an ideal environment for the industry to thrive.
After Deusch and Company, other firms specializing in silver overlay were founded. In particular, the firms of Friedrich Wilhelm Spahr [ 1 ] and Alfred and Manfred Veyhl were established.
Parallel to the development of German silver overlay, silver overlay production was also initiated in the United States. [ 14 ]
The specific feature of German silver overlay is the degree of purity – 925 for Sterling silver or 999 for fine silver. The quality of silver used for German overlay can be seen by identifying the impressed 1000 mark (usually on the base or side of an item). The purity and thickness of the silver overlay ensures the beauty of the item is maintained without any loss to the silver even after many years of cleaning. Although other kinds of silver, such as nickel silver, can be used for silver overlay, the effect is not as vibrant. [ 15 ] [ 16 ]
Bohemian and Venetian Murano glass are often described as silver overlay, but the silver is so thin that it looks as though it has been painted onto the surface, producing a flat effect.
Friedrich Deusch invented a way to combine silver and a non-conductive surface such as porcelain or glass with galvanization . He achieved this with a special conductive fluid (a type of flux ) which was fixed permanently on the prepared form. The particular objects (such as a vase) were first roughened by engraving or using hydrofluoric acid to etch a design. This implies that a very exact covering of the surfaces had to be achieved to prevent any damage to areas which were not to be overlaid. Maybe they used a masking lacquer which could withstand the following baking in the kiln which was used to fuse the flux with the surface of the item. The next step was to galvanize the item with the purest silver (1000). [ 17 ]
It was very important to monitor items being overlaid with silver – waiting too long resulted in visible dark spots and slight roughness where the cathode or anode were fixed. The cathode and anode were used to charge the item electronically and this allowed the fusion of silver to the area painted with the silver flux. The thickness of silver desired on the finished item determined how long the item needed to be left in the silver bath; this could be more than 30 hours. Finally, if the masking lacquer (discussed earlier) did not burn in the kiln, it must have been removed later (probably with chemical fluids).
When colored enamels were to be used on the finished product, they had to be fired prior to the final stage of the silver overlay process. [ 18 ] Engraving the silver was the last, and sometimes most laborious, work; it was brought to the highest level by Friedrich Wilhelm Spahr and his workers.
Early items designed and produced by Friedrich Deusch are very classical, and this was followed by an abstract phase of Art Déco in its purest form. From the 1950s, it was more a concrete style with flowers and so forth. Deusch applied silver overlay to vases, plates, coffee and tea services, and other items.
From the outset, the firm of Alfred Veyhl had its own style. It was mostly a combination of polychromatic painted details of birds, flowers, and similar motifs, framed with silver.
The more abstract designs are rare. Alfred, and later his son Manfred Veyhl, were the only ones who used varnish to avoid silver oxidation . Alfred used softer and rounder lines in his designs, whereas Manfred had a more angular, expressive style. A specialty for this company was that clients could choose from a certain range of porcelain forms and décors. The items were then produced exclusively in a single production run. [ 18 ]
An outstanding figure is Friedrich Wilhelm Spahr. There is evidence that he learned his skill from Friedrich Deusch (some items of both firms have very similar formal designs). He was not only an artisan but an artist in developing repeating circumferential forms in perfect and harmonic proportion. Very often it is the pure arrangement of lines (curved or straight), or their combination, with flowers or birds. Never over-designed, but enough to divide the small surface (for example, a vase) in a self-evident and harmonious way. Like the others, not only did he design and apply the silver overlay, but he also prepared the porcelain with his own enamel colors, painted the motifs, and engraved the silver. He did not produce all these items by himself, instead, Spahr's factory employed about forty specialized workers. The outstanding engraved pieces show the unrivaled quality of Spahr. [ 17 ]
The early items typically have a thicker silver layer. One can also see the stroke of the brush which proves the overlay and painted surface were handcrafted. Printed designs were used more often on items produced later, especially those of Manfred Vehyl. These can be recognized by studying the design: if the color is flat and full of small dots, this strongly indicates a printed design. Also, the silver work on printed color designs appears not to cover the design closely, as it should.
The three companies bought and used porcelain blanks from several well-known producers such as Rosenthal , Hutschenreuther , Thomas Bavaria , Krautheim & Adelberg and marketed the finished products under their own names. They also produced silver overlay glass in the same manner. A large amount of glassware came from WMF [ 19 ] in Geislingen , which is not far from Schwäbisch Gmünd. A respectable amount of glass to be overlaid also came from Jean Beck , [ 20 ] a famous glass designer in Munich . Until recently, it was believed that Beck created the brilliant silver designs himself and that Deusch only produced them. However, this was not the case. As with the porcelain, Deusch and others bought the delightfully stylized glass blanks, decorated them in silver overlay, and sold them under their own names.
Friedrich Deusch used the impressed mark "Deusch 1000 / 1000" on the early items. This mark was punched directly into the silver. Very often one may also find a red three-digit number on the bottom of the porcelain or glass which indicates this early production. Later, it was replaced by a red stamp which shows a coffeepot and the name Deusch. In addition, to these marks, the following marks may also be found: "1000 / 1000 Silber" or "1000 / 1000 Feinsilber". Later items may have the additional mark "Made in Western Germany".
Alfred and Manfred Veyhl used many different marks, stamps, and labels (always placed on the bottom of the item). Vehyl's work often shows the "1000/1000 silver" mark included in the body of the design. Some rare items are signed by a handwritten monogram (MV for Manfred Veyhl) and the word "Handgemalt" (handpainted).
Friedrich Wilhelm Spahr mostly used marks impressed directly into the silver. The very earliest and rarest of Spahr's marks began with "MSG 1000 10" ("MSG" standing for "Manufaktur Schwäbisch Gmünd"). This mark was followed by "Spahr 1000 10" (sometimes stamped in black letters on a porcelain base), later with "Spahr 1000", and finally with transparent plastic labels on the bottom printed "Spahr Feinsilberauflage 1000 / 1000".
Alvin Corporation, which was later owned by the Gorham Mfg. Co. after 1928, also used special marks. They manufacture pieces of sterling silver flatware, as well as hollowware and special toilet ware. [ 21 ]
The La Pierre Manufacturing Company also sued special marks. It was established by Frank H. La Pierre in 1885, and headquartered at 18 East 14th Street, NY . It relocated its offices to Newark, NJ before its incorporation in 1895. Their special marks appear on their silver overlay items such as hollowware and novelty items. [ 22 ]
The Rockwell Silver Company established in Meriden, CT around 1905 created a number of designs that featured silver overlay, however, they were merged with Silver City Glass Company in 1978, so even though they have done extensive work, there are no unique marks associated with the company. [ 23 ]
The Gorham Manufacturing Co ., which was active from 1848 till 1865, used a lion as their mark. They also used a ram head and the phrase "coin" to mark their items.
These luxurious products were most often sold in important jewellery stores. Sometimes the retailer's paper labels survived the cleaning attempts of the last decades, and these labels are always a keen addition for any collector. They confirm that silver overlay porcelain and glass were sold all over Germany.
Friedrich Deusch, the oldest and biggest firm, also sold internationally and even produced a large amount of silver overlay tableware for the Royal House of Saudi Arabia . Deusch is the only firm that has survived (as of 2013), although the focus of production has
changed from fine art to galvanizing parts for the automobile industry. In 1976, after three generations, the Deusch family relinquished interest in the firm of Friedrich Deusch and Company Today, there is scant knowledge and interest in this firm's history. [ 24 ]
Veyhl (father and son) traveled a lot offering their newest items to different jewellery stores. Later, they opened their own shop in Plüderhausen (close to Schwäbisch Gmünd). [ 18 ] Friedrich Wilhelm Spahr created timeless designs that can be found today all over Europe and even in the United States. These are rare, desirable, and mostly exquisite.
Silver overlay was a very exclusive luxury ware from the beginning because of the very complicated and time-consuming steps of manufacturing. Silver overlay items were never mass-produced and were made in limited numbers. The development of silver overlay was forged by a technical alliance between artists, artisans, and advances in chemistry, physics, electronics, and, ultimately, the industrialized techniques of the late 19th century. The arts movements of the day were philosophically against industrialized techniques. Yet, ironically, many delightfully decorated pieces of silver overlay porcelain and glass can be seen with superb handicraft and Art Nouveau -inspired designs. Thus, while the handicraft movement died after a single incandescent generation, their designs live on, as do the stunning works of Friedrich Deusch, Friedrich Wilhelm Spahr, and Alfred & Manfred Vehyl. | https://en.wikipedia.org/wiki/Silver_overlay |
Silver perchlorate is the chemical compound with the formula AgClO 4 . This white solid forms a monohydrate and is mildly deliquescent . It is a useful source of the Ag + ion, although the presence of perchlorate presents risks. It is used as a catalyst in organic chemistry.
Silver perchlorate is created by heating a mixture of perchloric acid with silver nitrate .
Alternatively, it can be prepared by the reaction between barium perchlorate and silver sulfate , or from the reaction of perchloric acid with silver oxide .
Silver perchlorate is noteworthy for its solubility in aromatic solvents such as benzene (52.8 g/L) and toluene (1010 g/L). [ 1 ] In these solvents, the silver cation binds to the arene, as has been demonstrated by X-ray crystallographic studies on crystals obtained from such solutions. [ 2 ] [ 3 ] Its solubility in water is extremely high, up to 500 g per 100 mL water. X-ray diffraction experiments show that aqueous solutions contain [Ag(H 2 O) 2 ] + with Ag-O distances near 240 picometer. [ 4 ]
Similar to silver nitrate , silver perchlorate is an effective reagent for replacing halides ligands with perchlorate, which is a weakly or non-coordinating anion . The use of silver perchlorate in chemical synthesis has declined due to concerns about explosiveness of perchlorate salts. Other silver reagents are silver tetrafluoroborate , and the related silver trifluoromethanesulfonate and silver hexafluorophosphate . | https://en.wikipedia.org/wiki/Silver_perchlorate |
In mathematics, the silver ratio is a geometrical proportion close to 70/29 . Its exact value is 1 + √2, the positive solution of the equation x 2 = 2 x + 1.
The name silver ratio results from analogy with the golden ratio , the positive solution of the equation x 2 = x + 1.
Although its name is recent, the silver ratio (or silver mean) has been studied since ancient times because of its connections to the square root of 2 , almost-isosceles Pythagorean triples , square triangular numbers , Pell numbers , the octagon , and six polyhedra with octahedral symmetry .
If the ratio of two quantities a > b > 0 is proportionate to the sum of two and their reciprocal ratio, they are in the silver ratio: a b = 2 a + b a {\displaystyle {\frac {a}{b}}={\frac {2a+b}{a}}} The ratio a b {\displaystyle {\frac {a}{b}}} is here denoted σ . {\displaystyle \sigma .} [ a ]
Based on this definition, one has 1 = ( 2 a + b a ) b a = ( 2 a + b a ) ( 2 a + b a − 2 ) ⟹ σ ( σ − 2 ) = 1 {\displaystyle {\begin{aligned}1&=\left({\frac {2a+b}{a}}\right){\frac {b}{a}}\\&=\left({\frac {2a+b}{a}}\right)\left({\frac {2a+b}{a}}-2\right)\\&\implies \sigma \left(\sigma -2\right)=1\end{aligned}}}
It follows that the silver ratio is found as the positive solution of the quadratic equation σ 2 − 2 σ − 1 = 0. {\displaystyle \sigma ^{2}-2\sigma -1=0.} The quadratic formula gives the two solutions 1 ± 2 , {\displaystyle 1\pm {\sqrt {2}},} the decimal expansion of the positive root begins as 2.414 213 562 373 095... {\displaystyle 2.414\,213\,562\,373\,095...} (sequence A014176 in the OEIS ).
Using the tangent function
or the hyperbolic sine
σ {\displaystyle \sigma } is the superstable fixed point of the iteration x ← 1 2 ( x 2 + 1 ) / ( x − 1 ) , with x 0 ∈ [ 2 , 3 ] {\displaystyle x\gets {\tfrac {1}{2}}(x^{2}+1)/(x-1),{\text{ with }}x_{0}\in [2,3]}
The iteration x ← 1 + 2 x / {\displaystyle x\gets {\sqrt {1+2x{\vphantom {/}}}}} results in the continued radical σ = 1 + 2 1 + 2 1 + ⋯ . {\displaystyle \sigma ={\sqrt {1+2{\sqrt {1+2{\sqrt {1+\cdots }}}}}}\;.}
The defining equation can be written 1 = 1 σ − 1 + 1 σ + 1 = 2 σ + 1 + 1 σ . {\displaystyle {\begin{aligned}1&={\frac {1}{\sigma -1}}+{\frac {1}{\sigma +1}}\\&={\frac {2}{\sigma +1}}+{\frac {1}{\sigma }}.\end{aligned}}}
The silver ratio can be expressed in terms of itself as fractions σ = 1 σ − 2 σ 2 = σ − 1 σ − 2 + σ + 1 σ − 1 . {\displaystyle {\begin{aligned}\sigma &={\frac {1}{\sigma -2}}\\\sigma ^{2}&={\frac {\sigma -1}{\sigma -2}}+{\frac {\sigma +1}{\sigma -1}}.\end{aligned}}}
Similarly as the infinite geometric series σ = 2 ∑ n = 0 ∞ σ − 2 n σ 2 = − 1 + 2 ∑ n = 0 ∞ ( σ − 1 ) − n . {\displaystyle {\begin{aligned}\sigma &=2\sum _{n=0}^{\infty }\sigma ^{-2n}\\\sigma ^{2}&=-1+2\sum _{n=0}^{\infty }(\sigma -1)^{-n}.\end{aligned}}}
For every integer n {\displaystyle n} one has σ n = 2 σ n − 1 + σ n − 2 = σ n − 1 + 3 σ n − 2 + σ n − 3 = 2 σ n − 1 + 2 σ n − 3 + σ n − 4 {\displaystyle {\begin{aligned}\sigma ^{n}&=2\sigma ^{n-1}+\sigma ^{n-2}\\&=\sigma ^{n-1}+3\sigma ^{n-2}+\sigma ^{n-3}\\&=2\sigma ^{n-1}+2\sigma ^{n-3}+\sigma ^{n-4}\end{aligned}}} From this an infinite number of further relations can be found.
Continued fraction pattern of a few low powers σ − 1 = [ 0 ; 2 , 2 , 2 , 2 , . . . ] ≈ 0.4142 ( 17 / 41 ) σ 0 = [ 1 ] σ 1 = [ 2 ; 2 , 2 , 2 , 2 , . . . ] ≈ 2.4142 ( 70 / 29 ) σ 2 = [ 5 ; 1 , 4 , 1 , 4 , . . . ] ≈ 5.8284 ( 5 + 29 / 35 ) σ 3 = [ 14 ; 14 , 14 , 14 , . . . ] ≈ 14.0711 ( 14 + 1 / 14 ) σ 4 = [ 33 ; 1 , 32 , 1 , 32 , . . . ] ≈ 33.9706 ( 33 + 33 / 34 ) σ 5 = [ 82 ; 82 , 82 , 82 , . . . ] ≈ 82.0122 ( 82 + 1 / 82 ) {\displaystyle {\begin{aligned}\sigma ^{-1}&=[0;2,2,2,2,...]\approx 0.4142\;(17/41)\\\sigma ^{0}&=[1]\\\sigma ^{1}&=[2;2,2,2,2,...]\approx 2.4142\;(70/29)\\\sigma ^{2}&=[5;1,4,1,4,...]\approx 5.8284\;(5+29/35)\\\sigma ^{3}&=[14;14,14,14,...]\approx 14.0711\;(14+1/14)\\\sigma ^{4}&=[33;1,32,1,32,...]\approx 33.9706\;(33+33/34)\\\sigma ^{5}&=[82;82,82,82,...]\approx 82.0122\;(82+1/82)\end{aligned}}}
The silver ratio is a Pisot number , [ 5 ] the next quadratic Pisot number after the golden ratio. By definition of these numbers, the absolute value 2 − 1 {\displaystyle {\sqrt {2}}-1} of the algebraic conjugate is smaller than 1, thus powers of σ {\displaystyle \sigma } generate almost integers and the sequence σ n mod 1 {\displaystyle \sigma ^{n}{\bmod {1}}} is dense at the borders of the unit interval . [ 6 ]
σ {\displaystyle \sigma } is the fundamental unit of real quadratic field K = Q ( 2 ) . {\displaystyle K=\mathbb {Q} \left({\sqrt {2}}\right).}
The silver ratio can be used as base of a numeral system , here called the sigmary scale . [ b ] Every real number x in [0,1] can be represented as a convergent series
Sigmary expansions are not unique. Due to the identities σ n + 1 = 2 σ n + σ n − 1 σ n + 1 + σ n − 1 = 2 σ n + 2 σ n − 1 , {\displaystyle {\begin{aligned}\sigma ^{n+1}&=2\sigma ^{n}+\sigma ^{n-1}\\\sigma ^{n+1}+\sigma ^{n-1}&=2\sigma ^{n}+2\sigma ^{n-1},\end{aligned}}} digit blocks 21 σ and 22 σ {\displaystyle 21_{\sigma }{\text{ and }}22_{\sigma }} carry to the next power of σ , {\displaystyle \sigma ,} resulting in 100 σ and 101 σ . {\displaystyle 100_{\sigma }{\text{ and }}101_{\sigma }.} The number one has finite and infinite representations 1.0 σ , 0.21 σ {\displaystyle 1.0_{\sigma },0.21_{\sigma }} and 0. 20 ¯ σ , 0.1 2 ¯ σ , {\displaystyle 0.{\overline {20}}_{\sigma },0.1{\overline {2}}_{\sigma },} where the first of each pair is in canonical form . The algebraic number 2 ( 3 σ − 7 ) {\displaystyle 2(3\sigma -7)} can be written 0.101 σ , {\displaystyle 0.101_{\sigma },} or non-canonically as 0.022 σ . {\displaystyle 0.022_{\sigma }.} The decimal number 10 = 111.12 σ , {\displaystyle 10=111.12_{\sigma },} 7 σ + 3 = 1100 σ {\displaystyle 7\sigma +3=1100_{\sigma }\,} and 1 σ − 1 = 0. 1 ¯ σ . {\displaystyle {\tfrac {1}{\sigma -1}}=0.{\overline {1}}_{\sigma }.}
Properties of canonical sigmary expansions, with coefficients a , b , c , d ∈ Z : {\displaystyle a,b,c,d\in \mathbb {Z} :}
Remarkably, the same holds mutatis mutandis for all quadratic Pisot numbers that satisfy the general equation x 2 = n x + 1 , {\displaystyle x^{2}=nx+1,} with integer n > 0. [ 9 ] It follows by repeated substitution of x = n + 1 x {\displaystyle x=n+{\frac {1}{x}}} that all positive solutions 1 2 ( n + n 2 + 4 / ) {\displaystyle {\tfrac {1}{2}}\left(n+{\sqrt {n^{2}+4{\vphantom {/}}}}\right)} have a purely periodic continued fraction expansion σ n = n + 1 n + 1 n + 1 ⋱ {\displaystyle \sigma _{n}=n+{\cfrac {1}{n+{\cfrac {1}{n+{\cfrac {1}{\ddots }}}}}}} Vera de Spinadel described the properties of these irrationals and introduced the moniker metallic means . [ 10 ]
These numbers are related to the silver ratio as the Fibonacci numbers and Lucas numbers are to the golden ratio .
The fundamental sequence is defined by the recurrence relation P n = 2 P n − 1 + P n − 2 for n > 1 , {\displaystyle P_{n}=2P_{n-1}+P_{n-2}{\text{ for }}n>1,} with initial values P 0 = 0 , P 1 = 1. {\displaystyle P_{0}=0,P_{1}=1.}
The first few terms are 0, 1, 2, 5, 12, 29, 70, 169,... (sequence A000129 in the OEIS ). The limit ratio of consecutive terms is the silver mean.
Fractions of Pell numbers provide rational approximations of σ {\displaystyle \sigma } with error | σ − P n + 1 P n | < 1 8 P n 2 {\displaystyle \left\vert \sigma -{\frac {P_{n+1}}{P_{n}}}\right\vert <{\frac {1}{{\sqrt {8}}P_{n}^{2}}}}
The sequence is extended to negative indices using P − n = ( − 1 ) n − 1 P n . {\displaystyle P_{-n}=(-1)^{n-1}P_{n}.}
Powers of σ {\displaystyle \sigma } can be written with Pell numbers as linear coefficients σ n = σ P n + P n − 1 , {\displaystyle \sigma ^{n}=\sigma P_{n}+P_{n-1},} which is proved by mathematical induction on n. The relation also holds for n < 0.
The generating function of the sequence is given by
The characteristic equation of the recurrence is x 2 − 2 x − 1 = 0 {\displaystyle x^{2}-2x-1=0} with discriminant D = 8. {\displaystyle D=8.} If the two solutions are silver ratio σ {\displaystyle \sigma } and conjugate σ ¯ , {\displaystyle {\bar {\sigma }},} so that σ + σ ¯ = 2 and σ ⋅ σ ¯ = − 1 , {\displaystyle \sigma +{\bar {\sigma }}=2\;{\text{ and }}\;\sigma \cdot {\bar {\sigma }}=-1,} the Pell numbers are computed with the Binet formula
Since | a σ ¯ n | < 1 / σ 2 n , {\displaystyle \left\vert a\,{\bar {\sigma }}^{n}\right\vert <1/\sigma ^{2n},} the number P n {\displaystyle P_{n}} is the nearest integer to a σ n , {\displaystyle a\,\sigma ^{n},} with a = 1 / 8 {\displaystyle a=1/{\sqrt {8}}} and n ≥ 0.
The Binet formula σ n + σ ¯ n {\displaystyle \sigma ^{n}+{\bar {\sigma }}^{n}} defines the companion sequence Q n = P n + 1 + P n − 1 . {\displaystyle Q_{n}=P_{n+1}+P_{n-1}.}
The first few terms are 2, 2, 6, 14, 34, 82, 198,... (sequence A002203 in the OEIS ).
This Pell-Lucas sequence has the Fermat property : if p is prime, Q p ≡ Q 1 mod p . {\displaystyle Q_{p}\equiv Q_{1}{\bmod {p}}.} The converse does not hold, the least odd pseudoprimes n ∣ ( Q n − 2 ) {\displaystyle \,n\mid (Q_{n}-2)} are 13 2 , 385, 31 2 , 1105, 1121, 3827, 4901. [ 12 ] [ c ]
Pell numbers are obtained as integral powers n > 2 of a matrix with positive eigenvalue σ {\displaystyle \sigma } M = ( 2 1 1 0 ) , {\displaystyle M={\begin{pmatrix}2&1\\1&0\end{pmatrix}},}
M n = ( P n + 1 P n P n P n − 1 ) {\displaystyle M^{n}={\begin{pmatrix}P_{n+1}&P_{n}\\P_{n}&P_{n-1}\end{pmatrix}}}
The trace of M n {\displaystyle M^{n}} gives the above Q n . {\displaystyle Q_{n}.}
A rectangle with edges in ratio √2 ∶ 1 can be created from a square piece of paper with an origami folding sequence. Considered a proportion of great harmony in Japanese aesthetics — Yamato-hi (大和比) — the ratio is retained if the √2 rectangle is folded in half, parallel to the short edges. Rabatment produces a rectangle with edges in the silver ratio (according to 1 / σ = √2 − 1 ). [ d ]
If the folding paper is opened out, the creases coincide with diagonal sections of a regular octagon . The first two creases divide the square into a silver gnomon with angles in the ratios 5 ∶ 2 ∶ 1, between two right triangles with angles in ratios 4 ∶ 2 ∶ 2 (left) and 4 ∶ 3 ∶ 1 (right). The unit angle is equal to 22 + 1 / 2 degrees.
If the octagon has edge length 1 , {\displaystyle 1,} its area is 2 σ {\displaystyle 2\sigma } and the diagonals have lengths σ + 1 / , σ {\displaystyle {\sqrt {\sigma +1{\vphantom {/}}}},\;\sigma } and 2 ( σ + 1 ) / . {\displaystyle {\sqrt {2(\sigma +1){\vphantom {/}}}}.} The coordinates of the vertices are given by the 8 permutations of ( ± 1 2 , ± σ 2 ) . {\displaystyle \left(\pm {\tfrac {1}{2}},\pm {\tfrac {\sigma }{2}}\right).} [ 15 ] The paper square has edge length σ − 1 {\displaystyle \sigma -1} and area 2. {\displaystyle 2.} The triangles have areas 1 , σ − 1 σ {\displaystyle 1,{\frac {\sigma -1}{\sigma }}} and 1 σ ; {\displaystyle {\frac {1}{\sigma }};} the rectangles have areas σ − 1 and 1 σ . {\displaystyle \sigma -1{\text{ and }}{\frac {1}{\sigma }}.}
Divide a rectangle with sides in ratio 1 ∶ 2 into four congruent right triangles with legs of equal length and arrange these in the shape of a silver rectangle, enclosing a similar rectangle that is scaled by factor 1 σ {\displaystyle {\tfrac {1}{\sigma }}} and rotated about the centre by π 4 . {\displaystyle {\tfrac {\pi }{4}}.} Repeating the construction at successively smaller scales results in four infinite sequences of adjoining right triangles, tracing a whirl of converging silver rectangles. [ 16 ]
The logarithmic spiral through the vertices of adjacent triangles has polar slope k = 4 π ln ( σ ) . {\displaystyle k={\frac {4}{\pi }}\ln(\sigma ).} The parallelogram between the pair of grey triangles on the sides has perpendicular diagonals in ratio σ {\displaystyle \sigma } , hence is a silver rhombus .
If the triangles have legs of length 1 {\displaystyle 1} then each discrete spiral has length σ σ − 1 = ∑ n = 0 ∞ σ − n . {\displaystyle {\frac {\sigma }{\sigma -1}}=\sum _{n=0}^{\infty }\sigma ^{-n}.} The areas of the triangles in each spiral region sum to σ 4 = 1 2 ∑ n = 0 ∞ σ − 2 n ; {\displaystyle {\frac {\sigma }{4}}={\tfrac {1}{2}}\sum _{n=0}^{\infty }\sigma ^{-2n};} the perimeters are equal to σ + 2 {\displaystyle \sigma +2} (light grey) and 2 σ − 1 {\displaystyle 2\sigma -1} (silver regions).
Arranging the tiles with the four hypotenuses facing inward results in the diamond-in-a-square shape. Roman architect Vitruvius recommended the implied ad quadratura ratio as one of three for proportioning a town house atrium . The scaling factor is 1 σ − 1 , {\displaystyle {\tfrac {1}{\sigma -1}},} and iteration on edge length 2 gives an angular spiral of length σ + 1. {\displaystyle \sigma +1.}
The silver mean has connections to the following Archimedean solids with octahedral symmetry ; all values are based on edge length = 2.
The coordinates of the vertices are given by 24 distinct permutations of ( ± σ , ± 1 , ± 1 ) , {\displaystyle (\pm \sigma ,\pm 1,\pm 1),} thus three mutually-perpendicular silver rectangles touch six of its square faces. The midradius is 2 ( σ + 1 ) / , {\displaystyle {\sqrt {2(\sigma +1){\vphantom {/}}}},} the centre radius for the square faces is σ . {\displaystyle \sigma .} [ 17 ]
Coordinates: 24 permutations of ( ± σ , ± σ , ± 1 ) . {\displaystyle (\pm \sigma ,\pm \sigma ,\pm 1).} Midradius: σ + 1 , {\displaystyle \sigma +1,} centre radius for the octagon faces: σ . {\displaystyle \sigma .} [ 18 ]
Coordinates: 48 permutations of ( ± ( 2 σ − 1 ) , ± σ , ± 1 ) . {\displaystyle (\pm (2\sigma -1),\pm \sigma ,\pm 1).} Midradius: 6 ( σ + 1 ) / , {\displaystyle {\sqrt {6(\sigma +1){\vphantom {/}}}},} centre radius for the square faces: σ + 2 , {\displaystyle \sigma +2,} for the octagon faces: 2 σ − 1. {\displaystyle 2\sigma -1.} [ 19 ]
See also the dual Catalan solids
The acute isosceles triangle formed by connecting two adjacent vertices of a regular octagon to its centre point, is here called the silver triangle . It is uniquely identified by its angles in ratios 2 : 3 : 3. {\displaystyle 2:3:3.} The apex angle measures 360 / 8 = 45 , {\displaystyle 360/8=45,} each base angle 67 1 2 {\displaystyle 67{\tfrac {1}{2}}} degrees. It follows that the height to base ratio is 1 2 tan ( 67 1 2 ) = σ 2 . {\displaystyle {\tfrac {1}{2}}\tan(67{\tfrac {1}{2}})={\tfrac {\sigma }{2}}.}
By trisecting one of its base angles, the silver triangle is partitioned into a similar triangle and an obtuse silver gnomon . The trisector is collinear with a medium diagonal of the octagon. Sharing the apex of the parent triangle, the gnomon has angles of 67 1 2 / 3 = 22 1 2 , 45 and 112 1 2 {\displaystyle 67{\tfrac {1}{2}}/3=22{\tfrac {1}{2}},45{\text{ and }}112{\tfrac {1}{2}}} degrees in the ratios 1 : 2 : 5. {\displaystyle 1:2:5.} From the law of sines , its edges are in ratios 1 : σ + 1 : σ . {\displaystyle 1:{\sqrt {\sigma +1}}:\sigma .}
The similar silver triangle is likewise obtained by scaling the parent triangle in base to leg ratio 2 cos ( 67 1 2 ) {\displaystyle 2\cos(67{\tfrac {1}{2}})} , accompanied with an 112 1 2 {\displaystyle 112{\tfrac {1}{2}}} degree rotation. Repeating the process at decreasing scales results in an infinite sequence of silver triangles, which converges at the centre of rotation . It is assumed without proof that the centre of rotation is the intersection point of sequential median lines that join corresponding legs and base vertices. [ 20 ] The assumption is verified by construction, as demonstrated in the vector image.
The centre of rotation has barycentric coordinates ( σ + 1 σ + 5 : 2 σ + 5 : 2 σ + 5 ) ∼ ( σ + 1 2 : 1 : 1 ) , {\displaystyle \left({\tfrac {\sigma +1}{\sigma +5}}:{\tfrac {2}{\sigma +5}}:{\tfrac {2}{\sigma +5}}\right)\sim \left({\tfrac {\sigma +1}{2}}:1:1\right),} the three whorls of stacked gnomons have areas in ratios ( σ + 1 2 ) 2 : σ + 1 2 : 1. {\displaystyle \left({\tfrac {\sigma +1}{2}}\right)^{2}:{\tfrac {\sigma +1}{2}}:1.}
The logarithmic spiral through the vertices of all nested triangles has polar slope
The long, medium and short diagonals of the regular octagon concur respectively at the apex, the circumcenter and the orthocenter of a silver triangle.
Assume a silver rectangle has been constructed as indicated above, with height 1 , length σ {\displaystyle \sigma } and diagonal length σ 2 + 1 {\displaystyle {\sqrt {\sigma ^{2}+1}}} . The triangles on the diagonal have altitudes 1 / 1 + σ − 2 ; {\displaystyle 1/{\sqrt {1+\sigma ^{-2}}}\,;} each perpendicular foot divides the diagonal in ratio σ 2 . {\displaystyle \sigma ^{2}.}
If an horizontal line is drawn through the intersection point of the diagonal and the internal edge of a rabatment square , the parent silver rectangle and the two scaled copies along the diagonal have areas in the ratios σ 2 : 2 : 1 , {\displaystyle \sigma ^{2}:2:1\,,} the rectangles opposite the diagonal both have areas equal to 2 σ + 1 . {\displaystyle {\tfrac {2}{\sigma +1}}.} [ 21 ]
Relative to vertex A , the coordinates of feet of altitudes U and V are ( σ σ 2 + 1 , 1 σ 2 + 1 ) and ( σ 1 + σ − 2 , 1 1 + σ − 2 ) . {\displaystyle \left({\tfrac {\sigma }{\sigma ^{2}+1}},{\tfrac {1}{\sigma ^{2}+1}}\right){\text{ and }}\left({\tfrac {\sigma }{1+\sigma ^{-2}}},{\tfrac {1}{1+\sigma ^{-2}}}\right).}
If the diagram is further subdivided by perpendicular lines through U and V , the lengths of the diagonal and its subsections can be expressed as trigonometric functions of argument α = 67 1 2 {\displaystyle \alpha =67{\tfrac {1}{2}}} degrees, the base angle of the silver triangle:
A B ¯ = σ 2 + 1 = sec ( α ) A V ¯ = σ 2 / A B ¯ = σ sin ( α ) U V ¯ = 2 / A S ¯ = 2 sin ( α ) S B ¯ = 4 / A B ¯ = 4 cos ( α ) S V ¯ = 3 / A B ¯ = 3 cos ( α ) A S ¯ = 1 + σ − 2 = csc ( α ) h ¯ = 1 / A S ¯ = sin ( α ) U S ¯ = A V ¯ − S B ¯ = ( 2 σ − 3 ) cos ( α ) A U ¯ = 1 / A B ¯ = cos ( α ) , {\displaystyle {\begin{aligned}{\overline {AB}}={\sqrt {\sigma ^{2}+1}}&=\sec(\alpha )\\{\overline {AV}}=\sigma ^{2}/{\overline {AB}}&=\sigma \sin(\alpha )\\{\overline {UV}}=2/{\overline {AS}}&=2\sin(\alpha )\\{\overline {SB}}=4/{\overline {AB}}&=4\cos(\alpha )\\{\overline {SV}}=3/{\overline {AB}}&=3\cos(\alpha )\\{\overline {AS}}={\sqrt {1+\sigma ^{-2}}}&=\csc(\alpha )\\{\overline {h}}=1/{\overline {AS}}&=\sin(\alpha )\\{\overline {US}}={\overline {AV}}-{\overline {SB}}&=(2\sigma -3)\cos(\alpha )\\{\overline {AU}}=1/{\overline {AB}}&=\cos(\alpha ),\end{aligned}}}
Both the lengths of the diagonal sections and the trigonometric values are elements of biquadratic number field K = Q ( 2 + 2 ) . {\displaystyle K=\mathbb {Q} \left({\sqrt {2+{\sqrt {2}}}}\right).}
The silver rhombus with edge 1 {\displaystyle 1} has diagonal lengths equal to U V ¯ {\displaystyle {\overline {UV}}} and 2 A U ¯ . {\displaystyle 2{\overline {AU}}.} The regular octagon with edge 2 {\displaystyle 2} has long diagonals of length 2 A B ¯ {\displaystyle 2{\overline {AB}}} that divide it into eight silver triangles. Since the regular octagon is defined by its side length and the angles of the silver triangle, it follows that all measures can be expressed in powers of σ and the diagonal segments of the silver rectangle, as illustrated above, pars pro toto on a single triangle.
The leg to base ratio A B ¯ / 2 ≈ 1.306563 {\displaystyle {\overline {AB}}/2\approx 1.306563} has been dubbed the Cordovan proportion by Spanish architect Rafael de la Hoz Arderius. According to his observations, it is a notable measure in the architecture and intricate decorations of the mediæval Mosque of Córdoba , Andalusia . [ 22 ]
A silver spiral is a logarithmic spiral that gets wider by a factor of σ {\displaystyle \sigma } for every quarter turn. It is described by the polar equation r ( θ ) = a exp ( k θ ) , {\displaystyle r(\theta )=a\exp(k\theta ),} with initial radius a {\displaystyle a} and parameter k = 2 π ln ( σ ) . {\displaystyle k={\frac {2}{\pi }}\ln(\sigma ).} If drawn on a silver rectangle, the spiral has its pole at the foot of altitude of a triangle on the diagonal and passes through vertices of paired squares which are perpendicularly aligned and successively scaled by a factor 1 / σ . {\displaystyle 1/\sigma .}
The silver ratio appears prominently in the Ammann–Beenker tiling , a non-periodic tiling of the plane with octagonal symmetry, build from a square and silver rhombus with equal side lengths. Discovered by Robert Ammann in 1977, its algebraic properties were described by Frans Beenker five years later. [ 23 ] If the squares are cut into two triangles, the inflation factor for Ammann A5-tiles is σ 2 , {\displaystyle \sigma ^{2},} the dominant eigenvalue of substitution matrix M = ( 3 2 4 3 ) . {\displaystyle M={\begin{pmatrix}3&2\\4&3\end{pmatrix}}.} | https://en.wikipedia.org/wiki/Silver_ratio |
In pathology , silver staining is the use of silver to selectively alter the appearance of a target in microscopy of histological sections ; in temperature gradient gel electrophoresis ; and in polyacrylamide gels .
In traditional stained glass , silver stain is a technique to produce yellow to orange or brown shades (or green on a blue glass base), by adding a mixture containing silver compounds (notably silver nitrate ), and firing lightly. It was introduced soon after 1800, and is the "stain" in the term "stained glass". Silver compounds [ 1 ] are mixed with binding substances, applied to the surface of glass, and then fired in a furnace or kiln. [ 2 ] [ 3 ] [ 4 ]
Camillo Golgi perfected silver staining for the study of the nervous system . Although the exact chemical mechanism by which this occurs is unknown, [ 5 ] Golgi's method stains a limited number of cells at random in their entirety. [ 6 ]
Silver staining was introduced by Kerenyi and Gallyas as a sensitive procedure to detect trace amounts of proteins in gels . [ 7 ] The technique has been extended to the study of other biological macromolecules that have been separated in a variety of supports. [ 8 ]
Classical Coomassie brilliant blue staining can usually detect a 50 ng protein band; silver staining increases the sensitivity typically 50 times.
Many variables can influence the color intensity and every protein has its own staining characteristics; clean glassware, pure reagents, and water of highest purity are the key points to successful staining. [ 9 ]
Some cells are argentaffin . These reduce silver solution to metallic silver after formalin fixation . Other cells are argyrophilic . These reduce silver solution to metallic silver after being exposed to the stain that contains a reductant , for example hydroquinone or formalin.
Silver nitrate forms insoluble silver phosphate with phosphate ions; this method is known as the Von Kossa Stain . When subjected to a reducing agent, usually hydroquinone , it forms black elementary silver. This is used for study of formation of calcium phosphate particles during bone growth.
Silver staining aids the visualization of targets of interest, namely intracellular and extracellular cellular components such as DNA and proteins , such as type III collagen and reticulin fibres by the deposition of metallic silver particles on the targets of interest. [ 10 ]
Pseudomonas , [ 11 ] Legionella , Leptospira , H. pylori , Bartonella and Treponema , and fungi such as Pneumocystis , Cryptococcus , and Candida are organisms that are stained with silver. [ citation needed ]
Silver staining is used in karyotyping . Silver nitrate stains the nucleolar organization region (NOR)-associated protein, producing a dark region wherein the silver is deposited and denoting the activity of rRNA genes within the NOR. Human chromosomes 13, 14, 15, 21, and 22 have NORs, which increase the silver stain activity by at least 50 times. [ citation needed ]
Silver staining is used to stain gels. The silver stain of proteins in Agarose gels was developed in 1973 by Kerenyi and Gallyas. [ 12 ] Later it was adapted to polyacrylamide gels used in SDS-PAGE , [ 13 ] [ 14 ] [ 15 ] [ 16 ] [ 17 ] and also for staining DNA or RNA. [ 18 ] The glycosylations of glycoproteins and polysaccharides can be oxidised by a 1-hour pre-treatment with 0.1% periodic acid at 4 °C, which improves the binding of silver ions and the staining result. [ 19 ]
First, the proteins are denatured in the gel by a fixative solution of 10% acetic acid and 30% ethanol and precipitated, at the same time the detergent (mostly SDS ) is extracted. The diffusion of the proteins is thus significantly reduced. After repeated washing with water, the gel is incubated in a silver nitrate solution. Silver ions bind to negatively charged side chains of the proteins. Excess silver ions are then washed off with water. In the final development step, the silver ions are reduced to elemental silver by addition of alkaline formaldehyde . This stains the sites where proteins are present, brown to black.
The intensity of the staining depends on the primary structure of the protein. Furthermore, the cleanliness of the vessels used and the purity of the reagents influence the silver stain. [ 20 ] Common artifacts in silver stained gels are bands of keratin in the ranges of 54–57 kDa and 65–68 kDa [ 21 ] as a contamination of the sample prior to the electrophoresis.
There are several silver stains incorporating methenamine , including: | https://en.wikipedia.org/wiki/Silver_staining |
Silver standards refer to the standards of millesimal fineness for the silver alloy used in the manufacture or crafting of silver objects. This list is organized from highest to lowest millesimal fineness, or purity of the silver. | https://en.wikipedia.org/wiki/Silver_standards |
Silver telluride (Ag 2 Te) is a chemical compound, a telluride of silver , also known as disilver telluride or silver(I) telluride. It forms a monoclinic crystal. In a wider sense, silver telluride can be used to denote AgTe (silver(II) telluride, a metastable compound) or Ag 5 Te 3 .
Silver(I) telluride occurs naturally as the mineral hessite , whereas silver(II) telluride is known as empressite .
Silver telluride is a semiconductor which can be doped both n-type and p-type. Stoichiometric Ag 2 Te has n-type conductivity. On heating silver is lost from the material.
Non-stoichiometric silver telluride has shown extraordinary magnetoresistance .
Porous silver telluride (AgTe) is synthesized by an electrochemical deposition method. The experiment can be performed using a potentiostat and a three-electrode cell with 200 mL of 0.5 M sulfuric acid electrolyte solution containing Ag nanoparticles at room temperature. Then a silver paste used in the tungsten ditelluride (WTe 2 ) attachment leach into the electrolyte which causes small amounts of Ag to dissolve in the electrolyte. The electrolyte was stirred by a magnetic bar to remove hydrogen bubbles. A silver- silver chloride electrode and a platinum wire can be used as reference and counter electrodes. All the potentials can be measured against the reference electrode, and it was calibrated using the equation ERHE = EAg/AgCl + .059 pH + .197. In order to grow the porous AgTe, the WTe 2 was treated using multiple cyclic voltammetry between -1.2 and 0 volts with a scan rate of 100 mV/s. [ 1 ]
Glutathione coated Ag 2 Te Nanoparticles can be synthesized by preparing a 9 mL solution containing 10 mM AgNO 3 , 5mM Na 2 TeO 3 , and 30 mM glutathione. Place that solution in an ice bath. N 2 H 4 was added to the solution and the reaction is allowed to proceed for 5 min under constant stirring. Then the nanoparticles are washed three times by a way of centrifugation, after the three washes the nanoparticles are suspended in PBS and washed again with that same method. [ 2 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silver_telluride |
Silver tetrafluoroborate is an inorganic compound with the molecular formula AgBF 4 . It is a white solid, although commercial samples often are gray, that dissolves in polar organic solvents as well as water. [ 2 ]
Silver tetrafluoroborate can be prepared by several methods. A simple route entails dissolving silver carbonate in aqueous tetrafluoroboric acid . [ 3 ] It can also be produced by treating silver(I) fluoride with boron trifluoride in nitromethane solution. The reaction between boron trifluoride and a benzene suspension of silver oxide is yet another route, one that exploits the solubility of the compound in benzene. This method however affords silver fulminate , a sensitive explosive. [ 4 ]
In the inorganic and organometallic chemistry laboratory, silver tetrafluoroborate, sometimes referred to "silver BF-4", is a used as a reagent to remove halide ligands and to oxidize electron-rich complexes. In dichloromethane, silver tetrafluoroborate is a moderately strong oxidant. [ 5 ] Similar to silver hexafluorophosphate , it is commonly used to replace halide anions or ligands with the weakly coordinating tetrafluoroborate anions. The abstraction of the halide is driven by the precipitation of the corresponding silver halide .
According to X-ray crystallography , the solid compound consists of Ag + centers bound to four fluoride sites of the BF 4 − . [ 6 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Silver_tetrafluoroborate |
Silvering is the chemical process of coating a non-conductive substrate such as glass with a reflective substance, to produce a mirror . While the metal is often silver , the term is used for the application of any reflective metal.
Most common household mirrors are "back-silvered" or "second-surface", meaning that the light reaches the reflective layer after passing through the glass. A protective layer of paint is usually applied to protect the back side of the reflective surface . [ 1 ] This arrangement protects the fragile reflective layer from corrosion, scratches, and other damage. [ 2 ] However, the glass layer may absorb some of the light and cause distortions and optical aberrations due to refraction at the front surface, and multiple additional reflections on it, giving rise to "ghost images" (although some optical mirrors such as Mangins take advantage of it).
Therefore, precision optical mirrors normally are "front-silvered" or " first-surface ", meaning that the reflective layer is on the surface towards the incoming light. The substrate normally provides only physical support, and need not be transparent. A hard, protective, transparent overcoat may be applied to prevent oxidation of the reflective layer and scratching of the metal. Front-coated mirrors achieve reflectivities of 90–95% when new.
Ptolemaic Egypt had manufactured small glass mirrors backed by lead , tin, or antimony . [ 4 ] In the early 10th century, the Persian scientist al-Razi described ways of silvering and gilding in a book on alchemy , [ citation needed ] but this was not done for the purpose of making mirrors.
Tin-coated mirrors were first made in Europe in the 15th century. The thin tinfoil used to silver mirrors was known as "tain". [ 5 ] When glass mirrors first gained widespread usage in Europe during the 16th century , most were silvered with an amalgam of tin and mercury , [ 6 ]
In 1835 German chemist Justus von Liebig developed a process for depositing silver on the rear surface of a piece of glass; this technique gained wide acceptance after Liebig improved it in 1856. [ 7 ] [ 8 ] The process was further refined and made easier by the chemist Tony Petitjean (1856). [ 9 ] This reaction is a variation of the Tollens' reagent for aldehydes. A diamminesilver(I) solution is mixed with a sugar and sprayed onto the glass surface. The sugar is oxidized by silver(I), which is itself reduced to silver(0), i.e. elemental silver , and deposited onto the glass.
In 1856-1857 Karl August von Steinheil and Léon Foucault introduced the process of depositing an ultra-thin layer of silver on the front surface of a piece of glass, making the first optical-quality first surface glass mirrors, replacing the use of speculum metal mirrors in reflecting telescopes . [ 10 ] [ dead link ] These techniques soon became standard for technical equipment.
An aluminum vacuum-deposition process invented in 1930 by Caltech physicist and astronomer John Strong , led to most reflecting telescopes shifting to aluminum. [ 11 ] Nevertheless, some modern telescopes use silver, such as the Kepler Space Telescope . The Kepler mirror's silver was deposited using ion assisted evaporation . [ 12 ] [ 13 ]
Silvering aims to produce a non-crystalline coating of amorphous metal (metallic glass), with no visible artifacts from grain boundaries. The most common methods in current use are electroplating , chemical "wet process" deposition, and vacuum deposition .
Electroplating of a substrate of glass or other non- conductive material requires the deposition of a thin layer of conductive but transparent material, such as carbon. This layer tends to reduce the adhesion between the metal and the substrate. [ 2 ] (pp 3 & 107) Chemical deposition can result in better adhesion, directly or by pre-treatment of the surface.
Vacuum deposition can produce very uniform coating with very precisely controlled thickness. [ 2 ]
The reflective layer on a second surface mirror such as a household mirror is often actual silver. A modern "wet" process for silver coating treats the glass with tin(II) chloride to improve the bonding between silver and glass. An activator is applied after the silver has been deposited to harden the tin and silver coatings. A layer of copper may be added for long-term durability. [ 14 ]
Silver would be ideal for telescope mirrors and other demanding optical applications, since it has the best initial front-surface reflectivity in the visible spectrum. However, it quickly oxidizes and absorbs atmospheric sulfur to create a dark, low-reflectivity tarnish.
The "silvering" on precision optical instruments such as telescopes is usually aluminum. Although aluminum also oxidizes quickly, the thin aluminum oxide (sapphire) layer is transparent, and so the high-reflectivity underlying aluminum stays visible.
In modern aluminum silvering, a sheet of glass is placed in a vacuum chamber with electrically heated nichrome coils that can evaporate aluminum. In a vacuum, the hot aluminum atoms travel in straight lines. When they hit the surface of the mirror, they cool and stick.
Some mirror makers evaporate a layer of quartz or beryllia on the mirror; others expose it to pure oxygen or air in an oven so that it will form a tough, clear layer of aluminum oxide .
The first tin-coated glass mirrors were produced by applying a tin-mercury amalgam to the glass and heating the piece to evaporate the mercury.
The "silvering" on infrared instruments is usually gold. It has the best reflectivity in the infrared spectrum, and has high resistance to oxidation and corrosion. Conversely, a thin gold coating is used to create optical filters which block infrared (by mirroring it back towards the source) while passing visible light. | https://en.wikipedia.org/wiki/Silvering |
In mathematics , the Silverman–Toeplitz theorem , first proved by Otto Toeplitz , is a result in series summability theory characterizing matrix summability methods that are regular. A regular matrix summability method is a linear sequence transformation that preserves the limits of convergent sequences . [ 1 ] The linear sequence transformation can be applied to the divergent sequences of partial sums of divergent series to give those series generalized sums.
An infinite matrix ( a i , j ) i , j ∈ N {\displaystyle (a_{i,j})_{i,j\in \mathbb {N} }} with complex -valued entries defines a regular matrix summability method if and only if it satisfies all of the following properties:
An example is Cesàro summation , a matrix summability method with
Let the aforementioned inifinite matrix ( a i , j ) i , j ∈ N {\displaystyle (a_{i,j})_{i,j\in \mathbb {N} }} of complex elements satisfy the following conditions:
and z n {\displaystyle z_{n}} be a sequence of complex numbers that converges to lim n → ∞ z n = z ∞ {\displaystyle \lim _{n\to \infty }z_{n}=z_{\infty }} . We denote S n {\displaystyle S_{n}} as the weighted sum sequence: S n = ∑ m = 1 n ( a n , m z n ) {\displaystyle S_{n}=\sum _{m=1}^{n}{\left(a_{n,m}z_{n}\right)}} .
Then the following results hold:
For the fixed j ∈ N {\displaystyle j\in \mathbb {N} } the complex sequences z n {\displaystyle z_{n}} , S n {\displaystyle S_{n}} and a i , j {\displaystyle a_{i,j}} approach zero if and only if the real-values sequences | z n | {\displaystyle \left|z_{n}\right|} , | S n | {\displaystyle \left|S_{n}\right|} and | a i , j | {\displaystyle \left|a_{i,j}\right|} approach zero respectively. We also introduce M = sup i ∈ N ∑ j = 1 i | a i , j | > 0 {\displaystyle M=\sup _{i\in \mathbb {N} }\sum _{j=1}^{i}\vert a_{i,j}\vert >0} .
Since | z n | → 0 {\displaystyle \left|z_{n}\right|\to 0} , for prematurely chosen ε > 0 {\displaystyle \varepsilon >0} there exists N ε = N ε ( ε ) {\displaystyle N_{\varepsilon }=N_{\varepsilon }\left(\varepsilon \right)} , so for every n > N ε ( ε ) {\displaystyle n>N_{\varepsilon }\left(\varepsilon \right)} we have | z n | < ε 2 M {\displaystyle \left|z_{n}\right|<{\frac {\varepsilon }{2M}}} . Next, for some N a = N a ( ε ) > N ε ( ε ) {\displaystyle N_{a}=N_{a}\left(\varepsilon \right)>N_{\varepsilon }\left(\varepsilon \right)} it's true, that | a n , m | < M N ε {\displaystyle \left|a_{n,m}\right|<{\frac {M}{N_{\varepsilon }}}} for every n > N a ( ε ) {\displaystyle n>N_{a}\left(\varepsilon \right)} and 1 ⩽ m ⩽ n {\displaystyle 1\leqslant m\leqslant n} . Therefore, for every n > N a ( ε ) {\displaystyle n>N_{a}\left(\varepsilon \right)}
| S n | = | ∑ m = 1 n ( a n , m z n ) | ⩽ ∑ m = 1 n ( | a n , m | ⋅ | z n | ) = ∑ m = 1 N ε ( | a n , m | ⋅ | z n | ) + ∑ m = N ε n ( | a n , m | ⋅ | z n | ) < < N ε ⋅ M N ε ⋅ ε 2 M + ε 2 M ∑ m = N ε n | a n , m | ⩽ ε 2 + ε 2 M ∑ m = 1 n | a n , m | ⩽ ε 2 + ε 2 M ⋅ M = ε {\displaystyle {\begin{aligned}&\left|S_{n}\right|=\left|\sum _{m=1}^{n}\left(a_{n,m}z_{n}\right)\right|\leqslant \sum _{m=1}^{n}\left(\left|a_{n,m}\right|\cdot \left|z_{n}\right|\right)=\sum _{m=1}^{N_{\varepsilon }}\left(\left|a_{n,m}\right|\cdot \left|z_{n}\right|\right)+\sum _{m=N_{\varepsilon }}^{n}\left(\left|a_{n,m}\right|\cdot \left|z_{n}\right|\right)<\\&<N_{\varepsilon }\cdot {\frac {M}{N_{\varepsilon }}}\cdot {\frac {\varepsilon }{2M}}+{\frac {\varepsilon }{2M}}\sum _{m=N_{\varepsilon }}^{n}\left|a_{n,m}\right|\leqslant {\frac {\varepsilon }{2}}+{\frac {\varepsilon }{2M}}\sum _{m=1}^{n}\left|a_{n,m}\right|\leqslant {\frac {\varepsilon }{2}}+{\frac {\varepsilon }{2M}}\cdot M=\varepsilon \end{aligned}}}
which means, that both sequences | S n | {\displaystyle \left|S_{n}\right|} and S n {\displaystyle S_{n}} converge zero. [ 3 ]
lim n → ∞ ( z n − z ∞ ) = 0 {\displaystyle \lim _{n\to \infty }\left(z_{n}-z_{\infty }\right)=0} . Applying the already proven statement yields lim n → ∞ ∑ m = 1 n ( a n , m ( z n − z ∞ ) ) = 0 {\displaystyle \lim _{n\to \infty }\sum _{m=1}^{n}{\big (}a_{n,m}\left(z_{n}-z_{\infty }\right){\big )}=0} . Finally,
lim n → ∞ S n = lim n → ∞ ∑ m = 1 n ( a n , m z n ) = lim n → ∞ ∑ m = 1 n ( a n , m ( z n − z ∞ ) ) + z ∞ lim n → ∞ ∑ m = 1 n ( a n , m ) = 0 + z ∞ ⋅ 1 = z ∞ {\displaystyle \lim _{n\to \infty }S_{n}=\lim _{n\to \infty }\sum _{m=1}^{n}{\big (}a_{n,m}z_{n}{\big )}=\lim _{n\to \infty }\sum _{m=1}^{n}{\big (}a_{n,m}\left(z_{n}-z_{\infty }\right){\big )}+z_{\infty }\lim _{n\to \infty }\sum _{m=1}^{n}{\big (}a_{n,m}{\big )}=0+z_{\infty }\cdot 1=z_{\infty }} , which completes the proof. | https://en.wikipedia.org/wiki/Silverman–Toeplitz_theorem |
Silverquant is a labeling and detection method for DNA microarrays or protein microarrays. A synonym is colorimetric detection. In contrast to the classical signal detection on microarrays by using fluorescence , the colorimetric detection is more sensitive and ozone-stable.
The probe to be detected is labeled with some biotin -molecules. After incubation with a gold-coupled anti-biotin conjugate, silver nitrate and a reducing agent are added. The reaction starts whereas the gold particle serves as a starting point for the silver precipitation.
The reaction needs to be stopped after a specific time. The constant reaction time is essential to obtain comparable results.
The silver-stained spots on the microarray are clearly visible. By using a transmission microarray scanner, the signals are transformed into digital values which are finally available as an image file.
Alexandre I et al. Anal Biochem. 2001 Aug 1;295(1):1-8. | https://en.wikipedia.org/wiki/Silverquant |
Silvilization is a conceptual framework or a vision of the world whereby the forest, a metaphor for primordial living, is the best place for human development and fulfilment. [ 1 ] [ 2 ] It is a portmanteau of the Latin word silva , meaning forest, and civilization . [ 1 ]
The term was first coined by Pierre-Doris Maltais, leader of the Iriadamant eco-cult. [ 3 ] Erkki Pulliainen , an MP of the Green League , in collaboration with Maltais and the University of Helsinki , implemented the interdisciplinary ESSOC project (“Ecological Sylvilisation and Survival with the Aid of Original Cultures”) in 1991. The project was considered a failure. [ 4 ]
In 1997, a publication in the journal Interculture by the Intercultural Institute of Montreal was devoted entirely to the theme of silvilization and ecosophy . The articles were written by authors such as Edward Goldsmith , Gary Snyder , and Gita Mehta . [ 1 ] | https://en.wikipedia.org/wiki/Silvilization |
In organosilicon chemistry , silyl enol ethers are a class of organic compounds that share the common functional group R 3 Si−O−CR=CR 2 , composed of an enolate ( R 3 C−O−R ) bonded to a silane ( SiR 4 ) through its oxygen end and an ethene group ( R 2 C=CR 2 ) as its carbon end. They are important intermediates in organic synthesis . [ 1 ] [ 2 ]
Silyl enol ethers are generally prepared by reacting an enolizable carbonyl compound with a silyl electrophile and a base , or just reacting an enolate with a silyl electrophile. [ 3 ] Since silyl electrophiles are hard and silicon-oxygen bonds are very strong, the oxygen (of the carbonyl compound or enolate) acts as the nucleophile to form a Si-O single bond. [ 3 ]
The most commonly used silyl electrophile is trimethylsilyl chloride . [ 3 ] To increase the rate of reaction, trimethylsilyl triflate may also be used in the place of trimethylsilyl chloride as a more electrophilic substrate. [ 4 ] [ 5 ]
When using an unsymmetrical enolizable carbonyl compound as a substrate, the choice of reaction conditions can help control whether the kinetic or thermodynamic silyl enol ether is preferentially formed. [ 6 ] For instance, when using lithium diisopropylamide (LDA) , a strong and sterically hindered base, at low temperature (e.g., −78°C), the kinetic silyl enol ether (with a less substituted double bond) preferentially forms due to sterics. [ 6 ] [ 7 ] When using triethylamine , a weak base, the thermodynamic silyl enol ether (with a more substituted double bond) is preferred. [ 6 ] [ 8 ] [ 9 ]
Alternatively, a rather exotic way of generating silyl enol ethers is via the Brook rearrangement of appropriate substrates. [ 10 ]
Silyl enol ethers are neutral, mild nucleophiles (milder than enamines ) that react with good electrophiles such as aldehydes (with Lewis acid catalysis ) and carbocations . [ 11 ] [ 12 ] [ 13 ] [ 14 ] Silyl enol ethers are stable enough to be isolated, but are usually used immediately after synthesis. [ 11 ]
Lithium enolates, one of the precursors to silyl enol ethers, [ 6 ] [ 7 ] can also be generated from silyl enol ethers using methyllithium . [ 15 ] [ 3 ] The reaction occurs via nucleophilic substitution at the silicon of the silyl enol ether, producing the lithium enolate and tetramethylsilane . [ 15 ] [ 3 ]
Silyl enol ethers are used in many reactions resulting in alkylation , e.g., Mukaiyama aldol addition , Michael reactions , and Lewis-acid-catalyzed reactions with S N 1 -reactive electrophiles (e.g., tertiary , allylic , or benzylic alkyl halides ). [ 16 ] [ 17 ] [ 18 ] [ 13 ] [ 12 ] Alkylation of silyl enol ethers is especially efficient with tertiary alkyl halides, which form stable carbocations in the presence of Lewis acids like TiCl 4 or SnCl 4 . [ 12 ]
Halogenation of silyl enol ethers gives haloketones . [ 19 ] [ 20 ]
Acyloins form upon organic oxidation with an electrophilic source of oxygen such as an oxaziridine or mCPBA . [ 21 ]
In the Saegusa–Ito oxidation , certain silyl enol ethers are oxidized to enones with palladium(II) acetate .
Reacting a silyl enol ether with PhSCl, a good and soft electrophile, provides a carbonyl compound sulfenylated at an alpha carbon . [ 22 ] [ 20 ] In this reaction, the trimethylsilyl group of the silyl enol ether is removed by the chloride ion released from the PhSCl upon attack of its electrophilic sulfur atom. [ 20 ]
Hydrolysis of a silyl enol ether results in the formation of a carbonyl compound and a disiloxane . [ 23 ] [ 24 ] In this reaction, water acts as an oxygen nucleophile and attacks the silicon of the silyl enol ether. [ 23 ] This leads to the formation of the carbonyl compound and a trimethylsilanol intermediate that undergoes nucleophilic substitution at silicon (by another trimethylsilanol) to give the disiloxane. [ 23 ]
Cyclic silyl enol ethers undergo regiocontrolled one-carbon ring contractions. [ 25 ] [ 26 ] These reactions employ electron-deficient sulfonyl azides, which undergo chemoselective, uncatalyzed [3+2] cycloaddition to the silyl enol ether, followed by loss of dinitrogen, and alkyl migration to give ring-contracted products in good yield. These reactions may be directed by substrate stereochemistry, giving rise to stereoselective ring-contracted product formation.
Silyl enol ethers of esters ( −OR ) or carboxylic acids ( −COOH ) are called silyl ketene acetals [ 13 ] and have the general structure R 3 Si−O−C(OR)=CR 2 . These compounds are more nucleophilic than the silyl enol ethers of ketones ( >C=O ). [ 13 ] | https://en.wikipedia.org/wiki/Silyl_enol_ether |
Silyl ethers are a group of chemical compounds which contain a silicon atom covalently bonded to an alkoxy group. The general structure is R 1 R 2 R 3 Si−O−R 4 where R 4 is an alkyl group or an aryl group. Silyl ethers are usually used as protecting groups for alcohols in organic synthesis . Since R 1 R 2 R 3 can be combinations of differing groups which can be varied in order to provide a number of silyl ethers, this group of chemical compounds provides a wide spectrum of selectivity for protecting group chemistry. Common silyl ethers are: trimethylsilyl ( TMS ), tert -butyldiphenylsilyl (TBDPS), tert -butyldimethylsilyl ( TBS/TBDMS ) and triisopropylsilyl ( TIPS ). They are particularly useful because they can be installed and removed very selectively under mild conditions.
Commonly silylation of alcohols requires a silyl chloride and an amine base. One reliable and rapid procedure is the Corey protocol in which the alcohol is reacted with a silyl chloride and imidazole at high concentration in DMF . [ 1 ] If DMF is replaced by dichloromethane, the reaction is somewhat slower, but the purification of the compound is simplified. A common hindered base for use with silyl triflates is 2,6-lutidine . [ 2 ] Primary alcohols can be protected in less than one hour while some hindered alcohols may require days of reaction time.
When using a silyl chloride, no special precautions are usually required, except for the exclusion of large amounts of water. An excess of silyl chloride can be employed but is not necessary. If excess reagent is used, the product will require flash chromatography to remove excess silanol and siloxane .
Sometimes silyl triflate and a hindered amine base are used. Silyl triflates are more reactive than their corresponding chlorides, so they can be used to install silyl groups onto hindered positions. Silyl triflate is more reactive and also converts ketones to silyl enol ethers . Silyl triflates are water sensitive and must be run under inert atmosphere conditions. Purification involves the addition of an aqueous acid such as saturated ammonium chloride solution. Water quenches remaining silyl reagent and protonates amine bases prior to their removal from the reaction mixture. Following extraction, the product can be purified by flash chromatography.
Ketones react with hydrosilanes in the presence of metal catalysts. [ 3 ] [ 4 ]
Reaction with acids or fluorides such as tetra-n-butylammonium fluoride removes the silyl group when protection is no longer needed. Larger substituents increase resistance to hydrolysis , but also make introduction of the silyl group more difficult. [ 5 ]
In acidic media, the relative resistance is:
In basic media, the relative resistance is:
It is possible to monosilylate a symmetrical diol, although this is known to be problematic occasionally. For example, the following monosilylation was reported: [ 6 ]
However, it turns out that this reaction is hard to repeat. If the reaction were controlled solely by thermodynamics, and if the dianion is of similar reactivity to the monoanion, then a corresponding statistical mixture of 1:2:1 disilylated:monosilylated:unsilylated diol would be expected. However, the reaction in THF is made selective by two factors: 1. kinetic deprotonation of the first anion and 2. the insolubility of the monoanion. At the initial addition of TBSCl, there is only a minor amount of monoanion in solution with the rest being in suspension. This small portion reacts and shifts the equilibrium of the monoanion to draw more into solution, thereby allowing for high yields of the mono-TBS compound to be obtained. Superior results in some cases may be obtained with butyllithium : [ 7 ]
A third method uses a mixture of DMF and DIPEA . [ 8 ]
Alternatively, an excess (4 eq) of the diol can be used, forcing the reaction toward monoprotection.
Selective deprotection of silyl groups is possible in many instances. For example, in the synthesis of taxol : [ 9 ]
Silyl ethers are mainly differentiated on the basis of sterics or electronics. In general, acidic deprotections deprotect less hindered silyl groups faster, with the steric bulk on silicon being more significant than the steric bulk on oxygen. Fluoride-based deprotections deprotect electron-poor silyl groups faster than electron-rich silyl groups. There is some evidence that some silyl deprotections proceed via hypervalent silicon species.
The selective deprotection of silyl ethers has been extensively reviewed. [ 10 ] [ 11 ] Although selective deprotections have been achieved under many different conditions, some procedures, outlined below, are more reliable. A selective deprotection will likely be successful if there is a substantial difference in sterics (e.g., primary TBS vs. secondary TBS or primary TES vs primary TBS) or electronics (e.g. primary TBDPS vs. primary TBS). Unfortunately, some optimization is inevitably required and it is often necessary to run deprotections partway and recycle material. | https://en.wikipedia.org/wiki/Silyl_ether |
Silylation is the introduction of one or more (usually) substituted silyl groups (R 3 Si) to a molecule. Silylations are core methods for production of organosilicon chemistry . Silanization , while similar to silylation, usually refers to attachment of silyl groups to solids. [ 1 ] Silyl groups are commonly used for: alcohol protection, enolate trapping, gas chromatography , electron-impact mass spectrometry (EI-MS), and coordinating with metal complexes.
Silylation is often used to protect alcohols, as well as amines, carboxylic acids, and terminal alkynes. The products after silylation, namely silyl ethers and silyl amines, are resilient toward basic conditions. [ 2 ] Protection is typically done by reacting the functional group with a silyl halide by an SN2 reaction mechanism, typically in the presence of base. [ 3 ]
The protection mechanism begins with the base deprotonating the alcohol group. Next, the deprotonated alcohol group attacks the silyl atom of the silyl halide compound. The halide acts as a leaving group and ends up in solution. A workup step follows to remove any excess base within the solution. The overall reaction scheme is as follows:
Other silylating agents include bis(trimethylsilyl)acetamide (BSA). The reaction of BSA with alcohols gives the corresponding trimethyl silyl ether , together with acetamide as a byproduct (Me = CH 3 ): [ 4 ]
Due to the strength of the Si-F bond, fluoride salts are commonly used as a deprotecting agent of silyl groups. [ 2 ] The primary fluorous deprotecting agent is tetra-n-butylammonium fluoride (TBAF), as its aliphatic chains in help incorporate the fluoride ion into organic solvents. [ 5 ] [ 6 ] [ 7 ]
Deprotection with a fluoride ion occurs by an S N 2 mechanism, followed by acidic workup to protonate the resulting alkoxide:
ROSiMe 3 + NBu 4 F → RO − + NBu + 4 + SiMe 3 F
Deprotection of the alcohol can also be done using either Brønsted acids or Lewis acid conditions. [ 8 ] Brønsted acids, like PyBr 3 (pyridinium tribromide), deprotect the alcohol by acting as a proton donor. [ 8 ]
Sterically bulkier alkyl substituents tend to decrease the reactivity of the silyl group. [ 9 ] Consequently, bulky substituents increase the silyl group's protective abilities. To add bulkier alkyl silyls, more strenuous conditions are required for alcohol protection. As bulkier groups require more strenuous conditions to add, they also require more strenuous conditions to remove. Additionally, bulkier silyl groups are more selective for the type of alcohols they react with, resulting in a preference for primary alcohols over secondary alcohols. Thus, silyl groups such as TBDMS and TIPS can be used to selectively protect primary alcohols over secondary alcohols. [ 9 ]
In acidic conditions, alkyl substituents acting as electron withdrawing groups decrease the reaction rate. [ 10 ] As bulker silyl groups are more likely to be electron withdrawing, it is easier to differentiate between less and more bulky silyl groups. [ 10 ] Therefore, acidic deprotection occurs fastest for less sterically bulky alkyl silyl groups. [ 8 ] In basic conditions, alkyl substituents acting as electron donating groups decrease reaction rate. [ 10 ]
Silylation can also be used to trap reactive compounds for isolation or identification. A common example of this is by trapping reactive enolates into silyl enol ethers , which represent reactive tautomers of many carbonyl compounds. [ 11 ] The original enolate can be reformed upon reaction with an organolithium, or other strong base. [ 11 ]
The introduction of a silyl group(s) gives derivatives of enhanced volatility, making the derivatives suitable for analysis by gas chromatography and electron-impact mass spectrometry (EI-MS). For EI-MS, the silyl derivatives give more favorable diagnostic fragmentation patterns of use in structure investigations, or characteristic ions of use in trace analyses employing selected ion monitoring and related techniques. [ 12 ] [ 13 ]
Coordination complexes with silyl ligands are well known. An early example is CpFe(CO) 2 Si(CH 3 ) 3 , prepared by silylation of CpFe(CO) 2 Na with trimethylsilyl chloride . Typical routes include oxidative addition of Si-H bonds to low-valent metals. Metal silyl complexes are intermediates in hydrosilation , a process used to make organosilicon compounds on both laboratory and commercial scales. [ 14 ] [ 15 ] | https://en.wikipedia.org/wiki/Silylation |
Silylene is a chemical compound with the formula SiR 2 . It is the silicon analog of carbene . Silylene rapidly when condensed.
Silylenes are formal derivatives of silylene with its hydrogens replaced by other substituents. [ 2 ] Most examples feature amido (NR 2 ) or alkyl/aryl groups. [ 3 ] [ 4 ]
Silylenes have been proposed as reactive intermediates . They are carbene analogs . [ 5 ]
Silylenes have been generated by thermolysis or photolysis of polysilanes , by silicon atom reactions ( insertion , addition or abstraction), by pyrolysis of silanes , or by reduction of 1,1-dihalosilane. It has long been assumed that the conversion of metallic Si to tetravalent silicon compounds proceeds via silylene intermediates:
Similar considerations apply to the direct process , the reaction of methyl chloride and bulk silicon.
Early observations of silylenes involved generation of dimethylsilylene by dechlorination of dimethyldichlorosilane : [ 6 ]
The formation of dimethylsilylene was demonstrated by conducting the dechlorination in the presence of trimethylsilane : the trapped product being pentamethyldisilane:
A room-temperature isolable N -heterocyclic silylene is N , N ′-di- tert -butyl-1,3-diaza-2-silacyclopent-4-en-2-ylidene: [ 7 ]
The α-amido centers stabilize silylenes by π-donation. The dehalogenation of diorganosilicon dihalides is a widely exploited. [ 8 ]
In one study diphenylsilylene is generated by flash photolysis of a trisilane: [ 9 ]
In this reaction diphenylsilylene is extruded from the trisila ring. The silylene can be observed with UV spectroscopy at 520 nm and is short-lived with a chemical half-life of two microseconds . Added methanol acts as a chemical trap with a second order rate constant of 1.3 × 10 10 mol −1 s −1 which is close to diffusion control. | https://en.wikipedia.org/wiki/Silylene |
SimThyr is a free continuous dynamic simulation program for the pituitary-thyroid feedback control system. [ 1 ] The open-source program is based on a nonlinear model of thyroid homeostasis. [ 2 ] [ 3 ] [ 4 ] In addition to simulations in the time domain the software supports various methods of sensitivity analysis . Its simulation engine is multi-threaded and supports multiple processor cores . SimThyr provides a GUI , which allows for visualising time series , modifying constant structure parameters of the feedback loop (e.g. for simulation of certain diseases), storing parameter sets as XML files (referred to as "scenarios" in the software) and exporting results of simulations in various formats that are suitable for statistical software. SimThyr is intended for both educational purposes and in-silico research. [ 4 ] [ 5 ]
The underlying model of thyroid homeostasis is based on fundamental biochemical, physiological and pharmacological principles, e.g. Michaelis-Menten kinetics , non-competitive inhibition and empirically justified kinetic parameters. [ 1 ] The model has been validated in healthy controls and in cohorts of patients with hypothyroidism and thyrotoxicosis . [ 6 ]
Multiple studies have employed SimThyr for in silico research on the control of thyroid function. [ 7 ] [ 8 ]
The original version was developed to check hypotheses about the generation of pulsatile TSH release. [ 9 ] Later and expanded versions of the software were used to develop the hypothesis of the TSH-T3 shunt in the hypothalamus-pituitary-thyroid axis, [ 10 ] to assess the validity of calculated parameters of thyroid homeostasis (including SPINA-GT and SPINA-GD ) [ 11 ] [ 12 ] and to study allostatic mechanisms leading to non-thyroidal illness syndrome . [ 13 ] [ 14 ]
SimThyr was also used to show that the release rate of thyrotropin is controlled by multiple factors other than T4 and that the relation between free T4 and TSH may be different in euthyroidism , hypothyroidism and thyrotoxicosis . [ 15 ]
SimThyr is free and open-source software. This ensures the source code to be available, which facilitates scientific discussion and reviewing of the underlying model. [ 16 ] [ 17 ] Additionally, the fact that it is freely available may result in economical benefits. [ 18 ] [ 19 ]
The software provides an editor that enables users to modify most structure parameters of the information processing structure. [ 20 ] This functionality fosters simulation of several functional diseases of the thyroid and the pituitary gland. Parameter sets may be stored as MIRIAM- and MIASE -compliant XML files.
On the other hand, the complexity of the user interface and the lack of the ability to model treatment effects have been criticized. [ 21 ] | https://en.wikipedia.org/wiki/SimThyr |
Sim is a two-player paper-and-pencil game .
Six dots ( vertices ) are drawn. Each dot is connected to every other dot by a line ( edge ).
Two players take turns coloring any uncolored lines. One player colors in one color, and the other colors in another color, with each player trying to avoid the creation of a triangle made solely of their color (only triangles with the dots as all corners count; intersections of lines are not relevant); the player who completes such a triangle loses immediately.
Ramsey theory can also be used to show that no game of Sim can end in a tie. Specifically, since the Ramsey number R (3, 3) is equal to 6, any two-coloring of the complete graph on 6 vertices ( K 6 ) must contain a monochromatic triangle, and therefore is not a tied position. This will also apply to any super-graph of K 6 . For another proof that there must eventually be a triangle of either color, see the Theorem on friends and strangers .
Computer search techniques verified in 1974 that the second player can win Sim with perfect play. [ 1 ] A strategy that could be easily implemented by human players was found in 2020. [ 2 ]
The game of Sim is one example of a Ramsey game. Other Ramsey games are possible. For instance, the players can be allowed to color more than one line during their turns. Another Ramsey game similar to Sim and related to the Ramsey number R (4, 4) = 18 is played on 18 vertices and the 153 edges between them. The two players must avoid to color all six edges connecting four vertices.
Because the Ramsey number R (3, 3, 3) is equal to 17, any three-coloring of the complete graph on 17 vertices must contain a monochromatic triangle. A corresponding Ramsey game uses pencils of three colors. One approach can have three players compete, while another would allow two players to alternately select any of the three colors to paint an edge of the graph, until a player loses by completing a monochromatic triangle. Finding perfect winning strategies for these variants is most likely out of reach.
A technical report [ 3 ] by Wolfgang Slany is available online, with many references to literature on Sim, going back to the game's introduction by Gustavus Simmons in 1969, [ 4 ] including proofs and estimates of the difficulty as well as computational complexity of Sim and other Ramsey games.
An app including its source code in the visual multi-platform Catrobat programming language is available [ 5 ] for playing it against one's smartphone. | https://en.wikipedia.org/wiki/Sim_(game) |
Sim Scanner is a feature of the Olympus FluoView FV1000 confocal laser scanning microscope . The system incorporates two laser scanners, one for confocal imaging and the other for simultaneous stimulation. They can be illuminated separately and independently, making it possible to stimulate the specimen during observation. As a result, the rapid cell reactions that occur right after laser stimulation can be captured, making the Sim Scanner suitable for such applications as Fluorescence recovery after photobleaching (FRAP), Fluorescence loss in photobleaching (FLIP), photoactivation and photoconversion.
Sim Scanner in Nature Methods | https://en.wikipedia.org/wiki/Sim_scanner |
SIMATIC is a series of programmable logic controller and automation systems, developed by Siemens . Introduced in 1958, the series has gone through four major generations, the latest being the SIMATIC S7 generation. The series is intended for industrial automation and production.
The name SIMATIC is a registered trademark of Siemens. It is a portmanteau of " Si emens" and "Auto matic ".
As with other programmable logic controllers ,
SIMATIC devices are intended to separate the control of a machine from the machine's direct operation,
in a more lightweight and versatile manner than controls hard-wired for a specific
machine. Early SIMATIC devices were transistor-based, intended to replace relays attached and customized to a specific machine. Microprocessors were introduced in 1973, allowing programs
similar to those on general-purpose digital computers to be stored and used for machine control. [ 1 ] SIMATIC devices have input and output modules to connect with controlled machines. The programs on the SIMATIC devices respond in real time to inputs from sensors on the controlled machines, and send output signals to actuators on the machines that direct their subsequent operation.
Depending on the device and its connection modules, signals may be a simple binary value ("high" or "low") or more complex. More complex inputs, outputs, and calculations were also supported as the SIMATIC line developed. For example, the SIMATIC 505 could handle floating point quantities and trigonometric functions. [ 2 ]
Siemens has developed four product lines to date:
The S5 line was sold in 90U, 95U, 101U, 100U, 105, 110, 115,115U, 135U, and 155U chassis styles. Within each chassis style, several CPUs were available, with varying speed, memory, and capabilities. Some systems provided redundant CPU operation for ultra-high-reliability control, as used in pharmaceutical manufacturing , for example.
Each chassis consisted of a power supply , and a backplane with slots for the addition of various option boards. Available options included serial and Ethernet communications, digital input and output cards, analog signal processing boards, counter cards, and other specialized interface and function modules.
The first entries in the S7 line were released in 1994, available under three performance classes: S7-200, S7-300 and S7-400. The introduction of SIMATIC S7 saw also the release of a new fieldbus standard Profibus , and the pioneer use of industrial Ethernet to facilitate communication between automation devices. The great success of the S7-300 CPU family in particular helped to cement the role of Siemens as one of the global leaders in automation technology. These series are expected to be phased out in 2033. [ 3 ]
The first generation of S7 CPUs were later succeeded by the S7-1200 and S7-1500, released in 2012. [ 4 ] These models came with standard Profinet interface.
Programs running on SIMATIC devices run in software environments created by Siemens. The environment varies by product line:
The S5 product line was usually programmed with a PC based software programming tool called STEP 5 . STEP 5 was used for programming, testing, and commissioning, and for documentation of programs for S5 PLCs.
The original STEP 5 versions ran on the CP/M operating system . Later versions ran on MS-DOS , and then versions of Windows through Windows XP . The final version of STEP 5 was version 7.2 (upgradable to version 7.23 Hotfix 1 with patches).
In addition to STEP 5, Siemens offered a proprietary State logic programming package called Graph5. Graph5 is a sequential programming language intended for use on machines that normally run through a series of discrete steps. It simulates a State machine on the S5 platform.
Several third-party programming environments were released for the S5. Most closely emulated STEP 5, some adding macros and other minor enhancements, others functioning drastically differently from STEP 5. One allowed STEP 5 programs to be cross-compiled to and from the C programming language and BASIC .
STEP 5 allowed the creation of structured or unstructured programming, from simple AND/OR operations up to complex subroutines. A STEP 5 program may, therefore, contain thousands of statements.
To maintain maximum transparency, STEP 5 offers a number of structuring facilities:
STEP 5 programs can be represented in three different ways:
Absolute or symbolic designations can be used for operands with all three methods of representation.
In LAD and FBD complex functions and function block calls can be entered via function keys . They are displayed on the screen as graphical symbols.
There are several program editors, from either genuine Siemens, or from other suppliers. After Siemens discontinued support, other suppliers started to develop new STEP 5 version which can run on Windows XP, or Windows 7.
Five types of blocks are available:
Some S5 PLCs also have block types FX (Extended Function Blocks), and DX(Extended Data Blocks); these are not distinct block types, but rather are another set of available blocks due to the CPU having more memory and addressing space.
STEP 5 differentiates between three types of operations:
The Stuxnet computer worm specifically targets SIMATIC S7 PLCs via its STEP 7 programming environment. | https://en.wikipedia.org/wiki/Simatic |
SimBioSys (short for Simulated Biological Systems) is a technology company deploying a combination of artificial intelligence and biophysical simulations to improve the personalized and patient-specific understanding of cancer.
SimBioSys developed a simulation engine, TumorScope, [ 1 ] which utilizes current standard of care diagnostic data (imaging & pathology) to create spatially resolved virtual replicas of an individual tumor and microenvironment and uses mechanistic models to incorporate the major hallmarks of cancer including drug sensitivity & delivery, metabolism, mechanical forces. The simulations enable precise & comprehensive predictions of response to therapy while providing researchers and clinicians keys insights into mechanisms of resistance. By virtualizing cancer, clinicians and patients are empowered with a better understanding of the disease and can assess all available options computationally to truly individualize treatment.
In the crowded world of genomics, new approaches have many barriers to becoming a new standard of care. SimBioSys complements and/or supersedes current precision medicine techniques while only relying on readily available and previously acquired datasets.
The first indication to market will be Early Stage Breast Cancer where there is significant opportunity to improve outcomes by selecting the right first line therapy while de-escalating care and lowering costs and side effects.
A retrospective study across 800 patients demonstrated volumetric errors under 4%. A recent pivotal study at University of Chicago , TumorScope™ produced 91% sensitivity and 93% specificity rates of predicting complete response to the physician's choice of therapy at the time of diagnosis. SimBioSys collaborates with over 130 oncologists across the country representing 16 premier cancer centers such University of Chicago, University of North Carolina, OHSU, among others.
SimBioSys anticipates FDA clearance for its breast cancer surgical planning tool in late 2023 with an expansion to other solid tumors to follow. Validation to lung and prostate cancer is already underway. While awaiting FDA approval, SimBioSys is commercializing the technology for use in patient education and drug development . | https://en.wikipedia.org/wiki/Simbiosys |
Simeon Chituru Achinewhu (born 15 August, 1946) [ 1 ] [ 2 ] is a Nigerian food and nutrition biochemist, scholar and university administrator who served as the past president-general of Ogbakor Ikwerre Socio-cultural Organisation Worldwide. [ 3 ] He was vice–chancellor of River State University (formerly Rivers State University of Science and Technology), from October 2000 until May 2007. In 2005 he was named the most research active vice-chancellor in the Nigerian university system.
Born on 15 August 1946 in Ikwerre Local Government Area, Rivers State , Nigeria, Achinewhu had his primary education in his home town Aluu. He finished from County Grammar School, Ikwerre/Etche in 1963 with Grade One. He later proceeded to Government Secondary School, Owerri and got his Higher School Certificate in physics, chemistry, and zoology in 1965. In 1970, Achinewhu graduated from the University of Ibadan , B.Sc. second class honors, M.Sc. in 1972 and Ph.D. 1975 in food science and technology from University of Reading , UK. [ 1 ]
Starting as lecturer at Rivers State University in food chemistry/biochemistry, food process technology, safety and fermentation, toxicology and nutrition in 1975, he has remained there to-date. He is also a researcher in Rivers State University, Port Harcourt (formerly Rivers State University of Science and Technology) and research is mostly centered on the composition and quality evaluation of Nigerian local foodstuff. [ 2 ]
As of 2021, Achinewhu serves as professor emeritus at the Rivers State University.
Prior to being appointed vice-chancellor of Rivers State University 2000, Achinewhu held the following positions:
In course of his research and scholastic endeavors, Achinewhu has visited many universities and has received a number of international as well as local awards.
In 2010 he was selected and worked as an expert in Europe-Africa Quality Connect: A collaborative project in five African universities between European Universities Association (EUA) and the Association of African Universities (AAU), sponsored by European Commission .
Achinewhu has analyzed more than fifty homegrown foodstuffs, which include seeds, nuts, tubers, spices, and herbs. These indigenous food items where examined and explored for their nutrient compositions and quality of protein content. Details of his findings are being used along with others in the compendium of Nigeria's food composition table. [ 4 ] [ 5 ]
He evolved the processing and production of coffee from coffee seed grown in Bayelsa State , Nigeria.
He did research on cassava processing, which identified upgrade cassava cultivars with superior quality food values with regards to product output and other physico-chemical properties. He identified new cultivars with high starch yield and therefore high export potentials. [ 6 ]
He developed a baby food (weaning) supplement employing the use of a combination of fermented plant food products. This was used to nourish children who were undernourished, in the days of Better Life Programme for Rural Women . [ 7 ]
Achinewhu married Eunice Achinewhu (nee Eunice Nyema Otto) in 1972 and they have four children. [ 1 ]
He is a reverend canon of the Church of Nigeria Anglican Communion . He is a crown of peace, justice of peace, and the national president of Peace Builders Association (Council of Ambassadors for Peace and Unification) | https://en.wikipedia.org/wiki/Simeon_Chituru_Achinewhu |
In Euclidean geometry , two objects are similar if they have the same shape , or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation , rotation and reflection . This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other.
For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other. This is because two ellipses can have different width to height ratios, two rectangles can have different length to breadth ratios, and two isosceles triangles can have different base angles.
If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure.
Two congruent shapes are similar, with a scale factor of 1. However, some school textbooks specifically exclude congruent triangles from their definition of similar triangles by insisting that the sizes must be different if the triangles are to qualify as similar. [ citation needed ]
Two triangles, △ ABC and △ A'B'C' are similar if and only if corresponding angles have the same measure: this implies that they are similar if and only if the lengths of corresponding sides are proportional . [ 1 ] It can be shown that two triangles having congruent angles ( equiangular triangles ) are similar, that is, the corresponding sides can be proved to be proportional. This is known as the AAA similarity theorem. [ 2 ] Note that the "AAA" is a mnemonic: each one of the three A's refers to an "angle". Due to this theorem, several authors simplify the definition of similar triangles to only require that the corresponding three angles are congruent. [ 3 ]
There are several criteria each of which is necessary and sufficient for two triangles to be similar:
A B ¯ A ′ B ′ ¯ = B C ¯ B ′ C ′ ¯ = A C ¯ A ′ C ′ ¯ . {\displaystyle {\frac {\overline {AB}}{\overline {A'B'}}}={\frac {\overline {BC}}{\overline {B'C'}}}={\frac {\overline {AC}}{\overline {A'C'}}}.}
A B ¯ A ′ B ′ ¯ = B C ¯ B ′ C ′ ¯ , ∠ A B C ≅ ∠ A ′ B ′ C ′ . {\displaystyle {\frac {\overline {AB}}{\overline {A'B'}}}={\frac {\overline {BC}}{\overline {B'C'}}},\quad \angle ABC\cong \angle A'B'C'.}
Symbolically, we write the similarity and dissimilarity of two triangles △ ABC and △ A'B'C' as follows: [ 8 ]
△ A B C ∼ △ A ′ B ′ C ′ △ A B C ≁ △ A ′ B ′ C ′ {\displaystyle {\begin{aligned}\triangle ABC&\sim \triangle A'B'C'\\\triangle ABC&\nsim \triangle A'B'C'\end{aligned}}}
There are several elementary results concerning similar triangles in Euclidean geometry: [ 9 ]
Given a triangle △ ABC and a line segment DE one can, with a ruler and compass , find a point F such that △ ABC ~ △ DEF . The statement that point F satisfying this condition exists is Wallis's postulate [ 11 ] and is logically equivalent to Euclid's parallel postulate . [ 12 ] In hyperbolic geometry (where Wallis's postulate is false) similar triangles are congruent.
In the axiomatic treatment of Euclidean geometry given by George David Birkhoff (see Birkhoff's axioms ) the SAS similarity criterion given above was used to replace both Euclid's parallel postulate and the SAS axiom which enabled the dramatic shortening of Hilbert's axioms . [ 7 ]
Similar triangles provide the basis for many synthetic (without the use of coordinates) proofs in Euclidean geometry. Among the elementary results that can be proved this way are: the angle bisector theorem , the geometric mean theorem , Ceva's theorem , Menelaus's theorem and the Pythagorean theorem . Similar triangles also provide the foundations for right triangle trigonometry . [ 13 ]
The concept of similarity extends to polygons with more than three sides. Given any two similar polygons, corresponding sides taken in the same sequence (even if clockwise for one polygon and counterclockwise for the other) are proportional and corresponding angles taken in the same sequence are equal in measure. However, proportionality of corresponding sides is not by itself sufficient to prove similarity for polygons beyond triangles (otherwise, for example, all rhombi would be similar). Likewise, equality of all angles in sequence is not sufficient to guarantee similarity (otherwise all rectangles would be similar). A sufficient condition for similarity of polygons is that corresponding sides and diagonals are proportional.
For given n , all regular n -gons are similar.
Several types of curves have the property that all examples of that type are similar to each other. These include:
A similarity (also called a similarity transformation or similitude ) of a Euclidean space is a bijection f from the space onto itself that multiplies all distances by the same positive real number r , so that for any two points x and y we have
where d ( x , y ) is the Euclidean distance from x to y . [ 16 ] The scalar r has many names in the literature including; the ratio of similarity , the stretching factor and the similarity coefficient . When r = 1 a similarity is called an isometry ( rigid transformation ). Two sets are called similar if one is the image of the other under a similarity.
As a map f : R n → R n , {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} ^{n},} a similarity of ratio r takes the form
where A ∈ O n ( R ) {\displaystyle A\in O^{n}(\mathbb {R} )} is an n × n orthogonal matrix and t ∈ R n {\displaystyle t\in \mathbb {R} ^{n}} is a translation vector.
Similarities preserve planes, lines, perpendicularity, parallelism, midpoints, inequalities between distances and line segments. [ 17 ] Similarities preserve angles but do not necessarily preserve orientation, direct similitudes preserve orientation and opposite similitudes change it. [ 18 ]
The similarities of Euclidean space form a group under the operation of composition called the similarities group S . [ 19 ] The direct similitudes form a normal subgroup of S and the Euclidean group E ( n ) of isometries also forms a normal subgroup. [ 20 ] The similarities group S is itself a subgroup of the affine group , so every similarity is an affine transformation .
One can view the Euclidean plane as the complex plane , [ b ] that is, as a 2-dimensional space over the reals . The 2D similarity transformations can then be expressed in terms of complex arithmetic and are given by
where a and b are complex numbers, a ≠ 0 . When | a |= 1 , these similarities are isometries.
The ratio between the areas of similar figures is equal to the square of the ratio of corresponding lengths of those figures (for example, when the side of a square or the radius of a circle is multiplied by three, its area is multiplied by nine — i.e. by three squared). The altitudes of similar triangles are in the same ratio as corresponding sides. If a triangle has a side of length b and an altitude drawn to that side of length h then a similar triangle with corresponding side of length kb will have an altitude drawn to that side of length kh . The area of the first triangle is A = 1 2 b h , {\displaystyle A={\tfrac {1}{2}}bh,} while the area of the similar triangle will be A ′ = 1 2 ⋅ k b ⋅ k h = k 2 A . {\displaystyle A'={\frac {1}{2}}\cdot kb\cdot kh=k^{2}A.} Similar figures which can be decomposed into similar triangles will have areas related in the same way. The relationship holds for figures that are not rectifiable as well.
The ratio between the volumes of similar figures is equal to the cube of the ratio of corresponding lengths of those figures (for example, when the edge of a cube or the radius of a sphere is multiplied by three, its volume is multiplied by 27 — i.e. by three cubed).
Galileo's square–cube law concerns similar solids. If the ratio of similitude (ratio of corresponding sides) between the solids is k , then the ratio of surface areas of the solids will be k 2 , while the ratio of volumes will be k 3 .
If a similarity has exactly one invariant point : a point that the similarity keeps unchanged, then this only point is called " center " of the similarity.
On the first image below the title, on the left, one or another similarity shrinks a regular polygon into a concentric one , the vertices of which are each on a side of the previous polygon. This rotational reduction is repeated , so the initial polygon is extended into an abyss of regular polygons. The center of the similarity is the common center of the successive polygons. A red segment joins a vertex of the initial polygon to its image under the similarity, followed by a red segment going to the following image of vertex, and so on to form a spiral . Actually we can see more than three direct similarities on this first image, because every regular polygon is invariant under certain direct similarities, more precisely certain rotations the center of which is the center of the polygon, and a composition of direct similarities is also a direct similarity. For example we see the image of the initial regular pentagon under a homothety of negative ratio −k , which is a similarity of ±180° angle and a positive ratio equal to k .
Below the title on the right, the second image shows a similarity decomposed into a rotation and a homothety. Similarity and rotation have the same angle of +135 degrees modulo 360 degrees . Similarity and homothety have the same ratio of 2 2 , {\displaystyle {\tfrac {\sqrt {2}}{2}},} multiplicative inverse of the ratio 2 {\displaystyle {\sqrt {2}}} ( square root of 2 ) of the inverse similarity. Point S is the common center of the three transformations: rotation, homothety and similarity. For example point W is the image of F under the rotation, and point T is the image of W under the homothety, more briefly T = H ( W ) = ( R ( F ) ) = ( H ∘ R ) ( F ) = D ( F ) , {\displaystyle T=H(W)=(R(F))=(H\circ R)(F)=D(F),} by naming R , H and D the previous rotation, homothety and similarity, with “ D " like "Direct".
This direct similarity that transforms triangle △ EFA into triangle △ ATB can be decomposed into a rotation and a homothety of same center S in several manners. For example, D = R ○ H = H ○ R , the last decomposition being only represented on the image. To get D we can also compose in any order a rotation of −45° angle and a homothety of ratio − 2 2 . {\displaystyle {\tfrac {-{\sqrt {2}}}{2}}.}
With " M " like "Mirror" and " I " like "Indirect", if M is the reflection with respect to line CW , then M ○ D = I is the indirect similarity that transforms segment BF like D into segment CT , but transforms point E into B and point A into A itself. Square ACBT is the image of ABEF under similarity I of ratio 1 2 . {\displaystyle {\tfrac {1}{\sqrt {2}}}.} Point A is the center of this similarity because any point K being invariant under it fulfills A K = A K 2 , {\displaystyle AK={\tfrac {AK}{\sqrt {2}}},} only possible if AK = 0 , otherwise written A = K .
How to construct the center S of direct similarity D from square ABEF , how to find point S center of a rotation of +135° angle that transforms ray S E → {\displaystyle {\overset {}{\overrightarrow {SE}}}} into ray S A → {\displaystyle {\overset {}{\overrightarrow {SA}}}} ? This is an inscribed angle problem plus a question of orientation . The set of points P such that P E → , P A → = + 135 ∘ {\displaystyle {\overset {}{{\overrightarrow {PE}},{\overrightarrow {PA}}=+135^{\circ }}}} is an arc of circle EA that joins E and A , of which the two radius leading to E and A form a central angle of 2(180° − 135°) = 2 × 45° = 90° . This set of points is the blue quarter of circle of center F inside square ABEF . In the same manner, point S is a member of the blue quarter of circle of center T inside square BCAT . So point S is the intersection point of these two quarters of circles.
In a general metric space ( X , d ) , an exact similitude is a function f from the metric space X into itself that multiplies all distances by the same positive scalar r , called f 's contraction factor, so that for any two points x and y we have
d ( f ( x ) , f ( y ) ) = r d ( x , y ) . {\displaystyle d(f(x),f(y))=rd(x,y).}
Weaker versions of similarity would for instance have f be a bi- Lipschitz function and the scalar r a limit
lim d ( f ( x ) , f ( y ) ) d ( x , y ) = r . {\displaystyle \lim {\frac {d(f(x),f(y))}{d(x,y)}}=r.}
This weaker version applies when the metric is an effective resistance on a topologically self-similar set.
A self-similar subset of a metric space ( X , d ) is a set K for which there exists a finite set of similitudes { f s } s ∈ S with contraction factors 0 ≤ r s < 1 such that K is the unique compact subset of X for which
⋃ s ∈ S f s ( K ) = K . {\displaystyle \bigcup _{s\in S}f_{s}(K)=K.}
These self-similar sets have a self-similar measure μ D with dimension D given by the formula
∑ s ∈ S ( r s ) D = 1 {\displaystyle \sum _{s\in S}(r_{s})^{D}=1}
which is often (but not always) equal to the set's Hausdorff dimension and packing dimension . If the overlaps between the f s ( K ) are "small", we have the following simple formula for the measure:
μ D ( f s 1 ∘ f s 2 ∘ ⋯ ∘ f s n ( K ) ) = ( r s 1 ⋅ r s 2 ⋯ r s n ) D . {\displaystyle \mu ^{D}(f_{s_{1}}\circ f_{s_{2}}\circ \cdots \circ f_{s_{n}}(K))=(r_{s_{1}}\cdot r_{s_{2}}\cdots r_{s_{n}})^{D}.\,}
In topology , a metric space can be constructed by defining a similarity instead of a distance . The similarity is a function such that its value is greater when two points are closer (contrary to the distance, which is a measure of dissimilarity : the closer the points, the lesser the distance).
The definition of the similarity can vary among authors, depending on which properties are desired. The basic common properties are
∀ ( a , b ) , S ( a , b ) ≥ 0 {\displaystyle \forall (a,b),S(a,b)\geq 0}
S ( a , b ) ≤ S ( a , a ) and ∀ ( a , b ) , S ( a , b ) = S ( a , a ) ⇔ a = b {\displaystyle S(a,b)\leq S(a,a)\quad {\text{and}}\quad \forall (a,b),S(a,b)=S(a,a)\Leftrightarrow a=b}
More properties can be invoked, such as:
The upper value is often set at 1 (creating a possibility for a probabilistic interpretation of the similitude).
Note that, in the topological sense used here, a similarity is a kind of measure . This usage is not the same as the similarity transformation of the § In Euclidean space and § In general metric spaces sections of this article.
Self-similarity means that a pattern is non-trivially similar to itself, e.g., the set {..., 0.5, 0.75, 1, 1.5, 2, 3, 4, 6, 8, 12, ...} of numbers of the form {2 i , 3·2 i } where i ranges over all integers. When this set is plotted on a logarithmic scale it has one-dimensional translational symmetry : adding or subtracting the logarithm of two to the logarithm of one of these numbers produces the logarithm of another of these numbers. In the given set of numbers themselves, this corresponds to a similarity transformation in which the numbers are multiplied or divided by two.
The intuition for the notion of geometric similarity already appears in human children, as can be seen in their drawings. [ 21 ] Certain perceptual categorization models in psychology are based on geometric similarity, assuming that learning involves the storage of specific instances ( i.e. of general object specifications) in memory. The categorization of another object ist subsequently based on the similarity of the object to the instances in memory. [ 22 ] | https://en.wikipedia.org/wiki/Similarity_(geometry) |
The similarity heuristic is a psychological heuristic pertaining to how people make judgments based on similarity . More specifically, the similarity heuristic is used to account for how people make judgments based on the similarity between current situations and other situations or prototypes of those situations.
At its most basic level, the similarity heuristic is an adaptive strategy . The goal of the similarity heuristic is maximizing productivity through favorable experience while not repeating unfavorable experiences. Decisions based on how favorable or unfavorable the present seems are based on how similar the past was to the current situation.
For example, a person may use the similarity heuristic when deciding on a book purchase. If a novel has a plot similar to that of novels read and enjoyed or the author has a writing style similar to that of favored authors, the purchasing decision will be positively influenced. A book with similar characteristics to previously pleasurable books is likely to also be enjoyed, causing the person to decide to obtain it.
The similarity heuristic directly emphasizes learning from past experience. For example, the similarity heuristic has been observed indirectly in experiments such as phonological similarity tests . These tests observe how well a person can distinguish similar sounds from dissimilar ones based on a comparison to previously heard sounds. While not involving a decision making process characteristic to heuristics in general, these studies show a reliance on past experience and comparison to the current experience. In addition, the similarity heuristic has become a valuable tool in the field of economics and consumerism.
The similarity heuristic is very easy to observe in the world of business, both from a marketing standpoint and from the position of the consumer. People tend to let past experience shape their world view; thus, if something presents itself as similar to a good experience had in the past, it is likely that the individual will partake in the current experience. The reverse holds true for situations that have proven unfavorable. A very basic example of this concept is a person deciding to get a meal at a particular restaurant because it reminds them of a similar establishment.
Companies often use the similarity heuristic as a marketing strategy. For example, companies will often advertise their services as something similar to a successful competitor, but better — such a concept is evident in the motion picture industry. Trailers for upcoming films will promote the latest movie as being made by a particular director, citing said director's past film credentials. In effect, a similarity heuristic is created in an audience's mind; creating a similarity between the coming attraction and past successes will likely make people decide to see the upcoming film.
Automotive parts companies and their distributors and dealers leverage similarity heuristics when they interchange the term, "OEM" (original equipment manufacturer), and "OE" (original equipment). For example, the OE design specifications may ask for a certain durability factor, corrosion resistance, and material composition. The OEM realizes they can produce the same part less expensively and with possibly greater profit, if they do not adhere to all or most of the OE design specifications. By marketing their product as "OEM" against a well-known brand or product (e.g., Mercedes-Benz), they predict that enough customers will purchase their OEM product vs. the OE product. The converse happens when the OE factory (e.g., Mercedes-Benz) promotes their brand of a commodity product (e.g., anti-freeze/coolant, spark plugs, etc.) as superior or better quality than the commodity product.
In addition, the use of a reverse similarity heuristic can be a highly valuable marketing tool. For example, when Nintendo wished to launch its Nintendo Entertainment System (NES) in the United States, it did so in the middle of a video game depression ; Atari had managed to make video games one of the least popular American pastimes. Initial showing of the NES were met poorly — clearly, a similarity heuristic was in place, and people had created biases against anything relating to interactive television gaming. Nintendo's goal, then, became the differentiation of their system from the past examples. Employing a dissimilarity heuristic, Nintendo managed to create enough of a gap from the former video game industry and market a successful product.
Job interviews often use similarity heuristic in identifying candidates suitable for the culture within the company. The Human Resource rounds of job interviews often focus on educational background and experiences of candidates that can qualify them for similarity or dissimilarity with the employees promoted within the company.
Similarity heuristic is sometimes used in legacy preferences to strengthen the candidacy of applicants in admissions of educational institutions. [ 1 ] It's argued, implicitly, that kids of alumni will often find themselves in the company of other similarly situated family friends, and hence be more likely to be successful themselves.
Some professions, such as software developers , regularly utilize the similarity heuristic. For software developers, the similarity heuristic is utilized when performing debugging tasks. A software bug exhibits a set of symptoms indicating the existence of a problem. In general, similar symptoms are caused by similar types of programming errors. By comparing these symptoms with those of previously corrected software flaws, a developer is able to determine the most probable cause and take an effective course of action. Over time, a developer’s past experiences will allow their use of the similarity heuristic to be highly effective, quickly choosing the debugging approach that will likely reveal the problem’s source.
Problem solving in general is benefited by the similarity heuristic. When new problems arise similar to previous problems, the similarity heuristic selects an approach that previously yielded favorable results. Even if the current problem is novel, any similarity to previous issues will help choose a proper course of action. | https://en.wikipedia.org/wiki/Similarity_heuristic |
A similarity system of triangles is a specific configuration involving a set of triangles. [ 1 ] A set of triangles is considered a configuration when all of the triangles share a minimum of one incidence relation with one of the other triangles present in the set. [ 1 ] An incidence relation between triangles refers to when two triangles share a point. For example, the two triangles to the right, A H C {\displaystyle AHC} and B H C {\displaystyle BHC} , are a configuration made up of two incident relations, since points C {\displaystyle C} and H {\displaystyle H} are shared. The triangles that make up configurations are known as component triangles. [ 1 ] Triangles must not only be a part of a configuration set to be in a similarity system, but must also be directly similar. [ 1 ] Direct similarity implies that all angles are equal between two given triangle and that they share the same rotational sense. [ 2 ] As is seen in the adjacent images, in the directly similar triangles, the rotation of B {\displaystyle B} onto C {\displaystyle C} and B 1 {\displaystyle B^{1}} onto C 1 {\displaystyle C^{1}} occurs in the same direction. In the opposite similar triangles, the rotation of B {\displaystyle B} onto C {\displaystyle C} and B 1 {\displaystyle B^{1}} onto C 1 {\displaystyle C^{1}} occurs in the opposite direction. In sum, a configuration is a similarity system when all triangles in the set, lie in the same plane and the following holds true: if there are n triangles in the set and n − 1 triangles are directly similar, then n triangles are directly similar. [ 1 ]
J.G. Mauldon introduced the idea of similarity systems of triangles in his paper in Mathematics Magazine "Similar Triangles". [ 1 ] Mauldon began his analyses by examining given triangles A B C , X Y Z {\displaystyle ABC,XYZ} for direct similarity through complex numbers, specifically the equation | a b c x y z 1 1 1 | = 0 {\displaystyle {\begin{vmatrix}a&b&c\\x&y&z\\1&1&1\end{vmatrix}}=0} . [ 1 ] He then furthered his analyses to equilateral triangles, showing that if a triangle A B C {\displaystyle ABC} satisfied the equation a + w b + w 2 c = 0 {\displaystyle a+wb+w^{2}c=0} when w = − 1 + i √ 3 2 {\displaystyle w={\frac {-1+i\surd 3}{2}}} , it was equilateral. [ 1 ] As evidence of this work, he applied his conjectures on direct similarity and equilateral triangles in proving Napoleon's theorem . [ 1 ] He then built off Napoleon by proving that if an equilateral triangle was constructed with equilateral triangles incident on each vertex, the midpoints of the connecting lines between the non-incident vertices of the outer three equilateral triangles create an equilateral triangle. [ 1 ] Other similar work was done by the French Geometer Thébault in his proof that given a parallelogram and squares that lie on each side of the parallelogram, the centers of the squares create a square. [ 3 ] Mauldon then analyzed coplanar sets of triangles, determining if they were similarity systems based on the criterion, if all but one of the triangles were directly similar, then all of the triangles are directly similar. [ 1 ]
If we construct a rectangle A B C D {\displaystyle ABCD} with directly similar triangles P A B , Q B C , R C D , S D A {\displaystyle PAB,QBC,RCD,SDA} on each side of the rectangle that are similar to P Q S {\displaystyle PQS} , then R Q S {\displaystyle RQS} is directly similar and the set of triangles { P A B , Q B C , R C D , S D A , P Q S , R Q S } {\displaystyle \{PAB,QBC,RCD,SDA,PQS,RQS\}} is a similarity system. [ 1 ]
However, if we acknowledge that the triangles can be degenerate and take points B {\displaystyle B} and P {\displaystyle P} to lie on each other and Q , R , D {\displaystyle Q,R,D} and S {\displaystyle S} to lie on each other, then the set of triangles is no longer a direct similarity system since the second triangle has area and the others do not. [ 1 ]
Given a figure where three sets of lines are parallel, but not equivalent in length (formally known as a rectangular parallelepiped ) with all points of order two being labelled as follows:
Then we can take the above points, analyze them as triangles and we can show that they form a similarity system. [ 1 ]
Proof:
In order for any given triangle, K L M {\displaystyle KLM} , to be directly similar to A 1 , B 1 , C 1 {\displaystyle A_{1},B_{1},C_{1}} the following equation should be satisfied:
If the same pattern is followed for the rest of the triangles, one will notice that the summation of the equations for the first four triangles and the summation of the equations for the last four triangles provides the same result. [ 1 ] Therefore, by the definition of a similarity system of triangles, no matter the seven similar triangles selected, the eighth will satisfy the system, making them all directly similar. [ 1 ] | https://en.wikipedia.org/wiki/Similarity_system_of_triangles |
Simjacker is a cellular software exploit for SIM cards discovered by AdaptiveMobile Security . [ 1 ] 29 countries are vulnerable according to ZDNet . [ 2 ] The vulnerability has been exploited primarily in Mexico, but also Colombia and Peru, according to the Wall Street Journal , [ 3 ] where it was used to track the location of mobile phone users without their knowledge.
The vulnerability was discovered and reported to the GSM Association through its coordinated vulnerability disclosure process by Cathal Mc Daid of AdaptiveMobile Security in 2019. [ 4 ] It was first reported publicly on 12 September 2019. [ 5 ] A technical paper and presentation was made available at the VirusBulletin conference on 3 October 2019. [ 6 ] [ 7 ]
The attack works by exploiting a vulnerability in a UICC /SIM card library called the S@T Browser. [ 8 ] A specially formatted binary text message is sent to the victim handset, which contains a set of commands to be executed by the S@T Browser environment in the UICC. As the S@T Browser environment has access to a subset of SIM Toolkit commands, the attackers used this vulnerability to instruct the UICC to request IMEI and location information from the handset via SIM Toolkit commands. Once this was obtained the UICC then instructs the handset to exfiltrate this information to the attackers within another text message. Other types of attacks are also possible using the S@T Browser, such as forcing a mobile device to open a webpage or to make a phone call. [ 9 ]
The attack differed from previously reported SIM card attacks as those required the SIM key to be obtained. [ 10 ] The Simjacker attack does not require a SIM key, only that the SIM card has the S@T Browser library installed on it, and that the binary messages containing the S@T Browser commands can be sent to the victim.
Simjacker was registered in the Common Vulnerabilities and Exposures database as CVE - 2019-16256 [ 11 ] and CVE - 2019-16257 , [ 12 ] and by the GSM Association in its Coordinated Vulnerability Disclosure process as CVD-2019-0026 [ 13 ]
The vulnerability was estimated to affect UICCs in at least 61 mobile operators in 29 countries, with estimates between a few hundred million to over a billion [ 14 ] SIM cards affected. The researcher reported that the most probable, conservative estimate is that mid to high hundreds of millions of SIM cards globally are affected. [ 15 ]
The vulnerability was being actively exploited primarily in Mexico, with thousands of mobile phone users being tracked by a surveillance company over the previous 2 years using this exploit. [ 16 ]
Mobile phone users can use a tool from SRLabs to see if their SIM card is vulnerable. [ 17 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Simjacker |
The Simmons–Smith reaction is an organic cheletropic reaction involving an organozinc carbenoid that reacts with an alkene (or alkyne ) to form a cyclopropane . [ 1 ] [ 2 ] [ 3 ] It is named after Howard Ensign Simmons, Jr. and Ronald D. Smith . It uses a methylene free radical intermediate that is delivered to both carbons of the alkene simultaneously, therefore the configuration of the double bond is preserved in the product and the reaction is stereospecific. [ 4 ]
Thus, cyclohexene , diiodomethane , and a zinc-copper couple (as iodomethylzinc iodide , ICH 2 ZnI ) yield norcarane (bicyclo[4.1.0]heptane). [ 5 ] [ 6 ]
The Simmons–Smith reaction is generally preferred over other methods of cyclopropanation, [ 7 ] however it can be expensive due to the high cost of diiodomethane. Modifications involving cheaper alternatives have been developed, such as dibromomethane [ 8 ] or diazomethane and zinc iodide . [ 9 ] The reactivity of the system can also be increased by using the Furukawa modification, exchanging the zinc‑copper couple for diethylzinc . [ 10 ]
The Simmons–Smith reaction is generally subject to steric effects , and thus cyclopropanation usually takes place on the less hindered face. [ 11 ] [ 12 ] [ verification needed ] However, when a hydroxy substituent is present in the substrate in proximity to the double bond, the zinc coordinates with the hydroxy substituent, directing cyclopropanation cis to the hydroxyl group (which may not correspond to cyclopropanation of the sterically most accessible face of the double bond): [ 13 ] An interactive 3D model of this reaction can be seen at ChemTube3D .
Although asymmetric cyclopropanation methods based on diazo compounds (the Metal-catalyzed cyclopropanations ) exist since 1966, the asymmetric Simmons–Smith reaction was introduced in 1992 [ 14 ] with a reaction of cinnamyl alcohol with diethylzinc , diiodomethane and a chiral disulfonamide in dichloromethane :
The hydroxyl group is a prerequisite serving as an anchor for zinc. An interactive 3D model of a similar reaction [ 15 ] can be seen here (java required). In another version of this reaction the ligand is based on salen and Lewis acid DIBAL is added: [ 16 ]
The Simmons–Smith reaction can be used to cyclopropanate simple alkenes without complications. Unfunctionalized achiral alkenes are best cyclopropanated with the Furukawa modification (see below), using Et 2 Zn and CH 2 I 2 in 1,2-dichloroethane . [ 17 ] Cyclopropanation of alkenes activated by electron donating groups proceed rapidly and easily. For example, enol ethers like trimethylsilyloxy -substituted olefins are often used because of the high yields obtained. [ 18 ]
Despite the electron-withdrawing nature of halides , many vinyl halides are also easily cyclopropanated, yielding fluoro-, bromo-, and iodo-substituted cyclopropanes. [ 19 ] [ 20 ]
The cyclopropanation of N -substituted alkenes is made complicated by N -alkylation as a competing pathway. This can be circumvented by adding a protecting group to nitrogen, however the addition of electron-withdrawing groups decreases the nucleophilicity of the alkene, lowering yield. The use of highly electrophilic reagents such as CHFI 2 , in place of CH 2 I 2 , has been shown to increase yield in these cases. [ 21 ]
Without the presence of a directing group on the olefin, very little chemoselectivity is observed. [ 22 ] However, an alkene which is significantly more nucleophilic than any others will be highly favored. For example, cyclopropanation occurs highly selectively at enol ethers . [ 23 ]
An important aspect of the Simmons–Smith reaction that contributes to its wide usage is its ability to be used in the presence of many functional groups. Among others, the haloalkylzinc-mediated reaction is compatible with alkynes , alcohols , ethers , aldehydes , ketones , carboxylic acids and derivatives, carbonates , sulfones , sulfonates , silanes , and stannanes . However, some side reactions are commonly observed.
Most side reactions occur due to the Lewis-acidity of the byproduct, ZnI 2 . In reactions that produce acid-sensitive products, excess Et 2 Zn can be added to scavenge the ZnI 2 that is formed, forming the less acidic EtZnI . The reaction can also be quenched with pyridine , which will scavenge ZnI 2 and excess reagents. [ 3 ]
Methylation of heteroatoms is also observed in the Simmons–Smith reaction due to the electrophilicity of the zinc carbenoids. For example, the use of excess reagent for long reaction times almost always leads to the methylation of alcohols. [ 24 ] Furthermore, Et 2 Zn and CH 2 I 2 react with allylic thioethers to generate sulfur ylides , which can subsequently undergo a 2,3-sigmatropic rearrangement , and will not cyclopropanate an alkene in the same molecule unless excess Simmons–Smith reagent is used. [ 25 ]
The Simmons–Smith reaction is rarely used in it original form and a number of modifications to both the zinc reagent and carbenoid precursor have been developed and are more commonly employed.
The Furukawa modification involves the replacement of the zinc-copper couple with dialkyl zinc, the most active of which was found to be Et 2 Zn . The modification was proposed in 1968 as a way to turn cationically polymerizable olefins such as vinyl ethers into their respective cyclopropanes. [ 26 ] It has also been found to be especially useful for the cyclopropanation of carbohydrates, being far more reproducible than other methods. [ 27 ] Like the unmodified reaction, the Furukawa-modified reaction is stereospecific , and is often much faster than the unmodified reaction. However, the Et 2 Zn reagent is pyrophoric , and as such must be handled with care. [ 28 ]
The Charette modification replaces the CH 2 I 2 normally found in the Simmons–Smith reaction with aryldiazo compounds, such as phenyldiazomethane , in Pathway A. [ 29 ] Upon treatment with stoichiometric amounts of zinc halide, an organozinc compound similar to the carbenoid discussed above is produced. This can react with almost all alkenes and alkynes, including styrenes and alcohols. This is especially useful, as the unmodified Simmons-Smith is known to deprotonate alcohols. Unfortunately, as in Pathway B shown the intermediate can also react with the starting diazo compound, giving cis - or trans - 1,2-diphenylethene. Additionally, the intermediate can react with alcohols to produce iodophenylmethane, which can further undergo an S N 2 reaction to produce ROCHPh , as in Pathway C.
The highly electrophilic nature of the zinc carbenoid reduces the useful scope of the Simmons-Smith cyclopropanation to electron-rich alkenes and those bearing pendant coordinating groups, most commonly alcohols. In 1998, the Shi group identified a novel zinc carbenoid formed from diethylzinc, trifluoroacetic acid and diiodomethane of the form CF 3 CO 2 ZnCH 2 I . [ 30 ] This zinc carbenoid is far more nucleophilic and allows for reaction with unfunctionalized and electron-deficient alkenes, like vinyl boronates . [ 31 ] A number of acidic modifiers have a similar effect, but trifluoroacetic acid is the most commonly used. The Shi modification of the cyclopropanation is also stereospecific . Further exploration of amino acids led to the development of an asymmetric variant of this cyclopropanation. [ 32 ]
Although not commonly used, Simmons-Smith reagents that display similar reactive properties to those of zinc have been prepared from aluminum and samarium compounds in the presence of CH 2 IX . [ 33 ] With the use of these reagents, allylic alcohols and isolated olefins can be selectively cyclopropanated in the presence of each other. Iodo- or chloro- methylsamarium iodide in THF is an excellent reagent to selectively cyclopropanate the allylic alcohol, presumably directed by chelation to the hydroxyl group. [ 34 ] In contrast, use of dialkyl(iodomethyl)aluminum reagents in CH 2 Cl 2 will selectively cyclopropanate the isolated olefin. [ 35 ] The specificity of these reagents allow cyclopropanes to be placed in poly-unsaturated systems that zinc-based reagents will cyclopropanate fully and unselectively. For example, i -Bu 3 Al will cyclopropanate geraniol at the 6 position, while Sm/Hg, will cyclopropanate at the 2 position, as shown below.
However, both reactions require near stoichiometric amounts of the starting metal compound, and Sm/Hg must be activated with the highly toxic HgCl 2 .
Most modern applications of the Simmons–Smith reaction use the Furukawa modification. Especially relevant and reliable applications are listed below.
A Furukawa-modified Simmons-Smith generated cyclopropane intermediate is formed in the synthesis of γ-keto esters from β-keto esters. The Simmons-Smith reagent binds first to the carbonyl group and subsequently to the α- carbon of the pseudo- enol that the first reaction forms. This second reagent forms the cyclopropyl intermediate which rapidly fragments into the product. [ 36 ] [ 37 ]
A Furukawa-modified Simmons–Smith reaction cyclopropanates both double bonds in an allenamide to form amido-spiro [2.2] cyclopentanes , featuring two cyclopropyl rings which share one carbon. The product of monocyclopropanation is also formed. [ 38 ] [ 39 ]
Cyclopropanation reactions in natural products synthesis have been reviewed. [ 40 ] The β-lactamase inhibitor Cilastatin provides an instructive example of Simmons-Smith reactivity in natural products synthesis. An allyl substituent on the starting material is Simmons-Smith cyclopropanated, and the carboxylic acid is subsequently deprotected via ozonolysis to form the precursor .
The Simmons–Smith reaction is used in the syntheses of GSK1360707F , [ 41 ] ropanicant [ 42 ] and Onglyza (Saxagliptan). [ 43 ] | https://en.wikipedia.org/wiki/Simmons–Smith_reaction |
Simon's reagent is used as a simple spot-test to presumptively identify alkaloids as well as other compounds. It reacts with secondary amines like MDMA and methamphetamine to give a blue solution.
The primary use of this reagent is for detecting secondary amines, such as MDMA and methamphetamine , and is typically used after the mecke or marquis reagents to differentiate between the two mentioned and amphetamine or MDA . [ 1 ]
The reagent is typically provided in two parts: [ 2 ] [ 1 ] [ 3 ]
Separate storage of the aldehyde and base are necessary to prevent aldol polymerisation of the aldehyde.
When exposed to an amine, reaction with acetaldehyde produces the enamine , which subsequently reacts with sodium nitroprusside to the imine . Finally, the iminium salt is hydrolysed to the bright blue [ 1 ] Simon-Awe complex. [ 3 ] [ 5 ]
Acetaldehyde can be replaced with acetone , in which case the reagent detects primary amines instead, giving a purple coloured product. [ 3 ]
A drop from each solution (A and B) is dripped onto the substance being tested, causing the two solutions to mix together. | https://en.wikipedia.org/wiki/Simon's_reagent |
Simon Cornelis Johannes Olivier (Amsterdam, June 13, 1879 – Wageningen, August 9, 1961) [ 1 ] was a Dutch chemist. [ 2 ] He was professor at the Wageningen Agricultural College (predecessor of what is currently Wageningen University [ 3 ] ) from 1919 to 1949. During the Second World War he was imprisoned for almost two years for his resistance against the German occupier. [ 4 ]
Olivier studied chemistry at the Delft University of Technology. [ 2 ] He received his doctorate in 1913 cum laude (“with high distinction”) as a doctor of technical science for his study of “Velocity measurements in the reaction of Friedel and Crafts” [translated from Dutch]. [ 5 ] He subsequently worked as an assistant at the National Agricultural Research Station in Groningen, and as a physics and chemistry teacher at the HBS in Nijmegen. [ 6 ] Subsequently, he got a job at the Wageningen Agricultural College. [ 3 ] [ failed verification ] In 1918 he was appointed professor of Organic Chemistry, the first professor of the current Laboratory of Organic Chemistry [ 7 ] . [ failed verification ] Olivier's publications also attracted attention abroad, especially in the field of organic chemistry. [ 8 ]
Olivier was concerned about Nazism well before the German invasion of the Netherlands. Already in 1936 he became a member of the Committee of Vigilance of Anti-National Socialist Intellectuals. He also advocated admission of Jewish refugees from Nazi Germany. [ 9 ]
Olivier was one of the few employees of the Wageningen Agricultural College who objected when they were asked to hand in an Aryan declaration in 1940. According to him, the statement was "the introduction of discrimination against Jews in the Netherlands". When he was informed that this could give him terrorist status, he crossed out the form and completed a new questionnaire. Nevertheless, Olivier continued to speak out against National Socialist ideas. [ 3 ] [ failed verification ]
After members of the National Socialist Movement (in Dutch: NSB) –a Dutch fascist movement that affiliated with the Nazis– had plastered Wageningen on July 18, 1941 with notes from the German V-action (the taking over of 'V=Victory' by the Germans “because Germany is winning on all fronts”) and especially the main building of the Wageningen Agricultural College, Olivier ordered a worker to remove everything. A few days later he was taken into custody. [ 2 ] After 11 months in prison in Amersfoort, where, as he put it, “he became more closely acquainted with the methods the Germans use to bring opponents to reason”, he was dismissed from his academic position and expelled from Wageningen. He was initially locked up in the infamous Oranjehotel in Scheveningen, and subsequently imprisoned in various German concentration camps until 1943, when he was released due to his poor health. [ 2 ] However, Olivier was banned from publishing and was no longer allowed to appear in university cities. [ 2 ] [ 4 ]
After the war, Olivier was appointed Rector Magnificus of the Wageningen Agricultural College for the year 1945-1946. [ 4 ] He had previously been rector in Wageningen in the academic year 1923-1924. Olivier retired in 1949. [ 4 ] | https://en.wikipedia.org/wiki/Simon_Olivier |
In mathematics, the Simon problems (or Simon's problems ) are a series of fifteen questions posed in the year 2000 by Barry Simon , an American mathematical physicist. [ 1 ] [ 2 ] Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert , the Simon problems concern quantum operators . [ 3 ] Eight of the problems pertain to anomalous spectral behavior of Schrödinger operators, and five concern operators that incorporate the Coulomb potential . [ 1 ] [ 4 ]
In 2014, Artur Avila won a Fields Medal for work including the solution of three Simon problems. [ 5 ] [ 6 ] Among these was the problem of proving that the set of energy levels of one particular abstract quantum system was, in fact, the Cantor set , a challenge known as the "Ten Martini Problem" after the reward that Mark Kac offered for solving it. [ 6 ] [ 7 ]
The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984. [ 8 ] [ 9 ]
Background definitions for the "Coulomb energies" problems ( N {\displaystyle N} non-relativistic particles (electrons) in R 3 {\displaystyle \mathbb {R} ^{3}} with spin 1 / 2 {\displaystyle 1/2} and an infinitely heavy nucleus with charge Z {\displaystyle Z} and Coulombic mutual interaction):
Simon listed the following problems in 1984: [ 8 ]
In 1991, Gerver showed that 3n-body problems in the plane for some sufficiently large value of n also undergo non-collisional singularities. [ 13 ]
Sinai once proved that the hard sphere gas is ergodic, but no complete proof has appeared except for the case of two particles, and a sketch for three, four, and five particles. [ 8 ]
In 2000, Simon claimed that five [ which? ] of the problems he listed had been solved. [ 1 ]
The Simon problems as listed in 2000 (with original categorizations), are: [ 1 ] [ 14 ]
Solved entirely by Kiselev (2005). [ 14 ] [ 17 ] [ 18 ] | https://en.wikipedia.org/wiki/Simon_problems |
Simonellite (1,1-dimethyl-1,2,3,4-tetrahydro-7-isopropyl phenanthrene) is a polycyclic aromatic hydrocarbon with a chemical formula C 19 H 24 . It is similar to retene .
Simonellite occurs naturally as an organic mineral derived from diterpenes present in conifer resins . [ 1 ] It is named after its discoverer, Vittorio Simonelli (1860–1929), an Italian geologist . It forms colorless to white orthorhombic crystals. [ 2 ] It occurs in Fognano, Tuscany , Italy.
Simonellite, together with cadalene , retene and ip-iHMN , is a biomarker of higher plants , which makes it useful for paleobotanic analysis of rock sediments . [ citation needed ]
This article about a specific mineral or mineraloid is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Simonellite |
In geometry and geometric measure theory , the Simons cone refers to a specific minimal hypersurface in R 8 {\displaystyle \mathbb {R} ^{8}} that plays a crucial role in resolving Bernstein's problem in higher dimensions. It is named after American mathematician Jim Simons .
The Simons cone is defined as the hypersurface given by the equation
This 7-dimensional cone has the distinctive property that its mean curvature vanishes at every point except at the origin, where the cone has a singularity . [ 1 ] [ 2 ]
The classical Bernstein theorem states that any minimal graph in R 3 {\displaystyle \mathbb {R} ^{3}} must be a plane. This was extended to R 4 {\displaystyle \mathbb {R} ^{4}} by Wendell Fleming in 1962 and Ennio De Giorgi in 1965, and to dimensions up to R 5 {\displaystyle \mathbb {R} ^{5}} by Frederick J. Almgren Jr. in 1966 and to R 8 {\displaystyle \mathbb {R} ^{8}} by Jim Simons in 1968. The existence of the Simons cone as a minimizing cone in R 8 {\displaystyle \mathbb {R} ^{8}} demonstrated that the Bernstein theorem could not be extended to R 9 {\displaystyle \mathbb {R} ^{9}} and higher dimensions. Bombieri, De Giorgi, and Enrico Giusti proved in 1969 that the Simons cone is indeed area-minimizing, thus providing a negative answer to the Bernstein problem in higher dimensions. [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Simons_cone |
The Simon–Glatzel equation [ 1 ] is an empirical correlation describing the pressure dependence of the melting temperature of a solid . The pressure dependence of the melting temperature is small for small pressure changes because the volume change during fusion or melting is rather small. However, at very high pressures higher melting temperatures are generally observed as the liquid usually occupies a larger volume than the solid making melting more thermodynamically unfavorable at elevated pressure. If the liquid has a smaller volume than the solid (as for ice and liquid water) a higher pressure leads to a lower melting point.
T ref {\displaystyle T_{\text{ref}}} and P ref {\displaystyle P_{\text{ref}}} are normally the temperature and the pressure of the triple point , but the normal melting temperature at atmospheric pressure are also commonly used as reference point because the normal melting point is much more easily accessible. Typically P ref {\displaystyle P_{\text{ref}}} is then set to 0. a {\displaystyle a} and b {\displaystyle b} are component-specific parameters.
The Simon–Glatzel equation can be viewed as a combination of the Murnaghan equation of state and the Lindemann law, [ 2 ] and an alternative form was proposed by J. J. Gilvarry (1956): [ 3 ]
T m = T ref ( K 0 ′ P − P ref K 0 + 1 ) 2 ( γ − 1 ) 3 + f {\displaystyle T_{m}=T_{\text{ref}}\left(K_{0}^{'}{\frac {P-P_{\text{ref}}}{K_{0}}}+1\right)^{\frac {2(\gamma -1)}{3+f}}}
where K 0 {\displaystyle K_{0}} is general K {\displaystyle K} at P = 0 {\displaystyle P=0} , K 0 ′ {\displaystyle K_{0}^{'}} is pressure derivative K {\displaystyle K} at P = 0 {\displaystyle P=0} , γ {\displaystyle \gamma } is Grüneisen ratio, and f {\displaystyle f} is the coefficient in Morse potential .
For methanol the following parameters [ 4 ] can be obtained:
The reference temperature has been T ref = 174.61 K and the reference pressure P ref has been set to 0 kPa.
Methanol is a component where the Simon–Glatzel works well in the given validity range.
The Simon–Glatzel equation is a monotonically increasing function. It can only describe the melting curves that rise indefinitely with increasing pressure. It may fail to describe the melting curves with a negative pressure dependence or local maximums. A damping term that asymptotically slopes down under pressure, D ( P ) = exp [ − c ( P − P ref ) ] {\displaystyle D(P)=\exp[-c(P-P_{\text{ref}})]} ( c is another component-specific parameter), is introduced by Vladimir V. Kechin to extend the Simon–Glatzel equation [ 5 ] so that all melting curves, rising, falling, and flattening, as well as curves with a maximum, can be described by a unified equation:
T m = F ( P ) ⋅ D ( P ) {\displaystyle T_{m}=F(P)\cdot D(P)}
where F ( P ) {\displaystyle F(P)} is the Simon–Glatzel equation (rising) and D ( P ) {\displaystyle D(P)} is the damping term (falling or flattening).
The unified equation may be rewritten as:
T m = T ref ( P − P ref a + 1 ) b ⋅ exp [ − c ( P − P ref ) ] {\displaystyle T_{m}=T_{\text{ref}}\left({\frac {P-P_{\text{ref}}}{a}}+1\right)^{b}\cdot \exp[-c(P-P_{\text{ref}})]}
This form predicts that all solids have a maximum melting temperature at a positive or (fictitious) negative pressure. | https://en.wikipedia.org/wiki/Simon–Glatzel_equation |
In mathematics , the term simple is used to describe an algebraic structure which in some sense cannot be divided by a smaller structure of the same type. Put another way, an algebraic structure is simple if the kernel of every homomorphism is either the whole structure or a single element. Some examples are:
The general pattern is that the structure admits no non-trivial congruence relations .
The term is used differently in semigroup theory. A semigroup is said to be simple if it has no nontrivial ideals , or equivalently, if Green's relation J is
the universal relation. Not every congruence on a semigroup is associated with an ideal, so a simple semigroup may
have nontrivial congruences. A semigroup with no nontrivial congruences is called congruence simple . | https://en.wikipedia.org/wiki/Simple_(abstract_algebra) |
Simple Modular Architecture Research Tool ( SMART ) is a biological database that is used in the identification and analysis of protein domains within protein sequences. [ 1 ] [ 2 ] SMART uses profile-hidden Markov models built from multiple sequence alignments to detect protein domains in protein sequences. The most recent release of SMART contains 1,204 domain models. [ 3 ] Data from SMART was used in creating the Conserved Domain Database collection and is also distributed as part of the InterPro database. [ 4 ] The database is hosted by the European Molecular Biology Laboratory in Heidelberg.
This database -related article is a stub . You can help Wikipedia by expanding it .
This bioinformatics-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Simple_Modular_Architecture_Research_Tool |
A simple or regular continued fraction is a continued fraction with numerators all equal one, and denominators built from a sequence { a i } {\displaystyle \{a_{i}\}} of integer numbers. The sequence can be finite or infinite, resulting in a finite (or terminated ) continued fraction like
or an infinite continued fraction like
Typically, such a continued fraction is obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In the finite case, the iteration/ recursion is stopped after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression . In either case, all integers in the sequence, other than the first, must be positive . The integers a i {\displaystyle a_{i}} are called the coefficients or terms of the continued fraction. [ 1 ]
Simple continued fractions have a number of remarkable properties related to the Euclidean algorithm for integers or real numbers . Every rational number p {\displaystyle p} / q {\displaystyle q} has two closely related expressions as a finite continued fraction, whose coefficients a i can be determined by applying the Euclidean algorithm to ( p , q ) {\displaystyle (p,q)} . The numerical value of an infinite continued fraction is irrational ; it is defined from its infinite sequence of integers as the limit of a sequence of values for finite continued fractions. Each finite continued fraction of the sequence is obtained by using a finite prefix of the infinite continued fraction's defining sequence of integers. Moreover, every irrational number α {\displaystyle \alpha } is the value of a unique infinite regular continued fraction, whose coefficients can be found using the non-terminating version of the Euclidean algorithm applied to the incommensurable values α {\displaystyle \alpha } and 1. This way of expressing real numbers (rational and irrational) is called their continued fraction representation .
Consider, for example, the rational number 415 / 93 , which is around 4.4624. As a first approximation , start with 4, which is the integer part ; 415 / 93 = 4 + 43 / 93 . The fractional part is the reciprocal of 93 / 43 which is about 2.1628. Use the integer part, 2, as an approximation for the reciprocal to obtain a second approximation of 4 + 1 / 2 = 4.5. Now, 93 / 43 = 2 + 7 / 43 ;
the remaining fractional part, 7 / 43 , is the reciprocal of 43 / 7 , and 43 / 7 is around 6.1429. Use 6 as an approximation for this to obtain 2 + 1 / 6 as an approximation for 93 / 43 and 4 + 1 / 2 + 1 / 6 , about 4.4615, as the third approximation. Further, 43 / 7 = 6 + 1 / 7 . Finally, the fractional part, 1 / 7 , is the reciprocal of 7, so its approximation in this scheme, 7, is exact ( 7 / 1 = 7 + 0 / 1 ) and produces the exact expression 4 + 1 2 + 1 6 + 1 7 {\displaystyle 4+{\cfrac {1}{2+{\cfrac {1}{6+{\cfrac {1}{7}}}}}}} for 415 / 93 .
That expression is called the continued fraction representation of 415 / 93 . This can be represented by the abbreviated notation 415 / 93 = [4; 2, 6, 7]. It is customary to place a semicolon after the first number to indicate that it is the whole part. Some older textbooks use all commas in the ( n + 1) -tuple, for example, [4, 2, 6, 7]. [ 2 ] [ 3 ]
If the starting number is rational, then this process exactly parallels the Euclidean algorithm applied to the numerator and denominator of the number. In particular, it must terminate and produce a finite continued fraction representation of the number. The sequence of integers that occur in this representation is the sequence of successive quotients computed by the Euclidean algorithm. If the starting number is irrational , then the process continues indefinitely. This produces a sequence of approximations, all of which are rational numbers, and these converge to the starting number as a limit. This is the (infinite) continued fraction representation of the number. Examples of continued fraction representations of irrational numbers are:
Continued fractions are, in some ways, more "mathematically natural" representations of a real number than other representations such as decimal representations , and they have several desirable properties:
A continued fraction in canonical form is an expression of the form
where a i are integer numbers, called the coefficients or terms of the continued fraction. [ 1 ]
When the expression contains finitely many terms, it is called a finite continued fraction.
When the expression contains infinitely many terms, it is called an infinite continued fraction. [ 5 ] When the terms eventually repeat from some point onwards, the continued fraction is called periodic . [ 4 ]
Thus, all of the following illustrate valid finite simple continued fractions:
For simple continued fractions of the form
the a n {\displaystyle a_{n}} term can be calculated from the following recursive sequence:
f n + 1 = 1 f n − ⌊ f n ⌋ {\displaystyle f_{n+1}={\frac {1}{f_{n}-\lfloor f_{n}\rfloor }}}
where f 0 = r {\displaystyle f_{0}=r} and a n = ⌊ f n ⌋ {\displaystyle a_{n}=\left\lfloor f_{n}\right\rfloor } .
from which it can be understood that the a n {\displaystyle a_{n}} sequence stops if f n = ⌊ f n ⌋ {\displaystyle f_{n}=\lfloor f_{n}\rfloor } is an integer.
Consider a continued fraction expressed as
Because such a continued fraction expression may take a significant amount of vertical space, a number of methods have been tried to shrink it.
Gottfried Leibniz sometimes used the notation [ 6 ]
and later the same idea was taken even further with the nested fraction bars drawn aligned, for example by Alfred Pringsheim as
or in more common related notations as [ 7 ]
or
Carl Friedrich Gauss used a notation reminiscent of summation notation ,
or in cases where the numerator is always 1, eliminated the fraction bars altogether, writing a list-style
Sometimes list-style notation uses angle brackets instead,
The semicolon in the square and angle bracket notations is sometimes replaced by a comma. [ 2 ] [ 3 ]
One may also define infinite simple continued fractions as limits :
This limit exists for any choice of a 0 {\displaystyle a_{0}} and positive integers a 1 , a 2 , … {\displaystyle a_{1},a_{2},\ldots } . [ 8 ] [ 9 ]
Consider a real number r {\displaystyle r} .
Let i = ⌊ r ⌋ {\displaystyle i=\lfloor r\rfloor } and let f = r − i {\displaystyle f=r-i} .
When f ≠ 0 {\displaystyle f\neq 0} , the continued fraction representation of r {\displaystyle r} is [ i ; a 1 , a 2 , … ] {\displaystyle [i;a_{1},a_{2},\ldots ]} , where [ a 1 ; a 2 , … ] {\displaystyle [a_{1};a_{2},\ldots ]} is the continued fraction representation of 1 / f {\displaystyle 1/f} . When r ≥ 0 {\displaystyle r\geq 0} , then i {\displaystyle i} is the integer part of r {\displaystyle r} , and f {\displaystyle f} is the fractional part of r {\displaystyle r} .
In order to calculate a continued fraction representation of a number r {\displaystyle r} , write down the floor of r {\displaystyle r} . Subtract this value from r {\displaystyle r} . If the difference is 0, stop; otherwise find the reciprocal of the difference and repeat. The procedure will halt if and only if r {\displaystyle r} is rational. This process can be efficiently implemented using the Euclidean algorithm when the number is rational.
The table below shows an implementation of this procedure for the number 3.245 = 649 / 200 {\displaystyle 3.245=649/200} :
The continued fraction for 3.245 {\displaystyle 3.245} is thus [ 3 ; 4 , 12 , 4 ] , {\displaystyle [3;4,12,4],} or, expanded:
649 200 = 3 + 1 4 + 1 12 + 1 4 . {\displaystyle {\frac {649}{200}}=3+{\cfrac {1}{4+{\cfrac {1}{12+{\cfrac {1}{4}}}}}}.}
The continued fraction representations of a positive rational number and its reciprocal are identical except for a shift one place left or right depending on whether the number is less than or greater than one respectively. In other words, the numbers represented by [ a 0 ; a 1 , a 2 , … , a n ] {\displaystyle [a_{0};a_{1},a_{2},\ldots ,a_{n}]} and [ 0 ; a 0 , a 1 , … , a n ] {\displaystyle [0;a_{0},a_{1},\ldots ,a_{n}]} are reciprocals.
For instance if a {\displaystyle a} is an integer and x < 1 {\displaystyle x<1} then
If x > 1 {\displaystyle x>1} then
The last number that generates the remainder of the continued fraction is the same for both x {\displaystyle x} and its reciprocal.
For example,
Every finite continued fraction represents a rational number , and every rational number can be represented in precisely two different ways as a finite continued fraction, with the conditions that the first coefficient is an integer and the other coefficients are positive integers. These two representations agree except in their final terms. In the longer representation the final term in the continued fraction is 1; the shorter representation drops the final 1, but increases the new final term by 1. The final element in the short representation is therefore always greater than 1, if present. In symbols:
Every infinite continued fraction is irrational , and every irrational number can be represented in precisely one way as an infinite continued fraction.
An infinite continued fraction representation for an irrational number is useful because its initial segments provide rational approximations to the number. These rational numbers are called the convergents of the continued fraction. [ 10 ] [ 11 ] The larger a term is in the continued fraction, the closer the corresponding convergent is to the irrational number being approximated. Numbers like π have occasional large terms in their continued fraction, which makes them easy to approximate with rational numbers. Other numbers like e have only small terms early in their continued fraction, which makes them more difficult to approximate rationally. The golden ratio φ has terms equal to 1 everywhere—the smallest values possible—which makes φ the most difficult number to approximate rationally. In this sense, therefore, it is the "most irrational" of all irrational numbers. Even-numbered convergents are smaller than the original number, while odd-numbered ones are larger.
For a continued fraction [ a 0 ; a 1 , a 2 , ...] , the first four convergents (numbered 0 through 3) are
The numerator of the third convergent is formed by multiplying the numerator of the second convergent by the third coefficient, and adding the numerator of the first convergent. The denominators are formed similarly. Therefore, each convergent can be expressed explicitly in terms of the continued fraction as the ratio of certain multivariate polynomials called continuants .
If successive convergents are found, with numerators h 1 , h 2 , ... and denominators k 1 , k 2 , ... then the relevant recursive relation is that of Gaussian brackets :
The successive convergents are given by the formula
Thus to incorporate a new term into a rational approximation, only the two previous convergents are necessary. The initial "convergents" (required for the first two terms) are 0 ⁄ 1 and 1 ⁄ 0 . For example, here are the convergents for [0;1,5,2,2].
When using the Babylonian method to generate successive approximations to the square root of an integer, if one starts with the lowest integer as first approximant, the rationals generated all appear in the list of convergents for the continued fraction. Specifically, the approximants will appear on the convergents list in positions 0, 1, 3, 7, 15, ... , 2 k −1 , ... For example, the continued fraction expansion for 3 {\displaystyle {\sqrt {3}}} is [1; 1, 2, 1, 2, 1, 2, 1, 2, ...] . Comparing the convergents with the approximants derived from the Babylonian method:
The Baire space is a topological space on infinite sequences of natural numbers. The infinite continued fraction provides a homeomorphism from the Baire space to the space of irrational real numbers (with the subspace topology inherited from the usual topology on the reals). The infinite continued fraction also provides a map between the quadratic irrationals and the dyadic rationals , and from other irrationals to the set of infinite strings of binary numbers (i.e. the Cantor set ); this map is called the Minkowski question-mark function . The mapping has interesting self-similar fractal properties; these are given by the modular group , which is the subgroup of Möbius transformations having integer values in the transform. Roughly speaking, continued fraction convergents can be taken to be Möbius transformations acting on the (hyperbolic) upper half-plane ; this is what leads to the fractal self-symmetry.
The limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1) is the Gauss–Kuzmin distribution .
If a 0 , {\displaystyle \ a_{0}\ ,} a 1 , {\displaystyle a_{1}\ ,} a 2 , {\displaystyle a_{2}\ ,} … {\displaystyle \ \ldots \ } is an infinite sequence of positive integers, define the sequences h n {\displaystyle \ h_{n}\ } and k n {\displaystyle \ k_{n}\ } recursively:
Theorem 1. For any positive real number x {\displaystyle \ x\ }
Theorem 2. The convergents of [ a 0 ; {\displaystyle \ [\ a_{0}\ ;} a 1 , {\displaystyle a_{1}\ ,} a 2 , {\displaystyle a_{2}\ ,} … ] {\displaystyle \ldots \ ]\ } are given by
or in matrix form, [ h n h n − 1 k n k n − 1 ] = [ a 0 1 1 0 ] ⋯ [ a n 1 1 0 ] {\displaystyle {\begin{bmatrix}h_{n}&h_{n-1}\\k_{n}&k_{n-1}\end{bmatrix}}={\begin{bmatrix}a_{0}&1\\1&0\end{bmatrix}}\cdots {\begin{bmatrix}a_{n}&1\\1&0\end{bmatrix}}}
Theorem 3. If the n {\displaystyle \ n} th convergent to a continued fraction is h n k n , {\displaystyle \ {\frac {h_{n}}{k_{n}}}\ ,} then
or equivalently
Corollary 1: Each convergent is in its lowest terms (for if h n {\displaystyle \ h_{n}\ } and k n {\displaystyle \ k_{n}\ } had a nontrivial common divisor it would divide k n h n − 1 − k n − 1 h n , {\displaystyle \ k_{n}\ h_{n-1}-k_{n-1}\ h_{n}\ ,} which is impossible).
Corollary 2: The difference between successive convergents is a fraction whose numerator is unity:
Corollary 3: The continued fraction is equivalent to a series of alternating terms:
Corollary 4: The matrix
has determinant ( − 1 ) n + 1 {\displaystyle (-1)^{n+1}} , and thus belongs to the group of 2 × 2 {\displaystyle \ 2\times 2\ } unimodular matrices G L ( 2 , Z ) . {\displaystyle \ \mathrm {GL} (2,\mathbb {Z} )~.}
Corollary 5: The matrix [ h n h n − 2 k n k n − 2 ] = [ h n − 1 h n − 2 k n − 1 k n − 2 ] [ a n 0 1 1 ] {\displaystyle {\begin{bmatrix}h_{n}&h_{n-2}\\k_{n}&k_{n-2}\end{bmatrix}}={\begin{bmatrix}h_{n-1}&h_{n-2}\\k_{n-1}&k_{n-2}\end{bmatrix}}{\begin{bmatrix}a_{n}&0\\1&1\end{bmatrix}}} has determinant ( − 1 ) n a n {\displaystyle (-1)^{n}a_{n}} , or equivalently, h n k n − h n − 2 k n − 2 = ( − 1 ) n k n − 2 k n a n {\displaystyle {\frac {h_{n}}{\ k_{n}\ }}-{\frac {h_{n-2}}{\ k_{n-2}\ }}={\frac {(-1)^{n}}{\ k_{n-2}\ k_{n}\ }}a_{n}} meaning that the odd terms monotonically decrease, while the even terms monotonically increase.
Corollary 6: The denominator sequence k 0 , k 1 , k 2 , … {\displaystyle k_{0},k_{1},k_{2},\dots } satisfies the recurrence relation k − 1 = 0 , k 0 = 1 , k n = k n − 1 a n + k n − 2 {\displaystyle k_{-1}=0,k_{0}=1,k_{n}=k_{n-1}a_{n}+k_{n-2}} , and grows at least as fast as the Fibonacci sequence , which itself grows like O ( ϕ n ) {\displaystyle O(\phi ^{n})} where ϕ = 1.618 … {\displaystyle \phi =1.618\dots } is the golden ratio .
Theorem 4. Each ( s {\displaystyle \ s} th) convergent is nearer to a subsequent ( n {\displaystyle \ n} th) convergent than any preceding ( r {\displaystyle \ r} th) convergent is. In symbols, if the n {\displaystyle \ n} th convergent is taken to be [ a 0 ; a 1 , … , a n ] = x n , {\displaystyle \ \left[\ a_{0};\ a_{1},\ \ldots ,\ a_{n}\ \right]=x_{n}\ ,} then
for all r < s < n . {\displaystyle \ r<s<n~.}
Corollary 1: The even convergents (before the n {\displaystyle \ n} th) continually increase, but are always less than x n . {\displaystyle \ x_{n}~.}
Corollary 2: The odd convergents (before the n {\displaystyle \ n} th) continually decrease, but are always greater than x n . {\displaystyle \ x_{n}~.}
Theorem 5.
Corollary 1: A convergent is nearer to the limit of the continued fraction than any fraction whose denominator is less than that of the convergent.
Corollary 2: A convergent obtained by terminating the continued fraction just before a large term is a close approximation to the limit of the continued fraction.
Theorem 6: Consider the set of all open intervals with end-points [ 0 ; a 1 , … , a n ] , [ 0 ; a 1 , … , a n + 1 ] {\displaystyle [0;a_{1},\dots ,a_{n}],[0;a_{1},\dots ,a_{n}+1]} . Denote it as C {\displaystyle {\mathcal {C}}} . Any open subset of [ 0 , 1 ] ∖ Q {\displaystyle [0,1]\setminus \mathbb {Q} } is a disjoint union of sets from C {\displaystyle {\mathcal {C}}} .
Corollary: The infinite continued fraction provides a homeomorphism from the Baire space to [ 0 , 1 ] ∖ Q {\displaystyle [0,1]\setminus \mathbb {Q} } .
If
are consecutive convergents, then any fractions of the form
where m {\displaystyle m} is an integer such that 0 ≤ m ≤ a n + 1 {\displaystyle 0\leq m\leq a_{n+1}} , are called semiconvergents , secondary convergents , or intermediate fractions . The ( m + 1 ) {\displaystyle (m+1)} -st semiconvergent equals the mediant of the m {\displaystyle m} -th one and the convergent h n k n {\displaystyle {\tfrac {h_{n}}{k_{n}}}} . Sometimes the term is taken to mean that being a semiconvergent excludes the possibility of being a convergent (i.e., 0 < m < a n + 1 {\displaystyle 0<m<a_{n+1}} ), rather than that a convergent is a kind of semiconvergent.
It follows that semiconvergents represent a monotonic sequence of fractions between the convergents h n − 1 k n − 1 {\displaystyle {\tfrac {h_{n-1}}{k_{n-1}}}} (corresponding to m = 0 {\displaystyle m=0} ) and h n + 1 k n + 1 {\displaystyle {\tfrac {h_{n+1}}{k_{n+1}}}} (corresponding to m = a n + 1 {\displaystyle m=a_{n+1}} ). The consecutive semiconvergents a b {\displaystyle {\tfrac {a}{b}}} and c d {\displaystyle {\tfrac {c}{d}}} satisfy the property a d − b c = ± 1 {\displaystyle ad-bc=\pm 1} .
If a rational approximation p q {\displaystyle {\tfrac {p}{q}}} to a real number x {\displaystyle x} is such that the value | x − p q | {\displaystyle \left|x-{\tfrac {p}{q}}\right|} is smaller than that of any approximation with a smaller denominator, then p q {\displaystyle {\tfrac {p}{q}}} is a semiconvergent of the continued fraction expansion of x {\displaystyle x} . The converse is not true, however.
One can choose to define a best rational approximation to a real number x as a rational number n / d , d > 0 , that is closer to x than any approximation with a smaller or equal denominator. The simple continued fraction for x can be used to generate all of the best rational approximations for x by applying these three rules:
For example, 0.84375 has continued fraction [0;1,5,2,2]. Here are all of its best rational approximations.
The strictly monotonic increase in the denominators as additional terms are included permits an algorithm to impose a limit, either on size of denominator or closeness of approximation.
The "half rule" mentioned above requires that when a k is even, the halved term a k /2 is admissible if and only if | x − [ a 0 ; a 1 , ..., a k − 1 ]| > | x − [ a 0 ; a 1 , ..., a k − 1 , a k /2]| . [ 12 ] This is equivalent to: [ 13 ]
The convergents to x are "best approximations" in a much stronger sense than the one defined above. Namely, n / d is a convergent for x if and only if | dx − n | has the smallest value among the analogous expressions for all rational approximations m / c with c ≤ d ; that is, we have | dx − n | < | cx − m | so long as c < d . (Note also that | d k x − n k | → 0 as k → ∞ .)
A rational that falls within the interval ( x , y ) , for 0 < x < y , can be found with the continued fractions for x and y . When both x and y are irrational and
where x and y have identical continued fraction expansions up through a k −1 , a rational that falls within the interval ( x , y ) is given by the finite continued fraction,
This rational will be best in the sense that no other rational in ( x , y ) will have a smaller numerator or a smaller denominator. [ 14 ] [ 15 ]
If x is rational, it will have two continued fraction representations that are finite , x 1 and x 2 , and similarly a rational y will have two representations, y 1 and y 2 . The coefficients beyond the last in any of these representations should be interpreted as +∞ ; and the best rational will be one of z ( x 1 , y 1 ) , z ( x 1 , y 2 ) , z ( x 2 , y 1 ) , or z ( x 2 , y 2 ) .
For example, the decimal representation 3.1416 could be rounded from any number in the interval [3.14155, 3.14165) . The continued fraction representations of 3.14155 and 3.14165 are
and the best rational between these two is
Thus, 355 / 113 is the best rational number corresponding to the rounded decimal number 3.1416, in the sense that no other rational number that would be rounded to 3.1416 will have a smaller numerator or a smaller denominator.
A rational number, which can be expressed as finite continued fraction in two ways,
will be one of the convergents for the continued fraction expansion of a number, if and only if the number is strictly between (see this proof )
The numbers x and y are formed by incrementing the last coefficient in the two representations for z . It is the case that x < y when k is even, and x > y when k is odd.
For example, the number 355 / 113 ( Zu's fraction ) has the continued fraction representations
and thus 355 / 113 is a convergent of any number strictly between
In his Essai sur la théorie des nombres (1798), Adrien-Marie Legendre derives a necessary and sufficient condition for a rational number to be a convergent of the continued fraction of a given real number. [ 16 ] A consequence of this criterion, often called Legendre's theorem within the study of continued fractions, is as follows: [ 17 ]
Theorem . If α is a real number and p , q are positive integers such that | α − p q | < 1 2 q 2 {\displaystyle \left|\alpha -{\frac {p}{q}}\right|<{\frac {1}{2q^{2}}}} , then p / q is a convergent of the continued fraction of α .
Proof . We follow the proof given in An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright . [ 18 ]
Suppose α , p , q are such that | α − p q | < 1 2 q 2 {\displaystyle \left|\alpha -{\frac {p}{q}}\right|<{\frac {1}{2q^{2}}}} , and assume that α > p / q . Then we may write α − p q = θ q 2 {\displaystyle \alpha -{\frac {p}{q}}={\frac {\theta }{q^{2}}}} , where 0 < θ < 1/2. We write p / q as a finite continued fraction [ a 0 ; a 1 , ..., a n ], where due to the fact that each rational number has two distinct representations as finite continued fractions differing in length by one (namely, one where a n = 1 and one where a n ≠ 1), we may choose n to be even. (In the case where α < p / q , we would choose n to be odd.)
Let p 0 / q 0 , ..., p n / q n = p / q be the convergents of this continued fraction expansion. Set ω := 1 θ − q n − 1 q n {\displaystyle \omega :={\frac {1}{\theta }}-{\frac {q_{n-1}}{q_{n}}}} , so that θ = q n q n − 1 + ω q n {\displaystyle \theta ={\frac {q_{n}}{q_{n-1}+\omega q_{n}}}} and thus, α = p q + θ q 2 = p n q n + 1 q n ( q n − 1 + ω q n ) = ( p n q n − 1 + 1 ) + ω p n q n q n ( q n − 1 + ω q n ) = p n − 1 q n + ω p n q n q n ( q n − 1 + ω q n ) = p n − 1 + ω p n q n − 1 + ω q n , {\displaystyle \alpha ={\frac {p}{q}}+{\frac {\theta }{q^{2}}}={\frac {p_{n}}{q_{n}}}+{\frac {1}{q_{n}(q_{n-1}+\omega q_{n})}}={\frac {(p_{n}q_{n-1}+1)+\omega p_{n}q_{n}}{q_{n}(q_{n-1}+\omega q_{n})}}={\frac {p_{n-1}q_{n}+\omega p_{n}q_{n}}{q_{n}(q_{n-1}+\omega q_{n})}}={\frac {p_{n-1}+\omega p_{n}}{q_{n-1}+\omega q_{n}}},} where we have used the fact that p n −1 q n - p n q n −1 = (-1) n and that n is even.
Now, this equation implies that α = [ a 0 ; a 1 , ..., a n , ω ]. Since the fact that 0 < θ < 1/2 implies that ω > 1, we conclude that the continued fraction expansion of α must be [ a 0 ; a 1 , ..., a n , b 0 , b 1 , ...], where [ b 0 ; b 1 , ...] is the continued fraction expansion of ω , and therefore that p n / q n = p / q is a convergent of the continued fraction of α .
This theorem forms the basis for Wiener's attack , a polynomial-time exploit of the RSA cryptographic protocol that can occur for an injudicious choice of public and private keys (specifically, this attack succeeds if the prime factors of the public key n = pq satisfy p < q < 2 p and the private key d is less than (1/3) n 1/4 ). [ 19 ]
Consider x = [ a 0 ; a 1 , ...] and y = [ b 0 ; b 1 , ...] . If k is the smallest index for which a k is unequal to b k then x < y if (−1) k ( a k − b k ) < 0 and y < x otherwise.
If there is no such k , but one expansion is shorter than the other, say x = [ a 0 ; a 1 , ..., a n ] and y = [ b 0 ; b 1 , ..., b n , b n + 1 , ...] with a i = b i for 0 ≤ i ≤ n , then x < y if n is even and y < x if n is odd.
To calculate the convergents of π we may set a 0 = ⌊ π ⌋ = 3 , define u 1 = 1 / π − 3 ≈ 7.0625 and a 1 = ⌊ u 1 ⌋ = 7 , u 2 = 1 / u 1 − 7 ≈ 15.9966 and a 2 = ⌊ u 2 ⌋ = 15 , u 3 = 1 / u 2 − 15 ≈ 1.0034 . Continuing like this, one can determine the infinite continued fraction of π as
The fourth convergent of π is [3;7,15,1] = 355 / 113 = 3.14159292035..., sometimes called Milü , which is fairly close to the true value of π .
Let us suppose that the quotients found are, as above, [3;7,15,1]. The following is a rule by which we can write down at once the convergent fractions which result from these quotients without developing the continued fraction.
The first quotient, supposed divided by unity, will give the first fraction, which will be too small, namely, 3 / 1 . Then, multiplying the numerator and denominator of this fraction by the second quotient and adding unity to the numerator, we shall have the second fraction, 22 / 7 , which will be too large. Multiplying in like manner the numerator and denominator of this fraction by the third quotient, and adding to the numerator the numerator of the preceding fraction, and to the denominator the denominator of the preceding fraction, we shall have the third fraction, which will be too small. Thus, the third quotient being 15, we have for our numerator (22 × 15 = 330) + 3 = 333 , and for our denominator, (7 × 15 = 105) + 1 = 106 . The third convergent, therefore, is 333 / 106 . We proceed in the same manner for the fourth convergent. The fourth quotient being 1, we say 333 times 1 is 333, and this plus 22, the numerator of the fraction preceding, is 355; similarly, 106 times 1 is 106, and this plus 7 is 113.
In this manner, by employing the four quotients [3;7,15,1], we obtain the four fractions:
To sum up, the pattern is Numerator i = Numerator ( i − 1 ) ⋅ Quotient i + Numerator ( i − 2 ) {\displaystyle {\text{Numerator}}_{i}={\text{Numerator}}_{(i-1)}\cdot {\text{Quotient}}_{i}+{\text{Numerator}}_{(i-2)}} Denominator i = Denominator ( i − 1 ) ⋅ Quotient i + Denominator ( i − 2 ) {\displaystyle {\text{Denominator}}_{i}={\text{Denominator}}_{(i-1)}\cdot {\text{Quotient}}_{i}+{\text{Denominator}}_{(i-2)}}
These convergents are alternately smaller and larger than the true value of π , and approach nearer and nearer to π . The difference between a given convergent and π is less than the reciprocal of the product of the denominators of that convergent and the next convergent. For example, the fraction 22 / 7 is greater than π , but 22 / 7 − π is less than 1 / 7 × 106 = 1 / 742 (in fact, 22 / 7 − π is just more than 1 / 791 = 1 / 7 × 113 ).
The demonstration of the foregoing properties is deduced from the fact that if we seek the difference between one of the convergent fractions and the next adjacent to it we shall obtain a fraction of which the numerator is always unity and the denominator the product of the two denominators. Thus the difference between 22 / 7 and 3 / 1 is 1 / 7 , in excess; between 333 / 106 and 22 / 7 , 1 / 742 , in deficit; between 355 / 113 and 333 / 106 , 1 / 11978 , in excess; and so on. The result being, that by employing this series of differences we can express in another and very simple manner the fractions with which we are here concerned, by means of a second series of fractions of which the numerators are all unity and the denominators successively be the product of every two adjacent denominators. Instead of the fractions written above, we have thus the series:
The first term, as we see, is the first fraction; the first and second together give the second fraction, 22 / 7 ; the first, the second and the third give the third fraction 333 / 106 , and so on with the rest; the result being that the series entire is equivalent to the original value.
A non-simple continued fraction is an expression of the form
where the a n ( n > 0) are the partial numerators, the b n are the partial denominators, and the leading term b 0 is called the integer part of the continued fraction.
To illustrate the use of non-simple continued fractions, consider the following example. The sequence of partial denominators of the simple continued fraction of π does not show any obvious pattern:
or
However, several non-simple continued fractions for π have a perfectly regular structure, such as:
The first two of these are special cases of the arctangent function with π = 4 arctan (1) and the fourth and fifth one can be derived using the Wallis product . [ 20 ] [ 21 ]
The continued fraction of π {\displaystyle \pi } above consisting of cubes uses the Nilakantha series and an exploit from Leonhard Euler. [ 22 ]
The numbers with periodic continued fraction expansion are precisely the irrational solutions of quadratic equations with rational coefficients; rational solutions have finite continued fraction expansions as previously stated. The simplest examples are the golden ratio φ = [1;1,1,1,1,1,...] and √ 2 = [1;2,2,2,2,...], while √ 14 = [3;1,2,1,6,1,2,1,6...] and √ 42 = [6;2,12,2,12,2,12...]. All irrational square roots of integers have a special form for the period; a symmetrical string, like the empty string (for √ 2 ) or 1,2,1 (for √ 14 ), followed by the double of the leading integer.
Because the continued fraction expansion for φ doesn't use any integers greater than 1, φ is one of the most "difficult" real numbers to approximate with rational numbers. Hurwitz's theorem [ 23 ] states that any irrational number k can be approximated by infinitely many rational m / n with
While virtually all real numbers k will eventually have infinitely many convergents m / n whose distance from k is significantly smaller than this limit, the convergents for φ (i.e., the numbers 5 / 3 , 8 / 5 , 13 / 8 , 21 / 13 , etc.) consistently "toe the boundary", keeping a distance of almost exactly 1 n 2 5 {\displaystyle {\scriptstyle {1 \over n^{2}{\sqrt {5}}}}} away from φ, thus never producing an approximation nearly as impressive as, for example, 355 / 113 for π . It can also be shown that every real number of the form a + b φ / c + d φ , where a , b , c , and d are integers such that a d − b c = ±1 , shares this property with the golden ratio φ; and that all other real numbers can be more closely approximated.
While there is no discernible pattern in the simple continued fraction expansion of π , there is one for e , the base of the natural logarithm :
which is a special case of this general expression for positive integer n :
Another, more complex pattern appears in this continued fraction expansion for positive odd n :
with a special case for n = 1 :
Other continued fractions of this sort are
where n is a positive integer; also, for integer n :
with a special case for n = 1 :
If I n ( x ) is the modified, or hyperbolic, Bessel function of the first kind, we may define a function on the rationals p / q by
which is defined for all rational numbers, with p and q in lowest terms. Then for all nonnegative rationals, we have
with similar formulas for negative rationals; in particular we have
Many of the formulas can be proved using Gauss's continued fraction .
Most irrational numbers do not have any periodic or regular behavior in their continued fraction expansion. Nevertheless, for almost all numbers on the unit interval, they have the same limit behavior.
The arithmetic average diverges: lim n → ∞ 1 n ∑ k = 1 n a k = + ∞ {\displaystyle \lim _{n\to \infty }{\frac {1}{n}}\sum _{k=1}^{n}a_{k}=+\infty } , and so the coefficients grow arbitrarily large: lim sup n a n = + ∞ {\displaystyle \limsup _{n}a_{n}=+\infty } . In particular, this implies that almost all numbers are well-approximable, in the sense that lim inf n → ∞ | x − p n q n | q n 2 = 0 {\displaystyle \liminf _{n\to \infty }\left|x-{\frac {p_{n}}{q_{n}}}\right|q_{n}^{2}=0} Khinchin proved that the geometric mean of a i tends to a constant (known as Khinchin's constant ): lim n → ∞ ( a 1 a 2 . . . a n ) 1 / n = K 0 = 2.6854520010 … {\displaystyle \lim _{n\rightarrow \infty }\left(a_{1}a_{2}...a_{n}\right)^{1/n}=K_{0}=2.6854520010\dots } Paul Lévy proved that the n th root of the denominator of the n th convergent converges to Lévy's constant lim n → ∞ q n 1 / n = e π 2 / ( 12 ln 2 ) = 3.2758 … {\displaystyle \lim _{n\rightarrow \infty }q_{n}^{1/n}=e^{\pi ^{2}/(12\ln 2)}=3.2758\ldots } Lochs' theorem states that the convergents converge exponentially at the rate of lim n → ∞ 1 n ln | x − p n q n | = − π 2 6 ln 2 {\displaystyle \lim _{n\to \infty }{\frac {1}{n}}\ln \left|x-{\frac {p_{n}}{q_{n}}}\right|=-{\frac {\pi ^{2}}{6\ln 2}}}
Continued fractions play an essential role in the solution of Pell's equation . For example, for positive integers p and q , and non-square n , it is true that if p 2 − nq 2 = ±1 , then p / q is a convergent of the regular continued fraction for √ n . The converse holds if the period of the regular continued fraction for √ n is 1, and in general the period describes which convergents give solutions to Pell's equation. [ 24 ]
Continued fractions also play a role in the study of dynamical systems , where they tie together the Farey fractions which are seen in the Mandelbrot set with Minkowski's question-mark function and the modular group Gamma.
The backwards shift operator for continued fractions is the map h ( x ) = 1/ x − ⌊1/ x ⌋ called the Gauss map , which lops off digits of a continued fraction expansion: h ([0; a 1 , a 2 , a 3 , ...]) = [0; a 2 , a 3 , ...] . The transfer operator of this map is called the Gauss–Kuzmin–Wirsing operator . The distribution of the digits in continued fractions is given by the zero'th eigenvector of this operator, and is called the Gauss–Kuzmin distribution . | https://en.wikipedia.org/wiki/Simple_continued_fraction |
A simple lipid is a fatty acid ester of different alcohols and carries no other substance. These lipids belong to a heterogeneous class of predominantly nonpolar compounds, mostly insoluble in water , but soluble in nonpolar organic solvents such as chloroform and benzene . [ 1 ]
"Simple lipid" can refer to many different types of lipid depending on the classification system used, but the most basic definitions usually classify simple lipids as those that do not contain acyl groups . The simple lipids are then divided further into glycerides , cholesteryl esters , and waxes . [ 2 ] The term was first used by T. P. Hidlich [ de ] in 1947 to separate "simple" greases and waxes from "mixed" triglycerides found in animal fats. [ 3 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Simple_lipid |
Simple Task-Actor Protocol (STAP) is a machine-readable format for specifying user-interface changes. STAP enables symmetric user-interface access for AI and human users.
Main focus of STAP is in providing a functionally-equivalent task experience for human and computational users alike.
In its focus to make human software usable by machine agents, STAP aims to eliminate non-task-essential design choices (e.g. font type/size may be irrelevant for many task types), leaving those to be optionally specified via customizable templates (e.g. CSS).
STAP messages adhere to JSON formatting, and can be deserialized with any standard JSON library.
Deploying a STAP application is similar to deploying a web application, where STAP takes place of HTML as the language for UI description.
Much like HTML, STAP is a means for serializing task interface display and interactions.
Unlike HTML documents, STAP messages are incremental updates to the display.
Whereas HTML is focused on hypertext look and feel, STAP is focused on function, structure, and affordances of task display.
Benefits of task development with STAP:
Benefits of agent development for STAP-compliant tasks: | https://en.wikipedia.org/wiki/Simple_task-actor_protocol |
A simple wave is a flow in a region adjacent to a region of constant state. [ 1 ] In the language of Riemann invariant , the simple wave can also be defined as the zone where all but one of the Riemann invariants are constant in the region of interest, and consequently, a simple wave zone is covered by arcs of characteristics that are straight lines. [ 2 ] [ 3 ] [ 4 ]
Simple waves occur quite often in nature. There is a theorem (see Courant and Friedrichs) that states that a non-constant state of flow adjacent to a constant value is always a simple wave . All expansion fans including Prandtl–Meyer expansion fan are simple waves. Compressive waves until shock wave forms are also simple waves. Weak shocks (including sound waves ) are also simple waves up to second-order approximation in the shock strength.
Simple waves are also defined by the behavior that all the characteristics under hodograph transformation collapses into a single curve. This means that the Jacobian involved in the hodographic transformation is zero.
Let ρ {\displaystyle \rho } be the gas density , u {\displaystyle u} the velocity, p {\displaystyle p} the pressure and c = ( ∂ p / ∂ ρ ) s {\displaystyle c={\sqrt {(\partial p/\partial \rho )_{s}}}} the speed of sound . In isentropic flows, entropy s {\displaystyle s} is constant and if the initial state of the gas is homogenous, then entropy is a constant everywhere at all times and therefore the pressure is a function only of ρ {\displaystyle \rho } , i.e., p = p ( ρ ) {\displaystyle p=p(\rho )} In simple waves, all dependent variables are just function of any one of the dependent variables (this is certainly the case in one-dimensional sound waves) and therefore we can assume the velocity to be also a function only of ρ {\displaystyle \rho } . i.e., u = u ( ρ ) . {\displaystyle u=u(\rho ).} This latter property is the cause of origin of the name simple wave, although the wave is nonlinear.
From the one-dimensional Euler equations , we have
which, because u = u ( ρ ) {\displaystyle u=u(\rho )} , can be written as
Further, since (remember that the time derivative of a function f ( x , t ) {\displaystyle f(x,t)} integrated along a curve x = φ ( t ) {\displaystyle x=\varphi (t)} is given by ( d f / d t ) φ = ∂ f / ∂ t + ( d x / d t ) φ ∂ f / ∂ x {\displaystyle (df/dt)_{\varphi }=\partial f/\partial t+(dx/dt)_{\varphi }\partial f/\partial x} )
the two equations lead to
However, since ρ {\displaystyle \rho } determines u {\displaystyle u} and therefore the above derivatives must be equal so that ρ d u / d ρ = ( 1 / ρ ) d p / d u = ( c 2 / ρ ) d ρ / d u {\displaystyle \rho du/d\rho =(1/\rho )dp/du=(c^{2}/\rho )d\rho /du} . Thus, we obtain d u / d ρ = ± c / ρ {\displaystyle du/d\rho =\pm c/\rho } , whence
This equation provides the required relation u = u ( ρ ) {\displaystyle u=u(\rho )} or, c = c ( u ) {\displaystyle c=c(u)} or, u = u ( p ) {\displaystyle u=u(p)} etc. The above equation is just a statement that either the J + {\displaystyle J_{+}} or the J − {\displaystyle J_{-}} Riemann invariant is constant.
Thus, we obtain
which upon integration becomes
where f ( u ) {\displaystyle f(u)} is an arbitrary function. This equation indicates that the characteristics in the x {\displaystyle x} - t {\displaystyle t} plane are just straight lines. When f ( u ) = 0 {\displaystyle f(u)=0} and when consequently length scale and time scale associated with the initial function disappears, the problem is self-similar and the solution depends only on the ratio x / t {\displaystyle x/t} . This particular case is referred as the centred simple wave .
Similar to the unsteady one-dimensional waves, simple waves in steady two-dimensional system cab be derived. In this case, the solution is given by
where f 1 ( p ) = ( ∂ y / ∂ x ) p {\displaystyle f_{1}(p)=(\partial y/\partial x)_{p}} and f 2 ( p ) {\displaystyle f_{2}(p)} is an arbitrary function of pressure. The characteristics in the x {\displaystyle x} - y {\displaystyle y} plane are straight lines. Similarly, the case corresponding to f 2 ( p ) = 0 {\displaystyle f_{2}(p)=0} is referred as the centred simple wave ; the Prandtl–Meyer expansion fan is a special case of this centred wave. | https://en.wikipedia.org/wiki/Simple_wave |
In algebra, a simplicial Lie algebra is a simplicial object in the category of Lie algebras . In particular, it is a simplicial abelian group , and thus is subject to the Dold–Kan correspondence .
This algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Simplicial_Lie_algebra |
In physics , the term simplicial manifold commonly refers to one of several loosely defined objects, commonly appearing in the study of Regge calculus . These objects combine attributes of a simplex with those of a manifold . There is no standard usage of this term in mathematics , and so the concept can refer to a triangulation in topology , or a piecewise linear manifold , or one of several different functors from either the category of sets or the category of simplicial sets to the category of manifolds .
A simplicial manifold is a simplicial complex for which the geometric realization is homeomorphic to a topological manifold . This is essentially the concept of a triangulation in topology . This can mean simply that a neighborhood of each vertex (i.e. the set of simplices that contain that point as a vertex) is homeomorphic to a n -dimensional ball .
A simplicial manifold is also a simplicial object in the category of manifolds . This is a special case of a simplicial space in which, for each n , the space of n -simplices is a manifold.
For example, if G is a Lie group , then the simplicial nerve of G has the manifold G n {\displaystyle G^{n}} as its space of n -simplices. More generally, G can be a Lie groupoid .
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Simplicial_manifold |
In geometry and combinatorics , a simplicial (or combinatorial ) d -sphere is a simplicial complex homeomorphic to the d -dimensional sphere . Some simplicial spheres arise as the boundaries of convex polytopes , however, in higher dimensions most simplicial spheres cannot be obtained in this way.
One important open problem in the field was the g-conjecture , formulated by Peter McMullen , which asks about possible numbers of faces of different dimensions of a simplicial sphere. In December 2018, the g-conjecture was proven by Karim Adiprasito in the more general context of rational homology spheres. [ 1 ] [ 2 ]
It follows from Euler's formula that any simplicial 2-sphere with n vertices has 3 n − 6 edges and 2 n − 4 faces. The case of n = 4 is realized by the tetrahedron. By repeatedly performing the barycentric subdivision , it is easy to construct a simplicial sphere for any n ≥ 4. Moreover, Ernst Steinitz gave a characterization of 1-skeleta (or edge graphs) of convex polytopes in R 3 implying that any simplicial 2-sphere is a boundary of a convex polytope.
Branko Grünbaum constructed an example of a non-polytopal simplicial sphere (that is, a simplicial sphere that is not the boundary of a polytope). Gil Kalai proved that, in fact, "most" simplicial spheres are non-polytopal. The smallest example is of dimension d = 4 and has f 0 = 8 vertices.
The upper bound theorem gives upper bounds for the numbers f i of i -faces of any simplicial d -sphere with f 0 = n vertices. This conjecture was proved for simplicial convex polytopes by Peter McMullen in 1970 [ 3 ] and by Richard Stanley for general simplicial spheres in 1975.
The g -conjecture , formulated by McMullen in 1970, asks for a complete characterization of f -vectors of simplicial d -spheres. In other words, what are the possible sequences of numbers of faces of each dimension for a simplicial d -sphere? In the case of polytopal spheres, the answer is given by the g -theorem , proved in 1979 by Billera and Lee (existence) and Stanley (necessity). It has been conjectured that the same conditions are necessary for general simplicial spheres. The conjecture was proved by Karim Adiprasito in December 2018. [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Simplicial_sphere |
In graph theory , a simplicial vertex v {\displaystyle v} is a vertex whose closed neighborhood N G [ v ] {\displaystyle N_{G}[v]} in a graph G {\displaystyle G} forms a clique , where every pair of neighbors is adjacent to each other. [ 1 ]
A vertex of a graph is bisimplicial if the set of it and its neighbours is the union of two cliques, and is k -simplicial if the set is the union of k cliques. A vertex is co-simplicial if its non-neighbours form an independent set . [ 2 ]
Addario-Berry et al. [ 3 ] demonstrated that every even-hole-free graph (or more specifically, even-cycle-free graph , as 4-cycles are also excluded here) contains a bisimplicial vertex, which settled a conjecture by Reed. The proof was later shown to be flawed by Chudnovsky & Seymour, [ 4 ] who gave a correct proof. Due to this property, the family of all even-cycle-free graphs is χ {\displaystyle \chi } -bounded .
This graph theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Simplicial_vertex |
Simplicity is the state or quality of being simple . Something easy to understand or explain seems simple, in contrast to something complicated. Alternatively, as Herbert A. Simon suggests, something is simple or complex depending on the way we choose to describe it. [ 1 ] In some uses, the label "simplicity" can imply beauty , purity, or clarity. In other cases, the term may suggest a lack of nuance or complexity relative to what is required.
The concept of simplicity is related to the field of epistemology and philosophy of science (e.g., in Occam's razor ). Religions also reflect on simplicity with concepts such as divine simplicity . In human lifestyles , simplicity can denote freedom from excessive possessions or distractions, such as having a simple living style. In some cases, the term may have negative connotations, as when referring to someone as a simpleton .
There is a widespread philosophical presumption that simplicity is a theoretical virtue. This presumption that simpler theories are preferable appears in many guises. Often it remains implicit; sometimes it is invoked as a primitive, self-evident proposition; other times it is elevated to the status of a ‘Principle’ and labeled as such (for example, the 'Principle of Parsimony'. [ 2 ]
According to Occam's razor , all other things being equal, the simplest theory is most likely true. In other words, simplicity is a meta-scientific criterion by which scientists evaluate competing theories.
A distinction is often made by many persons [ by whom? ] between two senses of simplicity: syntactic simplicity (the number and complexity of hypotheses), and ontological simplicity (the number and complexity of things postulated). These two aspects of simplicity are often referred to as elegance and parsimony respectively. [ 3 ]
John von Neumann defines simplicity as an important esthetic criterion of scientific models:
[...] (scientific model) must satisfy certain esthetic criteria - that is, in relation to how much it describes, it must be rather simple. I think it is worth while insisting on these vague terms - for instance, on the use of word rather. One cannot tell exactly how "simple" simple is. [...] Simplicity is largely a matter of historical background, of previous conditioning, of antecedents, of customary procedures, and it is very much a function of what is explained by it. [ 4 ]
The recognition that too much complexity can have a negative effect on business performance was highlighted in research undertaken in 2011 by Simon Collinson of the Warwick Business School and the Simplicity Partnership, which found that managers who are orientated towards finding ways of making business "simpler and more straightforward" can have a beneficial impact on their organisation.
Most organizations contain some amount of complexity that is not performance enhancing, but drains value out of the company. Collinson concluded that this type of 'bad complexity' reduced profitability ( EBITDA ) by more than 10%. [ 5 ]
Collinson identified a role for "simplicity-minded managers", managers who were "predisposed towards simplicity", and identified a set of characteristics related to the role, namely "ruthless prioritisation", the ability to say "no", willingness to iterate, to reduce communication to the essential points of a message and the ability to engage a team. [ 5 ] His report, the Global Simplicity Index 2011 , was the first ever study to calculate the cost of complexity in the world's largest organisations. [ 6 ]
The Global Simplicity Index identified that complexity occurs in five key areas of an organisation: people, processes, organisational design, strategy, and products and services. [ 7 ] As the "global brands report", the research is repeated and published annually. [ 8 ] : 3 The 2022 report incorporates a " brand simplicity score" and an "industry simplicity score". [ 9 ]
Research by Ioannis Evmoiridis at Tilburg University found that earnings reported by "high simplicity firms" are higher than among other businesses, and that such firms "exhibit[ed] a superior performance during the period 2010 - 2015", whilst requiring lower average capital expenditure and lower leverage . [ 8 ] : 18
Simplicity is a theme in the Christian religion. According to St. Thomas Aquinas , God is infinitely simple . The Roman Catholic and Anglican religious orders of Franciscans also strive for personal simplicity. Members of the Religious Society of Friends (Quakers) practice the Testimony of Simplicity , which involves simplifying one's life to focus on what is important and disregard or avoid what is least important. Simplicity is tenet of Anabaptistism, and some Anabaptist groups like the Bruderhof , make an effort to live simply. [ 10 ] [ 11 ]
In the context of human lifestyle , simplicity can denote freedom from excessive material consumption and psychological distractions.
"Receive with simplicity everything that happens to you." — Rashi (French rabbi, 11th century), citation at the beginning of the film A Serious Man (2009), Coen Brothers | https://en.wikipedia.org/wiki/Simplicity |
The Simplified Molecular Input Line Entry System ( SMILES ) is a specification in the form of a line notation for describing the structure of chemical species using short ASCII strings . SMILES strings can be imported by most molecule editors for conversion back into two-dimensional drawings or three-dimensional models of the molecules.
The original SMILES specification was initiated in the 1980s. It has since been modified and extended. In 2007, an open standard called OpenSMILES was developed in the open source chemistry community.
The original SMILES specification was initiated by David Weininger at the USEPA Mid-Continent Ecology Division Laboratory in Duluth in the 1980s. [ 1 ] [ 2 ] [ 3 ] [ 4 ] Acknowledged for their parts in the early development were "Gilman Veith and Rose Russo (USEPA) and Albert Leo and Corwin Hansch ( Pomona College ) for supporting the work, and Arthur Weininger (Pomona; Daylight CIS) and Jeremy Scofield (Cedar River Software, Renton, WA) for assistance in programming the system." [ 5 ] The Environmental Protection Agency funded the initial project to develop SMILES. [ 6 ] [ 7 ]
It has since been modified and extended by others, most notably by Daylight Chemical Information Systems . In 2007, an open standard called "OpenSMILES" was developed by the Blue Obelisk open-source chemistry community. Other 'linear' notations include the Wiswesser Line Notation (WLN), ROSDAL and SLN (Tripos Inc).
In July 2006, the IUPAC introduced the InChI as a standard for formula representation. SMILES is generally considered to have the advantage of being more human-readable than InChI; it also has a wide base of software support with extensive theoretical backing (such as graph theory ).
The term SMILES refers to a line notation for encoding molecular structures and specific instances should strictly be called SMILES strings. However, the term SMILES is also commonly used to refer to both a single SMILES string and a number of SMILES strings; the exact meaning is usually apparent from the context. The terms "canonical" and "isomeric" can lead to some confusion when applied to SMILES. The terms describe different attributes of SMILES strings and are not mutually exclusive.
Typically, a number of equally valid SMILES strings can be written for a molecule. For example, CCO , OCC and C(O)C all specify the structure of ethanol . Algorithms have been developed to generate the same SMILES string for a given molecule; of the many possible strings, these algorithms choose only one of them. This SMILES is unique for each structure, although dependent on the canonicalization algorithm used to generate it, and is termed the canonical SMILES. These algorithms first convert the SMILES to an internal representation of the molecular structure; an algorithm then examines that structure and produces a unique SMILES string. Various algorithms for generating canonical SMILES have been developed and include those by Daylight Chemical Information Systems, OpenEye Scientific Software , MEDIT , Chemical Computing Group , MolSoft LLC, and the Chemistry Development Kit . A common application of canonical SMILES is indexing and ensuring uniqueness of molecules in a database .
The original paper that described the CANGEN [ 2 ] algorithm claimed to generate unique SMILES strings for graphs representing molecules, but the algorithm fails for a number of simple cases (e.g. cuneane , 1,2-dicyclopropylethane) and cannot be considered a correct method for representing a graph canonically. [ 8 ] There is currently no systematic comparison across commercial software to test if such flaws exist in those packages.
SMILES notation allows the specification of configuration at tetrahedral centers , and double bond geometry. These are structural features that cannot be specified by connectivity alone, and therefore SMILES which encode this information are termed isomeric SMILES. A notable feature of these rules is that they allow rigorous partial specification of chirality. The term isomeric SMILES is also applied to SMILES in which isomers are specified.
In terms of a graph-based computational procedure, SMILES is a string obtained by printing the symbol nodes encountered in a depth-first tree traversal of a chemical graph . The chemical graph is first trimmed to remove hydrogen atoms and cycles are broken to turn it into a spanning tree . Where cycles have been broken, numeric suffix labels are included to indicate the connected nodes. Parentheses are used to indicate points of branching on the tree.
The resultant SMILES form depends on the choices:
From the view point of a formal language theory, SMILES is a word. A SMILES is parsable with a context-free parser. The use of this representation has been in the prediction of biochemical properties (incl. toxicity and biodegradability ) based on the main principle of chemoinformatics that similar molecules have similar properties. The predictive models implemented a syntactic pattern recognition approach (which involved defining a molecular distance) [ 9 ] as well as a more robust scheme based on statistical pattern recognition. [ 10 ]
Atoms are represented by the standard abbreviation of the chemical elements , in square brackets, such as [Au] for gold . Brackets may be omitted in the common case of atoms which:
All other elements must be enclosed in brackets, and have charges and hydrogens shown explicitly. For instance, the SMILES for water may be written as either O or [OH2] . Hydrogen may also be written as a separate atom; water may also be written as [H]O[H] .
When brackets are used, the symbol H is added if the atom in brackets is bonded to one or more hydrogen, followed by the number of hydrogen atoms if greater than 1, then by the sign + for a positive charge or by - for a negative charge. For example, [NH4+] for ammonium ( NH + 4 ). If there is more than one charge, it is normally written as digit; however, it is also possible to repeat the sign as many times as the ion has charges: one may write either [Ti+4] or [Ti++++] for titanium (IV) Ti 4+ . Thus, the hydroxide anion ( OH − ) is represented by [OH-] , the hydronium cation ( H 3 O + ) is [OH3+] and the cobalt (III) cation (Co 3+ ) is either [Co+3] or [Co+++] .
A bond is represented using one of the symbols . - = # $ : / \ .
Bonds between aliphatic atoms are assumed to be single unless specified otherwise and are implied by adjacency in the SMILES string. Although single bonds may be written as - , this is usually omitted. For example, the SMILES for ethanol may be written as C-C-O , CC-O or C-CO , but is usually written CCO .
Double, triple, and quadruple bonds are represented by the symbols = , # , and $ respectively as illustrated by the SMILES O=C=O ( carbon dioxide CO 2 ), C#N ( hydrogen cyanide HCN) and [Ga+]$[As-] ( gallium arsenide ).
An additional type of bond is a "non-bond", indicated with . , to indicate that two parts are not bonded together. For example, aqueous sodium chloride may be written as [Na+].[Cl-] to show the dissociation.
An aromatic "one and a half" bond may be indicated with : ; see § Aromaticity below.
Single bonds adjacent to double bonds may be represented using / or \ to indicate stereochemical configuration; see § Stereochemistry below.
Ring structures are written by breaking each ring at an arbitrary point (although some choices will lead to a more legible SMILES than others) to make an acyclic structure and adding numerical ring closure labels to show connectivity between non-adjacent atoms.
For example, cyclohexane and dioxane may be written as C1CCCCC1 and O1CCOCC1 respectively. For a second ring, the label will be 2. For example, decalin (decahydronaphthalene) may be written as C1CCCC2C1CCCC2 .
SMILES does not require that ring numbers be used in any particular order, and permits ring number zero, although this is rarely used. Also, it is permitted to reuse ring numbers after the first ring has closed, although this usually makes formulae harder to read. For example, bicyclohexyl is usually written as C1CCCCC1C2CCCCC2 , but it may also be written as C0CCCCC0C0CCCCC0 .
Multiple digits after a single atom indicate multiple ring-closing bonds. For example, an alternative SMILES notation for decalin is C1CCCC2CCCCC12 , where the final carbon participates in both ring-closing bonds 1 and 2. If two-digit ring numbers are required, the label is preceded by % , so C%12 is a single ring-closing bond of ring 12.
Either or both of the digits may be preceded by a bond type to indicate the type of the ring-closing bond. For example, cyclopropene is usually written C1=CC1 , but if the double bond is chosen as the ring-closing bond, it may be written as C=1CC1 , C1CC=1 , or C=1CC=1 . (The first form is preferred.) C=1CC-1 is illegal, as it explicitly specifies conflicting types for the ring-closing bond.
Ring-closing bonds may not be used to denote multiple bonds. For example, C1C1 is not a valid alternative to C=C for ethylene . However, they may be used with non-bonds; C1.C2.C12 is a peculiar but legal alternative way to write propane , more commonly written CCC .
Choosing a ring-break point adjacent to attached groups can lead to a simpler SMILES form by avoiding branches. For example, cyclohexane-1,2-diol is most simply written as OC1CCCCC1O ; choosing a different ring-break location produces a branched structure that requires parentheses to write.
Aromatic rings such as benzene may be written in one of three forms:
In the latter case, bonds between two aromatic atoms are assumed (if not explicitly shown) to be aromatic bonds. Thus, benzene , pyridine and furan can be represented respectively by the SMILES c1ccccc1 , n1ccccc1 and o1cccc1 .
Aromatic nitrogen bonded to hydrogen, as found in pyrrole must be represented as [nH] ; thus imidazole is written in SMILES notation as n1c[nH]cc1 .
When aromatic atoms are singly bonded to each other, such as in biphenyl , a single bond must be shown explicitly: c1ccccc1-c2ccccc2 . This is one of the few cases where the single bond symbol - is required. (In fact, most SMILES software can correctly infer that the bond between the two rings cannot be aromatic and so will accept the nonstandard form c1ccccc1c2ccccc2 .)
The Daylight and OpenEye algorithms for generating canonical SMILES differ in their treatment of aromaticity.
Branches are described with parentheses, as in CCC(=O)O for propionic acid and FC(F)F for fluoroform . The first atom within the parentheses, and the first atom after the parenthesized group, are both bonded to the same branch point atom. The bond symbol must appear inside the parentheses; outside (e.g. CCC=(O)O ) is invalid.
Substituted rings can be written with the branching point in the ring as illustrated by the SMILES COc(c1)cccc1C#N ( see depiction ) and COc(cc1)ccc1C#N ( see depiction ) which encode the 3 and 4-cyanoanisole isomers. Writing SMILES for substituted rings in this way can make them more human-readable.
Branches may be written in any order. For example, bromochlorodifluoromethane may be written as FC(Br)(Cl)F , BrC(F)(F)Cl , C(F)(Cl)(F)Br , or the like. Generally, a SMILES form is easiest to read if the simpler branch comes first, with the final, unparenthesized portion being the most complex. The only caveats to such rearrangements are:
The one form of branch which does not require parentheses are ring-closing bonds: the SMILES fragment C1N is equivalent to C(1)N , both denoting a bond between the C and the N . Choosing ring-closing bonds adjacent to branch points can reduce the number of parentheses required. For example, toluene is normally written as Cc1ccccc1 or c1ccccc1C , avoiding the parentheses required if written as c1cc(C)ccc1 or c1cc(ccc1)C .
SMILES permits, but does not require, specification of stereoisomers .
Configuration around double bonds is specified using the characters / and \ to show directional single bonds adjacent to a double bond. For example, F/C=C/F ( see depiction ) is one representation of trans - 1,2-difluoroethylene , in which the fluorine atoms are on opposite sides of the double bond (as shown in the figure), whereas F/C=C\F ( see depiction ) is one possible representation of cis -1,2-difluoroethylene, in which the fluorines are on the same side of the double bond.
Bond direction symbols always come in groups of at least two, of which the first is arbitrary. That is, F\C=C\F is the same as F/C=C/F . When alternating single-double bonds are present, the groups are larger than two, with the middle directional symbols being adjacent to two double bonds. For example, the common form of (2,4)-hexadiene is written C/C=C/C=C/C .
As a more complex example, beta-carotene has a very long backbone of alternating single and double bonds, which may be written CC1CCC/C(C)=C1/C=C/C(C)=C/C=C/C(C)=C/C=C/C=C(C)/C=C/C=C(C)/C=C/C2=C(C)/CCCC2(C)C .
Configuration at tetrahedral carbon is specified by @ or @@ . Consider the four bonds in the order in which they appear, left to right, in the SMILES form. Looking toward the central carbon from the perspective of the first bond, the other three are either clockwise or counter-clockwise. These cases are indicated with @@ and @ , respectively (because the @ symbol itself is a counter-clockwise spiral).
For example, consider the amino acid alanine . One of its SMILES forms is NC(C)C(=O)O , more fully written as N[CH](C)C(=O)O . L -Alanine , the more common enantiomer , is written as N[C@@H](C)C(=O)O ( see depiction ). Looking from the nitrogen–carbon bond, the hydrogen ( H ), methyl ( C ), and carboxylate ( C(=O)O ) groups appear clockwise. D -Alanine can be written as N[C@H](C)C(=O)O ( see depiction ).
While the order in which branches are specified in SMILES is normally unimportant, in this case it matters; swapping any two groups requires reversing the chirality indicator. If the branches are reversed so alanine is written as NC(C(=O)O)C , then the configuration also reverses; L -alanine is written as N[C@H](C(=O)O)C ( see depiction ). Other ways of writing it include C[C@H](N)C(=O)O , OC(=O)[C@@H](N)C and OC(=O)[C@H](C)N .
Normally, the first of the four bonds appears to the left of the carbon atom, but if the SMILES is written beginning with the chiral carbon, such as C(C)(N)C(=O)O , then all four are to the right, but the first to appear (the [CH] bond in this case) is used as the reference to order the following three: L -alanine may also be written [C@@H](C)(N)C(=O)O .
The SMILES specification includes elaborations on the @ symbol to indicate stereochemistry around more complex chiral centers, such as trigonal bipyramidal molecular geometry .
Isotopes are specified with a number equal to the integer isotopic mass preceding the atomic symbol. Benzene in which one atom is carbon-14 is written as [14c]1ccccc1 and deuterochloroform is [2H]C(Cl)(Cl)Cl .
To illustrate a molecule with more than 9 rings, consider cephalostatin -1, [ 12 ] a steroidic 13-ringed pyrazine with the empirical formula C 54 H 74 N 2 O 10 isolated from the Indian Ocean hemichordate Cephalodiscus gilchristi :
Starting with the left-most methyl group in the figure:
% appears in front of the index of ring closure labels above 9; see § Rings above.
The SMILES notation is described extensively in the SMILES theory manual provided by Daylight Chemical Information Systems and a number of illustrative examples are presented. Daylight's depict utility provides users with the means to check their own examples of SMILES and is a valuable educational tool.
SMARTS is a line notation for specification of substructural patterns in molecules. While it uses many of the same symbols as SMILES, it also allows specification of wildcard atoms and bonds, which can be used to define substructural queries for chemical database searching. One common misconception is that SMARTS-based substructural searching involves matching of SMILES and SMARTS strings. In fact, both SMILES and SMARTS strings are first converted to internal graph representations which are searched for subgraph isomorphism .
SMIRKS, a superset of "reaction SMILES" and a subset of "reaction SMARTS", is a line notation for specifying reaction transforms. The general syntax for the reaction extensions is REACTANT>AGENT>PRODUCT (without spaces), where any of the fields can either be left blank or filled with multiple molecules delineated with a dot ( . ), and other descriptions dependent on the base language. Atoms can additionally be identified with a number (e.g. [C:1] ) for mapping, [ 13 ] for example in . [ 14 ]
SMILES corresponds to discrete molecular structures. However many materials are macromolecules, which are too large (and often stochastic) to conveniently generate SMILES for. BigSMILES is an extension of SMILES that aims to provide an efficient representation system for macromolecules. [ 15 ]
SMILES can be converted back to two-dimensional representations using structure diagram generation (SDG) algorithms. [ 16 ] This conversion is sometimes ambiguous. Conversion to three-dimensional representation is achieved by energy-minimization approaches. There are many downloadable and web-based conversion utilities. | https://en.wikipedia.org/wiki/Simplified_Molecular_Input_Line_Entry_System |
Simplified perturbations models are a set of five mathematical models (SGP, SGP4, SDP4, SGP8 and SDP8) used to calculate orbital state vectors of satellites and space debris relative to the Earth-centered inertial coordinate system. This set of models is often referred to collectively as SGP4 due to the frequency of use of that model particularly with two-line element sets produced by NORAD and NASA .
These models predict the effect of perturbations caused by the Earth’s shape, drag, radiation, and gravitation effects from other bodies such as the sun and moon. [ 1 ] [ 2 ] Simplified General Perturbations (SGP) models apply to near earth objects with an orbital period of less than 225 minutes. Simplified Deep Space Perturbations (SDP) models apply to objects with an orbital period greater than 225 minutes, which corresponds to an altitude of 5,877.5 km, assuming a circular orbit. [ 3 ]
The SGP4 and SDP4 models were published along with sample code in FORTRAN IV in 1988 with refinements over the original model to handle the larger number of objects in orbit since. SGP8/SDP8 introduced additional improvements for handling orbital decay . [ 3 ]
The SGP4 model has an error ~1 km at epoch and grows at ~1–3 km per day. [ 3 ] This data is updated frequently in NASA and NORAD sources due to this error. The original SGP model was developed by Kozai in 1959, refined by Hilton & Kuhlman in 1966 and was originally used by the National Space Surveillance Control Center (and later the United States Space Surveillance Network ) for tracking of objects in orbit. The SDP4 model has an error of 10 km at epoch. [ 1 ]
Deep space models SDP4 and SDP8 use only 'simplified drag' equations. Accuracy is not a great concern here as high drag satellite cases do not remain in "deep space" for very long as the orbit quickly becomes lower and near circular. SDP4 also adds Lunar–Solar gravity perturbations to all orbits, and Earth resonance terms specifically for 24-hour geostationary and 12-hour Molniya orbits . [ 2 ]
Additional revisions of the model were developed and published by 2010 by the NASA Goddard Space Flight Center in support of tracking of the SeaWiFS mission and the Navigation and Ancillary Information Facility at the Jet Propulsion Laboratory in support of Planetary Data System for navigational purposes of numerous, mostly deep space, missions. [ 1 ] [ 4 ] Current code libraries [ 5 ] [ 6 ] use SGP4 and SDP4 algorithms merged into a single codebase in 1990 [ 7 ] handling the range of orbital periods which are usually referred to generically as SGP4. [ 7 ]
Source code for algorithm implementations, and TLE interpretation in some cases: | https://en.wikipedia.org/wiki/Simplified_perturbations_models |
Simplified sewerage , also called small-bore sewerage , is a sewer system that collects all household wastewater ( blackwater and greywater ) in small-diameter pipes laid at fairly flat gradients . Simplified sewers are laid in the front yard or under the pavement (sidewalk) or - if feasible - inside the back yard, rather than in the centre of the road as with conventional sewerage. It is suitable for existing unplanned low-income areas, as well as new housing estates with a regular layout. [ 2 ] It allows for a more flexible design. [ 1 ] With simplified sewerage it is crucial to have management arrangements in place to remove blockages, which are more frequent than with conventional sewers. It has been estimated that simplified sewerage reduces investment costs by up to 50% compared to conventional sewerage.
Simplified sewerage is sometimes also referred to as conventional sewerage with appropriate standards, implying that most conventional sewers are overdesigned.
The concept of simplified sewerage emerged in parallel in Natal , Brazil and Karachi , Pakistan in the early 1980s without any interaction or communication.
In both cases particular emphasis was given to community mobilization, an essential element for the success of simplified sewerage. In Latin America, and particularly in Brazil, simplified sewerage is also known as condominial sewerage , a term that underscores the importance of community participation in planning and maintenance at the level of a housing block (known as condominio in the Spanish and Portuguese use of the term).
In developing countries, connection to sewer systems is often costly for poor households, despite typically low monthly sewer tariffs. This apparent paradox is explained by the high costs of in-plot and in-house sanitary installations that have to be paid entirely by the user, by sometimes high sewer connection fees levied by utilities, and by a lack of community consultation. As a result, in many cities in developing countries conventional sewers are laid at high costs under a street, while many users on that street do not connect to them. In Brazil, in some cities connection rates in the early 1990s were less than 40% of the intended beneficiary population. [ 3 ]
Simplified sewerage is most widely used in Brazil . It is estimated that in Brazil some 5 million people in over 200 towns and cities are served with simplified sewerage - or condominial sewerage. [ 4 ] This corresponds to about 3% of the population of Brazil and about 6% of the population connected to sewers. They serve poor and rich alike.
Simplified sewerage has also been used in
In Pakistan , beginning with the Orangi Pilot Project in Karachi , a variation of simplified sewerage using larger diameter pipes has been used.
Community participation in the planning of any sewer system is a fundamental requirement to achieve higher household connection rates and to increase the likelihood of proper maintenance of in-block sewers. In addition, it can motivate users to assume parts of the costs of the sewer system that they are able to assume, such as contribution of labor for construction and/or maintenance.
Typically, in the planning process for a simplified sewerage system, meetings are carried out at the housing block ( condominio ) level for information, discussions and clarifications required for a joint group decision on network design, community contributions during construction and maintenance responsibilities. Users might finance and implement in-house sanitary installations and household connections and would agree on a suitable type of condominial branch. They are asked to comply with agreements established for construction and operation of the condominial branch, as well as payment of tariffs. In turn, the service provider agrees to fulfill his responsibilities as established in the “Terms of Connection ” between the parties. [ 4 ] The community participation process also provides a good opportunity for complementary actions like hygiene promotion, which can have a significant impact on public health at a relatively limited cost.
Simplified sewers are usually laid in the front yard or under the pavement (sidewalk). In some rare cases it is possible to lay them in the back yard. [ 10 ] Sidewalk branches are usually preferred in regular urbanizations, while the front and back yard branches are particularly suited to neighborhoods with challenging topography or urbanization patterns. However, in some cases neither of these options is possible. For example, in South Asia, in many cities there is no sidewalk or front yard, so pipes have to be laid in the middle of the street as with conventional sewers. [ 11 ]
In Latin America typical simplified sewer diameters are 100 mm, laid at a gradient of 1 in 200 (0.5 percent). Such a sewer will serve around 200 households of 5 people with a wastewater flow of 80 litres per person per day. In Pakistan, however, there are no rigorous standards for sewer diameters. In a small pilot as part of the Orangi Pilot Project pipes with a diameter of 150mm were used. [ 12 ]
Laying small diameter pipes at fairly flat gradients requires careful construction techniques. Plastic pipes are best used as they are more easily jointed correctly. This reduces wastewater leakage from the sewer and groundwater infiltration into it. With simplified sewerage there is no need to have the large expensive manholes of the type used for conventional sewerage — simple brick or plastic junction chambers are used instead. [ 2 ]
Construction can be carried out by contractors or by trained and properly supervised community members. Training and proper supervision are actually needed in both cases, since contractors in many cities are not familiar with simplified sewerage.
The cost of sewerage - conventional or simplified - are always site-specific, and estimates are subject to controversies. Construction costs of simplified sewerage are up to half the costs of conventional sewerage. Investment cost savings come from various design features that may or may not be present in a particular simplified sewerage system. Cost-saving features of any simplified sewerage system are a smaller diameter of pipes, smaller and shallower trenches and simplified manholes. The two latter features are estimated to account for most of the cost savings. Other features that could further reduce costs may only be present in some systems, such as:
An element that may slightly increase costs compared to conventional sewerage is the introduction of grease traps or of interceptor chambers for the settlement of sludge. The latter are more common in South Asia and are not used in the condominial model. A 2006 study of four countries showed cost savings of 31-57% from the use of simplified sewerage compared to conventional sewerage with unit costs varying from US$119 per connection in a neighborhood in Bolivia and to US$759 per connection in a small town in Paraguay. [ 13 ] A detailed estimate gives the costs of simplified sewerage in Lima as at least US$700 per household (US$120–140 per person), including in-house sanitary facilities (US$100 per household) and including design, supervision and social intermediation costs (US$126 per household, which are common costs shared with water infrastructure), but excluding taxes. [ 14 ]
In general, at higher population densities sewer systems are cheaper than on-site sanitation (such as septic tanks ). The switching value at which sewerage becomes less costly is largely determined by the type of sewerage, conventional or simplified. A 1983 study in Natal showed that the investment costs for simplified sewerage were lower than for on-site systems at the quite low population density of about 160 people per hectare . Conventional sewerage, however, was cheaper only at densities above 400 people per hectare. [ 2 ]
Good operation and maintenance (O&M) is essential for the long-term sustainability of any sewerage system, but particularly for simplified sewerage, since the small diameter of pipes and low gradients make the system highly vulnerable to clogging. Solids can readily block the small diameter piping and the shallow grade of pipe alignment prevents sewage flow from reaching scouring velocity, meaning that solids fall out of suspension and depositing within the low gradient pipe before reaching the downstream receiving body.
The original concept of householders being responsible for O&M of in-block condominial sewers has not worked well in the long term. [ 15 ] A study of simplified sewerage systems in Brazil has shown that effective maintenance of sewers by utilities has often been the result of community pressure by neighborhood associations. Without such pressure maintenance by utilities has often been inadequate, and community maintenance has not come about either. [ 16 ]
Few situation exist where simplified sewers are appropriate sanitation solutions to install. Therefore, alternative management systems had to be developed to mitigate the high issues of simplified sewers, and a few examples are provided below:
Concerning maintenance costs, available information indicates similar costs and requirements for the simplified and the conventional system under the same conditions. Simplified systems typically require more interventions, but the cost per intervention is lower. Comparative analytical studies are not yet available, however.
According to Jose Carlos Melo, who is considered to be the "father" of condominial sewers in Brazil, some important constraints for the application of simplified sewerage are: [ 4 ]
Over the last years, countries like Bolivia and Peru reviewed and modernized technical standards according to methods and criteria established and accepted in Brazil in the 1980s, thus overcoming the latter constraint. | https://en.wikipedia.org/wiki/Simplified_sewerage |
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