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In astronomy , the velocity dispersion ( σ ) is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects , such as an open cluster , globular cluster , galaxy , galaxy cluster , or supercluster . By measuring the radial velocities of the group's members through astronomical spectroscopy , the velocity dispersion of that group can be estimated and used to derive the group's mass from the virial theorem . [ 1 ] Radial velocity is found by measuring the Doppler width of spectral lines of a collection of objects; the more radial velocities one measures, the more accurately one knows their dispersion. A central velocity dispersion refers to the σ of the interior regions of an extended object, such as a galaxy or cluster.
The relationship between velocity dispersion and matter (or the observed electromagnetic radiation emitted by this matter) takes several forms – specific correlations – in astronomy based on the object(s) being observed. Notably, the M – σ relation applies for material orbiting many black holes , the Faber–Jackson relation for elliptical galaxies , and the Tully–Fisher relation for spiral galaxies . For example, the σ found for objects about the Milky Way 's supermassive black hole (SMBH) is about 100 km/s, which provides an approximation of the mass of this SMBH. [ 2 ] The Andromeda Galaxy ( Messier 31) hosts a SMBH about 10 times larger than our own, and has a σ ≈ 160 km/s . [ 3 ]
Groups and clusters of galaxies have more disparate (contrasting in degree) velocity dispersions than smaller objects. For example, while our own poor group , the Local Group , has a σ = 61±8 km/s , [ 4 ] rich clusters of galaxies, such as the Coma Cluster , have a σ ≈ 1,000 km/s . [ 5 ] The dwarf elliptical galaxies within Coma, as with all galaxies, have their own internal velocity dispersion for their stars, which is a σ ≲ 80 km/s , typically. [ 6 ] Normal elliptical galaxies , by comparison, have an average σ ≈ 200 km/s . [ 7 ]
For spiral galaxies , the increase in velocity dispersion in population I stars is a gradual process which likely results from the near-random incidence of momentum exchanges, specifically dynamical friction , between individual stars and large interstellar media (gas and dust clouds) with masses greater than 10 5 M ☉ . [ 8 ] Face-on spiral galaxies have a central σ ≲ 90 km/s ; slightly more if viewed edge-on. [ 9 ]
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https://en.wikipedia.org/wiki/Velocity_dispersion
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A velocity potential is a scalar potential used in potential flow theory. It was introduced by Joseph-Louis Lagrange in 1788. [ 1 ]
It is used in continuum mechanics , when a continuum occupies a simply-connected region and is irrotational . In such a case, ∇ × u = 0 , {\displaystyle \nabla \times \mathbf {u} =0\,,} where u denotes the flow velocity . As a result, u can be represented as the gradient of a scalar function ϕ : u = ∇ φ = ∂ φ ∂ x i + ∂ φ ∂ y j + ∂ φ ∂ z k . {\displaystyle \mathbf {u} =\nabla \varphi \ ={\frac {\partial \varphi }{\partial x}}\mathbf {i} +{\frac {\partial \varphi }{\partial y}}\mathbf {j} +{\frac {\partial \varphi }{\partial z}}\mathbf {k} \,.}
ϕ is known as a velocity potential for u .
A velocity potential is not unique. If ϕ is a velocity potential, then ϕ + f ( t ) is also a velocity potential for u , where f ( t ) is a scalar function of time and can be constant. Velocity potentials are unique up to a constant, or a function solely of the temporal variable.
The Laplacian of a velocity potential is equal to the divergence of the corresponding flow. Hence if a velocity potential satisfies Laplace equation , the flow is incompressible .
Unlike a stream function , a velocity potential can exist in three-dimensional flow.
In theoretical acoustics , [ 2 ] it is often desirable to work with the acoustic wave equation of the velocity potential ϕ instead of pressure p and/or particle velocity u . ∇ 2 φ − 1 c 2 ∂ 2 φ ∂ t 2 = 0 {\displaystyle \nabla ^{2}\varphi -{\frac {1}{c^{2}}}{\frac {\partial ^{2}\varphi }{\partial t^{2}}}=0} Solving the wave equation for either p field or u field does not necessarily provide a simple answer for the other field. On the other hand, when ϕ is solved for, not only is u found as given above, but p is also easily found—from the (linearised) Bernoulli equation for irrotational and unsteady flow —as p = − ρ ∂ φ ∂ t . {\displaystyle p=-\rho {\frac {\partial \varphi }{\partial t}}\,.}
This fluid dynamics –related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Velocity_potential
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In turbomachinery , a velocity triangle or a velocity diagram is a triangle representing the various components of velocities of the working fluid in a turbomachine . Velocity triangles may be drawn for both the inlet and outlet sections of any turbomachine. The vector nature of velocity is utilized in the triangles, and the most basic form of a velocity triangle consists of the tangential velocity, the absolute velocity and the relative velocity of the fluid making up three sides of the triangle.
A general velocity triangle consists of the following vectors: [ 1 ] [ 2 ]
The following angles are encountered during the analysis:
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https://en.wikipedia.org/wiki/Velocity_triangle
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Velvet is an algorithm package that has been designed to deal with de novo genome assembly and short read sequencing alignments . This is achieved through the manipulation of de Bruijn graphs for genomic sequence assembly via the removal of errors and the simplification of repeated regions. [ 2 ] Velvet has also been implemented in commercial packages, such as Sequencher , Geneious , MacVector and BioNumerics .
The development of next-generation sequencers (NGS) allowed for increased cost effectiveness on very short read sequencing. The manipulation of de Bruijn graphs as a method for alignment became more realistic but further developments were needed to address issues with errors and repeats. [ 3 ] This led to the development of Velvet by Daniel Zerbino and Ewan Birney at the European Bioinformatics Institute in the United Kingdom. [ 4 ]
Velvet works by efficiently manipulating de Bruijn graphs through simplification and compression, without the loss of graph information, by converging non-intersecting paths into single nodes. It eliminates errors and resolves repeats by first using an error correction algorithm that merges sequences together. Repeats are then removed from the sequence via the repeat solver that separates paths which share local overlaps.
The combination of short reads and read pairs allows Velvet to resolve small repeats and produce contigs of reasonable length. This application of Velvet can produce contigs with a N50 length of 50 kb on paired-end prokaryotic data and a 3 kb length for regions of mammalian data.
As already mentioned Velvet uses the de Bruijn graph to assemble short reads. More specifically Velvet represents each different k-mer obtained from the reads by a unique node on the graph. Two nodes are connected if its k-mers have a k-1 overlap. In other words, an arc from node A to node B exists if the last k-1 characters of the k-mer, represented by A, are the first k-1 characters of the k-mer represented by B. The following figure shows an example of a de Bruijn graph generated with Velvet:
The same process is simultaneously done with the reverse complement of all the k-mers to take into account the overlaps between the reads of opposite strands.
A number of optimizations can be done over the graph which includes simplification and error removal.
An easy way to save memory costs is to merge nodes that do not affect the path generated in the graph, i.e., whenever a node A has only one outgoing arc that points to node B, with only one ingoing arc, the nodes can be merged. It is possible to represent both nodes as one, merging them and all their information together. The next figure illustrates this process in the simplification of the initial example.
Errors in the graph can be caused by the sequencing process or it could simply be that the biological sample contains some errors (for example polymorphisms ).
Velvet recognizes three kinds of errors: tips; bubbles; and erroneous connections.
A node is considered a tip and should be erased if it is disconnected on one of its ends, the length of the information stored in the node is shorter than 2k, and the arc leading to this node has a low multiplicity (number of times the arc was found during the construction of the graph) and as a result cannot be compared to other alternative paths. Once these errors are removed, the graph once again undergoes simplification.
Bubbles are generated when two distinct paths start and end at the same nodes. Normally bubbles are caused by errors or biological variants. These errors are removed using the Tour Bus algorithm, which is similar to a Dijkstra's algorithm , a breadth-first search that detects the best path to follow and determines which ones should be erased. A simple example is shown in figure 4.
This process is also shown in figure 5 following on from the examples shown in figures 1 and 2.
These are connections that do not generate correct paths or do not create any recognizable structures within the graph. Velvet erases these errors after completion of the Tour Bus algorithm, applying a simple coverage cut-off that must be defined by the user.
Velvet provides the following functions:
After running velvetg a number of files are generated. Most importantly, a file of contigs contains the sequences of the contigs longer than 2k, where k is the word-length used in velveth.
For more detail and examples refer to the Velvet Manual [ 5 ]
Current DNA sequencing technologies, including NGS, are limited on the basis that genomes are much larger than any read length. Typically, NGS operate with small reads, less than 400 bp, and have a much lower cost per read than previous first generation machines . They are also simpler to operate with higher parallel operation and higher yield. [ 3 ]
However, short reads contain less information than larger reads thus requiring a higher assembly read coverage to allow for detectable overlaps. This in turn increases the complexity of the sequencing and significantly increases computational requirements. A larger number of reads also increases the size of the overlap graph, making it more difficult and lengthy to compute. The connections between the reads become more indistinct due to the decrease in overlapping sections leading to a greater possibility of errors.
To overcome these issues, dynamic sequencing programs that are efficient, highly cost effective and able to resolve errors and repeats were developed. Velvet algorithms was designed for this and are able to perform short read de novo sequencing alignment in relatively short computational time and with lower memory usage compared to other assemblers. [ 6 ]
One of the main drawbacks in the use of Velvet is the use of the command-line interface and the difficulties users, especially beginners, face in the implementation of their data. A graphical user interface for the Velvet assembler was developed in 2012 and designed to overcome this problem and simplify the running of Velvet. [ 7 ]
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https://en.wikipedia.org/wiki/Velvet_assembler
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Venetia Katharine Douglas Burney (married name Phair , 11 July 1918 – 30 April 2009) was an English accountant and teacher. She is remembered as the first person to suggest the name Pluto for the dwarf planet discovered by Clyde Tombaugh in 1930. At the time, she was 11 years old.
Venetia Burney was the daughter of Rev. Charles Fox Burney , Oriel Professor of the Interpretation of Holy Scripture at Oxford, and his wife Ethel Wordsworth Burney (née Madan). She was the granddaughter of Falconer Madan (1851–1935), Librarian of the Bodleian Library of the University of Oxford . [ 1 ] Falconer Madan's brother, Henry Madan (1838–1901), Science Master of Eton , had in 1878 suggested the names Phobos and Deimos for the moons of Mars . [ 2 ]
On 14 March 1930, Falconer Madan read the story of the new planet's discovery in The Times and mentioned it to his granddaughter Venetia. She suggested the name Pluto – the Roman god of the Underworld, who was able to make himself invisible − and Madan forwarded the suggestion to astronomer Herbert Hall Turner , who cabled his American colleagues at Lowell Observatory . Clyde Tombaugh liked the proposal because it started with the initials of Percival Lowell , who had predicted the existence of Planet X , which they thought was Pluto because it was coincidentally in that position in space. On 1 May 1930, the name Pluto was formally adopted for the new celestial body. [ 3 ] Whether she was really the first person to propose the name has been doubted on plausibility grounds, [ 4 ] but the historical fact is that she was credited as such.
Most news coverage done at the time of the discovery of Pluto didn't mention her and the role she played in terms of naming Pluto was mostly forgotten about until a 1984 article from Sky & Telescope publicized her role. [ 5 ]
Burney was educated at Downe House School in Berkshire and Newnham College, Cambridge , where she studied economics from 1938-41. [ 6 ] After graduation she became a chartered accountant . Later she became a teacher of economics and mathematics at girls’ schools in southwest London [ 7 ] teaching until she retired in the 1980s. [ 8 ] She was married to Edward Maxwell Phair from 1947 until his death in 2006. Her husband, a classicist , later became housemaster and head of English at Epsom College . She died on 30 April 2009, aged 90, in Banstead in Surrey. [ 7 ] She was buried at Randalls Park Crematorium in Leatherhead in Surrey.
Only a few months before the reclassification of Pluto from a planet to a dwarf planet , with a debate going on about the issue, she said in an interview, "At my age, I've been largely indifferent [to the debate]; though I suppose I would prefer it to remain a planet." [ 3 ]
The asteroid 6235 Burney and the Burney impact basin on Pluto were named in her honour. [ 9 ] [ 10 ] In July 2015 the New Horizons spacecraft was the first to visit Pluto and carried an instrument named Venetia Burney Student Dust Counter in her honour. [ 11 ] Mihaly Horanyi, Principal Investigator for the instrument, and Alan Stern visited Mrs Phair at home to present her with a plaque, certificate, and spacecraft model. [ 12 ]
Massachusetts rock band The Venetia Fair came up with their name after reading about Venetia Phair, shortly after Pluto was reclassified as a dwarf planet. [ 13 ]
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https://en.wikipedia.org/wiki/Venetia_Burney
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Venkataraman Thangadurai is a scientist recognized for his work in solid state ionics and chemistry . He is a professor at the University of St Andrews , specializing in Chemistry. [ 1 ] [ 2 ]
Thangadurai, who was born in India , earned his Chemistry degrees from various institutions in Tamil Nadu and a Ph.D. from the Indian Institute of Science in 1999. He pursued postdoctoral studies in Germany , receiving a fellowship from the Alexander von Humboldt Foundation and a Habilitation degree in 2004 from the University of Kiel . [ 3 ] [ citation needed ]
Thangadurai works on creating new materials for energy storage and conversion, particularly in solid oxide fuel cells , batteries and gas separation membranes . His research focuses on ion transport in solid electrolytes and high-performance materials for energy applications. [ 4 ] [ citation needed ] Thangadurai has done work on advancing Li-based garnets within all-solid-state Lithium metal batteries. Thangadurai co-founded Ion Storage Systems and Superionics Inc. [ 5 ] [ 6 ] [ 7 ] Thangadurai submitted 13 patent applications and has 443 publications [ 8 ] [ 9 ] He moved to the University of St Andrews in early July 2024.
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https://en.wikipedia.org/wiki/Venkataraman_Thangadurai
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Venom-induced consumption coagulopathy (VICC) is a medical condition caused by the effects of some snake and caterpillar venoms on the blood. [ 1 ] Important coagulation factors are activated by the specific serine proteases in the venom and as they become exhausted, coagulopathy develops. Symptoms are consistent with uncontrolled bleeding. Diagnosis is made using blood tests that assess clotting ability along with recent history of envenomation. Treatment generally involves pressure dressing, confirmatory blood testing, and antivenom administration.
Symptoms are similar to those seen in other consumptive coagulopathies. These include obvious bleeding from the nose, gums, intravenous lines , or puncture sites. More serious symptoms such as vomiting blood, intestinal bleeding, and hemorrhage of internal organs may also be seen. [ 2 ]
Venom-induced coagulopathy is caused by over-activation of the body's natural clotting system. This decreases clotting factor availability, thus impairing hemostasis . The exact mechanism by which this is accomplished varies greatly venom to venom. [ 3 ] Some venoms cause something akin to disseminated intravascular coagulation , while others lack the microthrombi characteristic in this disorder. [ 4 ] Procoagulant metalloproteinases in the venom promote a consumption coagulopathy by activating prothrombin , factor V , factor X or thrombin-like enzymes (fibrinogenases). [ 5 ] Venom induced coagulopathy may also be accompanied by a thrombotic microangiopathy consisting of thrombocytopenia (low platelets), microangiopathic hemolytic anemia and acute kidney injury . [ 5 ]
Diagnosis is established using various laboratory tests designed to test the function of the clotting system and other blood components. These tests include a complete blood count , prothrombin time with international normalized ratio , activated partial thromboplastin time , serum direct fibrinogen , and D-dimer . Abnormal values of these tests in combination with recent history of snakebite suggest VICC. The anticoagulation effects of snake venom can last for up to two weeks in some species without the administration of antivenom and should thus be considered as the relevant time course when distinguishing symptom causes. [ 6 ]
Treatment revolves around rapid identification and prompt administration of antivenom. General principles of treatment also include application of pressure dressing, baseline blood tests, swabbing of bite site for venom, urinalysis , and follow-up serial bloodwork to monitor disease progression. However, there is some controversy as some venoms may work too quickly for antivenom to be of any use. [ 7 ]
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https://en.wikipedia.org/wiki/Venom-induced_consumption_coagulopathy
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Venom optimization hypothesis , also known as venom metering , is a biological hypothesis which postulates that venomous animals have physiological control over their production and use of venoms . It explains the economic use of venom because venom is a metabolically expensive product, and that there is a biological mechanism for controlling their specific use. The hypothetical concept was proposed by Esther Wigger, Lucia Kuhn-Nentwig, and Wolfgang Nentwig of the Zoological Institute at the University of Bern , Switzerland , in 2002. [ 1 ] [ 2 ]
A number of venomous animals have been experimentally found to regulate the amount of venom they use during predation or defensive situations. Species of anemones, jellyfish, ants, scorpions, spiders, and snakes are found to use their venoms frugally depending on the situation and size of their preys or predators. [ 3 ]
Venom optimization hypothesis was postulated by Wigger, Kuhn-Nentwig, and Nentwig from their studies of the amount of venom used by a wandering spider Cupiennius salei . This spider produces a neurotoxic peptide called CsTx-1 for paralysing its prey. [ 4 ] It does not weave webs for trapping preys, and therefore, entirely depends on its venom for predation. It is known to prey on a variety of insects including butterflies, moths, earwigs, cockroaches, flies and grasshoppers. [ 5 ] Its venom glands store only about 10 μl of crude venom. Refilling of the glands takes 2–3 days and the lethal efficacy of the venom is, initially, very low for several days, requiring 8 to 18 days for full effect. [ 6 ] It was found that the amount of venom released differed for each specific prey. For example, for bigger and stronger insects like beetles, the spider uses the entire amount of its venom; while for small ones, it uses only a small amount, thus economizing its costly venom. [ 1 ] In fact, experiments show that the amount of venom released is just sufficient (at the lethal dose) to paralyze the target organism depending on the size or strength, and is not more than what is necessary. [ 7 ]
Animal venoms are complex biomolecules and hence, their biological synthesis require high metabolic activity. A particular venom itself is a complex chemical mixture composed of hundreds of proteins and non-proteinaceous compounds, resulting in a potent weapon for prey immobilization and predator deterrence. The metabolic cost of venom is sufficiently high to result in secondary loss of venom whenever its use becomes non-essential to survival of the animal. This suggests that venomous animals may have evolved strategies for minimizing venom expenditure, that they should use them only as and when required, and that too in optimal amount. [ 2 ]
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https://en.wikipedia.org/wiki/Venom_optimization_hypothesis
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Venom in medicine is the medicinal use of venoms for therapeutic benefit in treating diseases .
Venom is any poisonous compound secreted by an animal intended to harm or disable another. When an organism produces a venom, its final form may contain hundreds of different bioactive elements that interact with each other inevitably producing its toxic effects. [ 1 ] This mixture of ingredients includes various proteins , peptides , and non-peptidic small molecules . [ 2 ] The active components of these venoms are isolated, purified, and screened in assays . These may be either phenotypic assays to identify component that may have desirable therapeutic properties ( forward pharmacology ) or target directed assays to identify their biological target and mechanism of action ( reverse pharmacology ). [ 3 ]
Venoms are naturally occurring substances that organisms evolved to deploy against other organisms, in defense or attack. [ 2 ] They are often mixtures of proteins that act together or singly to attack their specific targets within the organism against which they are used, generally with high specificity and generally easily accessible through the vascular system. [ 2 ] This has made venoms a subject of study for people who work in drug discovery . [ 2 ] With developments in omic technologies ( proteomics , genomics , etc.), researchers in this field became able to identify genes that produce certain elements in an animal's venom, as well as protein domains that have been used as building blocks across many species. [ 2 ] In conjunction with methods of separation and purification of compounds, scientists are able to study each individual compound that exists within a venom "concoction", looking for compounds to serve as drug leads or other use. [ 2 ] Each venomous organism produces thousands of different proteins giving access to millions of different molecules that still have potential uses. In addition, nature is continuously evolving; as prey develop resistance to these venoms, the predators also evolve as well, creating novel toxins that can continue to act upon its respective prey. [ 4 ]
The earliest known use of venom in medicine dates back to 380 B.C. in ancient Greece. [ 5 ] Aristotle 's "Historia Animalium", describes how venom can be used in the production of antidotes for the venom. [ 5 ] During the height of the Roman empire, there is evidence of venom being added into medicine used to treat smallpox, leprosy, fever, and wounds. [ 5 ] Despite this, early uses of venom were primarily involved in the process of making antidotes. This use of venom continued into the Middle Ages and well into the 19th century. The first modern study of venom in a medical light occurred in the late 19th century. A scientist, Albert Calmatte, injected animals with small amounts of venom, using their blood as the antidote. [ 5 ]
Captopril emulates the function of the toxin found in Brazilian pit viper ( Bothrops jararaca ) venom and is generally accepted as the first venom "success" story. Captopril is an ACE inhibitor (angiotensin-converting enzyme) that was approved by the FDA approved in April 1981. It lowers blood pressure by inhibiting the production of angiotensin II which acts in a pathway that leads to vasoconstriction which raises blood pressure. After the creation of this drug, many analogues ( enalapril , lisinopril , perindopril , ramipril , etc.) were produced. [ 6 ]
Ziconotide is a synthetically made version of the ω- conotoxin made by the cone snail , [ 7 ] that is used to treat severe pain and is delivered as an infusion into the cerebrospinal fluid using an intrathecal pump system . [ 8 ] Ziconitide acts presynaptically on N-type calcium channels , blocking the receptors of this channel with high selectivity and affinity, [ 7 ]
Eptifibatide was modeled after a component in southeastern pygmy rattlesnake venom and is used in anticoagulation therapies in an effort to reduce the risk of heart attacks ; it is used in only severe cases because of the possible side effect of thrombocytopenia , a condition where platelets are unable to aggregate at all. [ 9 ] [ 10 ] [ 11 ] Eptifibatide binds reversibly to platelets reducing the risk of thrombosis . It is an antagonist of glycoprotein IIb/IIIa . [ 9 ]
Exenatide is a 39- amino-acid peptide that is a synthetic version of exendin-4, a hormone found in the saliva of the Gila monster . [ 12 ] It is used to treat Type II Diabetes as an adjunct to insulin and other drugs. [ 13 ] [ 14 ] It is GLP-1 receptor agonist that was first isolated by John Eng in 1992 while working at the Veterans Administration Medical Center in the Bronx, New York. [ 12 ]
Batroxobin , is a serine protease found in snake venom produced by Bothrops atrox and Bothrops moojeni , venomous species of pit viper found east of the Andes in South America. It cleaves fibrinogen , similarly to thrombin . Batroxobin from B atrox is used as a drug called "Reptilase" that is used to stop bleeding, while batroxobin from B moojeni is a drug called "Defibrase", used to break up blood clots. It is also used in a system called "Vivostat", where a person's blood is taken just before surgery and exposed to batroxobin; the resulting clots are then harvested, and then dissolved, forming a fibrin glue that is then used on the person during the surgery. [ 15 ]
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https://en.wikipedia.org/wiki/Venoms_in_medicine
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Vensim is a simulation software developed by Ventana Systems. It primarily supports continuous simulation ( system dynamics ), with some discrete event and agent-based modelling capabilities. It is available commercially and as a free "Personal Learning Edition".
Vensim provides a graphical modeling interface with stock and flow and causal loop diagrams , on top of a text-based system of equations in a declarative programming language. It includes a patented method for interactive tracing of behavior through causal links in model structure (the patent expired in 2012), [ 1 ] [ 2 ] [ 3 ] as well as a language extension for automating quality control experiments on models called Reality Check. [ 4 ]
The modeling language supports arrays (subscripts) and permits mapping among dimensions and aggregation. Built-in allocation functions satisfy constraints that are sometimes not met by conventional approaches like logit . [ 5 ] It supports discrete delays, queues and a variety of stochastic processes.
There are multiple paths for cross sectional and time-series data import and export, including text files, spreadsheets and ODBC. Models may be calibrated against data using optimization, Kalman Filtering [ 6 ] or Markov chain Monte Carlo methods. Sensitivity analysis options provide a variety of ways to test and sample models, including Monte Carlo simulation with Latin Hypercube sampling.
Vensim model files can be packaged and published in a customizable read-only format that can be executed by a freely available Model Reader. This allows sharing of interactive models with users who do not own the program and/or who the model author does not wish to have access to the model's code base. [ 7 ]
Vensim is general-purpose software, used in a wide variety of problem domains. Common or high-profile applications include:
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https://en.wikipedia.org/wiki/Vensim
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Vent polymerase is a archean thermostable DNA polymerase used for the polymerase chain reaction . It was isolated from the thermophile Thermococcus litoralis . [ 1 ]
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https://en.wikipedia.org/wiki/Vent_DNA_polymerase
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Ventilation is the intentional introduction of outdoor air into a space. Ventilation is mainly used to control indoor air quality by diluting and displacing indoor effluents and pollutants . It can also be used to control indoor temperature, humidity, and air motion to benefit thermal comfort , satisfaction with other aspects of the indoor environment, or other objectives.
The intentional introduction of outdoor air is usually categorized as either mechanical ventilation, natural ventilation , or mixed-mode ventilation . [ 2 ]
Ventilation is typically described as separate from infiltration.
The design of buildings that promote occupant health and well-being requires a clear understanding of the ways that ventilation airflow interacts with, dilutes, displaces, or introduces pollutants within the occupied space. Although ventilation is an integral component of maintaining good indoor air quality, it may not be satisfactory alone. [ 6 ] A clear understanding of both indoor and outdoor air quality parameters is needed to improve the performance of ventilation in terms of occupant health and energy. [ 7 ] In scenarios where outdoor pollution would deteriorate indoor air quality, other treatment devices such as filtration may also be necessary. [ 8 ] In kitchen ventilation systems, or for laboratory fume hoods , the design of effective effluent capture can be more important than the bulk amount of ventilation in a space. More generally, the way that an air distribution system causes ventilation to flow into and out of a space impacts the ability of a particular ventilation rate to remove internally generated pollutants. The ability of a system to reduce pollution in space is described as its "ventilation effectiveness". However, the overall impacts of ventilation on indoor air quality can depend on more complex factors such as the sources of pollution, and the ways that activities and airflow interact to affect occupant exposure.
An array of factors related to the design and operation of ventilation systems are regulated by various codes and standards. Standards dealing with the design and operation of ventilation systems to achieve acceptable indoor air quality include the American Society of Heating, Refrigerating and Air-Conditioning Engineers ( ASHRAE ) Standards 62.1 and 62.2, the International Residential Code, the International Mechanical Code , and the United Kingdom Building Regulations Part F . Other standards that focus on energy conservation also impact the design and operation of ventilation systems, including ASHRAE Standard 90.1, and the International Energy Conservation Code .
When indoor and outdoor conditions are favorable, increasing ventilation beyond the minimum required for indoor air quality can significantly improve both indoor air quality and thermal comfort through ventilative cooling , which also helps reduce the energy demand of buildings. [ 9 ] [ 10 ] During these times, higher ventilation rates, achieved through passive or mechanical means ( air-side economizer , ventilative pre-cooling), can be particularly beneficial for enhancing people's physical health. [ 11 ] Conversely, when conditions are less favorable, maintaining or improving indoor air quality through ventilation may require increased use of mechanical heating or cooling, leading to higher energy consumption.
Ventilation should be considered for its relationship to "venting" for appliances and combustion equipment such as water heaters , furnaces, boilers , and wood stoves. Most importantly, building ventilation design must be careful to avoid the backdraft of combustion products from "naturally vented" appliances into the occupied space. This issue is of greater importance for buildings with more air-tight envelopes. To avoid the hazard, many modern combustion appliances utilize "direct venting" which draws combustion air directly from outdoors, instead of from the indoor environment.
The air in a room can be supplied and removed in several ways, for example via ceiling ventilation, cross ventilation , floor ventilation or displacement ventilation . [ citation needed ]
Furthermore, the air can be circulated in the room using vortexes which can be initiated in various ways:
The ventilation rate, for commercial, industrial, and institutional (CII) buildings, is normally expressed by the volumetric flow rate of outdoor air, introduced to the building. The typical units used are cubic feet per minute (CFM) in the imperial system, or liters per second (L/s) in the metric system (even though cubic meter per second is the preferred unit for volumetric flow rate in the SI system of units). The ventilation rate can also be expressed on a per person or per unit floor area basis, such as CFM/p or CFM/ft², or as air changes per hour (ACH).
For residential buildings, which mostly rely on infiltration for meeting their ventilation needs, a common ventilation rate measure is the air change rate (or air changes per hour): the hourly ventilation rate divided by the volume of the space ( I or ACH ; units of 1/h). During the winter, ACH may range from 0.50 to 0.41 in a tightly air-sealed house to 1.11 to 1.47 in a loosely air-sealed house. [ 12 ]
ASHRAE now recommends ventilation rates dependent upon floor area, as a revision to the 62-2001 standard, in which the minimum ACH was 0.35, but no less than 15 CFM/person (7.1 L/s/person). As of 2003, the standard has been changed to 3 CFM/100 sq. ft. (15 L/s/100 sq. m.) plus 7.5 CFM/person (3.5 L/s/person). [ 13 ]
Ventilation Rate Procedure is rate based on standard and prescribes the rate at which ventilation air must be delivered to space and various means to the condition that air. [ 14 ] Air quality is assessed (through CO 2 measurement) and ventilation rates are mathematically derived using constants.Indoor Air Quality Procedure uses one or more guidelines for the specification of acceptable concentrations of certain contaminants in indoor air but does not prescribe ventilation rates or air treatment methods. [ 14 ] This addresses both quantitative and subjective evaluations and is based on the Ventilation Rate Procedure. It also accounts for potential contaminants that may have no measured limits, or for which no limits are not set (such as formaldehyde off-gassing from carpet and furniture).
Natural ventilation harnesses naturally available forces to supply and remove air in an enclosed space. Poor ventilation in rooms is identified to significantly increase the localized moldy smell in specific places of the room including room corners. [ 11 ] There are three types of natural ventilation occurring in buildings: wind-driven ventilation , pressure-driven flows, and stack ventilation . [ 15 ] The pressures generated by 'the stack effect ' rely upon the buoyancy of heated or rising air. Wind-driven ventilation relies upon the force of the prevailing wind to pull and push air through the enclosed space as well as through breaches in the building's envelope.
Almost all historic buildings were ventilated naturally. [ 16 ] The technique was generally abandoned in larger US buildings during the late 20th century as the use of air conditioning became more widespread. However, with the advent of advanced Building Performance Simulation (BPS) software, improved Building Automation Systems (BAS), Leadership in Energy and Environmental Design (LEED) design requirements, and improved window manufacturing techniques; natural ventilation has made a resurgence in commercial buildings both globally and throughout the US. [ 17 ]
The benefits of natural ventilation include:
Techniques and architectural features used to ventilate buildings and structures naturally include, but are not limited to:
Natural ventilation is a key factor in reducing the spread of airborne illnesses such as tuberculosis, the common cold, influenza, meningitis or COVID-19. [ 18 ] Opening doors and windows are good ways to maximize natural ventilation, which would make the risk of airborne contagion much lower than with costly and maintenance-requiring mechanical systems. Old-fashioned clinical areas with high ceilings and large windows provide the greatest protection. Natural ventilation costs little and is maintenance-free, and is particularly suited to limited-resource settings and tropical climates, where the burden of TB and institutional TB transmission is highest. In settings where respiratory isolation is difficult and climate permits, windows and doors should be opened to reduce the risk of airborne contagion. Natural ventilation requires little maintenance and is inexpensive. [ 19 ]
Natural ventilation is not practical in much of the infrastructure because of climate. This means that the facilities need to have effective mechanical ventilation systems and or use Ceiling Level UV or FAR UV ventilation systems.
Ventilation is measured in terms of air changes per hour (ACH). As of 2023 [update] , the CDC recommends that all spaces have a minimum of 5 ACH. [ 20 ] For hospital rooms with airborne contagions the CDC recommends a minimum of 12 ACH. [ 21 ] Challenges in facility ventilation are public unawareness, [ 22 ] [ 23 ] ineffective government oversight, poor building codes that are based on comfort levels, poor system operations, poor maintenance, and lack of transparency. [ 24 ]
Pressure, both political and economic, to improve energy conservation has led to decreased ventilation rates. Heating, ventilation, and air conditioning rates have dropped since the energy crisis in the 1970s and the banning of cigarette smoke in the 1980s and 1990s. [ 25 ] [ 26 ] [ better source needed ]
Mechanical ventilation of buildings and structures can be achieved by the use of the following techniques:
Demand-controlled ventilation ( DCV , also known as Demand Control Ventilation) makes it possible to maintain air quality while conserving energy. [ 27 ] [ 28 ] ASHRAE has determined that "It is consistent with the ventilation rate procedure that demand control be permitted for use to reduce the total outdoor air supply during periods of less occupancy." [ 29 ] In a DCV system, CO 2 sensors control the amount of ventilation. [ 30 ] [ 31 ] During peak occupancy, CO 2 levels rise, and the system adjusts to deliver the same amount of outdoor air as would be used by the ventilation-rate procedure. [ 32 ] However, when spaces are less occupied, CO 2 levels reduce, and the system reduces ventilation to conserves energy. DCV is a well-established practice, [ 33 ] and is required in high occupancy spaces by building energy standards such as ASHRAE 90.1 . [ 34 ]
Personalized ventilation is an air distribution strategy that allows individuals to control the amount of ventilation received. The approach delivers fresh air more directly to the breathing zone and aims to improve the air quality of inhaled air. Personalized ventilation provides much higher ventilation effectiveness than conventional mixing ventilation systems by displacing pollution from the breathing zone with far less air volume. Beyond improved air quality benefits, the strategy can also improve occupants' thermal comfort, perceived air quality, and overall satisfaction with the indoor environment. Individuals' preferences for temperature and air movement are not equal, and so traditional approaches to homogeneous environmental control have failed to achieve high occupant satisfaction. Techniques such as personalized ventilation facilitate control of a more diverse thermal environment that can improve thermal satisfaction for most occupants.
Local exhaust ventilation addresses the issue of avoiding the contamination of indoor air by specific high-emission sources by capturing airborne contaminants before they are spread into the environment. This can include water vapor control, lavatory effluent control, solvent vapors from industrial processes, and dust from wood- and metal-working machinery. Air can be exhausted through pressurized hoods or the use of fans and pressurizing a specific area. [ 35 ] A local exhaust system is composed of five basic parts:
In the UK, the use of LEV systems has regulations set out by the Health and Safety Executive (HSE) which are referred to as the Control of Substances Hazardous to Health ( CoSHH ). Under CoSHH, legislation is set to protect users of LEV systems by ensuring that all equipment is tested at least every fourteen months to ensure the LEV systems are performing adequately. All parts of the system must be visually inspected and thoroughly tested and where any parts are found to be defective, the inspector must issue a red label to identify the defective part and the issue.
The owner of the LEV system must then have the defective parts repaired or replaced before the system can be used.
Smart ventilation is a process of continually adjusting the ventilation system in time, and optionally by location, to provide the desired IAQ benefits while minimizing energy consumption, utility bills, and other non-IAQ costs (such as thermal discomfort or noise).
A smart ventilation system adjusts ventilation rates in time or by location in a building to be responsive to one or more of the following: occupancy, outdoor thermal and air quality conditions, electricity grid needs, direct sensing of contaminants, operation of other air moving and air cleaning systems. In addition, smart ventilation systems can provide information to building owners, occupants, and managers on operational energy consumption and indoor air quality as well as a signal when systems need maintenance or repair.
Being responsive to occupancy means that a smart ventilation system can adjust ventilation depending on demand such as reducing ventilation if the building is unoccupied. Smart ventilation can time-shift ventilation to periods when a) indoor-outdoor temperature differences are smaller (and away from peak outdoor temperatures and humidity), b) when indoor-outdoor temperatures are appropriate for ventilative cooling, or c) when outdoor air quality is acceptable.
Being responsive to electricity grid needs means providing flexibility to electricity demand (including direct signals from utilities) and integration with electric grid control strategies.
Smart ventilation systems can have sensors to detect airflow, systems pressures, or fan energy use in such a way that systems failures can be detected and repaired, as well as when system components need maintenance, such as filter replacement. [ 36 ]
Combustion (in a fireplace , gas heater , candle , oil lamp , etc.) consumes oxygen while producing carbon dioxide and other unhealthy gases and smoke , requiring ventilation air. An open chimney promotes infiltration (i.e. natural ventilation) because of the negative pressure change induced by the buoyant , warmer air leaving through the chimney. The warm air is typically replaced by heavier, cold air.
Ventilation in a structure is also needed for removing water vapor produced by respiration , burning, and cooking , and for removing odors. If water vapor is permitted to accumulate, it may damage the structure, insulation , or finishes. [ citation needed ] When operating, an air conditioner usually removes excess moisture from the air. A dehumidifier may also be appropriate for removing airborne moisture.
Ventilation guidelines are based on the minimum ventilation rate required to maintain acceptable levels of effluents. Carbon dioxide is used as a reference point, as it is the gas of highest emission at a relatively constant value of 0.005 L/s. The mass balance equation is:
Q = G/ (C i − C a )
ASHRAE standard 62 states that air removed from an area with environmental tobacco smoke shall not be recirculated into ETS-free air. A space with ETS requires more ventilation to achieve similar perceived air quality to that of a non-smoking environment.
The amount of ventilation in an ETS area is equal to the amount of an ETS-free area plus the amount V, where:
V = DSD × VA × A/60E
Primitive ventilation systems were found at the Pločnik archeological site (belonging to the Vinča culture ) in Serbia and were built into early copper smelting furnaces. The furnace, built on the outside of the workshop, featured earthen pipe-like air vents with hundreds of tiny holes in them and a prototype chimney to ensure air goes into the furnace to feed the fire and smoke comes out safely. [ 39 ]
Passive ventilation and passive cooling systems were widely written about around the Mediterranean by Classical times. Both sources of heat and sources of cooling (such as fountains and subterranean heat reservoirs) were used to drive air circulation, and buildings were designed to encourage or exclude drafts, according to climate and function. Public bathhouses were often particularly sophisticated in their heating and cooling. Icehouses are some millennia old, and were part of a well-developed ice industry by classical times.
The development of forced ventilation was spurred by the common belief in the late 18th and early 19th century in the miasma theory of disease , where stagnant 'airs' were thought to spread illness. An early method of ventilation was the use of a ventilating fire near an air vent which would forcibly cause the air in the building to circulate. English engineer John Theophilus Desaguliers provided an early example of this when he installed ventilating fires in the air tubes on the roof of the House of Commons . Starting with the Covent Garden Theatre , gas burning chandeliers on the ceiling were often specially designed to perform a ventilating role.
A more sophisticated system involving the use of mechanical equipment to circulate the air was developed in the mid-19th century. A basic system of bellows was put in place to ventilate Newgate Prison and outlying buildings, by the engineer Stephen Hales in the mid-1700s. The problem with these early devices was that they required constant human labor to operate. David Boswell Reid was called to testify before a Parliamentary committee on proposed architectural designs for the new House of Commons , after the old one burned down in a fire in 1834. [ 40 ] In January 1840 Reid was appointed by the committee for the House of Lords dealing with the construction of the replacement for the Houses of Parliament. The post was in the capacity of ventilation engineer, in effect; and with its creation there began a long series of quarrels between Reid and Charles Barry , the architect. [ 42 ]
Reid advocated the installation of a very advanced ventilation system in the new House. His design had air being drawn into an underground chamber, where it would undergo either heating or cooling. It would then ascend into the chamber through thousands of small holes drilled into the floor, and would be extracted through the ceiling by a special ventilation fire within a great stack. [ 43 ]
Reid's reputation was made by his work in Westminster. He was commissioned for an air quality survey in 1837 by the Leeds and Selby Railway in their tunnel. [ 44 ] The steam vessels built for the Niger expedition of 1841 were fitted with ventilation systems based on Reid's Westminster model. [ 45 ] Air was dried, filtered and passed over charcoal. [ 46 ] [ 47 ] Reid's ventilation method was also applied more fully to St. George's Hall, Liverpool , where the architect, Harvey Lonsdale Elmes , requested that Reid should be involved in ventilation design. [ 48 ] Reid considered this the only building in which his system was completely carried out. [ 49 ]
With the advent of practical steam power , ceiling fans could finally be used for ventilation. Reid installed four steam-powered fans in the ceiling of St George's Hospital in Liverpool , so that the pressure produced by the fans would force the incoming air upward and through vents in the ceiling. Reid's pioneering work provides the basis for ventilation systems to this day. [ 43 ] He was remembered as "Dr. Reid the ventilator" in the twenty-first century in discussions of energy efficiency , by Lord Wade of Chorlton . [ 50 ]
Ventilating a space with fresh air aims to avoid "bad air". The study of what constitutes bad air dates back to the 1600s when the scientist Mayow studied asphyxia of animals in confined bottles. [ 51 ] The poisonous component of air was later identified as carbon dioxide (CO 2 ), by Lavoisier in the very late 1700s, starting a debate as to the nature of "bad air" which humans perceive to be stuffy or unpleasant. Early hypotheses included excess concentrations of CO 2 and oxygen depletion . However, by the late 1800s, scientists thought biological contamination, not oxygen or CO 2 , was the primary component of unacceptable indoor air. However, it was noted as early as 1872 that CO 2 concentration closely correlates to perceived air quality.
The first estimate of minimum ventilation rates was developed by Tredgold in 1836. [ 52 ] This was followed by subsequent studies on the topic by Billings [ 53 ] in 1886 and Flugge in 1905. The recommendations of Billings and Flugge were incorporated into numerous building codes from 1900–the 1920s and published as an industry standard by ASHVE (the predecessor to ASHRAE ) in 1914. [ 51 ]
The study continued into the varied effects of thermal comfort , oxygen, carbon dioxide, and biological contaminants. The research was conducted with human subjects in controlled test chambers. Two studies, published between 1909 and 1911, showed that carbon dioxide was not the offending component. Subjects remained satisfied in chambers with high levels of CO 2 , so long as the chamber remained cool. [ 51 ] (Subsequently, it has been determined that CO 2 is, in fact, harmful at concentrations over 50,000ppm [ 54 ] )
ASHVE began a robust research effort in 1919. By 1935, ASHVE-funded research conducted by Lemberg, Brandt, and Morse – again using human subjects in test chambers – suggested the primary component of "bad air" was an odor, perceived by the human olfactory nerves. [ 55 ] Human response to odor was found to be logarithmic to contaminant concentrations, and related to temperature. At lower, more comfortable temperatures, lower ventilation rates were satisfactory. A 1936 human test chamber study by Yaglou, Riley, and Coggins culminated much of this effort, considering odor, room volume, occupant age, cooling equipment effects, and recirculated air implications, which guided ventilation rates. [ 56 ] The Yagle research has been validated, and adopted into industry standards, beginning with the ASA code in 1946. From this research base, ASHRAE (having replaced ASHVE) developed space-by-space recommendations, and published them as ASHRAE Standard 62-1975: Ventilation for acceptable indoor air quality.
As more architecture incorporated mechanical ventilation, the cost of outdoor air ventilation came under some scrutiny. In 1973, in response to the 1973 oil crisis and conservation concerns, ASHRAE Standards 62-73 and 62–81) reduced required ventilation from 10 CFM (4.76 L/s) per person to 5 CFM (2.37 L/s) per person. In cold, warm, humid, or dusty climates, it is preferable to minimize ventilation with outdoor air to conserve energy, cost, or filtration. This critique (e.g. Tiller [ 57 ] ) led ASHRAE to reduce outdoor ventilation rates in 1981, particularly in non-smoking areas. However subsequent research by Fanger, [ 58 ] W. Cain, and Janssen validated the Yagle model. The reduced ventilation rates were found to be a contributing factor to sick building syndrome . [ 59 ]
The 1989 ASHRAE standard (Standard 62–89) states that appropriate ventilation guidelines are 20 CFM (9.2 L/s) per person in an office building, and 15 CFM (7.1 L/s) per person for schools, while 2004 Standard 62.1-2004 has lower recommendations again (see tables below). ANSI/ASHRAE (Standard 62–89) speculated that "comfort (odor) criteria are likely to be satisfied if the ventilation rate is set so that 1,000 ppm CO 2 is not exceeded" [ 60 ] while OSHA has set a limit of 5000 ppm over 8 hours. [ 61 ]
ASHRAE continues to publish space-by-space ventilation rate recommendations, which are decided by a consensus committee of industry experts. The modern descendants of ASHRAE standard 62-1975 are ASHRAE Standard 62.1, for non-residential spaces, and ASHRAE 62.2 for residences.
In 2004, the calculation method was revised to include both an occupant-based contamination component and an area–based contamination component. [ 62 ] These two components are additive, to arrive at an overall ventilation rate. The change was made to recognize that densely populated areas were sometimes overventilated (leading to higher energy and cost) using a per-person methodology.
Occupant Based Ventilation Rates , [ 62 ] ANSI/ASHRAE Standard 62.1-2004
Area-based ventilation rates , [ 62 ] ANSI/ASHRAE Standard 62.1-2004
The addition of occupant- and area-based ventilation rates found in the tables above often results in significantly reduced rates compared to the former standard. This is compensated in other sections of the standard which require that this minimum amount of air is delivered to the breathing zone of the individual occupant at all times. The total outdoor air intake of the ventilation system (in multiple-zone variable air volume (VAV) systems) might therefore be similar to the airflow required by the 1989 standard. From 1999 to 2010, there was considerable development of the application protocol for ventilation rates. These advancements address occupant- and process-based ventilation rates, room ventilation effectiveness, and system ventilation effectiveness [ 63 ]
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In kinesiology , the ventilatory threshold (VT1) refers to the point during exercise at which the volume of air breathed out (expiratory ventilation ) starts to increase at an exponentially greater rate than VO 2 (breath-by-breath volume of oxygen (O 2 )). [ 1 ] VT1 is thought to reflect a person's anaerobic threshold — the point at which the oxygen supplied to the muscles no longer meets its oxygen requirements at a given work rate — and therefore lactate threshold — the point at which lactate begins to accumulate in the blood, because with ongoing dependence on anaerobic glycolysis, increasing amounts of CO2 need to be exhaled to accommodate its production during the conversion of lactic acid to lactate. [ 1 ]
As the intensity level of the activity being performed increases, breathing becomes faster; more steadily first and then more rapid as the intensity increases. When breathing surpasses normal ventilation rate, one has reached ventilatory threshold. For most people this threshold lies at exercise intensities between 50% and 75% of VO 2 max. A major factor affecting one's ventilatory threshold is their maximal ventilation (amount of air entering and exiting lungs). This is dependent on their personal experience with the activity and how physically fit the person is. Comparison studies of more athletic people have shown that your ventilatory threshold occurs at a higher intensity if you are more active or have been training for that exercise; although, in some cases shorter continuous tests can be used because of rapid alterations in ventilation.
Frangolias DD,
Rhodes EC
School of Human Kinetics, University of British Columbia, Vancouver, Canada.
Medicine and Science in Sports and Exercise [1995, 27(7):1007-1013]:
A government experiment to test ventilatory threshold was held between November and December 2004. Subjects included 32 physically active males (age: 22.3; TV: 180.5; TM: 75.5 kg; VO2max: 57.1 mL/kg/min) encountered a continuous test of increasing loads on a treadmill, cardiorespiratory and other variables were observed using ECG (recording of the electrical activity of the heart) and gas analyzer. During the test, subjects were asked to point at a scale from 6 to 20 reflecting their feeling of discomfort. The RPE threshold was recorded as constant value of 12-13. Averages of ventilatory and RPE threshold were conveyed by parameters that were monitored and then compared by using t-test for dependent samples. No significant difference was found between mean values of ventilatory and RPE threshold, when they were expressed by parameters such as: speed, load, heart rate, absolute and relative oxygen consumption. The conclusion of this experiment was: the fixed value (12-13) of RPE scale may be used to detect the exercise intensity that corresponds to ventilatory threshold.
Maximum oxygen intake, VO 2 , is one of the best measures of cardiovascular fitness and maximal aerobic power. VO 2 max averages around 35–40 mL/(kg∙ min) in a healthy male and 27–31 mL/ (kg∙ min) in a healthy female. These scores can improve with training. Factors that affect your VO 2 max are age, sex, fitness, training, and genetics. While scores in the upper 80s and 90s have been recorded by legendary endurance athletes such as Greg Lemond , Miguel Indurain , and Steve Prefontaine , most competitive endurance athletes have scores in the mid to high 60s. Cycling, rowing, swimming and running are some of the main sports that push VO 2 levels to the maximum. Ventilatory threshold and lactate threshold are expressed as a percentage of VO 2 max; beyond this percentage the ability to sustain the work rate rapidly declines as high intensity but short duration energy systems such as glycolysis and ATP-PC are relied on more heavily.
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Ventricose is an adjective describing the condition of a mushroom, gastropod or plant that it is "swollen, distended, or inflated especially on one side". [ 1 ]
In mycology , ventricose is a condition in which the cystidia , lamella or stipe of a mushroom is swollen in the middle.
In gastropods, if the shell of a snail is ventricose or subventricose , it means the whorl of the shell is swollen.
This Basidiomycota -related article is a stub . You can help Wikipedia by expanding it .
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Venturi Transport Protocol ( VTP ) is a patented proprietary transport layer protocol that is designed to transparently replace TCP in order to overcome inefficiencies [ which? ] in the design of TCP related to wireless data transport. It is owned by Venturi Wireless .
The protocol is employed by various wireless broadband internet service providers such as Verizon Wireless and Unwired (Unwired calls the Venturi Client application that provides transparent VTP connectivity the Unwired Optimizer) in order to speed up their network and to overcome latency issues.
U.S. patent 6115384A
This computer networking article is a stub . You can help Wikipedia by expanding it .
This article about wireless technology is a stub . You can help Wikipedia by expanding it .
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The Venturi effect is the reduction in fluid pressure that results when a moving fluid speeds up as it flows from one section of a pipe to a smaller section. The Venturi effect is named after its discoverer, the Italian physicist Giovanni Battista Venturi , and was first published in 1797.
The effect has various engineering applications, as the reduction in pressure inside the constriction can be used both for measuring the fluid flow and for moving other fluids (e.g. in a vacuum ejector ).
In inviscid fluid dynamics , an incompressible fluid's velocity must increase as it passes through a constriction in accord with the principle of mass continuity , while its static pressure must decrease in accord with the principle of conservation of mechanical energy ( Bernoulli's principle ) or according to the Euler equations . Thus, any gain in kinetic energy a fluid may attain by its increased velocity through a constriction is balanced by a drop in pressure because of its loss in potential energy .
By measuring the pressure difference without needing to measure the actual pressures at the two points, the flow rate can be determined, as in various flow measurement devices such as Venturi meters, Venturi nozzles and orifice plates .
Referring to the adjacent diagram, using Bernoulli's equation in the special case of steady, incompressible, inviscid flows (such as the flow of water or other liquid, or low-speed flow of gas) along a streamline, the theoretical static pressure drop at the constriction is given by
p 1 − p 2 = ρ 2 ( v 2 2 − v 1 2 ) , {\displaystyle p_{1}-p_{2}={\frac {\rho }{2}}(v_{2}^{2}-v_{1}^{2}),}
where ρ {\displaystyle \rho } is the density of the fluid, v 1 {\displaystyle v_{1}} is the (slower) fluid velocity where the pipe is wider, and v 2 {\displaystyle v_{2}} is the (faster) fluid velocity where the pipe is narrower (as seen in the figure). The static pressure at each position is measured using a small tube either outside and ending at the wall or into the pipe with the small tube end face parallel with the flow direction.
The limiting case of the Venturi effect is when a fluid reaches the state of choked flow , where the fluid velocity approaches the local speed of sound of the fluid. When a fluid system is in a state of choked flow, a further decrease in the downstream pressure environment will not lead to an increase in velocity, unless the fluid is compressed.
The mass flow rate for a compressible fluid will increase with increased upstream pressure, which will increase the density of the fluid through the constriction (though the velocity will remain constant). This is the principle of operation of a de Laval nozzle . Increasing source temperature will also increase the local sonic velocity, thus allowing increased mass flow rate, but only if the nozzle area is also increased to compensate for the resulting decrease in density.
The Bernoulli equation is invertible, and pressure should rise when a fluid slows down. Nevertheless, if there is a shortened expansion in the tube section, turbulence is more likely to appear, and the theorem will not hold. Generally in Venturi tubes, the pressure in the entrance is compared to the pressure in the middle section and the output section is never compared with them.
The simplest apparatus is a tubular setup known as a Venturi tube or simply a Venturi (plural: "Venturis" or occasionally "Venturies"). Fluid flows through a length of pipe of varying diameter. To avoid undue aerodynamic drag , a Venturi tube typically has an entry cone of 30 degrees and an exit cone of 5 degrees. [ 1 ]
Venturi tubes are often used in processes where permanent pressure loss is not tolerable and where maximum accuracy is needed in case of highly viscous liquids. [ citation needed ]
Venturi tubes are more expensive to construct than simple orifice plates , and both function on the same basic principle. However, for any given differential pressure, orifice plates cause significantly more permanent energy loss. [ 2 ]
Both Venturi tubes and orifice plates are used in industrial applications and in scientific laboratories for measuring the flow rate of liquids.
A Venturi can be used to measure the volumetric flow rate , Q {\displaystyle \scriptstyle Q} , using Bernoulli's principle .
Since Q = v 1 A 1 = v 2 A 2 p 1 − p 2 = ρ 2 ( v 2 2 − v 1 2 ) {\displaystyle {\begin{aligned}Q&=v_{1}A_{1}=v_{2}A_{2}\\[3pt]p_{1}-p_{2}&={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)\end{aligned}}}
then Q = A 1 2 ρ ⋅ p 1 − p 2 ( A 1 A 2 ) 2 − 1 = A 2 2 ρ ⋅ p 1 − p 2 1 − ( A 2 A 1 ) 2 {\displaystyle Q=A_{1}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1}}}}=A_{2}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{1-\left({\frac {A_{2}}{A_{1}}}\right)^{2}}}}}} A Venturi can also be used to mix a liquid with a gas. If a pump forces the liquid through a tube connected to a system consisting of a Venturi to increase the liquid speed (the diameter decreases), a short piece of tube with a small hole in it, and last a Venturi that decreases speed (so the pipe gets wider again), the gas will be sucked in through the small hole because of changes in pressure. At the end of the system, a mixture of liquid and gas will appear. See aspirator and pressure head for discussion of this type of siphon .
As fluid flows through a Venturi, the expansion and compression of the fluids cause the pressure inside the Venturi to change. This principle can be used in metrology for gauges calibrated for differential pressures. This type of pressure measurement may be more convenient, for example, to measure fuel or combustion pressures in jet or rocket engines.
The first large-scale Venturi meters to measure liquid flows were developed by Clemens Herschel who used them to measure small and large flows of water and wastewater beginning at the end of the 19th century. [ 3 ] While working for the Holyoke Water Power Company , Herschel would develop the means for measuring these flows to determine the water power consumption of different mills on the Holyoke Canal System , first beginning development of the device in 1886, two years later he would describe his invention of the Venturi meter to William Unwin in a letter dated June 5, 1888. [ 4 ]
Fundamentally, pressure-based meters measure kinetic energy density. Bernoulli's equation (used above) relates this to mass density and volumetric flow:
Δ P = 1 2 ρ ( v 2 2 − v 1 2 ) = 1 2 ρ ( ( A 1 A 2 ) 2 − 1 ) v 1 2 = 1 2 ρ ( 1 A 2 2 − 1 A 1 2 ) Q 2 = k ρ Q 2 {\displaystyle \Delta P={\frac {1}{2}}\rho (v_{2}^{2}-v_{1}^{2})={\frac {1}{2}}\rho \left(\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1\right)v_{1}^{2}={\frac {1}{2}}\rho \left({\frac {1}{A_{2}^{2}}}-{\frac {1}{A_{1}^{2}}}\right)Q^{2}=k\,\rho \,Q^{2}}
where constant terms are absorbed into k . Using the definitions of density ( m = ρ V {\displaystyle m=\rho V} ), molar concentration ( n = C V {\displaystyle n=CV} ), and molar mass ( m = M n {\displaystyle m=Mn} ), one can also derive mass flow or molar flow (i.e. standard volume flow):
Δ P = k ρ Q 2 = k 1 ρ m ˙ 2 = k ρ C 2 n ˙ 2 = k M C n ˙ 2 . {\displaystyle {\begin{aligned}\Delta P&=k\,\rho \,Q^{2}\\&=k{\frac {1}{\rho }}\,{\dot {m}}^{2}\\&=k{\frac {\rho }{C^{2}}}\,{\dot {n}}^{2}=k{\frac {M}{C}}\,{\dot {n}}^{2}.\end{aligned}}}
However, measurements outside the design point must compensate for the effects of temperature, pressure, and molar mass on density and concentration. The ideal gas law is used to relate actual values to design values :
C = P R T = ( P P ⊖ ) ( T T ⊖ ) C ⊖ {\displaystyle C={\frac {P}{RT}}={\frac {\left({\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}C^{\ominus }} ρ = M P R T = ( M M ⊖ P P ⊖ ) ( T T ⊖ ) ρ ⊖ . {\displaystyle \rho ={\frac {MP}{RT}}={\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }.}
Substituting these two relations into the pressure-flow equations above yields the fully compensated flows:
Δ P = k ( M M ⊖ P P ⊖ ) ( T T ⊖ ) ρ ⊖ Q 2 = Δ P max ( M M ⊖ P P ⊖ ) ( T T ⊖ ) ( Q Q max ) 2 = k ( T T ⊖ ) ( M M ⊖ P P ⊖ ) ρ ⊖ m ˙ 2 = Δ P max ( T T ⊖ ) ( M M ⊖ P P ⊖ ) ( m ˙ m ˙ max ) 2 = k M ( T T ⊖ ) ( P P ⊖ ) C ⊖ n ˙ 2 = Δ P max ( M M ⊖ T T ⊖ ) ( P P ⊖ ) ( n ˙ n ˙ max ) 2 . {\displaystyle {\begin{aligned}\Delta P&=k{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }\,Q^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\left({\frac {Q}{Q_{\max }}}\right)^{2}\\&=k{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)\rho ^{\ominus }}}{\dot {m}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {m}}{{\dot {m}}_{\max }}}\right)^{2}\\&=k{\frac {M\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)C^{\ominus }}}{\dot {n}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {n}}{{\dot {n}}_{\max }}}\right)^{2}.\end{aligned}}}
Q , m , or n are easily isolated by dividing and taking the square root . Note that pressure-, temperature-, and mass-compensation is required for every flow, regardless of the end units or dimensions. Also we see the relations:
k Δ P max = 1 ρ ⊖ Q max 2 = ρ ⊖ m ˙ max 2 = C ⊖ 2 ρ ⊖ n ˙ max 2 = C ⊖ M ⊖ n ˙ max 2 . {\displaystyle {\begin{aligned}{\frac {k}{\Delta P_{\max }}}&={\frac {1}{\rho ^{\ominus }Q_{\max }^{2}}}\\&={\frac {\rho ^{\ominus }}{{\dot {m}}_{\max }^{2}}}\\&={\frac {{C^{\ominus }}^{2}}{\rho ^{\ominus }{\dot {n}}_{\max }^{2}}}={\frac {C^{\ominus }}{M^{\ominus }{\dot {n}}_{\max }^{2}}}.\end{aligned}}}
The Venturi effect may be observed or used in the following:
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In hydrology , a Venturi flume is a device used for measuring the rate of flow of a liquid in situations with large flow rates, such as a river. [ 1 ] It is based on the Venturi effect , for which it is named. [ 2 ] It was first developed by V.M. Cone in Fort Collins, Colorado . [ 3 ]
The Venturi flume consists of a flume with a constricted section in the center. By the Venturi effect, this causes a drop in the fluid pressure at the center of the constriction. By comparing the fluid pressure at the center of the flume with that earlier in the device, the rate of flow can be measured. [ 4 ] [ 5 ]
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The Venus Spectral Rocket Experiment ( VeSpR ) was a suborbital rocket telescope that collected data on the ultraviolet (UV) light that is being emitted from Venus's atmosphere, which can provide information about the history of water on Venus . [ 3 ] [ 4 ] Measurements of this type cannot be done using Earth-based telescopes because Earth's atmosphere absorbs most UV light before it reaches the ground. [ 3 ]
The Venus Spectral Rocket Experiment (VeSpR) collected data on 27 November 2013, on the escape of water from Venus' atmosphere during the flight of the suborbital rocket. The sounding rocket carried the telescope above most of Earth's atmosphere where it could observe ultraviolet light from Venus that would normally be absorbed by Earth's atmosphere. Total flight time was less than 10 minutes, [ 1 ] and the telescope can be recovered and reused. [ 1 ]
VeSpR is a two-stage system, combining a Terrier missile – originally built as a surface-to-air missile and later repurposed to support science missions – and a Black Brant model Mk1 sounding rocket with a telescope inside developed by the Center for Space Physics at Boston University . [ 3 ] Integration took place at NASA's Wallops Flight Facility in Virginia.
The Terrier stage fires for only 6 seconds after launch before it burns out and separates from the Mk 1, having accelerating from zero to 2100 km/h (1300 mph). [ 2 ] The Black Brant coasts upward for 6 seconds, before firing for about 30 seconds, taking the payload to a speed of over 7800 km/h (4800 mph). At that point the rocket is 46 km high, but it already has enough speed to coast upward for almost four more minutes, reaching its peak of 300 km (186 miles) before starting its descent back to Earth. [ 2 ] The payload made its final descent with a parachute and touch down about 80 km (50 miles) downrange of the launch site, where it can be recovered.
The upper atmospheres of all three terrestrial planets are slowly evaporating into space, with the highest loss rate for the lightest atom, hydrogen . At Venus, solar UV radiation penetrates into the middle atmosphere, where photodissociation of H 2 O by solar UV radiation releases H and O, which diffuse into the upper atmosphere and eventually reach the exobase. [ 5 ] The H atoms may be lost into space, while relatively fewer O atoms escape, mainly due to non-thermal processes. Understanding the details of escape today is a requirement to be able to extrapolate into the past to learn the history of Venusian water. [ 5 ]
The atmosphere of Venus is known to have undergone substantial evolution over geologic time. [ 5 ] Evidence for this includes the present remarkable contrast between Venus’ atmosphere and the Earth's: Venus has very little water, a 95% CO 2 atmosphere, a surface temperature of 750 K, and a surface pressure of 90 bar. The early Venusian atmosphere is thought to have undergone either a moist or runaway greenhouse heating episode to produce these conditions, and this would have included hydrodynamic escape of light gases from the upper atmosphere to deplete possibly as much as an ocean of water. Support for this scenario comes from the measured ratio of D/H in Venus' atmosphere of roughly 1.6% from the Pioneer Venus mass spectrometer , orbiting ion mass spectrometer (OIMS) data, and IR spectra of the night-side atmosphere. This large enhancement over cosmic abundances is consistent with the loss of an ocean's worth of H 2 O over geologic time. [ 5 ]
The VeSpR telescope is a special-purpose Cassegrain design to accomplish observations that other missions are not able to perform. [ 4 ] The use of a pre-dispersing prism to prevent long wavelengths from entering the spectrograph permits a long-aperture approach to echelle spectroscopy , and the chosen combination of imaging and dispersion scales provides high spectral resolution of emission line profiles with a several arc sec wide aperture for good sensitivity. For comparable spectral resolution the HST/ STIS uses a 0.2 arc sec aperture, which provides 375 times less solid angle on the sky than a 3 x 5 arc sec region observed by this rocket telescope. For comparison, the ratio of telescope areas HST/rocket is roughly 50 times. With equivalent efficiencies, Hubble Space Telescope would need 4 hours of observing time to achieve the same S/N that the rocket obtains in 5 minutes. [ 4 ] However, Hubble telescope is not allowed to point too close to the Sun to avoid damaging its instruments, so it cannot be used for this. [ 2 ]
The VeSpR telescope is a Cassegrain design with a Dall-Kirkham figure, and with a 35 cm diameter ellipsoidal primary and a spherical secondary mirror providing 1–2 arc sec image quality within a few arc min of the optic axis. [ 4 ] The telescope delivers a f/21 beam to the focal plane with a plate scale of 26 arc sec/mm. The spectrograph has been designed and constructed for UV echelle line profile measurements with long-slit imaging. The Ebert-Fastie configuration employed in the design of the spectrograph has many characteristics well suited to the science needs of this mission. Symmetric off-axis reflections from a single collimating mirror are employed to remove aberrations: the spatial resolution is limited by the telescope and the spectral resolution by the grating and aperture characteristics. [ 4 ]
Use of a paraboloidal collimator, has produced 2 arc sec image quality with minimal astigmatism along the central 2–3 arc min. A 2 deg. magnesium fluoride (MgF 2 ) objective prism mounted forward of the aperture plate is used to disperse the converging beam from the telescope: with the 1216 Å image focused onto the primary aperture, other wavelengths are excluded from the spectrograph producing a very low level of scattered light on the detector. [ 4 ]
The spectrograph uses a replica of a prototype grating for the Hubble Space Telescope STIS. [ 4 ] For a 5 arc sec aperture width, the measured resolution in the last flight was 0.055 Å FWHM. A camera is included to re-image the focal plane onto a separate detector, providing an image of the telescope field of view minus the light which passes through the spectrograph aperture. The Venus image on the aperture plate will be sufficiently dispersed by the objective prism that the Ly α image will be clearly separated from the longer wavelength continuum and emissions. [ 4 ]
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Venus , as one of the brightest objects in the sky, has been known since prehistoric times and has been a major fixture in human culture for as long as records have existed. As such, it has a prominent position in human culture , religion , and myth . It has been made sacred to gods of many cultures, and has been a prime inspiration for writers and poets as the morning star and evening star . [ 1 ]
What is now known as the planet Venus has long been an object of fascination for cultures worldwide. It is the second brightest object in the night sky, and follows a synodic cycle by which it seems to disappear for several days due to its proximity to the Sun , then re-appear on the opposite side of the Sun and on the other horizon. Depending on the point in its cycle, Venus may appear before sunrise in the morning, or after sunset in the evening, but it never appears to reach the apex of the sky. Therefore, many cultures have recognized it with two names, even if their astronomers realized that it was really one object. [ 1 ]
In Old English , the planet was known as morgensteorra (morning star) and æfensteorra (evening star). It was not until the 13th century C.E. that the name "Venus" was adopted for the planet. [ 2 ] It was called Lucifer in classical Latin though the morning star was considered sacred to the goddess Venus. [ 3 ]
In Chinese the planet is called Jīn-xīng (金星), the golden planet of the metal element . It is known as "Kejora" in Indonesian and Malaysian Malay .
Modern Chinese , Japanese and Korean cultures refer to the planet literally as the "gold star" ( 金星 ), based on the Five elements . [ 4 ] [ 5 ] [ 6 ]
Because the movements of Venus appear to be discontinuous (it disappears due to its proximity to the Sun , for many days at a time, and then reappears on the other horizon), some cultures did not recognize Venus as single entity; instead, they assumed it to be two separate stars on each horizon: the morning and evening star. Nonetheless, a cylinder seal from the Jemdet Nasr period indicates that the ancient Sumerians already knew that the morning and evening stars were the same celestial object. The Sumerians associated the planet with the goddess Inanna , who was known as Ishtar by the later Akkadians and Babylonians . [ 7 ] She had a dual role as a goddess of both love and war, thereby representing a deity that presided over birth and death. [ 8 ] [ 9 ]
The discontinuous movements of Venus relate to both Inanna's mythology as well as her dual nature. [ 7 ] [ 10 ] [ 11 ] Inanna's actions in several of her myths, including Inanna and Shukaletuda and Inanna's Descent into the Underworld appear to parallel the motion of the planet Venus as it progresses through its synodic cycle. For example, in Inanna's Descent to the Underworld , Inanna is able to descend into the netherworld, where she is killed, and then resurrected three days later to return to the heavens. An interpretation of this myth by Clyde Hostetter holds that it is an allegory for the movements of the planet Venus, beginning with the spring equinox and concluding with a meteor shower near the end of one synodic period of Venus. The three-day disappearance of Inanna refers to the three-day planetary disappearance of Venus between its appearance as a morning and evening star. [ 12 ] An introductory hymn to this myth describes Inanna leaving the heavens and heading for Kur , what could be presumed to be the mountains, replicating the rising and setting of Inanna to the West. In the myth Inanna and Shukaletuda , Shukaletuda is described as scanning the heavens in search of Inanna, possibly searching the eastern and western horizons. In the same myth, while searching for her attacker, Inanna herself makes several movements that correspond with the movements of Venus in the sky. [ 7 ] Inanna-Ishtar's most common symbol was the eight-pointed star . [ 13 ] The eight-pointed star seems to have originally borne a general association with the heavens, but, by the Old Babylonian Period ( c. 1830 – c. 1531 BC), it had come to be specifically associated with the planet Venus , with which Ishtar was identified. [ 13 ]
In the Old Babylonian period, the planet Venus was known as Ninsi'anna , and later as Dilbat . [ 14 ] " Ninsi'anna" translates to "divine lady, illumination of heaven", which refers to Venus as the brightest visible "star". Earlier spellings of the name were written with the cuneiform sign si4 (= SU, meaning "to be red"), and the original meaning may have been "divine lady of the redness of heaven", in reference to the color of the morning and evening sky. [ 15 ] Venus is described in Babylonian cuneiform texts such as the Venus tablet of Ammisaduqa , which relates observations that possibly date from 1600 BC. [ 16 ] The Venus tablet of Ammisaduqa shows the Babylonians understood morning and evening star were a single object, referred to in the tablet as the "bright queen of the sky" or "bright Queen of Heaven ", and could support this view with detailed observations. [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ] [ 23 ]
In ancient Canaanite religion , the morning star is personified as the god Attar , a masculine variant of the name of the Babylonian goddess Ishtar. [ 24 ] In myth, Attar attempted to occupy the throne of Ba'al and, finding he was unable to do so, descended and ruled the underworld . [ 25 ] [ 26 ] The original myth may have been about a lesser god, Helel , trying to dethrone the Canaanite high god El , who was believed to live on a mountain to the north. [ 27 ] [ 28 ] Hermann Gunkel 's reconstruction of the myth told of a mighty warrior called Hêlal, whose ambition was to ascend higher than all the other stellar divinities, but who had to descend to the depths. It thus portrayed as a battle the process by which the bright morning star fails to reach the highest point in the sky before being faded out by the rising sun. [ 29 ]
Similarities have been noted with the story of Inanna 's descent into the underworld, [ 28 ] Ishtar and Inanna being associated with the planet Venus . [ 30 ] A connection has been seen also with the Babylonian myth of Etana . The Jewish Encyclopedia comments:
In the Hebrew language Book of Isaiah , chapter 14, the King of Babylon is condemned using imagery derived from Canaanite myth, and is called הֵילֵל בֶּן-שָׁחַר ( Helel ben Shachar , Hebrew for "shining one, son of the morning"). [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 36 ] [ 37 ] The title " Helel ben Shahar " may refer to the planet Venus as the morning star. [ 38 ] Helel ben Shahar was cast out of heaven for rebelling against Elion . [ 39 ]
The Ancient Egyptians possibly knew that the morning star ( Tioumoutiri ) and evening star ( Ouaiti ) [ 40 ] were one and the same by the second millennium BC or at the latest by the Later Period under Mesopotamian influence. [ 41 ] [ 42 ] At first described as either a phoenix or heron (or Bennu ), [ 41 ] calling it "the crosser" or "star with crosses", [ 41 ] and associated with Osiris , later during the Late Period under probably Mesopotamian influence Venus was depicted as a two-headed morning god (with human and falcon heads), as in the Dendera zodiac , and associated with Horus , [ 42 ] son of Isis (which during the even later Hellenistic period was together with Hathor identified with Aphrodite ).
The Ancient Greeks called the morning star Φωσφόρος , Phosphoros ( epithet of Hecate ), the "Bringer of Light". Another Greek name for the morning star was Heosphoros ( Greek Ἑωσφόρος Heōsphoros ), meaning "Dawn-Bringer". [ 43 ] They called the evening star, which was long considered a separate celestial object, Hesperos ( Ἓσπερος , the "star of the evening"). [ 44 ] Both were children of dawn Eos and therefore grandchildren of Aphrodite. By Hellenistic times, the ancient Greeks had identified these as a single planet, [ 45 ] [ 46 ] though the traditional use of two names for its appearance in the morning and the evening continued even into the Roman period.
The Greek myth of Phaethon , whose name means "Shining One", has also been seen as similar to those of other gods who cyclically descend from the heavens, like Inanna and Attar. [ 29 ]
In classical mythology, Lucifer ("light-bringer" in Latin) was the name of the planet Venus as the morning star (as the evening star it was called Vesper ), and it was often personified as a male figure bearing a torch. Lucifer was said to be "the fabled son of Aurora [ 3 ] and Cephalus , and father of Ceyx ". He was often presented in poetry as heralding the dawn. [ 47 ]
The Romans considered the planet Lucifer particularly sacred to the goddess Venus , whose name eventually became the scientific name for the planet. The second century Roman mythographer Pseudo-Hyginus said of the planet: [ 48 ]
Ovid , in his first century epic Metamorphoses , describes Lucifer as ordering the heavens: [ 49 ]
In the classical Roman period, Lucifer was not typically regarded as a deity and had few, if any, myths, [ 47 ] though the planet was associated with various deities and often poetically personified. Cicero pointed out that "You say that Sol the Sun and Luna the Moon are deities, and the Greeks identify the former with Apollo and the latter with Diana. But if Luna (the Moon) is a goddess, then Lucifer (the Morning-Star) also and the rest of the Wandering Stars (Stellae Errantes) will have to be counted gods; and if so, then the Fixed Stars (Stellae Inerrantes) as well." [ 50 ]
The Hebrew word transliterated as Hêlêl [ 51 ] or Heylel (pron. as Hay-LALE ), [ 52 ] occurs only once in the Hebrew Bible . [ 51 ] The Septuagint renders הֵילֵל in Greek as Ἑωσφόρος [ 53 ] [ 54 ] [ 55 ] [ 56 ] [ 57 ] ( heōsphoros ), [ 58 ] [ 59 ] [ 60 ] "bringer of dawn", the Ancient Greek name for the morning star. [ 61 ] Aquila of Sinope derives the word hêlêl , the Hebrew name for the morning star, from the verb yalal (to lament). This derivation was adopted as a proper name for an angel who laments the loss of his former beauty. [ 62 ] The Christian church fathers – for example Hieronymus, in his Vulgate – translated this as Lucifer. The equation of Lucifer with the fallen angel probably occurred in 1st century Palestinian Judaism. According to the King James Bible -based Strong's Concordance , the original Hebrew word means "shining one, light-bearer", and the translation given in the King James text is the Latin name for the planet Venus, "Lucifer". [ 52 ] However, the translation of הֵילֵל with the name "Lucifer" has been abandoned in modern English translations of Isaiah 14:12. In a modern translation from the original Hebrew, the passage in which the name Helel ben Shahar occurs begins with the statement: "On the day the Lord gives you relief from your suffering and turmoil and from the harsh labour forced on you, you will take up this taunt against the king of Babylon: How the oppressor has come to an end! How his fury has ended!" [ 63 ] After describing the death of the king, the taunt continues:
This passage was the origin of the later belief that the Devil was a fallen angel, who could also be referred to as "Lucifer". However, it originally referred to the rise and disappearance of the morning star as an allegory for the fall of a once-proud king. This allegorical understanding of Isaiah seems to be the most accepted interpretation in the New Testament , as well as among early Christians such as Origen , Eusebius , Tertullian , and Gregory the Great . The fallen angel motif may therefore be considered a Christian "remythologization" of Isaiah 14, returning its allegorical imagery of the hubris of a historical ruler to the original roots of the Canaanite myth of a lesser god trying and failing to claim the throne of the heavens, who is then cast down to the underworld. [ 65 ]
In Christian tradition the morning star is a symbol for the approaching Son of God and his light-filled appearance in the night of the world ( Epiphany ). Astronomical theories for dating the Star of Bethlehem relate, among other things, to various conjunctions of Venus and Jupiter. [ citation needed ] Sometimes Venus is also identified as the Stella maris , a title of Mary, mother of Jesus of Nazareth . [ citation needed ]
In Vietnamese folklore , the planet was regarded as two separate bodies: the morning star ( sao Mai ) and the evening star ( sao Hôm ). [ 66 ] Due to the position of these supposedly distinct bodies in the sky, they went down in folk poetry as a metaphor for separation, especially that between lovers.
When it was in the opposite direction of the Moon , the planet was also known as sao Vượt (the climbing/passing star, also spelled as sao Vược due to different Quốc ngữ interpretations of one Nôm character). Such an opposition, much like that between the morning star and the evening star, has also been likened in folk poetry to the separation of ill-fated lovers, as evidenced by this lục bát couplet:
In India Shukra Graha ("the planet Shukra") which is named after a powerful saint Shukra. Shukra which is used in Indian Vedic astrology [ 67 ] means "clear, pure" or "brightness, clearness" in Sanskrit . One of the nine Navagraha , it is held to affect wealth, pleasure and reproduction; it was the son of Bhrgu , preceptor of the Daityas, and guru of the Asuras. [ 68 ] The word Shukra is also associated with semen, or generation.
In Iranian mythology, especially in Persian mythology , the planet usually corresponds to the goddess Anahita . In some parts of Pahlavi literature the deities Aredvi Sura and Anahita are regarded as separate entities, the first one as a personification of the mythical river and the latter as a goddess of fertility, which is associated with the planet Venus. As the goddess Aredvi Sura Anahita —and simply called Anahita as well—both deities are unified in other descriptions, e. g. in the Greater Bundahishn , and are represented by the planet. In the Avestan text Mehr Yasht ( Yasht 10 ) there is a possible early link to Mithra . The Persian name of the planet today is "Nahid", which derives from Anahita and later in history from the Pahlavi language Anahid . [ 69 ] [ 70 ] [ 71 ] [ 72 ]
The deity Erkliğ Han (the Powerful) was identified with Venus as a great warrior. He was responsible for killing the stars when the sun rises. [ 73 ] For this reason, he was a symbol for warriors in general. [ 74 ] In the 11th century Turkic Kutadgu Bilig , under cross-cultural influences of Greek and Sumerian mythology, Venus became associated with love, beauty, and fertility. [ 73 ]
In Islamic traditions the morning star is called زُهْرَة , الزُّهَرَة Zohra or Zohrah and commonly related to a "beautiful woman". [ 75 ] According to myth, of which an echo is found in a play by the 17th-century English poet William Percy , two angels, Harut and Marut , descended to earth and were seduced by Zohra's beauty to commit shirk , murder, adultery and drinking wine. In their drunken state, Zohra elicited from these angels the secret words to ascend to heaven. When she spoke the secret words, she elevated herself to the first heaven, but was imprisoned there (i.e. transformed into the planet Venus). [ 76 ]
According to tafsir , some say that the woman literally became the morning star, as a reflection of her ability to blend the angels. Others say that during her ascend she was imprisoned on the planet and is tortured there. [ 77 ]
Venus was considered the most important celestial body observed by the Maya , who called it Chac ek , [ 78 ] or Noh Ek ', "the Great Star". The Maya monitored the movements of Venus closely and observed it in daytime. The positions of Venus and other planets were thought to influence life on Earth, so the Maya and other ancient Mesoamerican cultures timed wars and other important events based on their observations. In the Dresden Codex , the Maya included an almanac showing Venus's full cycle, in five sets of 584 days each (approximately eight years), after which the patterns repeated (since Venus has a synodic period of 583.92 days). [ 79 ]
The Maya civilization developed a religious calendar , based in part upon the motions of the planet, and held the motions of Venus to determine the propitious time for events such as war. They also named it Xux Ek ', the Wasp Star. The Maya were aware of the planet's synodic period, and could compute it to within a hundredth part of a day. [ 80 ]
In traditional Lakota star knowledge, the planet Venus is named Aŋpo Wiŋ or the Light of Dawn (sometimes also translated as Morningstar). It is believed to be a male Nāgī controlling beginnings, fate and all things cyclical. He is also sometimes credited as the father of Star Boy .
The Maasai people named the planet Kileken , and have an oral tradition about it called The Orphan Boy . [ 81 ]
Venus is important in many Australian aboriginal cultures , such as that of the Yolngu people in Northern Australia. The Yolngu gather after sunset to await the rising of Venus, which they call Barnumbirr . As she approaches, in the early hours before dawn, she draws behind her a rope of light attached to the Earth, and along this rope, with the aid of a richly decorated "Morning Star Pole", the people are able to communicate with their dead loved ones, showing that they still love and remember them. Barnumbirr is also an important creator-spirit in the Dreaming , and "sang" much of the country into life. [ 82 ]
Venus plays a prominent role in Pawnee mythology . One specific group of Pawnee , a North American native tribe, until as late as 1838, practiced a morning star ritual in which a girl was sacrificed to the morning star. [ 83 ]
Among the Mapuche of south-central Chile and southwestern Argentina ; the planet or Wünelve ("the First") is believed to have existed when spirits were attempting to ascend back from the World Below or Minchemapu after falling from the Middle World or Rangimapu ; the planet is believed to be an amalgamation of some of those spirits who were stuck on their way. [ 84 ] The planet is an important symbol for this people; it was eventually incorporated into the flag of Chile simplified as a five-pointed star [ 85 ] symbolizing a beacon of progress and honor.
In western astrology , derived from its historical connotation with goddesses of femininity and love, Venus is held to influence desire and sexual fertility. [ 86 ]
In the metaphysical system of Theosophy , it is believed that on the etheric plane of Venus there is a civilization that existed hundreds of millions of years before Earth's [ 87 ] and it is also believed that the governing deity of Earth, Sanat Kumara , is from Venus. [ 88 ]
The discovery in the modern era that Venus was a distant world covered in impenetrable cloud cover gave science fiction writers free rein to speculate on conditions at its surface; all the more so when early observations showed that not only was it similar in size to Earth, it possessed a substantial atmosphere. Closer to the Sun than Earth, the planet was frequently depicted as warmer, but still habitable by humans. [ 89 ] The genre reached its peak between the 1930s and 1950s, at a time when science had revealed some aspects of Venus, but not yet the harsh reality of its surface conditions. Findings from the first missions to Venus showed the reality to be quite different, and brought this particular genre to an end. [ 90 ] As scientific knowledge of Venus advanced, science fiction authors tried to keep pace, particularly by conjecturing human attempts to terraform Venus . [ 91 ]
Scientists who had reported 2020 possible signs of life in the clouds of Venus stated that the found biosignature phosphine is found on Earth and among others produced by penguins . Subsequently some public news reports and public responses wrongly cited the scientists' interest in the processes that create phosphine, suggesting that penguins lived in the clouds of Venus. [ 92 ] The Planetary Society picked up on the misunderstanding for entertainment purposes. [ 93 ]
Solar System → Local Interstellar Cloud → Local Bubble → Gould Belt → Orion Arm → Milky Way → Milky Way subgroup → Local Group → Local Sheet → Virgo Supercluster → Laniakea Supercluster → Local Hole → Observable universe → Universe Each arrow ( → ) may be read as "within" or "part of".
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Planetary symbols are used in astrology and traditionally in astronomy to represent a classical planet (which includes the Sun and the Moon) or one of the modern planets. The classical symbols were also used in alchemy for the seven metals known to the ancients , which were associated with the planets , and in calendars for the seven days of the week associated with the seven planets. The original symbols date to Greco-Roman astronomy ; their modern forms developed in the 16th century, and additional symbols would be created later for newly discovered planets.
The seven classical planets, their symbols, days and most commonly associated planetary metals are:
The International Astronomical Union (IAU) discourages the use of these symbols in modern journal articles, and their style manual proposes one- and two-letter abbreviations for the names of the planets for cases where planetary symbols might be used, such as in the headings of tables. [ 1 ] The modern planets with their traditional symbols and IAU abbreviations are:
The symbols of Venus and Mars are also used to represent female and male in biology following a convention introduced by Carl Linnaeus in the 1750s.
The origins of the planetary symbols can be found in the attributes given to classical deities. The Roman planisphere of Bianchini (2nd century, currently in the Louvre , inv. Ma 540) [ 2 ] shows the seven planets represented by portraits of the seven corresponding gods, each a bust with a halo and an iconic object or dress, as follows: Mercury has a caduceus and a winged cap; Venus has a necklace and a shining mirror; Mars has a war-helmet and a spear; Jupiter has a laurel crown and a staff; Saturn has a conical headdress and a scythe; the Sun has rays emanating from his head; and the Moon has a crescent atop her head.
The written symbols for Mercury, Venus, Jupiter, and Saturn have been traced to forms found in late Greek papyri. [ 3 ] [ b ]
Early forms are also found in medieval Byzantine codices which preserve horoscopes. [ 4 ]
A diagram in the astronomical compendium by Johannes Kamateros (12th century) closely resembles the 11th-century forms shown above, with the Sun represented by a circle with a single ray, Jupiter by the letter zeta (the initial of Zeus , Jupiter's counterpart in Greek mythology), Mars by a round shield in front of a diagonal spear, and the remaining classical planets by symbols resembling the modern ones, though without the crosses seen in modern versions of Mercury, Venus, Jupiter and Saturn. [ citation needed ] These crosses first appear in the late 15th or early 16th century. According to Maunder, the addition of crosses appears to be "an attempt to give a savour of Christianity to the symbols of the old pagan gods." [ 5 ] The modern forms of the classical planetary symbols are found in a woodcut of the seven planets in a Latin translation of Abu Ma'shar al-Balkhi 's De Magnis Coniunctionibus printed at Venice in 1506, represented as the corresponding gods riding chariots. [ 6 ]
Earth is not one of the classical planets, as "planets" by definition were "wandering stars" as seen from Earth's surface.
Earth's status as planet is a consequence of heliocentrism in the 16th century.
Nonetheless, there is a pre-heliocentric symbol for the world, now used as a planetary symbol for the Earth. This is a circle crossed by two lines, horizontal and vertical, representing the world divided by four rivers into the four quarters of the world (often translated as the four "corners" of the world): . A variant, now obsolete, had only the horizontal line: . [ 7 ]
A medieval European symbol for the world – the globus cruciger , (the globe surmounted by a Christian cross ) – is also used as a planetary symbol; it resembles an inverted symbol for Venus.
The planetary symbols for Earth are encoded in Unicode at U+1F728 🜨 ALCHEMICAL SYMBOL FOR VERDIGRIS and U+2641 ♁ EARTH .
The crescent shape has been used to represent the Moon since antiquity. In classical antiquity, it is worn by lunar deities ( Selene/Luna , Artemis/Diana , Men , etc.) either on the head or behind the shoulders, with its horns pointing upward.
The representation of the moon as a simple crescent with the horns pointing to the side (as a heraldic crescent increscent or crescent decrescent ) is attested from late Classical times.
The same symbol can be used in a different context not for the Moon itself but for a lunar phase , as part of a sequence of four symbols
for "new moon" (U+1F311 🌑︎), "waxing" (U+263D ☽︎), "full moon" (U+1F315 🌕︎) and "waning" (U+263E ☾︎).
The symbol ☿ for Mercury is a caduceus (a staff intertwined with two serpents), a symbol associated with Mercury / Hermes throughout antiquity. Some time after the 11th century, a cross was added to the bottom of the staff to make it seem more Christian. [ 3 ]
The ☿ symbol has also been used to indicate intersex , transgender , or non-binary gender . [ 8 ] A related usage is for the 'worker' or 'neuter' sex among social insects that is neither male nor (due to its lack of reproductive capacity) fully female, such as worker bees . [ 9 ] It was also once the designated symbol for hermaphroditic or 'perfect' flowers , [ 10 ] but botanists now use ⚥ for these. [ 11 ]
Its Unicode codepoint is U+263F ☿ MERCURY .
The Venus symbol , ♀, consists of a circle with a small cross below it.
It has been interpreted as a depiction of the hand-mirror of the goddess, which may also explain Venus's association with the planetary metal copper, as mirrors in antiquity were made of polished copper, [ 12 ] [ d ] though this is not certain. [ 3 ] In the Greek Oxyrhynchus Papyri 235 , the symbols for Venus and Mercury did not have the cross on the bottom stem, [ 3 ] and Venus appears without the cross (⚲) in Johannes Kamateros (12th century). [ citation needed ]
In botany and biology , the symbol for Venus is used to represent the female sex , alongside the symbol for Mars representing the male sex, [ 13 ] following a convention introduced by Linnaeus in the 1750s. [ 10 ] [ e ] Arising from the biological convention, the symbol also came to be used in sociological contexts to represent women or femininity . This gendered association of Venus and Mars has been used to pair them heteronormatively , describing women and men stereotypically as being so different that they can be understood as coming from different planets, an understanding popularized in 1992 by the book titled Men Are from Mars, Women Are from Venus . [ 14 ] [ 15 ]
Unicode encodes the symbol as U+2640 ♀ FEMALE SIGN , in the Miscellaneous Symbols block. [ f ]
The modern astronomical symbol for the Sun, the circumpunct ( U+2609 ☉ SUN ), was first used in the Renaissance . It possibly represents Apollo's golden shield with a boss ; it is unknown if it traces descent from the nearly identical Egyptian hieroglyph for the Sun.
Bianchini's planisphere , produced in the 2nd century, shows a circlet with rays radiating from it. [ 5 ] [ 2 ] In late Classical times, the Sun is attested as a circle with a single ray. A diagram in Johannes Kamateros' 12th century Compendium of Astrology shows the same symbol. [ 18 ] This older symbol is encoded by Unicode as U+1F71A 🜚 ALCHEMICAL SYMBOL FOR GOLD in the Alchemical Symbols block. Both symbols have been used alchemically for gold, as have more elaborate symbols showing a disk with multiple rays or even a face.
The Mars symbol , ♂, is a depiction of a circle with an arrow emerging from it, pointing at an angle to the upper right in Europe and to the upper left in India. [ 19 ] [ 20 ] It is also the old and obsolete symbol for iron in alchemy. In zoology and botany, it is used to represent the male sex (alongside the astrological symbol for Venus representing the female sex), [ 13 ] following a convention introduced by Linnaeus in the 1750s. [ 10 ]
The symbol dates from at latest the 11th century, at which time it was an arrow across or through a circle, thought to represent the shield and spear of the god Mars; in the medieval form, for example in the 12th-century Compendium of Astrology by Johannes Kamateros, the spear is drawn across the shield. [ 18 ] The Greek Oxyrhynchus Papyri show a different symbol, [ 3 ] perhaps simply a spear. [ 2 ]
Its Unicode codepoint is U+2642 ♂ MALE SIGN ( ♂ ).
The symbol for Jupiter , ♃, was originally a Greek zeta, Ζ , with a stroke indicating that it is an abbreviation (for Zeus , the Greek equivalent of Roman Jupiter).
Its Unicode codepoint is U+2643 ♃ JUPITER .
Salmasius and earlier attestations show that the symbol for Saturn, ♄, derives from the initial letters ( Kappa , rho ) of its ancient Greek name Κρόνος ( Kronos ), with a stroke to indicate an abbreviation . [ 10 ] By the time of Kamateros (12th century), the symbol had been reduced to a shape similar to a lower-case letter eta η, with the abbreviation stroke surviving (if at all) in the curl on the bottom-right end.
Its Unicode codepoint is U+2644 ♄ SATURN .
The symbols for Uranus were created shortly after its discovery in 1781. One symbol, ⛢, invented by J. G. Köhler and refined by Bode , was intended to represent the newly discovered metal platinum ; since platinum, commonly called white gold, was found by chemists mixed with iron, the symbol for platinum combines the alchemical symbols for iron , ♂, and gold , ☉. [ 21 ] [ 22 ] Gold and iron are the planetary metals for the Sun and Mars, and so share their symbols. Several orientations were suggested, but an upright arrow is now universal.
Another symbol, , was suggested by Lalande in 1784. In a letter to Herschel , Lalande described it as "a globe surmounted by the first letter of your name". [ 23 ] The platinum symbol tends to be used by astronomers, and the monogram by astrologers. [ 24 ]
For use in computer systems, the symbols are encoded U+26E2 ⛢ ASTRONOMICAL SYMBOL FOR URANUS and U+2645 ♅ URANUS .
Several symbols were proposed for Neptune to accompany the suggested names for the planet. Claiming the right to name his discovery, Urbain Le Verrier originally proposed to name the planet for the Roman god Neptune [ 25 ] and the symbol of a trident , [ 26 ] while falsely stating that this had been officially approved by the French Bureau des Longitudes . [ 25 ] In October, he sought to name the planet Leverrier , after himself, and he had loyal support in this from the observatory director, François Arago , [ 27 ] who in turn proposed a new symbol for the planet, . [ 28 ] However, this suggestion met with resistance outside France, [ 27 ] and French almanacs quickly reintroduced the name Herschel for Uranus , after that planet's discoverer Sir William Herschel , and Leverrier for the new planet, [ 29 ] though it was used by anglophone institutions. [ 30 ] Professor James Pillans of the University of Edinburgh defended the name Janus for the new planet, and proposed a key for its symbol. [ 26 ] Meanwhile, Struve presented the name Neptune on December 29, 1846, to the Saint Petersburg Academy of Sciences . [ 31 ] In August 1847, the Bureau des Longitudes announced its decision to follow prevailing astronomical practice and adopt the choice of Neptune , with Arago refraining from participating in this decision. [ 32 ] The planetary symbol was Neptune's trident , with the handle stylized either as a crossed , following Mercury, Venus, Jupiter, Saturn, and the asteroids, or as an orb , following the symbols for Uranus, Earth, and Mars. [ 7 ] The crossed variant is the more common today.
For use in computer systems, the symbols are encoded as U+2646 ♆ NEPTUNE and U+2BC9 ⯉ NEPTUNE FORM TWO .
Pluto was almost universally considered a planet from its discovery in 1930 until its re-classification as a dwarf planet (planetoid) by the IAU in 2006. Planetary geologists [ 33 ] and astrologers continue to treat it as a planet. The original planetary symbol for Pluto was , a monogram of the letters P and L. Astrologers generally use a bident with an orb. NASA has used the bident symbol since Pluto's reclassification. These symbols are encoded as U+2647 ♇ PLUTO and U+2BD3 ⯓ PLUTO FORM TWO .
In the 19th century, planetary symbols for the major asteroids were also in use, including 1 Ceres (a reaper's sickle , encoded U+26B3 ⚳ CERES ), 2 Pallas (a lance, U+26B4 ⚴ PALLAS ) and 3 Juno (a sceptre, encoded U+26B5 ⚵ JUNO ).
Encke (1850) used symbols for 5 Astraea , 6 Hebe , 7 Iris , 8 Flora and 9 Metis in the Berliner Astronomisches Jahrbuch . [ 34 ]
In the late 20th century, astrologers abbreviated the symbol for 4 Vesta (the sacred fire of Vesta , encoded U+26B6 ⚶ VESTA ), [ 35 ] and introduced new symbols for 5 Astraea ( , a stylised % sign, shift-5 on QWERTY keyboards for asteroid 5), 10 Hygiea encoded U+2BDA ⯚ HYGIEA ) [ 36 ] and for 2060 Chiron , discovered in 1977 (a key, U+26B7 ⚷ CHIRON ). [ 35 ] Chiron's symbol was adapted as additional centaurs were discovered; symbols for 5145 Pholus and 7066 Nessus have been encoded in Unicode. [ 36 ] The abbreviated Vesta symbol is now universal, and the astrological symbol for Pluto has been used astronomically for Pluto as a dwarf planet. [ 37 ]
In the early 21st century, symbols for the trans-Neptunian dwarf planets have been given Unicode codepoints , particularly Eris (the hand of Eris , ⯰, but also ⯱), Sedna , Haumea , Makemake , Gonggong , Quaoar and Orcus which are in Unicode. All (except Eris, for which the hand of Eris is a traditional Discordian symbol) were devised by Denis Moskowitz, a software engineer in Massachusetts. [ 37 ] [ 38 ]
Other symbols have also been invented by Moskowitz, for some smaller TNOs as well as many planetary moons. (Charon in particular coincidentally matches a symbol already existing in Unicode as an astrological Pluto.) However, these have not been broadly adopted. [ 37 ] [ 39 ]
From 1845 to 1855, many symbols were created for newly discovered asteroids. But by 1851, the spate of discoveries had led to a general abandonment of these symbols in favour of numbering all asteroids instead. [ 41 ]
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The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors .
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The Vera Rubin Early Career Prize is named after Vera Rubin and is awarded by the Division on Dynamical Astronomy of the American Astronomical Society . [ 1 ] The prize recognizes excellence in dynamical astronomy . Recipients must have received their doctorate no more than ten years prior.
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Verastem, Inc. , doing business as Verastem Oncology , is an American pharmaceutical company that develops medicines to treat certain cancers. [ 2 ] Headquartered and founded in Boston, Massachusetts , the firm is a member of NASDAQ Biotechnology Index . [ 3 ]
Verastem Oncology (Verastem Inc) was co-founded in 2010 by entrepreneur Christoph H. Westphal and venture capitalist Michelle Dipp , who provided seed funding and initial office space in Cambridge, MA. The company was formed to commercialize the work of the three other co-founders, MIT biologists Robert F. Weinberg, Eric S. Lander and Piyush Gupta , by discovering and developing drugs to treat cancer by targeting cancer stem cells . [ 4 ]
The company raised $16 million in the initial Series A financing. [ 5 ]
Westphal served as CEO and chairman of the board from 2010 to 2013. Under his leadership, the company raised $55 million through an IPO in 2012. [ 6 ] Mr. Robert Forrester succeeded Christoph Westphal as Verastem's president and CEO in 2013. [ 7 ] In July 2019, Brian Stuglik was appointed to chief executive officer (CEO) of Verastem Oncology. [ 8 ]
Their leading investigational drug is defactinib (VS-6063), is a small-molecule focal adhesion kinase (FAK) inhibitor designed to kill cancer stem cells, intended for the treatment of malignant pleural mesothelioma . [ 9 ] In October 2015, they announced the premature termination of the company's late-stage clinical trial for defactinib after data analysis of the Phase II COMMAND trial found no significant differences in efficacy versus placebo. . [ 10 ] [ 11 ] [ 12 ] Following the failure of the study, the company had to cut 50% of its workforce. [ 13 ]
In November 2016, Verastem Oncology licensed global rights from Infinity Pharmaceuticals to duvelisib (IPI-145), a novel inhibitor of PI3K delta and gamma . [ 14 ] [ 15 ] In April 2018, Verastem filed a New Drug Application (NDA) for duvelisib for the treatment of relapsed or refractory chronic lymphocytic leukemia / small lymphocytic lymphoma (CLL/SLL) and accelerated approval for relapsed or refractory follicular lymphoma (FL). The results of the clinical study DUO were published in Blood Journal . [ 16 ]
Verastem Oncology received FDA approval for duvelisib on September 24, 2018, as a treatment for adults with 3rd-line chronic lymphocytic leukemia/small lymphocytic lymphoma, and an accelerated approval as a 3rd-line treatment for follicular lymphoma, contingent on the results of a confirmatory trial. [ 17 ] The drug label carries a black box warning due to the risk of potentially fatal or serious toxicities: infections, diarrhea or colitis , cutaneous reactions and pneumonitis . [ 18 ]
In July 2019, Verastem Oncology signed an exclusive agreement with Sanofi for the commercialization of duvelisib in Russia and CIS , Turkey, the Middle East and Africa. [ 19 ]
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Veratric acid , also known as 3,4-dimethoxybenzoic acid, is a benzoic acid . It is a plant metabolite found in species such as Hypericum laricifolium , Artemisia sacrorum , and Zeyheria montana . [ 1 ] [ 2 ]
A 2023 study at SRM Institute of Science and Technology suggests that veratric acid has apoptotic and antiproliferative effects against triple negative breast cancer cells. These effects were substantially increased when polydopamine nanoparticles were used as a sustained release drug carrier. [ 3 ]
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Verbal reasoning is understanding and reasoning using concepts framed in words. It aims at evaluating ability to think constructively, rather than at simple fluency or vocabulary recognition.
Verbal reasoning tests of intelligence provide an assessment of an individual's ability to think, reason and solve problems in different ways. For this reason, verbal reasoning tests are often used as entrance examinations by schools, colleges and universities to select the most able applicants. Additionally, such tests are also used by a growing number of employers as part of the selection/ recruitment process.
The Wechsler Adult Intelligence Scale III (WAIS-III) divides Verbal IQ (VIQ) into two categories:
The Law School Admission Test (LSAT) is a classic measure that evaluates the verbal reasoning ability of participants who are applying to a graduate law school. The multiple choice sections are broken up into three parts:
Large graduate training schemes are increasingly using verbal reasoning tests (verbals) to distinguish between applicants. The types of verbals candidates face in these assessments are typically looking to assess understanding and comprehension skills.
Verbal reasoning tests are often used during recruitment for positions in many industries, such as banking, finance, management consulting, mining and accounting. The tests are used as an efficient way to short list candidates for later stages of the recruitment process, such as interview. When used in recruitment, the tests normally include a series of text passages regarding a random topic. Then there will be a series of statements regarding the passages. The candidate must then determine if the statement is true, false or they can not tell (it is ambiguous). The candidate is not expected to know anything about the topics, and the answer is to be based purely on the information in the passage. [ 4 ]
This section of the article briefly elucidates the general elements relating to verbal reasoning in order of increasing complexity.
Vocabulary (the knowledge of words' meanings in a language) and grammar (knowledge of words' proper relation to one another in a language) can function both as prerequisites as well as topics of focus of verbal reasoning. In the former capacity, they are used to form propositions and arguments (see below), while in the latter capacity they are the subject of analysis and evaluation, where verbal reasoning synthesizes linguistic information and analyzes relationships among component parts of sentences, words, and concepts. [ 5 ] [ 6 ]
The basic element of reasoning (verbal, or otherwise) is the proposition . A proposition is simply the meaning behind a declarative sentence that can be either true or false (note: special care is taken here to mention that the proposition is specifically what is meant by such a sentence, and is not the actual sentence itself). In other words, a proposition is something that one can know, believe, think, assume, or so on. [ 7 ] Worth explicitly mentioning here is that only some (and not necessarily all) statements count as propositions. This is because the defining feature of a proposition is that it is necessarily making some assertion which can intelligibly be assigned a truth value . In other words: statements are only propositions if they are Truth-apt. To illustrate this principled distinction, let us consider the following two statements:
The first sentence is a proposition because it purports a fact which is either true or untrue. The second sentence, however, is not a proposition, because it does not appear to make any true/false assertion (that is, there is nothing meant by the sentence that one could say were or weren't "true").
A premise is a proposition in an argument which will justify or induce a conclusion. That is, premises are propositions which, if true , allow for the logical inference of an associated proposition which is known as the "conclusion". To give an example: the statement "John is a bachelor" is a premise in the one-sentence argument " John is a bachelor, therefore John is unmarried ", and the conclusion is that "John is unmarried".
Premises may be treated somewhat differently according to the specific type of argument in which they occur. In a deductive argument , premises are often assumed to be true — regardless of whether or not they really are. This is juxtaposed against inductive arguments , in which there is merely a chance of some premise(s) (and/or conclusion(s)) being true.
An argument is a series of premises together with one or more conclusion(s). Arguments can serve a variety of purposes, ranging from determining the degree of truth of a conclusion, to persuading individuals to accept or reject some belief(s) (as in the case of rhetoric ). An additional note on arguments is that they may take a number of different forms, including that of a syllogism , essay , or dialogue (among others). To the extent which argument overlaps with and is reliant upon language, it may be considered one of the central concerns of verbal reasoning (or for that matter any reasoning, at large).
At this point a sort of maximal scope has been reached, wherein it is appropriate to point out and address the issue of circularity . Insofar as verbal reasoning is used to create and analyze arguments of language, while at the same time arguments (using language as their vehicle) are used to exercise and analyze reasoning , there will be some inevitable degree of circularity between the two. This point offers a fitting conclusion to the current section, and serves to reiterate the importance of verbal reasoning.
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The Verband Deutscher Tonmeister e.V. (VDT) is a registered association for audio industry professionals. [ 1 ] [ 2 ] The VDT has evolved from the Deutsche Filmtonmeister-Vereinigung (which focused on film sound professionals) that was founded in Munich in 1950. [ 3 ]
There are currently more than 1900 members [ 4 ] in the VDT that are either freelancers or employed in various institutions; e.g. in the film business, radio broadcasting, television, recording studios, record labels, theaters and performance venues, the audio equipment producing industry, research and development, multimedia education and other audio related areas of occupation. Students preparing for a job in the audio industry are also members of the VDT, making up roughly 10%. [ 5 ]
Even though the designation of Tonmeister is a fixed part of the name of the association its members carry many other job titles like audio engineer , sound director , music director , sound designer , producer, record producer and music supervisor . The occupational title Tonmeister, although created in the 1930s, is not protected in Germany and does not describe a clearly defined occupation. Thematically the goals and activities of the VDT are related to those of the Audio Engineering Society (AES), even if there is no formal connection.
The biennial Tonmeistertagung [ 6 ] (VDT International convention) combines an international scientific conference and workshop program with a trade fair, focusing on applied research and technical excellence. [ 7 ] It has been in existence since 1949. [ 8 ] Similarly the International Tonmeister Symposium, dedicated to one thematic complex, is analogous to the AES-conferences. The Tonmeister Academy as initiated by the VDT offers educational classes and advanced training sessions.
The VDT award Golden Bobby [ 9 ] is awarded in seven categories for outstanding performance in sound recording and mixing. Since 2002 the VDT also bestows a medal of honour [ 10 ] on members who have rendered outstanding services to the profession of sound engineers and the audio industry. Prominent recipients are Peter K. Burkowitz [ 11 ] (developer of the REDD mixing console at EMI's Abbey Road Studios ; writer of the technical part of Recording the Beatles ), David Griesinger (of Lexicon ) and Eberhard Sengpiel .
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In computing , Verbose mode is an option available in many computer operating systems and programming languages that provides additional details as to what the computer is doing and what drivers and software it is loading during startup. Used as a flag in a computer program, it produces detailed output for diagnostic purposes thus making it easier to debug.
When running programs in the command line , verbose output is typically outputted in standard output or standard error .
Many command line programs, such as cURL [ 1 ] or Bash , [ 2 ] can be set to verbose mode by using a flag, such as -v or --verbose .
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The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors .
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In mathematics , Verdier duality is a cohomological duality in algebraic topology that generalizes Poincaré duality for manifolds . Verdier duality was introduced in 1965 by Jean-Louis Verdier ( 1965 ) as an analog for locally compact topological spaces of Alexander Grothendieck 's theory of Poincaré duality in étale cohomology for schemes in algebraic geometry . It is thus (together with the said étale theory and for example Grothendieck's coherent duality ) one instance of Grothendieck's six operations formalism.
Verdier duality generalises the classical Poincaré duality of manifolds in two directions: it applies to continuous maps from one space to another (reducing to the classical case for the unique map from a manifold to a one-point space), and it applies to spaces that fail to be manifolds due to the presence of singularities. It is commonly encountered when studying constructible or perverse sheaves .
Verdier duality states that (subject to suitable finiteness conditions discussed below)
certain derived image functors for sheaves are actually adjoint functors . There are two versions.
Global Verdier duality states that for a continuous map f : X → Y {\displaystyle f\colon X\to Y} of locally compact Hausdorff spaces, the derived functor of the direct image with compact (or proper) supports R f ! {\displaystyle Rf_{!}} has a right adjoint f ! {\displaystyle f^{!}} in the derived category of sheaves , in other words, for (complexes of) sheaves (of abelian groups) F {\displaystyle {\mathcal {F}}} on X {\displaystyle X} and G {\displaystyle {\mathcal {G}}} on Y {\displaystyle Y} we have
Local Verdier duality states that
in the derived category of sheaves on Y .
It is important to note that the distinction between the global and local versions is that the former relates morphisms between
complexes of sheaves in the derived categories, whereas the latter relates internal Hom-complexes and so can be evaluated locally. Taking global sections of both sides in the local statement gives the global Verdier duality.
These results hold subject to the compactly supported direct image functor f ! {\displaystyle f_{!}} having finite cohomological dimension .
This is the case if there is a bound d ∈ N {\displaystyle d\in \mathbf {N} } such that the compactly supported cohomology H c r ( X y , Z ) {\displaystyle H_{c}^{r}(X_{y},\mathbf {Z} )} vanishes for all fibres X y = f − 1 ( y ) {\displaystyle X_{y}=f^{-1}(y)} (where y ∈ Y {\displaystyle y\in Y} )
and r > d {\displaystyle r>d} . This holds if all the fibres X y {\displaystyle X_{y}} are at most d {\displaystyle d} -dimensional manifolds or more generally at most d {\displaystyle d} -dimensional CW-complexes .
The discussion above is about derived categories of sheaves of abelian groups. It is instead possible to consider a ring A {\displaystyle A} and (derived categories of) sheaves of A {\displaystyle A} -modules; the case above corresponds to A = Z {\displaystyle A=\mathbf {Z} } .
The dualizing complex D X {\displaystyle D_{X}} on X {\displaystyle X} is defined to be
where p is the map from X {\displaystyle X} to a point. Part of what makes Verdier duality interesting in the singular setting is that when X {\displaystyle X} is not a manifold (a graph or singular algebraic variety for example) then the dualizing complex is not quasi-isomorphic to a sheaf concentrated in a single degree. From this perspective the derived category is necessary in the study of singular spaces.
If X {\displaystyle X} is a finite-dimensional locally compact space, and D b ( X ) {\displaystyle D^{b}(X)} the bounded derived category of sheaves of abelian groups over X {\displaystyle X} , then the Verdier dual is a contravariant functor
defined by
It has the following properties:
Poincaré duality can be derived as a special case of Verdier duality. Here one explicitly calculates cohomology of a space using the machinery of sheaf cohomology .
Suppose X is a compact orientable n -dimensional manifold, k is a field and k X {\displaystyle k_{X}} is the constant sheaf on X with coefficients in k . Let f = p {\displaystyle f=p} be the constant map to a point. Global Verdier duality then states
To understand how Poincaré duality is obtained from this statement, it is perhaps easiest to understand both sides piece by piece. Let
be an injective resolution of the constant sheaf. Then by standard facts on right derived functors
is a complex whose cohomology is the compactly supported cohomology of X . Since morphisms between complexes of sheaves (or vector spaces) themselves form a complex we find that
where the last non-zero term is in degree 0 and the ones to the left are in negative degree. Morphisms in the derived category are obtained from the homotopy category of chain complexes of sheaves by taking the zeroth cohomology of the complex, i.e.
For the other side of the Verdier duality statement above, we have to take for granted the fact that when X is a compact orientable n -dimensional manifold
which is the dualizing complex for a manifold. Now we can re-express the right hand side as
We finally have obtained the statement that
By repeating this argument with the sheaf k X replaced with the same sheaf placed in degree i we get the classical Poincaré duality
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Verdigris ( / ˈ v ɜːr d ɪ ɡ r iː ( s )/ ) [ 1 ] is a common name for any of a variety of somewhat toxic [ 2 ] [ 3 ] [ 4 ] copper salts of acetic acid , which range in colour from green to a bluish-green depending on their chemical composition . [ 5 ] : 132 Once used as a medicine [ 6 ] [ 7 ] and pharmaceutical preparation, [ 8 ] : 176 [ 9 ] verdigris occurs naturally, creating a patina on copper, bronze , and brass , and is the main component of a historic green pigment used for artistic purposes from antiquity until the late 20th century, including in easel painting , polychromatic sculptures , and illumination of maps. [ 9 ] : 414–423 [ 10 ] However, due to its instability, its popularity declined as other green pigments became readily available. [ 8 ] : 171 The instability of its appearance stems from its hydration level and basicity , which change as the pigment interacts with other materials over time. [ 11 ] : 637
The name verdigris comes from the Middle English vertegrez , from the Old French verte grez . According to one view, it comes from vert d'aigre , [ 12 ] "green [made by action] of vinegar". The modern French writing of this word is vert-de-gris ("green of grey"), sounding like the older name verdet gris ("grey greenish"), itself a deformation of verte grez . It was used as a pigment in paintings and other art objects (as green color), mostly imported from Greece, and hence it is more usually given another etymology as vert-de-Grèce ("green of Greece "). [ 13 ] [ 14 ]
Copper(II) acetate is prepared by treatment of copper(II) hydroxide with acetic acid . [ 15 ] The historical methods used for producing verdigris have been recorded in artistic treaties, manuscripts on alchemy, works in natural history, and texts on medicine. [ 9 ] : 414 The most common ingredients used were copper and vinegar. Throughout history, recipes changed. In the Middle Ages , copper strips were attached to a wooden block with acetic acid; the block was then buried in dung . A few weeks later, the block was to be dug up, and the verdigris scraped off. [ 16 ] Another method of production was developed in 18th-century Montpellier , France, a locale which had the ideal climate to produce verdigris for pulverization . [ 8 ] : 177 The industry there was long dominated by women, with verdigris manufactured in household cellars using copper plates stacked in clay pots that were filled with distilled wine. [ 15 ] The acid in the grapes caused the copper to develop crystals. The crystals ripened into verdigris and were scraped off when matured. [ 8 ] : 172 It was a profitable business, and 80% of production was sold abroad through certified female brokers. At the height of its popularity, in the 1710s, the government had to enforce inspection systems to address growing fraudulent practices. By the 20th century, the production of verdigris had moved away from Montpellier and more cost-efficient methods of producing green pigments sent the industry into decline after WWI . [ 8 ] : 179–182
Verdigris is a collective term for copper acetate, whose chemical varieties produce different hues. The technical literature is inconsistent in describing these variations. Some sources refer to "neutral verdigris" as copper(II) acetate monohydrate ( Cu(CH 3 CO 2 ) 2 ·(H 2 O) ) and to "blue verdigris" as Cu(CH 3 CO 2 ) 2 ·CuO·(H 2 O) 6 . [ 17 ] Other sources describe the main copper salt in natural verdigris as Cu 4 SO 4 (OH) 6 ( brochantite ). [ 18 ] Still other sources describe it as basic copper carbonate ( Cu 2 CO 3 (OH) 2 ), [ 19 ] or as Cu(CH 3 CO 2 ) 2 ·(Cu(OH) 2 ) n where n varies from 0 to 3. [ 20 ] In marine environments, the main copper salt is tribasic copper chloride ( Cu 2 (OH) 3 Cl ). [ 18 ] [ 19 ]
Overall, variations of verdigris can be divided into two groups: basic verdigris and neutral verdigris. [ 5 ] : 132 The difference in colour depends on the hydration level and degrees of basicity . [ 11 ] : 637
Verdigris, which was once used as a medicine [ 6 ] [ 7 ] and pharmaceutical preparation [ 8 ] : 176 [ 9 ] : 414 is mildly poisonous. [ clarify ] [ 2 ] [ 3 ] [ 4 ] [ better source needed ] Symptoms of toxicity include nausea, anemia and death, although widespread acquired immunity has been documented, as occurred with female workers in Montpellier . [ 21 ] Nontoxic substitutes have been developed for some applications, such as art pigments.
Verdigris is a naturally occurring protective layer on metals such as copper, brass, and bronze. In addition to be a desirable artistic effect, it has been used primarily as a pigment and now-outdated medicinal preparations.
When burned, verdigris produces a green flame. [ 22 ]
Verdigris has been used as a pigment since antiquity, including in paintings in Rome and Pompeii. The use of verdigris continued into the Middle Ages , Renaissance and Baroque paintings. [ 5 ] : 132 It has been identified in The Last Supper (1306) by Giotto . [ 5 ] : 142 During the 15th and 16th centuries, it was used in paintings for its transparency and brilliance. [ 11 ] : 637 It was difficult to create strong green colors in paintings due to the limitations of the existing green, yellow and blue pigments. In early Italian, Netherlandish, and German paintings, verdigris was widely used to create pure green tones for landscapes and drapery , such as the green coat of Saint John in the Mond Crucifixion by Raphael . [ 23 ] : 46 Verdigris was used as both glaze and opaque paint. When verdigris glaze was combined with lead white or lead-tin yellow , it created a deeply saturated green. [ 5 ] : 132–136 It was used in oil-based house paint for French and Dutch country houses. Verdigris also was used as an imitation of 'Chinese varnish' on European lacquer . [ 8 ] : 175–176 However, during the 19th century, the use of verdigris began to decrease as alternatives such as Emerald Green and viridian became more popular. [ 5 ] : 132
As a pigment, verdigris is subject to colour change. The changes are most pronounced during the first month of exposure to air. The changes also depend on the type of binding agent and type of verdigris used. For example, changes are less pronounced with neutral verdigris in oil and egg tempera compared to basic verdigris. [ 5 ] : 135 With aging, the green pigment in these applications will show signs of browning or darkening. [ 11 ] : 637 For example, in Botticelli 's The Mystical Nativity , from 1500, the blue-green costumes of the angels have darkened to a dark green colour. [ 24 ]
Verdigris pigment is lightfast in oil paint, as numerous examples of 15th-century paintings show. However, its lightfastness and air resistance are very low in other media. Copper resinate, made from verdigris by boiling it in a resin , is not lightfast, even in oil paint. In the presence of light and air, green copper resinate becomes stable brown copper oxide. [ 13 ] The browning mechanism is attributed to the transient formation of Cu(I) in the pigment and oil system. The reduction of Cu(II) into Cu(I) due to the release of a carboxylate, causes changes in the optical properties of pigment . Furthermore, linseed oil induces the transformation of the copper acetate bimetallic structure, and forms monomeric series. Dioxygen that reacts with partially decarboxylated dimers to form a peroxy-Cu dimer complex is responsible for the darkening of the pigment. [ 11 ] : 635–638
In previous literature on painting, verdigris has been described as unstable when combined with other pigments which leads to further deterioration. Due to the fickle nature of the pigment, it required special preparation of paint, carefully layered application, and immediate sealing with varnish to avoid rapid discoloration (but not in the case of oil paint). [ 13 ] However, further scientific research suggests that the difficulties are less extreme than previously described. The pigment nonetheless has the ability to degrade cellulosic materials, such as paper. [ 5 ] : 137 In terms of identification and reproduction, modern technology and reproducible synthesis procedures have been developed to be used for museums and collections to identify distinct verdigris phases in historical artworks. [ 23 ] : 14857 Certain components of historical verdigris pigments, copper(II) acetates , are partially irreproducible based on the given historical recipes. [ 23 ] : 14847
Verdigris has also been used in medicine, [ 6 ] [ 7 ] and is identified in the Pharmacologia of John Ayrton Paris as the healing rust of the Spear of Telephus mentioned by Homer . [ 6 ] [ 7 ] Verdigris solids were also used for pharmaceutical preparations [ 9 ] : 414 in the 18th century to treat canker sores . [ 8 ] : 176
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VEREX was an ad hoc committee assembled in 1991 by the Third Review Conference of the Biological Weapons Convention (BWC) to research verification measures to enforce the BWC from a scientific and technical standpoint. [ 1 ] [ 2 ] [ 3 ]
VEREX was mandated to “identify and examine potential verification measures from a scientific and technical standpoint”. [ 1 ] These verification measures sought to determine
Whether a State Party is developing, producing, stockpiling, acquiring or retaining microbial or other biological agents or toxins, of types and in quantities that have no justification for prophylactic, protective or other peaceful purposes. [ 1 ]
The measures, which could be assessed singly or in combination, were to be evaluated against the following set of criteria: [ 1 ]
The VEREX committee, which consisted of governmental experts, met in a series of four sessions in 1992 and 1993. [ 4 ]
The first session of the committee assembled 21 potential methods for verification, including surveillance, declaration of activities, and ways to inspect suspicious facilities. [ 4 ] The second sessions focused on the uses and limitations of technologies that could be used to implement the methods discussed in the previous session. [ 4 ] The third session examined the advantages and disadvantages of each of the 21 potential verification methods. [ 4 ]
In September 1993, VEREX submitted its report, concluding that "some of the verification measures would contribute to strengthening the effectiveness and improve the implementation of the Convention". [ 4 ] Moreover, the report states that these verification measures "could be useful to varying degrees in enhancing confidence, through increased transparency, that States Parties were fulfilling their obligations under the BWC". [ 4 ]
The following is a list of the 21 potential verifications measures that were identified and evaluated by VEREX: [ 4 ]
In 1994, a Special Conference of BWC States Parties convened to consider the VEREX report. The conference decided to establish an Ad Hoc Group to negotiate a legally-binding verification protocol for the BWC. [ 5 ] The Ad Hoc Group convened 24 sessions between 1995 and 2001, during which it negotiated a draft protocol to the BWC which would establish a verification system supported by an international organization. [ 6 ] This organization would regularly conduct on-site visits to declared biological facilities as well as investigate specific suspect facilities and activities. [ 7 ] However, states disagreed on several fundamental issues, including the scope of on-site visits and export controls. [ 7 ] By early 2001, the “rolling text” of the draft protocol still contained many areas on which views diverged widely.
A 210-page draft protocol, circulated in March 2001 by the chairman of the Ad Hoc Group, attempted to resolve the contested issues. [ 8 ] However, in July 2001 the George W. Bush administration rejected both the draft protocol circulated by the Group's Chairman and the entire approach on which the draft was based, resulting in the collapse of the negotiation process. [ 9 ] To justify its decision, the United States asserted that the protocol would not have improved BWC compliance and would have harmed U.S. national security and commercial interests. [ 10 ] Many analysts, including Matthew Meselson and Amy Smithson, criticized the U.S. decision as undermining international efforts against non-proliferation and as contradicting U.S. government rhetoric regarding the alleged biological weapons threat posed by Iraq and other U.S. adversaries. [ 11 ]
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16th century: Aepke Onsta, Eylco Onsta until 1564.
1576: Ecke Claessen
1587: Hidde Onsta
Verhildersum is a borg directly to the east of the town of Leens in the Dutch province of Groningen . It is now a museum.
The name Verhildersum comes from Verhildert , where Ver means 'woman' or 'noble woman' and Hilder(t) is a proper name. When this woman lived is unknown. The ending -um in Verhildersum stands for 'house'.
The borg dates, as a heerd (a word for farm in Gronings ), from the 14th century. It became a borg in the 17th century.
In 1398 a certain Aylko Ferhildema is mentioned, the same person as Aylko Onsta from Sauwerd . The surname Ferhildema could indicate that he (had) lived in Verhildersum. It is unknown whether, after Aylko Onsta, other members of the Onsta family lived in Verhildersum, but it is considered highly probable that the Onsta's kept possession of the borg for some time. One clue to this is that the borg was destroyed in both 1400 and 1514 by the city-Groningers (inhabitants of the city Groningen ), just like the Onstaborg . However, in between these two battles no mention of the borg is made in official records. In a document mention is made of the reconstruction of the borg after 1514 for the sum of 1200 gold pieces, excluding some exterior buildings.
After the death of the inhabitant Aepke Onsta in 1564, Ecke Claessen is mentioned as the inhabitant of the borg in 1576. Complaints by him are made with regard to troubles caused by billeted soldiers with their two wives and a child, who reside at the borg due to the Eighty Years' War . During the war Eylco Onsta flees to East Frisia , but despite this keeps calling himself hoofdeling of Wetsinge , Sauwerd and Verhildersum. However, in reality, in 1587, twenty years after the death of Aepke Onsta, it is arranged in the property settlement that not he alone, but he and his sister Hidde Onsta together become owner of the borg Verhildersum. Verhildersum was then a heerd (farm) of 150 yokes (about 75 hectares ) on which stood 'the old borg'. [ 1 ]
Around the borg lies the Verhildersum Estate of 32 hectares . In the borg gardens are a carriage house , a farmhouse , and a garden shed .
The schathuis was built originally built in 1833 on the estate of Saaksumborg, a borg which is now demolished. The schathuis used to be a farmhouse and derives its name from the old Frysian word skat , which means cattle. [ 2 ] In 1972, the schathuis was moved to the Verhildersum Estate.
From 1994 to 2012, the fine dining restaurant Schathoes Verhildersum of chef Dick Soek was housed in the building. [ 3 ] The restaurant had one Michelin star from 2004 to 2012. Since 2012, the grand cafe 't Schathuys is housed in the building.
The late-nineteenth-century garden shed is the former 'tramhouse' of the Emmaplein in Haren, Groningen . The borg garden is laid out according to the golden ratio with characteristics from the Renaissance and the Baroque . The garden is also home to a herb garden , more than ninety types of roses and fifty types of Clematis . The garden is surrounded by moates .
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The Verhoeff algorithm [ 1 ] is a checksum for error detection first published by Dutch mathematician Jacobus Verhoeff in 1969. [ 2 ] [ 3 ] It was the first decimal check digit algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits, [ 4 ] which was at the time thought impossible with such a code.
The method was independently discovered by H. Peter Gumm in 1985, this time including a formal proof and an extension to any base. [ 5 ]
Verhoeff had the goal of finding a decimal code—one where the check digit is a single decimal digit—which detected all single-digit errors and all transpositions of adjacent digits. At the time, supposed proofs of the nonexistence [ 6 ] of these codes made base-11 codes popular, for example in the ISBN check digit .
His goals were also practical, and he based the evaluation of different codes on live data from the Dutch postal system, using a weighted points system for different kinds of error. The analysis broke the errors down into a number of categories: first, by how many digits are in error; for those with two digits in error, there are transpositions ( ab → ba ), twins ( aa → 'bb'), jump transpositions ( abc → cba ), phonetic ( 1a → a0 ), and jump twins ( aba → cbc ). Additionally there are omitted and added digits. Although the frequencies of some of these kinds of errors might be small, some codes might be immune to them in addition to the primary goals of detecting all singles and transpositions.
The phonetic errors in particular showed linguistic effects, because in Dutch, numbers are typically read in pairs; and also while 50 sounds similar to 15 in Dutch, 80 doesn't sound like 18.
Taking six-digit numbers as an example, Verhoeff reported the following classification of the errors:.
The general idea of the algorithm is to represent each of the digits (0 through 9) as elements of the dihedral group D 5 {\displaystyle D_{5}} . That is, map digits to D 5 {\displaystyle D_{5}} , manipulate these, then map back into digits. Let this mapping be m : [ 0 , 9 ] → D 5 {\displaystyle m:[0,9]\to D_{5}}
m = ( 0 1 2 3 4 5 6 7 8 9 e r r 2 r 3 r 4 s r s r 2 s r 3 s r 4 s ) {\displaystyle m={\begin{pmatrix}0&1&2&3&4&5&6&7&8&9\\e&r&r^{2}&r^{3}&r^{4}&s&rs&r^{2}s&r^{3}s&r^{4}s\end{pmatrix}}}
Let the nth digit be a n {\displaystyle a_{n}} and let the number of digits be k {\displaystyle k} .
For example given the code 248 then k {\displaystyle k} is 3 and a 3 = m ( 8 ) = r 3 s {\displaystyle a_{3}=m(8)=r^{3}s} .
Now define the permutation f : D 5 → D 5 {\displaystyle f:D_{5}\to D_{5}}
f = ( e r r 2 r 3 r 4 s r s r 2 s r 3 s r 4 s r s r 2 s r s r 2 r 3 s r 3 e r 4 s r 4 ) {\displaystyle f={\begin{pmatrix}e&r&r^{2}&r^{3}&r^{4}&s&rs&r^{2}s&r^{3}s&r^{4}s\\r&s&r^{2}s&rs&r^{2}&r^{3}s&r^{3}&e&r^{4}s&r^{4}\end{pmatrix}}}
For example f ( r 3 ) = r s {\displaystyle f(r^{3})=rs} . Another example is f 2 ( r 3 ) = r 3 {\displaystyle f^{2}(r^{3})=r^{3}} since f ( f ( r 3 ) ) = f ( r s ) = r 3 {\displaystyle f(f(r^{3}))=f(rs)=r^{3}}
Using multiplicative notation for the group operation of D 5 {\displaystyle D_{5}} , the check digit is then simply a value c {\displaystyle c} such that
f ( a 1 ) ⋅ f 2 ( a 2 ) ⋅ … ⋅ f k ( a k ) ⋅ f k + 1 ( c ) = e {\displaystyle f(a_{1})\cdot f^{2}(a_{2})\cdot \ldots \cdot f^{k}(a_{k})\cdot f^{k+1}(c)=e}
c {\displaystyle c} is explicitly given by inverse permutation
c = f − 1 − k ( ∏ n = 1 k f n ( a n ) − 1 ) {\displaystyle c=f^{-1-k}\left(\prod _{n=1}^{k}f^{n}(a_{n})^{-1}\right)}
For example the check digit for 248 is 5. To verify this, use the mapping to D 5 {\displaystyle D_{5}} and insert into the LHS of the previous equation
f ( r 2 ) ⋅ f 2 ( r 4 ) ⋅ f 3 ( r 3 s ) ⋅ f 4 ( s ) = e {\displaystyle f(r^{2})\cdot f^{2}(r^{4})\cdot f^{3}(r^{3}s)\cdot f^{4}(s)=e}
To evaluate this permutation quickly use that
f 4 ( s ) = f 3 ( r 3 s ) = f 2 ( r 4 ) = f ( r 2 ) = r 2 s {\displaystyle f^{4}(s)=f^{3}(r^{3}s)=f^{2}(r^{4})=f(r^{2})=r^{2}s}
to get that
r 2 s ⋅ r 2 s ⋅ r 2 s ⋅ r 2 s = e {\displaystyle r^{2}s\cdot r^{2}s\cdot r^{2}s\cdot r^{2}s=e}
This is the same reflection being iteratively multiplied. Use that reflections are their own inverse. [ 7 ]
( r 2 s ⋅ r 2 s ) ⋅ ( r 2 s ⋅ r 2 s ) = e 2 = e {\displaystyle (r^{2}s\cdot r^{2}s)\cdot (r^{2}s\cdot r^{2}s)=e^{2}=e}
In practice the algorithm is implemented using simple lookup tables without needing to understand how to generate those tables from the underlying group and permutation theory. This is more properly considered a family of algorithms, as other permutations work too. Verhoeff's notes that the particular permutation, given above, is special as it has the property of detecting 95.3% of the phonetic errors. [ 8 ]
The strengths of the algorithm are that it detects all transliteration and transposition errors, and additionally most twin, twin jump, jump transposition and phonetic errors.
The main weakness of the Verhoeff algorithm is its complexity. The calculations required cannot easily be expressed as a formula in say Z / 10 Z {\displaystyle {\displaystyle \mathbb {Z} /10\mathbb {Z} }} . Lookup tables are required for easy calculation. A similar code is the Damm algorithm , which has similar qualities.
The Verhoeff algorithm can be implemented using three tables:
a multiplication table d , an inverse table inv , and a permutation table p .
The first table, d , is based on multiplication in the dihedral group D 5 . [ 7 ] and is simply the Cayley table of the group. Note that this group is not commutative , that is, for some values of j and k , d ( j , k ) ≠ d ( k , j ).
The inverse table inv represents the multiplicative inverse of a digit, that is, the value that satisfies d ( j , inv ( j )) = 0.
The permutation table p applies a permutation to each digit based on its position in the number. This is actually a single permutation (1 5 8 9 4 2 7 0)(3 6) applied iteratively; i.e. p ( i + j , n ) = p ( i , p ( j , n )).
The Verhoeff checksum calculation is performed as follows:
The original number is valid if and only if c = 0 {\displaystyle c=0} .
To generate a check digit, append a 0 , perform the calculation: the correct check digit is i n v ( c ) {\displaystyle inv(c)} .
Generate a check digit for 236 :
c is 2, so the check digit is inv (2), which is 3.
Validate the check digit 2363 :
c is zero, so the check is correct.
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https://en.wikipedia.org/wiki/Verhoeff_algorithm
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Verification in the field of space systems engineering covers two verification processes: Qualification and Acceptance
In the field of spaceflight verification standards are developed by DoD , NASA and the ECSS , among others. Large aerospace corporations may also developed their own internal standards. These standards exist in order to specify requirements for the verification of a space system product, such as: [ 1 ]
Verification or qualification, is one main reason that costs for space systems are high. All data are to be documented and to stay accessible for potential, later failure analyses. In previous times that approach was executed down to piece-parts level (resistors, switches etc.) whereas nowadays it is tried to reduce cost by usage of "CAM (Commercial, Avionics, Military) equipment" for non-safety relevant units.
Qualification is the formal proof that the design meets all requirements of the specification and the parameters agreed in the Interface Control Documents (ICD) requirements with adequate margin, including tolerances due to manufacturing imperfections, wear-out within specified life-time, faults, etc. The end of the qualification process is the approval signature of the customer on the Certificate of Qualification (CoQ), or Qualification Description Document (QDD) agreeing that all the requirements are met by the product to be delivered under the terms of a contract.
Acceptance is the formal proof that the product identified is free of workmanship defects and meets preset performance requirements with adequate margin. Acceptance is based on the preceding qualification by reference to the used design / manufacturing documentation. The end of the acceptance process is the approval signature of the customer on the CoA, or QDD, agreeing that all the requirements are met by the product to be delivered under the terms of a contract.
There are five generally accepted Qualification methods:
Being qualified means demonstrating with margin that the design, and the implementation of the design, meets the intended preset requirements. There are many different Qualification strategies in order to reach the same goals. It consists of designing hardware (or software) to qualification requirements (including margin), testing dedicated hardware (or software) to qualification requirements to verify the design, followed by acceptance testing of flight hardware to screen workmanship defects. There are other strategies as well, the Proto-Qualification strategy for instance. Proto-Qualification consists of testing the first flight hardware to Proto-Qualification requirements to verify design, and testing subsequent flight hardware to acceptance levels to screen workmanship defects. This first Proto-Qualification unit is flight-worthy.
There are three generally accepted Acceptance methods:
If a deviation against the qualified item is detected (higher tolerances, scratches etc.) a Non-Conformance is to be processed; to justify that this item can be used despite this deviation an Analysis might be required.
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https://en.wikipedia.org/wiki/Verification_(spaceflight)
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Verily Life Sciences LLC , [ 2 ] also known as Verily (formerly Google Life Sciences ), is Alphabet Inc. 's research organization devoted to the study of life sciences . [ 3 ] [ 4 ] The organization was formerly a division of Google X , until August 10, 2015, when Sergey Brin announced that the organization would become an independent subsidiary of Alphabet Inc . [ 5 ] with restructuring completed on October 2, 2015. On December 7, 2015, Google Life Sciences was renamed Verily. [ 6 ] [ 7 ] As of 2025, Verily is the first “bet” to successfully divest from Google and is now operating as a standalone company under Alphabet.
On 9 September 2014, the division acquired Lift Labs, the makers of Liftware . [ 8 ]
Verily Life Sciences in January 2019 raised $1 billion in funding.
At the end of 2019, Verily sold its stake in robot-assisted surgery joint venture Verb Surgical to development partner Johnson & Johnson . [ 9 ]
In August 2020, Verily announced that it is entering into the insurance market with the launch of Coefficient Insurance Company. The new subsidiary will be backed by Swiss Re Group's commercial insurance unit. [ 10 ]
In September 2022, Verily announced longtime CEO Andy Conrad would step down as CEO in January 2023, to be replaced by Stephen Gillett [ 11 ] who became CEO on January 3, 2023. [ 12 ]
In January 2023, fifteen percent of Verily's workforce was laid off as part of a broader restructuring by parent company, Alphabet. [ 13 ] The Information reported in August that Gillett had told employees they would stop relying on Alphabet on "a wide range of corporate services", signaling a potential spin-out as an independent company. [ 14 ]
In June 2024, Verily decided to close its operations in Israel three years after opening a research and development center in the country. Verily staff in Israel are expected to leave by the third quarter of 2024. The company cited an effort to refocus its strategy on core products and projects as the reason for the closure. [ 15 ]
In August 2024, Verily moved its headquarters from South San Francisco to Dallas citing significant investment and involvement in the Texas healthcare and technology sectors. [ 16 ]
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https://en.wikipedia.org/wiki/Verily
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Verkís Consulting Engineers is the oldest consulting firm in Iceland and is one of the largest engineering firms in Iceland with around 350 employees. Verkís is a multidisciplinary consulting firm, providing services in all fields of engineering and related professional disciplines of consulting. Verkís offers engineering , consulting, management, operational and EPCM services. Core disciplines include geothermal and hydroelectric power and Verkís has participated in nearly all geothermal and hydroelectric projects in Iceland as well as in several projects abroad. Other core disciplines include geothermal district heating , power transmission , buildings, transport, infrastructure and industry.
Ever since the early 1930s, Verkís has participated in the engineering of most of Iceland's biggest and most prominent construction projects, covering disciplines such as civil and structural design, mechanical engineering , electrical HV, MV, and LV engineering, systems engineering , automation and control.
Egill Viðarsson is the CEO and Snæbjörn Jónsson is the chairman of the board. The headquarters are in Reykjavík but in addition there are eleven branches around Iceland .
Verkís traces its origin back to 1932, making it the oldest consulting company in Iceland, and has a firm background in the energy- and construction industry both in Iceland and abroad. Verkís was formed in 2008 by the merger of five well established Icelandic engineering consulting firms: [ 2 ]
VST was established in 1932 and has over the years provided a wide range of services. Consultancy services in the building industry, energy and infrastructure has been the main area of activity and VST took part in most hydropower projects in Iceland. In recent years, VST has offered a variety of other services, especially within the aluminium industry, and also in the fields of project management, construction, safety and environmental management.
Rafteikning was established in 1965 and has been one of the leading electrical consulting service firms in Iceland. The main focus of activity has been on power and control engineering and the firm has participated in the electrical design of several hydropower and geothermal power plants .
Fjarhitun was established in 1962 and has been a leader in designing district heating systems, utilizing the geothermal hot water in Iceland and has also participated in the design of many geothermal power plants . Fjarhitun has provided a wide range of services in other fields of mechanical engineering .
Fjölhönnun was established in 1970 and has been active in the design of roads, bridges and similar structures and the structural design of buildings. The firm has also participated in many projects, providing supervision and project management.
RT Rafagnatækni was established in 1961 and has specialized in the planning, design and programming of control systems for power plants and other systems in the field of automation, measurements and communication. RT has also been providing services in field of electronics.
On 17 April 2013 Almenna Consulting teamed up with Verkís.
Almenna Consulting Engineers Ltd. was founded in 1941 as "Almenna byggingarfélagið", it played an important role in modernising the infrastructure of the country as it took part in developing the country's first large hydroelectric power plants in the 1960s. In 1971, the company was reorganized as Almenna Consulting Engineers Ltd .
Verkís is divided into seven divisions, five of which are business segment divisions. In addition to the business segment divisions, there is an office support division and a branch office division. Each business segment division is split into discipline sections. The management team consist of the CEO and seven division managers. The board represents the owners of the company and has five members and two alternate members. [ 3 ]
Verkís provides consultancy services in most fields of engineering and related disciplines. The services offered includes: Project Management and EPCM , Cost Estimation and Planning, Engineering and Design, Project Controls, Feasibility studies, Inspection services, Procurement , and Commissioning. Support functions such as Risk Assessment , Quality Management , Health Safety and Environment, and the development of Environmental Impact Assessments are also an integral part of the services.
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https://en.wikipedia.org/wiki/Verkís
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Verlet integration ( French pronunciation: [vɛʁˈlɛ] ) is a numerical method used to integrate Newton's equations of motion . [ 1 ] It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics . The algorithm was first used in 1791 by Jean Baptiste Delambre and has been rediscovered many times since then, most recently by Loup Verlet in the 1960s for use in molecular dynamics. It was also used by P. H. Cowell and A. C. C. Crommelin in 1909 to compute the orbit of Halley's Comet , and by Carl Størmer in 1907 to study the trajectories of electrical particles in a magnetic field (hence it is also called Størmer's method ). [ 2 ] The Verlet integrator provides good numerical stability , as well as other properties that are important in physical systems such as time reversibility and preservation of the symplectic form on phase space , at no significant additional computational cost over the simple Euler method .
For a second-order differential equation of the type x ¨ ( t ) = A ( x ( t ) ) {\displaystyle {\ddot {\mathbf {x} }}(t)=\mathbf {A} {\bigl (}\mathbf {x} (t){\bigr )}} with initial conditions x ( t 0 ) = x 0 {\displaystyle \mathbf {x} (t_{0})=\mathbf {x} _{0}} and x ˙ ( t 0 ) = v 0 {\displaystyle {\dot {\mathbf {x} }}(t_{0})=\mathbf {v} _{0}} , an approximate numerical solution x n ≈ x ( t n ) {\displaystyle \mathbf {x} _{n}\approx \mathbf {x} (t_{n})} at the times t n = t 0 + n Δ t {\displaystyle t_{n}=t_{0}+n\,\Delta t} with step size Δ t > 0 {\displaystyle \Delta t>0} can be obtained by the following method:
Newton's equation of motion for conservative physical systems is
or individually
where
This equation, for various choices of the potential function V {\displaystyle V} , can be used to describe the evolution of diverse physical systems, from the motion of interacting molecules to the orbit of the planets .
After a transformation to bring the mass to the right side and forgetting the structure of multiple particles, the equation may be simplified to
with some suitable vector-valued function A ( x ) {\displaystyle \mathbf {A} (\mathbf {x} )} representing the position-dependent acceleration. Typically, an initial position x ( 0 ) = x 0 {\displaystyle \mathbf {x} (0)=\mathbf {x} _{0}} and an initial velocity v ( 0 ) = x ˙ ( 0 ) = v 0 {\displaystyle \mathbf {v} (0)={\dot {\mathbf {x} }}(0)=\mathbf {v} _{0}} are also given.
To discretize and numerically solve this initial value problem , a time step Δ t > 0 {\displaystyle \Delta t>0} is chosen, and the sampling-point sequence t n = n Δ t {\displaystyle t_{n}=n\,\Delta t} considered. The task is to construct a sequence of points x n {\displaystyle \mathbf {x} _{n}} that closely follow the points x ( t n ) {\displaystyle \mathbf {x} (t_{n})} on the trajectory of the exact solution.
Where Euler's method uses the forward difference approximation to the first derivative in differential equations of order one, Verlet integration can be seen as using the central difference approximation to the second derivative:
Verlet integration in the form used as the Størmer method [ 3 ] uses this equation to obtain the next position vector from the previous two without using the velocity as
The time symmetry inherent in the method reduces the level of local errors introduced into the integration by the discretization by removing all odd-degree terms, here the terms in Δ t {\displaystyle \Delta t} of degree three. The local error is quantified by inserting the exact values x ( t n − 1 ) , x ( t n ) , x ( t n + 1 ) {\displaystyle \mathbf {x} (t_{n-1}),\mathbf {x} (t_{n}),\mathbf {x} (t_{n+1})} into the iteration and computing the Taylor expansions at time t = t n {\displaystyle t=t_{n}} of the position vector x ( t ± Δ t ) {\displaystyle \mathbf {x} (t\pm \Delta t)} in different time directions:
where x {\displaystyle \mathbf {x} } is the position, v = x ˙ {\displaystyle \mathbf {v} ={\dot {\mathbf {x} }}} the velocity, a = x ¨ {\displaystyle \mathbf {a} ={\ddot {\mathbf {x} }}} the acceleration, and b = a ˙ = x … {\displaystyle \mathbf {b} ={\dot {\mathbf {a} }}={\overset {\dots }{\mathbf {x} }}} the jerk ( third derivative of the position with respect to the time).
Adding these two expansions gives
We can see that the first- and third-order terms from the Taylor expansion cancel out, thus making the Verlet integrator an order more accurate than integration by simple Taylor expansion alone.
Caution should be applied to the fact that the acceleration here is computed from the exact solution, a ( t ) = A ( x ( t ) ) {\displaystyle \mathbf {a} (t)=\mathbf {A} {\bigl (}\mathbf {x} (t){\bigr )}} , whereas in the iteration it is computed at the central iteration point, a n = A ( x n ) {\displaystyle \mathbf {a} _{n}=\mathbf {A} (\mathbf {x} _{n})} . In computing the global error, that is the distance between exact solution and approximation sequence, those two terms do not cancel exactly, influencing the order of the global error.
To gain insight into the relation of local and global errors, it is helpful to examine simple examples where the exact solution, as well as the approximate solution, can be expressed in explicit formulas. The standard example for this task is the exponential function .
Consider the linear differential equation x ¨ ( t ) = w 2 x ( t ) {\displaystyle {\ddot {x}}(t)=w^{2}x(t)} with a constant w {\displaystyle w} . Its exact basis solutions are e w t {\displaystyle e^{wt}} and e − w t {\displaystyle e^{-wt}} .
The Størmer method applied to this differential equation leads to a linear recurrence relation
or
It can be solved by finding the roots of its characteristic polynomial q 2 − 2 ( 1 + 1 2 ( w h ) 2 ) q + 1 = 0 {\displaystyle q^{2}-2\left(1+{\tfrac {1}{2}}(wh)^{2}\right)q+1=0} . These are
The basis solutions of the linear recurrence are x n = q + n {\displaystyle x_{n}=q_{+}^{n}} and x n = q − n {\displaystyle x_{n}=q_{-}^{n}} . To compare them with the exact solutions, Taylor expansions are computed:
The quotient of this series with the exponential e w h {\displaystyle e^{wh}} starts with 1 − 1 24 ( w h ) 3 + O ( h 5 ) {\displaystyle 1-{\tfrac {1}{24}}(wh)^{3}+{\mathcal {O}}\left(h^{5}\right)} , so
From there it follows that for the first basis solution the error can be computed as
That is, although the local discretization error is of order 4, due to the second order of the differential equation the global error is of order 2, with a constant that grows exponentially in time.
Note that at the start of the Verlet iteration at step n = 1 {\displaystyle n=1} , time t = t 1 = Δ t {\displaystyle t=t_{1}=\Delta t} , computing x 2 {\displaystyle \mathbf {x} _{2}} , one already needs the position vector x 1 {\displaystyle \mathbf {x} _{1}} at time t = t 1 {\displaystyle t=t_{1}} . At first sight, this could give problems, because the initial conditions are known only at the initial time t 0 = 0 {\displaystyle t_{0}=0} . However, from these the acceleration a 0 = A ( x 0 ) {\displaystyle \mathbf {a} _{0}=\mathbf {A} (\mathbf {x} _{0})} is known, and a suitable approximation for the position at the first time step can be obtained using the Taylor polynomial of degree two:
The error on the first time step then is of order O ( Δ t 3 ) {\displaystyle {\mathcal {O}}\left(\Delta t^{3}\right)} . This is not considered a problem because on a simulation over a large number of time steps, the error on the first time step is only a negligibly small amount of the total error, which at time t n {\displaystyle t_{n}} is of the order O ( e L t n Δ t 2 ) {\displaystyle {\mathcal {O}}\left(e^{Lt_{n}}\Delta t^{2}\right)} , both for the distance of the position vectors x n {\displaystyle \mathbf {x} _{n}} to x ( t n ) {\displaystyle \mathbf {x} (t_{n})} as for the distance of the divided differences x n + 1 − x n Δ t {\displaystyle {\tfrac {\mathbf {x} _{n+1}-\mathbf {x} _{n}}{\Delta t}}} to x ( t n + 1 ) − x ( t n ) Δ t {\displaystyle {\tfrac {\mathbf {x} (t_{n+1})-\mathbf {x} (t_{n})}{\Delta t}}} . Moreover, to obtain this second-order global error, the initial error needs to be of at least third order.
A disadvantage of the Størmer–Verlet method is that if the time step ( Δ t {\displaystyle \Delta t} ) changes, the method does not approximate the solution to the differential equation. This can be corrected using the formula [ 4 ]
A more exact derivation uses the Taylor series (to second order) at t i {\displaystyle t_{i}} for times t i + 1 = t i + Δ t i {\displaystyle t_{i+1}=t_{i}+\Delta t_{i}} and t i − 1 = t i − Δ t i − 1 {\displaystyle t_{i-1}=t_{i}-\Delta t_{i-1}} to obtain after elimination of v i {\displaystyle \mathbf {v} _{i}}
so that the iteration formula becomes
The velocities are not explicitly given in the basic Størmer equation, but often they are necessary for the calculation of certain physical quantities like the kinetic energy . This can create technical challenges in molecular dynamics simulations, because kinetic energy and instantaneous temperatures at time t {\displaystyle t} cannot be calculated for a system until the positions are known at time t + Δ t {\displaystyle t+\Delta t} . This deficiency can either be dealt with using the velocity Verlet algorithm or by estimating the velocity using the position terms and the mean value theorem :
Note that this velocity term is a step behind the position term, since this is for the velocity at time t {\displaystyle t} , not t + Δ t {\displaystyle t+\Delta t} , meaning that v n = x n + 1 − x n − 1 2 Δ t {\displaystyle \mathbf {v} _{n}={\tfrac {\mathbf {x} _{n+1}-\mathbf {x} _{n-1}}{2\Delta t}}} is a second-order approximation to v ( t n ) {\displaystyle \mathbf {v} (t_{n})} . With the same argument, but halving the time step, v n + 1 2 = x n + 1 − x n Δ t {\displaystyle \mathbf {v} _{n+{\frac {1}{2}}}={\tfrac {\mathbf {x} _{n+1}-\mathbf {x} _{n}}{\Delta t}}} is a second-order approximation to v ( t n + 1 2 ) {\displaystyle \mathbf {v} \left(t_{n+{\frac {1}{2}}}\right)} , with t n + 1 2 = t n + 1 2 Δ t {\displaystyle t_{n+{\frac {1}{2}}}=t_{n}+{\tfrac {1}{2}}\Delta t} .
One can shorten the interval to approximate the velocity at time t + Δ t {\displaystyle t+\Delta t} at the cost of accuracy:
A related, and more commonly used algorithm is the velocity Verlet algorithm, [ 5 ] similar to the leapfrog method , except that the velocity and position are calculated at the same value of the time variable (leapfrog does not, as the name suggests). This uses a similar approach, but explicitly incorporates velocity, solving the problem of the first time step in the basic Verlet algorithm:
It can be shown that the error in the velocity Verlet is of the same order as in the basic Verlet. Note that the velocity algorithm is not necessarily more memory-consuming, because, in basic Verlet, we keep track of two vectors of position, while in velocity Verlet, we keep track of one vector of position and one vector of velocity. The standard implementation scheme of this algorithm is:
This algorithm also works with variable time steps, and is identical to the 'kick-drift-kick' form of leapfrog method integration.
Eliminating the half-step velocity, this algorithm may be shortened to
Note, however, that this algorithm assumes that acceleration a ( t + Δ t ) {\displaystyle \mathbf {a} (t+\Delta t)} only depends on position x ( t + Δ t ) {\displaystyle \mathbf {x} (t+\Delta t)} and does not depend on velocity v ( t + Δ t ) {\displaystyle \mathbf {v} (t+\Delta t)} .
One might note that the long-term results of velocity Verlet, and similarly of leapfrog are one order better than the semi-implicit Euler method . The algorithms are almost identical up to a shift by half a time step in the velocity. This can be proven by rotating the above loop to start at step 3 and then noticing that the acceleration term in step 1 could be eliminated by combining steps 2 and 4. The only difference is that the midpoint velocity in velocity Verlet is considered the final velocity in semi-implicit Euler method.
The global error of all Euler methods is of order one, whereas the global error of this method is, similar to the midpoint method , of order two. Additionally, if the acceleration indeed results from the forces in a conservative mechanical or Hamiltonian system , the energy of the approximation essentially oscillates around the constant energy of the exactly solved system, with a global error bound again of order one for semi-explicit Euler and order two for Verlet-leapfrog. The same goes for all other conserved quantities of the system like linear or angular momentum, that are always preserved or nearly preserved in a symplectic integrator . [ 6 ]
The velocity Verlet method is a special case of the Newmark-beta method with β = 0 {\displaystyle \beta =0} and γ = 1 2 {\displaystyle \gamma ={\tfrac {1}{2}}} .
Since velocity Verlet is a generally useful algorithm in 3D applications, a solution written in C++ could look like below. This type of position integration will significantly increase accuracy in 3D simulations and games when compared with the regular Euler method.
The global truncation error of the Verlet method is O ( Δ t 2 ) {\displaystyle {\mathcal {O}}\left(\Delta t^{2}\right)} , both for position and velocity.
This is in contrast with the fact that the local error in position is only O ( Δ t 4 ) {\displaystyle {\mathcal {O}}\left(\Delta t^{4}\right)} as described above. The difference is due to the accumulation of the local truncation error over all of the iterations.
The global error can be derived by noting the following:
and
Therefore
Similarly:
which can be generalized to (it can be shown by induction, but it is given here without proof):
If we consider the global error in position between x ( t ) {\displaystyle x(t)} and x ( t + T ) {\displaystyle x(t+T)} , where T = n Δ t {\displaystyle T=n\Delta t} , it is clear that [ citation needed ]
and therefore, the global (cumulative) error over a constant interval of time is given by
Because the velocity is determined in a non-cumulative way from the positions in the Verlet integrator, the global error in velocity is also O ( Δ t 2 ) {\displaystyle {\mathcal {O}}\left(\Delta t^{2}\right)} .
In molecular dynamics simulations, the global error is typically far more important than the local error, and the Verlet integrator is therefore known as a second-order integrator.
Systems of multiple particles with constraints are simpler to solve with Verlet integration than with Euler methods. Constraints between points may be, for example, potentials constraining them to a specific distance or attractive forces. They may be modeled as springs connecting the particles. Using springs of infinite stiffness, the model may then be solved with a Verlet algorithm.
In one dimension, the relationship between the unconstrained positions x ~ i ( t ) {\displaystyle {\tilde {x}}_{i}^{(t)}} and the actual positions x i ( t ) {\displaystyle x_{i}^{(t)}} of points i {\displaystyle i} at time t {\displaystyle t} , given a desired constraint distance of r {\displaystyle r} , can be found with the algorithm
Verlet integration is useful because it directly relates the force to the position, rather than solving the problem using velocities.
Problems, however, arise when multiple constraining forces act on each particle. One way to solve this is to loop through every point in a simulation, so that at every point the constraint relaxation of the last is already used to speed up the spread of the information. In a simulation this may be implemented by using small time steps for the simulation, using a fixed number of constraint-solving steps per time step, or solving constraints until they are met by a specific deviation.
When approximating the constraints locally to first order, this is the same as the Gauss–Seidel method . For small matrices it is known that LU decomposition is faster. Large systems can be divided into clusters (for example, each ragdoll = cluster). Inside clusters the LU method is used, between clusters the Gauss–Seidel method is used. The matrix code can be reused: The dependency of the forces on the positions can be approximated locally to first order, and the Verlet integration can be made more implicit.
Sophisticated software, such as SuperLU [ 7 ] exists to solve complex problems using sparse matrices. Specific techniques, such as using (clusters of) matrices, may be used to address the specific problem, such as that of force propagating through a sheet of cloth without forming a sound wave . [ 8 ]
Another way to solve holonomic constraints is to use constraint algorithms .
One way of reacting to collisions is to use a penalty-based system, which basically applies a set force to a point upon contact. The problem with this is that it is very difficult to choose the force imparted. Use too strong a force, and objects will become unstable, too weak, and the objects will penetrate each other. Another way is to use projection collision reactions, which takes the offending point and attempts to move it the shortest distance possible to move it out of the other object.
The Verlet integration would automatically handle the velocity imparted by the collision in the latter case; however, note that this is not guaranteed to do so in a way that is consistent with collision physics (that is, changes in momentum are not guaranteed to be realistic). Instead of implicitly changing the velocity term, one would need to explicitly control the final velocities of the objects colliding (by changing the recorded position from the previous time step).
The two simplest methods for deciding on a new velocity are perfectly elastic and inelastic collisions . A slightly more complicated strategy that offers more control would involve using the coefficient of restitution .
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https://en.wikipedia.org/wiki/Verlet_integration
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A Verlet list (named after Loup Verlet ) is a data structure in molecular dynamics simulations to efficiently maintain a list of all particles within a given cut-off distance of each other. [ 1 ]
This method may easily be applied to Monte Carlo simulations . For short-range interactions, a cut-off radius is typically used, beyond which particle interactions are considered "close enough" to zero to be safely ignored. For each particle, a Verlet list is constructed that lists all other particles within the potential cut-off distance, plus some extra distance so that the list may be used for several consecutive Monte Carlo "sweeps" (set of Monte Carlo steps or moves) before being updated. If we wish to use the same Verlet list n {\displaystyle n} times before updating, then the cut-off distance for inclusion in the Verlet list should be R c + 2 n d {\displaystyle R_{c}+2nd} , where R c {\displaystyle R_{c}} is the cut-off distance of the potential, and d {\displaystyle d} is the maximum Monte Carlo step (move) of a single particle. Thus, we will spend of order N 2 {\displaystyle N^{2}} time to compute the Verlet lists ( N {\displaystyle N} is the total number of particles), but are rewarded with n {\displaystyle n} Monte Carlo "sweeps" of order N n 2 {\displaystyle Nn^{2}} instead of N N {\displaystyle NN} . By optimizing our choice of n {\displaystyle n} it can be shown that Verlet lists allow converting the O ( N 2 ) {\displaystyle O(N^{2})} problem of Monte Carlo sweeps to an O ( N 5 / 3 ) {\displaystyle O(N^{5/3})} problem.
Using cell lists to identify the nearest neighbors in O ( N ) {\displaystyle O(N)} further reduces the computational cost.
This computational chemistry -related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Verlet_list
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Vermeology (from Latin vermes , worms) is the field of biology dedicated to the study of worms . [ 1 ] A person who studies vermeology is referred to as a vermeologist .
The umbrella term "vermeology" has fallen out of common use, as the animals known as worms belong to multiple phyla that are not closely related. Subfields of vermeology include nematology , the study of nematodes , oligochaetology [ 2 ] (also called lumbricology [ 3 ] ), the study of earthworms , and helminthology , [ 4 ] which focuses on parasitic worms, also known as helminths . The field of malacology was also historically included within vermeology.
The final book that Charles Darwin published in his lifetime focused on bioturbation by earthworms.
This zoology –related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Vermeology
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Vermes (" vermin/vermes ") is an obsolete taxon used by Carl Linnaeus and Jean-Baptiste Lamarck for non- arthropod invertebrate animals .
In Linnaeus's Systema Naturae , the Vermes had the rank of class , occupying the 6th (and last) slot of his animal systematics. It was divided into the following orders , all except the Lithophyta containing (in modern terms) organisms from a variety of phyla: [ 1 ]
Apart from the Mollusca , understood very differently from the modern phylum of that name, Linnaeus included a very diverse and rather mismatched assemblage of animals in the categories. The Intestina group encompassed various parasitic animals, among them the hagfish , which Linnaeus would have found in dead fish. Shelled molluscs were placed in the Testacea, together with barnacles and tube worms . Cnidarians (jellyfish and corals), echinoderms and polychaetes were spread across the other orders.
Linnaeus's system was revised by Jean-Baptiste Lamarck in his 1801 Système des Animaux sans Vertebres . In this work, he categorized echinoderms , arachnids , crustaceans and annelids , which he separated from Vermes . [ 2 ]
After Linnaeus, and especially with the advent of Darwinism , it became apparent that the Vermes animals are not closely related. Systematic works on phyla since Linnaeus continued to split up Vermes and sort the animals into natural systematic units.
Of the classes of Vermes proposed by Linnaeus, only Mollusca has been kept as a phylum, and its composition has changed almost entirely. Linnaeus's early classification of the soft-bodied organisms was revolutionary in its day. A number of the organisms classified as Vermes by Linnaeus were very poorly known, and a number of them were not even viewed as animals.
While the Vermes is no longer a taxonomic group, anatomists continue to use the description "vermiform" of animals or organs that are worm -shaped. The word root is Latin , vermes ( worms ) and formes ( shaped ) . [ 3 ] A well known example is the vermiform appendix , a small, blind section of the gut in humans and a number of other mammals . [ 4 ]
Several soft-bodied animal phyla including the annelids (earthworm and relatives) and the roundworms (mainly parasites), but also the minute parasitic mesozoans and some larger-bodied free-living phyla like the ribbon worms , peanut worms , and priapulids .
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https://en.wikipedia.org/wiki/Vermiform
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Vermilion (sometimes vermillion ) [ 1 ] is a color family and pigment most often used between antiquity and the 19th century from the powdered mineral cinnabar (a form of mercury sulfide ). It is synonymous with red orange , which often takes a modern form, but is 11% brighter (at full brightness). [ contradictory ]
Used first in English in the 13th century, the word vermilion came from the Old French word vermeillon , which was derived from vermeil , from the Latin vermiculus – the diminutive of the Latin word vermis for worm. [ 2 ]
The name originated because it had a similar color to the natural red dye made from an insect, Kermes vermilio , which was widely used in Europe. [ 2 ] [ 3 ] The first recorded use of "vermilion" as a color name in English was in 1289. [ 4 ] [ 5 ]
The term cinnabar is used in mineralogy and crystallography for the red crystalline form of mercury sulfide HgS. Thus, the natural mineral pigment is called "cinnabar", and its synthetic form is called "vermilion" from red lead . [ 2 ]
Vermilion is a dense, opaque pigment with a clear, brilliant hue. [ 6 ] The pigment was originally made by grinding a powder of cinnabar ( mercury sulfide ). [ 7 ] Like most mercury compounds, it is toxic . [ 8 ]
Vermilion is not one specific hue; mercuric sulfides make a range of warm hues, from bright orange-red to a duller reddish-purple that resembles fresh liver. Differences in hue are caused by the size of the ground particles of pigment. Larger crystals produce duller and less orange hues.
Cinnabar pigment was a side product of the mining of mercury, and mining cinnabar was difficult, expensive, and dangerous, because of the toxicity of mercury. Greek philosopher Theophrastus of Eresus (371–286 BC) described the process in De Lapidibus , the first scientific book on minerals. Efforts began early to find a better way to make the pigment.
The Chinese were probably the first to make a synthetic vermilion as early as the fourth century BC. Greek alchemist Zosimus of Panopolis (third–fourth century AD) wrote that such a method existed. In the early 9th century, the process was accurately described by Persian alchemist Jabir ibn Hayyan (722–804) in his book of recipes of colors, and the process began to be widely used in Europe. [ 6 ] [ 9 ]
The process described by Jabir ibn Hayyan was fairly simple:
When first created, the material is almost black. As it is ground, the red color appears. The longer the compound is ground, the finer the color becomes. Italian Renaissance artist Cennino Cennini wrote: "If you were to grind it every day, even for 20 years, it would keep getting better and more perfect." [ 10 ]
In the 17th century, a new method of making the pigment was introduced, known as the Dutch method. [ 8 ] Mercury and melted sulfur were mashed to make black mercury sulfide , then heated in a retort , producing vapors condensing as a bright, red mercury sulfide. To remove the sulfur, these crystals were treated with a strong alkali, washed, and finally ground under water to yield the commercial powder form of the pigment. [ 11 ] The pigment is still made today using essentially the same process.
Vermilion has one important defect; it is liable to darken, or develop a purplish-gray surface sheen. [ 6 ] Cennino Cennini wrote, "Bear in mind ... that it is not in its character to be exposed to air, but it is more resistant on panel than on walls since, when it is used and laid on a wall, over a period of time, standing in the air, it turns black." [ 12 ] Newer research indicates that chlorine ions and light may aid in decomposing vermilion into elemental mercury, which is black when in finely dispersed form. [ 13 ] [ 14 ]
Vermilion was the primary red pigment used by European painters, from the Renaissance until the 20th century. Because of its cost and toxicity, though, it was almost entirely replaced by a new synthetic pigment, cadmium red , in the 20th century. As cadmium can also be toxic, some scientists propose replacing this with solid solutions of the perovskites CaTaO2N and LaTaON2. [ 15 ]
Genuine vermilion pigment today comes mostly from China; it is a synthetic mercuric sulfide, labeled on paint tubes as PR-106 (Red Pigment 106). The synthetic pigment is of higher quality than vermilion made from ground cinnabar, which has many impurities. The pigment is very toxic, and should be used with great care. [ 16 ]
The colors are widely used in the art and decoration of Ancient Rome and the Byzantine Empire , then in the illuminated manuscripts of the Middle Ages , in the paintings of the Renaissance , and in the art and lacquerware of China . [ 17 ] [ 18 ]
The first documented use of vermilion pigment, made with ground cinnabar, dates to 8000–7000 BC, and was found at the Neolithic village of Çatalhöyük , in modern-day Turkey. Cinnabar was mined in Spain beginning in about 5300 BC. In China, the first documented use of cinnabar as a pigment was by the Yangshao culture (5000–4000 BC), where it was used to paint ceramics, to cover the walls and floors of rooms, and for ritual ceremonies. [ 19 ]
The principal source of cinnabar for the ancient Romans was the Almaden mine in northwest Spain, which was worked by prisoners. Since the ore of mercury was highly toxic, a term in the mines was a near-guaranteed death sentence. Pliny the Elder described the mines this way:
Nothing is more carefully guarded. It is forbidden to break up or refine the cinnabar on the spot. They send it to Rome in its natural condition, under seal, to the extent of some ten thousand librae ( Roman pounds thus 3289 kg) a year. The sales price is fixed by law to keep it from becoming impossibly expensive, and the price fixed is seventy sesterces a pound. [ 20 ]
In Rome, the precious pigment was used to paint frescoes, decorate statues, and even as a cosmetic . In Roman triumphs , the victors had their faces covered with vermilion powder, and the face of Jupiter on the Capitoline Hill was also colored vermilion. [ 7 ] Cinnabar was used to paint the walls of some of the most luxurious villas in Pompeii , including the Villa of the Mysteries (Italian: Villa dei Misteri ). [ 7 ] Pliny reported its painters stole a large portion of the expensive pigment by frequently washing their brushes and saving the wash water. [ 21 ]
In the Byzantine Empire , the use of cinnabar/the vermilion color was reserved for the use of the imperial family and administrators; official letters and imperial decrees were written in vermilion ink, made with cinnabar. [ 21 ]
It is known as sindoor . Sindoor is commonly used by married women in Hindu religion. [ 17 ]
Vermilion was also used by the native peoples of America, to paint ceramics, figurines, and murals, and for the decoration of burials. It was used in the Chavin civilization (400 BC – 200 AD), and in the Maya , Sican, Moche, and Inca empires. The major source was the Huancavelica mine in the Andes mountains in central Peru.
The most dramatic example of vermilion use in the Americas was the so-called Tomb of the Red Queen , located in Temple XIII, in the ruins of the Mayan city of Palenque in Chiapas, Mexico. The temple is dated to between 600 and 700 AD. It was discovered in 1994 by Mexican archeologist Fanny López Jiménez . The body and all objects in the sarcophagus were covered with bright red vermilion powder made from cinnabar. [ 22 ] [ 23 ] [ 19 ]
The technique for making a synthetic vermilion by combining sulfur and mercury was in use in Europe in the 9th century, but the pigment was still expensive. Since it was almost as expensive as gold leaf, it was used only in the most important decoration of illuminated manuscripts, while the less expensive minium , made with red lead , was used for the red letters and symbols in the text.
Vermilion was also used by painters in the Renaissance as a very vivid and bright red, though it did have the weakness of sometimes turning dark with time. Florentine artist Cennino Cennini described it in his handbook for artists:
This pigment is made by alchemy , prepared in a retort , which subject I will leave be since to put every method and recipe into my discussion would be too longwinded. The reason? Because if you care to take the trouble, you will find a lot of recipes for it, and particularly if you cultivate friendships with monks. But, so that you do not waste your time with the many different techniques, I advise you, just take what you can find at the apothecary's for your money. And I want to teach you how to buy it and how to recognise the good vermilion. Always buy solid vermilion and not crushed or ground. The reason? Because more often than not you are cheated either with red lead or crushed brick. [ 24 ]
By the 20th century, the cost and toxicity of vermilion led to its gradually being replaced by synthetic pigments, particularly cadmium red, which had a comparable color and opacity.
In China, the color vermilion was also playing an important role in national culture. The color was mostly used in creating Chinese lacquerware , which was exported around the world, giving rise to the term "Chinese red".
The lacquer came from the Chinese lacquer tree , or Toxicodendron vernicifluum , a relative of poison ivy and poison sumac (not to be confused with sumac , which is in a different genus and is not toxic), which grew in regions of China, Korea , and Japan. The sap or resin of the tree, called urushiol , was caustic and toxic (it contained the same chemical compound as poison ivy ), but painted onto wood or metal, it hardened into a fine natural plastic, or lacquer surface. The pure sap was dark brown, but beginning in about the third century BC, during the Han dynasty , Chinese artisans colored it with powdered cinnabar or with red ochre ( ferric oxide ), giving it an orange-red color. [ 25 ] [ 26 ] Beginning in about the 8th century, Chinese chemists began making synthetic vermilion from mercury and sulfur, which reduced the price of the pigment and allowed the production of Chinese lacquerware on a larger scale.
The shade of red of the lacquerware has changed over the centuries. During the Eastern Han dynasty (25–220 AD) the Chinese word for red referred to a light red. However, during the Tang dynasty (618–907), when the synthetic vermilion was introduced, that color became darker and richer. The poet Bai Juyi (772–846) wrote in a song poem praising Jiangnan , "the flowers by the river when the sun rises are redder than flames", and the word he used for red was the word for vermilion, or Chinese red. [ 27 ]
When Chinese lacquerware and the ground cinnabar used to color it were exported to Europe in the 17th and 18th centuries, European collectors considered it to be finer than the European vermilion. In 1835, "Chinese vermilion" was described as a cinnabar so pure that it only had to be ground into powder to become a perfect vermilion. Historically, European vermilion often included adulterants including brick, orpiment , iron oxide , Persian red , iodine scarlet —and minium (red lead), an inexpensive and bright, but fugitive lead-oxide pigment. [ 28 ]
Since ancient times, vermilion was regarded as the color of blood, thus the color of life. It was used to paint temples and the carriages of the emperor, and as the printing paste for personal seals . It was also used for unique red calligraphic ink reserved for emperors. Chinese Taoists associated vermilion with eternity.
The Dutch singer Simone Simons , released her debut solo album called Vermillion in 2024. On this album, the word vermillion was used for one of the song titles called "Vermillion Dreams" and also the album was called vermillion.
The Crayola color red-orange has been a Crayola color since 1930.
The web color orange-red was formulated in 1987 as one of the X11 colors , which became known as the X11 web colors after the invention of the World Wide Web in 1991.
This color is the medium tone of vermilion called vermilion on the Plochere color list, which was formulated in 1948 and is used widely by interior designers.
Chinese red or China red is the name used for the vermilion shade used in Chinese lacquerware . The shade of the color can vary from dark to light depending upon how the pigment is made and how the lacquer was applied. Chinese red was originally made from the powdered mineral cinnabar, but beginning in about the 8th century it was made more commonly by a chemical process combining mercury and sulfur. Vermilion has significance in Taoist culture, and is regarded as the color of life and eternity.
"Chinese red" appears in English in 1924. [ 33 ]
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Vermin ( colloquially varmint(s) [ 1 ] or varmit(s) ) are pests or nuisance animals that spread diseases and destroy crops , livestock , and property . Since the term is defined in relation to human activities, which species are included vary by region and enterprise.
The term derives from the Latin vermis ( worm ), and was originally used for the worm-like larvae of certain insects , many of which infest foodstuffs. [ 2 ] The term varmint (and vermint ) has been found in sources from c. 1530–1540s. [ 1 ] [ 3 ]
The term "vermin" is used to refer to a wide scope of organisms, including rodents (such as rats ), cockroaches , termites , bed bugs , [ 4 ] stoats , sables .
Historically, in the 16th and 17th century, the expression also became used as a derogatory term associated with groups of persons typically plagued by vermin, namely beggars and vagabonds , and more generally the poor . [ 5 ]
Disease-carrying rodents and insects are the usual case, but the term is also applied to larger animals—especially small predators —typically because they consume resources which humans consider theirs, such as livestock and crops. Birds which eat cereal crops and fruit are an example. The American crow ( Corvus brachyrhynchos ), is widely hated by farmers because of crop depredation. Pigeons , which have been widely introduced in urban environments, are also sometimes considered vermin. Some varieties of snakes and arachnids may also be referred to as vermin. "Vermin" is also used by some people as a term of abuse, either individually or collectively. [ 1 ]
Varmint or varmit is an American-English colloquialism , a corruption of "vermin" particularly common to the American East and South-east within the nearby bordering states of the vast Appalachia region. The term describes species which raid farms from without, as opposed to vermin (such as rats) that infest from within, thus referring mainly to predators such as feral dogs , foxes , weasels , and coyotes , sometimes even wolves or rarely bears , but also, to a lesser degree, herbivores and burrowing animals that directly damage crops and land.
Although "varmint/varmit" is not the prevalent usage in Standard Written English , it is a common descriptor for certain kinds of weapons and pest control situations in the Appalachian and nearby states and the American West and South-west which have adopted terms such as varmint rifle and varmint hunting .
Any species can develop into vermin if introduced into a region where there are favorable living conditions and few natural predators. In such cases, they are seen as an invasive species and humans often choose to fill the role of the predator to limit the danger to the environment. Examples of vermin include goats on the Galápagos Islands , rabbits in Australia or cats on Prince Edward Islands . Rats , mice , and cockroaches are common urban and suburban vermin. The introduction of Hippos into Colombia by Pablo Escobar led to the Hippos becoming an invasive species. The transplanted Hippos thrived and flourished in Colombia due to the favorable living conditions and few predators leading to a invasively rapid increase of the Hippo population.
Under Tudor "vermin laws", many creatures were seen as competitors for the produce of the countryside and bounties were paid by the parish for their carcasses. The declaration of the red kite as vermin led to its decline to the point of extirpation in the UK by the 20th century. However, the red kite has since been reintroduced to much of Scotland and the majority of England and Wales by the trans-location of breeding pairs from other parts of Europe. [ 6 ]
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Vermitechnology is an overarching term for the following subtopics:
Vermitechnology includes the study and commercial application of technologies that utilise earthworms for degrading waste organic materials for sanitation and agricultural re-use. [ 1 ] Organic wastes degraded and stabilised by earthworms include those suspended or dissolved in water and also solid organic material.
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Vermixocins A and B are isolates of Penicillium vermiculatum . Both compounds have cytotoxic activity in vitro . [ 1 ]
This article about an organic compound is a stub . You can help Wikipedia by expanding it .
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Vermont SportsCar ( VSC ) is a race car manufacturer that designs, engineers, and builds rally , rallycross and other specialty vehicles for teams and private clients. Since 2006 Vermont SportsCar has been the technical partner to Subaru of America and manages the automaker's racing division Subaru Motorsports USA . [ 1 ]
Founded by Lance Smith in 1988, [ 2 ] VSC operates in Milton, Vermont, with more than 70 full-time employees. [ 3 ] VSC manages motorsports programs primarily within the American Rally Association Championship, Nitro Rallycross series, and the Mount Washington Hill Climb . Additionally VSC designs, builds and campaigns the Gymkhana Subaru vehicles driven by Travis Pastrana . [ 4 ]
VSC manufactures and sells aftermarket performance parts for Subaru vehicles under the name VSC Performance. [ 5 ] VSC also offers prototyping and engineering services for private race teams and builds custom race and road cars.
In early 2022 VSC launched a multi-car effort in the 2022–23 Nitro Rallycross Championship ’s all-electric Group E class. [ 6 ]
VSC was founded in 1988 by Lance Smith. A native of Williston, Vermont, Smith started as a mechanic preparing race cars for car builder and racer Tivvy Shenton and then in the 1980s for rally driver John Buffum . [ 7 ] In 1988, he modified a Volkswagen Golf for a private team in the SCCA ProRally series and spent the next several years competing as a co-driver for several seasons in other cars he built, including a Toyota Celica , Mitsubishi Eclipse , and Mitsubishi Galant VR4 . [ 8 ] In 1992, Smith won the co-driver's championship in the North American Rally Cup and the Subaru "Pride and Professionalism" award for the best-prepped car. [ 9 ] Smith reduced the amount of his co-driving in 1997 to focus on building a Mitsubishi Evolution V for Buffum and growing his business. In 2001 VSC supported Prodrive and Subaru of America with the launch of Subaru Rally Team USA competing in the SCCA ProRally Championship in the USA. [ 10 ] In 2003, VSC helped manage the Mitsubishi factory rally effort in the USA and competed in the SCCA ProRally Championship utilizing Mitsubishi EVO VIII rally cars. [ 11 ]
In 2006, VSC partnered again with Subaru of America to relaunch Subaru Rally Team USA and serve as the technical partner for Subaru of America's motorsports efforts. [ 12 ] That program, rebranded in 2019 as Subaru Motorsports USA, continues today and is currently the world's largest Subaru motorsports program. In its debut 2006 season, VSC won the Rally America National Championship with driver Travis Pastrana . [ 13 ] Additionally in 2006 VSC fielded Subaru WRX STI rally cars in the first rally car competition held by the ESPN X Games , where Pastrana beat former WRC Champion Colin McRae for the gold medal. [ 14 ] Pastrana won the Rally America National Championship for the next three years driving alongside Subaru teammate Ken Block , who himself won 10 rallies, two X Games medals and three podiums for Subaru in Rally America. BMX rider and racer Dave Mirra replaced Block for the 2010 season . [ 15 ] In 2011 , David Higgins replaced Pastrana and went on to clinch six consecutive championships through 2016 . Pastrana returned to the team in 2014 and won the 2017 Rally America and 2021 American Rally Association championships while Higgins secured another two championships in 2018 and 2019. [ 16 ]
VSC managed the Subaru Puma Rallycross Team for the 2012 - 2014 seasons. [ 17 ] Drivers included David Higgins , Dave Mirra , Sverre Isachsen , Bucky Lasek , Patrik Sandell , and Chris Atkinson . After the Global Rallycross series dissolved in the U.S., Subaru entered the Americas Rallycross Championship in 2018 where Subaru driver Patrik Sandell earned third place in the driver's championship. [ 18 ] Scott Speed joined the Subaru team in 2019 and led the ARX Driver's Championship until a back injury sustained at the Nitro Rallycross event in Utah forced him to miss the remainder of the ARX season. [ 19 ] The team went on to win the ARX Team's Championship in 2019, despite Speed's absence from the final two rounds (due to his injury) earning 4 wins from 6 ARX rounds. [ 20 ]
After a 2020 hiatus due to the COVID-19 pandemic, VSC and Subaru Motorsports USA entered a new rallycross series spearheaded by Subaru driver Travis Pastrana and Nitro Circus . [ 21 ] The inaugural 2021 Nitro Rallycross Championship was won by Pastrana after a close fought season with teammate Scott Speed , who finished in second in the standings after the duo was tied on points after the final round, with Pastrana winning the series based on tie-break rules; [ 22 ] Subaru Motorsports USA won the NRX Team Championship as well.
VSC built several record-winning cars for the Mount Washington Hill Climb , a 7.6-mile sprint to the summit of Mount Washington in New Hampshire . VSC entered Travis Pastrana at the wheel of the Airslayer STI, the car utilized in the Gymkhana 2020 video with Pastrana, at the 2021 Mt. Washington Hillclimb. He set a new record of 5:28.67 and broke his 5:44.72 record from 2017. [ 23 ] David Higgins had set the record twice with a VSC-prepped Subaru: in 2014 at 6:09.09 and in 2011 at 6:11.54. [ 24 ]
In 2015, VSC provided their VT15R Subaru WRX STI rally car body kit to Universal Studios for the film The Fate of the Furious , the eighth release in the Fast & Furious series. The movie featured the body kit on the Subaru WRX STI driven by the character Little Nobody, played by Scott Eastwood , and was featured in an ice racing scene. [ 25 ] The movie car was later released as a Hot Wheels scale model.
In 2020, VSC built the Airslayer STI (internally referenced as the VT20G) for Hoonigan ’s eleventh installment of the Gymkhana video series, “Gymkhana 2020,” featuring Travis Pastrana behind the wheel. [ 26 ] Pastrana subsequently drove the Airslayer STI at the 2021 Mount Washington Hill Climb where he beat his previous record and won the event overall.
VSC specializes in designing and building Subaru race cars. [ 27 ] At its Vermont shop, VSC performs nearly all facets of the build process from design to fabrication and carbon composites to wiring, engine development and paint.
Subaru WRX ARA24 Rally Car
The Subaru WRX ARA24 runs in the American Rally Association Open 4WD Class. While based on the stock model, the Subaru WRX ARA24 has a 2.0-liter four-cylinder boxer engine with a custom crankshaft, pistons, connecting rods, block, heads, and turbocharger to produce 320 horsepower and 380 pound-feet of torque when fitted with a 33mm series-mandated intake restrictor. [ 28 ] The latest rules make the car less powerful than the outgoing VT22r. A custom six-speed sequential gearbox and two limited-slip differentials handle the engine's output. Driver Brandon Semenuk and co-driver Keaton Williams won the 2023 Ojibwe Forests Rally in the VT23r, which is identical to the Subaru WRX ARA24. [ 29 ]
VT21x
The VT21x is designed for Nitro Rallycross competition. The rear doors are sealed to accommodate a rear-mounted radiator setup due to the high likelihood of front-end damage in Rallycross racing. The 2.0-liter four-cylinder boxer engine is fitted with a larger 45mm turbo restrictor to produce more than 600 horsepower and 680 pound-feet of torque. The race weight in 2021 was a minimum of 2915 pounds. [ 30 ]
Omaze Gymkhana STI
Built in tandem with the VT20g, the Omaze Gymkhana STI was a one-off road car that VSC and Hoonigan , the owner of the Gymkhana brand, donated as a prize to Omaze as part of a charity contest. The car features a custom exhaust and modified sway bars, chassis bracing, coilover springs, and a carbon fiber VSC Performance motorsport wing. It also has a unique interior featuring a rally-style hydraulic hand brake and a custom wrap inspired by the VT20g livery design. [ 31 ]
TRAX STI & Sleigh
VSC built this 2009 STI for Ken Block and billed it as the "world's fastest cat-track operation automobile for back-country snowboarding access." VSC also built a fiberglass sleigh that can be towed by the TRAX STI. [ 32 ]
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Verna Natural Mineral Water is a brand of bottled water from the Twellium Industrial Company , produced and marketed primarily in Ghana, [ 1 ] and considered by reviewers to be among the top selling bottled water brands in Ghana. [ 2 ] [ 3 ] [ 4 ]
Verna Natural Mineral Water is produced from protected underground water and bottled by the Twellium Industrial Company headquartered in Medie Kotoku in the Eastern Region of Ghana. [ 3 ] While marketing is focused on Ghana , Verna Natural Mineral Water is also sold in Burkina Faso and Togo.
Verna Natural Mineral Water appeared on the market in 2014. In 2017, Verna Natural Mineral Water underwent a rebranding exercise in line with market trends; focusing on its style and appeal to the younger generation. The plastic bottle containers now involved the display of blue and pink colors on its paper labeling, a pronounced logo for the product, and a yoghurt-pink colored cap. The rebranding of Verna Natural Mineral Water also reflected a logo of the "Changing Lives" social action project associated with the brand. [ 5 ] [ 6 ] In June 2019, Verna Natural Mineral Water won the product of the year award in at the third edition of Ghana Manufacturing Awards. [ 7 ]
Verna Natural Mineral Water offers a poverty intervention program dubbed Changing Lives , as part of its corporate social responsibility to support the underprivileged and vulnerable members of society. [ 5 ] Changing Lives is organised around a television series made up of different episodes, where each episode tells a different story of a successful intervention project the company has carried out. Beneficiaries of Changing Lives have included autistic patients who have received mentorship support from role models to enable them build a career. [ 5 ] [ 8 ]
In 2017, Changing Lives was extended to Kumasi in the Ashanti Region of Ghana. At its lunch, Otumfuo Osei Tutu II endorsed and extended his support for the initiative. [ 9 ] [ 10 ]
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The Verneuil method (or Verneuil process or Verneuil technique ), also called flame fusion , was the first commercially successful method of manufacturing synthetic gemstones , developed in the late 1883 [ 1 ] by the French chemist Auguste Verneuil . It is primarily used to produce the ruby , sapphire and padparadscha varieties of corundum , as well as the diamond simulants rutile , strontium titanate and spinel. The principle of the process involves melting a finely powdered substance using an oxyhydrogen flame, and crystallising the melted droplets into a boule . The process is considered to be the founding step of modern industrial crystal growth technology, and remains in wide use to this day. [ 2 ] [ 3 ]
Since the study of alchemy began, there have been attempts to synthetically produce precious stones, and ruby , being one of the prized cardinal gems , has long been a prime candidate. In the 19th century, significant advances were achieved, with the first ruby formed by melting two smaller rubies together in 1817, and the first microscopic crystals created from alumina ( aluminium oxide ) in a laboratory in 1837. [ 4 ] By 1877, chemist Edmond Frémy had devised an effective method for commercial ruby manufacture by using molten baths of alumina, yielding the first gemstone-quality synthetic stones. The Parisian chemist Auguste Verneuil, who applied to work with Frémy at age 17, became Frémy 's assistant in 1876 and helped develop the method, [ 4 ] but soon went on to independently develop the flame fusion process, which would eventually come to bear his name.
One of Verneuil's sources of inspiration for developing his own method was the appearance of synthetic rubies sold by an unknown Genevan merchant in 1885. [ 4 ] These "Geneva rubies" were determined to be artificial at the time but are now believed to be the first rubies produced by flame fusion, predating Verneuil's work by several years. After being introduced to the "Geneva rubies" by a mineralogist at the Natural Museum of History in Paris, Verneuil came to the conclusion that it was possible to recrystallise finely ground aluminium oxide into a large gemstone. This realisation, along with the availability of the recently developed oxyhydrogen torch and growing demand for synthetic rubies, led him to design the Verneuil furnace, where finely ground purified alumina and chromium oxide were melted by a flame of at least 2,000 °C (3,630 °F), and recrystallised on a support below the flame, creating a large crystal. Verneuil documented his work in sealed documents during the 1890s and publicly announced his work in 1902, publishing details outlining the process in 1904. [ 4 ]
By 1910, Verneuil's laboratory had expanded into a 30-furnace production facility, with annual gemstone production by the Verneuil process having reached 1,000 kg (2,200 lb) in 1907. By 1912, production reached 3,200 kg (7,100 lb), and would go on to reach 200,000 kg (440,000 lb) in 1980 and 250,000 kg (550,000 lb) in 2000, led by Hrand Djevahirdjian 's factory in Monthey , Switzerland , founded in 1914. The most notable improvements in the process were made in 1932, by S. K. Popov , who helped establish the capability for producing high-quality sapphires in the Soviet Union through the next 20 years. A large production capability was also established in the United States during World War II , when European sources were not available, and jewels were in high demand for their military applications such as for timepieces.
The process was designed primarily for the synthesis of rubies, which became the first gemstone to be produced on an industrial scale. However, the Verneuil process could also be used for the production of other stones, including blue sapphire which required oxides of iron and titanium to be used in place of chromium oxide. [ 4 ] The basic process can be used to form even more elaborate gemstones such as star sapphires , where titania ( titanium dioxide ) was added and the boule was kept in the heat longer, allowing needles of rutile to crystallise within it. In 1947, the Linde Air Products division of Union Carbide pioneered the use of the Verneuil process for creating such star sapphires, [ 5 ] until production was discontinued in 1974 owing to overseas competition.
Despite some improvements in the method, the Verneuil process remains virtually unchanged to this day, while maintaining a leading position in the manufacture of synthetic corundum and spinel gemstones. Its most significant setback came in 1917, when Jan Czochralski introduced the Czochralski process , which has found numerous applications in the semiconductor industry , where a much higher quality of crystals is required than the Verneuil process can produce. Other alternatives to the process emerged in 1957, when Bell Labs introduced the hydrothermal process , and in 1958, when Carroll Chatham introduced the flux method . In 1989 Larry P Kelley of ICT, Inc. also developed a variant of the Czochralski process where natural ruby is used as the 'feed' material.
One of the most crucial factors in successfully crystallising an artificial gemstone is obtaining highly pure starting material, with at least 99.9995% purity. [ 6 ] In the case of manufacturing rubies, sapphires or padparadscha , this material is alumina. The presence of sodium impurities is especially undesirable, as it makes the crystal opaque . [ 6 ] But because the bauxite from which alumina is obtained is most likely by way of the Bayer process (the first stage of which introduces caustic soda in order to separate the Al 2 O 3 ) particular attention must be paid to the feedstock. [ 7 ]
Depending on the desired colouration of the crystal, small quantities of various oxides are added, such as chromium oxide for a red ruby, or ferric oxide and titania for a blue sapphire. Other starting materials include titania for producing rutile, or titanyl double oxalate for producing strontium titanate. Alternatively, small, valueless crystals of the desired product can be used.
This starting material is finely powdered, and placed in a container within a Verneuil furnace, with an opening at the bottom through which the powder can escape when the container is vibrated. While the powder is being released, oxygen is supplied into the furnace, and travels with the powder down a narrow tube. This tube is located within a larger tube, into which hydrogen is supplied. At the point where the narrow tube opens into the larger one, combustion occurs, with a flame of at least 2,000 °C (3,630 °F) at its core. As the powder passes through the flame, it melts into small droplets, which fall onto an earthen support rod placed below. The droplets gradually form a sinter cone on the rod, the tip of which is close enough to the core to remain liquid. It is at that tip that the seed crystal eventually forms. As more droplets fall onto the tip, a single crystal , called a boule , starts to form, and the support is slowly moved downward, allowing the base of the boule to crystallise, while its cap always remains liquid. The boule is formed in the shape of a tapered cylinder, with a diameter broadening away from the base and eventually remaining more or less constant. With a constant supply of powder and withdrawal of the support, very long cylindrical boules can be obtained. Once removed from the furnace and allowed to cool, the boule is split along its vertical axis to relieve internal pressure, otherwise the crystal will be prone to fracture when the stalk is broken due to a vertical parting plane . [ 8 ]
When initially outlining the process, Verneuil specified a number of conditions crucial for good results. These include: a flame temperature that is not higher than necessary for fusion; always keeping the melted product in the same part of the oxyhydrogen flame; and reducing the point of contact between the melted product and support to as small an area as possible. The average commercially produced boule using the process is 13 mm (0.51 in) in diameter and 25 to 50 mm (0.98 to 1.97 in) long, weighing about 125 carats (25.0 g). The process can also be performed with a custom-oriented seed crystal to achieve a specific desired crystallographic orientation .
Crystals produced by the Verneuil process are chemically and physically equivalent to their naturally occurring counterparts, and strong magnification is usually required to distinguish between the two. A telltale characteristic is the Verneuil crystal is curved growth lines (curved striae) form, [ 9 ] as the cylindrical boule grows upwards in an environment with a high thermal gradient , while the equivalent lines in natural crystals are straight. Another distinguishing feature is the common presence of microscopic gas bubbles formed due to an excess of oxygen in the furnace; imperfections in natural crystals are usually solid impurities. [ 8 ]
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https://en.wikipedia.org/wiki/Verneuil_method
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Calipers or callipers are an instrument used to measure the linear dimensions of an object or hole; namely, the length , width, thickness, diameter or depth of an object or hole. The word "caliper" comes from a corrupt form of caliber . [ 1 ] [ 2 ] [ 3 ]
Many types of calipers permit reading out a measurement on a ruled scale , a dial , or an electronic digital display . A common association is to calipers using a sliding vernier scale .
Some calipers can be as simple as a compass with inward or outward-facing points, but with no scale (measurement indication). The tips of the caliper are adjusted to fit across the points to be measured, and then kept at that span while moved to separate measuring device, such as a ruler .
Calipers are used in many fields such as mechanical engineering , metalworking , forestry , woodworking , science and medicine .
Caliper is the American spelling , while calliper (double "L") is the British spelling.
A single tool might be referred to as a caliper or as calipers — a plural only ( plurale tantum ) form, like scissors or glasses .
Colloquially, the phrase "pair of verniers" or just "vernier" might refer to a vernier caliper. In loose colloquial usage, these phrases may also refer to other kinds of calipers, although they involve no vernier scale. In machine-shop usage, the term "caliper" is often used in contradistinction to micrometer , even though outside micrometers are technically a form of caliper. In this usage, caliper implies only the form factor of the instrument.
The earliest caliper has been found in the Greek Giglio wreck near the Italian coast. The ship's find dates to the 6th century BC. The wooden piece already featured a fixed and a movable jaw. [ 4 ] [ 5 ] Although rare finds, calipers remained in use by the Greeks and Romans . [ 5 ] [ 6 ]
A bronze caliper, dating from 9 AD, was used for minute measurements during the Chinese Xin dynasty . The caliper had an inscription stating that it was "made on the gui-you day, [ a ] the first day [ b ] of the first month of the first year of Shijianguo . [ c ] " The calipers included a "slot and pin" and "graduated in inches and tenths of an inch." [ 7 ] [ 8 ]
The modern vernier caliper was invented by Pierre Vernier , as an improvement of the nonius of Pedro Nunes .
Inside calipers are used to measure the internal size of an object.
Outside calipers are used to measure the external size of an object.
The same observations and technique apply to this type of caliper, as for the inside caliper. With some understanding of their limitations and usage, these instruments can provide a high degree of accuracy and repeatability. They are especially useful when measuring over very large distances; consider if the calipers are used to measure a large-diameter pipe. A vernier caliper does not have the depth capacity to straddle this large diameter and at the same time reach the outermost points of the pipe's diameter. They are made from high-carbon steel.
In the metalworking field, a divider caliper, popularly called a compass, is used to mark out locations. The points are sharpened so that they act as scribers; one leg can then be placed in the dimple created by a center or prick punch and the other leg pivoted so that it scribes a line on the workpiece's surface, thus forming an arc or circle.
Their namesake use is in dividing a workpiece of arbitrary width into equal-width sections: by "walking" the tool from one end to the other by pivoting it from one point to the next until reaching the other end, then adjusting the gap between the points until the "walk" ends directly on the end point, equal divisions can be easily marked out without any measuring.
A divider caliper is also used to measure a distance between two points on a map. The two caliper ends are brought to the two points whose distance is being measured. The caliper's opening is then either measured on a separate ruler and then converted to the actual distance, or measured directly on a scale drawn on the map. On a nautical chart the distance is often measured on the latitude scale appearing on the sides of the map: one minute of arc along any great circle , e.g. any longitude meridian, is approximately one nautical mile or 1852 meters .
Dividers are also used in the medical profession. An ECG (also EKG) caliper transfers distance on an electrocardiogram ; in conjunction with the appropriate scale, the heart rate can be determined. A pocket caliper version was invented by cardiologist Robert A. Mackin. [ 9 ] [ failed verification ]
Oddleg calipers , Hermaphrodite calipers , or Oddleg Jennys , as pictured on the left, are generally used to scribe a line at a set distance from the edge of a workpiece. The bent leg is used to run along the workpiece edge while the scriber makes its mark at a predetermined distance, this ensures a line parallel to the edge.
In the diagram at left, the uppermost caliper has a slight shoulder in the bent leg allowing it to sit on the edge more securely. The lower caliper lacks this feature but has a renewable scriber that can be adjusted for wear, as well as being replaced when excessively worn.
The labelled parts are
The calipers in the diagram show a primary reading on the metric scale of about 2.475 cm (2.4 cm read from the main scale plus about 0.075 cm from the vernier scale).
Calipers often have a "zero point error": meaning that the calipers do not read 0.000 cm when the jaws are closed. The zero point error must always be subtracted from the primary reading. Let us assume these calipers have a zero-point error of 0.013 cm. This would give us a length reading of 2.462 cm.
For any measurement, reporting the error on the measurement is also important. Ignoring the possibility of interpolation by eye, both the primary reading and the zero point reading are bounded by plus/minus half the length corresponding to the width of the smallest interval on the vernier scale (0.0025 cm). These are "absolute" errors and absolute errors add, so the length reading is then bounded by
plus/minus the length corresponding to the full width of the smallest interval on the vernier scale (0.005 cm). Assuming no systematics affect the measurement (the instrument works perfectly), a complete measurement would then read 2.462 cm ± 0.005 cm.
The vernier, dial, and digital calipers directly read the distance measured with high accuracy and precision . They are functionally identical, with different ways of reading the result. These calipers comprise a calibrated scale with a fixed jaw, and another jaw, with a pointer, that slides along the scale. The distance between the jaws is then read in different ways for the three types.
The simplest method is to read the position of the pointer directly on the scale. When the pointer is between two markings, the user can mentally interpolate to improve the precision of the reading. This would be a simply calibrated caliper, but the addition of a vernier scale allows more accurate interpolation and is the universal practice; this is the vernier caliper .
Vernier, dial, and digital calipers can measure internal dimensions (using the uppermost jaws in the picture at right), external dimensions using the pictured lower jaws, and in many cases depth by the use of a probe that is attached to the movable head and slides along the centre of the body. This probe is slender and can get into deep grooves that may prove difficult for other measuring tools.
The vernier scales may include metric measurements on the lower part of the scale and inch measurements on the upper, or vice versa, in countries that use inches. Vernier calipers commonly used in industry provide a precision to 0.01 mm (10 micrometres ), or one thousandth of an inch. They are available in sizes that can measure up to 1828 mm (72 in). [ 10 ]
Instead of using a vernier mechanism, which requires some practice to use, the dial caliper reads the final fraction of a millimeter or inch on a simple dial.
In this instrument, a small, precise rack and pinion drives a pointer on a circular dial , allowing direct reading without the need to read a vernier scale. Typically, the pointer rotates once every inch, tenth of an inch, or 1 millimeter. This measurement must be added to the coarse whole inches or centimeters read from the slide. The dial is usually arranged to be rotatable beneath the pointer, allowing for "differential" measurements (the measuring of the difference in size between two objects, or the setting of the dial using a master object and subsequently being able to read directly the plus-or-minus variance in the size of subsequent objects relative to the master object).
The slide of a dial caliper can usually be locked at a setting using a small lever or screw; this allows simple go/no-go checks of part sizes.
Rather than a rack and pinion , digital calipers use a linear encoder . A liquid-crystal display shows the measurement, which often can switch units between millimeters and fractional or decimal inches. All provide for zeroing the display at any point along the slide, allowing the same sort of differential measurements as with the dial caliper. Digital calipers may contain a "reading hold" feature, allowing the reading of dimensions after use in awkward locations where the display cannot be seen. Like analog calipers, the slide of many digital calipers can be locked using a lever or screw.
Ordinary 150 mm (6 in ) digital calipers made of stainless steel have a rated accuracy of 0.02 mm ( 0.001 in ) and a resolution of 0.01 mm (0.0005 in). [ 11 ] The same technology is used for longer calipers, but accuracy declines to 0.03 mm (0.001 in) for 100–200 mm (4–8 in) and 0.04 mm (0.0015 in) for 200–300 mm (8–12 in) measurements. [ 12 ]
Many digital calipers contain a capacitive linear encoder . Inexpensive Chinese models have 56 narrow emitter plates and one long receiver plate etched on the sliding display's printed circuit board , which intersect with a repeating pattern of T-shaped plates in the longer "stator" board. The top of the "T" plates intersect with the receiver plate, while the vertical bars of each "T" intersect with the emitter plates. The pitch of each "T" in the stator is slightly less than 8 times the pitch of each emitter plate, so their intersecting capacitive area is not perfectly aligned but rather forms an interference pattern . [ 15 ] As the slider moves, these variable capacitances change in a repeating linear fashion. The slider's circuitry counts these repetitions as it slides and achieves finer resolution using linear interpolation of the capacitances. [ 16 ] One model sends 8 periodic pulse-width modulation voltage signals (which appear identical but out of phase by 1 ⁄ 8 of the period), [ 17 ] each connected to 7 emitter plates, and the resulting analog signal is read through a single receiver plate. [ 18 ] The 1983 German patent DE3340782C2 (see figure) is said to describe the workings. [ 19 ]
Other digital calipers contain an inductive linear encoder, which allows robust performance in the presence of contamination such as coolants. [ 20 ] Magnetic linear encoders are used in yet other digital calipers. [ citation needed ]
Digital calipers nowadays offer serial data output to expedite repeated measurements, avoid human error , and allow direct data entry into a digital recorder, spreadsheet , statistical process control program, or similar software on a personal computer . Interfacing devices based on RS-232 , Universal Serial Bus , or wireless can be built or purchased. The serial digital output varies among manufacturers, but common options are:
A caliper using a calibrated screw for measurement, rather than a slide, is called an external micrometer caliper gauge , a micrometer caliper or, more often, simply a micrometer . (Sometimes the term caliper , referring to any other type in this article, is held in contradistinction to micrometer .)
Each of the above types of calipers has its relative merits and faults.
Vernier calipers are rugged and have long-lasting accuracy, are coolant proof, are not affected by magnetic fields, and are largely shockproof. They may have both centimeter and inch scales. However, vernier calipers require good eyesight or a magnifying glass to read and can be difficult to read from a distance or from awkward angles. It is relatively easy to misread the last digit. In production environments, reading vernier calipers all day long is error-prone and is annoying to the workers.
Dial calipers are comparatively easy to read, especially when seeking the exact center by rocking and observing the needle movement. They can be set to 0 at any point for comparisons. They are usually fairly susceptible to shock damage. They are also very prone to getting dirt in the gears, which can cause accuracy problems.
Digital calipers switch easily between centimeter and inch systems. They can be set to zero easily at any point with a full count in either direction and can take measurements even if the display is completely hidden, either by using a "hold" key, or by zeroing the display and closing the jaws, showing the correct measurement, but negative. They can be mechanically and electronically fragile. Most also require batteries and do not resist coolant well. They are also only moderately shockproof and can be vulnerable to dirt.
Calipers may read to a resolution of 0.01 mm or 0.0005 in, but accuracy may not be better than about ±0.02 mm or 0.001 in for 150 mm (6 in) calipers, and worse for longer ones. [ 28 ]
A caliper must be properly applied against the part in order to take the desired measurement. For example, when measuring the thickness of a plate, a vernier caliper must be held at right angles to the piece. Some practice may be needed to measure round or irregular objects correctly.
Accuracy of measurement when using a caliper is highly dependent on the skill of the operator. Regardless of type, a caliper's jaws must be forced into contact with the part being measured. As both part and caliper are always to some extent elastic , the amount of force used affects the indication. A consistent, firm touch is correct. Too much force results in an under indication as part and tool distort; too little force gives insufficient contact and an over indication. This is a greater problem with a caliper incorporating a wheel, which lends mechanical advantage . This is especially the case with digital calipers, calipers out of adjustment, or calipers with a poor quality beam.
Simple calipers are uncalibrated; the measurement taken must be compared against a scale. Whether the scale is part of the caliper or not, all analog calipers—verniers and dials—require good eyesight in order to achieve the highest precision. Digital calipers have an advantage in this area.
Calibrated calipers may be mishandled, leading to loss of zero . When a caliper's jaws are fully closed, it should, of course, indicate zero. If it does not, it must be recalibrated or repaired. A vernier caliper does not easily lose its calibration, but a sharp impact or accidental damage to the measuring surface in the caliper jaw can be significant enough to displace zero. [ 29 ] Digital calipers have zero set buttons, for quick recalibration.
Vernier, dial and digital calipers can be used with accessories that extend their usefulness. Examples are a base that extends their usefulness as a depth gauge and a jaw attachment that all allows measuring the center distance between holes. Since the 1970s, a clever modification of the moveable jaw on the back side of any caliper allows for step or depth measurements in addition to external caliper measurements, similarly to a universal micrometer (e.g., Starrett Mul-T-Anvil or Mitutoyo Uni-Mike).
The method to use a vernier scale or caliper with zero error is to use the formula "actual reading = main scale + vernier scale − (zero error)". Zero error may arise due to knocks that affect the calibration at 0.00 mm when the jaws are perfectly closed or just touching each other. Positive zero error refers to the fact that when the jaws of the vernier caliper are just closed, the reading is a positive reading away from the actual reading of 0.00 mm. If the reading is 0.10 mm, the zero error is referred to as +0.10 mm. Negative zero error refers to the fact that when the jaws of the vernier caliper are just closed, the reading is a negative reading away from the actual reading of 0.00 mm. If the reading is −0.08 mm, the zero error is referred to as −0.08 mm.
Calipers with measurement axes displaced from the object being measured suffer from Abbe error if the jaws are not perpendicular due to manufacturing tolerances. Unlike zero error, the amount of Abbe error depends on the offset. [ 30 ]
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https://en.wikipedia.org/wiki/Vernier_calipers
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In French interior design , vernis Martin is a type (or a number of types) of japanning or imitation lacquer named after the 18th century French Martin brothers: Guillaume (died 1749), Etienne-Simon, Robert and Julien. They ran a leading factory from between about 1730 and 1770, and were vernisseurs du roi ("varnishers to the king"). But they did not invent the process, nor were they the only producers, nor does the term cover a single formula or technique. [ 1 ] It imitated Chinese lacquer and European subjects, and was applied to a wide variety of items, from furniture to coaches . It is said to have been made by heating oil and copal and then adding Venetian turpentine .
Oriental lacquer had speedily acquired high favour in France, and many attempts were made to imitate it. Some of these attempts were passably successful, and it is likely that many of the examples in the possession of Louis XIV at his death were of European manufacture. Chinese lacquer was, however, imported in large quantities, and sometimes panels were made in China from designs prepared in Paris.
Biographical details of the career of the brothers Martin are scanty, but it is known that Guillaume, the eldest, was already in business in 1724. Their method and work must have come rapidly into vogue, for in 1730 Guillaume and Simon Martin were granted by letters patent a twenty years' monopoly, subsequently renewed, of making " toutes sortes d'ouvrages en relief de la Chine et du Japon " ("all kinds of relief works from China and Japan"). At the height of their fame the brothers directed at least three factories in Paris, and in 1748 they were all classed together as a "Manufacture nationale." One of them was still in existence in 1785. [ 2 ]
The literature of their day had much to say of the Martin brothers. In Voltaire 's comedy Nadine , produced in 1749, mention is made of a berline (carriage) " bonne et brillante, tous les panneaux par Martin sont vernis " ("good and bright, all the panels varnished by Martin"). The marquis de Mirabeau in L'Ami des hommes refers to the enamelled snuff-boxes and varnished carriages which came from the Martins' factory. As with many great artists, their names were attached to many works they never saw, and the Martins suffered considerably in this respect. That the quality of their production varied between very wide limits is established by existing and undoubted examples; but it is extremely improbable that even their three factories could have turned out the quantity of examples that has been attributed to them. Yet their production was large and miscellaneous, for such was the rage for their lacquer that it was applied to every possible object. [ 2 ]
The fashion was not confined to France. At its best Vernis Martin has a sheen, polish, and translucence which compel admiration. Every variety of Asian lacquer of the Far East was imitated and often improved upon by the Martins—the black with raised gold ornaments, the red, and finally in the green ground, powdered with gold, they reached the high-water mark of their art. This delicate work, poudré and wavy-lined with gold or semi with flowers overlaid with transparent enamel, is seen at its best on small boxes, fans, needle-cases and such-like. Of the larger specimens from the Martins' factories many have disappeared, or been cut up into decorative panels. It would appear that none of the work they placed in the famous hotels of old Paris is now in situ, and the really fine examples are in museums. Even the decorations of the apartments of the Dauphin at the Palace of Versailles , executed, or at least begun, in 1749, have vanished; so have those at the Château de Bellevue . [ 2 ]
Critics have accepted that of the four brothers Robert Martin accomplished the most original and the most completely artistic work. He left a son, Jean Alexandre, who described himself in 1767 as Vernisseur du Roi de Prusse ("varnisher to the king of Prussia "). He was employed at the palace of Sanssouci , but failed to continue the great traditions of his father and his uncles. The French Revolution finally extinguished a taste which had lasted for a large part of the 18th century. [ 2 ]
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The Verona astrolabe is an archaeological discovery unearthed in the vaults of a museum in Verona , Italy. [ 1 ] Dating back to the eleventh century, this Islamic astrolabe is one of the oldest examples of its kind and is among the few known to exist worldwide. It appears to have been employed by Muslim, Jewish, and Christian communities spanning Spain, North Africa, and Italy over several centuries. [ 2 ]
Described by historian Tom Almeroth-Williams of the University of Cambridge as the "world's first smartphone," the astrolabe served as a portable astronomical instrument capable of diverse functionalities. It provided users with a two-dimensional representation of the universe, enabling the plotting of star positions, calculation of time and distances, and even the development of horoscopes. [ 3 ]
Initially doubted to be authentic, the Verona Astrolabe was authenticated as an eleventh-century artifact by Dr. Federica Gigante of Cambridge University's History Faculty. Her analysis, published in the journal Nuncius , confirmed its origins in Al-Andalus , the Muslim-ruled region of Spain during the medieval period. The astrolabe bears Hebrew inscriptions alongside Arabic , indicating its circulation within the Jewish diaspora community in Italy, where Hebrew was used in place of Arabic. [ 4 ] [ 5 ]
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https://en.wikipedia.org/wiki/Verona_astrolabe
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In mathematics , the Veronese surface is an algebraic surface in five-dimensional projective space , and is realized by the Veronese embedding , the embedding of the projective plane given by the complete linear system of conics . It is named after Giuseppe Veronese (1854–1917). Its generalization to higher dimension is known as the Veronese variety .
The surface admits an embedding in the four-dimensional projective space defined by the projection from a general point in the five-dimensional space. Its general projection to three-dimensional projective space is called a Steiner surface .
The Veronese surface is the image of the mapping
given by
where [ x : ⋯ ] {\displaystyle [x:\cdots ]} denotes homogeneous coordinates . The map ν {\displaystyle \nu } is known as the Veronese embedding.
The Veronese surface arises naturally in the study of conics . A conic is a degree 2 plane curve, thus defined by an equation:
The pairing between coefficients ( A , B , C , D , E , F ) {\displaystyle (A,B,C,D,E,F)} and variables ( x , y , z ) {\displaystyle (x,y,z)} is linear in coefficients and quadratic in the variables; the Veronese map makes it linear in the coefficients and linear in the monomials. Thus for a fixed point [ x : y : z ] , {\displaystyle [x:y:z],} the condition that a conic contains the point is a linear equation in the coefficients, which formalizes the statement that "passing through a point imposes a linear condition on conics".
The Veronese map or Veronese variety generalizes this idea to mappings of general degree d in n +1 variables. That is, the Veronese map of degree d is the map
with m given by the multiset coefficient , or more familiarly the binomial coefficient , as:
The map sends [ x 0 : … : x n ] {\displaystyle [x_{0}:\ldots :x_{n}]} to all possible monomials of total degree d (of which there are m + 1 {\displaystyle m+1} ); we have n + 1 {\displaystyle n+1} since there are n + 1 {\displaystyle n+1} variables x 0 , … , x n {\displaystyle x_{0},\ldots ,x_{n}} to choose from; and we subtract 1 {\displaystyle 1} since the projective space P m {\displaystyle \mathbb {P} ^{m}} has m + 1 {\displaystyle m+1} coordinates. The second equality shows that for fixed source dimension n, the target dimension is a polynomial in d of degree n and leading coefficient 1 / n ! . {\displaystyle 1/n!.}
For low degree, d = 0 {\displaystyle d=0} is the trivial constant map to P 0 , {\displaystyle \mathbf {P} ^{0},} and d = 1 {\displaystyle d=1} is the identity map on P n , {\displaystyle \mathbf {P} ^{n},} so d is generally taken to be 2 or more.
One may define the Veronese map in a coordinate-free way, as
where V is any vector space of finite dimension, and S y m d V {\displaystyle {\rm {{Sym}^{d}V}}} are its symmetric powers of degree d . This is homogeneous of degree d under scalar multiplication on V , and therefore passes to a mapping on the underlying projective spaces .
If the vector space V is defined over a field K which does not have characteristic zero , then the definition must be altered to be understood as a mapping to the dual space of polynomials on V . This is because for fields with finite characteristic p , the p th powers of elements of V are not rational normal curves , but are of course a line. (See, for example additive polynomial for a treatment of polynomials over a field of finite characteristic).
For n = 1 , {\displaystyle n=1,} the Veronese variety is known as the rational normal curve , of which the lower-degree examples are familiar.
The image of a variety under the Veronese map is again a variety, rather than simply a constructible set ; furthermore, these are isomorphic in the sense that the inverse map exists and is regular – the Veronese map is biregular . More precisely, the images of open sets in the Zariski topology are again open.
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https://en.wikipedia.org/wiki/Veronese_surface
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The Veronica bucket [ 1 ] is a mechanism for hand washing originating in Ghana which consists of a bucket of water with a tap fixed at the bottom, mounted at hand height, and a bowl underneath to collect waste water. The Veronica bucket was developed by Veronica Bekoe . The Veronica bucket serves as a simple way to encourage proper hand washing using flowing water. Bekoe in an interview stated that the bucket was originally made to help her and her colleagues wash their hands under running water after each lab session. She said, "We are used to washing hands in a bowl with others washing in the same water, which will do more harm than good." These colleagues were contaminating their hands rather than decontaminating them. In addition to the COVID benefit of hand washing, the Veronica bucket is also essential for areas where potable water is not readily available. [ 2 ]
The bucket is also used in other African countries. It is common in places such as schools, hospitals, churches and areas with no running taps. [ 2 ] It has become very popular in Ghana following the outbreak of the novel coronavirus ( COVID-19 ) as citizens engage in frequent hand washing to stem its spread. [ 3 ] [ 4 ] In Ekiti State , Nigeria , the governor Kayode Fayemi directed all public places to provide running tap water or Veronica buckets "to encourage frequent handwashing" as part of the measures to contain COVID-19. [ 5 ]
Before the COVID-19 outbreak, the invention was used in some schools and hospitals but now it is in high demand due to its role in curbing the outbreak. Now, the setup could be spotted in places like malls, hospitals, corporate institutions and government offices. It was invented by a Ghanaian, Veronica Bekoe , [ 6 ] whom the invention was named after. She claimed the bucket was named after her in 1993 by Joan Hetrick. [ 7 ] Bekoe is a biologist who has worked at the Public Health and Reference Laboratory of the Ghana Health Service from 1972 to 2008. [ 8 ]
The invention was initially produced by local artisans with aluminium utensils used in selling Hausa koko attached with a tap which was a prototype , popularly known as Akorlaa gyae su and is currently made of plastic with a tap attached to it which has an area for holding soap and towels. Variations available today come in all colours. [ 9 ] [ 10 ] [ 11 ]
In February 2021, Veronica Bekoe launched an updated version of the bucket to reduce physical contact with the unit and further help halt the spread of COVID-19 . [ 12 ]
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https://en.wikipedia.org/wiki/Veronica_bucket
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Veronte Autopilot is a family of autopilot systems developed by Embention, a Spanish company specializing in safety-critical avionics for unmanned aerial vehicles (UAVs) and electric vertical take-off and landing (eVTOL) aircraft. [ 1 ] Known for its advanced control capabilities, the Veronte Autopilot systems are designed to meet stringent reliability and certification requirements, allowing their integration into both manned and unmanned aircraft. [ 1 ]
Veronte Autopilot is used in various autonomous flight systems for both civil and military applications. It is a fully user-programmable flight controller that can be adapted to different aircraft through model-based design, enabling it to meet specific operational needs. The autopilot supports features such as obstacle avoidance, geofencing, satellite communications, and real-time telemetry, with built-in remote identification (Remote ID) and Automatic Dependent Surveillance–Broadcast (ADS-B) functionalities. [ 2 ]
The product family includes configurations for single core, redundant, and distributed redundancy setups, enhancing reliability for critical operations. It is equipped with advanced safety measures, making it suitable for use in applications requiring high safety standards, such as urban air mobility (UAM) and certified drone operations. [ 3 ]
Veronte Autopilot is developed in compliance with key aviation standards, including DO-178C, DO-254, and DO-160. [ 4 ] The company behind the product, Embention, is certified under ISO9001 and EN9100 , ensuring a robust quality management system. In 2024, the European Union Aviation Safety Agency (EASA) approved the certification basis for Veronte Autopilot under the ETSO -C198 framework, [ 5 ] making it the first flight control system for UAS and eVTOL to undergo this process. [ 6 ] This certification paves the way for Veronte Autopilot to be used in both manned and unmanned aircraft that require formal certification. [ 7 ]
Veronte Autopilot is utilized in a variety of sectors, including defense, emergency response, and UAM . Its systems have been integrated into both drones and eVTOL aircraft used for air taxis and cargo transport. [ 8 ] By achieving certifications that meet manned aviation standards, Veronte Autopilot enables seamless integration into broader aerospace operations, promoting the use of autonomous systems in regulated airspaces. [ 1 ]
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https://en.wikipedia.org/wiki/Veronte_Autopilot
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The Versatile Laboratory Aid ( VELA ) is a 4-channel data logging tool that was created as part of a joint venture by Ashley Clarke, Keith Jones and David Binney of Leeds University and Educational Electronics. The VELA was designed to be used as a stand-alone data logger that could be used out in the field and it could then be taken back to the laboratory where it could be connected to a chart printer, oscilloscope or microcomputer for data analysis purposes.
The VELA was designed and built with the intention that it would be used in schools and Universities to monitor Physics [ 2 ] [ 3 ] and Chemistry experiments as it could be attached to all manner or analogue probes and sensors such as pH meters , temperature sensors , light gates , Signal generator and microphones . Each of the VELA's four channels can be independently set to record voltages in the ranges of +/–250mV, +/–2.5V and +/–25V [ 4 ] allowing a range of different input devices to be connected simultaneously.
The basic VELA carries a single 4KB EPROM (ISL1 or ISL1*) which contains the basic input and output routines that handle the keyboard input and 8-digit LED display output together with seventeen user selectable programs which range from a 4-channel digital volt meter to a random event monitor which could be used with a Geiger Counter Probe to measure and log radiation levels from a source material.
In total, the VELA could record a maximum of 4096 data points either from one channel or split equally between the four channels depending on the selected monitoring program. In later versions of the VELA firmware (ISL1*), the number of data points was reduced by 7 bytes per data channel as these bytes were reserved for storing channel and program configuration data when transferring data to a microcomputer. [ 5 ]
The VELA went through at least two hardware revisions going from the Mark I to Mark II and subsequently the VELA PLUS but the ISL ROMs remained compatible between all three devices although the Mark I VELA required a daughter board to carry the extra ROMs that were developed after the VELA's initial release.
The VELA Mark I was based around the Motorola MC6802 central processor and carried 4KB of RAM. It shipped with the original ISL1 ROM fitted and has space for a further 2 ROMs to be fitted on board. The PCB of the Mark I was split into two parts which connected to each other through a ribbon cable. [ 6 ] The ROMs were generally shipped on 2732 EPROM chips and they could be sent back to Educational Electronics to be updated with enhanced firmware when it became available. [ 7 ]
The VELA Mark II was a refinement to the Mark I design and was based on the same processor and hardware. The Mark II PCB was condensed onto a single board and carried space for a further three EPROM's to be fitted in addition to the ISL1* EPROM that it shipped with. There were modifications to the connectors on the VELA Mark II with the addition of a 5V 70mA output and a revised power supply connector although early Mark II VELA's continued to use the original 3.5mm power supply plug socket as used on the VELA Mark I.
The VELA PLUS was again a refinement on the Mark II VELA and the PCB carried alterations to the op-amps and circuitry associated with the channel inputs. The VELA front panel was also revised to make it clearer to understand as the usability of the VELA had been a source of issues amongst the teaching community.
With the advent of the VELA PLUS, the name Ve rsatile L aboratory A id which was displayed on the front panel was changed to Ve rsatile La boratory Instrument whilst retaining the VELA contraction.
The VELA was 50/50 subsidised [ 8 ] [ 9 ] by the DTI , an arm of the British Government to encourage take up within the education sector and many thousands of VELA units were sold to schools.
In 1986 an article in the Electronic Systems News Spring Journal [ 10 ] stated "4000 teachers now possess a VELA, but it is suspected that more than half of these have never been used."
The VELA was designed to be connected to three different types of device, being a chart printer, an oscilloscope or a microcomputer. Connecting the VELA to a chart printer allowed the captured data to be printed directly from the VELA for analysis and making a permanent record of the data captured. Connecting the VELA to an oscilloscope allowed users to have a real-time view of the data the VELA was recording or a playback view of pre-existing captured data. When connected to a microcomputer, the data captured could be stored and manipulated using a variety of different software applications that were available for the VELA.
Using the Digital Out port, the VELA can also be used as a control device using 8 of the 16 data lines provided. [ 11 ] [ 12 ]
Software was produced for several microcomputers including the Apple II , BBC Micro , Commodore PET , Commodore 64 , Research Machines 380Z and early IBM-PC compatible . A partial list of known software titles is listed below. [ 13 ] [ 14 ] [ 15 ] [ 16 ]
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https://en.wikipedia.org/wiki/Versatile_Laboratory_Aid
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The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors .
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https://en.wikipedia.org/wiki/Versed_cosine
|
The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors .
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https://en.wikipedia.org/wiki/Versed_sine
|
The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit Aryabhatia , [ 1 ] Section I) trigonometric tables . The versine of an angle is 1 minus its cosine .
There are several related functions, most notably the coversine and haversine . The latter, half a versine, is of particular importance in the haversine formula of navigation.
The versine [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] or versed sine [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] is a trigonometric function already appearing in some of the earliest trigonometric tables. It is symbolized in formulas using the abbreviations versin , sinver , [ 13 ] [ 14 ] vers , or siv . [ 15 ] [ 16 ] In Latin , it is known as the sinus versus (flipped sine), versinus , versus , or sagitta (arrow). [ 17 ]
Expressed in terms of common trigonometric functions sine, cosine, and tangent, the versine is equal to versin θ = 1 − cos θ = 2 sin 2 θ 2 = sin θ tan θ 2 {\displaystyle \operatorname {versin} \theta =1-\cos \theta =2\sin ^{2}{\frac {\theta }{2}}=\sin \theta \,\tan {\frac {\theta }{2}}}
There are several related functions corresponding to the versine:
Special tables were also made of half of the versed sine, because of its particular use in the haversine formula used historically in navigation .
hav θ = sin 2 ( θ 2 ) = 1 − cos θ 2 {\displaystyle {\text{hav}}\ \theta =\sin ^{2}\left({\frac {\theta }{2}}\right)={\frac {1-\cos \theta }{2}}}
The ordinary sine function ( see note on etymology ) was sometimes historically called the sinus rectus ("straight sine"), to contrast it with the versed sine ( sinus versus ). [ 31 ] The meaning of these terms is apparent if one looks at the functions in the original context for their definition, a unit circle :
For a vertical chord AB of the unit circle, the sine of the angle θ (representing half of the subtended angle Δ ) is the distance AC (half of the chord). On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos( θ ) (equal to the length of line OC ) and versin( θ ) (equal to the length of line CD ) is the radius OD (with length 1). Illustrated this way, the sine is vertical ( rectus , literally "straight") while the versine is horizontal ( versus , literally "turned against, out-of-place"); both are distances from C to the circle.
This figure also illustrates the reason why the versine was sometimes called the sagitta , Latin for arrow . [ 17 ] [ 30 ] If the arc ADB of the double-angle Δ = 2 θ is viewed as a " bow " and the chord AB as its "string", then the versine CD is clearly the "arrow shaft".
In further keeping with the interpretation of the sine as "vertical" and the versed sine as "horizontal", sagitta is also an obsolete synonym for the abscissa (the horizontal axis of a graph). [ 30 ]
In 1821, Cauchy used the terms sinus versus ( siv ) for the versine and cosinus versus ( cosiv ) for the coversine. [ 15 ] [ 16 ] [ nb 1 ]
As θ goes to zero, versin( θ ) is the difference between two nearly equal quantities, so a user of a trigonometric table for the cosine alone would need a very high accuracy to obtain the versine in order to avoid catastrophic cancellation , making separate tables for the latter convenient. [ 12 ] Even with a calculator or computer, round-off errors make it advisable to use the sin 2 formula for small θ .
Another historical advantage of the versine is that it is always non-negative, so its logarithm is defined everywhere except for the single angle ( θ = 0, 2 π , …) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines.
In fact, the earliest surviving table of sine (half- chord ) values (as opposed to the chords tabulated by Ptolemy and other Greek authors), calculated from the Surya Siddhantha of India dated back to the 3rd century BC, was a table of values for the sine and versed sine (in 3.75° increments from 0 to 90°). [ 31 ]
The versine appears as an intermediate step in the application of the half-angle formula sin 2 ( θ / 2 ) = 1 / 2 versin( θ ), derived by Ptolemy , that was used to construct such tables.
The haversine, in particular, was important in navigation because it appears in the haversine formula , which is used to reasonably accurately compute distances on an astronomic spheroid (see issues with the Earth's radius vs. sphere ) given angular positions (e.g., longitude and latitude ). One could also use sin 2 ( θ / 2 ) directly, but having a table of the haversine removed the need to compute squares and square roots. [ 12 ]
An early utilization by José de Mendoza y Ríos of what later would be called haversines is documented in 1801. [ 14 ] [ 32 ]
The first known English equivalent to a table of haversines was published by James Andrew in 1805, under the name "Squares of Natural Semi-Chords". [ 33 ] [ 34 ] [ 17 ]
In 1835, the term haversine (notated naturally as hav. or base-10 logarithmically as log. haversine or log. havers. ) was coined [ 35 ] by James Inman [ 14 ] [ 36 ] [ 37 ] in the third edition of his work Navigation and Nautical Astronomy: For the Use of British Seamen to simplify the calculation of distances between two points on the surface of the Earth using spherical trigonometry for applications in navigation. [ 3 ] [ 35 ] Inman also used the terms nat. versine and nat. vers. for versines. [ 3 ]
Other high-regarded tables of haversines were those of Richard Farley in 1856 [ 33 ] [ 38 ] and John Caulfield Hannyngton in 1876. [ 33 ] [ 39 ]
The haversine continues to be used in navigation and has found new applications in recent decades, as in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 [ 40 ] [ 41 ] or in a more compact method for sight reduction since 2014. [ 29 ]
While the usage of the versine, coversine and haversine as well as their inverse functions can be traced back centuries, the names for the other five cofunctions appear to be of much younger origin.
One period (0 < θ < 2 π ) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function (including Hann , Hann–Poisson and Tukey windows ), because it smoothly ( continuous in value and slope ) "turns on" from zero to one (for haversine) and back to zero. [ nb 2 ] In these applications, it is named Hann function or raised-cosine filter .
The functions are circular rotations of each other.
Inverse functions like arcversine (arcversin, arcvers, [ 8 ] avers, [ 43 ] [ 44 ] aver), arcvercosine (arcvercosin, arcvercos, avercos, avcs), arccoversine (arccoversin, arccovers, [ 8 ] acovers, [ 43 ] [ 44 ] acvs), arccovercosine (arccovercosin, arccovercos, acovercos, acvc), archaversine (archaversin, archav, haversin −1 , [ 45 ] invhav, [ 46 ] [ 47 ] [ 48 ] ahav, [ 43 ] [ 44 ] ahvs, ahv, hav −1 [ 49 ] [ 50 ] ), archavercosine (archavercosin, archavercos, ahvc), archacoversine (archacoversin, ahcv) or archacovercosine (archacovercosin, archacovercos, ahcc) exist as well:
These functions can be extended into the complex plane . [ 42 ] [ 19 ] [ 24 ]
Maclaurin series : [ 24 ]
When the versine v is small in comparison to the radius r , it may be approximated from the half-chord length L (the distance AC shown above) by the formula [ 51 ] v ≈ L 2 2 r . {\displaystyle v\approx {\frac {L^{2}}{2r}}.}
Alternatively, if the versine is small and the versine, radius, and half-chord length are known, they may be used to estimate the arc length s ( AD in the figure above) by the formula s ≈ L + v 2 r {\displaystyle s\approx L+{\frac {v^{2}}{r}}} This formula was known to the Chinese mathematician Shen Kuo , and a more accurate formula also involving the sagitta was developed two centuries later by Guo Shoujing . [ 52 ]
A more accurate approximation used in engineering [ 53 ] is v ≈ s 3 2 L 1 2 8 r {\displaystyle v\approx {\frac {s^{\frac {3}{2}}L^{\frac {1}{2}}}{8r}}}
The term versine is also sometimes used to describe deviations from straightness in an arbitrary planar curve, of which the above circle is a special case. Given a chord between two points in a curve, the perpendicular distance v from the chord to the curve (usually at the chord midpoint) is called a versine measurement. For a straight line, the versine of any chord is zero, so this measurement characterizes the straightness of the curve. In the limit as the chord length L goes to zero, the ratio 8 v / L 2 goes to the instantaneous curvature . This usage is especially common in rail transport , where it describes measurements of the straightness of the rail tracks [ 54 ] and it is the basis of the Hallade method for rail surveying .
The term sagitta (often abbreviated sag ) is used similarly in optics , for describing the surfaces of lenses and mirrors .
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https://en.wikipedia.org/wiki/Versinus
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In mathematics , a versor is a quaternion of norm one (a unit quaternion ). Each versor has the form
where the r 2 = −1 condition means that r is a unit-length vector quaternion (or that the first component of r is zero, and the last three components of r are a unit vector in 3 dimensions). The corresponding 3-dimensional rotation has the angle 2 a about the axis r in axis–angle representation . In case a = π/2 (a right angle ), then q = r {\displaystyle q=\mathbf {r} } , and the resulting unit vector is termed a right versor .
The collection of versors with quaternion multiplication forms a group , and the set of versors is a 3-sphere in the 4-dimensional quaternion algebra.
Hamilton denoted the versor of a quaternion q by the symbol U q . He was then able to display the general quaternion in polar coordinate form
where T q is the norm of q . The norm of a versor is always equal to one; hence they occupy the unit 3-sphere in H {\displaystyle \ \mathbb {H} \ } . Examples of versors include the eight elements of the quaternion group . Of particular importance are the right versors , which have angle π/2 . These versors have zero scalar part, and so are vectors of length one (unit vectors). The right versors form a sphere of square roots of −1 in the quaternion algebra. The generators i , j , and k are examples of right versors, as well as their additive inverses . Other versors include the twenty-four Hurwitz quaternions that have the norm 1 and form vertices of a 24-cell polychoron.
Hamilton defined a quaternion as the quotient of two vectors. A versor can be defined as the quotient of two unit vectors. For any fixed plane Π the quotient of two unit vectors lying in Π depends only on the angle (directed) between them, the same a as in the unit vector–angle representation of a versor explained above. That's why it may be natural to understand corresponding versors as directed arcs that connect pairs of unit vectors and lie on a great circle formed by intersection of Π with the unit sphere , where the plane Π passes through the origin. Arcs of the same direction and length (or, the same, subtended angle in radians ) are equipollent and correspond to the same versor. [ 1 ]
Such an arc, although lying in the three-dimensional space , does not represent a path of a point rotating as described with the sandwiched product with the versor. Indeed, it represents the left multiplication action of the versor on quaternions that preserves the plane Π and the corresponding great circle of 3-vectors. The 3-dimensional rotation defined by the versor has the angle two times the arc's subtended angle, and preserves the same plane. It is a rotation about the corresponding vector r , that is perpendicular to Π .
On three unit vectors, Hamilton writes [ 2 ]
Multiplication of quaternions of norm one corresponds to the (non-commutative) "addition" of great circle arcs on the unit sphere. Any pair of great circles either is the same circle or has two intersection points . Hence, one can always move the point B and the corresponding vector to one of these points such that the beginning of the second arc will be the same as the end of the first arc.
An equation
implicitly specifies the unit vector–angle representation for the product of two versors. Its solution is an instance of the general Campbell–Baker–Hausdorff formula in Lie group theory. As the 3-sphere represented by versors in H {\displaystyle \ \mathbb {H} \ } is a 3-parameter Lie group, practice with versor compositions is a step into Lie theory . Evidently versors are the image of the exponential map applied to a ball of radius π in the quaternion subspace of vectors.
Versors compose as aforementioned vector arcs, and Hamilton referred to this group operation as "the sum of arcs", but as quaternions they simply multiply.
The geometry of elliptic space has been described as the space of versors. [ 3 ]
The orthogonal group in three dimensions, rotation group SO(3) , is frequently interpreted with versors via the inner automorphism q ↦ u − 1 q u {\displaystyle \ q\mapsto u^{-1}q\ u\ } where u is a versor. Indeed, if
then
by calculation. [ 4 ] The plane { x + y r : ( x , y ) ∈ R 2 } ⊂ H {\displaystyle \ \{\ x+y\ \mathbf {r} \ :\ (x,y)\in \mathbb {R} ^{2}\ \}\subset \mathbb {H} \ } is isomorphic to C {\displaystyle \ \mathbb {C} \ } and the inner automorphism, by commutativity, reduces to the identity mapping there.
Since quaternions can be interpreted as an algebra of two complex dimensions, the rotation action can also be viewed through the special unitary group SU(2) .
For a fixed r , versors of the form exp ( a r ) {\displaystyle \ \exp(a\ \mathbf {r} )\ } where a ∈ ( − π , π ] , {\displaystyle \ a\in \left(-\pi ,\pi \ \right]\ ,} form a subgroup isomorphic to the circle group . Orbits of the left multiplication action of this subgroup are fibers of a fiber bundle over the 2-sphere, known as Hopf fibration in the case r = i ; other vectors give isomorphic, but not identical fibrations. Lyons (2003) gives an elementary introduction to quaternions to elucidate the Hopf fibration as a mapping on unit quaternions. He writes "the fibers of the Hopf map are circles in S 3 ". [ 5 ]
Versors have been used to represent rotations of the Bloch sphere with quaternion multiplication. [ 6 ]
The facility of versors illustrate elliptic geometry , in particular elliptic space , a three-dimensional realm of rotations. The versors are the points of this elliptic space, though they refer to rotations in 4-dimensional Euclidean space . Given two fixed versors u and v , the mapping q ↦ u q v {\displaystyle \ q\mapsto u\ q\ v\ } is an elliptic motion . If one of the fixed versors is 1, then the motion is a Clifford translation of the elliptic space, named after William Kingdon Clifford who was a proponent of the space. An elliptic line through versor u is { u exp ( a r ) : 0 ≤ a < π } . {\displaystyle \ \{\ u\ \exp(a\ \mathbf {r} )\ :\ 0\leq a<\pi \ \}~.} Parallelism in the space is expressed by Clifford parallels . One of the methods of viewing elliptic space uses the Cayley transform to map the versors to R 3 . {\displaystyle \ \mathbb {R} ^{3}~.}
The set of all versors, with their multiplication as quaternions, forms a continuous group G . For a fixed pair { − r , + r } {\displaystyle \ \{-\mathbf {r} ,+\mathbf {r} \ \}\ } of right versors, G 1 = { exp ( a r ) : a ∈ R } {\displaystyle \ G_{1}=\{\ \exp(a\ \mathbf {r} )\ :\ a\in \mathbb {R} \ \}\ } is a one-parameter subgroup that is isomorphic to the circle group .
Next consider the finite subgroups, beyond the quaternion group Q 8 : [ 7 ] [ 8 ]
As noted by Hurwitz , the 16 quaternions 1 2 ( ± 1 ± i ± j ± k ) {\displaystyle \ {\tfrac {\ 1\ }{2}}\left(\pm \mathbf {1} \pm \mathbf {i} \pm \mathbf {j} \pm \mathbf {k} \right)\ } all have norm one, so they are in G . Joined with Q 8 , these unit Hurwitz quaternions form a group G 2 of order 24 called the binary tetrahedral group . The group elements, taken as points on S 3 , form a 24-cell .
By a process of bitruncation of the 24-cell, the 48-cell on G is obtained, and these versors multiply as the binary octahedral group .
Another subgroup is formed by 120 icosians which multiply in the manner of the binary icosahedral group .
A hyperbolic versor is a generalization of quaternionic versors to indefinite orthogonal groups , such as Lorentz group .
It is defined as a quantity of the form
Such elements arise in split algebras , for example split-complex numbers or split-quaternions . It was the algebra of tessarines discovered by James Cockle in 1848 that first provided hyperbolic versors. In fact, Cockle wrote the above equation (with j in place of r ) when he found that the tessarines included the new type of imaginary element.
This versor was used by Homersham Cox (1882/1883) in relation to quaternion multiplication. [ 9 ] [ 10 ] The primary exponent of hyperbolic versors was Alexander Macfarlane , as he worked to shape quaternion theory to serve physical science. [ 11 ] He saw the modelling power of hyperbolic versors operating on the split-complex number plane, and in 1891 he introduced hyperbolic quaternions to extend the concept to 4-space. Problems in that algebra led to use of biquaternions after 1900. In a widely seen review, Macfarlane wrote:
Today the concept of a one-parameter group subsumes the concepts of versor and hyperbolic versor as the terminology of Sophus Lie has replaced that of Hamilton and Macfarlane.
In particular, for each r such that r r = +1 or r r = −1 , the mapping a ↦ exp ( a r ) {\displaystyle a\mapsto \exp(a\,\mathbf {r} )} takes the real line to a group of hyperbolic or ordinary versors. In the ordinary case, when r and − r are antipodes on a sphere, the one-parameter groups have the same points but are oppositely directed. In physics, this aspect of rotational symmetry is termed a doublet .
Robb (1911) defined the parameter rapidity , which specifies a change in frame of reference . This rapidity parameter corresponds to the real variable in a one-parameter group of hyperbolic versors. With the further development of special relativity the action of a hyperbolic versor came to be called a Lorentz boost . [ 13 ]
Sophus Lie was less than a year old when Hamilton first described quaternions, but Lie's name has become associated with all groups generated by exponentiation. The set of versors with their multiplication has been denoted Sl(1,q) by Gilmore (1974) . [ 14 ] Sl(1,q) is the special linear group of one dimension over quaternions, the "special" indicating that all elements are of norm one. The group is isomorphic to SU(2,c), a special unitary group , a frequently used designation since quaternions and versors are sometimes considered archaic for group theory. The special orthogonal group SO(3,r) of rotations in three dimensions is closely related: it is a 2:1 homomorphic image of SU(2,c).
The subspace { x i + y j + z k : x , y , z ∈ R } ⊂ H {\displaystyle \ \{\ xi+yj+zk\ :\ x,y,z\in \mathbb {R} \ \}\subset \mathbb {H} \ } is called the Lie algebra of the group of versors. The commutator product [ u , v ] = u v − v u , {\displaystyle [u,v]=uv-vu\ ,} is just double the cross product of two vectors, which forms the multiplication operation in the Lie algebra. The close relation to SU(1,c) and SO(3,r) is evident in the isomorphism of their Lie algebras. [ 14 ]
Lie groups that contain hyperbolic versors include the group on the unit hyperbola and the special unitary group SU(1,1) .
The word is derived from Latin versari = "to turn" with the suffix -or forming a noun from the verb (i.e. versor = "the turner"). It was introduced by William Rowan Hamilton in the 1840s in the context of his quaternion theory.
The term "versor" is generalised in geometric algebra to indicate a member R {\displaystyle R} of the algebra that can be expressed as the product of invertible vectors, R = v 1 v 2 ⋯ v k {\displaystyle R=v_{1}v_{2}\cdots v_{k}} . [ 15 ] [ 16 ]
Just as a quaternion versor u {\displaystyle u} can be used to represent a rotation of a quaternion q {\displaystyle q} with mapping q ↦ u − 1 q u {\displaystyle q\mapsto u^{-1}qu} , so can a versor R {\displaystyle R} in Geometric Algebra be used to represent the result of k {\displaystyle k} reflections on a member A {\displaystyle A} of the algebra with mapping A ↦ ( − 1 ) k R A R − 1 {\displaystyle A\mapsto (-1)^{k}RAR^{-1}} .
A rotation can be considered the result of two reflections, so it turns out a quaternion versor u {\displaystyle u} can be identified as a 2-versor R = v 1 v 2 {\displaystyle R=v_{1}v_{2}} in the geometric algebra of three real dimensions G ( 3 , 0 ) {\displaystyle {\mathcal {G}}(3,0)} .
In a departure from Hamilton's definition, multivector versors are not required to have unit norm, just to be invertible. Normalisation can still be useful however, so it is convenient to designate versors as unit versors in a geometric algebra if R R ~ = ± 1 {\displaystyle R{\tilde {R}}=\pm 1} , where the tilde denotes reversion of the versor.
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The Thermoproteota are prokaryotes that have been classified as a phylum of the domain Archaea . [ 3 ] [ 4 ] [ 5 ] Initially, the Thermoproteota were thought to be sulfur-dependent extremophiles but recent studies have identified characteristic Thermoproteota environmental rRNA indicating the organisms may be the most abundant archaea in the marine environment. [ 6 ] Originally, they were separated from the other archaea based on rRNA sequences; other physiological features, such as lack of histones , have supported this division, although some crenarchaea were found to have histones. [ 7 ] Until 2005 all cultured Thermoproteota had been thermophilic or hyperthermophilic organisms, some of which have the ability to grow at up to 113 °C. [ 8 ] These organisms stain Gram negative and are morphologically diverse, having rod, cocci , filamentous and oddly-shaped cells. [ 9 ] Recent evidence shows that some members of the Thermoproteota are methanogens.
Thermoproteota were initially classified as a part of regnum Eocyta in 1984, [ 10 ] but this classification has been discarded. The term "eocyte" now applies to either TACK (formerly Crenarchaeota) or to Thermoproteota.
One of the best characterized members of the Crenarchaeota is Sulfolobus solfataricus . This organism was originally isolated from geothermally heated sulfuric springs in Italy, and grows at 80 °C and pH of 2–4. [ 11 ] Since its initial characterization by Wolfram Zillig , a pioneer in thermophile and archaean research, similar species in the same genus have been found around the world. Unlike the vast majority of cultured thermophiles, Sulfolobus grows aerobically and chemoorganotrophically (gaining its energy from organic sources such as sugars). These factors allow a much easier growth under laboratory conditions than anaerobic organisms and have led to Sulfolobus becoming a model organism for the study of hyperthermophiles and a large group of diverse viruses that replicate within them.
Nitrososphaerota
Thermoproteales
Fervidicoccales
Desulfurococcales 1
Desulfurococcales
Sulfolobales
" Panguiarchaeales "
"Korarchaeales"
"Bifangarchaeales" [B24]
"Hecatellales" [B25]
"Xuanwuarculales" [RBG-16-48-13]
"Houtuarculales" [40CM-2-53-6]
"Wuzhiqiibiales" [TCS64]
"Zhuquarculales" [EX4484-135]
"Bathyarchaeales" [B26-1]
" Caldarchaeales "
"Geothermarchaeales"
Conexivisphaerales
Nitrososphaerales
" Nezhaarchaeales "
" Culexarchaeles "
" Methanomethylicales "
"Gearchaeales"
Thermofilales
Thermoproteales
" Marsarchaeales "
Sulfolobales
Verstraetearchaeota is a candidate phylum in Thermoproteota . [ 2 ] Other valid names for this phylum are Nitrososphaerota and Thermoproteota . This candidate phylum has not been cultured . [ 18 ] This domain is capable of Methanogenesis . [ 19 ]
Irradiation of S. solfataricus cells with ultraviolet light strongly induces formation of type IV pili that can then promote cellular aggregation. [ 20 ] Ultraviolet light-induced cellular aggregation was shown by Ajon et al. [ 21 ] to mediate high frequency inter-cellular chromosome marker exchange. Cultures that were ultraviolet light-induced had recombination rates exceeding those of uninduced cultures by as much as three orders of magnitude. S. solfataricus cells are only able to aggregate with other members of their own species. [ 21 ] Frols et al. [ 20 ] [ 22 ] and Ajon et al. [ 21 ] considered that the ultraviolet light-inducible DNA transfer process, followed by homologous recombinational repair of damaged DNA , is an important mechanism for promoting chromosome integrity.
This DNA transfer process can be regarded as a primitive form of sexual interaction .
Beginning in 1992, data were published that reported sequences of genes belonging to the Thermoproteota in marine environments. [ 23 ] , [ 24 ] Since then, analysis of the abundant lipids from the membranes of Thermoproteota taken from the open ocean have been used to determine the concentration of these “low temperature Crenarchaea” (See TEX-86 ). Based on these measurements of their signature lipids, Thermoproteota are thought to be very abundant and one of the main contributors to the fixation of carbon . [ citation needed ] DNA sequences from Thermoproteota have also been found in soil and freshwater environments, suggesting that this phylum is ubiquitous to most environments. [ 25 ]
In 2005, evidence of the first cultured “low temperature Crenarchaea” was published. Named Nitrosopumilus maritimus , it is an ammonia -oxidizing organism isolated from a marine aquarium tank and grown at 28 °C. [ 26 ]
The research about two-domain system of classification has paved the possibilities of connections between crenarchaea and eukaryotes . [ 27 ]
DNA analysis from 2008 (and later, 2017) has shown that eukaryotes possible evolved from thermoproteota-like organisms. Other candidates for the ancestor of eukaryotes include closely related asgards . This could suggest that eukaryotic organisms possibly evolved from prokaryotes.
These results are similar to the eocyte hypothesis of 1984, proposed by James A. Lake . [ 10 ] The classification according to Lake, states that both crenarchaea and asgards belong to Kingdom Eocyta. Though this has been discarded by scientists, the main concept remains. The term "Eocyta" now either refers to the TACK group or to Phylum Thermoproteota itself.
However, the topic is highly debated and research is still going on.
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Versus populum ( Latin for "towards the people") is the liturgical stance of a priest who, while celebrating Mass , faces the people from the other side of the altar. The opposite stance, that of a priest facing in the same direction as the people, is today called ad orientem (literally, "towards the east" − even if the priest is really facing in some other direction) or ad apsidem ("towards the apse" − even if the altar is unrelated to the apse of the church or even if the church or chapel has no apse).
In the early history of Christianity it was considered the norm to pray facing the geographical east. [ 1 ] From the middle of the 17th century, almost all new Roman Rite altars were built against a wall or backed by a reredos , with a tabernacle placed on the main altar or inserted into the reredos. This meant that the priest turned to the people, putting his back to the altar, for a few short moments at Mass. However, the Tridentine Missal is not celebrated versus populum since the Ritus Servandus gives corresponding instructions for the priest when performing actions that require him to face the people. In the Ritus Servandus, the rubrics say "with his hands joined before his breast, and with his eyes downcast, he turns toward the people from left to right." This would otherwise not make sense in the context of versus populum since versus populum assumes that he is already facing the people. [ 2 ]
It has been said that the reason the Pope always faced the people when celebrating Mass in St Peter's was that early Christians faced eastward when praying and, due to the difficult terrain, the basilica was built with its apse to the west. Some have attributed this orientation in other early Roman churches to the influence of Saint Peter's. [ 3 ] However, the arrangement whereby the apse with the altar is at the west end of the church and the entrance on the east is found also in Roman churches contemporary with Saint Peter's (such as the original Basilica of Saint Paul Outside the Walls ) that were under no such constraints of terrain, and the same arrangement remained the usual one until the sixth century. [ 4 ] According to Klaus Gamber, in this early layout the people were situated not in the central nave but in the side aisles of the church and, while the priest faced both the altar and east throughout the Mass, the people faced the altar (from the sides) until the high point of the Mass, when they would turn to face east, the direction in which the priest was already facing. [ 5 ] This view is strongly criticized on the grounds of the unlikelihood that, in churches where the altar was to the west, they would turn their backs on the altar (and the priest) at the celebration of the Eucharist. [ 6 ]
It was in the 8th or 9th century that the position whereby the priest faced the apse, not the people, when celebrating Mass was adopted in Rome, [ 7 ] under the influence of the Frankish Empire , [ 8 ] where it had become general. [ 9 ] However, in several churches in Rome, it was physically impossible, even before the twentieth-century liturgical reforms, for the priest to celebrate Mass facing away from the people, because of the presence, immediately in front of the altar, of the "confession" ( Latin : confessio ), an area sunk below floor level to enable people to come close to the tomb of the saint buried beneath the altar. The best-known such "confession" is that in St Peter's Basilica , but many other churches in Rome have the same architectural feature, including at least one, the present Basilica of Saint Paul Outside the Walls , which, although the original Constantinian basilica was arranged like St Peter's, is oriented since 386 in such a way that the priest faces west when celebrating Mass.
The earliest Christian churches were not built with any particular orientation in mind, but by the fifth century it became the rule in the Eastern Roman Empire to have the altar at the east end of the church, an arrangement that became normal but not universal in northern Europe. [ 9 ] The old Roman custom of having the altar at the west end and the entrance at the east was sometimes followed as late as the 11th century even in areas under Frankish rule, as seen in Petershausen (Constance) , Bamberg Cathedral , Augsburg Cathedral , Regensburg Cathedral , and Hildesheim Cathedral (all in present-day Germany). [ 10 ] In the east also, the original Constantinian Church of the Holy Sepulchre in Jerusalem had its apse to the west until it was Byzantinized in 1048. [ 11 ] [ 12 ] [ 13 ] [ 14 ]
In the Roman Rite of the Catholic Church, the altar is "the center of thanksgiving that the Eucharist accomplishes" and the point around which the other rites are in some manner arrayed. [ 15 ] Its importance was made evident by Romano Guardini (1885–1968), about whom Robert R. Kuehn wrote: "with him [Guardini] on the altar, the sacred table became the center of the universe" [...] The impact of the sacred action was all the more profound because Guardini celebrated the Mass versus populum – facing the people." [ 16 ]
The present (2002) General Instruction of the Roman Missal says, in the official English translation: "The altar should be built separate from the wall, in such a way that it is possible to walk around it easily and that Mass can be celebrated at it facing the people, which is desirable wherever possible." [ 17 ] Where practicable, the church altar should be built in such a way that the priest can easily walk around it and can celebrate Mass versus populum . But at least one popular priest, who resists the liturgical reforms of Vatican II ecumenical council, tends to suggest that the text does not oblige the priest to avail of these possibilities. [ 18 ] In actual practice throughout the Roman Catholic Church, popes, cardinals, archbishops, bishops and priests, by their constant examples since the Novus Ordo form of the Roman Missal was initially promulgated, have been nearly unanimous in adopting versus populum as the defining orientation for the priest during the Mass.
In practice, after the Second Vatican Council, altars that obliged the priest to have his back to the people were generally moved away from the wall or reredos, or, where this was unsuitable, a new freestanding altar was built closer to the people. This, however, is not universal, and in some older churches and chapels it is physically impossible for the priest to face the people throughout the Mass, as before 1970 some churches, especially in Rome, had altars at which it was physically impossible for the priest not to face the people throughout the Mass.
The present Roman Missal prescribes that the priest should face the people at six points of the Mass:
The Tridentine Roman Missal requires the priest to face the people, without looking at them, since he is directed to have his eyes cast down to the ground ( Ritus servandus , V, 1; VII, 7; XII, 1), and, if he is at the same side of the altar as the people, to turn his back to the altar, eight times:
The Tridentine and the Vatican II editions of the Roman Missal expressly direct the priest to face the altar at exactly the same points. His position in relation to the altar and the people determines whether facing the altar means also facing the people.
However, the present Roman Missal does not direct the priest to turn, that is, to change his direction from toward the people to away from the people. In this sense, the word face , as it is defined, can readily be understood as focusing one's attention, whether on the people gathered in front of the priest or on the altar in front of the priest, while the priest is in a versus populum posture.
In the second half of the 17th century, it became customary to place the tabernacle on the main altar of the church. When a priest celebrates Mass at such an altar with his back to the people, he sometimes necessarily turns his back directly to the Blessed Sacrament , as when he turns to the people at the Orate fratres . This seeming disrespect is absent when the priest stands on the side of the altar away from the people; but locating so large an object on the altar is arguably inconvenient for a celebration in which the priest faces the people. Accordingly, the revised Roman Missal states:
The Missal does, however, direct that the tabernacle be situated "in a part of the church that is truly noble, prominent, readily visible, beautifully decorated, and suitable for prayer" (GIRM 314).
For the majority of its history, ad orientem worship was the norm, apart from a relatively brief period following the Reformation when priests in the Church of England and other churches of the Anglican Communion celebrated the Holy Eucharist standing at the north-end (i.e. the left side) of the communion table, according to the rubric in the Book of Common Prayer. By the 1630s, Archbishop Laud 's refors had returned the altar to its traditional eastern position - there was an Elizabethan injunction on the matter, which Laud used to defend his requirement that the communion tables be stood permanently altar-wise at the east end. Thereafter followed a time of back-and-forth, but at the Restoration, altars in the Chapels Royal were restored to their proper positions, and many Cathedrals followed suit, although there was a notable disuniformity from church to church, with the non-conformists having differing views.
When the City of London churches were rebuilt following the great fire, there was a noticiable uniformity in the chancel layouts of the rebuilt churches, with the communion table stood on a marble floor, raised on one or two steps, railed and most backed by a reredos. The shallow depth of these steps meant that the communion table could only be placed altar-wise, that is, facing east in the traditional arrangement. It is thought that this is partly due to Wren being the son and nephew of distinguished Laudian churchmen, who would certainly have had the traditional ad orientem arrangement in their churches. [ 19 ] This also applied to the city churches that survived the fire, such as St Helen, Bishopsgate , which retained its ad orientem orientation until the end of the 20th century. It is thought that celebrations from this period were at the "north end", the celebrant was actually facing east, while standing at the north end of the altar, as the altar arrangements leave little other space for the celebrant to stand. 18th Century Churches also follow suit, with similar altar arrangements to Wren's City Churches, with the baroque church of St Martin-in-the-Fields and the neighbouring Palladian church of St Giles-in-the-Fields both with railed altars at their east ends, preclude any arrangement of the altar other than the eastward position - the sanctuary of the latter (still largely in its original form) is so shallow that the swing of the communion rail gate does not even allow the communion table to be pulled away from the wall (the former has since been enlarged, with a modern stone altar positioned for versus populum celebration)
The rubric was further challenged in the 19th century by the Oxford Movement , many of whose leaders preferred the traditional ad orientem position, - indeed what is considered the "English Use" altar arrangement has curtains on 3 sides of the altar, only allowing the eastward celebration of the Eucharist. The practices reintroduced by the Anglo-Catholic revival soon became the norm throughout the Church of England, with most mainstream parish churches adopting, among other catholic practices, Eucharistic vestments, altar candlesticks and crucifixes, and most 19th century churches being constructed with ad orientem celebration in mind. Notable examples include the 19th century high altar at St Paul's Cathedral by Bodley and Garner constructed in marble with a large marble reredos, and the various Oxford Movement churches such as All Saints, Margaret Street and St Cyprian's, Clarence Gate by Comper, built to a Sarum Rite ideal. In America, the rubric requiring that the priest stand at the north end of the table, facing liturgical South, was removed from the 1928 American Book of Common Prayer (the Church of England never adopted the 1928 prayer book, as it was rejected by parliament). This was controversial, despite many notable 19th century Anglican churches and cathedrals in America had been built to Anglo-Catholic ideals, complete with stone eastward-facing altars and using full Eucharistic vestments, but nonetheless regularized a practice that was already widespread. Praying ad orientem then became common especially at the Gloria Patri , Gloria in Excelsis and Ecumenical creeds in that direction. [ 20 ] However, following the reforms of the Second Vatican Council in the Roman Catholic Church, many mainstream Anglican churches that had re-adopted many of the traditional catholic practices, likewise adopted the reforms of Vatican II. "the course of the last forty years or so, a great many of those altars have either been removed and pulled out away from the wall or replaced by the kind of freestanding table-like altar", in "response to the popular sentiment that the priest ought not turn his back to the people during the service; the perception was that this represented an insult to the laity and their centrality in worship. Thus developed today’s widespread practice in which the clergy stand behind the altar facing the people." [ 21 ] Today, it is not uncommon to find ad orientem celebrations of the Eucharist in more traditional Anglican churches, but the reformed late 20th century Roman Catholic practice of versus populum is undoubtedly more widespread despite never being the historical norm.
The United Methodist Book of Worship mandates that:
In our churches, the Communion table is to be placed in such a way that the presider is able to stand behind it, facing the people, and the people can visually if not physically gather around it. The table should be high enough so that the presider does not need to stoop to handle the bread and cup. Adaptations may be necessary to facilitate gracious leadership. While architectural integrity should be respected, it is important for churches to carefully adapt or renovate their worship spaces more fully to invite the people to participate in the Holy Meal. If altars are for all practical purposes immovable, then congregations should make provisions for creating a table suitable to the space so that the presiding minister may face the people and be closer to them. [ 22 ]
In the Lutheran German Mass ( Deutsche Messe ), Martin Luther , the founder of that denomination, wrote that:
Here [in Wittenberg] we retain the vestments, altar, and candles until they are used up or we are pleased to make a change. But we do not oppose anyone who would do otherwise. In the true mass, however, of real Christians, the altar should not remain where it is, and the priest should always face the people as Christ doubtlessly did in the Last Supper. [ 23 ]
In discussing the Divine Service , Lorraine S. Brugh and Gordon W. Lathrop write that "Many Lutherans, in concert with many other Christians, think that the time of which Luther spoke has indeed come, and that the pastor should preside at the table facting the people, i.e., versus populum . The assembly needs to have a sense that it is gathered around that table, sees and hears what happens there, has a promise of Christ clearly addressed to it, participates in the thanksgiving, and is made into a community through God's gift." [ 24 ] Thus, in the Lutheran Church , many altars are now built to be freestanding. In churches where the former altar attached to the wall cannot be moved, it has often been converted to be used as a credence table , as a "significant new table is set up, closer to the people and standing free". [ 25 ]
Cardinal Joseph Ratzinger (later Pope Benedict XVI ) in his book The Spirit of the Liturgy criticised the use of versus populum as ahistorical and even harmful to the liturgy. He stated that versus populum "turns the community into a self-enclosed circle", where the presider becomes the real point of reference instead of God. He also maintained that praying toward the east ( ad orientem ) is a tradition that goes back to the beginning of Christianity and that is a "fundamental expression of the Christian synthesis of cosmos and history" and urged Catholics to gradually return to this tradition. On the other hand, he warned against quick and frequent changes to the liturgy, so he proposed a temporary solution - placing the cross in the middle of the altar, so the entire congregation "turns toward the Lord", who should be the real center of the Mass. [ 26 ]
Edward Slattery , from 1993 to 2016 Bishop of the Roman Catholic Diocese of Tulsa , argued that the change towards versus populum has had a number of unforeseen and largely negative effects. First of all, he said, "it is a serious rupture with the Church's ancient tradition. Secondly, it can give the appearance that the priest and the people were engaged in a conversation about God, rather than the worship of God. Thirdly, it places an inordinate importance on the personality of the celebrant by placing him on a kind of liturgical stage". [ 27 ]
On the other hand, the Jesuit theologian John Zupez, in an article in Emmanuel based on modern studies in scriptural exegesis, found that the New Testament word for sacrifice ( hilasterion) refers to our expiation from sin, not propitiation impacting or appeasing God. This current translation, accepted in the Catholic lectionary, should "eliminate a strong argument for the priest at Mass facing toward God ( ad orientem )" and "support the practice of the priest facing the people to elicit their active involvement." [ 28 ] However, the Council of Trent had already authoritatively confirmed that "this sacrifice [of the Mass] is truly propitiatory ."
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Eclipse Vert.x is a polyglot event-driven application framework that runs on the Java Virtual Machine. [ 2 ] [ 3 ]
Similar environments written in other programming languages include Node.js for JavaScript , Twisted for Python , Perl Object Environment for Perl , libevent for C , reactPHP and amphp for PHP and EventMachine for Ruby .
Vert.x was started by Tim Fox in 2011 while he was employed by VMware .
Fox initially named the project "Node.x", a play on the naming of Node.js , with the "x" representing the fact that the new project was polyglot in nature, and didn't simply support JavaScript. The project was later renamed to "Vert.x" to avoid any potential legal issues as "Node" was a trademark owned by Joyent Inc. [ 4 ] The new name was also a play on the name node, as a vertex is a synonym for a node in mathematics.
In December 2012, after he left their employment, VMware served legal papers on Tim Fox to take control of the Vert.x trademark, domain name, blog, GitHub account, and Google Group from the Vert.x community [ 5 ] [ 6 ]
After much discussion with other parties, in January 2013, VMware was persuaded that it would be in the best interests of the Vert.x community to move the project and associated IP to the Eclipse Foundation, a neutral legal entity. [ 7 ]
In August 2013, the core Vert.x project completed its move to the Eclipse Foundation. The other projects that make up the Vert.x stack did not migrate to Eclipse but continued to use the "Vert.x" trademark with tacit approval of the Eclipse Foundation.
In May 2014, Vert.x won the award for "Most Innovative Java Technology" at the JAX Innovation awards. [ 8 ]
On January 12, 2016, Tim Fox stepped down as the lead of the Vert.x project. [ 9 ] and Julien Viet, a long-time contributor, took his place.
Vert.x uses low level IO library Netty . [ 10 ]
The application framework includes these features:
A web server serving "Hello from Vert.x!" could be written in Java:
And in JavaScript :
Both cases will result in a web server serving content in a highly scalable manner.
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The Vertebrate Genomes Project (VGP) is a project which aims to generate high-quality, complete reference genomes of all 66,000 vertebrate species. It is an international cooperation project with members from more than 50 separate institutions and was launched in February 2017. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]
In October 2021, VGP partnered with Colossal Biosciences to sequence and assemble elephant genomes for preservation purposes. [ 6 ]
In April 2022, VGP partnered with the Human Genome Project [ 7 ] and the African BioGenome Project for sequencing research. [ 8 ]
In July 2022, VGP and Colossal Biosciences announced that they successfully sequenced the entire Asian elephant genome; this is the first time that mammalian genetic code has been fully sequenced to this degree since the Human Genome Project was completed in the early 2000s. [ 9 ]
In November 2022, VGP successfully sequenced the Nile Rat genome in order to facilitate research on type 2 diabetes and the health effects of circadian rhythm disruption. Not only did researchers sequence an individual rat, but they also sequenced both its parents, allowing them to separate the original rat’s alleles by parental haplotype. The resulting sequence showed that the vast majority of expected protein-coding genes were accounted for. [ 10 ] [ 11 ]
Vertebrate Genomes Project
This article about a scientific organization is a stub . You can help Wikipedia by expanding it .
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The vertebrate mitochondrial code (translation table 2 ) is the genetic code found in the mitochondria of all vertebrata .
AGA and AGG were thought to have become mitochondrial stop codons early in vertebrate evolution. [ 1 ] However, at least in humans it has now been shown that AGA and AGG sequences are not recognized as termination codons . A -1 mitoribosome frameshift occurs at the AGA and AGG codons predicted to terminate the CO1 and ND6 open reading frames (ORFs), and consequently both ORFs terminate in the standard UAG codon. [ 2 ]
Mitochondrial genes in some vertebrates (including humans) have incomplete stop codons ending in U or UA, which become complete termination codons (UAA) upon subsequent polyadenylation . [ 3 ] [ 4 ] [ 5 ] [ 6 ]
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Vertebrate zoology is the biological discipline that consists of the study of Vertebrate animals, i.e., animals with a backbone , such as fish , amphibians , reptiles , birds and mammals . Many natural history museums have departments named Vertebrate Zoology . In some cases whole museums bear this name, e.g. the Museum of Vertebrate Zoology at the University of California , Berkeley . [ 1 ]
This subdivision of zoology has many further subdivisions, including:
These divisions are sometimes further divided into more specific specialties.
This zoology –related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Vertebrate_zoology
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In the mathematical field of graph theory , an automorphism is a permutation of the vertices such that edges are mapped to edges and non-edges are mapped to non-edges. [ 1 ] A graph is a vertex-transitive graph if, given any two vertices v 1 and v 2 of G , there is an automorphism f such that
In other words, a graph is vertex-transitive if its automorphism group acts transitively on its vertices. [ 1 ] A graph is vertex-transitive if and only if its graph complement is, since the group actions are identical.
Every symmetric graph without isolated vertices is vertex-transitive, and every vertex-transitive graph is regular . However, not all vertex-transitive graphs are symmetric (for example, the edges of the truncated tetrahedron ), and not all regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's graph ).
Finite vertex-transitive graphs include the symmetric graphs (such as the Petersen graph , the Heawood graph and the vertices and edges of the Platonic solids ). The finite Cayley graphs (such as cube-connected cycles ) are also vertex-transitive, as are the vertices and edges of the Archimedean solids (though only two of these are symmetric). Potočnik, Spiga and Verret have constructed a census of all connected cubic vertex-transitive graphs on at most 1280 vertices. [ 2 ]
Although every Cayley graph is vertex-transitive, there exist other vertex-transitive graphs that are not Cayley graphs. The most famous example is the Petersen graph, but others can be constructed including the line graphs of edge-transitive non- bipartite graphs with odd vertex degrees. [ 3 ]
The edge-connectivity of a connected vertex-transitive graph is equal to the degree d , while the vertex-connectivity will be at least 2( d + 1)/3. [ 1 ] If the degree is 4 or less, or the graph is also edge-transitive , or the graph is a minimal Cayley graph , then the vertex-connectivity will also be equal to d . [ 4 ]
Infinite vertex-transitive graphs include:
Two countable vertex-transitive graphs are called quasi-isometric if the ratio of their distance functions is bounded from below and from above. A well known conjecture stated that every infinite vertex-transitive graph is quasi-isometric to a Cayley graph . A counterexample was proposed by Diestel and Leader in 2001. [ 5 ] In 2005, Eskin, Fisher, and Whyte confirmed the counterexample. [ 6 ]
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In geometry , a vertex ( pl. : vertices or vertexes ), also called a corner , is a point where two or more curves , lines , or line segments meet or intersect . For example, the point where two lines meet to form an angle and the point where edges of polygons and polyhedra meet are vertices. [ 1 ] [ 2 ] [ 3 ]
The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments, and lines that result in two straight "sides" meeting at one place. [ 3 ] [ 4 ]
A vertex is a corner point of a polygon , polyhedron , or other higher-dimensional polytope , formed by the intersection of edges , faces or facets of the object. [ 4 ]
In a polygon, a vertex is called " convex " if the internal angle of the polygon (i.e., the angle formed by the two edges at the vertex with the polygon inside the angle) is less than π radians (180°, two right angles ); otherwise, it is called "concave" or "reflex". [ 5 ] More generally, a vertex of a polyhedron or polytope is convex, if the intersection of the polyhedron or polytope with a sufficiently small sphere centered at the vertex is convex, and is concave otherwise.
Polytope vertices are related to vertices of graphs , in that the 1-skeleton of a polytope is a graph, the vertices of which correspond to the vertices of the polytope, [ 6 ] and in that a graph can be viewed as a 1-dimensional simplicial complex the vertices of which are the graph's vertices.
However, in graph theory , vertices may have fewer than two incident edges, which is usually not allowed for geometric vertices. There is also a connection between geometric vertices and the vertices of a curve , its points of extreme curvature: in some sense the vertices of a polygon are points of infinite curvature, and if a polygon is approximated by a smooth curve, there will be a point of extreme curvature near each polygon vertex. [ 7 ]
A vertex of a plane tiling or tessellation is a point where three or more tiles meet; [ 8 ] generally, but not always, the tiles of a tessellation are polygons and the vertices of the tessellation are also vertices of its tiles. More generally, a tessellation can be viewed as a kind of topological cell complex , as can the faces of a polyhedron or polytope; the vertices of other kinds of complexes such as simplicial complexes are its zero-dimensional faces.
A polygon vertex x i of a simple polygon P is a principal polygon vertex if the diagonal [ x (i − 1) , x (i + 1) ] intersects the boundary of P only at x (i − 1) and x (i + 1) . There are two types of principal vertices: ears and mouths . [ 9 ]
A principal vertex x i of a simple polygon P is called an ear if the diagonal [ x (i − 1) , x (i + 1) ] that bridges x i lies entirely in P . (see also convex polygon ) According to the two ears theorem , every simple polygon has at least two ears. [ 10 ]
A principal vertex x i of a simple polygon P is called a mouth if the diagonal [ x (i − 1) , x (i + 1) ] lies outside the boundary of P .
Any convex polyhedron 's surface has Euler characteristic
where V is the number of vertices, E is the number of edges , and F is the number of faces . This equation is known as Euler's polyhedron formula . Thus the number of vertices is 2 more than the excess of the number of edges over the number of faces. For example, since a cube has 12 edges and 6 faces, the formula implies that it has eight vertices.
In computer graphics , objects are often represented as triangulated polyhedra in which the object vertices are associated not only with three spatial coordinates but also with other graphical information necessary to render the object correctly, such as colors, reflectance properties, textures, and surface normal . [ 11 ] These properties are used in rendering by a vertex shader , part of the vertex pipeline .
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Vertex Pharmaceuticals Incorporated is an American biopharmaceutical company based in Boston, Massachusetts . It was one of the first biotech firms to use an explicit strategy of rational drug design rather than combinatorial chemistry . It maintains headquarters in Boston, Massachusetts, and three research facilities, in San Diego, California , and Milton Park , Oxfordshire, England .
Vertex was founded in 1989 by Joshua Boger [ 3 ] and Kevin J. Kinsella [ 4 ] to "transform the way serious diseases are treated." [ 5 ]
The company's beginnings were profiled by Barry Werth in the 1994 book The Billion-Dollar Molecule . [ 4 ] His 2014 book, The Antidote: Inside the World of New Pharma , chronicled the company's subsequent development over the next two decades. [ 6 ]
By 2004, its product pipeline focused on viral infections, inflammatory and autoimmune disorders, and cancer . [ 7 ]
In 2009, the company had about 1,800 employees, including 1,200 in the Boston area. [ 3 ] By 2019 there were about 2,500 employees. [ 8 ]
Since late 2011, Vertex has ranked among the top 15 best-performing companies on the Standard & Poor's 500 . Vertex shares increased 250 percent in the same period. [ 9 ] In January 2014, Vertex completed its move from Cambridge, Massachusetts , to Boston, Massachusetts , and took residence in a new, $800 million complex. Located on the South Boston waterfront, it marked the first time in the company's history that all of the roughly 1,200 Vertex employees in the Greater Boston area worked together. [ 10 ]
On 23 January 2019, Ian Smith, the COO and interim CFO of Vertex, was terminated from his position for undisclosed personal behavior that violated established company code of conduct rules. [ 11 ] In June of the same year, Vertex announced it would acquire Exonics Therapeutics for up to $1 billion and collaborate with CRISPR Therapeutics, boosting its development of treatments for Duchenne muscular dystrophy and myotonic dystrophy type 1. [ 12 ] [ 13 ]
In September 2019 the company announced it would acquire Semma Therapeutics for $950 million in cash. [ 14 ] Semma Therapeutics created a "small, implantable device that holds millions of replacement beta cells, letting glucose and insulin through but keeping immune cells out." [ 15 ]
On 1 April 2020, Reshma Kewalramani , then the chief medical officer, became president and chief executive officer of Vertex Pharmaceuticals. [ 16 ] Former CEO and president Jeffrey Leiden transitioned to the role of executive chairman of the board of directors, as of 1 April 2020. [ 16 ] Leiden was to serve as executive chairman until April 2023, [ 17 ] [ 18 ] although As of September 2024 [update] he remains in that post. [ 19 ]
In July 2022, the business announced it would acquire ViaCyte, Inc. for $320 million. [ 20 ]
In April 2024, it was announced Vertex had agreed to acquire the Seattle -headquartered clinical stage biopharmaceutical company Alpine Immune Sciences for $4.9 billion. [ 21 ]
In 2012 ivacaftor was designated as an orphan drug , identifying cystic fibrosis as affecting fewer than 200,000 people in the United States. On 31 January 2012, Vertex gained FDA approval [ 22 ] of the first drug, Kalydeco, [ 23 ] to treat the underlying cause of cystic fibrosis rather than the symptoms, in patients 6 years or older who have the G551D gene mutation .
In the US, 30,000 people have cystic fibrosis. About 4% of those, or 1,200, have the G551D gene mutation. In 2017 Vertex marketed the drug for $311,000 per person per year. [ 24 ] [ 25 ]
Vertex also studied ivacaftor in combination with another drug ( lumacaftor [ 26 ] ) for the most common mutation in cystic fibrosis (CF), known as F508del, and published the first set of results in 2012. Vertex produced the drug after 13 years of research and development, with $70 million in support from the Cystic Fibrosis Foundation . [ 27 ] [ 28 ]
In the UK, the company provided the drug free for a limited time for certain patients. Subsequently, the hospitals decided to continue to pay for the drug for those patients. UK agencies estimated the cost per quality adjusted life year (QALY) at between £335,000 and £1,274,000—far above the NICE thresholds [ 29 ] of £20,000-£30,000.
On 5 November 2014 Vertex announced the submission of a New Drug Application (NDA) to the FDA for a fully co-formulated combination of lumacaftor and ivacaftor for people with cystic fibrosis ages 12 and older who have two copies of the F508del mutation in the cystic fibrosis transmembrane conductance regulator (CFTR) gene. [ 30 ] In 2015, FDA approved the combination of lumacaftor and ivacaftor to treat CF in patients 12 years and older, who have the F 508del mutation. The combination drug is marketed under the tradename Orkambi . [ 31 ]
On 28 March 2017, Vertex announced Phase 3 data from a dual combination treatment, tezacaftor plus ivacaftor, in patients with cystic fibrosis. [ 32 ] On 12 February 2018, the FDA approved the combination, marketed as Symdeko. [ 33 ]
In 2016, Vertex began developing a new group of CFTR modulators in combination with tezacaftor and ivacaftor. [ 33 ] In 2017, the company reported results that showed benefits for patients with different mutations that represent 90% of the CF population. [ 34 ] On 22 October 2019, two months after a new drug application was filed with it, the FDA approved Vertex's Triple-combo therapy Trikafta ( elexacaftor/tezacaftor/ivacaftor ) for patients 12 and older with at least one F508del mutation. [ 35 ] The FDA approval covers approximately 90% of patients with cystic fibrosis. [ 36 ]
Vertex has refused to make Trikafta available in developing countries and works to block generic alternatives, making it inaccessible for thousands of patients. [ 37 ]
In January 2025, Vertex became the first drugmaker in 25 years to gain U.S. approval for a new type of pain medicine when the FDA approved Journavx ( suzetrigine ), a novel non-opioid treatment for moderate to severe acute pain. [ 44 ] [ 45 ] Journavx was evaluated via two randomized, double-blind, placebo- and active-controlled trials of acute surgical pain. [ 46 ]
In 2014, Vertex discontinued telaprevir. [ 47 ] In May 2011, the Food and Drug Administration (FDA) had approved the drug telaprevir (Incivek) as an oral treatment for hepatitis C . Development and commercialization of telaprevir was shared with Johnson & Johnson for European distribution and Mitsubishi for Asia. Telaprevir is a protease inhibitor . [ 48 ]
In 2015, several media outlets reported CEO Jeffrey Leiden's 2014 compensation to be approximately US$48.5 million. [ 49 ] Vertex shareholders opted for a reduction in CEO compensation in 2015 and 2016, resulting in 2016 earnings of US$17.4 million. [ 50 ]
The initial pricing of Orkambi at US$ 135,000 to US$ 270,000 per patient per year, depending on the patient's country, led to campaigns by parent groups concerned that it limited access to the drug for children and young adults with cystic fibrosis, and also led to allegations of unfair pricing by the UK's National Health Service . [ 51 ] [ 52 ] [ 53 ] [ 54 ] [ 55 ]
In March 2019, Vertex was legally required to destroy 7,880 packs of Orkambi that reached their expiry dates during price negotiations with the NHS. [ 56 ] [ 57 ]
On October 24, 2019, NHS England agreed to fund wider access to all of the pharmaceutical company's cystic fibrosis medications that were already licensed at that time, such as Orkambi, Symkevi and Kalydeco, and any future indications of these medicines. The funding agreement was finalized soon after Vertex signed reimbursement deals elsewhere, including NHS Scotland , Spain and Australia. [ 58 ] [ 36 ] Vertex agreed to offer equivalent pricing to the NHS in Wales and Northern Ireland . [ 59 ] On June 30, 2020, Vertex and NHS expanded the agreement to include reimbursement of Kaftrio (the name used for marketing Trikafta in the UK), making England one of the first countries in Europe to fund it. [ 60 ]
In October 2023, NICE declined to recommend Vertex's cystic fibrosis drugs Kaftrio, Symkevi, and Orkambi for use in CF patients, citing their high costs as beyond the acceptable range for NHS resources. However, in June 2024, NICE and Vertex reached an agreement on acceptable pricing terms, extending the pricing deal originally established in 2019 to include these drugs. The extended agreement also ensures that patients will have access to future license extensions for these CF medications. [ 61 ] [ 62 ] [ 63 ]
Pricing and public funding varies by country beyond the USA and the UK.
By October 2019, Vertex's CF medicines were publicly funded in 17 countries. [ 64 ]
By 2023, Vertex had reimbursement agreements in 36 countries for their CF medicines, of which 35 are considered high-income countries. About 27% (51,322) of the estimated CF patients were treated with Trikafta, of whom nearly half (49%) lived in the U.S., 42% in Europe, and 9% in Canada, Israel, Australia, and New Zealand combined. [ 65 ]
Trikafta has become increasingly available worldwide since its initial approval in 2019. As of 2023, the medication is reimbursed in over 30 countries, primarily in high-income nations across North America, Europe, and Oceania. [ 66 ] By 2024, the company's group of CF medications were "broadly available" in over 60 countries. [ 67 ] Although access to Cystic Fibrosis medications is still limited in many countries, as of 2024 about two-thirds of people diagnosed are receiving the treatment around the world. [ 61 ] The high cost of Trikafta presents a significant barrier to access. [ 68 ] In countries where it is reimbursed, patients typically pay a fraction of this cost, but the financial burden on healthcare systems remains substantial. Price negotiations and managed entry agreements (which for example link reimbursement to clinical performance) are common strategies used by countries to make Trikafta more affordable, though the details of these arrangements are often confidential. [ 69 ]
In the late 1990s the Bethesda-based Cystic Fibrosis Foundation , encouraged by then-President Robert Beall, began investing in Vertex— when it was a small start-up biotechnology company— to help fund the development of Kalydeco in the form of venture philanthropy . The total investment amounted to $150 million. [ 73 ] In 2014, the CF Foundation sold the rights to the royalties of the drugs for $3.3 billion, twenty times the foundation's 2013 budget. [ 73 ] [ 74 ] Proponents of venture philanthropy say the high financial return helps speed drug development and also provides potential monetary rewards that can go to more research. [ 73 ]
By 2015 the annual price of Kalydeco had been increased to more than $300,000 per patient. [ 75 ]
According to an article published in the Milwaukee Journal Sentinel Vertex executives "grossed more than $100 million by cashing in stocks and stock options" and at "one point, the value of company's stock increased more $6 billion in a single day." [ 76 ]
Twenty-nine physicians and scientists working with people with cystic fibrosis (CF) wrote to Jeff Leiden, CEO of Vertex Pharmaceuticals to plead for lower prices. [ 77 ]
We are aware of the financial complexities of the huge expenses for R & D with respect to the small number of patients or the market system that enables these advances to become reality. Yet – notwithstanding all your patient support programs – it is at best unseemly for Vertex to charge our patients' insurance plans (including strapped state medical assistance plans), $294,000 annually for two pills a day (a 10-fold increase in a typical patient's total drug costs). This action could appear to be leveraging pain and suffering into huge financial gain for speculators, some of whom were your top executives who reportedly made millions of dollars in a single day (Boston Globe, 29 May).
The company responded in an email that "while publicly funded academic research provided important early understanding of the cause of cystic fibrosis, it took Vertex scientists 14 years of their own research, funded mostly by the company, before the drug won approval." [ 76 ]
On 15 April 2015 in Cambridge, Massachusetts, Joan Finnegan Brooks of the Cystic Fibrosis Foundation spoke about the role of Vertex and venture philanthropy to a panel of biotech leaders hosted by Life Sciences Foundation on the topic of patient advocacy in the biotech industry. [ 78 ] While Brooks, who has cystic fibrosis, expressed gratitude for Vertex's development of Kalydeco, she observed that "More than 25% of people are saying (in surveys conducted by the CFF) that they are skipping medications or delaying medications or skipping doctor appointments because of cost of care issues." She added that "one of the things that the Foundation has done," is to "develop resources that can help patients bridge that gap through patient access programs, and so forth." [ 79 ]
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In geometry , a vertex configuration is a shorthand notation for representing a polyhedron or tiling as the sequence of faces around a vertex . It has variously been called a vertex description , [ 1 ] [ 2 ] [ 3 ] vertex type , [ 4 ] [ 5 ] vertex symbol , [ 6 ] [ 7 ] vertex arrangement , [ 8 ] vertex pattern , [ 9 ] face-vector, [ 10 ] vertex sequence. [ 11 ] It is also called a Cundy and Rollett symbol for its usage for the Archimedean solids in their 1952 book Mathematical Models . [ 12 ] [ 13 ] [ 14 ] For uniform polyhedra , there is only one vertex type and therefore the vertex configuration fully defines the polyhedron. ( Chiral polyhedra exist in mirror-image pairs with the same vertex configuration.)
For example, " 3.5.3.5 " indicates a vertex belonging to 4 faces, alternating triangles and pentagons . This vertex configuration defines the vertex-transitive icosidodecahedron . The notation is cyclic and therefore is equivalent with different starting points, so 3.5.3.5 is the same as 5.3.5.3. The order is important, so 3.3.5.5 is different from 3.5.3.5 (the first has two triangles followed by two pentagons). Repeated elements can be collected as exponents so this example is also represented as (3.5) 2 .
3 6 Defect 0°
4 4 Defect 0°
6 3 Defect 0°
A vertex configuration is written as one or more numbers separated by either dots or commas. Each number represents the number of sides in each face that meets at each vertex. [ 15 ] An icosidodecahedron is denoted as 3.5.3.5 {\displaystyle 3.5.3.5} because there are four faces at each vertex, alternating between triangles (with 3 sides) and pentagons (with 5 sides). This can also be written as ( 3.5 ) 2 {\displaystyle (3.5)^{2}} .
The vertex configuration can also be considered an expansive form of the simple Schläfli symbol for regular polyhedra . The Schläfli notation has the form { p , q } {\displaystyle \{p,q\}} , where p {\displaystyle p} is the number of sides in each face and q {\displaystyle q} is the number of faces that meet at each vertex. Hence, the Schläfli notation { p , q } {\displaystyle \{p,q\}} can be written as p . p . p ⋯ {\displaystyle p.p.p\cdots } (where p {\displaystyle p} appears q {\displaystyle q} times), or simply p q {\displaystyle p^{q}} . [ 15 ]
This notation applies to polygonal tilings as well as polyhedra. A planar vertex configuration denotes a uniform tiling just like a nonplanar vertex configuration denotes a uniform polyhedron.
The notation is ambiguous for chiral forms. For example, the snub cube has clockwise and counterclockwise forms which are identical across mirror images. Both have a 3.3.3.3.4 vertex configuration.
The notation also applies for nonconvex regular faces, the star polygons . For example, a pentagram has the symbol {5/2}, meaning it has 5 sides going around the centre twice.
For example, there are 4 regular star polyhedra with regular polygon or star polygon vertex figures. The small stellated dodecahedron has the Schläfli symbol of {5/2,5} which expands to an explicit vertex configuration 5/2.5/2.5/2.5/2.5/2 or combined as (5/2) 5 . The great stellated dodecahedron , {5/2,3} has a triangular vertex figure and configuration (5/2.5/2.5/2) or (5/2) 3 . The great dodecahedron , {5,5/2} has a pentagrammic vertex figure, with vertex configuration is (5.5.5.5.5)/2 or (5 5 )/2. A great icosahedron , {3,5/2} also has a pentagrammic vertex figure, with vertex configuration (3.3.3.3.3)/2 or (3 5 )/2.
Faces on a vertex figure are considered to progress in one direction. Some uniform polyhedra have vertex figures with inversions where the faces progress retrograde. A vertex figure represents this in the star polygon notation of sides p/q such that p <2 q , where p is the number of sides and q the number of turns around a circle. For example, "3/2" means a triangle that has vertices that go around twice, which is the same as backwards once. Similarly "5/3" is a backwards pentagram 5/2.
Semiregular polyhedra have vertex configurations with positive angle defect .
NOTE: The vertex figure can represent a regular or semiregular tiling on the plane if its defect is zero. It can represent a tiling of the hyperbolic plane if its defect is negative.
For uniform polyhedra, the angle defect can be used to compute the number of vertices. Descartes' theorem states that all the angle defects in a topological sphere must sum to 4 π radians or
720 degrees.
Since uniform polyhedra have all identical vertices, this relation allows us to compute the number of vertices, which is 4 π / defect or
720/ defect .
Example: A truncated cube 3.8.8 has an angle defect of 30 degrees. Therefore, it has 720/30 = 24 vertices.
In particular it follows that { a , b } has 4 / (2 − b (1 − 2/ a )) vertices.
Every enumerated vertex configuration potentially uniquely defines a semiregular polyhedron. However, not all configurations are possible.
Topological requirements limit existence. Specifically p.q.r implies that a p -gon is surrounded by alternating q -gons and r -gons, so either p is even or q equals r . Similarly q is even or p equals r , and r is even or p equals q . Therefore, potentially possible triples are 3.3.3, 3.4.4, 3.6.6, 3.8.8, 3.10.10, 3.12.12, 4.4. n (for any n >2), 4.6.6, 4.6.8, 4.6.10, 4.6.12, 4.8.8, 5.5.5, 5.6.6, 6.6.6. In fact, all these configurations with three faces meeting at each vertex turn out to exist.
The number in parentheses is the number of vertices, determined by the angle defect.
The uniform dual or Catalan solids , including the bipyramids and trapezohedra , are vertically-regular ( face-transitive ) and so they can be identified by a similar notation which is sometimes called face configuration . [ 16 ] Cundy and Rollett prefixed these dual symbols by a V . In contrast, Tilings and patterns uses square brackets around the symbol for isohedral tilings.
This notation represents a sequential count of the number of faces that exist at each vertex around a face . [ 12 ] For example, V3.4.3.4 or V(3.4) 2 represents the rhombic dodecahedron which is face-transitive: every face is a rhombus , and alternating vertices of the rhombus contain 3 or 4 faces each.
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In mathematics, the vertex enumeration problem for a polytope , a polyhedral cell complex , a hyperplane arrangement , or some other object of discrete geometry , is the problem of determination of the object's vertices given some formal representation of the object. A classical example is the problem of enumeration of the vertices of a convex polytope specified by a set of linear inequalities : [ 1 ]
where A is an m × n matrix, x is an n ×1 column vector of variables, and b is an m ×1 column vector of constants. The inverse ( dual ) problem of finding the bounding inequalities given the vertices is called facet enumeration (see convex hull algorithms ).
The computational complexity of the problem is a subject of research in computer science . For unbounded polyhedra, the problem is known to be NP-hard, more precisely, there is no algorithm that runs in polynomial time in the combined input-output size, unless P=NP. [ 2 ]
A 1992 article by David Avis and Komei Fukuda [ 3 ] presents a reverse-search algorithm which finds the v vertices of a polytope defined by a nondegenerate system of n inequalities in d dimensions (or, dually, the v facets of the convex hull of n points in d dimensions, where each facet contains exactly d given points) in time O ( ndv ) and space O( nd ). The v vertices in a simple arrangement of n hyperplanes in d dimensions can be found in O( n 2 dv ) time and O( nd ) space complexity. The Avis–Fukuda algorithm adapted the criss-cross algorithm for oriented matroids.
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In graph theory , the metric k -center problem or vertex k-center problem is a classical combinatorial optimization problem studied in theoretical computer science that is NP-hard . Given n cities with specified distances, one wants to build k warehouses in different cities and minimize the maximum distance of a city to a warehouse. In graph theory , this means finding a set of k vertices for which the largest distance of any point to its closest vertex in the k -set is minimum. The vertices must be in a metric space , providing a complete graph that satisfies the triangle inequality . It has application in facility location and clustering . [ 1 ] [ 2 ]
The problem was first proposed by Hakimi in 1964. [ 3 ]
Let ( X , d ) {\displaystyle (X,d)} be a metric space where X {\displaystyle X} is a set and d {\displaystyle d} is a metric A set V ⊆ X {\displaystyle \mathbf {V} \subseteq {\mathcal {X}}} , is provided together with a parameter k {\displaystyle k} . The goal is to find a subset C ⊆ V {\displaystyle {\mathcal {C}}\subseteq \mathbf {V} } with | C | = k {\displaystyle |{\mathcal {C}}|=k} such that the maximum distance of a point in V {\displaystyle \mathbf {V} } to the closest point in C {\displaystyle {\mathcal {C}}} is minimized. The problem can be formally defined as follows: For a metric space ( X {\displaystyle {\mathcal {X}}} ,d),
That is, every point in a cluster is in distance at most r C ( V ) {\displaystyle r^{\mathcal {C}}(V)} from its respective center. [ 4 ]
The k-Center Clustering problem can also be defined on a complete undirected graph G = ( V , E ) as follows: Given a complete undirected graph G = ( V , E ) with distances d ( v i , v j ) ∈ N satisfying the triangle inequality, find a subset C ⊆ V with | C | = k while minimizing:
In a complete undirected graph G = ( V , E ), if we sort the edges in non-decreasing order of the distances: d ( e 1 ) ≤ d ( e 2 ) ≤ ... ≤ d ( e m ) and let G i = (V, E i ), where E i = { e 1 , e 2 , ..., e i }. The k -center problem is equivalent to finding the smallest index i such that G i has a dominating set of size at most k . [ 5 ]
Although Dominating Set is NP-complete , the k -center problem remains NP-hard . This is clear, since the optimality of a given feasible solution for the k -center problem can be determined through the Dominating Set reduction only if we know in first place the size of the optimal solution (i.e. the smallest index i such that G i has a dominating set of size at most k ), which is precisely the difficult core of the NP-hard problems. Although a Turing reduction can get around this issue by trying all values of k .
A simple greedy approximation algorithm that achieves an approximation factor of 2 builds C {\displaystyle {\mathcal {C}}} using a farthest-first traversal in k iterations.
This algorithm simply chooses the point farthest away from the current set of centers in each iteration as the new center. It can be described as follows:
The solution obtained using the simple greedy algorithm is a 2-approximation to the optimal solution. This section focuses on proving this approximation factor.
Given a set of n points V ⊆ X {\displaystyle \mathbf {V} \subseteq {\mathcal {X}}} , belonging to a metric space ( X {\displaystyle {\mathcal {X}}} ,d), the greedy K -center algorithm computes a set K of k centers, such that K is a 2-approximation to the optimal k -center clustering of V .
i.e. r K ( V ) ≤ 2 r o p t ( V , k ) {\displaystyle r^{\mathbf {K} }(\mathbf {V} )\leq 2r^{opt}(\mathbf {V} ,{\textit {k}})} [ 4 ]
This theorem can be proven using two cases as follows,
Case 1: Every cluster of C o p t {\displaystyle {\mathcal {C}}_{opt}} contains exactly one point of K {\displaystyle \mathbf {K} }
Case 2: There are two centers k ¯ {\displaystyle {\bar {k}}} and u ¯ {\displaystyle {\bar {u}}} of K {\displaystyle \mathbf {K} } that are both in Π ( C o p t , c ¯ ) {\displaystyle \Pi ({\mathcal {C}}_{opt},{\bar {c}})} , for some c ¯ ∈ C o p t {\displaystyle {\bar {c}}\in {\mathcal {C}}_{opt}} (By pigeon hole principle, this is the only other possibility)
r K ( V ) ≤ r C i − 1 ( V ) = d ( u ¯ , C i − 1 ) ≤ d ( u ¯ , k ¯ ) ≤ d ( u ¯ , c ¯ ) + d ( c ¯ , k ¯ ) ≤ 2 r o p t {\displaystyle {\begin{aligned}r^{\mathbf {K} }(\mathbf {V} )\leq r^{{\mathcal {C}}_{i-1}}(\mathbf {V} )&=d({\bar {u}},{\mathcal {C}}_{i-1})\\&\leq d({\bar {u}},{\bar {k}})\\&\leq d({\bar {u}},{\bar {c}})+d({\bar {c}},{\bar {k}})\\&\leq 2r^{opt}\end{aligned}}} [ 4 ]
Another algorithm with the same approximation factor takes advantage of the fact that the k -Center problem is equivalent to finding the smallest index i such that G i has a dominating set of size at most k and computes a maximal independent set of G i , looking for the smallest index i that has a maximal independent set with a size of at least k . [ 7 ] It is not possible to find an approximation algorithm with an approximation factor of 2 − ε for any ε > 0, unless P = NP. [ 8 ] Furthermore, the distances of all edges in G must satisfy the triangle inequality if the k -center problem is to be approximated within any constant factor, unless P = NP. [ 9 ]
It can be shown that the k -Center problem is W[2]-hard to approximate within a factor of 2 − ε for any ε > 0, when using k as the parameter. [ 10 ] This is also true when parameterizing by the doubling dimension (in fact the dimension of a Manhattan metric ), unless P=NP . [ 11 ] When considering the combined parameter given by k and the doubling dimension , k -Center is still W[1]-hard but it is possible to obtain a parameterized approximation scheme . [ 12 ] This is even possible for the variant with vertex capacities, which bound how many vertices can be assigned to an opened center of the solution. [ 13 ]
If P ≠ N P {\displaystyle P\neq NP} , the vertex k -center problem can not be (optimally) solved in polynomial time. However, there are some polynomial time approximation algorithms that get near-optimal solutions. Specifically, 2-approximated solutions . Actually, if P ≠ N P {\displaystyle P\neq NP} the best possible solution that can be achieved by a polynomial time algorithm is a 2-approximated one. [ 14 ] [ 15 ] [ 16 ] [ 17 ] In the context of a minimization problem, such as the vertex k -center problem, a 2-approximated solution is any solution C ′ {\displaystyle C'} such that r ( C ′ ) ≤ 2 × r ( OPT ) {\displaystyle r(C')\leq 2\times r({\text{OPT}})} , where r ( OPT ) {\displaystyle r({\text{OPT}})} is the size of an optimal solution. An algorithm that guarantees to generate 2-approximated solutions is known as a 2-approximation algorithm. The main 2-approximated algorithms for the vertex k -center problem reported in the literature are the Sh algorithm, [ 18 ] the HS algorithm, [ 17 ] and the Gon algorithm. [ 15 ] [ 16 ] Even though these algorithms are the (polynomial) best possible ones, their performance on most benchmark datasets is very deficient. Because of this, many heuristics and metaheuristics have been developed through the time. Contrary to common sense, one of the most practical (polynomial) heuristics for the vertex k -center problem is based on the CDS algorithm, which is a 3-approximation algorithm [ 19 ]
Formally characterized by David Shmoys in 1995, [ 18 ] the Sh algorithm takes as input a complete undirected graph G = ( V , E ) {\displaystyle G=(V,E)} , a positive integer k {\displaystyle k} , and an assumption r {\displaystyle r} on what the optimal solution size is. The Sh algorithm works as follows: selects the first center c 1 {\displaystyle c_{1}} at random. So far, the solution consists of only one vertex, C = { c 1 } {\displaystyle C=\{c_{1}\}} . Next, selects center c 2 {\displaystyle c_{2}} at random from the set containing all the vertices whose distance from C {\displaystyle C} is greater than 2 × r {\displaystyle 2\times r} . At this point, C = { c 1 , c 2 } {\displaystyle C=\{c_{1},c_{2}\}} . Finally, selects the remaining k − 2 {\displaystyle k-2} centers the same way c 2 {\displaystyle c_{2}} was selected. The complexity of the Sh algorithm is O ( k n ) {\displaystyle O(kn)} , where n {\displaystyle n} is the number of vertices.
Proposed by Dorit Hochbaum and David Shmoys in 1985, the HS algorithm takes the Sh algorithm as basis. [ 17 ] By noticing that the value of r ( OPT ) {\displaystyle r({\text{OPT}})} must equals the cost of some edge in E {\displaystyle E} , and since there are O ( n 2 ) {\displaystyle O(n^{2})} edges in E {\displaystyle E} , the HS algorithm basically repeats the Sh algorithm with every edge cost. The complexity of the HS algorithm is O ( n 4 ) {\displaystyle O(n^{4})} . However, by running a binary search over the ordered set of edge costs, its complexity is reduced to O ( n 2 log n ) {\displaystyle O(n^{2}\log n)} .
Proposed independently by Teofilo Gonzalez , [ 15 ] and by Martin Dyer and Alan Frieze [ 16 ] in 1985, the Gon algorithm is basically a more powerful version of the Sh algorithm. While the Sh algorithm requires a guess r {\displaystyle r} on r ( OPT ) {\displaystyle r({\text{OPT}})} , the Gon algorithm prescinds from such guess by noticing that if any set of vertices at distance greater than 2 × r ( OPT ) {\displaystyle 2\times r({\text{OPT}})} exists, then the farthest vertex must be inside such set. Therefore, instead of computing at each iteration the set of vertices at distance greater than 2 × r {\displaystyle 2\times r} and then selecting a random vertex, the Gon algorithm simply selects the farthest vertex from every partial solution C ′ {\displaystyle C'} . The complexity of the Gon algorithm is O ( k n ) {\displaystyle O(kn)} , where n {\displaystyle n} is the number of vertices.
Proposed by García Díaz et al. in 2017, [ 19 ] the CDS algorithm is a 3-approximation algorithm that takes ideas from the Gon algorithm (farthest point heuristic), the HS algorithm (parametric pruning), and the relationship between the vertex k -center problem and the Dominating Set problem. The CDS algorithm has a complexity of O ( n 4 ) {\displaystyle O(n^{4})} . However, by performing a binary search over the ordered set of edge costs, a more efficiente heuristic named CDSh is proposed. The CDSh algorithm complexity is O ( n 2 log n ) {\displaystyle O(n^{2}\log n)} . Despite the suboptimal performance of the CDS algorithm, and the heuristic performance of CDSh, both present a much better performance than the Sh, HS, and Gon algorithms.
It can be shown that the k -Center problem is W[2]-hard to approximate within a factor of 2 − ε for any ε > 0, when using k as the parameter. [ 20 ] This is also true when parameterizing by the doubling dimension (in fact the dimension of a Manhattan metric ), unless P=NP . [ 21 ] When considering the combined parameter given by k and the doubling dimension , k -Center is still W[1]-hard but it is possible to obtain a parameterized approximation scheme . [ 22 ] This is even possible for the variant with vertex capacities, which bound how many vertices can be assigned to an opened center of the solution. [ 23 ]
Some of the most widely used benchmark datasets for the vertex k -center problem are the pmed instances from OR-Lib., [ 24 ] and some instances from TSP-Lib. [ 25 ] Table 1 shows the mean and standard deviation of the experimental approximation factors of the solutions generated by each algorithm over the 40 pmed instances from OR-Lib [ 19 ]
The greedy pure algorithm (or Gr) follows the core idea of greedy algorithms : to take optimal local decisions. In the case of the vertex k -center problem, the optimal local decision consists in selecting each center in such a way that the size of the solution (covering radius) is minimum at each iteration. In other words, the first center selected is the one that solves the 1-center problem. The second center selected is the one that, along with the previous center, generates a solution with minimum covering radius. The remaining centers are selected the same way. The complexity of the Gr algorithm is O ( k n 2 ) {\displaystyle O(kn^{2})} . [ 26 ] The empirical performance of the Gr algorithm is poor on most benchmark instances.
The Scoring algorithm (or Scr) was introduced by Jurij Mihelič and Borut Robič in 2005. [ 27 ] This algorithm takes advantage of the reduction from the vertex k -center problem to the minimum dominating set problem. The problem is solved by pruning the input graph with every possible value of the optimal solution size and then solving the minimum dominating set problem heuristically. This heuristic follows the lazy principle, which takes every decision as slow as possible (opossed to the greedy strategy). The complexity of the Scr algorithm is O ( n 4 ) {\displaystyle O(n^{4})} . The empirical performance of the Scr algorithm is very good on most benchmark instances. However, its running time rapidly becomes impractical as the input grows. So, it seems to be a good algorithm only for small instances.
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A vertex model is a type of statistical mechanics model in which the Boltzmann weights are associated with a vertex in the model (representing an atom or particle). [ 1 ] [ 2 ] This contrasts with a nearest-neighbour model, such as the Ising model , in which the energy, and thus the Boltzmann weight of a statistical microstate is attributed to the bonds connecting two neighbouring particles. The energy associated with a vertex in the lattice of particles is thus dependent on the state of the bonds which connect it to adjacent vertices. It turns out that every solution of the Yang–Baxter equation with spectral parameters in a tensor product of vector spaces V ⊗ V {\displaystyle V\otimes V} yields an exactly-solvable vertex model.
Although the model can be applied to various geometries in any number of dimensions, with any number of possible states for a given bond, the most fundamental examples occur for two dimensional lattices, the simplest being a square lattice where each bond has two possible states. In this model, every particle is connected to four other particles, and each of the four bonds adjacent to the particle has two possible states, indicated by the direction of an arrow on the bond. In this model, each vertex can adopt 2 4 {\displaystyle 2^{4}} possible configurations. The energy for a given vertex can be given by ε i j k ℓ {\displaystyle \varepsilon _{ij}^{k\ell }} ,
with a state of the lattice is an assignment of a state of each bond, with the total energy of the state being the sum of the vertex energies. As the energy is often divergent for an infinite lattice, the model is studied for a finite lattice as the lattice approaches infinite size. Periodic or domain wall [ 3 ] boundary conditions may be imposed on the model.
For a given state of the lattice, the Boltzmann weight can be written as the product over the vertices of the Boltzmann weights of the corresponding vertex states
where the Boltzmann weights for the vertices are written
and the i , j , k , l range over the possible statuses of each of the four edges attached to the vertex. The vertex states of adjacent vertices must satisfy compatibility conditions along the connecting edges (bonds) in order for the state to be admissible.
The probability of the system being in any given state at a particular time, and hence the properties of the system are determined by the partition function , for which an analytic form is desired.
where β = 1/ kT , T is temperature and k is the Boltzmann constant . The probability that the system is in any given state ( microstate ) is given by
so that the average value of the energy of the system is given by
In order to evaluate the partition function, firstly examine the states of a row of vertices.
The external edges are free variables, with summation over the internal bonds. Hence, form the row partition function
This can be reformulated in terms of an auxiliary n -dimensional vector space V , with a basis { v 1 , … , v n } {\displaystyle \{v_{1},\ldots ,v_{n}\}} , and R ∈ E n d ( V ⊗ V ) {\displaystyle R\in End(V\otimes V)} as
and T ∈ E n d ( V ⊗ V ⊗ N ) {\displaystyle T\in End(V\otimes V^{\otimes N})} as
thereby implying that T can be written as
where the indices indicate the factors of the tensor product V ⊗ V ⊗ N {\displaystyle V\otimes V^{\otimes N}} on which R operates. Summing over the states of the bonds in the first row with the periodic boundary conditions i 1 = i 1 ′ {\displaystyle i_{1}=i'_{1}} , gives
where τ = trace V ( T ) {\displaystyle \tau =\operatorname {trace} _{V}(T)} is the row-transfer matrix.
By summing the contributions over two rows, the result is
which upon summation over the vertical bonds connecting the first two rows gives: ( ( trace V ( T ) ) 2 ) j 1 … j N ℓ 1 … ℓ N {\displaystyle ((\operatorname {trace} _{V}(T))^{2})_{j_{1}\dots j_{N}}^{\ell _{1}\dots \ell _{N}}} for M rows, this gives
and then applying the periodic boundary conditions to the vertical columns, the partition function can be expressed in terms of the transfer matrix τ {\displaystyle \tau } as
where λ m a x {\displaystyle \lambda _{max}} is the largest eigenvalue of τ {\displaystyle \tau } . The approximation follows from the fact that the eigenvalues of τ M {\displaystyle \tau ^{M}} are the eigenvalues of τ {\displaystyle \tau } to the power of M , and as M → ∞ {\displaystyle M\rightarrow \infty } , the power of the largest eigenvalue becomes much larger than the others. As the trace is the sum of the eigenvalues, the problem of calculating Z {\displaystyle \mathbb {Z} } reduces to the problem of finding the maximum eigenvalue of τ {\displaystyle \tau } . This in itself is another field of study. However, a standard approach to the problem of finding the largest eigenvalue of τ {\displaystyle \tau } is to find a large family of operators which commute with τ {\displaystyle \tau } . This implies that the eigenspaces are common, and restricts the possible space of solutions. Such a family of commuting operators is usually found by means of the Yang–Baxter equation , which thus relates statistical mechanics to the study of quantum groups .
Definition : A vertex model is integrable if, ∀ μ , ν , ∃ λ {\displaystyle \forall \mu ,\nu ,\exists \lambda } such that
This is a parameterized version of the Yang–Baxter equation, corresponding to the possible dependence of the vertex energies, and hence the Boltzmann weights R on external parameters, such as temperature, external fields, etc.
The integrability condition implies the following relation.
Proposition : For an integrable vertex model, with λ , μ {\displaystyle \lambda ,\mu } and ν {\displaystyle \nu } defined as above, then
as endomorphisms of V ⊗ V ⊗ V ⊗ N {\displaystyle V\otimes V\otimes V^{\otimes N}} , where R ( λ ) {\displaystyle R(\lambda )} acts on the first two vectors of the tensor product.
It follows by multiplying both sides of the above equation on the right by R ( λ ) − 1 {\displaystyle R(\lambda )^{-1}} and using the cyclic property of the trace operator that the following corollary holds.
Corollary : For an integrable vertex model for which R ( λ ) {\displaystyle R(\lambda )} is invertible ∀ λ {\displaystyle \forall \lambda } , the transfer matrix τ ( μ ) {\displaystyle \tau (\mu )} commutes with τ ( ν ) , ∀ μ , ν {\displaystyle \tau (\nu ),\ \forall \mu ,\nu } .
This illustrates the role of the Yang–Baxter equation in the solution of solvable lattice models. Since the transfer matrices τ {\displaystyle \tau } commute for all λ , ν {\displaystyle \lambda ,\nu } , the eigenvectors of τ {\displaystyle \tau } are common, and hence independent of the parameterization. It is a recurring theme which appears in many other types of statistical mechanical models to look for these commuting transfer matrices.
From the definition of R above, it follows that for every solution of the Yang–Baxter equation in the tensor product of two n -dimensional vector spaces, there is a corresponding 2-dimensional solvable vertex model where each of the bonds can be in the possible states { 1 , … , n } {\displaystyle \{1,\ldots ,n\}} , where R is an endomorphism in the space spanned by { | a ⟩ ⊗ | b ⟩ } , 1 ≤ a , b ≤ n {\displaystyle \{|a\rangle \otimes |b\rangle \},1\leq a,b\leq n} . This motivates the classification of all the finite-dimensional irreducible representations of a given Quantum algebra in order to find solvable models corresponding to it.
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In astronomy , geography , and related sciences and contexts, a direction or plane passing by a given point is said to be vertical if it contains the local gravity direction at that point. [ 1 ]
Conversely, a direction, plane, or surface is said to be horizontal (or leveled ) if it is everywhere perpendicular to the vertical direction.
In general, something that is vertical can be drawn from up to down (or down to up), such as the y-axis in the Cartesian coordinate system .
The word horizontal is derived from the Latin horizon , which derives from the Greek ὁρῐ́ζων , meaning 'separating' or 'marking a boundary'. [ 2 ] The word vertical is derived from the late Latin verticalis , which is from the same root as vertex , meaning 'highest point' or more literally the 'turning point' such as in a whirlpool. [ 3 ]
Girard Desargues defined the vertical to be perpendicular to the horizon in his 1636 book Perspective .
In physics, engineering and construction, the direction designated as vertical is usually that along which a plumb-bob hangs. Alternatively, a spirit level that exploits the buoyancy of an air bubble and its tendency to go vertically upwards may be used to test for horizontality. A water level device may also be used to establish horizontality.
Modern rotary laser levels that can level themselves automatically are robust sophisticated instruments and work on the same fundamental principle. [ 4 ] [ 5 ]
When the curvature of the Earth is taken into account, the concepts of vertical and horizontal take on yet another meaning. On the surface of a smoothly spherical, homogenous, non-rotating planet, the plumb bob picks out as vertical the radial direction. Strictly speaking, it is now no longer possible for vertical walls to be parallel: all verticals intersect. This fact has real practical applications in construction and civil engineering, e.g., the tops of the towers of a suspension bridge are further apart than at the bottom. [ 6 ]
Also, horizontal planes can intersect when they are tangent planes to separated points on the surface of the Earth. In particular, a plane tangent to a point on the equator intersects the plane tangent to the North Pole at a right angle . (See diagram).
Furthermore, the equatorial plane is parallel to the tangent plane at the North Pole and as such has claim to be a horizontal plane. But it is. at the same time, a vertical plane for points on the equator. In this sense, a plane can, arguably, be both horizontal and vertical, horizontal at one place , and vertical at another .
For a spinning earth, the plumb line deviates from the radial direction as a function of latitude. [ 7 ] Only on the equator and at the North and South Poles does the plumb line align with the local radius. The situation is actually even more complicated because Earth is not a homogeneous smooth sphere. It is a non homogeneous, non spherical, knobby planet in motion, and the vertical not only need not lie along a radial, it may even be curved and be varying with time. On a smaller scale, a mountain to one side may deflect the plumb bob away from the true zenith . [ 8 ]
On a larger scale the gravitational field of the Earth, which is at least approximately radial near the Earth, is not radial when it is affected by the Moon at higher altitudes. [ 9 ] [ 10 ]
Neglecting the curvature of the earth, horizontal and vertical motions of a projectile moving under gravity are independent of each other. [ 11 ] Vertical displacement of a projectile is not affected by the horizontal component of the launch velocity, and, conversely, the horizontal displacement is unaffected by the vertical component. The notion dates at least as far back as Galileo. [ 12 ]
When the curvature of the Earth is taken into account, the independence of the two motion does not hold. For example, even a projectile fired in a horizontal direction (i.e., with a zero vertical component) may leave the surface of the spherical Earth and indeed escape altogether. [ 13 ]
In the context of a 1-dimensional orthogonal Cartesian coordinate system on a Euclidean plane, to say that a line is horizontal or vertical, an initial designation has to be made. One can start off by designating the vertical direction, usually labelled the Y direction. [ 14 ] The horizontal direction, usually labelled the X direction, [ 15 ] is then automatically determined. Or, one can do it the other way around, i.e., nominate the x -axis, in which case the y -axis is then automatically determined. There is no special reason to choose the horizontal over the vertical as the initial designation: the two directions are on par in this respect.
The following hold in the two-dimensional case:
Not all of these elementary geometric facts are true in the 3-D context.
In the three-dimensional case, the situation is more complicated as now one has horizontal and vertical planes in addition to horizontal and vertical lines. Consider a point P and designate a direction through P as vertical. A plane which contains P and is normal to the designated direction is the horizontal plane at P. Any plane going through P, normal to the horizontal plane is a vertical plane at P. Through any point P, there is one and only one horizontal plane but a multiplicity of vertical planes. This is a new feature that emerges in three dimensions. The symmetry that exists in the two-dimensional case no longer holds.
In the 2-dimension case, as mentioned already, the usual designation of the vertical coincides with the y-axis in co-ordinate geometry. This convention can cause confusion in the classroom. For the teacher, writing perhaps on a white board, the y -axis really is vertical in the sense of the plumbline verticality but for the student the axis may well lie on a horizontal table.
Although the word horizontal is commonly used in daily life and language (see below), it is subject to many misconceptions.
In general or in practice, something that is horizontal can be drawn from left to right (or right to left), such as the x-axis in the Cartesian coordinate system . [ citation needed ]
The concept of a horizontal plane is thus anything but simple, although, in practice, most of these effects and variations are rather small: they are measurable and can be predicted with great accuracy, but they may not greatly affect our daily life.
This dichotomy between the apparent simplicity of a concept and an actual complexity of defining (and measuring) it in scientific terms arises from the fact that the typical linear scales and dimensions of relevance in daily life are 3 orders of magnitude (or more) smaller than the size of the Earth. Hence, the world appears to be flat locally, and horizontal planes in nearby locations appear to be parallel. Such statements are nevertheless approximations; whether they are acceptable in any particular context or application depends on the applicable requirements, in particular in terms of accuracy.
In graphical contexts, such as drawing and drafting and Co-ordinate geometry on rectangular paper, it is very common to associate one of the dimensions of the paper with a horizontal, even though the entire sheet of paper is standing on a flat horizontal (or slanted) table. In this case, the horizontal direction is typically from the left side of the paper to the right side. This is purely conventional (although it is somehow 'natural' when drawing a natural scene as it is seen in reality), and may lead to misunderstandings or misconceptions, especially in an educational context.
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In spherical geometry , a vertical circle is a great circle on the celestial sphere that is perpendicular to the horizon . [ 1 ] Therefore, it contains the vertical direction , passing through the zenith and the nadir . There is a vertical circle for any given azimuth , where azimuth is the angle measured east from the north on the celestial horizon. The vertical circle which is in the east–west direction is called the prime vertical . The vertical circle which is on the north–south direction is called the local celestial meridian (LCM), or principal vertical. Vertical circles are part of the horizontal coordinate system . [ 2 ]
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A vertical ecosystem is an architectural gardening system developed by Ignacio Solano from the mur vegetal created by Patrick Blanc . This new approach enhances the previous archetype of mur vegetal and considers the relationship that exists between a set of living organisms, biocenosis , inhabiting a physical component, biotope . The system is based on the automated control of nutrients and plant parameters of the original wall, adding strains of bacteria, mycorrhizal fungi and interspecific symbiosis in plant selection, creating an artificial ecosystem from inert substrates. The system was created in 2007 and patented in 2010. [ 1 ]
Amongst abiotic factors that influence vertical ecosystems, namely the substrate and its environmental conditions, the physio-chemical characteristics possessed by the means are decisive. [ 2 ] The texture, porosity and depth of the substrate, those that in a natural ecosystem are edaphic factors, have been tested to the point of finding fitogenerate [ clarification needed ] materials with perfect levels of absorption and humidity for the development of more than forty living families of plants represented by around 120 species. Moreover, the substrate used in the system developed by Ignacio Solano provides the ecosystem with the necessary resistance to serve as a high-durability biotope . [ 3 ]
Environmental factors such as light, temperature and humidity are controlled by automated systems in interior vertical ecosystems. Ecosystems that are situated outside require study and analysis of the natural variables of their particular area, combined with a study of the behaviour of the numerous plant species in the biotope in each location. The selection and combination of species is one of the key factors for correct development. This is known as positive allelopathy .
Hydrological factors, such as pH levels, the conductivity of the water, dissolved gases and salinity, are balanced with precision so that the hydroponic system functions at its maximum capacity. The objective required by this system is to incorporate all the nutrients and micronutrients necessary for the health of the plants, and therefore the whole ecosystem, in a constant manner. To control these variables, the vertical ecosystem implements a system of sensors and warnings that inform of any anomaly of measurements in real time, allowing remote monitoring and control of the system. [ 4 ]
Vertical ecosystems enable plant species, fungi, and bacteria to live in an environment of almost unlimited resources, generating interactions favourable to the system. [ 5 ] In this way, they encourage healthy and exponential growth in their evolutionary stages, until they manage to adjust to their maximum value, known as the load capacity: the optimum capacity of living species interacting without stress in a limited space in search of mutualisms and intraspecific associations that benefit all the species involved. The success of a vertical ecosystem depends on the control of abiotic and biotic factors that limit the growth of plant populations, the control of environmental resistance .
Vertical ecosystems aim to prolong the life of planted species and bring the benefits of a traditional vertical garden, including: absorption of CO 2 , heavy metals and dust, natural thermal insulation , and reduction of noise pollution .
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Vertical exaggeration ( VE ) is a scale that is used in raised-relief maps , plans and technical drawings ( cross section perspectives), in order to emphasize vertical features, which might be too small to identify relative to the horizontal scale. [ 1 ]
The vertical exaggeration is given by:
where VS is the vertical scale and HS is the horizontal scale, both given as representative fractions.
For example, if 1 centimetre (0.39 in) vertically represents 200 metres (660 ft) and 1 centimetre (0.39 in) horizontally represents 4,000 metres (13,000 ft), the vertical exaggeration, 20×, is given by:
Vertical exaggeration is given as a number; for example 5× means vertical measurements appear 5 times greater than horizontal measurements. A value of 1× indicates that horizontal and vertical scales are identical, and is regarded as having "no vertical exaggeration." Vertical exaggerations less than 1 are not common, but would indicate a reduction in vertical scale (or, equivalently, a horizontal exaggeration).
Some scientists [ 2 ] [ 3 ] object to vertical exaggeration as a tool that makes an oblique visualization dramatic at the cost of misleading the viewer about the true appearance of the landscape.
In some cases, if the vertical exaggeration is too high, the map reader may get confused.
This geometry-related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Vertical_exaggeration
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A vertical form fill sealing machine is a type of automated assembly-line product packaging system, commonly used in the packaging industry for food and many other products. Walter Zwoyer, the inventor of the technology, patented his idea for the VFFS machine in 1936 while working with the Henry Heide Candy Company . [ 1 ] The machine constructs plastic bags and stand-up pouches out of a flat roll of film, fills them with product, and seals them. Both solids and liquids can be bagged. [ 2 ]
The typical machine is loaded with a continuous flat roll of plastic film , which has usually had labeling and artwork applied. Plastic is the most commonly used packaging material in the food industry , but the technology can be used to form continuous metallized foil/film, paper, and fabric product containers by changing the edge sealing/seaming methods. For some products the film may first be fed through a sterilizing chemical bath and dryer. [ 3 ]
Vertical or Inclined Form-Fill-Seal Packaging machine
For a vertical form-fill-seal the film approaches the back of a long hollow conical tube, which is called the forming tube. When the center of the plastic is near the tube, the outer edges of the film form flaps that wrap around the conical forming tube. The film is pulled downward around the outside of the tube and a vertical heat-sealing bar clamps onto the edges of the film to create the "fin Seal", bonding the film by melting the seam edges together. [ 4 ]
To start the bagging process, a horizontal sealing bar creates the "Bottom Seal" by clamping across the bottom edge of the tube, bonding the film together, and cutting off any film below. This sealing bar can be on a fixed height, which is called an intermittent sealing process. Faster systems include a sealing bar that moves down with the bag while sealing. This is called a continuous process. The product is either pre-measured by a multi-head weighing system or the sealed tube end is then lowered onto a precision weighing table and the product to be bagged is dispensed through the long conical tube in the center of the bag. When the gross weight of the product-filled bag is reached, filling stops, and the horizontal sealing bar seals the top of the bag, simultaneously forming the bottom of the next bag above. This bag is then cut off from the tube and is now a sealed package, ready to advance onward into the product boxing and shipping processes.
During the final sealing process, the bag may be filled with air from a blower or from an inert gas supply such as nitrogen. Inflating the bag helps reduce the crushing of fragile products such as potato chips , while inflating with inert gas drives out oxygen and retards the growth of bacteria that would spoil the product. Other product finishes such as hole punching for retail hanging racks will be done concurrently or just after the "Top Seal" is made.
The feeding of material and cutting of the bag/pouch can be determined either by pouch length, or by indexing to an eyespot (photo registration mark), which is detected by a visual sensor. While single web systems are popular for food applications, the dual web four side seal system is often popular for IVD and Medical device products. Closely related is the horizontal form-fill-seal machine, which generally uses more floor space than a vertical system. Modern advancements in pouch forming technology have allowed for smaller and smaller Vertical pouch forming systems.
Many food-filled packages are filled with nitrogen to extend shelf life without the use of chemicals. Many manufacturers create and control their own nitrogen supply by using an on demand nitrogen generators .
Dual-web systems are available for pouches requiring different materials for each side, or with four sides. Dual-web systems use two rolls of material fed in from opposite sides of the machine. The bottom and sides are heat-sealed together to form the pouch, and the product is loaded from the top. The pouch with the loaded product then advances downwards; the top is sealed and the pouch is cut off. The sealing of the top of the pouch forms the bottom of the next pouch. During this process a tear notch may be punched.
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https://en.wikipedia.org/wiki/Vertical_form_fill_sealing_machine
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Vertical handover or vertical handoff refers to a network node changing the type of connectivity it uses to access a supporting infrastructure, usually to support node mobility. For example, a suitably equipped laptop might be able to use both high-speed wireless LAN and cellular technology for Internet access. Wireless LAN connections generally provide higher speeds, while cellular technologies generally provide more ubiquitous coverage. Thus the laptop user might want to use a wireless LAN connection whenever one is available and to revert to a cellular connection when the wireless LAN is unavailable. Vertical handovers refer to the automatic transition from one technology to another in order to maintain communication. This is different from a horizontal handover between different wireless access points that use the same technology.
Vertical handoffs between WLAN and UMTS (WCDMA) have attracted a great deal of attention in all the research areas of the 4G wireless network, due to the benefit of utilizing the higher bandwidth and lower cost of WLAN as well as better mobility support and larger coverage of UMTS. Vertical handovers among a range of wired and wireless access technologies including WiMAX can be achieved using Media independent handover which is standardized as IEEE 802.21 .
To support vertical handover , a mobile terminal needs to have a dual mode card, for example one that can work under both WLAN and UMTS frequency bands and modulation schemes.
For the vertical handover between UMTS and WLAN, there are two main interworking architecture: tight coupling and loose coupling .
The tight coupling scheme, which 3GPP adopted, introduces two more elements: WAG (Wireless Access Gateway) and PDG (Packet Data Gateway). So the data transfers from WLAN AP to a Corresponding Node on the internet must go through the Core Network of UMTS.
Loose coupling is more used when the WLAN is not operated by cellular operator but any private user. So the data transmitted through WLAN will not go through Cellular Networks.
In traditional handovers, such as a handover between cellular networks, the handover decision is based mainly on RSS (Received Signal Strength) in the border region of two cells, and may also be based on call drop rate, etc. for resource management reasons.
In vertical handover, the situation is more complex. Two different kinds of wireless networks normally have incomparable signal strength metrics, for example, WLAN compared to UMTS. In, WLAN and UMTS networks both cover an area at the same time.
The handover metrics in this situation should include RSS, user preference, network conditions, application types, cost etc.
Based on the handover metrics mentioned above, the decision about how and when to switch the interface to which network will be made.
Many papers have given reasonable flow charts based on the better service and lower cost, etc. while some others, using fuzzy logic, neuron network or MADM methods to solve the problem.
When a mobile station transfers a user's session from one network to another, the IP address will change. In order to allow the Corresponding Node that the MS is communicating with to find it correctly and allow the session to continue, Mobility Management is used.
The Mobility Management problem can be solved in different layers, such as the Application Layer, Transport Layer, IP Layer, etc. The most common method is to use SIP (Session Initiation Protocol) and Mobile IP .
The handover procedure specifies the control signalling used to perform the handover and is invoked by the handover decision algorithm.
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https://en.wikipedia.org/wiki/Vertical_handover
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Vertical market software is aimed at addressing the needs of any given business within a discernible vertical market (specific industry or market). While horizontal market software can be useful to a wide array of industries (such as word processors or spreadsheet programs), vertical market software is developed for and customized to a specific industry's needs.
Vertical market software is readily identifiable by the application specific graphical user interface which defines it. One example of vertical market software is point-of-sale software.
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https://en.wikipedia.org/wiki/Vertical_market_software
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The term vertical resistance , used commonly in the context of plant selection, was first used in 1963 by James Edward Van der Plank to describe single-gene resistance. This contrasted with the term horizontal resistance which was used to describe many-gene resistance. [ 1 ]
In 1976, Raoul A. Robinson adapted the original definition of vertical resistance and argued that in vertical resistance there were individual genes for resistance in the host plant and also individual genes for parasitic ability in the parasite. This phenomenon is known as the gene-for-gene relationship , and it was the defining character of vertical resistance. [ 2 ]
This genetics article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Vertical_resistance
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Vertical roller mill is a type of grinder used to grind materials into extremely fine powder for use in mineral dressing processes , paints , pyrotechnics , cements and ceramics. It is an energy efficient alternative for a ball mill . [ 1 ]
The vertical roller mill is a kind of grinding machine for cement, raw material, cement clinker , slag and coal slag. It has the benefits of simple structure and low cost of manufacture and use. Vertical roller mills have many different forms, but they work basically the same. All of these forms come with a roller (or the equivalent of roller grinding parts), and roller along the track of the disc at the level of circular movement imposed by external grinding roller in the vertical pressure on the disc on the material being the joint action of compression and shear, and to crush.
Material grinding process motor through reducer rotating drive disc, the material falls from the mill under the central entrance and exit, under the action of centrifugal force to the disc edge by the roller to move and the crushing, grinding out lap after the material was speed up the flow to and vertical mill with one of the separator, after the meal by the separator back to the mill, the re-grinding; powder while grinding out with air, dust collection equipment in the system to collect down, that is, products. Established through the mill in the pneumatic conveying of materials, a larger air flow rate, which can use waste heat of gas, at the same time dry grinding operations.
Principle of Grinding for these mills are done by Attrition and Compression method. The grinding force are applied through the sets of rollers on to the material bed spread over the rotating grinding table. This causes attrition initially followed by compression from external grinding forces.
Used in cement grinding production grinding parts of its various forms, there is a cylinder, cone type, ball type, etc., and roller surface is also flat, curved, convex round noodles. Applied to the grinding roller to roller grinding along the track bed in close contact with the material strength of a spring pressure, hydraulic, etc.
It has two pairs of grinding rollers, each pair of roller composed of two narrow rollers, mounted on the same axis and can rotate at different speeds. There are two circular disc slot, and roller to the tire shape, work pressure in the tank. Disc roller and the relative sliding velocity between small and roller can swing, even if the roller sleeve and the disc after the liner wear can guarantee a good abrasive, will not affect the grinding effect. Roller symmetrical structure, one side can be upside down after use and wear.
Material grinding process: hydraulic pneumatic roller device through the pressure applied to the material on the crushing of materials, the materials have been moved to crush the edge of disc, from the disc around the nozzle from the exhaust air to improve these materials to Separator.Meal to separate returns after a concentrated mill, fine powder was collected in the precipitator unloading. In the gas flow is small, the meal can not be increased to enhance air flow, they would fall through the nozzle discharged outside the mill, bucket elevator to be transported to the feeder of vertical roller mill , and was re-grinding mill feed people. This cycle features of the way there:
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https://en.wikipedia.org/wiki/Vertical_roller_mill
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In mathematics , particularly calculus , a vertical tangent is a tangent line that is vertical . Because a vertical line has infinite slope , a function whose graph has a vertical tangent is not differentiable at the point of tangency.
A function ƒ has a vertical tangent at x = a if the difference quotient used to define the derivative has infinite limit :
The graph of ƒ has a vertical tangent at x = a if the derivative of ƒ at a is either positive or negative infinity.
For a continuous function , it is often possible to detect a vertical tangent by taking the limit of the derivative. If
then ƒ must have an upward-sloping vertical tangent at x = a . Similarly, if
then ƒ must have a downward-sloping vertical tangent at x = a . In these situations, the vertical tangent to ƒ appears as a vertical asymptote on the graph of the derivative.
Closely related to vertical tangents are vertical cusps . This occurs when the one-sided derivatives are both infinite, but one is positive and the other is negative. For example, if
then the graph of ƒ will have a vertical cusp that slopes up on the left side and down on the right side.
As with vertical tangents, vertical cusps can sometimes be detected for a continuous function by examining the limit of the derivative. For example, if
then the graph of ƒ will have a vertical cusp at x = a that slopes down on the left side and up on the right side.
The function
has a vertical tangent at x = 0, since it is continuous and
Similarly, the function
has a vertical cusp at x = 0, since it is continuous,
and
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https://en.wikipedia.org/wiki/Vertical_tangent
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Vertical transmission of symbionts is the transfer of a microbial symbiont from the parent directly to the offspring. [ 1 ] Many metazoan species carry symbiotic bacteria which play a mutualistic , commensal , or parasitic role. [ 1 ] A symbiont is acquired by a host via horizontal , vertical, or mixed transmission. [ 2 ]
Vertical transmission, passage of symbiotic microflora from parents to offspring, is common in species of animals which have parental care . There are fitness benefits in providing youths with established microorganism community early on. [ 3 ]
Complex interdependence occurs between host and symbiont. [ 5 ] The genetic pool of the symbiont is generally smaller and more subject to genetic drift . [ 6 ] In true vertical transmission, the evolutionary outcomes of the host and symbiont are linked. [ 7 ] If there is mixed transmission, new genetic material may be introduced. [ 8 ] Generally, symbionts settle into specific niches and can even transfer part of their genome into the host nucleus.
The mechanism promotes tightly coupled evolutionary pressure, which causes the host and symbiont to function as a holobiont . [ 9 ]
Evolutionary bottlenecks lead to less symbiont diversity , and thus resilience . Similarly, this greatly reduces the effective population size . Ultimately, without an influx of new genetic material, the population becomes clonal . Mutations tend to persist in symbionts and build up over time. [ 10 ]
Since the egg contributes the organelles and has more space and opportunity for intracellular symbionts to be passed to subsequent generations, it is a very common method of vertical transmission. [ 1 ] Intracellular symbionts can migrate from the bacteriocyte to the ovaries and become incorporated in germ cells. [ 11 ]
In plants, vertical transmission of microbial endophytes through germline can occur matrilineally via seed. [ 12 ] There are several mechanisms by which a seed can matrilineally become infected with endophytes. The mother plant can produce vascular connections from its somatic microbiomes to the endosperm . [ 12 ] Alternatively, endophytes can be transmitted directly when reproductive organs are developing in the shoot apical meristem . [ 12 ]
Human infants acquire their microbiome from their mothers, from every sphere where there is contact. This includes potentially the mother's vagina , gastrointestinal tract , skin , mouth and breastmilk . [ 13 ] These routes are typical if the delivery is a vaginal birth and the infant is nursed. When other actions, such as Caesarian delivery , bottle feeding, or maternal antibiotics during nursing occur, these modes of vertical transmission are disrupted. [ 14 ] [ 15 ]
Though extremely rare, Rickettsia is transmitted to Nephotettix cincticep through the paternal line in the sperm . [ 16 ]
In plants, vertical transmission of microbial endophytes through germline can occur patrilineally via pollen . [ 12 ] Patrilineal transmission has been hypothesized to be a common mechanism for fungal endophyte transmission, [ 12 ] as well as bacteria. [ 17 ]
Microbes can be transmitted through the actions of parents caring for their offspring, such as the cultivation of gut microbes through regurgitation feeding. [ 18 ] This type of vertical transmission does not always occur via the behavior of the genetic parent; instead, other members of a social or family groups may transmit the microbial community, resulting in kin selection . [ 4 ] [ 19 ]
Earthworms (Eisenia) have an extracellular symbiont, Verminephrobacter . Rather than being passed through the egg in the germline, the young are aposymbiotic when still in the egg capsule; however, they acquire Verminephrobacter before the egg capsule ruptures, so it is still vertical transmission. [ 20 ]
Vertical transmission of endosymbiotic bacteria is very common in insects . [ 21 ]
It's estimated that about 70% of all insects carry the bacteria Wolbachia , which can be transmitted vertically as well as horizontally . [ 22 ] Depending on the host species, it may function as mutualist or a pathogen. [ 23 ] In order to maintain the infection within a host species, it must enter the forming egg cell and be transmitted through the germline. To improve the rate of vertical transmission, Wolbachia can alter its host's reproductive system [ 23 ] in a diverse array of mechanisms, such as induced parthenogenesis , male killing, or feminization . [ 24 ] All of these increase the ratio of infected females, which is beneficial to a matrilineally-spread infection.
Pea Aphids do not get all of the necessary amino acids from their diet. Their obligate symbiont, Buchnera , synthesize the remainder. [ 11 ] [ 25 ]
The head louse ( Pediculus humanus ) has an obligate symbiotic relationship with Candidatus Riesia pediculicola. The louse provides shelter and protection while bacteria provides essential B vitamins . C. riesia lives in the bacteriocyte but move to the ovaries to be transmitted to the next generation. [ 26 ] [ 27 ]
Tsetse flies have a fascinating life cycle. Tsetse gives life birth, which is extremely rare among insects. The fly fertilized one egg at the time and for the first three larval stages the single offspring developed inside the mother's uterus feeding on milk substance coming from milk glands in the uterus. [ 28 ] [ 29 ] [ 30 ] [ 31 ] Through the "milk" the youngsters receive parent microflora including Wigglesworthia glossinidia , the bacteria providing host with vitamins B scarce in the tsetse fly's blood-only diet. [ 32 ] [ 33 ]
Social spiders Stegodyphus dumicola live in Namibia and Botswana. The majority of females in the colony are virgins but participate in offspring care for reproducing females. [ 34 ] Offspring hatch symbiont-free, and bacterial symbionts are transmitted vertically across generations by social interactions with the onset of regurgitation feeding by (foster) mothers early in the development. [ 19 ]
Caecilians feed youngsters by mother skin, passing to them the microflora which colonize youngster's skin and gut. [ 35 ] The mother's skin is adapted for this purpose, thickening beforehand and regenerating quickly after being consumed to continue providing for her young. She repeats the process several times during early development without significant harm to herself. The repeated nature of skin feeding means that juveniles are exposed to their mother microbiome several times, enhancing the likelihood of microbial gut and skin successful colonization.
Bornean foam‑nesting frogs Leptomantis harrissoni tadpoles receive microbes from both their parents (vertically) and environment (horizontally). [ 3 ] Initially they have microbiomes resembling their parents and the exterior of the foam nest, but after one week in the pond tadpoles pick up new microbes from the pond environment.
A Ranitomeya imitator dart frog feeds tadpoles with unfertilized trophic eggs. Anaerobic parabasalian protists are passed to the tadpoles via vertical transmission. In the gut, these protists express digestive enzymes Proteinases. [ 36 ] By doing so, they help youngsters to have the ability to digest fat and protein in the mother egg versus plant debris in the mini pond they live in. Genes that code for Proteinases are not present in the Ranitomeya genome. The symbiosis allows Ranitpomeya imitator to expand into the new ecological niche and tadpoles to grow more robustly. [ 36 ] Another mechanism of vertical transmission via parental care occurs when the father carries a tadpole on its back from the egg to the breeding pool, which allows the tadpole an opportunity to receive microflora patrilinealy. [ 37 ]
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https://en.wikipedia.org/wiki/Vertical_transmission
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A vertical video is a video created either by a camera or computer that is intended for viewing in portrait mode , producing an image that is taller than it is wide. It thus sits in opposition to the multiple horizontal formats normalised by cinema and television, which trace their lineage from the proscenium theatre , Western landscape painting traditions, [ 1 ] and the human visual field . [ 2 ]
Vertical video has historically been shunned by professional video creators because it does not fit the aspect ratio of established moving image forms, such as film and television, as well as newer web-based video players such as YouTube , meaning that black spaces appeared on either side of the image. However, the popularity of mobile video apps such as Snapchat and especially TikTok , which use the more mobile-friendly portrait format, have led to an increase in the production of vertical videos by advertising companies. [ 3 ]
Vertical filmmaking has aesthetic roots reaching back at least to the tall painted frescoes and stained-glass windows of Christian churches. [ 4 ] The world’s first moving images of a cat ( Falling Cat , Étienne-Jules Marey, 1894 ) were shot vertically. When the first motion picture screenings were held in 1895, however, the format was standardised horizontally (though at 4:3 aspect ratio , the images were closer to a square format than to widescreen). Noting that the new cinematic art had taken on the old strictures of the theatre, on 17 September 1930 Russian filmmaker and theorist Sergei Eisenstein addressed the Technicians Branch of the Academy of Motion Picture Arts and Sciences in Hollywood, calling for a cinema screen of variable aspect ratio (a "dynamic square"), one which would be able to cope with whatever compositional format the filmmaker chose, including a vertical framing. [ 1 ] He lost the argument to a screen format standardised at a new Academy ratio (1.375:1) and vertical filmmaking has largely remained confined to experimental artists of the Expanded Cinema [ 5 ] movement, which flourished during the 1960s and 70s. It also made appearances in various World's Fair films such as In the Labyrinth [ 6 ] in Montréal in 1967.
If artists working with cinematic film were constrained by physical limitations from tipping the apparatus, the video medium made rotating the camera and/or projector somewhat easier. Artist Bill Viola frequently employs tall-screen video. In 1984, musician and artist Brian Eno created Thursday Afternoon , a series of "video paintings" presented in vertical format.
The 2005 music video for Imogen Heap 's song " Hide and Seek " was shot by Joel Peissig in portraiture, one of the first music videos in this format. [ 7 ] He felt that the vertical frame "complimented her face and her solitude"; as he used 35 mm film to shoot the music video, he also noticed that putting the camera on its side produced better-looking light streaks. [ 8 ]
Indian composer and record producer A. R. Rahman 's 2007 international single Pray for Me Brother , that was an initiative by Nokia Corporation , was then released as a vertical video. The song was conceived as an anti-poverty anthem for the Millennium Goals for the United Nations .
By 2013, a number of independent film and video makers had made the creative jump to vertical formats for narrative films [ 9 ] despite the limitations of using professional capture and projection apparatuses in vertical orientation. [ 10 ] The first festival of specially commissioned tall-screen films, Sonic Acts ' Vertical Cinema, [ 11 ] [ 12 ] was screened at Kontraste Dark As Light Festival in Austria in October 2013; [ 13 ] whilst the world's first open competition for vertical film and video, the Vertical Film Festival [ 14 ] was held one year later in Katoomba, New South Wales , Australia . Both organisations project onto large-format vertical cinema screens in suitably tall-roofed venues, but there have also been a number of online initiatives [ 15 ] to encourage filmmakers to explore the creative potential of the vertical frame, as well as dedicated groups and channels on Vimeo . [ 16 ] Similar exhibits took place in March 2015 at South by Southwest in Austin, Texas [ 17 ] and in November 2016 at the Vertifilms festival in Prague . [ 18 ]
Vertical video has presented significant challenges to video publishers, as many of them have been traditionally geared for horizontal video. In October 2015, social video platform Grabyo , which is used by major sports federations such as La Liga and the National Hockey League (NHL), launched technology to help video publishers adapt horizontal 16:9 video into mobile formats such as vertical and square. [ 19 ]
Mary Meeker, a partner at Silicon Valley venture capital firm Kleiner Perkins Caufield & Byers , highlighted the growth of vertical video viewing in her 2015 Internet Trends Report - growing from 5% of video viewing in 2010 to 29% in 2015. Vertical video ads like Snapchat's are watched in their entirety nine times more than landscape video ads. [ 20 ] Snapchat , DMG Media and WPP plc formed a content marketing agency called Truffle Pig in June 2015 that would be focused on creating content for vertical screens. [ 21 ] By 2015, vertical video was rapidly supported by many major social platforms including Facebook and Twitter. [ 22 ] YouTube introduced a vertical video viewing format compatible with mobile screens for Android in 2015; the new format was rolled out to all mobile devices two years later. [ 23 ]
By the late 2010s, many online video platforms began embracing the use of vertical video due to the growing use of mobile devices. In 2018, Instagram launched a vertical video application, IGTV . [ 24 ] The same year, YouTube introduced the capability for vertical video without black bars on its desktop website and in social media embeds. [ 23 ] YouTube also unveiled a new vertical video ad format in 2018, saying "more than 70 percent of YouTube watch time happens on mobile devices". [ 23 ] In March 2018, streaming media company Netflix announced the introduction of vertically-oriented 30-second previews of shows and movies to its platform; the company also cited the use of mobile devices as inspiration. [ 25 ] Vertical video has become more commonly used by news media, both for organizational social media profiles and increasingly on their own websites. [ 26 ]
Capitalizing on the rise of smartphones , whose default orientation is vertical, some music artists began releasing platform-exclusive vertical music videos . [ 27 ] These vertical videos are often shown on Snapchat's "Discover" section or within Spotify playlists. [ 28 ]
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https://en.wikipedia.org/wiki/Vertical_video
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The Vertically Generalized Production Model (VGPM) is a model commonly used to estimate primary production within the ocean. The VGPM was designed by Behrenfeld and Falkowski and was originally published in a 1997 article in Limnology and Oceanography. [ 1 ] It is one of the most frequently used models for primary production estimation due to its ability to be applied to chlorophyll a data from satellites, and its relatively simple design. [ 2 ] Chlorophyll a is a common measure of primary production, as it is a main component of photosynthesis. [ 1 ] [ 3 ] [ 2 ]
Primary production is often measured using three variables: the biomass (or amount in weight) of the phytoplankton, the availability of light, and the rate of carbon fixation. [ 2 ] The VGPM is now one of the most popular models to use for satellite chlorophyll data due to it being surface light dependent as well as using an estimated maximum value of primary production compared to the units of chlorophyll throughout the water column, known as PBopt. [ 3 ] [ 2 ] It also considers environmental factors that often influence primary production as well as allows for variables often collected using remote satellites to derive the primary production without having to physically sample the water. [ 2 ] This PBopt was found to be dependent on surface chlorophyll, and data for this can be collected using satellites. Satellites can only collect the parameters used to estimate primary production; they cannot calculate it themselves, which is why the need for a model to do so exists. [ 4 ]
Because of this being a generalized model, it is intended to reflect most accurately the open ocean. Other localized areas, especially coastal regions, may need to incorporate additional factors to get the most accurate representation of primary production. [ 2 ] [ 4 ] The values produced using the VGPM are estimates and there will be some level of uncertainty with using this model.
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https://en.wikipedia.org/wiki/Vertically_Generalized_Production_Model
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The Vertifolia effect is a well documented phenomenon in the fields of plant breeding and plant pathology . It is characterized by the erosion of a crop's horizontal resistance to disease during a breeding cycle due to the presence of strong vertical resistance , characterized by the presence of R genes . This effect was observed in late blight of potato. This phenomenon was first described by J.E. Van der Plank in his 1963 book Plant Disease: Epidemics and Control. [ 1 ] Van der Plank observed that under artificial selection the potato variety Vertifolia had stronger vertical resistance to the potato late blight pathogen, Phytophthora infestans , as measured by the presence of specific R genes . However, when the pathogen overcame these R genes Vertifolia exhibited a greater loss of horizontal resistance than varieties with fewer R genes and lower vertical resistance . [ 1 ] This effect suggests that when a pathogen evolves an avirulence gene to counteract a variety's R gene, that variety will be more susceptible to the pathogen than other varieties.
The Vertifolia effect has important implications for the breeding of disease resistant crops. To avoid it plant breeders may opt to cross in R genes or insert transgenes at the end of the breeding cycle to maintain levels of horizontal resistance during early rounds of selection. It is also suggests that breeders should focus on enhancing horizontal resistance to avoid potential catastrophic crop losses. [ citation needed ] Though the effect is a frequently observed phenomenon among plant breeders and plant pathologists, it is difficult to document and there are situations where it does not hold true. [ 2 ] [ 3 ]
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https://en.wikipedia.org/wiki/Vertifolia_effect
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The Verwey transition is a low-temperature phase transition in the mineral magnetite associated with changes in its magnetic, electrical, and thermal properties. [ 1 ] It typically occurs near a temperature of 120 K but is observed at a range of temperatures between 80 and 125 K, although the spread is generally tight around 118–120 K in natural magnetites. [ 1 ] [ 2 ] Upon warming through the Verwey transition temperature ( T V ), the magnetite crystal lattice changes from a monoclinic structure insulator to the metallic cubic inverse spinel structure that persists at room temperature. [ 3 ] The phenomenon is named after Evert Verwey , a Dutch chemist who first recognized, in the 1940s, the connection between the structural transition and the changes in the physical properties of magnetite. This was the first metal-insulator transition to be found. [ 4 ]
The Verwey transition is near in temperature, but distinct from, a magnetic isotropic point in magnetite, at which the first magnetocrystalline anisotropy constant changes sign from positive to negative. [ 5 ]
The temperature and physical expression of the Verwey transition are highly sensitive to the stress state of magnetite and the stoichiometry . Non-stoichiometry in the form of metal cation substitution or partial oxidation can lower the transition temperature or suppress it entirely. [ 5 ] [ 6 ]
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https://en.wikipedia.org/wiki/Verwey_transition
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Very-large-scale integration ( VLSI ) is the process of creating an integrated circuit (IC) by combining millions or billions of MOS transistors onto a single chip. VLSI began in the 1970s when MOS integrated circuit (metal oxide semiconductor) chips were developed and then widely adopted, enabling complex semiconductor and telecommunications technologies. The microprocessor and memory chips are VLSI devices.
Before the introduction of VLSI technology, most ICs had a limited set of functions they could perform. An electronic circuit might consist of a CPU , ROM , RAM and other glue logic . VLSI enables IC designers to add all of these into one chip .
The history of the transistor dates to the 1920s when several inventors attempted devices that were intended to control current in solid-state diodes and convert them into triodes. Success came after World War II, when the use of silicon and germanium crystals as radar detectors led to improvements in fabrication and theory. Scientists who had worked on radar returned to solid-state device development. With the invention of the first transistor at Bell Labs in 1947, the field of electronics shifted from vacuum tubes to solid-state devices . [ 1 ]
With the small transistor at their hands, electrical engineers of the 1950s saw the possibilities of constructing far more advanced circuits. However, as the complexity of circuits grew, problems arose. [ 2 ] One problem was the size of the circuit. A complex circuit like a computer was dependent on speed. If the components were large, the wires interconnecting them must be long. The electric signals took time to go through the circuit, thus slowing the computer. [ 2 ]
The invention of the integrated circuit by Jack Kilby and Robert Noyce solved this problem by making all the components and the chip out of the same block (monolith) of semiconductor material. [ 3 ] The circuits could be made smaller, and the manufacturing process could be automated. This led to the idea of integrating all components on a single-crystal silicon wafer, which led to small-scale integration (SSI) in the early 1960s, and then medium-scale integration (MSI) in the late 1960s. [ 4 ]
General Microelectronics introduced the first commercial MOS integrated circuit in 1964. [ 5 ] In the early 1970s, MOS integrated circuit technology allowed the integration of more than 10,000 transistors in a single chip. [ 6 ] This paved the way for VLSI in the 1970s and 1980s, with tens of thousands of MOS transistors on a single chip (later hundreds of thousands, then millions, and now billions).
The first semiconductor chips held two transistors each. Subsequent advances added more transistors, and as a consequence, more individual functions or systems were integrated over time. The first integrated circuits held only a few devices, perhaps as many as ten diodes , transistors , resistors and capacitors , making it possible to fabricate one or more logic gates on a single device. Now known retrospectively as small-scale integration (SSI), improvements in technique led to devices with hundreds of logic gates, known as medium-scale integration (MSI). Further improvements led to large-scale integration (LSI), i.e. systems with at least a thousand logic gates. Current technology has moved far past this mark and today's microprocessors have many millions of gates and billions of individual transistors.
At one time, there was an effort to name and calibrate various levels of large-scale integration above VLSI. Terms like ultra-large-scale integration (ULSI) were used. But the huge number of gates and transistors available on common devices has rendered such fine distinctions moot. Terms suggesting greater than VLSI levels of integration are no longer in widespread use.
In 2008, billion-transistor processors became commercially available. This became more commonplace as semiconductor fabrication advanced from the then-current generation of 65 nm processors. Current designs, unlike the earliest devices, use extensive design automation and automated logic synthesis to lay out the transistors, enabling higher levels of complexity in the resulting logic functionality. Certain high-performance logic blocks, like the SRAM ( static random-access memory ) cell, are still designed by hand to ensure the highest efficiency. [ citation needed ]
Structured VLSI design is a modular methodology originated by Carver Mead and Lynn Conway for saving microchip area by minimizing the interconnect fabric area. This is obtained by repetitive arrangement of rectangular macro blocks which can be interconnected using wiring by abutment . An example is partitioning the layout of an adder into a row of equal bit slices cells. In complex designs this structuring may be achieved by hierarchical nesting. [ 7 ]
Structured VLSI design had been popular in the early 1980s, but lost its popularity later [ citation needed ] because of the advent of placement and routing tools wasting a lot of area by routing , which is tolerated because of the progress of Moore's law . When introducing the hardware description language KARL in the mid-1970s, Reiner Hartenstein coined the term "structured VLSI design" (originally as "structured LSI design"), echoing Edsger Dijkstra 's structured programming approach by procedure nesting to avoid chaotic spaghetti-structured programs.
As microprocessors become more complex due to technology scaling , microprocessor designers have encountered several challenges which force them to think beyond the design plane, and look ahead to post-silicon:
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Very large floating structures ( VLFSs ) or very large floating platforms ( VLFPs ) are artificial islands, which may be constructed to create floating airports , bridges , breakwaters , piers and docks , storage facilities (for oil and natural gas), wind and solar power plants, for military purposes , to create industrial space, emergency bases, entertainment facilities (such as casinos ), recreation parks, mobile offshore structures and even for habitation . Currently, several different concepts have been proposed for building floating cities or huge living complexes. [ 1 ] Some units have been constructed and are presently in operation. [ 2 ]
Floating structures offer several advantages over more permanent structures which might extend from the shore into open water:
VLFSs differ from watercraft in that most or all of the usable area is the top surface instead of the internal (hold) areas. Thus a useful VLFS will cover significant area. It can be constructed by joining the necessary number of floating units together. The design of the floating structure must comport with safety and strength requirements, operating conditions, etc. Steel, concrete (prestressed or reinforced hybrid) or steel-concrete composite materials may be used to build the floating structure. The motion of the floating structure due to wind or wave action must be substantially neutralized, to ensure the safety of people and facilities on a VLFS, and to allow useful activities. VLFSs must be securely moored to the ocean bed. [ 3 ]
Current VLFS designs fall into two categories: semi-submersible , and pontoon .
The semi-submersible-type VLFS has a raised platform above sea level using column tubes; it is more suitable for deployment in high seas with large waves. In open sea, where the waves are relatively large, the semi-submersible VLFS minimizes the effects of waves while maintaining a constant buoyant force. Semi-submersible types are used for petroleum exploration in deep waters. They are fixed in place by column tubes, piles, or other bracing systems.
The pontoon-type VLFS platform rests on the water surface and is intended for deployment in calm waters such as a cove, a lagoon or a harbor. Its basic element is a simple box structure; it usually offers high stability, low manufacturing cost and easy maintenance and repair. The pontoon type is supported by its buoyancy on the sea surface. The pontoon type is flexible compared to other kinds of offshore structures, so that the elastic deformations are more important than their rigid body motions. Thus, hydroelastic analysis is uppermost in designing the pontoon-type VLFS. Together with the motion of the floating structure, the response of the structure to water waves and the impact on the entire fluid domain have to be studied.
Pontoon-type VLFSs are also known in the literature as mat-like VLFSs because of their small draft in relation to the length dimensions. Very large pontoon-type floating structures are often called ‘mega-floats'. As a rule, the mega-float is a floating structure having at least one length dimension greater than 60 metres (200 ft) Horizontally large floating structures can be from 500 to 5,000 metres (1,600 to 16,400 ft) in length and 100 to 1,000 metres (330 to 3,280 ft) in width, with typical thickness of 2 to 10 metres (6.6 to 32.8 ft).
Many large floating structures have been conceptualized, including a golf course , [ 4 ] a farm , [ 5 ] and habitable long-term living complexes ( seasteading ).
Some large floating structures that have been built include floating airports and floating landing platforms for returning rockets.
A Mega-Float floating airport prototype was constructed in Tokyo Bay from 1998 to 1999. [ 6 ] It was one kilometer in length and was primarily intended as a test vehicle, to research the loadings and responses of such installations. [ 7 ] This project was substituted as a study project to provide more definite information about a proposed floating runway at Kansai International Airport , which was not built (an artificial island was instead constructed to support the runway). However the choice to build an airport on two islands composed of sand landfill has resulted in the Kansai Airport sinking several centimeters per year. ( https://www.smithsonianmag.com/air-space-magazine/how-to-save-a-sinking-airport-180968985/ )
In the 2010s, SpaceX contracted with a Louisiana shipyard to build a floating landing platform for reusable orbital launch vehicles . The platform had an approximately 90 by 50 meters (300 ft × 160 ft) landing pad surface and was capable of precision positioning with diesel-powered azimuth thrusters [ 8 ] so the platform can hold its position for launch vehicle landing. This platform was first deployed in January 2015 [ 9 ] when SpaceX attempted a controlled descent flight test to land the first stage of Falcon 9 Flight 14 on a solid surface after it was used to loft a contracted payload toward Earth orbit. [ 10 ] [ 11 ] The platform utilizes GPS position information to navigate and hold its precise position. [ 12 ] The rocket landing leg span is 18 m (60 ft) and must not only land within the 52 m (170 ft)-wide barge deck, but must also deal with ocean swells and GPS errors .
SpaceX CEO Elon Musk first displayed a photograph of the " autonomous spaceport drone ship " in November 2014. The ship is designed to hold position to within 3 meters (9.8 ft), even under storm conditions. [ 13 ]
On 8 April 2016, the first stage of the rocket that launched the Dragon CRS-8 spacecraft, successfully landed on the drone ship named Of Course I Still Love You, the first successful landing of a rocket booster on a floating platform. [ 14 ]
As of 2018 [update] , Blue Origin is intending to make the first stage boosters of New Glenn be reusable , and recover launched boosters downrange on the Atlantic Ocean via a ship that is underway acting as a floating movable landing platform . The hydrodynamically-stabilized ship increases the likelihood of successful recovery in rough seas . [ 15 ]
A concept has been patented for a floating automotive parking barge with angled sides to deflect wind shear. [ 16 ]
The Shell floating LNG plant was constructed to process and liquify offshore natural gas into liquified natural gas for transport and storage. [ 17 ] [ 18 ] The Shell project was scheduled to begin processing gas in 2016. [ 19 ] In December 2018, Shell announced that the wells have been opened and the plant was ready to begin the initial phase of production. [ 20 ] In June 2019, it reached a significant milestone, shipping its first liquefied natural gas cargo to customers in Asia. [ 18 ]
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Very low frequency or VLF is the ITU designation [ 1 ] [ 2 ] for radio frequencies (RF) in the range of 3–30 kHz , corresponding to wavelengths from 100 to 10 km, respectively. The band is also known as the myriameter band or myriameter wave as the wavelengths range from one to ten myriameters (an obsolete metric unit equal to 10 kilometers). Due to its limited bandwidth , audio (voice) transmission is highly impractical in this band, and therefore only low- data-rate coded signals are used. The VLF band is used for a few radio navigation services, government time radio stations (broadcasting time signals to set radio clocks ) and secure military communication. Since VLF waves can penetrate at least 40 meters (130 ft) into saltwater, they are used for military communication with submarines .
Because of their long wavelengths, VLF radio waves can diffract around large obstacles and so are not blocked by mountain ranges, and they can propagate as ground waves following the curvature of the Earth and so are not limited by the horizon. Ground waves are absorbed by the resistance of the Earth and are less important beyond several hundred to a thousand kilometres/miles, and the main mode of long-distance propagation is an Earth–ionosphere waveguide mechanism. [ 3 ] The Earth is surrounded by a conductive layer of electrons and ions in the upper atmosphere at the bottom of the ionosphere called the D layer at 60–90 km (37–56 mi) altitude, [ 4 ] which reflects VLF radio waves. The conductive ionosphere and the conductive Earth form a horizontal "duct" a few VLF wavelengths high, which acts as a waveguide confining the waves so they don't escape into space. The waves travel in a zig-zag path around the Earth, reflected alternately by the Earth and the ionosphere, in transverse magnetic (TM) mode.
VLF waves have very low path attenuation, 2–3 dB per 1,000 km, [ 3 ] with little of the " fading " experienced at higher frequencies. [ 4 ] This is because VLF waves are reflected from the bottom of the ionosphere, while higher frequency shortwave signals are returned to Earth from higher layers in the ionosphere, the F1 and F2 layers, by a refraction process, and spend most of their journey in the ionosphere, so they are much more affected by ionization gradients and turbulence. Therefore, VLF transmissions are very stable and reliable, and are used for long-distance communication. Propagation distances of 5,000–20,000 km have been realized. [ 3 ] However, atmospheric noise (" sferics ") is high in the band, [ 4 ] including such phenomena as " whistlers ", caused by lightning .
A major practical drawback to the VLF band is that because of the length of the waves, full size resonant antennas ( half wave dipole or quarter wave monopole antennas) cannot be built because of their physical height. [ 6 ] : 14 Vertical antennas must be used because VLF waves propagate in vertical polarization, but a quarter-wave vertical antenna at 30 kHz (10 km wavelength) would be 2.5 kilometres (8,200 feet) high. So practical transmitting antennas are electrically short , a small fraction of the length at which they would be self-resonant. [ 7 ] [ 8 ] : 24.5–24.6 Due to their low radiation resistance (often less than one ohm) they are inefficient, radiating only 10% to 50% of the transmitter power at most, [ 3 ] [ 6 ] : 14 with the rest of the power dissipated in the antenna/ground system resistances. Very high power transmitters (~1 megawatt) are required for long-distance communication, so the efficiency of the antenna is an important factor.
High power VLF transmitting stations use capacitively-toploaded monopole antennas . These are very large wire antennas, up to several kilometers long. [ 9 ] : 3.9–3.21 [ 8 ] : 24.8–24.12 They consist of a series of steel radio masts , linked at the top with a network of cables, often shaped like an umbrella or clotheslines. [ 6 ] : p.14 Either the towers themselves or vertical wires serve as monopole radiators, and the horizontal cables form a capacitive top-load to increase the current in the vertical wires, increasing the radiated power and efficiency of the antenna. High-power stations use variations on the umbrella antenna such as the "delta" and " trideco " antennas, or multiwire flattop (triatic) antennas. [ 6 ] : p.129–162 For low-power transmitters, inverted-L and T antennas are used.
Due to the low radiation resistance, to minimize power dissipated in the ground these antennas require extremely low resistance ground (Earthing) systems, consisting of radial networks of buried copper wires under the antenna. To minimize dielectric losses in the soil, the ground conductors are buried shallowly, only a few inches in the ground, and the ground surface near the antenna is sometimes protected by copper ground screens. Counterpoise systems have also been used, consisting of radial networks of copper cables supported several feet above the ground under the antenna.
A large loading coil is required at the antenna feed point to cancel the capacitive reactance of the antenna to make it resonant . At VLF the design of this coil is challenging; it must have low resistance at the operating RF frequency, high Q , must handle very high currents, and must withstand the extremely high voltage on the antenna. These are usually huge air core coils 2–4 meters high wound on a nonconductive frame, with RF resistance reduced by using thick litz wire several centimeters in diameter, consisting of thousands of insulated strands of fine wire braided together. [ 6 ] : p.95
The high capacitance and inductance and low resistance of the antenna-loading coil combination makes it act electrically like a high Q tuned circuit . VLF antennas have very narrow bandwidth and to change the transmitting frequency requires a variable inductor ( variometer ) to tune the antenna. The large VLF antennas used for high-power transmitters usually have bandwidths of only 50–100 hertz. The high Q results in very high voltages (up to 250 kV) [ 6 ] : p.58 on the antenna and very good insulation is required. [ 6 ] : p.14,19 Large VLF antennas usually operate in 'voltage limited' mode: the maximum power of the transmitter is limited by the voltage the antenna can accept without air breakdown , corona , and arcing from the antenna.
The bandwidth of large capacitively loaded VLF antennas is so narrow (50–100 Hz) that even the small frequency shifts of FSK and MSK modulation may exceed it, throwing the antenna out of resonance , causing the antenna to reflect some power back down the feedline. The traditional solution is to use a "bandwidth resistor" in the antenna which reduces the Q , increasing the bandwidth; however this also reduces the power output. A recent alternative used in some military VLF transmitters is a circuit which dynamically shifts the antenna's resonant frequency between the two output frequencies with the modulation. [ 8 ] : 24.7 [ 9 ] : 3.36 This is accomplished with a saturable reactor in series with the antenna loading coil . This is a ferromagnetic core inductor with a second control winding through which a DC current flows, which controls the inductance by magnetizing the core, changing its permeability . The keying datastream is applied to the control winding. So when the frequency of the transmitter is shifted between the '1' and '0' frequencies, the saturable reactor changes the inductance in the antenna resonant circuit to shift the antenna resonant frequency to follow the transmitter's frequency.
The requirements for receiving antennas are less stringent, because of the high level of natural atmospheric noise in the band. At VLF frequencies atmospheric radio noise is far above the receiver noise introduced by the receiver circuit and determines the receiver signal-to-noise ratio . So small inefficient receiving antennas can be used, and the low voltage signal from the antenna can simply be amplified by the receiver without introducing significant noise. Ferrite loop antennas are usually used for reception.
Because of the small bandwidth of the band, and the extremely narrow bandwidth of the antennas used, it is impractical to transmit audio signals ( AM or FM radiotelephony ). [ 10 ] A typical AM radio signal with a bandwidth of 10 kHz would occupy one third of the VLF band. More significantly, it would be difficult to transmit any distance because it would require an antenna with 100 times the bandwidth of current VLF antennas, which due to the Chu-Harrington limit would be enormous in size. Therefore, only text data can be transmitted, at low bit rates . In military networks frequency-shift keying (FSK) modulation is used to transmit radioteletype data using 5 bit ITA2 or 8 bit ASCII character codes. A small frequency shift of 30–50 hertz is used due to the small bandwidth of the antenna.
In high power VLF transmitters, to increase the allowable data rate, a special form of FSK called minimum-shift keying (MSK) is used. This is required due to the high Q of the antenna. [ 9 ] : 3.2–3.4, §3.1.1 The huge capacitively-loaded antenna and loading coil form a high Q tuned circuit , which stores oscillating electrical energy. The Q of large VLF antennas is typically over 200; this means the antenna stores far more energy (200 times as much) than is supplied or radiated in any single cycle of the transmitter current. The energy is stored alternately as electrostatic energy in the topload and ground system, and magnetic energy in the vertical wires and loading coil. VLF antennas typically operate "voltage-limited", with the voltage on the antenna close to the limit that the insulation will stand, so they will not tolerate any abrupt change in the voltage or current from the transmitter without arcing or other insulation problems. As described below, MSK is able to modulate the transmitted wave at higher data rates without causing voltage spikes on the antenna.
The three types of modulation that have been used in VLF transmitters are:
Historically, this band was used for long distance transoceanic radio communication during the wireless telegraphy era between about 1905 and 1925. Nations built networks of high-power LF and VLF radiotelegraphy stations that transmitted text information by Morse code , to communicate with other countries, their colonies, and naval fleets. Early attempts were made to use radiotelephone using amplitude modulation and single-sideband modulation within the band starting from 20 kHz, but the result was unsatisfactory because the available bandwidth was insufficient to contain the sidebands .
In the 1920s the discovery of the skywave (skip) radio propagation method allowed lower power transmitters operating at high frequency to communicate at similar distances by reflecting their radio waves off a layer of ionized atoms in the ionosphere , and long-distance radio communication stations switched to the shortwave frequencies. The Grimeton VLF transmitter at Grimeton near Varberg in Sweden , one of the few remaining transmitters from that era that has been preserved as a historical monument, can be visited by the public at certain times, such as on Alexanderson Day .
Due to its long propagation distances and stable phase characteristics, during the 20th century the VLF band was used for long range hyperbolic radio navigation systems which allowed ships and aircraft to determine their geographical position by comparing the phase of radio waves received from fixed VLF navigation beacon transmitters.
The worldwide Omega system used frequencies from 10 to 14 kHz, as did Russia's Alpha .
VLF was also used for standard time and frequency broadcasts. In the US, the time signal station WWVL began transmitting a 500 W signal on 20 kHz in August 1963. It used frequency-shift keying ( FSK ) to send data, shifting between 20 kHz and 26 kHz. The WWVL service was discontinued in July 1972.
Naturally occurring signals in the VLF band are used by geophysicists for long range lightning location and for research into atmospheric phenomena such as the aurora. Measurements of whistlers are employed to infer the physical properties of the magnetosphere . [ 11 ]
Geophysicists use VLF- electromagnetic receivers to measure conductivity in the near surface of the Earth. [ 12 ]
VLF signals can be measured as a geophysical electromagnetic survey that relies on transmitted currents inducing secondary responses in conductive geologic units. A VLF anomaly represents a change in the attitude of the electromagnetic vector overlying conductive materials in the subsurface.
VLF can also penetrate soil and rock for some distance, so these frequencies are also used for through-the-earth mine communications systems.
Powerful VLF transmitters are used by the military to communicate with their forces worldwide. The advantage of VLF frequencies is their long range, high reliability, and the prediction that in a nuclear war VLF communications will be less disrupted by nuclear explosions than higher frequencies. Since it can penetrate seawater VLF is used by the military to communicate with submarines near the surface, while ELF frequencies are used for deeply submerged subs.
Examples of naval VLF transmitters are
Since 2004 the US Navy has stopped using ELF transmissions, with the statement that improvements in VLF communication has made them unnecessary, so it may have developed technology to allow submarines to receive VLF transmissions while at operating depth.
High power land-based and aircraft transmitters in countries that operate submarines send signals that can be received thousands of miles away. Transmitter sites typically cover great areas (many acres or square kilometers), with transmitted power anywhere from 20 kW to 2,000 kW. Submarines receive signals from land based and aircraft transmitters using some form of towed antenna that floats just under the surface of the water – for example a Buoyant Cable Array Antenna (BCAA).
Modern receivers use sophisticated digital signal processing techniques to remove the effects of atmospheric noise (largely caused by lightning strikes around the world) and adjacent channel signals, extending the useful reception range. Strategic nuclear bombers of the United States Air Force receive VLF signals as part of hardened nuclear resilient operations.
Two alternative character sets may be used: 5 bit ITA2 or 8 bit ASCII . Because these are military transmissions they are almost always encrypted for security reasons. Although it is relatively easy to receive the transmissions and convert them into a string of characters, enemies cannot decode the encrypted messages; military communications usually use unbreakable one-time pad ciphers since the amount of text is so small.
The frequency range below 8.3 kHz is not allocated by the International Telecommunication Union and in some nations may be used license-free.
Radio amateurs in some countries have been granted permission (or have assumed permission) to operate at frequencies below 8.3 kHz. [ 13 ]
Operations tend to congregate around the frequencies 8.27 kHz, 6.47 kHz, 5.17 kHz, and 2.97 kHz. [ 14 ] Transmissions typically last from one hour up to several days and both receiver and transmitter must have their frequency locked to a stable reference such as a GPS disciplined oscillator or a rubidium standard in order to support such long duration coherent detection and decoding.
Radiated power from amateur stations is very small, ranging from 1 μW to 100 μW for fixed base station antennas, and up to 10 mW from kite or balloon antennas. Despite the low power, stable propagation with low attenuation in the earth-ionosphere cavity enable very narrow bandwidths to be used to reach distances up to several thousand kilometers. The modes used are QRSS , MFSK , and coherent BPSK .
The transmitter generally consists of an audio amplifier of a few hundred watts, an impedance matching transformer, a loading coil and a large wire antenna. Receivers employ an electric field probe or magnetic loop antenna, a sensitive audio preamplifier, isolating transformers, and a PC sound card to digitise the signal. Extensive digital signal processing is required to retrieve the weak signals from beneath interference from power line harmonics and VLF radio atmospherics . Useful received signal strengths are as low as 3 × 10 −8 volts/meter (electric field) and 1 × 10 −16 tesla (magnetic field), with signaling rates typically between 1 and 100 bits per hour.
VLF signals are often monitored by radio amateurs using simple homemade VLF radio receivers based on personal computers (PCs). [ 15 ] [ 16 ] An aerial in the form of a coil of insulated wire is connected to the input of the soundcard of the PC (via a jack plug) and placed a few meters away from it. Fast Fourier transform (FFT) software in combination with a sound card allows reception of all frequencies below the Nyquist frequency simultaneously in the form of spectrogrammes .
Because CRT monitors are strong sources of noise in the VLF range, it is recommended to record the spectrograms with any PC CRT monitors turned off. These spectrograms show many signals, which may include VLF transmitters and the horizontal electron beam deflection of TV sets. The strength of the signal received can vary with a sudden ionospheric disturbance . These cause the ionization level to increase in the ionosphere producing a rapid change to the amplitude and phase of the received VLF signal.
For a more detailed list, see List of VLF-transmitters
ELF 3 Hz/100 Mm 30 Hz/10 Mm
SLF 30 Hz/10 Mm 300 Hz/1 Mm
ULF 300 Hz/1 Mm 3 kHz/100 km
VLF 3 kHz/100 km 30 kHz/10 km
LF 30 kHz/10 km 300 kHz/1 km
MF 300 kHz/1 km 3 MHz/100 m
HF 3 MHz/100 m 30 MHz/10 m
VHF 30 MHz/10 m 300 MHz/1 m
UHF 300 MHz/1 m 3 GHz/100 mm
SHF 3 GHz/100 mm 30 GHz/10 mm
EHF 30 GHz/10 mm 300 GHz/1 mm
THF 300 GHz/1 mm 3 THz/0.1 mm
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Ignoring gravity , experimental bounds seem to suggest that special relativity with its Lorentz symmetry and Poincaré symmetry describes spacetime. Surprisingly, Bogoslovsky [ 1 ] and independently Cohen and Glashow [ 2 ] have demonstrated that a small subgroup of the Lorentz group is sufficient to explain all the current bounds.
The minimal subgroup in question can be described as follows: The stabilizer of a null vector is the special Euclidean group SE(2), which contains T(2) as the subgroup of parabolic transformations . This T(2), when extended to include either parity or time reversal (i.e. subgroups of the orthochronous and time-reversal respectively), is sufficient to give us all the standard predictions. Their new symmetry is called very special relativity (VSR).
This relativity -related article is a stub . You can help Wikipedia by expanding it .
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Vesicle fusion is the merging of a vesicle with other vesicles or a part of a cell membrane . In the latter case, it is the end stage of secretion from secretory vesicles, where their contents are expelled from the cell through exocytosis . Vesicles can also fuse with other target cell compartments, such as a lysosome . Exocytosis occurs when secretory vesicles transiently dock and fuse at the base of cup-shaped structures at the cell plasma membrane called porosomes , the universal secretory machinery in cells. Vesicle fusion may depend on SNARE proteins in the presence of increased intracellular calcium (Ca 2+ ) concentration.
Stimuli that trigger vesicle fusion act by increasing intracellular Ca 2+ .
Model systems consisting of a single phospholipid or a mixture have been studied by physical chemists. Cardiolipin is found mainly in mitochondrial membranes, and calcium ions play an important role in the respiratory processes mediated by the mitochondrion . The forces involved have been postulated to explain [ 3 ] this process in terms of nucleation for agglomeration of smaller supramolecular entities or phase changes in the structure of the biomembranes. [ 4 ]
In synaptic vesicle fusion, the vesicle must be within a few nanometers of the target membrane for the fusion process to begin. This closeness allows the cell membrane and the vesicle to exchange lipids which is mediated by certain proteins which remove water that comes between the forming junction. Once the vesicle is in position it must wait until Ca 2+ enters the cell by the propagation of an action potential to the presynaptic membrane. [ 5 ] Ca 2+ binds to specific proteins, one of which is Synaptotagmin , in neurons which triggers the complete fusion of the vesicle with the target membrane. [ 6 ]
SNARE proteins are also thought to help mediate which membrane is the target of which vesicle. [ 7 ]
Assembly of the SNAREs into the "trans" complexes likely bridges the opposing lipid bilayers of membranes belonging to cell and secretory granule, bringing them in proximity and inducing their fusion. The influx of calcium into the cell triggers the completion of the assembly reaction, which is mediated by an interaction between the putative calcium sensor, synaptotagmin , with membrane lipids and/or the partially assembled SNARE complex.
One hypothesis implicates the molecule Complexin within the SNARE complex and its interaction with the molecule synaptotagmin. [ 9 ] Known as the "clamp" hypothesis, the presence of complexin normally inhibits the fusion of the vesicle to the cell membrane. However, binding of calcium ions to synaptotagmin triggers the complexin to be released or inactivated, so that the vesicle is then free to fuse. [ 10 ]
According to the "zipper" hypothesis, the complex assembly starts at the N-terminal parts of SNARE motifs and proceeds towards the C-termini that anchor interacting proteins in membranes. Formation of the "trans"-SNARE complex proceeds through an intermediate complex composed of SNAP-25 and syntaxin-1, which later accommodates synaptobrevin-2 (the quoted syntaxin and synaptobrevin isotypes participate in neuronal neuromediator release).
Based on the stability of the resultant cis-SNARE complex , it has been postulated that energy released during the assembly process serves as a means for overcoming the repulsive forces between the membranes. There are several models that propose explanation of a subsequent step – the formation of stalk and fusion pore, but the exact nature of these processes remains debated. Two of the most prominent models on fusion pore formation are the lipid-lined and protein-lined fusion pore theories. [ 11 ]
One possible model for fusion pore formation is the lipid-line pore theory. In this model, once the membranes have been brought into sufficiently close proximity via the "zipper" mechanism of the SNARE complex, membrane fusion occurs spontaneously. It has been shown that when the two membranes are brought within a critical distance, it is possible for hydrophilic lipid headgroups of one membrane to merge with the opposing membrane. [ 12 ] In the lipid-lined fusion pore model, the SNARE complex acts as a scaffold, pulling on the membrane, causing both membranes to pucker so they may reach the critical fusion distance. As the two membranes begin to fuse, a lipid-lined stalk is produced, expanding radially outward as fusion proceeds.
While a lipid-lined pore is possible and can achieve all the same properties observed in early pore formation, sufficient data does not exist to prove it is the sole method of formation. [ 13 ] There is not currently a proposed mechanism on inter-cellular regulation for fluctuation of lipid-lined pores, and they would have a substantially more difficult time producing effects such as the "kiss-and-run" when compared with their protein-lined counterparts. Lipid-lined pores effectiveness would also be highly dependent on the composition of both membranes, and its success or failure could vary wildly with changes in elasticity and rigidity. [ 13 ]
Another possible model for fusion pore formation is the protein-lined pore theory. In this model, after activation of synaptotagmin by calcium, several SNARE complexes come together to form a ring structure, with synaptobrevin forming the pore in the vesicle membrane and Syntaxin forming the pore in the cell membrane. [ 14 ] As the initial pore expands it incorporates lipids from both bilayers, eventually resulting in complete fusion of the two membranes. The SNARE complex has a much more active role in the protein-lined pore theory; because the pore consists initially entirely of SNARE proteins, the pore is easily able to undergo intercellular regulation, making fluctuation and "kiss-and-run" mechanisms easily attainable. [ 9 ]
A protein-lined pore perfectly meets all the observed requirements of the early fusion pore, and while some data does support this theory, [ 14 ] sufficient data does not exist to pronounce it the primary method of fusion. A protein-lined pore requires at least five copies of the SNARE complex while fusion has been observed with as few as two. [ 14 ]
In both theories the function of the SNARE complex remains largely unchanged, and the entire SNARE complex is necessary to initiate fusion. It has, however, been proven that in vitro Syntaxin per se is sufficient to drive spontaneous calcium independent fusion of synaptic vesicles containing v-SNAREs. [ 15 ] This suggests that in Ca 2+ -dependent neuronal exocytosis synaptotagmin is a dual regulator, in absence of Ca 2+ ions to inhibit SNARE dynamics, while in presence of Ca 2+ ions to act as agonist in the membrane fusion process.
In synaptic vesicles , some neurochemists have suggested that vesicles occasionally may not completely fuse with presynaptic membranes in neurotransmitter release into the synaptic cleft . The controversy lies in whether or not endocytosis always occurs in vesicle reforming after release of the neurotransmitter. Another proposed mechanism for release of vesicle contents into extracellular fluid is called kiss-and-run fusion .
There is some indication that vesicles may only form a small pore in the presynaptic membrane allowing contents to be released by standard diffusion for a short while before retreating back into the presynaptic cell. This mechanism may be a way around clathrin-mediated endocytosis . It is also proposed that the vesicle does not need to return to an endosome to refill, though it is not thoroughly understood by which mechanism it would refill. This does not exclude full vesicle fusion, but only states that both mechanisms may operate in synaptic clefts.
"Kiss and run" has been shown to occur in endocrine cells, though it has not been directly witnessed in synaptic gaps. [ 16 ]
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The vesicular monoamine transporter (VMAT) is a transport protein integrated into the membranes of synaptic vesicles of presynaptic neurons . It transports monoamine neurotransmitters – such as dopamine , serotonin , norepinephrine , epinephrine , and histamine – into the vesicles , which release the neurotransmitters into synapses, as chemical messages to postsynaptic neurons. VMATs utilize a proton gradient generated by V-ATPases in vesicle membranes to power monoamine import.
Pharmaceutical drugs that target VMATs have possible applications for many conditions, leading to a plethora of biological research, including hypertension , drug addiction , psychiatric disorders, Parkinson's disease , and other neurological disorders. Many drugs that target VMATs act as inhibitors and alter the kinetics of the protein. Much research regarding the effects of altered VMATs on biological systems is still ongoing.
Monoamines transported by VMATs are mainly noradrenaline , adrenaline , dopamine , serotonin , histamine , and trace amines . [ 1 ] Exogenous substrates include guanethidine and MPP + . [ 2 ]
VMAT research began in 1958 when Nils-Åke Hillarp discovered secretory vesicles . In the 1970s, scientists like Arvid Carlsson recognized the need to understand how transport systems and ion gradients work in different organisms in order to explore new treatment options such as reserpine (RES). Researchers discovered inhibitors that blocked the uptake of neurotransmitters into vesicles, suggesting the existence of VMATs. [ 3 ] A decade later, molecular genetic tools have improved methods for protein identification. Scientists have used these tools to analyze DNA and amino acid sequences, and discovered that transporters in bacteria and humans were very similar, which emphasized the importance and universality of transporters. [ 4 ] The transporters were first structurally identified by cloning VMATs in rats. [ 3 ] The VMAT were first isolated and purified in bovine chromaffin granules, in both its native and denatured forms. [ 5 ]
There are two types of VMATs expressed in humans: VMAT1 and VMAT2 . [ 4 ] VMAT1 is expressed mainly in large dense-core vesicles (LDCVs) of the peripheral nervous system. VMAT1 may be found in neuroendocrine cells , particularly chromaffin and enterochromaffin granules, which are primarily found in the medulla of the adrenal glands .
VMAT2 favors expression in a variety of monoaminergic cells of the central nervous system , such as the brain, sympathetic nervous system , mast cells , and cells containing histamine in the gut. [ citation needed ] It is prevalent in β-cells , [ 6 ] expressed in blood platelets , [ 7 ] [ 8 ] and co-expressed in chromaffin cells. [ 6 ] Expression of the two transporters in internal organs seems to differ between species: only VMAT1 is expressed in rat adrenal medulla cells, whereas VMAT2 is the major transporter in bovine adrenal medulla cells. [ 9 ]
VMAT1 and VMAT2 are acidic glycoproteins with a molecular weight of approximately 70 kDa . [ 4 ] [ 10 ] Both isoforms are transmembrane proteins with 12 transmembrane domains (TMDs). [ 4 ]
VMATs function by loading monoamines—dopamine, serotonin, histamine, norepinephrine, and epinephrine—into transport vesicles. [ 11 ] VMATs use the same transport mechanism for all types of monoamines, [ 5 ] and transport them from the cytosol into high-concentration storage vesicles. [ 4 ] Transport vesicles are released into the space between neurons, called the synaptic cleft , where they convey a chemical message to the next neuron. VMATs also function in sorting, storing, and releasing neurotransmitters, and are believed to participate in protecting these neurotransmitters from autoxidation . [ 4 ] The transporters are also known to continue biochemical modification after loading certain neurotransmitters. [ 4 ]
Vesicle packing requires a large energy source to store large quantities of neurotransmitters into a small vesicular space at high concentrations. VMAT transport relies on the pH and electrochemical gradient generated by a vesicular H + -ATPase . [ 4 ] [ 12 ] The current model of VMAT function proposes that the efflux of two protons (H + ) against the H + gradient is coupled with influx of one monoamine. [ 4 ] [ 12 ] The first H + efflux generates a transporter conformation associated with a high-affinity amine-binding site in the cytosolic phase, and the second H + efflux is coupled with a second large conformational change that leads to amine transport from the cytosolic side into the vesicle, reducing amine-binding affinity. [ 4 ]
Studies indicate that the amino acid residue His419, located on the domain between TMDs X and XI of rat VMAT1, plays a role in energy coupling to the amine transport by assisting the first proton-dependent conformational change. [ 4 ] [ 13 ] It has been proposed that RES inhibits VMAT by interacting with this conformation. [ citation needed ]
VMAT gene sequence analysis demonstrates that four aspartic acid residues in the middle region of TMDs I, VI, X, and XI and one lysine residue in TMD II have highly conserved gene sequences, suggesting these residues play a critical role in transporter structure and function. [ 4 ] [ 14 ] Specifically, the residues Lys139 and Asp427 are thought to compose an ion pair that promotes high-affinity interaction with VMAT substrates and inhibitors. [ 4 ] [ 14 ] The Asp431 residue located in TMD XI is believed to be critical for amine transport, but does not interact with RES binding; it is thought to complete the substrate transport cycle. [ 4 ] [ 15 ]
VMATs have a relatively low V max , with an estimated rate of 5–20/sec depending on the substrate. [ 16 ] Vesicle filling may limit monoamine release from neurons with high rates of firing.
Specific amine-binding affinity varies by VMAT isoform; studies indicate that catecholamines dopamine, norepinephrine, and epinephrine have a threefold higher affinity for VMAT2 than VMAT1 binding and uptake. [ 4 ] [ 12 ] [ 17 ] The imidazoleamine histamine has a thirtyfold higher affinity for VMAT2 compared to VMAT1, [ 4 ] and is thought to bind to a different site than other monoamines. [ 12 ] Unlike catecholamines and histamine, the indoleamine serotonin binds to VMAT1 and VMAT2 with a similar affinity for both transporter isoforms. [ 4 ] [ 17 ]
VMAT1 has a lower turnover number and a lower affinity for most monoamine substrates than VMAT2, which may be because of VMAT2's location in the central nervous system, which demands fast recovery from neurotransmitter release in order to prepare for subsequent releases. The uptake efficiencies of each VMAT substrate can be ranked in order of efficiency as: serotonin, dopamine, epinephrine, and norepinephrine. [ 4 ]
Methamphetamines decrease V max , while cocaine increases V max reversibly in rat brain. [ 4 ]
The effects of VMAT inhibition have been studied in-depth in animal models. Mutant homozygous VMAT(-/-) mice move little, feed poorly, and die within a few days of birth.
More specifically, inhibition of VMAT2 may cause an increase in cytosolic catecholamine levels, which can result in an increase in efflux of catecholamines through the cell membrane , depleting catecholamine concentrations and causing increased oxidative stress and oxidative damage to the neuron.
Heterozygous VMAT mutants display hypersensitivity to amphetamine , cocaine, and MPTP (1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine), the latter being a substance causally linked to Parkinson's disease (PD) in rodents. [ 7 ] This suggests a protective role of VMATs against oxidative stress through removal of such substances from the cytosol. [ 7 ]
VMAT inhibitors include:
Two known binding sites for VMAT inhibitors include the RES binding site and the TBZ binding site. Some evidence suggests these two sites may overlap or exist as two separate conformations of the same binding site. [ 4 ] [ 12 ] VMAT inhibitors tend to fall into two classes: those that interact with the RES binding site and those that interact with the TBZ binding site. [ 12 ]
RES, methoxytetrabenazine (MTBZ), and the drug amiodarone bind to the RES binding site. TBZ (also called Nitoman and Xenazine), dihydrotetrabenazine (DTBZOH), ketanserin (KET), and the drug lobeline bind to the TBZ binding site. Amphetamine, methamphetamine and GZ-7931 are also known to interact with VMAT2. [ 4 ] [ 18 ] [ 19 ] [ 20 ]
Inhibitor affinity varies among VMAT isoforms. RES and KET have higher inhibitory affinity for VMAT2–mediated 5HT transport than for that of VMAT1; TBZ seems to inhibit VMAT2 exclusively. [ 4 ]
The residues asp33 and ser180, 181, and 182 are believed to be involved in substrate recognition, and interact with the protonated amino group and hydroxyl group on the catechol or indole rings. [ 12 ]
Cocaine and methylphenidate (MPD, also known as Ritalin and Concerta) are believed to interact with VMAT2 to cause a shift in VMAT2 "from a plasmalemmal membrane-associated fraction to a vesicle-enriched, nonmembrane-associated fraction." [ 21 ]
Consistent with catecholamine-binding affinity, RES has a threefold higher affinity for VMAT2 than for VMAT1. [ 12 ] [ 17 ] The RES binding site is known to be hydrophobic , which is thought to contribute to ligand binding affinity. [ 4 ] Methamphetamine binds to the RES site on VMATs. [ 22 ]
The current working model proposes that RES and the substrate bind to a single site in a pH-gradient modulated conformational structure of the transporter. The conformation occurs after the transport of one H + across the membrane and into the vesicle; proton transport drives the substrate recognition site from the lumen to the cytoplasmic surface of the vesicle for RES and substrate binding. [ 4 ] [ 12 ] [ 23 ] Methoxytetrabenazine (MTBZ) may bind to the RES binding site, based on studies indicating that RES significantly inhibited MTBZ-binding. [ 4 ] Amiodarone is also believed to inhibit monoamine vesicular uptake by binding to the RES binding site. [ 4 ]
TBZ and dihydrotetrabenazine (DTBZOH) are believed to bind to a different binding site from the RES/substrate binding site, or to a different conformation of the RES/substrate binding site. [ 4 ] [ 12 ] [ 24 ] This site is believed to be located at the N-terminus , based on studies done in bovine VMAT2. [ 12 ] Tyr434 and asp461 are identified as being responsible for the high-affinity interaction of TBZ, serotonin, and histamine in VMAT2. [ 12 ] Unlike methamphetamine, amphetamine binds to the TBZ site on hVMAT2. [ 22 ]
Unlike RES inhibition, TBZ inhibition is only affected by very high concentrations of monoamines; however, single injections of RES can inhibit TBZ binding. [ 12 ] ketanserin (KET) [ 4 ] [ 23 ] and lobeline [ 4 ] [ 12 ] also bind to the TBZ binding site conformation.
Three to four glycosylation sites exist in the vesicular matrix on a loop between TMD I and TMD II. [ 4 ] In biology, the vesicle matrix refers to the material or tissue between cells in which more specialized structures are embedded. Two of the glycosylation sites, the N -linked glycosylation terminal and C -linked terminal , are located in the cytosolic portion of the vesicle. [ 4 ] [ 25 ]
The highest amount of genetic variance between VMAT1 and VMAT2 exists near the N- and C- terminals in the cytosolic phase, and in the glycosylated loop between TMDs I and II. [ 4 ]
Several motifs involved in the VMAT trafficking cycle are believed to be encoded in the C-terminus. A dileucine motif in the C-terminus is required for VMAT2 endocytosis . [ 6 ] Studies suggest the acidic residues in the dileucine motif sort VMAT2 away from constitutive secretory vesicles and into the regulated secretory pathway . [ 6 ] The hydrophobic residues in the dileucine motif are thought to couple with the acidic residues as a single unit to help sort VMAT2 to large dense course vesicles. [ 6 ] Acidic glutamate residues located upstream of the dileucine motif are known to be important for localization of VMAT2 to large dense core vesicles; these residues are also conserved in VMAT1. [ 6 ]
Although both VMAT1 and VMAT2 are encoded by two different genes , the individual genetic sequences demonstrate high homology. Polymorphisms in VMAT2 that affect regulation and quantitative expression may pose genetic risk factors for PD. A specific VMAT1 gene ( SLC18A1 ) has several associated polymorphisms , which have a locus 8p21.3 that has been strongly connected to schizophrenia susceptibility. [ 26 ]
Over-expression of VMAT2 results in increased secretion of neurotransmitter upon cell stimulation. Data suggests that deletion of the VMAT2 genes does not affect the size of small clear-core vesicles.
VMATs may be regulated by changes in transcription , post-transcriptional modifications such as phosphorylation and mRNA splicing of exons , and vesicular transport inactivation facilitated by heterotrimeric G-proteins , which are thought to be possessed by chromaffin granules, and have shown to regulate small clear-core vesicles. [ 6 ] [ 7 ]
Specific heterotrimeric G-protein type regulation is tissue-dependent for VMAT2; it is not known whether this is the case for VMAT1. Heterotrimeric G-protein Gαo2 decreases VMAT1 activity in pancreatic and adrenal medulla cells , and activates heterotrimeric G-proteins to inhibit VMAT2 activity in the brain, regardless of whether they are localized on small clear-core or large-dense-core vesicles. The activated heterotrimeric G-protein Gαq downregulates VMAT2-mediated serotonin transport in blood platelets, but not in the brain, where Gαq completely inhibits VMAT2 activity. [ 7 ] Although the exact signalling pathway for G-protein mediated regulation of VMATs is not known, [ 7 ] it has recently been described that implicated G-proteins act directly on the VMATs. [ 27 ]
VMAT2 has been shown to contribute to many clinical neurological disorders including drug addiction, mood disorders, and stress, [ 28 ] as well as Parkinson's disease [ 29 ] and Alzheimer's disease. [ 30 ] [ 31 ]
Studies indicate VMAT2 mRNA is present in all cell groups damaged by Parkinson's disease (PD); [ 32 ] these findings have identified VMAT2 as a target for preventing Parkinson's. VMAT2 presence does not independently protect neurons from PD, but a decrease in VMAT2 expression has been shown to correlate with susceptibility to the disease, [ 32 ] which may be due to a ratio between the dopamine transporter and VMAT2. [ 32 ]
Based on the understanding the increased cytosolic dopamine levels lead to dopaminergic cell death in PD, it has been proposed that regulatory polymorphisms in VMAT2 affect VMAT2 quantitative expression, and may serve as a genetic risk factor for PD. Specifically, the SLC18A2 promoter region for the VMAT2 gene has been identified as an area where several polymorphisms form discrete haplotypes . [ 4 ] [ 33 ]
Studies using a genetic rodent model to understand clinical depression in humans suggest that VMAT2 genetic or functional alterations may be involved in depression. [ 34 ] Reduced VMAT2 levels were identified in specific subregions of the striatum involved in clinical depression, including the nucleus accumbens shell but not the core, the ventral tegmental area , and the substantia nigra 's pars compacta . The reduced VMAT2 protein levels were not accompanied by similar levels of VMAT2 mRNA alterations. Based on these findings, it has been proposed that VMAT2 activity is not altered at the level of genetic expression, but may be altered at the functional level in ways that may correlate with clinical depression. [ 4 ]
Many psychostimulant drugs are known to interact with VMAT, including amphetamine analogs such as methamphetamine, cocaine, and ecstasy (MDMA). [ citation needed ]
VMAT inhibitors tend to fall into two classes; those that interact with the RES binding site and those that interact with the TBZ binding site. [ 12 ]
RES, methoxytetrabenazine, and amiodarone bind to the RES binding site.
TBZ, DTBZOH, ketanserin, and lobeline bind to the TBZ binding site.
Many psychostimulants , including substituted amphetamines and cocaine, are known to interact with VMAT2. Studies indicate that both amphetamines and cocaine act to increase non-exocytotic release of dopamine in specific regions of the brain by interacting directly with VMAT2 function. [ 4 ] [ 18 ] [ 21 ]
VMAT is a main target of methamphetamine. Studies indicate that substituted amphetamines including methamphetamine interact with VMAT2 at the TBZ/DTBZOH binding site. [ 4 ] [ 21 ] By acting as a negative allosteric modulator , methamphetamine blocks the presynaptic cell's ability to use VMAT for vesicular packaging.
Methamphetamine alters the subcellular location of VMAT2, which affects the distribution of dopamine in the cell. Treatment with methamphetamine relocates VMAT2 from a vesicle-enriched fraction to a location that is not continuous with synaptosomal preparations. [ 9 ]
Repeated amphetamine exposure may increase VMAT2 mRNA in certain brain regions with little or no decline upon withdrawal from the drug. [ 9 ]
A study performed by Sonsalla et al. demonstrated that methamphetamine treatment decreases DHTBZ binding and vesicular dopamine uptake. [ 4 ] [ 21 ] Another study demonstrated that multiple high doses of methamphetamine removed DTBZ binding sites from the vesicles. [ 12 ]
In addition to an interaction with the TBZ/DTBZOH binding site, some researchers propose that substituted amphetamines like methamphetamine decrease dopamine uptake because of the weak base properties of substituted amphetamines. [ 21 ] This “Weak Base Hypothesis” proposes that amphetamine analogs enter the cell through transport and lipophilic diffusion, then diffuses through the vesicular membrane where they accumulate in synaptic vesicles and offset the proton electrochemical gradient in the vesicle that drives monoamine transport through VMAT. [ 21 ] Amphetamine administration would prevent vesicular dopamine uptake through VMAT, and explain the finding that amphetamine administration correlates with decreased dopamine release from vesicles and a neurotoxic increase in intracellular dopamine. [ 4 ] [ 21 ]
Unlike methamphetamine, cocaine interacts with VMAT2 by mobilizing VMAT2-expressing vesicles, causing a shift in VMAT2 proteins from a plasmalemmal (synaptosomal) membrane fraction to a vesicle-enriched fraction that is not associated with the synaptosomal membrane and not retained in synaptosomal preparations. [ 4 ] [ 12 ] [ 21 ] Methylphenidate is believed to interact with VMAT2 in a similar fashion. [ 21 ]
In addition to mobilizing VMAT2-expressing vesicles, cocaine has been shown to increase the V max of VMAT2 for dopamine and increase the number of DTBZ binding sites. [ 12 ] It has also mobilized a synapsin -dependent reserve pool of dopamine-containing synaptic vesicles, which interacts with the vesicular trafficking cycle to increase dopamine release. [ 12 ]
Short-term exposure to cocaine increases VMAT2 density in the prefrontal cortex and striatum of mammalian brains. This is theorized to be a defensive mechanism against the depletive effects cocaine has on cytosolic dopamine through increasing monoamine storage capacity. [ 9 ] Chronic cocaine use has been implicated with a reduction in VMAT2 immunoreactivity as well as a decrease in DTBZOH binding in humans.
Research suggests a decline in VMAT2 protein through prolonged cocaine use could play an important role in the development of cocaine-induced mood disorders. [ 9 ]
MDMA is known to affect serotonergic neurons, but has been shown to inhibit synaptosomal and vesicular uptake of serotonin and dopamine [ 4 ] to roughly the same extent in vitro . [ 12 ] In vivo studies indicate short-term MDMA exposure causes short-term reduction in VMAT2 activity, which is reversed after 24 hours. [ 12 ]
Genetic research models have shown that polymorphisms in SLC18A1 and SLC18A2 , the genes that encode for VMAT1 and 2 proteins, respectively, may confer risk for some neuropsychiatric disorders; [ 4 ] [ 33 ] [ 35 ] however, no specific diseases have been identified yet as directly resulting from a genetic mutation in an SLC18 gene, which codes for VMAT proteins. [ 35 ]
Much of the current research related to VMAT explores the genetic underpinnings of neuropsychiatric disorders as they may be affected by SLC18A family mutations.
The dopaminergic neuron is known to play a central role in drug addiction and abuse and the potential role of the dopamine transporter has been well-explored as a target for amphetamine and cocaine. Current research looks toward VMAT2 as a target for such psychostimulants. A combination of imaging, neurochemical, biochemical, cell biological, genetic, and immunohistochemical evidence has been compiled to provide the most current comprehensive understanding of the role the VMAT2 plays in amphetamine and cocaine abuse and addiction through aminergic neurotransmission. [ 1 ] [ 35 ]
As VMATs are membrane proteins, structural information is limited and researchers have yet to completely understand the structure of both isoforms. Further studies are needed in order to determine the structure and therefore complete function of these proteins. There is preliminary evidence that the gene for VMAT1 may be linked to susceptibility to schizophrenia , bipolar disorder , and various anxiety disorders. [ 4 ] Further studies are needed in order to confirm these findings and to gain a better understanding of the role of VMATs in the central nervous system.
Multiple single-nucleotide polymorphisms (SNPs) have been identified in the coding region of VMATs. The effects of some of these SNPs have been alteration of VMAT function, structure and regulation. [ 36 ] Further investigation of these SNPs is required in order to distinguish whether they may be attributable to certain diseases with suspected SNP- mutation origins.
α-synuclein, a cytosolic protein found mainly in pre-synaptic nerve terminals, has been found to have regulatory interactions with the trafficking of VMATs; mutations involving α-synuclein have been linked to familial PD. [ 36 ] Further research is needed to clarify the extent to which these proteins modulate the trafficking of VMATs, and whether they may be exploited in order to gather more information about the exact mechanism of how disorders such as PD occurs, and how they may potentially be treated.
Studies have shown that at the synaptic membrane, enzymes responsible for the synthesis of dopamine, tyrosine hydroxylase and amino acid aromatic decarboxylase are physically and functionally coupled with VMAT2. [ 36 ] It was initially thought that the synthesis of these substances and the subsequent packaging of them into vesicles were two entirely separate processes.
Current research related to VMAT uses VMAT2 knockout mice to explore the behavioral genetics of this transporter in an animal model. VMAT2 knockouts are known to be lethal as homozygotes, but heterozygote knockouts are not lethal and are used in many studies as a durable animal model. [ 9 ] [ 35 ]
From knockout and knockdown mice, researchers have discovered that it is good to have over-expression or under-expression of the VMAT genes in some circumstances. [ 35 ] Mice are also used in drug studies, particularity studies involving the effect cocaine and methamphetamine have on VMATs. [ 35 ] Studies involving animals have prompted scientists to work on developing drugs that inhibit or enhance the function of VMATs. Drugs that inhibit VMATs may have use in addiction but further studies are needed. [ 35 ] Enhancing the function of VMATs may also have therapeutic value. [ 35 ]
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https://en.wikipedia.org/wiki/Vesicular_monoamine_transporter
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6570
110877
ENSG00000036565
ENSMUSG00000036330
P54219
Q8R090
NM_001135691 NM_001142324 NM_001142325 NM_003053
NM_153054
NP_001129163 NP_001135796 NP_001135797 NP_003044
NP_694694
Vesicular monoamine transporter 1 ( VMAT1 ), also known as chromaffin granule amine transporter ( CGAT ) or solute carrier family 18 member 1 ( SLC18A1 ), is a protein that in humans is encoded by the SLC18A1 gene . VMAT1 is an integral membrane protein , which is embedded in synaptic vesicles and serves to transfer monoamines , such as norepinephrine , epinephrine , dopamine , and serotonin , between the cytosol and synaptic vesicles. [ 5 ] SLC18A1 is an isoform of the vesicular monoamine transporter .
The idea that there must be specific transport proteins associated with the uptake of monoamines and acetylcholine into vesicles developed due to the discovery of specific inhibitors which interfered with monoamine neurotransmission and also depleted monoamines in neuroendocrine tissues. [ 5 ] VMAT1 and VMAT2 were first identified in rats upon cloning cDNAs for proteins which gave non-amine accumulating recipient cells the ability to sequester monoamines. [ 6 ] Subsequently, human VMATs were cloned using human cDNA libraries with the rat homologs as probes, and heterologous-cell amine uptake assays were performed to verify transport properties. [ 7 ]
Across mammalian species, VMATs have been found to be structurally well conserved; VMAT1s have an overall sequence identity exceeding 80%. However, there exists only a 60% sequence identity between the human VMAT1 and VMAT2. [ 8 ]
VMAT1 is an acidic glycoprotein with an apparent weight of 40 kDa . [ 9 ] Although the crystallographic structure has not yet been fully resolved, VMAT1 is known to have either twelve transmembrane domains (TMDs), based on Kyte-Doolittle hydrophobicity scale analysis [ 7 ] or ten TMDs, based on MAXHOM alignment. MAXHOM alignment was determined using the "profile-fed neural network systems from Heidelberg" (PHD) program. [ 5 ] The main difference between these two models arises from the placement of TMDs II and IV in the vesicle lumen or the cytoplasm .
VMATs are found in a variety of cell types throughout the body, however, VMAT1 is found exclusively in neuroendocrine cells , in contrast to VMAT2, which is also found in the PNS and CNS . Specifically, VMAT1 is found in chromaffin cells , enterochromaffin cells , and small intensely fluorescent cells (SIFs). [ 10 ] Chromaffin cells are responsible for releasing the catecholamines (norepinephrine and epinephrine ) into systemic circulation . Enterochromaffin cells are responsible for storing serotonin in the gastrointestinal tract. SIFs are interneurons associated with the sympathetic nervous system which are managed by dopamine.
VMAT1 is found in both large dense-core vesicles (LDCVs) as well as in small synaptic vesicles (SSVs). This was discovered via studying rat adrenal medulla cells (PC12 cells). [ 11 ] LDCVs are 70-200 nm in size and exist throughout the neuron ( soma , dendrites , etc.). SSVs are much smaller (usually about 40 nm) and typically exist as clusters in the presynaptic cleft.
The active transport of monoamines from the cytosol into storage vesicles operates against a large (>10 5 ) concentration gradient. Secondary active transport is the type of active transport used, meaning that VMAT1 is an antiporter . This transport is facilitated via proton gradient generated by the protein proton ATPase . The inward transport of the monoamine is coupled with the efflux of two protons per monoamine. [ 12 ] The first proton is thought to cause a change in VMAT1's conformation , which pushes a high affinity amine binding site , to which the monoamine attaches. The second proton then causes a second change in the conformation which pulls the monoamine into the vesicle and greatly reduces the affinity of the binding site for amines. A series of tests suggest that His 419, located between TMDs X and XI, plays the key role in the first of these conformational changes, and that Asp 431, located on TMD XI, does likewise during the second change. [ 9 ]
Several reuptake inhibitors of VMATs are known to exist, including reserpine (RES), tetrabenazine (TBZ), dihydrotetrabenazine (DTBZOH), and ketanserin (KET). It is thought that RES exhibits competitive inhibition , binding to the same site as the monoamine substrate, as studies have shown that it can be displaced via introduction of norepinephrine. TBZ, DTBZOH, and KET are thought to exhibit non-competitive inhibition , instead binding to allosteric sites and decreasing the activity of the VMAT rather than simply blocking its substrate binding site. [ 9 ] It has been found that these inhibitors are less effective at inhibiting VMAT1 than VMAT2, and the inhibitory effects of the tetrabenazines on VMAT1 is negligible. [ 10 ]
The expression of VMAT1 in healthy endocrine cells was compared to VMAT1 expression in infants with hyperinsulinemic hypoglycemia and adults with pancreatic endocrine tumors. [ 13 ] Through immunohistochemistry (IHC) and in situ hybridization (ISH), they found VMAT1 and VMAT2 were located in mutually exclusive cell types, and that in insulinomas VMAT2 activity disappeared, suggesting that if only VMAT1 activity is present in the endocrine system, this type of cancer is likely.
VMAT1 also has effects on the modulation of gastrin processing in G cells . These intestinal endocrine cells process amine precursors, and VMAT1 pulls them into vesicles for storage. The activity of VMAT1 in these cells has a seemingly inhibitory effect on the processing of gastrin. Essentially, this means that certain compounds in the gut can be taken into these G cells and either amplify or inhibit the function of VMAT1, which will impact gastrin processing (conversion from G34 to G17). [ 14 ]
Additionally, VMAT1 is known to play a role in the uptake and secretion of serotonin in the gut. Enterochromaffin cells in the intestines will secrete serotonin in response to the activation of certain mechanosensors . [ 15 ] The regulation of serotonin in the gut is critically important, as it modulates appetite and controls intestinal contraction.
Presence of VMAT1 in cells has been shown to protect them from the damaging effects of cooling and rewarming associated with hypothermia . [ 16 ] Experiments were carried out on aortic and kidney cells and tissues . Evidence was found that an accumulation of serotonin using VMAT1 and TPH1 allowed for the subsequent release of serotonin when exposed to cold temperatures. This allows cystathionine beta synthase (CBS) mediated generation of H 2 S . The protection against the damage caused by hypothermia is due to a reduction in the generation of reactive oxygen species (ROS), which can induce apoptosis , due to the presence of H 2 S. [ 17 ]
VMAT1 (SLC18A1) maps to a shared bipolar disorder (BPD)/ schizophrenia locus , which is located on chromosome 8p 21. [ 18 ] [ 19 ] It is thought that disruption in transport of monoamine neurotransmitters due to variation in the VMAT1 gene may be relevant to the etiology of these mental disorders. One study looked at a population of European descent, examining the genotypes of a bipolar group and a control group. The study confirmed expression of VMAT1 in the brain at a protein and mRNA level, and found a significant difference between the two groups, suggesting that, at least for people of European descent, variation in the VMAT1 gene may confer susceptibility. [ 18 ] A second study examined a population of Japanese individuals, one group healthy and the other schizophrenic. This study resulted in mostly inconclusive findings, but some indications that variation in the VMAT1 gene would confer susceptibility to schizophrenia in Japanese women. [ 20 ] While these studies provide some promising insight into the cause of some of the most prevalent mental disorders, it is clear that additional research will be necessary in order to gain a full understanding.
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https://en.wikipedia.org/wiki/Vesicular_monoamine_transporter_1
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6571
214084
ENSG00000165646
ENSMUSG00000025094
Q05940
Q8BRU6
NM_003054
NM_172523
NP_003045
NP_766111
The solute carrier family 18 member 2 ( SLC18A2 ) also known as vesicular monoamine transporter 2 ( VMAT2 ) is a protein that in humans is encoded by the SLC18A2 gene . [ 5 ] VMAT2 is an integral membrane protein that transports monoamines —particularly neurotransmitters such as dopamine , norepinephrine , serotonin , and histamine —from cellular cytosol into synaptic vesicles . [ 6 ] In nigrostriatal pathway and mesolimbic pathway dopamine-releasing neurons, VMAT2 function is also necessary for the vesicular release of the neurotransmitter GABA . [ 7 ]
VMAT2 is believed to possess at least two distinct binding sites, which are characterized by tetrabenazine (TBZ) and reserpine binding to the transporter. [ 8 ] Amphetamine (TBZ site) and methamphetamine (reserpine site) bind at distinct sites on VMAT2 to inhibit its function. [ 8 ] VMAT2 inhibitors like tetrabenazine and reserpine reduce the concentration of monoamine neurotransmitters in the synaptic cleft by inhibiting uptake through VMAT2; the inhibition of SLC18A2 uptake by these drugs prevents the storage of neurotransmitters in synaptic vesicles and reduces the quantity of neurotransmitters that are released through exocytosis . Although many substituted amphetamines induce the release of neurotransmitters from vesicles through VMAT2 while inhibiting uptake through VMAT2, they may facilitate the release of monoamine neurotransmitters into the synaptic cleft by simultaneously reversing the direction of transport through the primary plasma membrane transport proteins for monoamines (i.e., the dopamine transporter , norepinephrine transporter , and serotonin transporter ) in monoamine neurons. Other VMAT2 inhibitors such as GZ-793A inhibit the reinforcing effects of methamphetamine, but without producing stimulant or reinforcing effects themselves. [ 9 ]
Researchers have found that inhibiting the dopamine transporter (but not VMAT2) will block the effects of amphetamine and cocaine; while, in another experiment, observing that disabling VMAT2 (but not the dopamine transporter) prevents any notable action in test animals after amphetamine administration yet not cocaine administration. This suggests that amphetamine may be an atypical substrate with little to no ability to prevent dopamine reuptake via binding to the dopamine transporter but, instead, uses it to enter a neuron where it then interacts with VMAT2 to induce efflux of dopamine from their vesicles into the cytoplasm whereupon dopamine transporters with amphetamine substrates attached move this recently liberated dopamine into the synaptic cleft. [ 10 ]
Although most amphetamines and other monoamine releasing agents (MRA) act on VMAT2, several MRAs, including phentermine , phenmetrazine , and benzylpiperazine (BZP), are inactive at VMAT2. [ 11 ] [ 12 ] Others, including cathinones like mephedrone , methcathinone , and methylone , also show only weak VMAT2 activity (e.g., ~10-fold weaker than the corresponding amphetamines). [ 13 ] [ 14 ] [ 15 ] MRAs acting on VMAT2 additionally continue to induce monoamine release in in-vitro systems in which VMAT2 is absent or inhibited. [ 16 ] [ 17 ]
VMAT2 is essential for enabling the release of neurotransmitters from the axon terminals of monoamine neurons into the synaptic cleft . If VMAT2 function is inhibited or compromised, monoamine neurotransmitters such as dopamine cannot be released into the synapse via typical release mechanisms (i.e., exocytosis resulting from action potentials ).
Cocaine users display a marked reduction in VMAT2 immunoreactivity . Those with cocaine-induced mood disorders displayed a significant loss of VMAT2 immunoreactivity; this might reflect damage to dopamine axon terminals in the striatum . These neuronal changes could play a role in causing disordered mood and motivational processes in more severely addicted users. [ 27 ]
To date, no agent has been shown to directly interact with VMAT2 in a way that promotes its activity. A VMAT2 positive allosteric modulator remains an elusive target in addiction and Parkinson's disease research. [ 28 ] [ 29 ] However, it has been observed that certain tricylcic and tetracylcic antidepressants (as well as a high- mesembrine Sceletium tortuosum extract) can upregulate the activity of VMAT2 in vitro, though whether this is due to a direct interaction is unknown. [ 30 ] [ 31 ]
Geneticist Dean Hamer has suggested that a particular allele of the SLC18A2 gene correlates with spirituality using data from a smoking survey, which included questions intended to measure "self-transcendence". Hamer performed the spirituality study on the side, independently of the National Cancer Institute smoking study. His findings were published in the mass-market book The God Gene: How Faith Is Hard-Wired into Our Genes . [ 32 ] [ 33 ] Hamer himself notes that SLC18A2 plays at most a minor role in influencing spirituality. [ 34 ] Furthermore, Hamer's claim that the SLC18A2 gene contributes to spirituality is controversial. [ 34 ] Hamer's study has not been published in a peer-reviewed journal and a reanalysis of the correlation demonstrates that it is not statistically significant. [ 34 ] [ 35 ]
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https://en.wikipedia.org/wiki/Vesicular_monoamine_transporter_2
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Vesicular transport adaptor proteins are proteins involved in forming complexes that function in the trafficking of molecules from one subcellular location to another. [ 2 ] [ 3 ] [ 4 ] These complexes concentrate the correct cargo molecules in vesicles that bud or extrude off of one organelle and travel to another location, where the cargo is delivered. While some of the details of how these adaptor proteins achieve their trafficking specificity has been worked out, there is still much to be learned.
There are several human disorders associated with defects in components of these complexes [ 5 ] [ 6 ] including Alzheimer's and Parkinson's diseases . [ 7 ]
Most of the adaptor proteins are heterotetramers . In the AP complexes, there are two large proteins ( ~ 100 k D ) and two smaller proteins. One of the large proteins is termed β ( beta ), with β1 in the AP-1 complex, β2 in the AP-2 complex , and so on. [ 10 ] The other large protein has different designations in the different complexes. In AP-1 it is named γ ( gamma ), AP-2 has α ( alpha ), AP-3 has δ ( delta ), AP-4 has ε ( epsilon ) and AP-5 has ζ ( zeta ). [ 10 ] The two smaller proteins are a medium subunit named μ ( mu ~50 kD) and a small subunit σ ( sigma ~20 kD), and named 1 through 5 corresponding to the 5 AP complexes. [ 10 ] Components of COPI (cop one) a coatomer , and TSET (T-set) a membrane trafficking complex have similar heterotetramers of the AP complexes. [ 11 ]
Retromer is not closely related, has been reviewed, [ 12 ] and its proteins will not be described here. GGAs (Golgi-localising, Gamma-adaptin ear domain homology, ARF-binding proteins) are a group of related proteins (three in humans) that act as monomeric clathrin adaptor proteins in various important membrane vesicle traffickings , [ 13 ] but are not similar to any of the AP complexes and will not be discussed in detail in this article. Stonins (not shown in the lead figure) are also monomers similar in some regards to GGA [ 4 ] and will also not be discussed in detail in this article.
PTBs are protein domains that include NUMB , DAB1 and DAB2 . Epsin and AP180 in the ANTH domain are other adaptor proteins that have been reviewed. [ 4 ]
An important transport complex, COPII , was not shown in the lead figure. The COPII complex is a heterohexamer, but not closely related to the AP/TSET complexes. The individual proteins of the COPII complex are called SEC proteins, because they are encoded by genes identified in sec retory mutants of yeast. One especially interesting aspect of COPII is that it can form typical spherical vesicles and tubules to transport large molecules like collagen precursors, which cannot fit inside typical spherical vesicles. COPII structure has been discussed in an open article [ 14 ] and will not be a focus of this article. These are examples of the much larger set of cargo adaptors. [ 3 ]
The most recent common ancestor (MRCA) of the eukaryotes must have had a mechanism for trafficking molecules between its endomembranes and organelles , and the likely identity of the adaptor complex involved has been reported. [ 11 ] It is believed that the MRCA had 3 proteins involved in trafficking and that they formed a heterotrimer. That heterotrimer next "dimerized" to form a 6 membered-complex. The individual components further changed into the current complexes, in the order shown, with AP1 and AP2 being the last to diverge. [ 11 ]
In addition, one component of TSET, a muniscin also known as the TCUP protein, appears to have evolved into part of the proteins of opisthokonts (animals and fungi ). [ 11 ] Parts of the AP complexes have evolved into parts of the GGA and stonin proteins. [ 4 ] There is evidence indicating that parts of the nuclear pore complex and COPII may be evolutionarily related. [ 15 ]
The best characterized type of vesicle is the clathrin coated vesicle (CCV). The formation of a COPII vesicle at the endoplasmic reticulum and its transport to the Golgi body . The involvement of the heterotetramer of COPI is similar to that of the AP/clathrin situation, but the coat of COPI is not closely related to the coats of either CCVs or COPII vesicles. [ 16 ] [ 17 ] AP-5 is associated with 2 proteins, SPG11 and SPG15 , which have some structural similarity to clathrin , and may form the coat around the AP-5 complex, [ 18 ] but the ultrastructure of that coat is not known. The coat of AP-4 is unknown. [ 19 ] [ a ]
An almost universal feature of coat assembly is the recruitment of the various adaptor complexes to the "donor" membrane by the protein Arf1 . The one known exception is AP-2, which is recruited by a particular plasma membrane lipid . [ 20 ]
Another almost universal feature of coat assembly is that the adaptors are recruited first, and they then recruit the coats. The exception is COPI, in which the 7 proteins are recruited to the membrane as a heptamer. [ 16 ]
As illustrated in the accompanying image, the production of a coated vesicle is not instantaneous, and a considerable fraction of the maturation time is used by making "abortive" or "futile" [ 21 ] interactions until enough interactions occur simultaneously to allow the structure to continue to develop. [ 22 ]
The last step in the formation of a transport vesicle is "pinching off" from the donor membrane. This requires energy, but even in the well studied case of CCVs, not all require dynamin . The accompanying illustration shows the case for AP-2 CCVs, however AP-1 and AP-3 CCVs do not use dynamin. [ 23 ]
Which cargo molecules are incorporated into a particular type of vesicle relies on specific interactions. Some of these interactions are directly with AP complexes and some are indirectly with "alternative adaptors", as shown in this diagram . [ 4 ] As examples, membrane proteins can have direct interactions, while proteins that are soluble in the lumen of the donor organelle bind indirectly to AP complexes by binding to membrane proteins that traverse the membrane and bind at their lumenal end to the desired cargo molecule. Molecules that should not be included in the vesicle appear to be excluded by "molecular crowding". [ 24 ]
The "signals" or amino acid "motifs" in the cargo proteins that interact with the adaptor proteins can be very short. For example, one well-known example is the di leucine motif, in which a leucine amino acid (aa) residue is followed immediately by another leucine or isoleucine residue. [ 25 ] [ b ] An even simpler example is the tyrosine based signal, which is YxxØ (a t y rosine residue separated by 2 aa residues from another bulky, hydrophobic aa residue). The accompanying figure shows how a small part of a protein can interact specifically with another protein, so these short signalling motifs should not be surprising. [ 26 ] The sort of sequence comparisons used, in part, to define these motifs. [ 10 ]
In some cases, post- translational modifications, such as phosphorylations (shown in the figure) are important for cargo recognition.
Adaptor diseases have been reviewed. [ 6 ]
AP-2/CCVs are involved in autosomal recessive hypercholesterolemia through the associated low-density lipoprotein receptor adapter protein 1 . [ 27 ] [ 28 ]
Retromer is involved in recycling components of the plasma membrane. The importance of that recycling at a synapse is hinted at in one of the figures in the gallery. There are at least 3 ways in which retromer dysfunction can contribute to brain disorders, including Alzheimer and Parkinson diseases. [ 7 ]
AP-5 is the most recently described complex, and one reason supporting the idea that it is an authentic adaptor complex is that it is associated with hereditary spastic paraplegia , [ 18 ] as is AP-4. [ 6 ] AP-1 is linked to MEDNIK syndrome . AP-3 is linked to Hermansky–Pudlak syndrome . COPI is linked to an autoimmune disease . [ 29 ] COPII is linked to cranio-lenticulo-sutural dysplasia .
One of the GGA proteins may be involved in Alzheimer's disease. [ 30 ]
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Vespertine is a term used in the life sciences to indicate something of, relating to, or occurring in the evening. In botany , a vespertine flower is one that opens or blooms in the evening. [ 1 ] In zoology , the term is used for a creature that becomes active at dusk , such as bats and owls. Strictly speaking, however, the term means that activity ceases during the hours of full darkness and does not resume until the next evening. Activity that continues throughout the night should be described as nocturnal .
Vespertine behaviour is a special case of crepuscular behaviour; like crepuscular activity, vespertine activity is limited to dusk rather than full darkness. Unlike vespertine activity, crepuscular activity may resume in dim twilight before dawn. A related term is matutinal , referring to activity limited to the dawn twilight.
The word vespertine is derived from the Latin word vespertīnus , an adjective meaning "evening".
This ethology article is a stub . You can help Wikipedia by expanding it .
This botany article is a stub . You can help Wikipedia by expanding it .
This biology article is a stub . You can help Wikipedia by expanding it .
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A vessel traffic service is a marine traffic monitoring system established by harbour or port authorities, similar to air traffic control for aircraft. The International Maritime Organization defines vessel traffic service as "a service implemented by a competent authority designed to improve the safety and efficiency of vessel traffic and protect the environment. The service shall have the capability to interact with the traffic and respond to traffic situations developing in the vessel traffic service area". [ 1 ] [ 2 ] Typical vessel traffic service systems use radar , closed-circuit television , VHF radiotelephony and automatic identification system to keep track of vessel movements and provide navigational safety in a limited geographical area.
In the United States, vessel traffic services are established and operated by the Coast Guard Navigation Center. Some services operate as partnerships between the Coast Guard and private agencies.
Guidelines require that the vessel traffic service authority should be provided with sufficient staff, appropriately qualified, suitably trained and capable of performing the tasks required, taking into consideration the type and level of services to be provided in conformity with the current International Maritime Organization guidelines on the subject. [ 3 ]
International Association of Marine Aids to Navigation and Lighthouse Authorities Recommendation V-103 is the recommendation sn Standards for training and certification of vessel traffic service personnel. There are four associated model courses, V103/1 to V-103/4, which are approved by the International Maritime Organization and should be used when training personnel for the vessel traffic service qualifications. [ 4 ]
An information service is a service to ensure that essential information becomes available in time for onboard navigational decision-making.
The information service is provided by broadcasting information at fixed times and intervals or when deemed necessary by the vessel traffic service or at the request of a vessel, and may include for example reports on the position, identity and intentions of other traffic; waterway conditions; weather; hazards; or any other factors that may influence the vessel's transit. [ 4 ]
A traffic organization service is a service to prevent the development of dangerous maritime traffic situations and to provide for the safe and efficient movement of vessel traffic within the vessel traffic service area.
The traffic organization service concerns the operational management of traffic and the forward planning of vessel movements to prevent congestion and dangerous situations and is particularly relevant in times of high traffic density or when the movement of special transports may affect the flow of other traffic. The service may also include establishing and operating a system of traffic clearances or sailing plans, or both, in relation to priority of movements, allocation of space, mandatory reporting of movements in the service area, routes to be followed, speed limits to be observed or other appropriate measures which are considered necessary by the vessel traffic service authority. [ 4 ]
Navigational assistance service is a service to assist onboard navigational decision-making and to monitor its effects.
The navigational assistance service is especially important in difficult navigational or meteorological circumstances or in case of defects or deficiencies. This service is normally rendered at the request of a vessel or by the vessel traffic service when deemed necessary. [ 4 ]
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Vestibular paroxysmia (VP) is a rare vertigo syndrome, which is defined by recurring, short-lasting vertigo attacks. A neurovascular cross-compression is commonly assumed to cause these attacks. [ 1 ] [ 2 ]
The main symptoms of VP are short attacks lasting seconds to a few minutes with spinning or swaying vertigo , which typically occur dozens of times a day. [ 1 ] This may be accompanied by rhythmic tinnitus . In some patients, the attacks can be triggered by certain head positions or by hyperventilation . [ 3 ]
The vertigo attacks are caused by pulsatile compression of the vestibulocochlear nerve by blood vessels (in 70% of cases the anterior inferior cerebellar artery (AICA)) [ 4 ] in the cerebellopontine angle, which can cause demyelinsation of the nerve. The nerve is particularly susceptible in the area of the nerve entry zone into the brain stem , as the structure of the myelin sheath changes here (from oligodendrocytes to Schwann cells ). [ 5 ]
In terms of the diagnostic criteria we find that the following must be met: [ 1 ]
A definiteve diagnosis can usually only be made after a successful attempt at pharmacotherapy. Vascular-nerve contact demonstrated by magnetic resonance imaging is not part of the diagnostic criteria. [ 1 ] [ 6 ] Appropriate imaging should be performed to rule out other structural changes in the cerebellopontine angle. [ 6 ]
Pharmacotherapy often involves oxcarbazepine , carbamazepine or lacosamide . [ 6 ] In very rare cases, surgery in the form of microvascular decompression may also be indicated. [ 4 ]
In a long-term study (mean follow-up time 4.8 years), around 75% of patients remained without vertigo attacks, and in more than half of them no drug therapy was necessary. [ 3 ]
Depending on the origin, there are two peaks in frequency: in the case of causative vascular malformations, those affected become symptomatic at a young age, while age-associated vascular changes usually cause symptoms for the first time between the ages of 40 and 70. Men are affected twice as often as women. [ 4 ] Vestibular paroxysmia accounts for around 3% of diagnoses in specialized vertigo outpatient clinics. [ 6 ]
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A vestigial response or vestigial reflex in a species is a response that has lost its original function. In humans, vestigial responses include ear perking, goose bumps and the hypnic jerk .
It has been observed that some people have slight protrusions on the outer ear (also known as the auricle). These protrusions tend towards the top of the auricle. This has been tagged and coined Darwin's tubercle of the auricle. This phenomenon agrees with the accepted scientific explanation: the incidence of tubercles of the auricle among humans, are vestigial structures testifying to our evolutionary past. They are a throwback to the pointed ears of many mammals and just one more vestigial trace of human evolutionary history.
The focus on this part of the human anatomy has finally been followed by a much later observation testifying to our evolutionary past. The subsequent observation concerns an automatic ear-perking response seen, for example, in dogs when startled by a sudden noise. This response, though faint, fleeting and hardly discernible in humans nonetheless clearly manifests itself. [ 1 ] This phenomenon is an automatic-response mechanism that activates even before a human becomes consciously aware that a startling, unexpected or unknown sound has been "heard". [ 2 ]
That this vestigial response occurs even before becoming consciously aware of a startling noise would explain why the function of ear-perking had evolved in animals. The mechanism serves to give a split-second advantage to a startled animal – possibly an animal being stalked and hunted. The evolutionary advantage of the ear-perking response could spell the difference between life and death. The perking response serves to gather and focus that much more audible information that is fed into the brain and on its way to being analyzed even before the animal actually becomes aware of the sound. This fraction-of-a-second advantage would explain the evolutionary selection for this response.
The pilomotor reflex, more commonly known as goose bumps, was originally a reflex that assured the raising of fur for additional insulation against cold. When scared, this response also made the frightened animal seem bigger and a more formidable enemy. [ 3 ]
The sudden startled arm-jerking response sometimes experienced when on the verge of sleeping is known as the hypnic jerk .
The evolutionary explanation for the existence of the hypnic jerk is unclear, but a possibility is that it is a vestigial reflex humans evolved when they usually slept in trees. Experiencing a hypnic jerk prior to falling asleep may have been selected so that the individual would be able to readjust their sleeping position in the tree with a branch-grabbing response to avoid falling, [ 4 ] much like how orangutans grasp upper branches of trees while sleeping.
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Vestigiality is the retention, during the process of evolution , of genetically determined structures or attributes that have lost some or all of the ancestral function in a given species. [ 1 ] Assessment of the vestigiality must generally rely on comparison with homologous features in related species. The emergence of vestigiality occurs by normal evolutionary processes, typically by loss of function of a feature that is no longer subject to positive selection pressures when it loses its value in a changing environment. The feature may be selected against more urgently when its function becomes definitively harmful, but if the lack of the feature provides no advantage, and its presence provides no disadvantage, the feature may not be phased out by natural selection and persist across species.
Examples of vestigial structures (also called degenerate, atrophied, or rudimentary organs) are the loss of functional wings in island-dwelling birds; the human vomeronasal organ ; and the hindlimbs of the snake and whale .
Vestigial features may take various forms; for example, they may be patterns of behavior, anatomical structures, or biochemical processes. Like most other physical features, however functional, vestigial features in a given species may successively appear, develop, and persist or disappear at various stages within the life cycle of the organism, ranging from early embryonic development to late adulthood.
Vestigiality, biologically speaking, refers to organisms retaining organs that have seemingly lost their original function. Vestigial organs are common evolutionary knowledge. [ 2 ] In addition, the term vestigiality is useful in referring to many genetically determined features, either morphological, behavioral, or physiological; in any such context, however, it need not follow that a vestigial feature must be completely useless. A classic example at the level of gross anatomy is the human vermiform appendix , vestigial in the sense of retaining no significant digestive function.
Similar concepts apply at the molecular level—some nucleic acid sequences in eukaryotic genomes have no known biological function; some of them may be " junk DNA ", but it is a difficult matter to demonstrate that a particular sequence in a particular region of a given genome is truly nonfunctional. The simple fact that it is noncoding DNA does not establish that it is functionless. Furthermore, even if an extant DNA sequence is functionless, it does not follow that it has descended from an ancestral sequence of functional DNA. Logically such DNA would not be vestigial in the sense of being the vestige of a functional structure. In contrast pseudogenes have lost their protein-coding ability or are otherwise no longer expressed in the cell. Whether they have any extant function or not, they have lost their former function and in that sense, they do fit the definition of vestigiality.
Vestigial structures are often called vestigial organs , although many of them are not actually organs . Such vestigial structures typically are degenerate, atrophied, or rudimentary, [ 3 ] and tend to be much more variable than homologous non-vestigial parts. Although structures commonly regarded "vestigial" may have lost some or all of the functional roles that they had played in ancestral organisms, such structures may retain lesser functions or may have become adapted to new roles in extant populations. [ 4 ]
It is important to avoid confusion of the concept of vestigiality with that of exaptation . Both may occur together in the same example, depending on the relevant point of view. In exaptation, a structure originally used for one purpose is modified for a new one. For example, the wings of penguins would be exaptational in the sense of serving a substantial new purpose (underwater locomotion), but might still be regarded as vestigial in the sense of having lost the function of flight. In contrast Darwin argued that the wings of emus would be definitely vestigial, as they appear to have no major extant function; however, function is a matter of degree, so judgments on what is a "major" function are arbitrary; the emu does seem to use its wings as organs of balance in running. Similarly, the ostrich uses its wings in displays and temperature control, though they are undoubtedly vestigial as structures for flight.
Vestigial characters range from detrimental through neutral to favorable in terms of selection. Some may be of some limited utility to an organism but still degenerate over time if they do not confer a significant enough advantage in terms of fitness to avoid the effects of genetic drift or competing selective pressures . Vestigiality in its various forms presents many examples of evidence for biological evolution . [ 5 ]
Vestigial structures have been noticed since ancient times, and the reason for their existence was long speculated upon before Darwinian evolution provided a widely accepted explanation. In the 4th century BC, Aristotle was one of the earliest writers to comment, in his History of Animals , on the vestigial eyes of moles, calling them "stunted in development" due to the fact that moles can scarcely see. [ 6 ] However, only in recent centuries have anatomical vestiges become a subject of serious study. In 1798, Étienne Geoffroy Saint-Hilaire noted on vestigial structures:
Whereas useless in this circumstance, these rudiments... have not been eliminated, because Nature never works by rapid jumps , and She always leaves vestiges of an organ, even though it is completely superfluous, if that organ plays an important role in the other species of the same family. [ 7 ]
His colleague, Jean-Baptiste Lamarck , named a number of vestigial structures in his 1809 book Philosophie Zoologique . Lamarck noted " Olivier 's Spalax , which lives underground like the mole, and is apparently exposed to daylight even less than the mole, has altogether lost the use of sight: so that it shows nothing more than vestiges of this organ." [ 8 ]
Charles Darwin was familiar with the concept of vestigial structures, though the term for them did not yet exist. He listed a number of them in The Descent of Man , including the muscles of the ear , wisdom teeth , the appendix , the tail bone , body hair , and the semilunar fold in the corner of the eye . Darwin also noted, in On the Origin of Species , that a vestigial structure could be useless for its primary function, but still retain secondary anatomical roles: "An organ serving for two purposes, may become rudimentary or utterly aborted for one, even the more important purpose, and remain perfectly efficient for the other.... [A]n organ may become rudimentary for its proper purpose, and be used for a distinct object." [ 9 ]
In the first edition of On the Origin of Species , Darwin briefly mentioned inheritance of acquired characters under the heading " Effects of Use and Disuse ", expressing little doubt that use "strengthens and enlarges certain parts, and disuse diminishes them; and that such modifications are inherited". [ 10 ] In later editions he expanded his thoughts on this, [ 11 ] and in the final chapter of the 6th edition concluded that species have been modified "chiefly through the natural selection of numerous successive, slight, favorable variations; aided in an important manner by the inherited effects of the use and disuse of parts". [ 12 ]
In 1893, Robert Wiedersheim published The Structure of Man , a book on human anatomy and its relevance to man's evolutionary history. The Structure of Man contained a list of 86 human organs that Wiedersheim described as, "Organs having become wholly or in part functionless, some appearing in the Embryo alone, others present during Life constantly or inconstantly. For the greater part Organs which may be rightly termed Vestigial." [ 13 ] Since his time, the function of some of these structures have been discovered, while other anatomical vestiges have been unearthed, making the list primarily of interest as a record of the knowledge of human anatomy at the time. Later versions of Wiedersheim's list were expanded to as many as 180 human "vestigial organs". This is why the zoologist Horatio Newman said in a written statement read into evidence in the Scopes Trial that "There are, according to Wiedersheim, no less than 180 vestigial structures in the human body, sufficient to make of a man a veritable walking museum of antiquities." [ 14 ]
Vestigial structures are often homologous to structures that are functioning normally in other species. Therefore, vestigial structures can be considered evidence for evolution , the process by which beneficial heritable traits arise in populations over an extended period of time. The existence of vestigial traits can be attributed to changes in the environment and behavior patterns of the organism in question. Through an examination of these various traits, it is clear that evolution had a hard role in the development of organisms. Every anatomical structure or behavior response has origins in which they were, at one time, useful. As time progressed, the ancient common ancestor organisms did as well. Evolving with time, natural selection played a huge role. More advantageous structures were selected, while others were not. With this expansion, some traits were left to the wayside. As the function of the trait is no longer beneficial for survival, the likelihood that future offspring will inherit the "normal" form of it decreases. In some cases, the structure becomes detrimental to the organism (for example the eyes of a mole can become infected [ 9 ] ). In many cases the structure is of no direct harm, yet all structures require extra energy in terms of development, maintenance, and weight, and are also a risk in terms of disease (e.g., infection , cancer ), providing some selective pressure for the removal of parts that do not contribute to an organism's fitness. A structure that is not harmful will take longer to be 'phased out' than one that is. However, some vestigial structures may persist due to limitations in development, such that complete loss of the structure could not occur without major alterations of the organism's developmental pattern, and such alterations would likely produce numerous negative side-effects. The toes of many animals such as horses , which stand on a single toe , are still evident in a vestigial form and may become evident, although rarely, from time to time in individuals.
The vestigial versions of the structure can be compared to the original version of the structure in other species in order to determine the homology of a vestigial structure. Homologous structures indicate common ancestry with those organisms that have a functional version of the structure. [ 15 ] Douglas Futuyma has stated that vestigial structures make no sense without evolution, just as spelling and usage of many modern English words can only be explained by their Latin or Old Norse antecedents. [ 16 ]
Vestigial traits can still be considered adaptations . This is because an adaptation is often defined as a trait that has been favored by natural selection. Adaptations, therefore, need not be adaptive , as long as they were at some point. [ 17 ]
Vestigial characters are present throughout the animal kingdom, and an almost endless list could be given. Darwin said that "it would be impossible to name one of the higher animals in which some part or other is not in a rudimentary condition." [ 9 ]
The wings of ostriches , emus and other flightless birds are vestigial; they are remnants of their flying ancestors' wings. These birds go through the effort of developing wings, even though most birds are too large to use the wings successfully. Seeing vestigial wings in birds is also common when they no longer need to fly to escape predators, such as birds on the Galapagos Islands . [ 18 ] The eyes of certain cavefish and salamanders are vestigial, as they no longer allow the organism to see, and are remnants of their ancestors' functional eyes. Animals that reproduce without sex (via asexual reproduction ) generally lose their sexual traits, such as the ability to locate/recognize the opposite sex and copulation behavior. [ 19 ]
Boas and pythons have vestigial pelvis remnants, which are externally visible as two small pelvic spurs on each side of the cloaca. These spurs are sometimes used in copulation, but are not essential, as no colubrid snake (the vast majority of species) possesses these remnants. Furthermore, in most snakes, the left lung is greatly reduced or absent. Amphisbaenians , which independently evolved limblessness, also retain vestiges of the pelvis as well as the pectoral girdle, and have lost their right lung. [ citation needed ]
A case of vestigial organs was described in polyopisthocotylean Monogeneans ( parasitic flatworms ). These parasites usually have a posterior attachment organ with several clamps , which are sclerotised organs attaching the worm to the gill of the host fish. These clamps are extremely important for the survival of the parasite. In the family Protomicrocotylidae , species have either normal clamps, simplified clamps, or no clamps at all (in the genus Lethacotyle ). After a comparative study of the relative surface of clamps in more than 100 Monogeneans , this has been interpreted as an evolutionary sequence leading to the loss of clamps. Coincidentally, other attachment structures (lateral flaps, transverse striations) have evolved in protomicrocotylids. Therefore, clamps in protomicrocotylids were considered vestigial organs. [ 20 ]
In the foregoing examples the vestigiality is generally the (sometimes incidental) result of adaptive evolution . However, there are many examples of vestigiality as the product of drastic mutation , and such vestigiality is usually harmful or counter-adaptive. One of the earliest documented examples was that of vestigial wings in Drosophila . [ 21 ] Many examples in many other contexts have emerged since. [ 22 ]
Human vestigiality is related to human evolution , and includes a variety of characters occurring in the human species. Many examples of these are vestigial in other primates and related animals, whereas other examples are still highly developed. The human caecum is vestigial, as often is the case in omnivores , being reduced to a single chamber receiving the content of the ileum into the colon . The ancestral caecum would have been a large, blind diverticulum in which resistant plant material such as cellulose would have been fermented in preparation for absorption in the colon. [ 23 ] [ 24 ] [ 25 ] Analogous organs in other animals similar to humans continue to perform similar functions. The coccyx , [ 26 ] or tailbone, though a vestige of the tail of some primate ancestors, is functional as an anchor for certain pelvic muscles including: the levator ani muscle and the largest gluteal muscle, the gluteus maximus. [ 27 ]
Other structures that are vestigial include the plica semilunaris on the inside corner of the eye (a remnant of the nictitating membrane ); [ 28 ] and (as seen at right) muscles in the ear . [ 29 ] Other organic structures (such as the occipitofrontalis muscle ) have lost their original functions (to keep the head from falling) but are still useful for other purposes (facial expression). [ 30 ]
Humans also bear some vestigial behaviors and reflexes. The formation of goose bumps in humans under stress is a vestigial reflex ; [ 31 ] its function in human ancestors was to raise the body's hair, making the ancestor appear larger and scaring off predators. The arrector pili (muscle that connects the hair follicle to connective tissue) contracts and creates goosebumps on skin. [ 32 ]
There are also vestigial molecular structures in humans, which are no longer in use but may indicate common ancestry with other species. One example of this is a gene that is functional in most other mammals and which produces L-gulonolactone oxidase , an enzyme that can make vitamin C . A documented mutation deactivated the gene in an ancestor of the modern infraorder of monkeys, and apes , and it now remains in their genomes , including the human genome , as a vestigial sequence called a pseudogene . [ 33 ]
The shift in human diet towards soft and processed food over time caused a reduction in the number of powerful grinding teeth, especially the third molars (also known as wisdom teeth), which were highly prone to impaction . [ 34 ]
Plants also have vestigial parts, including functionless stipules and carpels , leaf reduction of Equisetum , paraphyses of Fungi . [ 35 ] Well known examples are the reductions in floral display, leading to smaller and/or paler flowers, in plants that reproduce without outcrossing , for example via selfing or obligate clonal reproduction. [ 36 ] [ 37 ]
Many objects in daily use contain vestigial structures. While not the result of natural selection through random mutation , much of the process is the same. Product design, like evolution, is iterative; it builds on features and processes that already exist, with limited resources available to make tweaks. To spend resources on completely weeding out a form that serves no purpose (if at the same time it is not an obstruction either) is not economically astute. These vestigial structures differ from the concept of skeuomorphism in that a skeuomorph is a design feature that has been specifically implemented as a reference to the past, enabling users to acclimatise quicker. A vestigial feature does not exist intentionally, or even usefully.
For example, men's business suits often contain a row of buttons at the bottom of the sleeve. These used to serve a purpose, allowing the sleeve to be split and rolled up. The feature has been lost entirely, though most suits still give the impression that it is possible, complete with fake button holes. There is also an example of exaptation to be found in the business suit: it was previously possible to button a jacket up all the way to the top. As it became the fashion to fold the lapel over, the top half of buttons and their accompanying buttonholes disappeared, save for a single hole at the top; it has since found a new use as a place to fasten pins, badges, or boutonnières . [ 38 ]
As a final example, soldiers in ceremonial or parade uniform can sometimes be seen wearing a gorget : a small decorative piece of metal suspended around the neck with a chain. The gorget serves no protection to the wearer, yet there exists an unbroken lineage from the gorget to the full suits of armour of the middle ages. With the introduction of gunpowder weapons, armour increasingly lost its usefulness on the battlefield. At the same time, military men were keen to retain the status it provided them. The result: a breastplate that "shrank" away over time, but never disappeared completely. [ 39 ]
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