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The Organization for Machine Automation and Control ( OMAC ) is a global organization that supports the machine automation and operational needs of manufacturing. [ 1 ] OMAC, has in conjunction with ISA , created the PackML industry standard for describing the state and transitions of packaging machines. [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] OMAC was formed by General Motors in the 1980s under the name Open Modular Architecture Controls to address the problem of each machine having different controls and/or software implementations. [ 7 ] In the late 1990s OMAC expanded into the packaging automation industry. [ 7 ]
This industry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Organization_for_Machine_Automation_and_Control |
Organizational space , sometimes called organizational architecture , describes the influence of the spatial environment on the health , the mind , and the behavior of humans in and around organizations . [ 1 ] It is an area of scientific research in which interdisciplinarity is a central perspective. It draws from management , organization and architecture [ 2 ] added with knowledge from, for instance, environmental psychology (Evans and Mitchell, 1998), social medicine (Macintyre et al., 2002), or spatial science (Festinger et al., 1950). In essence, it may be regarded as a special field of expertise of organization studies and change management applied to architecture. The knowledge area is related to evidence-based design in which the influence of the spatial environment on patient's health , healing , and customer satisfaction are being researched in health care . It is also related to practice-based areas of management such as facility management which is primarily devoted to the maintenance and care of commercial or institutional buildings and to property management in which the operation of real estate is central. The scientific field of organizational space must be distinguished from social architecture in which the development of information and communication technologies is central and also different from space science which is concerned with the study of the universe .
This research strand distinguishes three different environments : the spatial environment from the physical environment and the built environment .
The coherence between the organization and its spatial environment may be regarded as an interwoven interdisciplinary cyclical flux from contingencies, intermediates, performances to interventions (Mobach, 2009). The contingencies are the organizational , architectural , technological , and natural conditions under which organization function. In the end they influence the performance of an organization, but first they mix in the intermediates . In this way humans in and around organizations will, for instance, notice these contingencies and will give them meaning (Clegg and Kornberger, 2006; Van Marrewijk and Yanow, 2010). Moreover, the contingencies will also influence social contact (Becker, 1981; Steele, 1973) and the degree to which a spatial environment can be functional (Sharles, 1923). Subsequently, the intermediates influence different performances , for instance, the health , the mind , and the behavior of people in and around organizations . The spatial environment can cause illness , such as with the sick building syndrome (EPA, 1991), but it can also positively influence the vitality of people or the recovery after an operation (Ulrich, 1984). The performances can provoke managerial intervention. In turn, these interventions will change the contingencies, and by doing so, change the elements, relations, and properties of the conditions under which people function. | https://en.wikipedia.org/wiki/Organizational_space |
Organizational technoethics ( OT ) is a branch stemming from technoethics . Advances in technology and their ability to transmit vast amounts of information in a short amount of time have changed the way information is being shared amongst co-workers and managers throughout organizations across the globe. Starting in the 1980s with information and communications technologies ( ICTs ), organizations have seen an increase in the amount of technology that they rely on to communicate within and outside of the workplace. However, these implementations of technology in the workplace create various ethical concerns and in turn a need for further analysis of technology in organizations. As a result of this growing trend, a subsection of technoethics known as organizational technoethics has emerged to address these issues.
Organizational technoethics "focuses on how technological advances are redefining organizations and how they operate within an evolving knowledge economy". [ 1 ] : 182 This new focus on knowledge and information within organizations has changed the way they function on a daily basis and has made it apparent that "as knowledge-intensive work gradually becomes the cornerstone of this economy, understanding its control practices is consequential to organizational effectiveness, worker satisfaction and ethical conditions of organizational governance". [ 2 ] With this "knowledge intensive work" at the forefront of most organizations, the efficient transmission of this knowledge and information now becomes a major priority to be carried out in the workplace. The introduction of the Internet in the workplace allowed employees to transmit information electronically not only to others in their own office but those in other countries as well. Technology began to facilitate the rapid exchange of information for these organizations and thus contributed to a structural change in how they operate. These changes prompted researchers to delve deeper into the issues surrounding organizational technoethics in how technology was shaping the workplace, whether positively or negatively, and the ethical issues that may arise.
The use of ICTs within organizations have given way to a new kind of office setting where physically being in the office is not mandatory to get the job done. This recent trend coined by many as the virtual workplace involves several workplaces that are connected through technology and are not hindered by physical restraints. Remote work , hot desking , and virtual teams are the three major types of virtual workplaces that have been made possible through the use of technology and have changed the way many organizations communicate and transmit information.
The increasing use of ICTs in the workplace has presented organizations with new ethical challenges. It has been argued that ICT use in organizational settings can contribute to counterproductive behaviour and deviancy [ 3 ] as the line between personal and professional lives becomes blurred. [ citation needed ] Usually this behaviour consists of non-sanctioned use of ICTs during work hours, such as updating personal blogs, playing games, doing personal banking online, and using email for non-work related activities.
In response to these popular misuses of technology in the workplace, some organizations have implemented workplace surveillance technologies and content-control software to monitor and restrict employees' activities online.
ICT use in medical organizations has also given rise to new ethical dilemmas, such as the use of electronic medical records. These have created privacy concerns relating to potential breaches of doctor-patient confidentiality as well as concerns with information storage.
One area of technoethics that is growing increasingly popular [ citation needed ] is organizational ethics and technology. The introduction of technology into organizations has fueled many different questions. Among these many questions is whether or not the technology being used is ethical. Many different case studies have been conducted in organizations around the world. In these case studies, new technology that has been introduced to an organization is examined. During the examination, one ethical question that seems to be a main focus for researchers is whether or not the new technology maintains users' privacy.
The advent of technology has also opened up new avenues and opportunities for individuals to misbehave; for example, cyberloafing , the act of employees using their companies' Internet access for personal purposes during work hours. While access to the internet may not result in an increase in production deviance with more people engaging in loafing per se, the temptation to do so is certainly higher since the Internet makes it so much easier and convenient to loaf in this manner. It is suggested by Lim when organizations are distributively, procedurally and interactionally unjust in their treatment of their employees (i.e., organizations have not given expected rewards or fair treatment in exchange for fair work), these employees are more likely to invoke the neutralization technique to legitimize their subsequent engagement in the act of cyberloafing. (Lim 2002) [ 4 ] One technology that has grown in popularity in recent years [ 5 ] is social networking sites, as many people use sites such as Facebook for personal and professional reasons. Organizations all over the world, including those in the Canadian province of Ontario, have begun to block access to Facebook and have led to criticism of Facebook . For example, in May 2007, Ontario government employees, Federal public servants, MPPs and cabinet ministers were blocked from access to Facebook on government computers. Employees trying to access Facebook received a warning message that read "The Internet website that you have requested has been deemed unacceptable for use for government business purposes". [ 6 ] The use of social networking sites led to a fear that government offices would become more vulnerable to computer viruses and hackers . However, with the government denying the use of these websites in their offices, many ethical questions arise about whether or not denying employees access to something that is readily available to everyone else is an infringement on the employees' rights and freedoms as Canadian citizens.
Another area of organizational technoethics that has been becoming increasingly popular is in the field of medicine. Medical ethics are based on values and judgments in a practical clinical placement where six values are portrayed the most: autonomy, beneficence, non-maleficence, justice, dignity, truthfulness and honesty. Many of the issues in medical ethics are due to a lack of communication between the patients, family members, and health care team. An asset to medical ethics that has brought attention to its advantages and disadvantages are electronic medical records . This is a new way to update, organize and store patients' medical records in a database that can be accessible to other doctors by using the network.
An issue in organizational technoethics in the medical field that is an increasing matter is the privacy issue with electronic medical records. To start, some advantages of EMRs are that they can minimize errors, keep records safe in the database, it is cost efficient, translates into a better treatment for the patients and can even give some control over health records to the patients. On the other hand, EMRs have brought upon some disadvantages mainly around privacy issues. First, it threatens a patient's privacy. Having a patient's medical history recorded in the database loses the confidentiality between the doctor and patient since anyone who has access to the system is able to retrieve these files.
Moreover, some do not feel their medical records are safe in the database since others are able to get into personal files and potentially change medical records or misuse the information. [ 7 ] A group of researchers conducted a study on the privacy issues raised by the use of EMRs. They concluded that all electronic systems around us have this one-to-many exchange such as the internet and email just like the EMR system. However, more clarity needs to be provided around patient consent and patient restrictions as well as confidentiality issues. [ 8 ] With the issue of privacy at hand, many ethical questions have surfaced on whether this electronic system is safe or a hazard to patients due to the easy access and misuse of a patient's information.
Organizational surveillance is becoming a reoccurring issue in the modern day workforce. Today's organizations are facing the ethical dilemma of privacy rights and meeting the societal demands of efficient productivity performances from employees. Organizations have restrictions on employees Web pages and have also implemented surveillance over workers email, Web browsing , and even video surveillance at the workplace. Surveillance has become a technoethical challenge because the rapid development of surveillance technologies. Surveillance is a prominent technoethical challenge because it threatens democracy, privacy, power, as well as brings various types of rights together. Surveillance is a technoethical challenge because it encompasses many ethical dilemmas made by new technology. Surveillance is a technoethical challenges because it threatens personal liberties. [ 9 ] Surveillance is said to corrode interpersonal trust, which is essential for democratic governance. [ 9 ] Citizens with access to new technologies are becoming more aware of the pervasiveness of these technologies. [ 9 ] Surveillances has evolved from people called informers to technology. Citizens are now seen as consumers, and their preferences are monitored in order to feed citizens their preferences rather than serve them with broad perspective. [ 9 ] This poses the question: Is it ethical to implement informational narrowcasting (only feeding citizens their preferences)? Surveillance also falls under many other categories and raises other ethical dilemmas. Another ethical dilemma would be: Should citizens be involved in the design process of technological policy on surveillance?
Surveillance can be ethical if states use it to protect national security and do not monitor citizens in the privacy of their bedroom and public washrooms. [ 10 ] In 1998 " New surveillance" introduced by technological advances added to the degree of complexity and mobility, that society had not seen before. [ 10 ] Surveillance has captured many areas of ethics and technology which translates into Technoethics. Surveillance has looked at power relationships in society, trust and autonomy, privacy, causes, authority as well as necessity, means, distance and social sorting. [ 10 ] Technoethics refers to the systems approach taken to look at all of these issues surrounding dilemmas such as surveillance.
The branch of utilitarian ethical theories are "based on the assumption of the greatest happiness to the greatest number of people". [ 1 ] : 26–27 Under this perspective of ethical theories, organizational surveillance for the workers does not bring happiness; "Workplace surveillance has consequences for employees, affecting employee well-being, work culture, productivity, creativity and motivation". [ 11 ] According to this report, the results show that surveillance produces the exact opposite results in which surveillance was implemented for, to increase workplace productivity. With organizational surveillance creating a workplace environment where employees feel unmotivated and as a result productivity will decrease. If the productivity of employees lack than the organization may not experience the rate of growth and success as wanted by management and ultimately, will lead to an overall unhappiness for both parties, employees and the organization.
Another branch of ethical theories which can be applied is duty ethics . Duty ethics is "concerned with the obligations one has to others in society". [ 1 ] : 26–27 Under this perspective, organizations have the obligation to provide services and goods to society. In order to produce services and goods for society, organizations must be efficient in productivity. As result of this need, organizations have implemented surveillance on employees in order to meet this obligation. Also, employees have the obligation to meet their own performance goals at the workplace, which align with the overall goals of the organization.
The Internet has become a popular medium of expression and accessing information and data. As the Internet community expands, there has been great debate on whether or not the internet should be censored, and if so, by whom. In Canada, there are many public and private organisations with the authority to censor, including many self-censoring associations and service providers. Canadian internet censorship is not specifically regulated; however local laws do apply to websites hosted in Canada as well as to residents who host sites on servers in other jurisdictions. Canada has seen many cases regarding websites including defamatory material [ 12 ] and material promoting hatred or contempt .
Important Canadian cases that raise the question of control of the flow of content on the Internet include:
Many cases were ruled through Section 13(1) of the Canadian Human Rights Act, such as the Marc Lemire case, which featured a "white nationalist" website hosted out of Hamilton, Ontario, Canada. However, the Canadian Human Rights Tribunal (CHRT) found that Section 13 was unconstitutional and refused to apply the provisions against the individual for reasons of freedom of speech. [ 14 ] All other Section 13 cases in Canada have been postponed pending on final decision of the applicability of Section 13.
Organizational ethics and technology is a hot-bed for discussion. Whether it is about the maintenance of worker's privacy or the censoring of social network sites, organizations are striving to find a way to balance both their worker's agency and their productivity. It seems the fluid nature of the Internet is forcing the hand of companies to allow their workers some benefits to access the sites they normally would outside of the office, while at the same time maintaining a strict policy to not abuse any privileges meted out. [ citation needed ] The medical field has brought on a new technology that hopes to effectively and systematically ease the process of updating, storing, and organizing patient's records in a manner that suits both the patients and the doctors that treat them.
With the advent of electronic medical records (EMR), the field of medical ethics has also seen an influx in ethical discourse. While the technology is different from social media per se, the efforts to protect the worker's (or patient's) privacy is similar and equally paramount to their survival. Patients will look to online databases to ensure that their information is both correct and secure, while trying to maintain the pseudo-ageless " doctor-patient confidentiality ", even with full knowledge that their information is accessible worldwide with the click of a button. [ citation needed ] Looking ahead to how EMR advances, and whether or not organizations will always feel the need to block social network sites all depends on how they continue to be used as people become more complacent with the technology. There will always be instances of ethical debates concerning technology within an organizational context, as the only things that seem to change are the technologies surrounding them. | https://en.wikipedia.org/wiki/Organizational_technoethics |
Organizing center may refer to: | https://en.wikipedia.org/wiki/Organizing_center |
The organising vision (OV) is a term developed by E. Burton Swanson and Neil Ramiller that defines how a vision is formed, a vision of how to organize structures and processes in regards to an information systems innovation. Images and ideas about an innovation from a wider community are brought together. The vision can often be characterised by buzzwords . While these are often seen as hype, they can be useful in giving a title to an organizing vision.
The vision serves three key functions: | https://en.wikipedia.org/wiki/Organizing_vision |
Organoastatine chemistry describes the synthesis and properties of organoastatine compounds , chemical compounds containing a carbon to astatine chemical bond .
Astatine is extremely radioactive, with the longest-lived isotope ( 210 At) having a half-life of only 8.1 hours. Consequently, organoastatine chemistry can only be studied by tracer techniques on extremely small quantities. The problems caused by radiation damage as well as difficulties in separation and identification are worse for organic astatine derivatives than for inorganic compounds. Most studies of organoastatine chemistry focus on 211 At (half-life 7.21 hours), which is the subject of ongoing studies in nuclear medicine : it is better than 131 I at destroying abnormal thyroid tissue. [ 1 ]
Astatine-labelled iodine reagents have been used to synthesise RAt, RAtCl 2 , R 2 AtCl, and RAtO 2 (R = phenyl or p -tolyl ). [ 1 ] Alkyl and aryl astatides are relatively stable and have been analysed at high temperatures (120 °C) with radio gas chromatography. [ 2 ] Demercuration reactions have produced with good yields trace quantities of 211 At-containing aromatic amino acids, steroids, and imidazoles, among other compounds. [ 1 ]
Astatine has both halogen-like and metallic properties, so that analogies with iodine sometimes hold, but sometimes do not. Astatine can be incorporated into organic molecules via halogen exchange, halodediazotation (replacing a diazonium group), halodeprotonation, or halodemetallation. Initial attempts to radiolabel proteins with 211 At exemplify its intermediate behaviour, as astatination (analogous to radioiodination) produces unstable results and it is instead AtO + (or a hydrolysed species) that probably bonds to proteins. Two-step procedures are used today, first synthesising stable astatoaryl prosthetic groups before incorporating them into the protein. [ 3 ] Not only is the C–At bond the weakest of all carbon–halogen bonds (following periodic trends), but also the bond easily breaks as the astatine is oxidised back to free astatine. [ 3 ]
This chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Organoastatine_chemistry |
Organoberyllium chemistry involves the synthesis and properties of organometallic compounds featuring the group 2 alkaline earth metal beryllium (Be). [ 2 ] The area remains less developed relative to the chemistry of other main-group elements , because Be compounds are toxic and few applications have been found. [ 3 ]
The coordination number of Be in organoberyllium compounds ranges from two to four. [ 4 ]
Dimethylberyllium and dimethylmagnesium adopts the same structure. [ 5 ] Diethylberyllium, however, does not structurally resemble diethylmagnesium (which has the same structure as dimethylmagnesium). [ 6 ] This contrast is attributed to the small size of Be relative to its heavier congener Mg: Be is one of the smallest atoms on the periodic table . [ 7 ] Dineopentylberyllium and many other dialkyl derivatives has been reported. [ 8 ]
The phenyl derivative is represented by trimeric Be 3 Ph 6 . [ 1 ] A terphenyl derivative is known. [ 9 ] With bulky aryl ligands three-coordination is observed, see Be(mesityl) 2 O(C 2 H 5 ) 2 . [ 8 ]
Organoberyllium compounds are typically prepared by transmetallation or alkylation of beryllium chloride . [ 10 ]
Beryllocene features both pi- and sigma-bonded cyclopentadienyl ligands. [ 11 ] [ 12 ] [ 13 ] It is prepared from BeCl 2 and potassium cyclopentadienide :
Many mixed ligand complexes are simply formed by addition of Lewis bases to diaryl and dialkylberyllium compounds. Many derivatives are known of the type BeR 2 L 2 and BAr 2 L 2 are known where L = thioether, pyridine, NHC, [ 14 ] and 1,4- Diazabutadienes . [ 15 ] Beryllium forms a variety of complexes with N -hetereocyclic carbenes (NHCs). [ 16 ] [ 17 ] [ 18 ]
While the +2-oxidation state is by far the most common for Be, compounds containing Be(I) and Be(0) have been described. A number of beryllium complexes with cyclic alkyl amino carbene (CAAC) ligands have been proposed to feature low-oxidation state beryllium centres. [ 19 ] [ 20 ] However, these low-oxidation state formulations have been contested due to the redox non-innocence of CAAC ligands. [ 21 ] [ 22 ] [ 23 ] Unambiguous low-oxidation state organo-beryllium complexes with Be–Be bonds have been synthesized by the group of Simon Aldridge . [ 24 ] [ 25 ]
Dimethylberyllium was reported in 1876. A. Atterberg produced this first organoberyllium compound by treatment of dimethylmercury with elemental beryllium. [ 26 ] The alkylation of beryllium halides was studied by H. Gilman. [ 27 ] [ 10 ] Early systematic work was conducted by G. E. Coates. [ 2 ] | https://en.wikipedia.org/wiki/Organoberyllium_chemistry |
Organocalcium chemistry is the chemistry of compounds containing a calcium to carbon bond , [ 1 ] or in broader definitions, organic compounds that contain calcium. [ 2 ] Although discovered around the same time as the now commonly utilized organomagnesium compounds , [ 3 ] organocalcium compounds were subject to greatly reduced interest due to drastic differences in stability. However, recent advances in stabilization of these highly reactive compounds has spurred increased interest in organocalcium compounds and allowed for multiple research directions to form. Because calcium metal is less reactive to organic reagents than magnesium [ 4 ] and the organocalcium compounds are more reactive than organomagnesium compounds, synthesis of novel compounds still poses a significant challenge. Calcium also has access to empty d orbitals that the lighter alkaline earth metals cannot access, and the degree to which this affects bonding and reactivity has sparked a fundamental debate. [ 5 ] [ 6 ] Lastly, despite the inherent instability of most organocalcium complexes, the unique basicity and size of the calcium ion together with the highly polarized bonds formed has opened up applications for organocalcium compounds in organic transformations and catalytic cycles .
In general, organocalcium synthesis is complicated by relatively unreactive calcium metal (compared to magnesium or the alkali metals due to a high atomization energy ) [ 7 ] [ 8 ] and high reactivity of most organocalcium compounds to oxygen, water, and even ethereal solvents . [ 9 ] To sustain the highly electropositive calcium center, the vast majority of compounds have anionic ligands by which they can be categorized, with neutral coordinating ligands utilized for increased stability.
The earliest organocalcium compounds to receive some sustained interest were alkyl- and arylcalcium compounds. The first of these was reported in 1905 by Ernst Beckmann , where synthesis of phenylcalcium iodide was claimed following stirring of calcium shavings with iodobenzene in diethyl ether (Et 2 O). [ 3 ] Subsequent study by Henry Gilman and Ferdinand Schulze argued that the isolated product in this report was actually the Et 2 O adduct of CaI 2 , [ 10 ] and, although phenylcalcium halides have been reported numerous times, [ 11 ] [ 12 ] [ 13 ] they are usually characterized through subsequent derivatization products. It took a full century until, in 2005, Matthias Westerhausen and colleagues obtained the first structural characterization of an arylcalcium compound, crystallizing phenylcalcium iodide as an adduct of tetrahydrofuran (THF) and calcium oxide . [ 14 ] A consistent challenge in the formation of organocalcium compounds has been the activation of calcium metal. Recent advancements in mechanochemistry have opened up simpler synthetic setups, with unactivated calcium being used to form arylcalcium reagents in situ during ball-milling. [ 15 ]
Allylcalcium compounds have also seen recent synthetic success, beginning with Timothy Hanusa and colleagues’ synthesis of a bis(allyl)calcium complex stabilized by sterically large, silyl substituents. [ 16 ] These successes have largely been driven by the use of salt metathesis reactions , where potassium salts of allyl anions exchange metals with a calcium halide, typically CaI 2 . This same strategy has been used to synthesize the unsubstituted complex Ca(η 3 -C 3 H 5 ) 2 as a soluble triglyme adduct. [ 17 ] This has been proven to be a versatile strategy, with a full series of substituted allylcalcium complexes of different sizes also characterized through a salt metathesis pathway. [ 18 ]
The carbon atom in the calcium-carbon bond takes on a significant negative charge. Because of the greater nucleophilicity of alkyl ligands, the alkylcalcium reagents are in general harder to synthesize than the arylcalcium compounds. [ 8 ] A common stabilizing strategy is to use bulky silyl [ 19 ] and phenyl [ 20 ] substituents to stabilize this negative charge. When targeting a Grignard analogue, the decreased reactivity from this method and the poor stability of the less protected methyl- and ethylcalcium halides has led to in situ generation of reactive alkylcalcium halides as the preferred method over the synthesis of isolable compounds. [ 21 ] Because of this poor stability, the pure organometallic dimethylcalcium was only isolated in 2018 by Reiner Anwander and colleagues as an insoluble, amorphous solid, with the THF adduct being structurally characterizable as a heptametallic cluster. [ 22 ]
Few calcium metallocenes (“calcocenes”) have been isolated, but they are of particular interest due to the insights into bonding that have come from their study. [ 23 ] The first synthesis of Cp 2 Ca (Cp = cyclopentadienyl) from calcium metal and cyclopentadiene in THF produced an insoluble, polymeric product. [ 24 ] A crystal structure showed that, unlike most transition metal metallocenes, the Cp-Ca-Cp angle is significantly bent and Cp 2 Ca has an opening that can be utilized to access derivatives. As seen in the first monomeric synthesis of a calcocene, ethereal solvents such as Et 2 O and THF almost always coordinate in this opening and can be challenging to remove through sublimation. [ 25 ] This bent structure can be leveraged into different coordination environments. For example, two butenyl-substituted Cp ligand will coordinate to Ca through both the five-membered rings and the olefins, but the olefins will not coordinate to Mg, where the Cp-Mg-Cp angle is not bent. [ 26 ]
Although low oxidation state beryllium and magnesium chemistry has developed significantly in the last two decades, [ 27 ] only a few reports exist of organocalcium compounds stabilizing any oxidation state other than Ca(II). [ 28 ] The first and only report of an isolable Ca(I) compound came in 2009, where two THF-coordinated Ca(I) ions sit on either side of an arene ring. [ 29 ] The π-antibonding orbitals of the sandwiched arene help stabilize the two calcium ions, which are further stabilized by the coordinating solvent. Other studies of Ca(I) were done at low temperatures in exotic conditions [ 30 ] or examine formally Ca(II) compounds that imply Ca(I)-containing intermediates either during synthesis or further reactivity. [ 31 ] [ 32 ] A landmark example of this from Sjoerd Harder and coworkers is the reported reduction of arenes and N 2 by a bridged Ca(I)-Ca(I) species generated in situ. [ 31 ] The ease of activating the normally inert N 2 to turn it into a strong reductant even at room temperature highlights the instability of Ca(I) species. Although not isolable as a Ca(I)-Ca(I) dimer, it possesses similar reactivity as a stronger reducing agent than a Mg(I) dimer.
There are several classes of calcium complexes that have become especially relevant despite not necessarily containing a Ca-C bond. The calcium amides, for example, have been investigated for numerous applications as a stoichiometric or catalytic reagent. Several modern synthetic strategies have allowed for a wide range of calcium amides to realized. Transmetalation , such as from a Sn(II) amide, allowed for the early preparation of amides yet again stabilized by bulky silyl groups. [ 33 ] Additional electronic and kinetic stabilization can be provided through carbenes , despite lacking the π-backbonding that other main group elements are capable of. [ 34 ] [ 35 ] A breakthrough in eliminating side product formation and other contamination was the development of mechanochemical syntheses that forgo the use of solvent. Simply ball-milling CaI 2 with a potassium amide salt yielded the corresponding bis(amido) complex. [ 36 ]
Inspired by the well-studied and useful solid-state CaH 2 , several molecular calcium hydrides have been synthesized with the hope of interesting small molecule activation. In 2006, Sjoerd Harder and Julie Brettar accomplished the synthesis of a well-defined, dimeric calcium hydride through the reaction of a calcium amide with phenylsilane . [ 37 ] Subsequent studies have expanded the library of stabilizing ligands, but all are multidentate ligands that coordinate through nitrogen sites. [ 38 ]
Several recent advances have been made in the synthesis of molecular calcium fluorides. The solid-state CaF 2 is an important source of fluorides for organofluorine compounds , but rely on dangerous HF intermediates. [ 39 ] The early well-characterized molecular calcium fluorides are clusters and are formed by reacting CaF 2 with large, multidentate ligands. [ 40 ] Recent work from Simon Aldridge and coworkers have resulted in more accessible fluoride coordination environments that can act as reagents for nucleophilic fluoride addition to organic compounds. [ 41 ] [ 42 ]
The changes in properties going down the alkaline earth group causes calcium to possess qualitatively entirely distinct bonding characteristics than the lighter beryllium and magnesium ions. In particular, calcium is significantly larger , more reducing , and has a much lower electronegativity . This enforces a strong preference for the Ca(II) oxidation state and an essentially ionic bond with carbon, which can be reasonably described as a carbanion in the Ca-C bond. [ 27 ]
A key difference in calcium bonding descriptions compared to magnesium and beryllium is the occasional use of the unfilled 3d orbitals to fully explain bonding and structural patterns. For example, the bent nature of calcocene, and the potentially bent geometry of CaH 2 , can be explained by increased involvement of the 3d orbitals in bonding. [ 23 ] [ 43 ] This has been highly debated, however, with other explanations invoking the polarizability of the larger Ca core [ 44 ] and a stabilizing van der Waals interaction between the two ligands. [ 45 ] A similar debate [ 5 ] [ 6 ] [ 46 ] is ongoing regarding the degree of π-backbonding in a Ca(CO) 8 complex. [ 30 ] Although still controversial, computational studies on the degree of sp-d hybridization [ 47 ] have caused some to label Ca as an honorary transition metal . [ 46 ]
Organocalcium compounds show some more similarities to organolithium chemistry over organomagnesium compounds. This is largely due to differences in electronegativity, which allow organocalcium compounds to function as a base more often than typical magnesium-based Grignard reagents do. [ 8 ] This basicity is exemplified by the facile deprotonation and subsequent cleavage of ethers such as THF. [ 48 ]
Another point of differentiation from the magnesium-based Grignard reagents is the higher positive charge localized on the calcium atom, due to the higher degree of ionicity in the Ca-C bond versus the Mg-C bond, which can enable unique reactivity not seen in the lighter alkaline earth compounds. For example, a dimeric Ca alkynide complex was shown to enable the coupling of two anionic alkynides to form an extended, fully double bonded four-carbon chain. [ 49 ] The previously mentioned in situ generation of reactive alkylcalcium species has also been successfully used to react with amines to form calcium amides. [ 21 ] This reactivity relies on fast ligand exchange of calcium Grignard reagents due to the ionic nature of this bond – the initially formed product is a heteroleptic calcium monoamide monohalide, but ligand exchange quickly forms the full calcium diamide and an insoluble calcium dihalide that drives the Schlenk equilibrium to completion. Non-Grignard alkylcalcium complexes have also shown unique reactivity, such as alkylation of benzene driven by the formation of a calcium hydride. [ 50 ]
Catalysis with organocalcium compounds has historically been limited due to poor stability. However, significant recent progress has been made in multiple areas of catalytic applications. Inspired by alkali metal-based organometallic compounds use in anionic polymerization, organocalcium compounds have also been investigated as polymerization catalysts. [ 2 ] For example, fast polymerization has been seen for polylactide synthesis with excellent selectivity for the isotactic form. [ 51 ] This is not only enabled by the previously discussed electronic and electrostatic differences, but also by the larger size of calcium in comparison to the alkali metals or magnesium. The larger size of calcium allows an unusual trigonal prismatic coordination geometry utilized throughout the mechanism. [ 52 ] The ionic nature of Ca-C bonding can also be leveraged for living polymerization , as was demonstrated for a stereoselective synthesis of polystyrene . [ 53 ]
Catalysis has also been performed using organocalcium compounds for a series of organic transformations. This most prominently includes hydroamination , where numerous viable substrates and modes of selectivity have been demonstrated. [ 2 ] [ 54 ] [ 55 ] Catalytic activity has also been shown for the analogous hydrophosphination , [ 56 ] the hydrogenation of alkene with dihydrogen, [ 57 ] regioselective hydrosilylation of conjugated alkenes, [ 58 ] and the hydroboration of alkenes, although the role of calcium in the latter mechanism is still debated. [ 59 ] The redistribution of arylsilane and hydrosilane groups has also been performed catalytically, relying on the cleavage and reformation of C-Si and Si-H bonds driven by the simultaneous cleavage and reformation of Ca-C and Ca-H bonds. [ 60 ] [ 61 ] | https://en.wikipedia.org/wiki/Organocalcium_chemistry |
In organic chemistry , organocatalysis is a form of catalysis in which the rate of a chemical reaction is increased by an organic catalyst. This "organocatalyst" consists of carbon , hydrogen , sulfur and other nonmetal elements found in organic compounds. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] Because of their similarity in composition and description, they are often mistaken as a misnomer for enzymes due to their comparable effects on reaction rates and forms of catalysis involved.
Organocatalysts which display secondary amine functionality can be described as performing either enamine catalysis (by forming catalytic quantities of an active enamine nucleophile ) or iminium catalysis (by forming catalytic quantities of an activated iminium electrophile). This mechanism is typical for covalent organocatalysis. Covalent binding of substrate normally requires high catalyst loading (for proline-catalysis typically 20–30 mol%).
Noncovalent interactions such as hydrogen-bonding facilitates low catalyst loadings (down to 0.001 mol%).
Organocatalysis offers several advantages. There is no need for metal-based catalysis thus making a contribution to green chemistry . In this context, simple organic acids have been used as catalyst for the modification of cellulose in water on multi-ton scale. [ 9 ] When the organocatalyst is chiral an avenue is opened to asymmetric catalysis ; for example, the use of proline in aldol reactions is an example of chirality and green chemistry. [ 10 ] Organic chemists David MacMillan and Benjamin List were both awarded the 2021 Nobel Prize in chemistry for their work on asymmetric organocatalysis. [ 11 ]
Regular achiral organocatalysts are based on nitrogen such as piperidine used in the Knoevenagel condensation . [ 12 ] DMAP used in esterifications [ 13 ] and DABCO used in the Baylis-Hillman reaction . [ 14 ] Thiazolium salts are employed in the Stetter reaction . These catalysts and reactions have a long history but current interest in organocatalysis is focused on asymmetric catalysis with chiral catalysts, called asymmetric organocatalysis or enantioselective organocatalysis . A pioneering reaction developed in the 1970s is called the Hajos–Parrish–Eder–Sauer–Wiechert reaction . Between 1968 and 1997, there were only a few reports of the use of small organic molecules as catalysts for asymmetric reactions (the Hajos–Parrish reaction probably being the most famous), but these chemical studies were viewed more as unique chemical reactions than as integral parts of a larger, interconnected field. [ 15 ]
In this reaction, naturally occurring chiral proline is the chiral catalyst in an aldol reaction . The starting material is an achiral triketone and it requires just 3% of proline to obtain the reaction product, a ketol in 93% enantiomeric excess . This is the first example of an amino acid-catalyzed asymmetric aldol reaction. [ 16 ] [ 17 ]
The asymmetric synthesis of the Wieland-Miescher ketone (1985) is also based on proline and another early application was one of the transformations in the total synthesis of Erythromycin by Robert B. Woodward (1981). [ 18 ] A mini-review digest article focuses on selected recent examples of total synthesis of natural and pharmaceutical products using organocatalytic reactions. [ 19 ]
Many chiral organocatalysts are an adaptation of chiral ligands (which together with a metal center also catalyze asymmetric reactions) and both concepts overlap to some degree.
A breakthrough in the field of organocatalysis came in 1997 when Yian Shi reported the first general, highly enantioselective organocatalytic reaction with the catalytic asymmetric epoxidation of trans- and trisubstituted olefins with chiral dioxiranes. [ 20 ] Since that time, several different types of reactions have been developed.
Organocatalysts for asymmetric synthesis can be grouped in several classes:
Examples of asymmetric reactions involving organocatalysts are:
Proline catalysis has been reviewed. [ 22 ] [ 23 ]
Imidazolidinones are catalysts for many transformations such as asymmetric Diels-Alder reactions and Michael additions . Chiral catalysts induce asymmetric reactions , often with high enantioselectivities. This catalyst works by forming an iminium ion with carbonyl groups of α,β-unsaturated aldehydes ( enals ) and enones in a rapid chemical equilibrium . This iminium activation is similar to activation of carbonyl groups by a Lewis acid and both catalysts lower the substrate's LUMO : [ 24 ] [ 25 ]
The transient iminium intermediate is chiral which is transferred to the reaction product via chiral induction . The catalysts have been used in Diels-Alder reactions , Michael additions , Friedel-Crafts alkylations , transfer hydrogenations and epoxidations .
One example is the asymmetric synthesis of the drug warfarin (in equilibrium with the hemiketal ) in a Michael addition of 4-hydroxycoumarin and benzylideneacetone : [ 26 ]
A recent exploit is the vinyl alkylation of crotonaldehyde with an organotrifluoroborate salt : [ 27 ]
For other examples of its use: see organocatalytic transfer hydrogenation and asymmetric Diels-Alder reactions .
A large group of organocatalysts incorporate the urea or the thiourea moiety. These catalytically effective (thio)urea derivatives termed (thio)urea organocatalysts provide explicit double hydrogen-bonding interactions to coordinate and activate H-bond accepting substrates. [ 28 ]
Their current uses are restricted to asymmetric multicomponent reactions, including those involving Michael addition, asymmetric multicomponent reactions for the synthesis of spirocycles, asymmetric multicomponent reactions involving acyl Strecker reactions, asymmetric Petasis reactions, asymmetric Biginelli reactions, asymmetric Mannich reactions, asymmetric aza-Henry reactions, and asymmetric reductive coupling reactions. [ 29 ] | https://en.wikipedia.org/wiki/Organocatalysis |
Organocerium chemistry is the science of organometallic compounds that contain one or more chemical bond between carbon and cerium . These compounds comprise a subset of the organolanthanides . Most organocerium compounds feature Ce(III) but some Ce(IV) derivatives are known.
Simple alkylcerium reagents are well known. One example is [Li(tmeda)] 3 Ce(CH 3 ) 6 . [ 1 ]
Although they are described as RCeCl 2 , their structures are far more complex.. [ 2 ] Furthermore, the solvent seems to alter the solution structure of the complex, with differences noted between reagents prepared in diethyl ether and tetrahydrofuran . There is evidence that the parent chloride forms a polymeric species in THF solution, of the form [Ce( μ -Cl) 2 (H 2 O)(THF) 2 ] n , but whether this type of polymer exists once the organometallic reagent is formed is unknown. [ 3 ]
Cyclopentadienyl derivatives of Ce are particularly well characterized. Hundreds have been examined by X-ray crystallography . The depicted (C 5 (CH 3 ) 4 H) 3 Ce is one of many. [ 4 ]
Some of the best characterized organocerium(IV) compounds feature cyclopentadienyl ligands, e.g. Ce(C 5 H 5 ) 3 Cl [ 5 ]
As reagents in organic chemistry, organocerium compounds are typically prepared in situ by treatment of cerium trichloride with organolithium or Grignard reagent . Reagents are derived from alkyl , alkynyl , and alkenyl organometallic reagents as well as enolates have been described. [ 6 ] [ 2 ] [ 7 ] [ 3 ] [ 8 ] The most common cerium source for this purpose is cerium(III) chloride , [ 9 ] which can be obtained in anhydrous form via dehydration of the commercially available hepta hydrate . Precomplexation with tetrahydrofuran is important for the success of the transmetallation, with most procedures involving "vigorous stirring for a period of no less than 2 hours". [ 2 ] The structures depicted (as below) for organocerium reagent, however are highly simplified.
These reagents add 1,2 to conjugated ketones and aldehydes . [ 10 ] This preference for direct addition is attributed to the oxophilicity of the cerium reagent, which activates the carbonyl for nucleophilic attack. [ 11 ]
Organocerium reagents are used almost exclusively for addition reactions in the same vein as organolithium and Grignard reagents.They are highly nucleophilic , allowing additions to imines [ 12 ] in the absence of additional Lewis acid catalysts , making them useful for substrates in which typical conditions fail. [ 2 ]
Despite this high reactivity, organocerium reagents are almost entirely non- basic , tolerating the presence of free alcohols and amines as well as enolizable α-protons. [ 2 ] [ 7 ]
They undergo 1,2-addition in reactions with conjugated electrophiles . At the same time, organocerium reagents can be used to synthesize ketones from acyl compounds without over-addition, as seen with organocuprates . [ 2 ]
Organocerium reagents have been employed in a number of total syntheses . Shown below is a key coupling step in the total synthesis of roseophilin , a potent antitumor antibiotic . [ 3 ] | https://en.wikipedia.org/wiki/Organocerium_chemistry |
Organogenesis is the phase of embryonic development that starts at the end of gastrulation and continues until birth . During organogenesis, the three germ layers formed from gastrulation (the ectoderm , endoderm , and mesoderm ) form the internal organs of the organism. [ 1 ]
The cells of each of the three germ layers undergo differentiation , a process where less-specialized cells become more-specialized through the expression of a specific set of genes. Cell differentiation is driven by cell signaling cascades. [ 2 ] Differentiation is influenced by extracellular signals such as growth factors that are exchanged to adjacent cells which is called juxtracrine signaling or to neighboring cells over short distances which is called paracrine signaling . [ 3 ] Intracellular signals – a cell signaling itself ( autocrine signaling ) – also play a role in organ formation. These signaling pathways allow for cell rearrangement and ensure that organs form at specific sites within the organism. [ 1 ] The organogenesis process can be studied using embryos and organoids. [ 4 ]
The endoderm is the inner most germ layer of the embryo which gives rise to gastrointestinal and respiratory organs by forming epithelial linings and organs such as the liver, lungs, and pancreas. [ 5 ] The mesoderm or middle germ layer of the embryo will form the blood, heart, kidney, muscles, and connective tissues. [ 5 ] The ectoderm or outermost germ layer of the developing embryo forms epidermis, the brain, and the nervous system. [ 5 ]
While each germ layer forms specific organs, in the 1820s, embryologist Heinz Christian Pander discovered that the germ layers cannot form their respective organs without the cellular interactions from other tissues. [ 1 ] In humans, internal organs begin to develop within 3–8 weeks after fertilization. The germ layers form organs by three processes: folds, splits, and condensation. [ 6 ] Folds form in the germinal sheet of cells and usually form an enclosed tube which you can see in the development of vertebrates neural tube. Splits or pockets may form in the germinal sheet of cells forming vesicles or elongations. The lungs and glands of the organism may develop this way. [ 6 ]
A primary step in organogenesis for chordates is the development of the notochord , which induces the formation of the neural plate , and ultimately the neural tube in vertebrate development. The development of the neural tube will give rise to the brain and spinal cord. [ 1 ] Vertebrates develop a neural crest that differentiates into many structures, including bones, muscles, and components of the central nervous system . Differentiation of the ectoderm into the neural crest, neural tube, and surface ectoderm is sometimes referred to as neurulation and the embryo in this phase is the neurula. The coelom of the body forms from a split of the mesoderm along the somite axis [ 1 ]
Organogenesis in plants occurs continuously and only stops when the plant dies. In the shoot , the shoot apical meristems regularly produce new lateral organs ( leaves , flowers , or fruits) and lateral branches. In the root , new lateral roots form from weakly differentiated internal tissue (e.g. the xylem -pole pericycle in the model plant Arabidopsis thaliana ). In vitro and in response to specific cocktails of hormones (mainly auxins and cytokinins ), most plant tissues can de-differentiate and form a mass of dividing totipotent stem cells called a callus . Organogenesis can then occur from those cells. The type of organ that is formed depends on the relative concentrations of the hormones in the medium. Plant organogenesis can be induced in tissue culture and used to regenerate plants. [ 7 ] | https://en.wikipedia.org/wiki/Organogenesis |
Organography (from Greek όργανο , organo , " organ "; and -γραφή , -graphy ) is the scientific description of the structure and function of the organs of living things.
Organography as a scientific study starts with Aristotle , who considered the parts of plants as "organs" and began to consider the relationship between different organs and different functions. In the 17th century Joachim Jung, [ 1 ] clearly articulated that plants are composed of different organ types such as root, stem and leaf, and he went on to define these organ types on the basis of form and position.
In the following century Caspar Friedrich Wolff [ 2 ] was able to follow the development of organs from the "growing points" or apical meristems. He noted the commonality of development between foliage leaves and floral leaves (e.g. petals) and wrote: "In the whole plant, whose parts we wonder at as being, at the first glance, so extraordinarily diverse, I finally perceive and recognize nothing beyond leaves and stem (for the root may be regarded as a stem). Consequently all parts of the plant, except the stem, are modified leaves."
Similar views were propounded at by Goethe in his well-known treatise. [ 3 ] He wrote: "The underlying relationship between the various external parts of the plant, such as the leaves, the calyx, the corolla, the stamens, which develop one after the other and, as it were, out of one another, has long been generally recognized by investigators, and has in fact been specially studied; and the operation by which one and the same organ presents itself to us in various forms has been termed Metamorphosis of Plants." | https://en.wikipedia.org/wiki/Organography |
An organoid is a miniaturised and simplified version of an organ produced in vitro in three dimensions that mimics the key functional, structural, and biological complexity of that organ. [ 1 ] It is derived from one or a few cells from a tissue , embryonic stem cells , or induced pluripotent stem cells , which can self-organize in three-dimensional culture owing to their self-renewal and differentiation capacities. The technique for growing organoids has rapidly improved since the early 2010s, and The Scientist named it one of the biggest scientific advancements of 2013. [ 2 ] Scientists and engineers use organoids to study development and disease in the laboratory , for drug discovery and development in industry, [ 3 ] personalized diagnostics and medicine, gene and cell therapies, tissue engineering, and regenerative medicine.
Attempts to create organs in vitro started with one of the first dissociation-reaggregation experiments [ 4 ] where Henry Van Peters Wilson demonstrated that mechanically dissociated sponge cells can reaggregate and self-organize to generate a whole organism. [ 5 ] In the subsequent decades, multiple labs were able to generate different types of organs [ 4 ] in vitro through the dissociation and reaggregation of organ tissues obtained from amphibians [ 6 ] and embryonic chicks. [ 7 ] The formation of first tissue-like colonies in vitro was observed for the first time by co-culturing keratinocytes and 3T3 fibroblasts. [ 8 ] The phenomena of mechanically dissociated cells aggregating and reorganizing to reform the tissue they were obtained from subsequently led to the development of the differential adhesion hypothesis by Malcolm Steinberg . [ 4 ] With the advent of the field of stem cell biology, the potential of stem cells to form organs in vitro was realized early on with the observation that when stem cells form teratomas or embryoid bodies , the differentiated cells can organize into different structures resembling those found in multiple tissue types. [ 4 ] The advent of the field of organoids, started with a shift from culturing and differentiating stem cells in two dimensional (2D) media, to three dimensional (3D) media to allow for the development of the complex 3-dimensional structures of organs. [ 4 ] Utilization of 3D media culture media methods for the structural organization was made possible with the development of extracellular matrices (ECM). [ 9 ] In the late 1980s, Bissell and colleagues showed that a laminin rich gel can be used as a basement membrane for differentiation and morphogenesis in cell cultures of mammary epithelial cells. [ 10 ] [ 11 ] Since 1987, researchers have devised different methods for 3D culturing, and were able to utilize different types of stem cells to generate organoids resembling a multitude of organs. [ 4 ] In the 1990s, in addition to their role in physical support, the role of ECM components in gene expression by their interaction with integrin-based focal adhesion pathways was reported. [ 12 ] In 2006, Yaakov Nahmias and David Odde showed the self-assembly of vascular liver organoid maintained for over 50 days in vitro . [ 13 ] In 2008, Yoshiki Sasai and his team at RIKEN institute demonstrated that stem cells can be coaxed into balls of neural cells that self-organize into distinctive layers. [ 14 ] In 2009 the Laboratory of Hans Clevers at Hubrecht Institute and University Medical Center Utrecht , Netherlands, showed that single LGR5 -expressing intestinal stem cells self-organize to crypt-villus structures in vitro without necessity of a mesenchymal niche, making them the first organoids. [ 15 ] In 2010, Mathieu Unbekandt & Jamie A. Davies demonstrated the production of renal organoids from murine fetus-derived renogenic stem cells. [ 16 ] In 2014, Qun Wang and co-workers engineered collagen-I and laminin based gels and synthetic foam biomaterials for the culture and delivery of intestinal organoids [ 17 ] and encapsulated DNA-functionalized gold nanoparticles into intestinal organoids to form an intestinal Trojan horse for drug delivery and gene therapy. [ 18 ] Subsequent reports showed significant physiological function of these organoids in vitro [ 19 ] and in vivo . [ 20 ] [ 21 ]
Other significant early advancements included in 2013, Madeline Lancaster at the Institute of Molecular Biotechnology of the Austrian Academy of Sciences established a protocol starting from pluripotent stem cells to generate cerebral organoids that mimic the developing human brain's cellular organization. [ 22 ] Meritxell Huch and Craig Dorrell at Hubrecht Institute and University Medical Center Utrecht demonstrated that single Lgr5+ cells from damaged mouse liver can be clonally expanded as liver organoids in Rspo1-based culture medium over several months. [ 23 ] In 2014, Artem Shkumatov et al. at the University of Illinois at Urbana-Champaign demonstrated that cardiovascular organoids can be formed from ES cells through modulation of the substrate stiffness, to which they adhere. Physiological stiffness promoted three-dimensionality of EBs and cardiomyogenic differentiation. [ 24 ]
Lancaster and Knoblich [ 4 ] define an organoid as a collection of organ-specific cell types that develops from stem cells or organ progenitors, self-organizes through cell sorting and spatially restricted lineage commitment in a manner similar to in vivo , and exhibits the following properties:
Organoid formation generally requires culturing the stem cells or progenitor cells in a 3D medium. [ 4 ] Stem cells have the ability to self-renew and differentiate into various cell subtypes, and they enable understanding the processes of development and disease progression. [ 25 ] Therefore organoids derived from stem cells enable studying biology and physiology at the organ level. [ 26 ] The 3D medium can be made using an extracellular matrix hydrogel such as Matrigel or Cultrex BME, which is a laminin -rich extracellular matrix that is secreted by the Engelbreth-Holm-Swarm tumor line. [ 10 ] Organoid bodies can then be made through embedding stem cells in the 3D medium. [ 4 ] When pluripotent stem cells are used for the creation of the organoid, the cells are usually, but not all the time, allowed to form embryoid bodies . [ 4 ] Those embryoid bodies are then pharmacologically treated with patterning factors to drive the formation of the desired organoid identity. [ 4 ] Organoids have also been created using adult stem cells extracted from the target organ, and cultured in 3D media. [ 27 ]
Biochemical cues have been incorporated in 3D organoid cultures and with exposure of morphogenes, morphogen inhibitors, or growth factors, organoid models can be developed using embryonic stem cells (ESCs) or adult stem cells (ASCs). Vascularization techniques can be utilized to embody microenvironments that are close to their counterparts, physiologically. Vasculature systems that can facilitate oxygen or nutrients to the inner mass of organoids can be achieved through microfluidic systems, vascular endothelial growth factor delivery systems, and endothelial cell-coated modules. [ 9 ] With patient-derived induced pluripotent stem cells (iPSCs) [ 28 ] and CRISPR/Cas -based genome editing [ 29 ] technologies, genome-edited or mutated pluripotent stem cells (PSCs) with altered signaling cues can be generated to control intrinsic cues within organoids.
A multitude of organ structures have been recapitulated using organoids. [ 4 ] This section aims to outline the state of the field as of now through providing an abridged list of the organoids that have been successfully created, along with a brief outline based on the most recent literature for each organoid, and examples of how it has been utilized in research.
A cerebral organoid describes artificially grown, in vitro , miniature organs resembling the brain . Cerebral organoids are created by culturing human pluripotent stem cells in a three-dimensional structure using rotational bioreactor and develop over the course of months. [ 22 ] The procedure has potential applications in the study of brain development, physiology and function. Cerebral organoids may experience "simple sensations" in response to external stimulation and neuroscientists are among those expressing concern that such organs could develop sentience . They propose that further evolution of the technique needs to be subject to a rigorous oversight procedure. [ 30 ] [ 31 ] [ 32 ] In 2023, researchers have built a hybrid biocomputer that combines laboratory-grown human brain organoids with conventional circuits, and can complete tasks such as voice recognition. [ 33 ] Cerebral Organoids are currently being used to research and develop Organoid Intelligence (OI) technologies. [ 34 ]
Gastrointestinal organoids refer to organoids that recapitulate structures of the gastrointestinal tract . The gastrointestinal tract arises from the endoderm , which during development forms a tube that can be divided in three distinct regions, which give rise to, along with other organs, the following sections of the gastrointestinal tract: [ 4 ]
Organoids have been created for the following structures of the gastrointestinal tract:
Intestinal organoids [ 15 ] have thus far been among the gut organoids generated directly from intestinal tissues or pluripotent stem cells. [ 4 ] One way human pluripotent stem cells can be driven to form intestinal organoids is through first the application of activin A to drive the cells into a mesoendodermal identity, followed by the pharmacological upregulation of Wnt3a and Fgf4 signaling pathways as they have been demonstrated to promote posterior gut fate. [ 4 ] Intestinal organoids have also been generated from intestinal stem cells, extracted from adult tissue and cultured in 3D media. [ 27 ] These adult stem cell-derived organoids are often referred to as enteroids or colonoids, depending on their segment of origin, and have been established from both the human and murine intestine. [ 15 ] [ 35 ] [ 36 ] Intestinal organoids consist of a single layer of polarized intestinal epithelial cells surrounding a central lumen. As such, recapitulate the crypt-villus structure of the intestine, by recapitulating its function, physiology and organization, and maintaining all the cell types found normally in the structure including intestinal stem cells. [ 4 ] Thus, intestinal organoids are a valuable model to study intestinal nutrient transport, [ 37 ] [ 38 ] drug absorption and delivery, [ 39 ] [ 40 ] nanomaterials and nanomedicine, [ 41 ] [ 42 ] incretin hormone secretion, [ 43 ] [ 44 ] and infection by various enteropathogens. [ 45 ] [ 46 ] For example, Qun Wang's team rationally designed artificial virus nanoparticles as oral drug delivery vehicles (ODDVs) with gut organoid-derived mucosal models [ 47 ] and demonstrated a new concept of using newly established colon organoids as tools for high-throughput drug screening, toxicity testing, and oral drug development. [ 48 ] Or recently, Sakib, S., and Zou, S. developed graphene oxide nanoparticles for delivering siRNA regulating expression of tumor necrosis factor-α, that aimed to treat intestinal organoids exhibiting an inflammatory phenotype. [ 49 ] Intestinal organoids also recapitulate the crypt-Villus structure to such a high degree of fidelity that they have been successfully transplanted to mouse intestines, and are hence highly regarded as a valuable model for research. [ 4 ] One of the fields of research that intestinal organoids have been utilized is that of stem cell niche. Intestinal organoids were used to study the nature of the intestinal stem cell niche , and research done with them demonstrated the positive role IL-22 has in maintaining in intestinal stem cells, [ 50 ] along with demonstrating the roles of other cell types like neurons and fibroblasts in maintenance of intestinal stem cells. [ 27 ] In the field of infection biology, different intestinal organoid-based model systems have been explored. On one hand, organoids can be infected in bulk by simply mixing them with the enteropathogen of interest. [ 51 ] However, to model infection via a more natural route starting from the intestinal lumen, microinjection of the pathogen is required. [ 52 ] [ 53 ] In addition, the polarity of intestinal organoids can be inverted, [ 54 ] and they can even be dissociated into single cells and cultured as 2D monolayers [ 55 ] [ 56 ] in order to make both the apical and basolateral sides of the epithelium more easily accessible. Intestinal organoids have also demonstrated therapeutic potential. [ 57 ]
In order to more accurately recapitulate the intestine in vivo , co-cultures of intestinal organoids and immune cells have been developed. [ 56 ] Furthermore, organ-on-a-chip models combine intestinal organoids with other cell types such as endothelial or immune cells as well as peristaltic flow. [ 58 ] [ 59 ]
Gastric organoids recapitulate at least partly the physiology of the stomach . Gastric organoids have been generated directly from pluripotent stem cells through the temporal manipulation of the FGF , WNT , BMP , retinoic acid and EGF signalling pathways in three-dimensional culture conditions. [ 60 ] Gastric organoids have also been generated using LGR5 expressing stomach adult stem cells . [ 61 ] Gastric organoids have been used as model for the study of cancer [ 62 ] [ 63 ] along with human disease [ 60 ] and development. [ 60 ] For example, one study [ 63 ] investigated the underlying genetic alterations behind a patient's metastatic tumor population , and identified that unlike the patient's primary tumor, the metastasis had both alleles of the TGFBR2 gene mutated. To further assess the role of TGFBR2 in the metastasis, the investigators created organoids where TGFBR2 expression is knocked down, through which they were able to demonstrate that reduced TGFBR2 activity leads to invasion and metastasis of cancerous tumors both in vitro and in vivo .
Lingual organoids are organoids that recapitulate, at least partly, aspects of the tongue physiology. Epithelial lingual organoids have been generated using BMI1 expressing epithelial stem cells in three-dimensional culture conditions through the manipulation of EGF , WNT , and TGF-β . [ 64 ] This organoid culture, however, lacks taste receptors , as these cells do not arise from Bmi1 expressing epithelial stem cells. [ 64 ] Lingual taste bud organoids containing taste cells, however, have been created using the LGR5 + or CD44 + stem/progenitor cells of circumvallate (CV) papilla tissue. [ 65 ] These taste bud organoids have been successfully created both directly from isolated Lgr5- or LGR6 -expressing taste stem/progenitor cells. [ 66 ] and indirectly, through the isolation, digestion, and subsequent culturing of CV tissue containing Lgr5+ or CD44+ stem/progenitor cells. [ 65 ]
Cerebellar organoid or hind brain organoids tend to recapitulate the cellular diversity of the fetal cerebellum along with some of its distinct cytoarchitectural features. The generation of cerebellar tissue from PSCs requires a secondary induction which leads to the formation of isthmic organizer, which first appears in the cell aggregate in 3D culture. [ 67 ] [ 68 ] Over the years this area of research has led to cerebellar organoid development which involves the patterning of human pluripotent stem cells resulting in the generation of both cerebellar excitatory and inhibitory progenitor populations. This includes the rhombic lip and the ventricular zone progenitors. Although further resarch is still ongoing in context of functional and morphological development of Purkinje cells over a longer period of developmental time. [ 69 ] [ 70 ]
3D organoid models of brain cancer derived from either patient derived explants (PDX) or direct from cancer tissue is now easily achievable and affords high-throughput screening of these tumors against the current panel of approved drugs form around the world.
Self-assembled cell aggregates consisting of BMECs, astrocytes, and pericytes are emerging as a potential alternative to transwell and microfluidic models for certain applications. These organoides can generate many features of the BBB, such as the expression of tight junctions, molecular transporters, and drug efflux pumps, and can therefore be used to model drug transport across the BBB. Also, they can serve as a model for evaluating the interactions between the BBB and adjacent brain tissue and provide a platform for understanding the combined abilities of a new drug to overcome the BBB and its effect on brain tissue. In addition, such models are highly scalable and easier to manufacture and operate than microfluidic devices. However, they have limited ability to reconstruct the morphology and physiology of the BBB and are unable to simulate physiological flow and shear stress .
Organoids enable to study how cells interact together in an organ, their interaction with their environment, how diseases affect them and the effect of drugs. In vitro culture makes this system easy to manipulate and facilitates their monitoring. While organs are difficult to culture because their size limits the penetration of nutrients, the small size of organoids limits this problem. On the other hand, they do not exhibit all organ features and interactions with other organs are not recapitulated in vitro . While research on stem cells and regulation of stemness was the first field of application of intestinal organoids, [ 15 ] they are now also used to study e.g. uptake of nutrients, drug transport and secretion of incretin hormones. [ 106 ] This is of great relevance in the context of malabsorption diseases as well as metabolic diseases such as obesity , insulin resistance , and diabetes .
Organoids provide an opportunity to create cellular models of human disease, which can be studied in the laboratory to better understand the causes of disease and identify possible treatments. The power of organoids in this regard was first shown for a genetic form of microcephaly , where patient cells were used to make cerebral organoids , which were smaller and showed abnormalities in early generation of neurons. [ 22 ] In another example, the genome editing system called CRISPR was applied to human pluripotent stem cells to introduce targeted mutations in genes relevant to two different kidney diseases, polycystic kidney disease and focal segmental glomerulosclerosis . [ 87 ] These CRISPR-modified pluripotent stem cells were subsequently grown into human kidney organoids, which exhibited disease-specific phenotypes. Kidney organoids from stem cells with polycystic kidney disease mutations formed large, translucent cyst structures from kidney tubules. When cultured in the absence of adherent cues (in suspension), these cysts reached sizes of 1 cm in diameter over several months. [ 107 ] Kidney organoids with mutations in a gene linked to focal segmental glomerulosclerosis developed junctional defects between podocytes, the filtering cells affected in that disease. [ 108 ] Importantly, these disease phenotypes were absent in control organoids of identical genetic background, but lacking the CRISPR mutations. [ 87 ] [ 107 ] [ 108 ] Comparison of these organoid phenotypes to diseased tissues from mice and humans suggested similarities to defects in early development. [ 107 ] [ 108 ]
As first developed by Takahashi and Yamanaka in 2007, induced pluripotent stem cells (iPSC) can also be reprogrammed from patient skin fibroblasts. [ 109 ] These stem cells carry the exact genetic background of the patient including any genetic mutations which might contribute to the development of human disease. Differentiation of these cells into kidney organoids has been performed from patients with Lowe Syndrome due to ORCL1 mutations. [ 110 ] This report compared kidney organoids differentiated from patient iPSC to unrelated control iPSC and demonstrated an inability of patient kidney cells to mobilise transcription factor SIX2 from the golgi complex . [ 110 ] Because SIX2 is a well characterised marker of nephron progenitor cells in the cap mesenchyme , the authors concluded that renal disease frequently seen in Lowe Syndrome (global failure of proximal tubule reabsorption or renal Fanconi syndrome ) could be related to alteration in nephron patterning arising from nephron progenitor cells lacking this important SIX2 gene expression. [ 110 ]
Other studies have used CRISPR gene editing to correct the patient's mutation in the patient iPSC cells to create an isogenic control, which can be performed simultaneously with iPSC reprogramming. [ 111 ] [ 112 ] [ 113 ] Comparison of a patient iPSC derived organoid against an isogenic control is the current gold standard in the field as it permits isolation of the mutation of interest as the only variable within the experimental model. [ 114 ] In one such report, kidney organoids derived from iPSC of a patient with Mainzer-Saldino Syndrome due to compound heterozygous mutations in IFT140 were compared to an isogenic control organoid in which an IFT140 variant giving rise to a non-viable mRNA transcript was corrected by CRISPR. [ 112 ] Patient kidney organoids demonstrated abnormal ciliary morphology consistent with existing animal models which was rescued to wild type morphology in the gene corrected organoids. [ 112 ] Comparative transcriptional profiling of epithelial cells purified from patient and control organoids highlighted pathways involved in cell polarity , cell-cell junctions and dynein motor assembly, some of which had been implicated for other genotypes within the phenotypic family of renal ciliopathies. [ 112 ] Another report utilising an isogenic control demonstrated abnormal nephrin localisation in the glomeruli of kidney organoids generated from a patient with congenital nephrotic syndrome . [ 113 ]
Things such as epithelial metabolism can also be modelled. [ 115 ]
Intestinal organoids grown from rectal biopsies using culture protocols established by the Clevers group have been used to model cystic fibrosis , [ 116 ] and led to the first application of organoids for personalised treatment. [ 117 ] Cystic fibrosis is an inherited disease that is caused by gene mutations of the cystic fibrosis transmembrane conductance regulator gene that encodes an epithelial ion channel necessary for healthy epithelial surface fluids. Studies by the laboratory of Jeffrey Beekman (Wilhelmina Children's Hospital, University Medical Center Utrecht, The Netherlands) described in 2013 that stimulation of colorectal organoids with cAMP-raising agonists such as forskolin or cholera toxin induced rapid swelling of organoids in a fully CFTR dependent manner. [ 116 ] Whereas organoids from non-cystic fibrosis subjects swell in response to forskolin as a consequence of fluid transport into the organoids' lumens, this is severely reduced or absent in organoids derived from people with cystic fibrosis. Swelling could be restored by therapeutics that repair the CFTR protein (CFTR modulators), indicating that individual responses to CFTR modulating therapy could be quantitated in a preclinical laboratory setting. Schwank et al. also demonstrated that the intestinal cystic fibrosis organoid phenotype could be repaired by CRISPR-Cas9 gene editing in 2013. [ 118 ]
Follow-up studies by Dekkers et al. in 2016 revealed that quantitative differences in forskolin-induced swelling between intestinal organoids derived from people with cystic fibrosis associate with known diagnostic and prognostic markers such as CFTR gene mutations or in vivo biomarkers of CFTR function. [ 117 ] In addition, the authors demonstrated that CFTR modulator responses in intestinal organoids with specific CFTR mutations correlated with published clinical trial data of these treatments. This led to preclinical studies where organoids from patients with extremely rare CFTR mutations for who no treatment was registered were found to respond strongly to a clinically available CFTR modulator. The suggested clinical benefit of treatment for these subjects based on the preclinical organoid test was subsequently confirmed upon clinical introduction of treatment by members of the clinical CF center under supervision of Kors van der Ent (Department of Paediatric Pulmonology, Wilhelmina Children's Hospital, University Medical Center Utrecht, The Netherlands). These studies show for the first time that organoids can be used for the individual tailoring of therapy or personalised medicine .
The self-renewal and regenerative properties of intestinal organoids make them promising candidates for transplantation therapies, particularly for disease involving epithelial barrier disruption. Notably, transplantation of organoids into the duodenum of mice has been shown to aid in the recovery of mucosal damages on mice with ischemia-reperfusion injury. [ 119 ]
The first successful transplantation of an organoid into a human, a patient with ulcerative colitis whose cells were used for the organoid, was carried out in 2022. [ 120 ] [ 121 ]
Organoids offer researchers an exceptional model to study developmental biology . [ 122 ] Since the identification of pluripotent stem cells , there have been great advancements in directing pluripotent stem cells fate in vitro using 2D cultures. [ 122 ] These advancements in PSC fate direction, coupled with the advancements in 3D culturing techniques allowed for the creation of organoids that recapitulate the properties of various specific subregions of a multitude of organs. [ 122 ] The use of these organoids has thus greatly contributed to expanding our understanding of the processes of organogenesis , and the field of developmental biology. [ 122 ] In central nervous system development, for example, organoids have contributed to our understanding of the physical forces that underlie retinal cup formation. [ 122 ] [ 123 ] More recent work has extended cortical organoid growth periods extensively and at nearly a year under specific differentiation conditions, the organoids persist and have some features of human fetal development stages. [ 124 ] | https://en.wikipedia.org/wiki/Organoid |
Organoid intelligence ( OI ) is an emerging field of study in computer science and biology that develops and studies biological wetware computing using 3D cultures of human brain cells (or brain organoids ) and brain-machine interface technologies. [ 1 ] Such technologies may be referred to as OIs.
Oragnoid intelligent computer systems can be an example of biohybrid systems .
As opposed to traditional non-organic silicon-based approaches, OI seeks to use lab-grown cerebral organoids to serve as "biological hardware." Scientists hope that such organoids can provide faster, more efficient, and more powerful computing power than regular silicon-based computing and AI while requiring only a fraction of the energy. However, while these structures are still far from being able to think like a regular human brain and do not yet possess strong computing capabilities, OI research currently offers the potential to improve the understanding of brain development, learning and memory, potentially finding treatments for neurological disorders such as dementia . [ 1 ]
Thomas Hartung, [ 2 ] a professor from Johns Hopkins University , argues that "while silicon-based computers are certainly better with numbers, brains are better at learning." Furthermore, he claimed that with "superior learning and storing" capabilities than AIs, being more energy efficient, and that in the future, it might not be possible to add more transistors to a single computer chip , while brains are wired differently and have more potential for storage and computing power, OIs can potentially harness more power than current computers. [ 1 ]
Some researchers claim that even though human brains are slower than machines at processing simple information, they are far better at processing complex information as brains can deal with fewer and more uncertain data, perform both sequential and parallel processing, being highly heterogenous, use incomplete datasets, and is said to outperform non-organic machines in decision-making. [ 1 ]
Training OIs involve the process of biological learning (BL) as opposed to machine learning (ML) for AIs. BL is said to be much more energy efficient than ML. [ 1 ]
OI generates complex biological data, necessitating sophisticated methods for processing and analysis. [ 3 ] Bioinformatics provides the tools and techniques to decipher raw data, uncovering the patterns and insights. A Python interface is currently available for processing and interaction with brain organoids. [ 4 ]
Brain-inspired computing hardware aims to emulate the structure and working principles of the brain and could be used to address current limitations in artificial intelligence technologies. However, brain-inspired silicon chips are still limited in their ability to fully mimic brain function, as most examples are built on digital electronic principles. One study performed OI computation (which they termed Brainoware ) by sending and receiving information from the brain organoid using a high-density multielectrode array. By applying spatiotemporal electrical stimulation, nonlinear dynamics, and fading memory properties, as well as unsupervised learning from training data by reshaping the organoid functional connectivity, the study showed the potential of this technology by using it for speech recognition and nonlinear equation prediction in a reservoir computing framework. [ 5 ]
While researchers are hoping to use OI and biological computing to complement traditional silicon-based computing, there are also questions about the ethics of such an approach. Examples of such ethical issues include OIs gaining consciousness and sentience as organoids and the question of the relationship between a stem cell donor (for growing the organoid) and the respective OI system. [ 6 ]
Enforced amnesia and limits on duration of operation without memory reset have been proposed as a way to mitigate the potential risk of silent suffering in brain organoids. [ 7 ] | https://en.wikipedia.org/wiki/Organoid_intelligence |
Organometallic chemistry is the study of organometallic compounds , chemical compounds containing at least one chemical bond between a carbon atom of an organic molecule and a metal , including alkali , alkaline earth , and transition metals , and sometimes broadened to include metalloids like boron, silicon, and selenium, as well. [ 1 ] [ 2 ] Aside from bonds to organyl fragments or molecules, bonds to 'inorganic' carbon, like carbon monoxide ( metal carbonyls ), cyanide , or carbide , are generally considered to be organometallic as well. Some related compounds such as transition metal hydrides and metal phosphine complexes are often included in discussions of organometallic compounds, though strictly speaking, they are not necessarily organometallic. The related but distinct term " metalorganic compound " refers to metal-containing compounds lacking direct metal-carbon bonds but which contain organic ligands. Metal β-diketonates, alkoxides , dialkylamides, and metal phosphine complexes are representative members of this class. The field of organometallic chemistry combines aspects of traditional inorganic and organic chemistry . [ 3 ]
Organometallic compounds are widely used both stoichiometrically in research and industrial chemical reactions, as well as in the role of catalysts to increase the rates of such reactions (e.g., as in uses of homogeneous catalysis ), where target molecules include polymers, pharmaceuticals, and many other types of practical products.
Organometallic compounds are distinguished by the prefix "organo-" (e.g., organopalladium compounds), and include all compounds which contain a bond between a metal atom and a carbon atom of an organyl group . [ 2 ] In addition to the traditional metals ( alkali metals , alkali earth metals , transition metals , and post transition metals ), lanthanides , actinides , semimetals, and the elements boron , silicon , arsenic , and selenium are considered to form organometallic compounds. [ 2 ] Examples of organometallic compounds include Gilman reagents , which contain lithium and copper , and Grignard reagents , which contain magnesium . Boron-containing organometallic compounds are often the result of hydroboration and carboboration reactions. Tetracarbonyl nickel and ferrocene are examples of organometallic compounds containing transition metals . Other examples of organometallic compounds include organolithium compounds such as n -butyllithium (n-BuLi), organozinc compounds such as diethylzinc (Et 2 Zn), organotin compounds such as tributyltin hydride (Bu 3 SnH), organoborane compounds such as triethylborane (Et 3 B), and organoaluminium compounds such as trimethylaluminium (Me 3 Al). [ 3 ]
A naturally occurring organometallic complex is methylcobalamin (a form of Vitamin B 12 ), which contains a cobalt - methyl bond. This complex, along with other biologically relevant complexes are often discussed within the subfield of bioorganometallic chemistry . [ 4 ]
Many complexes feature coordination bonds between a metal and organic ligands . Complexes where the organic ligands bind the metal through a heteroatom such as oxygen or nitrogen are considered coordination compounds (e.g., heme A and Fe(acac) 3 ). However, if any of the ligands form a direct metal-carbon (M-C) bond, then the complex is considered to be organometallic. Although the IUPAC has not formally defined the term, some chemists use the term "metalorganic" to describe any coordination compound containing an organic ligand regardless of the presence of a direct M-C bond. [ 5 ]
The status of compounds in which the canonical anion has a negative charge that is shared between ( delocalized ) a carbon atom and an atom more electronegative than carbon (e.g. enolates ) may vary with the nature of the anionic moiety, the metal ion, and possibly the medium. In the absence of direct structural evidence for a carbon–metal bond, such compounds are not considered to be organometallic. [ 2 ] For instance, lithium enolates often contain only Li-O bonds and are not organometallic, while zinc enolates ( Reformatsky reagents ) contain both Zn-O and Zn-C bonds, and are organometallic in nature. [ 3 ]
The metal-carbon bond in organometallic compounds is generally highly covalent . [ 1 ] For highly electropositive elements, such as lithium and sodium, the carbon ligand exhibits carbanionic character, but free carbon-based anions are extremely rare, an example being cyanide .
Most organometallic compounds are solids at room temperature, however some are liquids such as methylcyclopentadienyl manganese tricarbonyl , or even volatile liquids such as nickel tetracarbonyl . [ 1 ] Many organometallic compounds are air sensitive (reactive towards oxygen and moisture), and thus they must be handled under an inert atmosphere . [ 1 ] Some organometallic compounds such as triethylaluminium are pyrophoric and will ignite on contact with air. [ 6 ]
As in other areas of chemistry, electron counting is useful for organizing organometallic chemistry. The 18-electron rule is helpful in predicting the stabilities of organometallic complexes, for example metal carbonyls and metal hydrides . The 18e rule has two representative electron counting models, ionic and neutral (also known as covalent) ligand models, respectively. [ 7 ] The hapticity of a metal-ligand complex, can influence the electron count. [ 7 ] Hapticity (η, lowercase Greek eta), describes the number of contiguous ligands coordinated to a metal. [ 7 ] For example, ferrocene , [(η 5 -C 5 H 5 ) 2 Fe], has two cyclopentadienyl ligands giving a hapticity of 5, where all five carbon atoms of the C 5 H 5 ligand bond equally and contribute one electron to the iron center. Ligands that bind non-contiguous atoms are denoted the Greek letter kappa, κ. [ 7 ] Chelating κ2-acetate is an example. The covalent bond classification method identifies three classes of ligands, X,L, and Z; which are based on the electron donating interactions of the ligand. Many organometallic compounds do not follow the 18e rule. The metal atoms in organometallic compounds are frequently described by their d electron count and oxidation state . These concepts can be used to help predict their reactivity and preferred geometry . Chemical bonding and reactivity in organometallic compounds is often discussed from the perspective of the isolobal principle .
A wide variety of physical techniques are used to determine the structure, composition, and properties of organometallic compounds. X-ray diffraction is a particularly important technique that can locate the positions of atoms within a solid compound, providing a detailed description of its structure. [ 1 ] [ 8 ] Other techniques like infrared spectroscopy and nuclear magnetic resonance spectroscopy are also frequently used to obtain information on the structure and bonding of organometallic compounds. [ 1 ] [ 8 ] Ultraviolet-visible spectroscopy is a common technique used to obtain information on the electronic structure of organometallic compounds. It is also used monitor the progress of organometallic reactions, as well as determine their kinetics . [ 8 ] The dynamics of organometallic compounds can be studied using dynamic NMR spectroscopy . [ 1 ] Other notable techniques include X-ray absorption spectroscopy , [ 9 ] electron paramagnetic resonance spectroscopy , and elemental analysis . [ 1 ] [ 8 ]
Due to their high reactivity towards oxygen and moisture, organometallic compounds often must be handled using air-free techniques . Air-free handling of organometallic compounds typically requires the use of laboratory apparatuses such as a glovebox or Schlenk line . [ 1 ]
Early developments in organometallic chemistry include Louis Claude Cadet 's synthesis of methyl arsenic compounds related to cacodyl , William Christopher Zeise 's [ 10 ] platinum-ethylene complex , [ 11 ] Edward Frankland 's discovery of diethyl- and dimethylzinc , Ludwig Mond 's discovery of Ni(CO) 4 , [ 1 ] and Victor Grignard 's organomagnesium compounds. (Although not always acknowledged as an organometallic compound, Prussian blue , a mixed-valence iron-cyanide complex, was first prepared in 1706 by paint maker Johann Jacob Diesbach as the first coordination polymer and synthetic material containing a metal-carbon bond. [ 12 ] ) The abundant and diverse products from coal and petroleum led to Ziegler–Natta , Fischer–Tropsch , hydroformylation catalysis which employ CO, H 2 , and alkenes as feedstocks and ligands.
Recognition of organometallic chemistry as a distinct subfield culminated in the Nobel Prizes to Ernst Fischer and Geoffrey Wilkinson for work on metallocenes . In 2005, Yves Chauvin , Robert H. Grubbs and Richard R. Schrock shared the Nobel Prize for metal-catalyzed olefin metathesis . [ 13 ]
Subspecialty areas of organometallic chemistry include:
Organometallic compounds find wide use in commercial reactions, both as homogenous catalysts and as stoichiometric reagents . For instance, organolithium , organomagnesium , and organoaluminium compounds , examples of which are highly basic and highly reducing, are useful stoichiometrically but also catalyze many polymerization reactions. [ 14 ]
Almost all processes involving carbon monoxide rely on catalysts, notable examples being described as carbonylations . [ 15 ] The production of acetic acid from methanol and carbon monoxide is catalyzed via metal carbonyl complexes in the Monsanto process and Cativa process . Most synthetic aldehydes are produced via hydroformylation . The bulk of the synthetic alcohols, at least those larger than ethanol, are produced by hydrogenation of hydroformylation-derived aldehydes. Similarly, the Wacker process is used in the oxidation of ethylene to acetaldehyde . [ 16 ]
Almost all industrial processes involving alkene -derived polymers rely on organometallic catalysts. The world's polyethylene and polypropylene are produced via both heterogeneously via Ziegler–Natta catalysis and homogeneously, e.g., via constrained geometry catalysts . [ 17 ]
Most processes involving hydrogen rely on metal-based catalysts. Whereas bulk hydrogenations (e.g., margarine production) rely on heterogeneous catalysts, for the production of fine chemicals such hydrogenations rely on soluble (homogenous) organometallic complexes or involve organometallic intermediates. [ 18 ] Organometallic complexes allow these hydrogenations to be effected asymmetrically.
Many semiconductors are produced from trimethylgallium , trimethylindium , trimethylaluminium , and trimethylantimony . These volatile compounds are decomposed along with ammonia , arsine , phosphine and related hydrides on a heated substrate via metalorganic vapor phase epitaxy (MOVPE) process in the production of light-emitting diodes (LEDs).
Organometallic compounds undergo several important reactions:
The synthesis of many organic molecules are facilitated by organometallic complexes. Sigma-bond metathesis is a synthetic method for forming new carbon-carbon sigma bonds . Sigma-bond metathesis is typically used with early transition-metal complexes that are in their highest oxidation state. [ 19 ] Using transition-metals that are in their highest oxidation state prevents other reactions from occurring, such as oxidative addition . In addition to sigma-bond metathesis, olefin metathesis is used to synthesize various carbon-carbon pi bonds . Neither sigma-bond metathesis or olefin metathesis change the oxidation state of the metal. [ 20 ] [ 21 ] Many other methods are used to form new carbon-carbon bonds, including beta-hydride elimination and insertion reactions .
Organometallic complexes are commonly used in catalysis. Major industrial processes include hydrogenation , hydrosilylation , hydrocyanation , olefin metathesis , alkene polymerization , alkene oligomerization , hydrocarboxylation , methanol carbonylation , and hydroformylation . [ 16 ] Organometallic intermediates are also invoked in many heterogeneous catalysis processes, analogous to those listed above. Additionally, organometallic intermediates are assumed for Fischer–Tropsch process .
Organometallic complexes are commonly used in small-scale fine chemical synthesis as well, especially in cross-coupling reactions [ 22 ] that form carbon-carbon bonds, e.g. Suzuki-Miyaura coupling , [ 23 ] Buchwald-Hartwig amination for producing aryl amines from aryl halides, [ 24 ] and Sonogashira coupling , etc.
Natural and contaminant organometallic compounds are found in the environment. Some that are remnants of human use, such as organolead and organomercury compounds, are toxicity hazards. Tetraethyllead was prepared for use as a gasoline additive but has fallen into disuse because of lead's toxicity. Its replacements are other organometallic compounds, such as ferrocene and methylcyclopentadienyl manganese tricarbonyl (MMT). [ 25 ] The organoarsenic compound roxarsone is a controversial animal feed additive. In 2006, approximately one million kilograms of it were produced in the U.S alone. [ 26 ] Organotin compounds were once widely used in anti-fouling paints but have since been banned due to environmental concerns. [ 27 ] | https://en.wikipedia.org/wiki/Organometallic_chemistry |
Organometallics is a biweekly journal published by the American Chemical Society . Its area of focus is organometallic and organometalloid chemistry. This peer-reviewed journal has an impact factor of 3.837 as reported by the 2021 Journal Citation Reports [ 1 ] by Thomson Reuters .
Since 2015 Paul Chirik is the editor-in-chief of Organometallics . [ 2 ] He is an American chemist and the Edwards S. Sanford Professor of Chemistry at Princeton University, and associate director for external partnerships of the Andlinger Center for Energy and the Environment. [ 3 ] He writes about the catalysis of hydrocarbons.
Past editors-in-chief are Dietmar Seyferth and John Gladysz. [ 4 ] This journal is indexed in Chemical Abstracts Service (CAS), British Library , CAB International , EBSCOhost , ProQuest , PubMed , SCOPUS , SwetsWise, and Web of Science .
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The Organon ( Ancient Greek : Ὄργανον , meaning "instrument, tool, organ") is the standard collection of Aristotle 's six works on logical analysis and dialectic . The name Organon was given by Aristotle's followers, the Peripatetics , who maintained against the Stoics that Logic was "an instrument" of Philosophy. [ 1 ]
Aristotle never uses the title Organon to refer to his logical works. The book, according to M. Barthélemy St. Hilaire , was not called "Organon" before the 15th century, and the treatises were collected into one volume, as is supposed, about the time of Andronicus of Rhodes ; and it was translated into Latin by Boethius about the 6th century. [ 1 ]
The six works of Organon are as follows:
The order of the works is not chronological (which is now hard to determine) but was deliberately chosen by Theophrastus to constitute a well-structured system. Indeed, parts of them seem to be a scheme of a lecture on logic. The arrangement of the works was made by Andronicus of Rhodes around 40 BC. [ 2 ]
Aristotle's Metaphysics has some points of overlap with the works making up the Organon but is not traditionally considered part of it; additionally, there are works on logic attributed, with varying degrees of plausibility, to Aristotle that were not known to the Peripatetics. [ 3 ]
Whereas the Organon of the Latin Scholastic tradition comprises only the above six works, its independent reception in the Arabic medieval world saw appended to this list of works Aristotle's Rhetoric and Poetics . [ 4 ]
The Organon was used in the school founded by Aristotle at the Lyceum , and some parts of the works seem to be a scheme of a lecture on logic. So much so that after Aristotle's death, his publishers ( Andronicus of Rhodes in 50 BC, for example) collected these works.
Following the collapse of the Western Roman Empire in the fifth century, much of Aristotle's work was lost in the Latin West. The Categories and On Interpretation are the only significant logical works that were available in the early Middle Ages . These had been translated into Latin by Boethius , along with Porphyry's Isagoge , which was also translated into Arabic by Ibn al-Muqaffa' via a Syriac intermediary. The other logical works were not available in Western Christendom until translated into Latin in the 12th century . However, the original Greek texts had been preserved in the Greek -speaking lands of the Eastern Roman Empire (aka Byzantium ). In the mid-twelfth century, James of Venice translated into Latin the Posterior Analytics from Greek manuscripts found in Constantinople.
The books of Aristotle were available in the early Muslim world, and after 750 AD Muslims had most of them [ dubious – discuss ] , including the Organon , translated into Arabic, normally via earlier Syriac translations. They were studied by Islamic and Jewish scholars, including Rabbi Moses Maimonides (1135–1204) and the Muslim Judge Ibn Rushd , known in the West as Averroes (1126–1198); both were originally from Córdoba, Spain , although the former left Iberia and by 1168 lived in Egypt .
All the major scholastic philosophers wrote commentaries on the Organon . Aquinas , Ockham and Scotus wrote commentaries on On Interpretation . Ockham and Scotus wrote commentaries on the Categories and Sophistical Refutations . Grosseteste wrote an influential commentary on the Posterior Analytics .
In the Enlightenment there was a revival of interest in logic as the basis of rational enquiry , and a number of texts, most successfully the Port-Royal Logic , polished Aristotelian term logic for pedagogy . During this period, while the logic certainly was based on that of Aristotle, Aristotle's writings themselves were less often the basis of study. There was a tendency in this period to regard the logical systems of the day to be complete, which in turn no doubt stifled innovation in this area. However, Francis Bacon published his Novum Organum ("The New Organon ") as a scathing attack in 1620 . [ 5 ] Immanuel Kant thought that there was nothing else to invent after the work of Aristotle, [ 6 ] and the famous logic historian Karl von Prantl claimed that any logician who said anything new about logic was "confused, stupid or perverse." These examples illustrate the force of influence which Aristotle's works on logic had. Indeed, he had already become known by the Scholastics (medieval Christian scholars) as "The Philosopher", due to the influence he had upon medieval theology and philosophy. His influence continued into the Early Modern period and Organon was the basis of school philosophy even in the beginning of the 18th century. [ 7 ] Since the logical innovations of the 19th century, particularly the formulation of modern predicate logic , Aristotelian logic had for a time fallen out of favor among many analytic philosophers .
However, the logic historian John Corcoran and others have shown that the works of George Boole and Gottlob Frege —which laid the groundwork for modern mathematical logic—each represent a continuation and extension to Aristotle's logic and in no way contradict or displace it. [ 8 ] [ 9 ] Boole fully accepted and endorsed Aristotle's logic, and Frege included Aristotle's square of opposition at the end of his groundbreaking Begriffsschrift to show the harmony of his theory with the Aristotelian tradition. [ 10 ]
Primary sources
Studies | https://en.wikipedia.org/wiki/Organon |
Organoniobium chemistry is the chemistry of compounds containing niobium - carbon (Nb-C) bonds. Compared to the other group 5 transition metal organometallics , the chemistry of organoniobium compounds most closely resembles that of organotantalum compounds. Organoniobium compounds of oxidation states +5, +4, +3, +2, +1, 0, −1, and −3 have been prepared, with the +5 oxidation state being the most common. [ 1 ]
Unlike vanadium, which forms the neutral hexacarbonyl, niobium does not easily form an analogous complex. The salts of the anionic binary carbonyl, [Nb(CO) 6 ] − , are however well characterized. They are obtained by reduction of NbCl 5 under an atmosphere of CO.
A wide variety of alkyl Nb compounds have been prepared. Low coordination number complexes require the absence of any β-hydrogen to prevent rapid β-hydride elimination. [ 2 ] The simplest compounds are salts of [Nb(CH 3 ) 6 ] − , which is prepared by alkylation of NbF 5 using methyl lithium : [ 3 ]
The first organoniobium compound fully characterized was Cp 2 NbBr 3 , [ 4 ] however the paramagnetic Nb(IV) metallocenes such as niobocene dichloride are more prevalent. Complexes are typically prepared by treatment of NbCl 5 with NaCp to form the bis(cyclopentadienyl) complex followed by further functionalization. Derivatives of pentamethylcyclopentadiene are also known, such as (C 5 Me 5 ) 2 NbH 3 . [ 2 ]
Niobium carbonyls supported by Cp ligands can be prepared at various oxidation states of Nb and serve as useful precursors in niobium carbonyl chemistry. [ 5 ]
Along with the related organotantalum species, niobium alkylidenes were among the first Scrock carbenes studied. The first syntheses of these complexes involved addition of organolithium reagents lacking β-hydrogens into hindered Nb(V) complexes followed by α-proton elimination. As compared to tantalum alkylidenes, niobium alkylidenes are less thermally and hydrolytically stable. [ 6 ]
Similar to other d 2 transition metals, Nb(III) produce adducts with alkynes. These derivatives are sometimes called Nb(V) alkenediyls metallacyclopropenes. [ 7 ] These alkendiyl complexes function as latent dianion equivalents. They react with electrophiles to give alkene derivatives. [ 7 ] [ 8 ]
No commercial applications of organoniobium compounds have been reported. They have found limited use in organic synthesis.
A prominent early synthetic application of organoniobium chemistry was the use of dimethoxyethane niobium trichloride, NbCl 3 (DME), as a reagent for the reductive coupling of imines with carbonyl compounds to form amino alcohols . [ 9 ] This reagent has found further use in other pinacol -type reductive couplings. [ 10 ] [ 8 ]
A number of formal [2+2+2] cycloadditions have been realized under Nb catalysis, including alkyne trimerizations and couplings of alkynes with alkenes or nitriles to form cyclohexadienes or pyridines, respectively. Typically a Nb(III) catalyst will form a Nb(V) metallocyclopropene with a terminal alkyne component and then engage in sequential migratory insertions and reductive elimination to furnish the six membered ring and regenerate the Nb(III). [ 8 ]
An organoniobium catalyst has also been developed for (Z)-selective semihydrogenation of alkynes. The mechanistic pathway for this reaction is distinct from other transition metal catalyzed hydrogenations, proceeding through the Nb(V) metallocyclopropene which engages with hydrogen either through direct sigma-bond metathesis or outer sphere 1,2-addition. [ 11 ] | https://en.wikipedia.org/wiki/Organoniobium_chemistry |
Organophosphines are organophosphorus compounds with the formula PR n H 3− n , where R is an organic substituent. These compounds can be classified according to the value of n : primary phosphines ( n = 1), secondary phosphines ( n = 2), tertiary phosphines ( n = 3). All adopt pyramidal structures. [ 1 ] Organophosphines are generally colorless, lipophilic liquids or solids. [ 2 ] The parent of the organophosphines is phosphine (PH 3 ). [ 3 ]
Organophophines are classified according to the number of organic substituents.
Primary (1°) phosphines, with the formula RPH 2 , in principle are derived by alkylation of phosphine. Some simple alkyl derivatives such as methylphosphine (CH 3 PH 2 ) can be prepared by alkylation of phosphine in the presence of base: [ 4 ]
A more common synthetic route involves reduction of chlorophosphines with hydride reagents. For example, reduction of dichlorophenylphosphine with lithium aluminium hydride affords phenylphosphine according to the following idealized equation: [ 5 ]
Most primary phosphines are pyrophoric in air. [ 6 ]
Secondary (2°) phosphines, with the formula R 2 PH, are prepared analogously to the primary phosphines. They are also obtained by alkali-metal reductive cleavage of triarylphosphines followed by hydrolysis of the resulting phosphide salt. The latter route is employed to prepare diphenylphosphine (Ph 2 PH). Diorganophosphinic acids, R 2 P(O)OH, can also be reduced with diisobutylaluminium hydride . Secondary phosphines are mildly protic in character.
Secondary phosphines occur in cyclic forms. Three-membered rings are phosphiranes (unsaturated: phosphirenes ), five-membered rings are phospholanes (unsaturated: phosphole ), and six-membered rings are phosphinanes .
Tertiary (3°) phosphines, with the formula R 3 P, are traditionally prepared by alkylation of phosphorus trichloride using Grignard reagents or related organolithium compounds:
In the case of trimethylphosphine , triphenyl phosphite is used in place of the highly electrophilic PCl 3 : [ 7 ]
Slightly more elaborate methods are employed for the preparation of unsymmetrical tertiary phosphines, with the formula R 2 R'P. The use of organophosphorus-based nucleophiles is typical. For example, lithium diphenylphosphide is readily methylated with methyl iodide to give methyldiphenylphosphine :
Phosphine is a precursor to some tertiary phosphines by hydrophosphination of alkenes. For example, in the presence of basic catalysts PH 3 adds of Michael acceptors such as acrylonitrile : [ 8 ]
Tertiary phosphines of the type PRR′R″ are " P -chiral " and optically stable.
From the commercial perspective, the most important phosphine is triphenylphosphine , several million kilograms being produced annually. It is prepared from the reaction of chlorobenzene , PCl 3 , and sodium. [ 9 ] Phosphines of a more specialized nature are usually prepared by other routes. [ 10 ]
Diphosphines are also available in primary, secondary, and tertiary phosphorus substituents. Triphosphines etc. are similar.
Organophosphines, like phosphine itself, are pyramidal molecules with approximate C 3 v symmetry . The C–P–C bond angles are approximately 98.6°. [ 3 ] The C–P–C bond angles are consistent with the notion that phosphorus predominantly uses the 3p orbitals for forming bonds and that there is little sp hybridization of the phosphorus atom. The latter is a common feature of the chemistry of phosphorus. As a result, the lone pair of trimethylphosphine has predominantly s-character as is the case for phosphine, PH 3 . [ 11 ]
Tertiary phosphines are pyramidal. When the organic substituents all differ, the phosphine is chiral and configurationally stable (in contrast to NRR'R"). Complexes derived from the chiral phosphines can catalyse reactions to give chiral , enantioenriched products.
The phosphorus atom in phosphines has a formal oxidation state −3 (σ 3 λ 3 ) and are the phosphorus analogues of amines . Like amines, phosphines have a trigonal pyramidal molecular geometry although often with smaller C-E-C angles (E = N, P), at least in the absence of steric effects. The C-P-C bond angle is 98.6° for trimethylphosphine increasing to 109.7° when the methyl groups are replaced by tert -butyl groups. When used as ligands, the steric bulk of tertiary phosphines is evaluated by their cone angle . The barrier to pyramidal inversion is also much higher than nitrogen inversion to occur, and therefore phosphines with three different substituents can be resolved into thermally stable optical isomers . Phosphines are often less basic than corresponding amines, for instance the phosphonium ion itself has a p K a of −14 compared to 9.21 for the ammonium ion; trimethylphosphonium has a p K a of 8.65 compared to 9.76 for trimethylammonium . However, triphenylphosphine (p K a 2.73) is more basic than triphenylamine (p K a −5), mainly because the lone pair of the nitrogen in NPh 3 is partially delocalized into the three phenyl rings. Whereas the lone pair on nitrogen is delocalized in pyrrole , the lone pair on phosphorus atom in the phosphorus equivalent of pyrrole ( phosphole ) is not. The reactivity of phosphines matches that of amines with regard to nucleophilicity in the formation of phosphonium salts with the general structure PR 4 + X − . This property is used in the Appel reaction for converting alcohols to alkyl halides . Phosphines are easily oxidized to the corresponding phosphine oxides , whereas amine oxides are less readily generated. In part for this reason, phosphines are very rarely encountered in nature.
Tertiary phosphines are often used as ligands in coordination chemistry. The binding of phosphines bind to metals, which serve as Lewis acids . For example, silver chloride reacts with triphenylphosphine to 1;1 and 1:2 complexes:
The adducts formed from phosphines and borane are useful reagents. These phosphine-boranes are air-stable, but the borane protecting group can be removed by treatment with amines. [ 12 ] [ 13 ]
Akin to complexation, phosphines are readily alkylated. For example, methyl bromide converts triphenylphosphine to the methyltriphenylphosphonium bromide , a "quat salt":
Phosphines are nucleophilic catalysts in organic synthesis , e.g. the Rauhut–Currier reaction and Baylis-Hillman reaction .
Like phosphine itself, but easier, organophosphines undergo protonation. The reaction is reversible. Whereas organophosphines are oxygen-sensitive, the protonated derivatives are not.
Primary and secondary derivatives, they can be deprotonated by strong bases to give organo phosphide derivatives. Thus diphenylphosphine reacts with organolithium reagent to give lithium diphenylphosphide :
Tertiary phosphines characteristically oxidize to give phosphine oxides with the formula R 3 PO. The reaction with oxygen is spin-forbidden but still proceeds at sufficient rate that samples of tertiary phosphines are characteristically contaminated with phosphine oxides. Qualitatively, the rates of oxidation are higher for trialkyl vs triarylphosphines. Faster still are oxidations using hydrogen peroxide . Primary and secondary phosphines also oxidize, but the product(s) are subject to tautomerization and further oxidation.
Tertiary phosphines characteristically oxidize to give phosphine sulfides .
The reducing properties of organophosphiines is also illustrated in the Staudinger reduction for the conversion of organic azides to amines and in the Mitsunobu reaction for converting alcohols into esters. In these processes, the phosphine is oxidized to phosphorus(V). Phosphines have also been found to reduce activated carbonyl groups, for instance the reduction of an α-keto ester to an α-hydroxy ester in scheme 2 . [ 14 ] In the proposed reaction mechanism , the first proton is on loan from the methyl group in trimethylphosphine (triphenylphosphine does not react).
Primary (RPH 2 ) and secondary phosphines (RRPH and R 2 PH) add to alkenes in presence of a strong base (e.g., KOH in DMSO ). Markovnikov's rules apply. Similar reactions occur involving alkynes . [ 15 ] Base is not required for electron-deficient alkenes (e.g., derivatives of acrylonitrile ) and alkynes.
Primary and secondary phosphines do not normally add to ketones and aldehydes unless the addition closes a ring: [ 16 ] | https://en.wikipedia.org/wiki/Organophosphine |
An organophosphinic acid is an organophosphorus compound with the formula R 2−n H n PO 2 H (R = alkyl , aryl ). One or both P-H bonds in the parent hypophosphorous acid (aka phosphinic acid) are replaced by organic groups. The Cyanex family of dialkylphosphinic acids are used in hydrometallurgy to extract metals from ores.
Monoalkylphosphinic acids have the formula OP(OH)(H)R, with the simplest example being methylphosphinic acid .
Phosphinic acid adds to Michael acceptors , for example with acrylamide it gives H(HO)P(O)CH 2 CH 2 C(O)NH 2 .
Dialkylphosphinic acids have the formula R 2 PO 2 H, where R is an alkyl or aryl group. The phosphorus(V) center has tetrahedral molecular geometry . Under the brand names Aerophine and Cyanex, dialkylphosphinic acids are used in extraction and separation of metals as one of the techniques of hydrometallurgy [ 1 ] Characteristically the organic substituents are branched to confer solubility and preclude crystallization. [ 2 ]
Formaldehyde and H 3 PO 2 react to give (HOCH 2 ) 2 PO 2 H.
The dithiodialkyphosphinic acids (R 2 PS 2 H) are related to the diorganodithiophosphates with the formula (RO) 2 PS 2 H, which are also used as complexing agents in the purification of metals. The phosphates are more prone to hydrolysis owing to the greater lability of the RO-P linkage vs the direct C-P bond. | https://en.wikipedia.org/wiki/Organophosphinic_acid |
Organophosphorus chemistry is the scientific study of the synthesis and properties of organophosphorus compounds , which are organic compounds containing phosphorus . [ 1 ] They are used primarily in pest control as an alternative to chlorinated hydrocarbons that persist in the environment. Some organophosphorus compounds are highly effective insecticides , although some are extremely toxic to humans, including sarin and VX nerve agents. [ 2 ]
Phosphorus, like nitrogen , is in group 15 of the periodic table, and thus phosphorus compounds and nitrogen compounds have many similar properties. [ 3 ] [ 4 ] [ 5 ] The definition of organophosphorus compounds is variable, which can lead to confusion. In industrial and environmental chemistry, an organophosphorus compound need contain only an organic substituent , but need not have a direct phosphorus-carbon (P-C) bond. [ citation needed ] Thus a large proportion of pesticides (e.g., malathion ), are often included in this class of compounds.
Phosphorus can adopt a variety of oxidation states , and it is general to classify organophosphorus compounds based on their being derivatives of phosphorus(V) vs phosphorus(III), which are the predominant classes of compounds. In a descriptive but only intermittently used nomenclature, phosphorus compounds are identified by their coordination number σ and their valency λ . In this system, a phosphine is a σ 3 λ 3 compound.
Phosphate esters have the general structure P(=O)(OR) 3 feature P(V). Such species are of technological importance as flame retardant agents, and plasticizers . Lacking a P−C bond, these compounds are in the technical sense not organophosphorus compounds but esters of phosphoric acid. Many derivatives are found in nature, such as phosphatidylcholine . Phosphate ester are synthesized by alcoholysis of phosphorus oxychloride. A variety of mixed amido-alkoxo derivatives are known, one medically significant example being the anti-cancer drug cyclophosphamide . Also derivatives containing the thiophosphoryl group (P=S) include the pesticide malathion . The organophosphates prepared on the largest scale are the zinc dithiophosphates , as additives for motor oil. Several million kilograms of this coordination complex are produced annually by the reaction of phosphorus pentasulfide with alcohols. [ 6 ]
Phosphoryl thioates are thermodynamically much stabler than thiophosphates, which can rearrange at high temperature or with a catalytic alkylant to the former: [ 7 ] : 73–76
In the environment, all these phosphorus(V) compounds break down via hydrolysis to eventually afford phosphate and the organic alcohol or amine from which they are derived.
Phosphonates are esters of phosphonic acid and have the general formula RP(=O)(OR') 2 . Phosphonates have many technical applications, a well-known member being glyphosate , better known as Roundup. With the formula (HO) 2 P(O)CH 2 NHCH 2 CO 2 H, this derivative of glycine is one of the most widely used herbicides. Bisphosphonates are a class of drugs to treat osteoporosis . The nerve gas agent sarin , containing both C–P and F–P bonds, is a phosphonate. [ citation needed ]
Phosphinates feature two P–C bonds, with the general formula R 2 P(=O)(OR'). A commercially significant member is the herbicide glufosinate . Similar to glyphosate mentioned above, it has the structure CH 3 P(O)(OH)CH 2 CH 2 CH(NH 2 )CO 2 H.
The Michaelis–Arbuzov reaction is the main method for the synthesis of these compounds. For example, dimethylmethylphosphonate (see figure above) arises from the rearrangement of trimethylphosphite , which is catalyzed by methyl iodide . In the Horner–Wadsworth–Emmons reaction and the Seyferth–Gilbert homologation , phosphonates are used in reactions with carbonyl compounds. The Kabachnik–Fields reaction is a method for the preparation of aminophosphonates. These compounds contain a very inert bond between phosphorus and carbon. Consequently, they hydrolyze to give phosphonic and phosphinic acid derivatives, but not phosphate. [ citation needed ]
Phosphine oxides (designation σ 4 λ 5 ) have the general structure R 3 P=O with formal oxidation state +5. Phosphine oxides form hydrogen bonds and some are therefore soluble in water. The P=O bond is very polar with a dipole moment of 4.51 D for triphenylphosphine oxide . [ citation needed ]
Compounds related to phosphine oxides include phosphine imides (R 3 PNR') and related chalcogenides (R 3 PE, where E = S , Se , Te ). These compounds are some of the most thermally stable organophosphorus compounds. In general, they are less basic than the corresponding phosphine oxides, which can adduce to thiophosphoryl halides: [ 7 ] : 73
Some phosphorus sulfides can undergo a reverse Arbuzov rearrangement to a dialkylthiophosphinate ester. [ 7 ] : 55
Compounds with the formula [PR 4 + ]X − comprise the phosphonium salts . These species are tetrahedral phosphorus(V) compounds. From the commercial perspective, the most important member is tetrakis(hydroxymethyl)phosphonium chloride , [P(CH 2 OH) 4 ]Cl, which is used as a fire retardant in textiles . Approximately 2M kg are produced annually of the chloride and the related sulfate. [ 6 ] They are generated by the reaction of phosphine with formaldehyde in the presence of the mineral acid:
A variety of phosphonium salts can be prepared by alkylation and arylation of organophosphines:
The methylation of triphenylphosphine is the first step in the preparation of the Wittig reagent.
The parent phosphorane (σ 5 λ 5 ) is PH 5 , which is unknown. [ citation needed ] Related compounds containing both halide and organic substituents on phosphorus are fairly common. Those with five organic substituents are rare, although P(C 6 H 5 ) 5 is known, being derived from P(C 6 H 5 ) 4 + by reaction with phenyllithium . [ citation needed ]
Phosphorus ylides are unsaturated phosphoranes, known as Wittig reagents , e.g. CH 2 P(C 6 H 5 ) 3 . These compounds feature tetrahedral phosphorus(V) and are considered relatives of phosphine oxides. They also are derived from phosphonium salts, but by deprotonation not alkylation. [ citation needed ]
Phosphites, sometimes called phosphite esters , have the general structure P(OR) 3 with oxidation state +3. Such species arise from the alcoholysis of phosphorus trichloride:
The reaction is general, thus a vast number of such species are known. Phosphites are employed in the Perkow reaction and the Michaelis–Arbuzov reaction . They also serve as ligands in organometallic chemistry.
Intermediate between phosphites and phosphines are phosphonites (P(OR) 2 R') and phosphinite (P(OR)R' 2 ). Such species arise via alcoholysis reactions of the corresponding phosphonous and phosphinous chlorides ((PCl 2 R') and (PClR' 2 ) , respectively). The latter are produced by reaction of a phosphorus trichloride with a poor metal -alkyl complex, e.g. organomercury , organolead , or a mixed lithium - organoaluminum compound. [ 8 ]
The parent compound of the phosphines is PH 3 , called phosphine in the US and British Commonwealth, but phosphane elsewhere. [ 9 ] Replacement of one or more hydrogen centers by an organic substituents (alkyl, aryl), gives PH 3−x R x , an organophosphine, generally referred to as phosphines. [ citation needed ]
From the commercial perspective, the most important phosphine is triphenylphosphine , several million kilograms being produced annually. It is prepared from the reaction of chlorobenzene , PCl 3 , and sodium. [ 6 ] Phosphines of a more specialized nature are usually prepared by other routes. [ 10 ] Phosphorus halides undergo nucleophilic displacement by organometallic reagents such as Grignard reagents . Organophosphines are nucleophiles and ligands . Two major applications are as reagents in the Wittig reaction and as supporting phosphine ligands in homogeneous catalysis . [ citation needed ]
Their nucleophilicity is evidenced by their reactions with alkyl halides to give phosphonium salts . Phosphines are nucleophilic catalysts in organic synthesis , e.g. the Rauhut–Currier reaction and Baylis-Hillman reaction . Phosphines are reducing agents , as illustrated in the Staudinger reduction for the conversion of organic azides to amines and in the Mitsunobu reaction for converting alcohols into esters. In these processes, the phosphine is oxidized to phosphorus(V). Phosphines have also been found to reduce activated carbonyl groups, for instance the reduction of an α-keto ester to an α-hydroxy ester. [ 11 ]
A few halophosphines are known, although phosphorus' strong nucleophilicity predisposes them to decomposition, and dimethylphosphinyl fluoride spontaneously disproportionates to dimethylphosphine trifluoride and tetramethylbiphosphine . [ 12 ] One common synthesis adds halogens to tetramethylbiphosphine disulfide . [ 13 ] Alternatively alkylation of phosphorus trichloride gives a halophosphonium cation, which metals reduce to halophosphines.
Compounds with carbon phosphorus(III) multiple bonds are called phosphaalkenes (R 2 C=PR) and phosphaalkynes (RC≡P). They are similar in structure, but not in reactivity, to imines (R 2 C=NR) and nitriles (RC≡N), respectively. In the compound phosphorine , one carbon atom in benzene is replaced by phosphorus. Species of this type are relatively rare but for that reason are of interest to researchers. A general method for the synthesis of phosphaalkenes is by 1,2-elimination of suitable precursors, initiated thermally or by base such as DBU , DABCO , or triethylamine :
Thermolysis of Me 2 PH generates CH 2 =PMe, an unstable species in the condensed phase.
Compounds where phosphorus exists in a formal oxidation state of less than III are uncommon, but examples are known for each class. Organophosphorus(0) species are debatably illustrated by the carbene adducts, [P(NHC)] 2 , where NHC is an N-heterocyclic carbene . [ 14 ] With the formulae (RP) n and (R 2 P) 2 , respectively, compounds of phosphorus(I) and (II) are generated by reduction of the related organophosphorus(III) chlorides: [ citation needed ]
Diphosphenes , with the formula R 2 P 2 , formally contain phosphorus-phosphorus double bonds. These phosphorus(I) species are rare but are stable provided that the organic substituents are large enough to prevent catenation . Bulky substituents also stabilize phosphorus radicals .
Many mixed-valence compounds are known, e.g. the cage P 7 (CH 3 ) 3 . | https://en.wikipedia.org/wiki/Organophosphorus_chemistry |
In industrial paper-making processes, organosolv is a pulping technique that uses an organic solvent to solubilise lignin and hemicellulose. It has been considered in the context of both pulp and paper manufacture and biorefining for subsequent conversion of cellulose to fuel ethanol. The process was invented by Theodor Kleinert in 1968 [ 1 ] as an environmentally benign alternative to kraft pulping .
Organosolv has several advantages when compared to other popular methods such as kraft or sulfite pulping . In particular, the ability to obtain relatively high quality lignin adds value to a process stream otherwise considered as waste. Organosolv solvents are easily recovered by distillation, leading to less water pollution and elimination of the odour usually associated with kraft pulping .
Organosolv pulping involves contacting a lignocellulosic feedstock such as chipped wood with an aqueous organic solvent at temperatures ranging from 140 to 220 °C. This causes lignin to break down by hydrolytic cleavage of alpha aryl-ether links into fragments that are soluble in the solvent system. Solvents used include acetone , methanol , ethanol , butanol , ethylene glycol , formic acid , and acetic acid . The concentration of solvent in water ranges from 40 to 80%. Higher boiling solvents have the advantage of a lower process pressure. This is weighed against the more difficult solvent recovery by distillation. [ 2 ] Ethanol has been suggested as the preferred solvent due to cost and easy recovery. Although butanol is shown to remove more lignin than other solvents and solvent recovery is simplified due to immiscibility in water, its high cost limits its use.
Numerous authors report that pulping with ethanol-water solutions gives a lignin free pulp yield 4–4.5% higher than that of kraft pulp. [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] The commonly used solvents acetone and ethanol have been examined with respect to pulp properties. The pulping of wheat straw with 40% mixtures of acetone or ethanol with water requires 60 minutes at 180 °C to give good pulp properties. [ 4 ] Organic solvents are almost always used as a mixture with water for process considerations such as reducing the vapour pressure and lowering the pH in order to also solubilise hemicellulose.
Only some small organosolv pulp mills are run today for production of pulp from annual renewable non wood fibre sources like straw, bagasse, etc. [ 8 ]
Recently, due to the popularity of second generation biofuels, the organosolv process has been considered in the context of bioethanol production. Cellulose from the organosolv process is susceptible to enzymatic hydrolysis into glucose followed by fermentation to dilute ethanol. The organosolv fractionation of mountain-beetle-killed lodgepole pine has yielded 97% conversion to glucose. Pan et al. [ 9 ] recovered 79% of the lignin using conditions of 170 °C, 1.1% w/w H 2 SO 4 , 65% v/v ethanol for 60 minutes.
Furthermore, ethanol organosolv pretreated rice straw was used to produce biohydrogen using Enterobacter aerogenes . The effect of temperature (120–180 °C), residence time (30–90 min), and ethanol concentration (45–75% v/v) on the hydrogen yield, residual biomass, and lignin recovery was investigated using RSM. The glucose concentration at the optimum conditions was 4.22-fold of untreated straw. [ 10 ]
The recovery of lignin from ethylene glycol organosolv pulping can be effected by 3 times dilution with acidified water. The lignin precipitates and forms spherical aggregates ranging from 0.5 to 2.5 μm. Filtration, while time-consuming, is then most effective while the mixture is hot (>100 °C). [ 11 ] Recovery can be achieved by filtration or centrifugation . Due to the hydrophobic nature of organosolv lignin, flotation of organosolv lignin is effective without the use of the collecting and precipitating agents [ 12 ] that are required for flotation of kraft lignin.
Organocell uses two-stage organosolv with roughly 50% methanol solutions. Sodium hydroxide is added in the second stage at a loading of 30% w/w of the dry wood. The lignin from the second stage is isolated by adding phosphoric acid until a pH of 4.0 is reached. [ 13 ]
The Alcohol Pulping and Recovery (APR) process treats wood in 3 stages, each using increasingly cleaner solvent. The important process parameters are extraction time, temperature, solvent composition and pH. Pilot plant operation has shown that ethanol pulping produces pulp superior to sulphite pulp at a lower cost. Lignin and hemicellulose are recovered in high yields. In 1987 the APR process was renamed the Alcell process. The process uses aqueous ethanol solutions (40–60% v/v) to delignifying wood at temperatures from 180 to 210 °C and 2–3.5 MPa. Solvent is recovered with flash evaporation, vapour condensation and vacuum stripping. [ 14 ]
A demonstration organosolv pulp mill operated in Miramichi, New Brunswick , Canada from 1989 to 1996 using the Alcell process. Repap owned the IP to the process when taken over by hedge funds in 1997. The pilot plant boasted superior environmental performance, excellent bleached pulp, an economically attractive scale of 300 tons/day and commercially attractive by-products. It is said that the technology can be used to exploit small regions of hardwood resource that could not support a modern sized kraft mill. [ 7 ]
Compagnie Industrielle de la Materière Végétale in France have developed a process where wheat straw is treated with acetic acid / formic acid / water (30/55/15 v/v/v) for 3.5 h at 105 °C under atmospheric pressure. The obtained fibres are screened and bleached. At this conditions the lignin is dissolved and hemicelluloses are hydrolysed to oligo and monosaccharides. Organic acids are collected by concentration of the cooking liquor and then lignin is precipitated by adding water and high pressure filtration. [ 8 ]
Chempolis Ltd in Oulu, Finland has developed, since 1995, a process concept where any lignocellulosic fibrous biomass sources are delignified with formic acid (biosolvent) in a compact process. The so-called "formico" technology incorporates full biosolvent recovery by evaporation and distillation in order to have a closed-loop process with minimal water need and effluent discharge. The delignification selectively fractionates lignocellulose components into cellulosic fibre, hemicellulose and lignin. Part of the hemicelluloses react to furfural and acetic acid, which are recovered in the distillation process to high-grade commercial products. The clean cellulosic fibre is used in various high-end packaging and textile purposes (bleached easily with hydrogen peroxide), or hydrolysed into high-purity glucose readily converted into biochemicals, or the glucose is easily fermented to bioethanol. The dissolved hemicelluloses and lignin after delignification are concentrated in evaporation and separated to produce hemicellulose fraction suitable for fermentation into ethanol or conversion to biochemicals. The separated lignin is sulfur-free and used in high-end applications replacing fossil aromatics. [ 8 ]
American Science and Technology (AST) based out of Chicago, Illinois, USA, has developed a process which uses a patented second generation Organosolv process to convert any kind of biomass to more than 10 industrial fine chemicals, organic intermediates and solvents. With a 2 ton/day production facility located in Wausau, Wisconsin , AST can also make high quality pulp, glucose, fructose and lignin. With the AST process, lignocellulosic biomass is treated with sulfuric acid, water, butanol and other organic solvents, water, an organic or inorganic acid, and catalyst for one to three hours at 150 to 200 °C. The results produce fibers that are screened and bleached for paper products. At these conditions, the lignin is dissolved in organic solvent and hemicelluloses are used to produce more organic solvent. Organic solvents are collected by separating water from the cooking liquor and then the lignin is precipitated by adding water, heat, and filtration.
The Bloom process was developed at EPFL in Lausanne [ 15 ] and is commercialised by Bloom Biorenewables Sàrl. [ 16 ] This method is based on a protection chemistry that prevents lignin and C5 sugars condensation. [ 17 ] | https://en.wikipedia.org/wiki/Organosolv |
Organostannane addition is reaction involving the nucleophilic addition of an allyl- , allenyl- , or propargyl- stannane to an aldehyde , imine , or (in rare cases) a ketone . [ 1 ] This reaction is widely used for carbonyl allylation .
The addition of an organostannane to carbonyl group is one of the most common and efficient methods for the production of contiguous, oxygen-containing stereocenters in organic molecules. Since many naturally-occurring polymers contain this stereochemical motif, such as poly propionate and poly acetate , organostannane addition has been studied extensively by natural products chemists as a synthetically and commercially-important reaction. [ 2 ] [ 3 ]
Organostannanes are very stable molecules, favoured for their ease of handling and selective reactivity. Chiral allylstannanes are known to react stereoselectively, yielding single diastereomers . The production of substituted allylstannanes containing either one or two new stereocenters can be achieved by this method with a very high degree of stereocontrol. (ref?)
(1)
However, stoichiometrically relative amounts of metal-containing byproducts are generated by this reaction, and addition to sterically-encumbered pi-bonds in ketones, are uncommon. (ref?)
Three modes allow the addition of allylstannanes to carbonyls: thermal addition, Lewis-acid-promoted addition, and addition involving prior transmetalation. Each of these modes invokes a unique model for stereocontrol, but in all cases, a distinction is made between reagent and substrate control. Substrate-controlled additions typically involve chiral aldehydes or imines and invoke the Felkin-Anh model . When all reagents are achiral, only simple diastereoselectivity ( syn versus anti , see above) must be considered. Addition takes place via an S E ' mechanism involving concerted dissociation of tin and C-C bond formation at the γ position.
With the allylstannane and aldehyde in high-temperature conditions, addition proceeds through a six-membered, cyclic transition state, with the tin center serving as an organizing element. The configuration of the double bond in the allylstannane controls the sense of diastereoselectivity of the reaction. [ 4 ]
(2)
This is not the case in Lewis-acid-promoted reactions, in which either the ( Z )- or ( E )-stannane affords the syn product predominantly (Type II). The origin of this selectivity has been debated, [ 5 ] and depends on the relative energies of a number of acyclic transition states. ( E )-Stannanes exhibit higher syn selectivity than the corresponding ( Z )-stannanes. [ 6 ]
(3)
In the presence of certain Lewis acids, transmetalation may occur before addition. Complex reaction mixtures may result if transmetalation is not complete or if an equilibrium between allylic isomers exists. Tin(IV) chloride [ 7 ] and indium(III) chloride [ 8 ] have been employed for useful reactions in this mode.
(4)
A wide variety of enantioselective additions employing chiral , non-racemic Lewis acids are known. The chiral (acyloxy)borane or "CAB" catalyst 1 , titanium - BINOL system 2 , and silver - BINAP system 3 provide addition products in high ee via the Lewis-acid-promoted mechanism described above.
Thermal additions of stannanes are limited (because of the high temperatures and pressures required) to only simple aldehyde substrates. Lewis acid promoted and transmetalation reactions are much milder and have achieved synthetic utility. Intramolecular addition gives five- or six-membered rings under Lewis acidic or thermal conditions.
(6)
The possibility of incorporating oxygen-containing substituents into allyl- and allenylstannanes expands their scope and utility substantially over methods relying on more reactive organometallics. These compounds are usually prepared by enantioselective reduction with a chiral reducing agent such as BINAL-H. [ 9 ] In the presence of a Lewis acid, isomerization of α-alkoxy allylstannanes to the corresponding γ-alkoxy isomers takes place. [ 10 ]
(7)
The use of chiral electrophiles is common and can provide "double diastereoselection" if the stannane is also chiral. [ 11 ] Chelation control using Lewis acids such as magnesium bromide can lead to high stereoselectivities for reactions of α-alkoxy aldehydes. [ 12 ]
(8)
Nucleophilic addition to propargyl mesylates or tosylates is used to form allenylstannanes. [ 13 ] These compounds react similarly to allylstannanes to afford homopropargyl alcohols, and any of the three reaction modes described above can be used with this class of reagents as well.
(9)
Imines are less reactive than the corresponding aldehydes, but palladium catalysis can be used to facilitate addition into imines. [ 14 ] The use of iminium ions as electrophiles has also been reported. [ 15 ]
(10)
The chiral allylic stannane 1 adds to acrolein to yield the 1,5- syn diastereomer as a single stereoisomer. A subsequent sigmatropic rearrangement increased the distance between the stereocenters even further. This step was carried out en route to (±)-patulolide C. [ 16 ]
(11)
Repeated use of the allylic stannane addition in an intramolecular sense was used in the synthesis of hemibrevetoxin B (one example is shown below). The pseudoequatorial positions of both "appendages" in the starting material lead to the observed stereoisomer. [ 17 ]
(12) | https://en.wikipedia.org/wiki/Organostannane_addition |
Organosulfur chemistry is the study of the properties and synthesis of organosulfur compounds , which are organic compounds that contain sulfur . [ 1 ] They are often associated with foul odors, but many of the sweetest compounds known are organosulfur derivatives, e.g., saccharin . Nature is abound with organosulfur compounds—sulfur is vital for life. Of the 20 common amino acids , two ( cysteine and methionine ) are organosulfur compounds, and the antibiotics penicillin and sulfa drugs both contain sulfur. While sulfur-containing antibiotics save many lives, sulfur mustard is a deadly chemical warfare agent. Fossil fuels , coal , petroleum , and natural gas , which are derived from ancient organisms, necessarily contain organosulfur compounds, the removal of which is a major focus of oil refineries .
Sulfur shares the chalcogen group with oxygen , selenium , and tellurium , and it is expected that organosulfur compounds have similarities with carbon–oxygen, carbon–selenium, and carbon–tellurium compounds.
A classical chemical test for the detection of sulfur compounds is the Carius halogen method .
Organosulfur compounds can be classified according to the sulfur-containing functional groups , which are listed (approximately) in decreasing order of their occurrence.
Sulfides, formerly known as thioethers, are characterized by C−S−C bonds [ 3 ] [ 4 ] Relative to C−C bonds, C−S bonds are both longer, because sulfur atoms are larger than carbon atoms, and about 10% weaker. Representative bond lengths in sulfur compounds are 183 pm for the S−C single bond in methanethiol and 173 pm in thiophene . The C−S bond dissociation energy for thiomethane is 89 kcal/mol (370 kJ/mol) compared to methane's 100 kcal/mol (420 kJ/mol) and when hydrogen is replaced by a methyl group the energy decreases to 73 kcal/mol (305 kJ/mol). [ 5 ] The single carbon to oxygen bond is shorter than that of the C−C bond. The bond dissociation energies for dimethyl sulfide and dimethyl ether are respectively 73 and 77 kcal/mol (305 and 322 kJ/mol).
Sulfides are typically prepared by alkylation of thiols. Alkylating agents include not only alkyl halides, but also epoxides, aziridines, and Michael acceptors . [ 6 ]
They can also be prepared via the Pummerer rearrangement .
In the Ferrario reaction , phenyl ether is converted to phenoxathiin by action of elemental sulfur and aluminium chloride . [ 7 ]
Thioacetals and thioketals feature C−S−C−S−C bond sequence. They represent a subclass of sulfides. The thioacetals are useful in " umpolung " of carbonyl groups. Thioacetals and thioketals can also be used to protect a carbonyl group in organic syntheses.
The above classes of sulfur compounds also exist in saturated and unsaturated heterocyclic structures, often in combination with other heteroatoms , as illustrated by thiiranes , thiirenes , thietanes , thietes , dithietanes , thiolanes , thianes , dithianes , thiepanes , thiepines , thiazoles , isothiazoles , and thiophenes , among others. The latter three compounds represent a special class of sulfur-containing heterocycles that are aromatic . The resonance stabilization of thiophene is 29 kcal/mol (121 kJ/mol) compared to 20 kcal/mol (84 kJ/mol) for the oxygen analogue furan . The reason for this difference is the higher electronegativity for oxygen drawing away electrons to itself at the expense of the aromatic ring current. Yet as an aromatic substituent the thio group is less electron-releasing than the alkoxy group. Dibenzothiophenes (see diagram ), tricyclic heterocycles consisting of two benzene rings fused to a central thiophene ring, occurs widely in heavier fractions of petroleum.
Thiol groups contain the functionality R−SH. Thiols are structurally similar to the alcohol group, but these functionalities are very different in their chemical properties. Thiols are more nucleophilic , more acidic, and more readily oxidized. This acidity can differ by 5 p K a units. [ 8 ]
The difference in electronegativity between sulfur (2.58) and hydrogen (2.20) is small and therefore hydrogen bonding in thiols is not prominent. Aliphatic thiols form monolayers on gold , which are topical in nanotechnology .
Certain aromatic thiols can be accessed through a Herz reaction .
Disulfides R−S−S−R with a covalent sulfur to sulfur bond are important for crosslinking : in biochemistry for the folding and stability of some proteins and in polymer chemistry for the crosslinking of rubber.
Longer sulfur chains are also known, such as in the natural product varacin which contains an unusual pentathiepin ring (5-sulfur chain cyclised onto a benzene ring).
Thioesters have general structure R−C(O)−S−R. They are related to regular esters (R−C(O)−O−R) but are more susceptible to hydrolysis and related reactions. Thioesters formed from coenzyme A are prominent in biochemistry, especially in fatty acid synthesis.
A sulfoxide , R−S(O)−R, is the S -oxide of a sulfide ("sulfide oxide"), a sulfone , R−S(O) 2 −R, is the S , S -dioxide of a sulfide, a thiosulfinate , R−S(O)−S−R, is the S -oxide of a disulfide, and a thiosulfonate , R−S(O) 2 −S−R, is the S , S -dioxide of a disulfide. All of these compounds are well known with extensive chemistry, e.g., dimethyl sulfoxide , dimethyl sulfone , and allicin (see drawing).
Sulfimides (also called a sulfilimines) are sulfur–nitrogen compounds of structure R 2 S=NR′, the nitrogen analog of sulfoxides. They are of interest in part due to their pharmacological properties. When two different R groups are attached to sulfur, sulfimides are chiral. Sulfimides form stable α-carbanions. [ 9 ]
Sulfoximides (also called sulfoximines) are tetracoordinate sulfur–nitrogen compounds, isoelectronic with sulfones, in which one oxygen atom of the sulfone is replaced by a substituted nitrogen atom, e.g., R 2 S(O)=NR′. When two different R groups are attached to sulfur, sulfoximides are chiral. Much of the interest in this class of compounds is derived from the discovery that methionine sulfoximide (methionine sulfoximine) is an inhibitor of glutamine synthetase . [ 10 ]
Sulfonediimines (also called sulfodiimines, sulfodiimides or sulfonediimides) are tetracoordinate sulfur–nitrogen compounds, isoelectronic with sulfones, in which both oxygen atoms of the sulfone are replaced by a substituted nitrogen atom, e.g., R 2 S(=NR′) 2 . They are of interest because of their biological activity and as building blocks for heterocycle synthesis. [ 11 ]
S -Nitrosothiols , also known as thionitrites, are compounds containing a nitroso group attached to the sulfur atom of a thiol, e.g. R−S−N=O. They have received considerable attention in biochemistry because they serve as donors of the nitrosonium ion, NO + , and nitric oxide, NO, which may serve as signaling molecules in living systems, especially related to vasodilation. [ 12 ]
A wide range of organosulfur compounds are known which contain one or more halogen atom ("X" in the chemical formulas that follow) bonded to a single sulfur atom, e.g.: sulfenyl halides , RSX; sulfinyl halides , RS(O)X; sulfonyl halides , RSO 2 X; alkyl and arylsulfur trichlorides, RSCl 3 and trifluorides, RSF 3 ; [ 13 ] and alkyl and arylsulfur pentafluorides, RSF 5 . [ 14 ] Less well known are dialkylsulfur tetrahalides, mainly represented by the tetrafluorides, e.g., R 2 SF 4 . [ 15 ]
Compounds with double bonds between carbon and sulfur are relatively uncommon, but include the important compounds carbon disulfide , carbonyl sulfide , and thiophosgene . Thioketones (RC(=S)R′) are uncommon with alkyl substituents, but one example is thiobenzophenone . Thioaldehydes are rarer still, reflecting their lack of steric protection (" thioformaldehyde " exists as a cyclic trimer). Thioamides , with the formula R 1 C(=S)N(R 2 )R 3 are more common. They are typically prepared by the reaction of amides with Lawesson's reagent . Isothiocyanates , with formula R−N=C=S, are found naturally. Vegetable foods with characteristic flavors due to isothiocyanates include wasabi , horseradish , mustard , radish , Brussels sprouts , watercress , nasturtiums , and capers .
The S -oxides of thiocarbonyl compounds are known as thiocarbonyl S -oxides: (R 2 C=S=O, and thiocarbonyl S , S -dioxides or sulfenes , R 2 C=SO 2 ). The thione S -oxides have also been known as sulfines , and while IUPAC considers this term obsolete, [ 16 ] the name persists in the literature. [ 17 ] These compounds are well known with extensive chemistry. [ 18 ] [ 19 ] Examples include syn -propanethial- S -oxide and sulfene .
Triple bonds between sulfur and carbon in sulfaalkynes are rare and can be found in carbon monosulfide (CS) [ 20 ] and have been suggested for the compounds F 3 CCSF 3 [ 21 ] [ 22 ] and F 5 SCSF 3 . [ 23 ] The compound HCSOH is also represented as having a formal triple bond. [ 24 ]
Thiocarboxylic acids (RC(O)SH) and dithiocarboxylic acids (RC(S)SH) are well known. They are structurally similar to carboxylic acids but more acidic. Thioamides are analogous to amides.
Sulfonic acids have functionality R−S(=O) 2 −OH. [ 25 ] They are strong acids that are typically soluble in organic solvents. Sulfonic acids like trifluoromethanesulfonic acid is a frequently used reagent in organic chemistry . Sulfinic acids have functionality R−S(O)−OH while sulfenic acids have functionality R−S−OH. In the series sulfonic—sulfinic—sulfenic acids, both the acid strength and stability diminish in that order. [ 26 ] [ 27 ] Sulfonamides, sulfinamides and sulfenamides , with formulas R−SO 2 NR′ 2 , R−S(O)NR′ 2 , and R−SNR′ 2 , respectively, each have a rich chemistry. For example, sulfa drugs are sulfonamides derived from aromatic sulfonation . Chiral sulfinamides are used in asymmetric synthesis, while sulfenamides are used extensively in the vulcanization process to assist cross-linking. Thiocyanates , R−S−CN, are related to sulfenyl halides and esters in terms of reactivity.
A sulfonium ion is a positively charged ion featuring three organic substituents attached to sulfur, with the formula [R 3 S] + . Together with their negatively charged counterpart, the anion, the compounds are called sulfonium salts. An oxosulfonium ion is a positively charged ion featuring three organic substituents and an oxygen attached to sulfur, with the formula [R 3 S=O] + . Together with their negatively charged counterpart, the anion, the compounds are called oxosulfonium salts. Related species include alkoxysulfonium and chlorosulfonium ions, [R 2 SOR] + and [R 2 SCl] + , respectively.
Deprotonation of sulfonium and oxosulfonium salts affords ylides , of structure R 2 S + −C − −R′ 2 and R 2 S(O) + −C − −R′ 2 . While sulfonium ylides , for instance in the Johnson–Corey–Chaykovsky reaction used to synthesize epoxides , are sometimes drawn with a C=S double bond, e.g., R 2 S=CR′ 2 , the ylidic carbon–sulfur bond is highly polarized and is better described as being ionic. Sulfonium ylides are key intermediates in the synthetically useful Stevens rearrangement . Thiocarbonyl ylides (RR′C=S + −C − −RR′) can form by ring-opening of thiiranes , photocyclization of aryl vinyl sulfides, [ 28 ] as well as by other processes.
Sulfuranes are relatively specialized functional group that feature tetravalent sulfur, with the formula SR 4 [ 2 ] Likewise, persulfuranes feature hexavalent SR 6 .
One of the few all-carbon persulfuranes has two methyl and two biphenylene ligands : [ 29 ]
It is prepared from the corresponding sulfurane 1 with xenon difluoride / boron trifluoride in acetonitrile to the sulfuranyl dication 2 followed by reaction with methyllithium in tetrahydrofuran to (a stable) persulfurane 3 as the cis isomer . X-ray diffraction shows C−S bond lengths ranging between 189 and 193 pm (longer than the standard bond length) with the central sulfur atom in a distorted octahedral molecular geometry .
A variety of organosulfur compounds occur in nature. Most abundant are the amino acids methionine , cysteine , and cystine . The vitamins biotin and thiamine , as well as lipoic acid contain sulfur heterocycles. Glutathione is the primary intracellular antioxidant . [ 6 ] Penicillin and cephalosporin are life-saving antibiotics , derived from fungi. Gliotoxin is a sulfur-containing mycotoxin produced by several species of fungi under investigation as an antiviral agent.
Common organosulfur compounds present in petroleum fractions at the level of 200–500 ppm. Common compounds are thiophenes , especially dibenzothiophenes . By the process of hydrodesulfurization (HDS) in refineries, these compounds are removed as illustrated by the hydrogenolysis of thiophene: C 4 H 4 S + 8 H 2 → C 4 H 10 + H 2 S
Compounds like allicin and ajoene are responsible for the odor of garlic . Lenthionine contributes to the flavor of shiitake mushrooms . Volatile organosulfur compounds also contribute subtle flavor characteristics to wine , nuts, cheddar cheese , chocolate , coffee , and tropical fruit flavors. [ 30 ] Many of these natural products also have important medicinal properties such as preventing platelet aggregation or fighting cancer.
Humans and other animals have an exquisitely sensitive sense of smell toward the odor of low-valent organosulfur compounds such as thiols, sulfides, and disulfides. Malodorous volatile thiols are protein-degradation products found in putrid food, so sensitive identification of these compounds is crucial to avoiding intoxication. Low-valent volatile sulfur compounds are also found in areas where oxygen levels in the air are low, posing a risk of suffocation.
Copper is required for the highly sensitive detection of certain volatile thiols and related organosulfur compounds by olfactory receptors in mice. Whether humans, too, require copper for sensitive detection of thiols is not yet known. [ 31 ] | https://en.wikipedia.org/wiki/Organosulfur_chemistry |
Organotantalum chemistry is the chemistry of chemical compounds containing a carbon -to- tantalum chemical bond . A wide variety of compound have been reported, initially with cyclopentadienyl and CO ligands. Oxidation states vary from −1 to +5.
Pentamethyltantalum was reported by Richard Schrock in 1974. [ 1 ]
Salts of [Ta(CH 3 ) 6 ] − are prepared by alkylation of TaF 5 using methyl lithium : [ 2 ]
Tantalum alkylidene complexes arise by treating trialkyltantalum dichloride with alkyl lithium reagents. This reaction initially forms a thermally unstable tetraalkyl-monochloro-tantalum complex, which undergoes α-hydrogen elimination, followed by alkylation of the remaining chloride. [ 1 ]
Tantalum alkylidene complexes are nucleophilic . [ 1 ] They effect a number of reactions including: olefinations, olefin metathesis, hydroaminoalkylation of olefins, and conjugate allylation of enones.
Ethylene , propylene , and styrene react with tantalum alkylidene complexes to yield olefin metathesis products. [ 3 ]
Some of the first reported organotantalum complexes were cyclopentadienyl derivatives. These arise from the salt metathesis reactions of sodium cyclopentadienide and tantalum pentachloride . An example of this is the first transition metal trihydride, Cp 2 TaH 3 . More soluble and better developed are derivatives of pentamethylcyclopentadiene such as Cp*TaCl 4 , Cp* 2 TaCl 2 , and Cp* 2 TaH 3 . [ 4 ]
Reduction of TaCl 5 under an atmosphere of CO gives the salts of [Ta(CO) 6 ] − . [ 5 ] These same anions can be obtained by carbonylation of tantalum arene complexes.
A number of tantalum isocyanide complexes are also known. [ 6 ]
Treatment of tantalum pentachloride with hexamethylbenzene (C 6 Me 6 ), aluminium , and aluminium trichloride gives [M(η 6 -C 6 Me 6 )AlCl 4 ] 2 . [ 7 ]
Tantalum-alkyne complexes [ 8 ] catalyze cyclotrimerizations . [ 9 ] [ 10 ] Some tantalum-alkyne complexes are precursors to allylic alcohols. [ 11 ] Tantalacyclopropenes are invoked as intermediates.
Organotantalum compounds are invoked as intermediates in C- alkylation of secondary amines with 1-alkenes using Ta(NMe 2 ) 5 . [ 12 ] The chemistry developed by Maspero was later brought to fruition when Hartwig and Herzon reported the hydroaminoalkylation of olefins to form alkylamines : [ 13 ]
The catalytic cycle may proceed by β-hydrogen abstraction of the bisamide, which forms the metallaaziridine . Subsequent olefin insertion , protonolysis of the tantalum-carbon bond, and β-hydrogen abstraction affords the alkylamine product. [ 14 ] [ 15 ] [ 16 ]
Organotantalum reagents arise via transmetalation of organotin compounds with tantalum(V) chloride. [ 17 ] These organotantalum reagents promote the conjugate allylation of enones. Although the direct allylation of carbonyl groups is prevalent throughout the literature, little has been reported on the conjugate allylation of enones. [ 18 ]
Organotantalum compounds are of academic interest, but few or no commercial applications have been described. | https://en.wikipedia.org/wiki/Organotantalum_chemistry |
Organotin chemistry is the scientific study of the synthesis and properties of organotin compounds or stannanes , which are organometallic compounds containing tin – carbon bonds. The first organotin compound was diethyltin diiodide ( (CH 3 CH 2 ) 2 SnI 2 ), discovered by Edward Frankland in 1849. [ 1 ] The area grew rapidly in the 1900s, especially after the discovery of the Grignard reagents , which are useful for producing Sn–C bonds. The area remains rich with many applications in industry and continuing activity in the research laboratory. [ 2 ]
Organotin compounds are generally classified according to their oxidation states. Tin(IV) compounds are much more common and more useful.
The tetraorgano derivatives are invariably tetrahedral. Compounds of the type SnRR'R''R''' have been resolved into individual enantiomers. [ 3 ]
Organotin chlorides have the formula R 4− n SnCl n for values of n up to 3. Bromides, iodides, and fluorides are also known, but are less important. These compounds are known for many R groups. They are always tetrahedral. The tri- and dihalides form adducts with good Lewis bases such as pyridine . The fluorides tend to associate such that dimethyltin difluoride forms sheet-like polymers. Di- and especially tri-organotin halides, e.g. tributyltin chloride , exhibit toxicities approaching that of hydrogen cyanide . [ 4 ]
Organotin hydrides have the formula R 4− n SnH n for values of n up to 3. The parent member of this series, stannane ( SnH 4 ), is an unstable colourless gas. Stability is correlated with the number of organic substituents. Tributyltin hydride is used as a source of hydride radical in some organic reactions.
Organotin oxides and hydroxides are common products from the hydrolysis of organotin halides. Unlike the corresponding derivatives of silicon and germanium, tin oxides and hydroxides often adopt structures with penta- and even hexacoordinated tin centres, especially for the diorgano- and monoorgano derivatives. The group Sn IV −O−Sn IV is called a stannoxane (which is a tin analogue of ethers ), and the group Sn IV −O−H is also called a stannanol (which is a tin analogue of alcohols ). [ 5 ] Structurally simplest of the oxides and hydroxides are the triorganotin derivatives. A commercially important triorganotin hydroxide is the acaricide cyhexatin (also called Plictran, tricyclohexyltin hydroxide and tricyclohexylstannanol), ( C 6 H 11 ) 3 SnOH . Such triorganotin hydroxides exist in equilibrium with the distannoxanes:
With only two organic substituents on each Sn centre, the diorganotin oxides and hydroxides are structurally more complex than the triorgano derivatives. [ 6 ] The simple tin geminal diols ( R 2 Sn(OH) 2 , the tin analogues of geminal diols R 2 C(OH) 2 ) and monomeric stannanones ( R 2 Sn=O , the tin analogues of ketones R 2 C=O ) are unknown. Diorganotin oxides ( R 2 SnO ) are polymers except when the organic substituents are very bulky, in which case cyclic trimers or, in the case where R is CH(Si(CH 3 ) 3 ) 2 dimers , with Sn 3 O 3 and Sn 2 O 2 rings. The distannoxanes exist as dimers with the formula [R 2 SnX] 2 O 2 wherein the X groups (e.g., chloride –Cl, hydroxide –OH, carboxylate RCO 2 − ) can be terminal or bridging (see Table). The hydrolysis of the monoorganotin trihalides has the potential to generate stannanoic acids, RSnO 2 H . As for the diorganotin oxides/hydroxides, the monoorganotin species form structurally complex because of the occurrence of dehydration/hydration, aggregation. Illustrative is the hydrolysis of butyltin trichloride to give [(CH 3 (CH 2 ) 3 Sn) 12 O 14 (OH) 6 ] 2+ .
Unlike carbon(IV) analogues but somewhat like silicon compounds, tin(IV) can also be coordinated to five and even six atoms instead of the regular four. These hypercoordinated compounds usually have electronegative substituents. Numerous examples of hypercoordinated compounds are provided by the organotin oxides and associated carboxylates and related pseudohalide derivatives. [ 6 ] The organotin halides for adducts, e.g. (CH 3 ) 2 SnCl 2 ( bipyridine ).
The all-organic penta- and hexaorganostannates(IV) have even been characterized, [ 7 ] while in the subsequent year a six-coordinated tetraorganotin compound was reported. [ 8 ] A crystal structure of room-temperature stable (in argon ) all-carbon pentaorganostannate(IV) was reported as the lithium salt with this structure: [ 9 ]
In this distorted trigonal bipyramidal structure the carbon to tin bond lengths (2.26 Å apical , 2.17 Å equatorial) are longer than regular C-Sn bonds (2.14 Å) reflecting its hypercoordinated nature.
Some reactions of triorganotin halides implicate a role for R 3 Sn + intermediates. Such cations are analogous to carbocations . They have been characterized crystallographically when the organic substituents are large, such as 2,4,6-triisopropylphenyl. [ 10 ]
Tin radicals, with the formula R 3 Sn , are called stannyl radicals . [ 2 ] They are a type of tetrel radical , and are invoked as intermediates in certain atom-transfer reactions. For example, tributyltin hydride (tris( n -butyl)stannane) serves as a useful source of "hydrogen atoms" because of the stability of the tributytin radical. [ 11 ]
Organotin(II) compounds are somewhat rare. Compounds with the empirical formula SnR 2 are somewhat fragile and exist as rings or polymers when R is not bulky. The polymers, called polystannanes , have the formula (SnR 2 ) n .
In principle, compounds of tin(II) might be expected to form a tin analogues of alkenes with a formal double bond between two tin atoms ( R 2 Sn=SnR 2 ) or between a tin atom and a carbon group atom (e.g. R 2 Sn=CR 2 and R 2 Sn=SiR 2 ). Indeed, compounds with the formula R 2 Sn=SnR 2 , called distannenes or distannylenes , which are tin analogues of ethylenes R 2 C=CR 2 , are known for certain organic substituents. The Sn centres in stannenes are trigonal. But, contrary to the C centres in alkenes which are trigonal planar , the Sn centres in stannenes tend to be highly pyramidal . Monomeric compounds with the formula SnR 2 , tin analogues of carbenes CR 2 are also known in a few cases. One example is Sn(SiR 3 ) 2 , where R is the very bulky CH(Si(CH 3 ) 3 ) 2 . Such species reversibly dimerize to the distannylene upon crystallization: [ 12 ]
Stannenes , compounds with tin-carbon double bonds, are exemplified by derivatives of stannabenzene . Stannoles , structural analogs of cyclopentadiene , exhibit little C-Sn double bond character.
Compounds of Sn(I) are rare and only observed with very bulky ligands. One prominent family of cages is accessed by pyrolysis of the 2,6-diethylphenyl-substituted tristannylene [Sn(C 6 H 3 -2,6-Et 2 ) 2 ] 3 , which affords the cubane-type cluster and a prismane . These cages contain Sn(I) and have the formula [Sn(C 6 H 3 -2,6-Et 2 )] n where n = 8, 10 and Et stands for ethyl group . [ 13 ] A stannyne contains a tin atom to carbon group atom triple bond (e.g. R−Sn≡C−R and R−Sn≡Si−R ), and a distannyne a triple bond between two tin atoms ( R−Sn≡Sn−R ). Distannynes only exist for extremely bulky substituents. Unlike alkynes , the C−Sn≡Sn−C core of these distannynes are nonlinear, although they are planar. The Sn-Sn distance is 3.066(1) Å, and the Sn-Sn-C angles are 99.25(14)°. Such compounds are prepared by reduction of bulky aryltin(II) halides. [ 14 ]
Organotin compounds can be synthesised by numerous methods. [ 15 ] Classic is the reaction of a Grignard reagent with tin halides for example tin tetrachloride . An example is provided by the synthesis of tetraethyltin: [ 16 ]
The symmetrical tetraorganotin compounds, especially tetraalkyl derivatives, can then be converted to various mixed chlorides by redistribution reactions (also known as the "Kocheshkov comproportionation" in the case of organotin compounds):
A related method involves redistribution of tin halides with organoaluminium compounds . [ 2 ] : 45–47
In principle, alkyltin halides can be formed from direct insertion of the metal into the carbon-halogen bond. However, such reactions are temperamental, typically requiring a very weak carbon-halogen bond (e.g. an alkyl iodide or an allyl halide) or crown-complexed alkali metal salt catalyst. Lewis acids or an ionic solvent may also promote the reaction. [ 2 ] : 51–52
The mixed organo-halo tin compounds can be converted to the mixed organic derivatives, as illustrated by the synthesis of dibutyldivinyltin: [ 17 ]
The organotin hydrides are generated by reduction of the mixed alkyl chlorides. For example, treatment of dibutyltin dichloride with lithium aluminium hydride gives the dibutyltin dihydride , a colourless distillable oil: [ 18 ]
The Wurtz-like coupling of alkyl sodium compounds with tin halides yields tetraorganotin compounds.
Hydrostannylation involves the metal-catalyzed addition of tin hydrides across unsaturated substrates. [ 19 ]
Alternatively, stannides attack organic electrophiles to give organostannanes, e.g.: [ 2 ] : 49
Important reactions, discussed above, usually focus on organotin halides and pseudohalides with nucleophiles . All-alkyl organotin compounds generally do not hydrolyze except in concentrated acid ; the major exception being tin acetylides . [ 20 ] An organostannane addition is nucleophilic addition of an allyl -, allenyl -, or propargylstannanes to aldehydes and imines , [ citation needed ] whereas hydrostannylation conveniently reduces only unpolarized multiple bonds. [ 21 ]
Organotin hydrides are unstable to strong base, disproportionating to hydrogen gas and distannanes. [ 2 ] : 295 The latter equilibrate with the corresponding radicals only in the continued presence of base, or if strongly sterically hindered. [ 2 ] : 299, 334–335 Conversely, mineral acids cleave distannanes to the organotin halide and more hydrogen gas. [ 2 ] : 300
In "pure" organic synthesis , the Stille reaction is considered is a key coupling technique . In the Stille reaction, sp 2 -hybridized organic halides (e.g. vinyl chloride CH 2 =CHCl ) catalyzed by palladium :
Organotin compounds are also used extensively in radical chemistry (e.g. radical cyclizations , Barton–McCombie deoxygenation , Barton decarboxylation , etc.).
An organotin compound is commercially applied as stabilizers in polyvinyl chloride . In this capacity, they suppress degradation by removing allylic chloride groups [ clarification needed ] and by absorbing hydrogen chloride . This application consumes about 20,000 tons of tin each year. The main class of organotin compounds are diorganotin dithiolates with the formula R 2 Sn(SR') 2 . The Sn-S bond is the reactive component. Diorganotin carboxylates, e.g., dibutyltin dilaurate , are used as catalysts for the formation of polyurethanes , for vulcanization of silicones , and transesterification . [ 2 ]
n -Butyltin trichloride is used in the production of tin dioxide layers on glass bottles by chemical vapor deposition .
" Tributyltins " are used as industrial biocides , e.g. as antifungal agents in textiles and paper, wood pulp and paper mill systems, breweries, and industrial cooling systems. Triphenyltin derivatives are used as active components of antifungal paints and agricultural fungicides. Other triorganotins are used as miticides and acaricides . Tributyltin oxide has been extensively used as a wood preservative . [ 2 ]
Tributyltin compounds were once widely used as marine anti- biofouling agents to improve the efficiency of ocean-going ships. Concerns over toxicity [ 22 ] of these compounds (some reports describe biological effects to marine life at a concentration of 1 nanogram per liter) led to a worldwide ban by the International Maritime Organization . As anti-fouling compounds, organotin compounds have been replaced by dichlorooctylisothiazolinone . [ 23 ]
The toxicities of tributyltin and triphenyltin derivative compounds are comparable to that of hydrogen cyanide . Furthermore, tri- n -alkyltins are phytotoxic and therefore cannot be used in agriculture. Depending on the organic groups, they can be powerful bactericides and fungicides . Reflecting their high bioactivity, "tributyltins" were once used in marine anti-fouling paint . [ 2 ]
In contrast to the triorganotin compounds, monoorgano, diorgano- and tetraorganotin compounds are far less dangerous, [ 4 ] although DBT may be immunotoxic. [ 25 ] | https://en.wikipedia.org/wiki/Organotin_chemistry |
An organotroph is an organism that obtains hydrogen or electrons from organic substrates. This term is used in microbiology to classify and describe organisms based on how they obtain electrons for their respiration processes. Some organotrophs such as animals and many bacteria , are also heterotrophs . Organotrophs can be either anaerobic or aerobic.
Antonym: Lithotroph , Adjective: Organotrophic .
The term was suggested in 1946 by Lwoff and collaborators. [ 1 ] | https://en.wikipedia.org/wiki/Organotroph |
In organic and organometallic chemistry , an organyl group (commonly denoted by the letter " R ") is an organic substituent with one (sometimes more) free valence electron(s) at a carbon atom . [ 1 ] The term is often used in chemical patent literature to protect claims over a broad scope. [ citation needed ]
This organic chemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Organyl_group |
Orgel's rules are a set of axioms attributed by Francis Crick to the evolutionary biologist Leslie Orgel . [ 1 ] [ 2 ]
"Whenever a spontaneous process is too slow or too inefficient a protein will evolve to speed it up or make it more efficient."
This "rule" comments on the fact that there are a great number of proteins in all organisms which fulfil a number of different functions through modifying chemical or physical processes. An example would be an enzyme that catalyses a chemical reaction that would take place too slowly to benefit an organism without being sped up by this enzyme.
" Evolution is cleverer than you are."
This rule is well known among biologists. It does not imply that evolution has conscious motives or method but that people who say "evolution can't do this" or "evolution can't do that" are simply lacking in imagination. [ 3 ]
Orgel's second rule tells us that the process of natural selection is not itself intelligent, clever or purposeful but that the products of evolution are ingenious. [ 4 ] | https://en.wikipedia.org/wiki/Orgel's_rules |
Orgel diagrams are correlation diagrams which show the relative energies of electronic terms in transition metal complexes , much like Tanabe–Sugano diagrams . They are named after their creator, Leslie Orgel . Orgel diagrams are restricted to only show weak field (i.e. high spin ) cases, and offer no information about strong field (low spin) cases. Because Orgel diagrams are qualitative , no energy calculations can be performed from these diagrams; also, Orgel diagrams only show the symmetry states of the highest spin multiplicity instead of all possible terms, unlike a Tanabe–Sugano diagram. [ 1 ] Orgel diagrams will, however, show the number of spin allowed transitions, along with their respective symmetry designations. In an Orgel diagram, the parent term (P, D, or F) in the presence of no ligand field is located in the center of the diagram, with the terms due to that electronic configuration in a ligand field at each side. There are two Orgel diagrams, one for d 1 , d 4 , d 6 , and d 9 configurations and the other with d 2 , d 3 , d 7 , and d 8 configurations.
In an Orgel diagram, lines with the same Russell–Saunders terms will diverge due to the non-crossing rule , but all other lines will be linear. Also, for the D Orgel diagram, the left side contains d 1 and d 6 tetrahedral and d 4 and d 9 octahedral complexes. The right side contains d 4 and d 9 tetrahedral and d 1 and d 6 octahedral complexes. For the F Orgel diagram, the left side contains d 2 and d 7 tetrahedral and d 3 and d 8 octahedral complexes. The right side contains d 3 and d 8 tetrahedral and d 2 and high spin d 7 octahedral complexes.
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it .
This spectroscopy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orgel_diagram |
Orichalcum or aurichalcum / ˌ ɔːr ɪ ˈ k æ l k ə m / is a metal mentioned in several ancient writings, including the story of Atlantis in the Critias of Plato . Within the dialogue, Critias (460–403 BC) says that orichalcum had been considered second only to gold in value and had been found and mined in many parts of Atlantis in ancient times, but that by Critias's own time, orichalcum was known only by name. [ 1 ]
Orichalcum may have been a noble metal such as platinum , [ 2 ] as it was supposed to be mined, but has been identified as pure copper or certain alloys of bronze , and especially brass alloys [ 3 ] in the case of antique Roman coins, the latter being of "similar appearance to modern brass" according to scientific research. [ 4 ]
The name is derived from the Greek ὀρείχαλκος , oreikhalkos (from ὄρος , oros , mountain and χαλκός , chalkos , copper), literally meaning "mountain copper".
The Romans transliterated "orichalcum" as "aurichalcum", which was thought to mean literally "gold copper". It is known from the writings of Cicero that the metal which they called orichalcum resembled gold in color but had a much lower value. [ 5 ] In Virgil 's Aeneid , the breastplate of Turnus is described as "stiff with gold and white orichalc".
Orichalcum has been vaguely identified by ancient Greek authors to be either a gold–copper alloy , a form of pure copper or a copper ore or various chemicals based on copper, but also copper– tin and copper– zinc alloys, or a metal or metallic alloy supposedly no longer known.
In later years "orichalcum" was used to describe the sulfide mineral chalcopyrite and also to describe brass. These usages are difficult to reconcile with the claims of Plato's Critias, who states that the metal was "only a name" by his time, [ 1 ] while brass and chalcopyrite were very important in the time of Plato, [ citation needed ] as they still are today.
Joseph Needham notes that Bishop Richard Watson , an 18th-century professor of chemistry, wrote of an ancient idea that there were "two sorts of brass or orichalcum". Needham also suggests that the Greeks may not have known how orichalcum was made and that they might even have had an imitation of the original. [ 6 ]
In 2015, 39 ingots were discovered in a sunken vessel on the coast of Gela in Sicily which have tentatively been dated at 2,100 years old . They were analyzed with X-ray fluorescence and found to be an alloy consisting of 75–80% copper, 15–20% zinc, and smaller percentages of nickel, lead, and iron. [ 7 ] Another cache of 47 ingots was recovered in February 2016 and found to have similar composition as measured with ICP-OES and ICP-MS : around 65–80% copper, 15–25% zinc, 4–7% lead, 0.5–1% nickel, and trace amounts of silver, antimony , arsenic , bismuth , and other elements. [ 8 ]
Orichalcum is first mentioned in the 7th century BC by Hesiod , and in the Homeric hymn dedicated to Aphrodite , dated to the 630s BC . [ citation needed ]
According to the Critias of Plato , the inner wall surrounding the citadel of Atlantis with the Temple of Poseidon "flashed with the red light of orichalcum". The interior walls, pillars, and floors of the temple were completely covered in orichalcum, and the roof was variegated with gold, silver, and orichalcum. In the center of the temple stood a pillar of orichalcum, on which the laws of Poseidon and records of the first son princes of Poseidon were inscribed. [ 9 ]
Pliny the Elder points out that orichalcum had lost currency due to the mines being exhausted. Pseudo-Aristotle in De mirabilibus auscultationibus (62) describes a type of copper that is "very shiny and white, not because there is tin mixed with it, but because some earth is combined and molten with it." This might be a reference to orichalcum obtained during the smelting of copper with the addition of " cadmia ", a kind of earth formerly found on the shores of the Black Sea, which is attributed to be zinc oxide . [ 10 ]
In numismatics , the term "orichalcum" is used to refer exclusively to a type of brass alloy used for minting Roman as , sestertius , dupondius , and semis type of coins. It is considered more valuable than copper, of which the as coin was previously made. [ 11 ] | https://en.wikipedia.org/wiki/Orichalcum |
In geometry , the orientation , attitude , bearing , direction , or angular position of an object – such as a line , plane or rigid body – is part of the description of how it is placed in the space it occupies. [ 1 ] More specifically, it refers to the imaginary rotation that is needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement, in which case it may be necessary to add an imaginary translation to change the object's position (or linear position). The position and orientation together fully describe how the object is placed in space. The above-mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, and its position does not change when it rotates.
Euler's rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis . This gives one common way of representing the orientation using an axis–angle representation . Other widely used methods include rotation quaternions , rotors , Euler angles , or rotation matrices . More specialist uses include Miller indices in crystallography, strike and dip in geology and grade on maps and signs.
A unit vector may also be used to represent an object's normal vector direction or the relative direction between two points.
Typically, the orientation is given relative to a frame of reference , usually specified by a Cartesian coordinate system .
In general the position and orientation in space of a rigid body are defined as the position and orientation, relative to the main reference frame, of another reference frame, which is fixed relative to the body, and hence translates and rotates with it (the body's local reference frame , or local coordinate system ). At least three independent values are needed to describe the orientation of this local frame. Three other values describe the position of a point on the object.
All the points of the body change their position during a rotation except for those lying on the rotation axis. If the rigid body has rotational symmetry not all orientations are distinguishable, except by observing how the orientation evolves in time from a known starting orientation. For example, the orientation in space of a line , line segment , or vector can be specified with only two values, for example two direction cosines . Another example is the position of a point on the Earth, often described using the orientation of a line joining it with the Earth's center, measured using the two angles of longitude and latitude . Likewise, the orientation of a plane can be described with two values as well, for instance by specifying the orientation of a line normal to that plane, or by using the strike and dip angles.
Further details about the mathematical methods to represent the orientation of rigid bodies and planes in three dimensions are given in the following sections.
In two dimensions the orientation of any object (line, vector, or plane figure ) is given by a single value: the angle through which it has rotated. There is only one degree of freedom and only one fixed point about which the rotation takes place.
When there are d dimensions, specification of an orientation of an object that does not have any rotational symmetry requires d ( d − 1) / 2 independent values.
Several methods to describe orientations of a rigid body in three dimensions have been developed. They are summarized in the following sections.
The first attempt to represent an orientation is attributed to Leonhard Euler . He imagined three reference frames that could rotate one around the other, and realized that by starting with a fixed reference frame and performing three rotations, he could get any other reference frame in the space (using two rotations to fix the vertical axis and another to fix the other two axes). The values of these three rotations are called Euler angles .
These are three angles, also known as yaw, pitch and roll, Navigation angles and Cardan angles. Mathematically they constitute a set of six possibilities inside the twelve possible sets of Euler angles, the ordering being the one best used for describing the orientation of a vehicle such as an airplane. In aerospace engineering they are usually referred to as Euler angles.
Euler also realized that the composition of two rotations is equivalent to a single rotation about a different fixed axis ( Euler's rotation theorem ). Therefore, the composition of the former three angles has to be equal to only one rotation, whose axis was complicated to calculate until matrices were developed.
Based on this fact he introduced a vectorial way to describe any rotation, with a vector on the rotation axis and module equal to the value of the angle. Therefore, any orientation can be represented by a rotation vector (also called Euler vector) that leads to it from the reference frame. When used to represent an orientation, the rotation vector is commonly called orientation vector, or attitude vector.
A similar method, called axis–angle representation , describes a rotation or orientation using a unit vector aligned with the rotation axis, and a separate value to indicate the angle (see figure).
With the introduction of matrices, the Euler theorems were rewritten. The rotations were described by orthogonal matrices referred to as rotation matrices or direction cosine matrices. When used to represent an orientation, a rotation matrix is commonly called orientation matrix, or attitude matrix.
The above-mentioned Euler vector is the eigenvector of a rotation matrix (a rotation matrix has a unique real eigenvalue ).
The product of two rotation matrices is the composition of rotations. Therefore, as before, the orientation can be given as the rotation from the initial frame to achieve the frame that we want to describe.
The configuration space of a non- symmetrical object in n -dimensional space is SO( n ) × R n . Orientation may be visualized by attaching a basis of tangent vectors to an object. The direction in which each vector points determines its orientation.
Another way to describe rotations is using rotation quaternions , also called versors. They are equivalent to rotation matrices and rotation vectors. With respect to rotation vectors, they can be more easily converted to and from matrices. When used to represent orientations, rotation quaternions are typically called orientation quaternions or attitude quaternions.
The attitude of a rigid body is its orientation as described, for example, by the orientation of a frame fixed in the body relative to a fixed reference frame. The attitude is described by attitude coordinates , and consists of at least three coordinates. [ 2 ] One scheme for orienting a rigid body is based upon body-axes rotation; successive rotations three times about the axes of the body's fixed reference frame, thereby establishing the body's Euler angles . [ 3 ] [ 4 ] Another is based upon roll, pitch and yaw , [ 5 ] although these terms also refer to incremental deviations from the nominal attitude | https://en.wikipedia.org/wiki/Orientation_(geometry) |
The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space , right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also be assigned a negative orientation. A vector space with an orientation selected is called an oriented vector space , while one not having an orientation selected, is called unoriented .
In mathematics , orientability is a broader notion that, in two dimensions, allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed. In linear algebra over the real numbers , the notion of orientation makes sense in arbitrary finite dimension, and is a kind of asymmetry that makes a reflection impossible to replicate by means of a simple displacement . Thus, in three dimensions, it is impossible to make the left hand of a human figure into the right hand of the figure by applying a displacement alone, but it is possible to do so by reflecting the figure in a mirror. As a result, in the three-dimensional Euclidean space , the two possible basis orientations are called right-handed and left-handed (or right-chiral and left-chiral).
Let V be a finite-dimensional real vector space and let b 1 and b 2 be two ordered bases for V . It is a standard result in linear algebra that there exists a unique linear transformation A : V → V that takes b 1 to b 2 . The bases b 1 and b 2 are said to have the same orientation (or be consistently oriented) if A has positive determinant ; otherwise they have opposite orientations . The property of having the same orientation defines an equivalence relation on the set of all ordered bases for V . If V is non-zero, there are precisely two equivalence classes determined by this relation. An orientation on V is an assignment of +1 to one equivalence class and −1 to the other. [ 1 ]
Every ordered basis lives in one equivalence class or another. Thus any choice of a privileged ordered basis for V determines an orientation: the orientation class of the privileged basis is declared to be positive.
For example, the standard basis on R n provides a standard orientation on R n (in turn, the orientation of the standard basis depends on the orientation of the Cartesian coordinate system on which it is built). Any choice of a linear isomorphism between V and R n will then provide an orientation on V .
The ordering of elements in a basis is crucial. Two bases with a different ordering will differ by some permutation . They will have the same/opposite orientations according to whether the signature of this permutation is ±1. This is because the determinant of a permutation matrix is equal to the signature of the associated permutation.
Similarly, let A be a nonsingular linear mapping of vector space R n to R n . This mapping is orientation-preserving if its determinant is positive. [ 2 ] For instance, in R 3 a rotation around the Z Cartesian axis by an angle α is orientation-preserving: A 1 = ( cos α − sin α 0 sin α cos α 0 0 0 1 ) {\displaystyle \mathbf {A} _{1}={\begin{pmatrix}\cos \alpha &-\sin \alpha &0\\\sin \alpha &\cos \alpha &0\\0&0&1\end{pmatrix}}} while a reflection by the XY Cartesian plane is not orientation-preserving: A 2 = ( 1 0 0 0 1 0 0 0 − 1 ) {\displaystyle \mathbf {A} _{2}={\begin{pmatrix}1&0&0\\0&1&0\\0&0&-1\end{pmatrix}}}
The concept of orientation degenerates in the zero-dimensional case. A zero-dimensional vector space has only a single point, the zero vector. Consequently, the only basis of a zero-dimensional vector space is the empty set ∅ {\displaystyle \emptyset } . Therefore, there is a single equivalence class of ordered bases, namely, the class { ∅ } {\displaystyle \{\emptyset \}} whose sole member is the empty set . This means that an orientation of a zero-dimensional space is a function { { ∅ } } → { ± 1 } . {\displaystyle \{\{\emptyset \}\}\to \{\pm 1\}.} It is therefore possible to orient a point in two different ways, positive and negative.
Because there is only a single ordered basis ∅ {\displaystyle \emptyset } , a zero-dimensional vector space is the same as a zero-dimensional vector space with ordered basis. Choosing { ∅ } ↦ + 1 {\displaystyle \{\emptyset \}\mapsto +1} or { ∅ } ↦ − 1 {\displaystyle \{\emptyset \}\mapsto -1} therefore chooses an orientation of every basis of every zero-dimensional vector space. If all zero-dimensional vector spaces are assigned this orientation, then, because all isomorphisms among zero-dimensional vector spaces preserve the ordered basis, they also preserve the orientation. This is unlike the case of higher-dimensional vector spaces where there is no way to choose an orientation so that it is preserved under all isomorphisms.
However, there are situations where it is desirable to give different orientations to different points. For example, consider the fundamental theorem of calculus as an instance of Stokes' theorem . A closed interval [ a , b ] is a one-dimensional manifold with boundary , and its boundary is the set { a , b } . In order to get the correct statement of the fundamental theorem of calculus, the point b should be oriented positively, while the point a should be oriented negatively.
The one-dimensional case deals with an oriented line or directed line , which may be traversed in one of two directions. In real coordinate space , an oriented line is also known as an axis . [ 3 ] There are two orientations to a line just as there are two orientations to an oriented circle (clockwise and anti-clockwise). A semi-infinite oriented line is called a ray . In the case of a line segment (a connected subset of a line), the two possible orientations result in directed line segments .
An orientable surface sometimes has the selected orientation indicated by the orientation of a surface normal .
An oriented plane can be defined by a pseudovector .
For any n -dimensional real vector space V we can form the k th- exterior power of V , denoted Λ k V . This is a real vector space of dimension ( n k ) {\displaystyle {\tbinom {n}{k}}} . The vector space Λ n V (called the top exterior power ) therefore has dimension 1. That is, Λ n V is just a real line. There is no a priori choice of which direction on this line is positive. An orientation is just such a choice. Any nonzero linear form ω on Λ n V determines an orientation of V by declaring that x is in the positive direction when ω ( x ) > 0. To connect with the basis point of view we say that the positively-oriented bases are those on which ω evaluates to a positive number (since ω is an n -form we can evaluate it on an ordered set of n vectors, giving an element of R ). The form ω is called an orientation form . If { e i } is a privileged basis for V and { e i ∗ } is the dual basis , then the orientation form giving the standard orientation is e 1 ∗ ∧ e 2 ∗ ∧ … ∧ e n ∗ .
The connection of this with the determinant point of view is: the determinant of an endomorphism T : V → V {\displaystyle T:V\to V} can be interpreted as the induced action on the top exterior power.
Let B be the set of all ordered bases for V . Then the general linear group GL( V ) acts freely and transitively on B . (In fancy language, B is a GL( V )- torsor ). This means that as a manifold , B is (noncanonically) homeomorphic to GL( V ). Note that the group GL( V ) is not connected , but rather has two connected components according to whether the determinant of the transformation is positive or negative (except for GL 0 , which is the trivial group and thus has a single connected component; this corresponds to the canonical orientation on a zero-dimensional vector space). The identity component of GL( V ) is denoted GL + ( V ) and consists of those transformations with positive determinant. The action of GL + ( V ) on B is not transitive: there are two orbits which correspond to the connected components of B . These orbits are precisely the equivalence classes referred to above. Since B does not have a distinguished element (i.e. a privileged basis) there is no natural choice of which component is positive. Contrast this with GL( V ) which does have a privileged component: the component of the identity. A specific choice of homeomorphism between B and GL( V ) is equivalent to a choice of a privileged basis and therefore determines an orientation.
More formally: π 0 ( GL ( V ) ) = ( GL ( V ) / GL + ( V ) = { ± 1 } {\displaystyle \pi _{0}(\operatorname {GL} (V))=(\operatorname {GL} (V)/\operatorname {GL} ^{+}(V)=\{\pm 1\}} ,
and the Stiefel manifold of n -frames in V {\displaystyle V} is a GL ( V ) {\displaystyle \operatorname {GL} (V)} - torsor , so V n ( V ) / GL + ( V ) {\displaystyle V_{n}(V)/\operatorname {GL} ^{+}(V)} is a torsor over { ± 1 } {\displaystyle \{\pm 1\}} , i.e., its 2 points, and a choice of one of them is an orientation.
The various objects of geometric algebra are charged with three attributes or features : attitude, orientation, and magnitude. [ 5 ] For example, a vector has an attitude given by a straight line parallel to it, an orientation given by its sense (often indicated by an arrowhead) and a magnitude given by its length. Similarly, a bivector in three dimensions has an attitude given by the family of planes associated with it (possibly specified by the normal line common to these planes [ 6 ] ), an orientation (sometimes denoted by a curved arrow in the plane) indicating a choice of sense of traversal of its boundary (its circulation ), and a magnitude given by the area of the parallelogram defined by its two vectors. [ 7 ]
Each point p on an n -dimensional differentiable manifold has a tangent space T p M which is an n -dimensional real vector space. Each of these vector spaces can be assigned an orientation. Some orientations "vary smoothly" from point to point. Due to certain topological restrictions, this is not always possible. A manifold that admits a smooth choice of orientations for its tangent spaces is said to be orientable . | https://en.wikipedia.org/wiki/Orientation_(vector_space) |
In mathematics, an orientation of a real vector bundle is a generalization of an orientation of a vector space ; thus, given a real vector bundle π: E → B , an orientation of E means: for each fiber E x , there is an orientation of the vector space E x and one demands that each trivialization map (which is a bundle map)
is fiberwise orientation-preserving, where R n is given the standard orientation . In more concise terms, this says that the structure group of the frame bundle of E , which is the real general linear group GL n ( R ), can be reduced to the subgroup consisting of those with positive determinant.
If E is a real vector bundle of rank n , then a choice of metric on E amounts to a reduction of the structure group to the orthogonal group O ( n ). In that situation, an orientation of E amounts to a reduction from O ( n ) to the special orthogonal group SO ( n ).
A vector bundle together with an orientation is called an oriented bundle . A vector bundle that can be given an orientation is called an orientable vector bundle .
The basic invariant of an oriented bundle is the Euler class . The multiplication (that is, cup product) by the Euler class of an oriented bundle gives rise to a Gysin sequence .
A complex vector bundle is oriented in a canonical way.
The notion of an orientation of a vector bundle generalizes an orientation of a differentiable manifold : an orientation of a differentiable manifold is an orientation of its tangent bundle. In particular, a differentiable manifold is orientable if and only if its tangent bundle is orientable as a vector bundle. (note: as a manifold, a tangent bundle is always orientable.)
To give an orientation to a real vector bundle E of rank n is to give an orientation to the (real) determinant bundle det E = ∧ n E {\displaystyle \operatorname {det} E=\wedge ^{n}E} of E . Similarly, to give an orientation to E is to give an orientation to the unit sphere bundle of E .
Just as a real vector bundle is classified by the real infinite Grassmannian , oriented bundles are classified by the infinite Grassmannian of oriented real vector spaces.
From the cohomological point of view, for any ring Λ, a Λ-orientation of a real vector bundle E of rank n means a choice (and existence) of a class
in the cohomology ring of the Thom space T ( E ) such that u generates H ~ ∗ ( T ( E ) ; Λ ) {\displaystyle {\tilde {H}}^{*}(T(E);\Lambda )} as a free H ∗ ( E ; Λ ) {\displaystyle H^{*}(E;\Lambda )} -module globally and locally: i.e.,
is an isomorphism (called the Thom isomorphism ), where "tilde" means reduced cohomology , that restricts to each isomorphism
induced by the trivialization π − 1 ( U ) ≃ U × R n {\displaystyle \pi ^{-1}(U)\simeq U\times \mathbf {R} ^{n}} . One can show, with some work, [ citation needed ] that the usual notion of an orientation coincides with a Z -orientation. | https://en.wikipedia.org/wiki/Orientation_of_a_vector_bundle |
The orientation of a building refers to the direction in which it is constructed and laid out, taking account of its planned purpose and ease of use for its occupants, its relation to the path of the sun and other aspects of its environment. [ 1 ] In church architecture , orientation is an arrangement by which the point of main interest in the interior is towards the east ( Latin : oriens ). The east end is where the altar is placed, often within an apse . The façade and main entrance are accordingly at the west end.
The opposite arrangement, in which the church is entered from the east and the sanctuary is at the other end, is called occidentation. [ 2 ] [ 3 ] [ 4 ] [ 5 ]
Since the eighth century most churches are orientated. Hence, even in the many churches where the altar end is not actually on the east side of the structure, terms such as "east end", "west door", "north aisle" are commonly used as if the church were orientated, treating the altar end as the liturgical east . [ 6 ]
Many early Christians faced east when praying. Due to this established custom, Tertullian says some non-Christians thought they worshipped the sun. [ 7 ] Origen says: "The fact that ... of all the quarters of the heavens, the east is the only direction we turn to when we pour out prayer, the reasons for this, I think, are not easily discovered by anyone." [ 8 ] Later on, various Church Fathers advanced mystical reasons for the custom. One such explanation is that Christ's Second Coming was expected to be from the east: "For as the lightning comes from the east and shines as far as the west, so will be the coming of the Son of Man". [ 9 ] [ 10 ] [ 11 ]
At first, the orientation of the building in which Christians met was unimportant, but after the legalization of the religion by the Roman Empire in the fourth century, customs developed in this regard. [ 12 ] These differed in Eastern and Western Christianity .
The Apostolic Constitutions , a work of Eastern Christianity written between 375 and 380 AD, gave it as a rule that churches should have the sanctuary (with apse and sacristies ) at the east end, to enable Christians to pray eastward in church as in private or in small groups. In the middle of the sanctuary was the altar , behind which was the bishop 's throne, flanked by the seats of the presbyters , while the laity were on the opposite side. However, even in the East there were churches (for example, in Tyre, Lebanon ) that had the entrance at the east end, and the sanctuary at the west end. During the readings all looked towards the readers, the bishop and presbyters looking westward, the people eastward. The Apostolic Constitutions , like the other documents that speak of the custom of praying towards the east, do not indicate on which side of the altar the bishop stood for "the sacrifice". [ 13 ] [ 14 ]
The earliest Christian churches in Rome were all built with the entrance on the opposite side: to the east, like the Jewish temple in Jerusalem . [ 15 ] Only in the 8th or 9th century did Rome accept the orientation that had become obligatory in the Byzantine Empire and was also generally adopted in the Frankish Empire and elsewhere in western and northern Europe. [ 12 ] [ 15 ] [ 16 ] The original Constantinian Church of the Holy Sepulchre in Jerusalem also had the altar in the west end. [ 17 ] [ 18 ]
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). [ 19 ]
The importance attached to orientation of churches declined in Europe after the 15th century. [ 20 ] In his instructions on the building and arrangement of churches, Charles Borromeo , archbishop of Milan from 1560 to 1584, expressed a preference for having the apse point exactly east, but accepted that, where that is impractical, a church could be built even on a north–south axis, preferably with the façade at the southern end. He stated that the altar can also be at the west end, where "in accordance with the rite of the Church it is customary for Mass to be celebrated at the main altar by a priest facing the people". [ 21 ]
The medieval mendicant orders generally built their churches inside towns and had to fit them into the town plans, regardless of orientation. Later, in the Spanish and Portuguese colonial empires they made no attempt to observe orientation, as is seen in San Francisco de Asis Mission Church near Taos, New Mexico . Today in the West, orientation is little observed in building churches, even by the Catholic church, and still less by Protestant denominations.
Borromeo stated that churches ought to be orientated exactly east, in line with the rising sun at the equinoxes , not at the solstices , but some churches seem to be orientated to sunrise on the feast day of their patron saint. Thus St. Stephen's Cathedral, Vienna is oriented in line with sunrise on Saint Stephen's Day , 26 December, in Julian calendar 1137, when it began to be built. However, a survey of old English churches published in 2006 showed practically no relationship with the feast days of the saints to whom they are dedicated. The results also did not conform to a theory that compass readings could have caused the variants. Taken as a body, those churches can only be said to have been orientated approximately but not exactly to the geographical east. [ 22 ]
Another survey of a smaller number of English churches examined other possible alignments also and found that, if sunset as well as sunrise is taken into account, the saint's day hypothesis covered 43% of the cases considered, and that there was a significant correspondence also with sunrise on Easter morning of the year of foundation. The results provided no support for the compass readings hypothesis. [ 23 ]
Yet another study of English churches found that a significant proportion of churches that showed a considerable deviation from true east were constrained by neighbouring buildings in town and perhaps by site topography in rural areas. [ 24 ]
Similarly, a survey of a total of 32 medieval churches with reliable metadata in Lower Austria and northern Germany discovered only a few aligned in accordance with the saint's feast, with no general trend. There was no evidence of the use of compasses; and there was a preferred alignment towards true east, with variations due to town and natural topography. [ 20 ]
A notable example of an (approximately) orientated church building that – to match the contours of its location and to avoid an area that was swampy at the time of its construction – bends slightly in the middle is Quimper Cathedral in Brittany .
Also the modern Coventry Cathedral faces north–south, perpendicular to the old cathedral that was bombed by the Luftwaffe during the blitz. The porch over the main entrance extends over the old wall and, while not connected to the original building does make a nod towards continuity of the structure. | https://en.wikipedia.org/wiki/Orientation_of_churches |
In the mathematical field of algebraic topology , the orientation sheaf on a manifold X of dimension n is a locally constant sheaf o X on X such that the stalk of o X at a point x is the local homology group
(in the integer coefficients or some other coefficients).
Let Ω M k {\displaystyle \Omega _{M}^{k}} be the sheaf of differential k -forms on a manifold M . If n is the dimension of M , then the sheaf
is called the sheaf of (smooth) densities on M . The point of this is that, while one can integrate a differential form only if the manifold is oriented , one can always integrate a density, regardless of orientation or orientability; there is the integration map:
If M is oriented; i.e., the orientation sheaf of the tangent bundle of M is literally trivial, then the above reduces to the usual integration of a differential form.
This topology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orientation_sheaf |
In solid-state physics , an orientational glass [ 1 ] is a molecular solid in which crystalline long-range order coexists with quenched disorder in some rotational degree of freedom .
An orientational glass is either obtained by quenching a plastic crystal , (e.g. cyclohexane , levoglucosan [ 2 ] ), or it is a mixed crystal in which positional disorder causes additional disorder of molecular orientations, e.g. CN orientations in KCN : KBr . [ 3 ]
This condensed matter physics -related article is a stub . You can help Wikipedia by expanding it .
This crystallography -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orientational_glass |
Oriented energy filters are used to grant sight to intelligent machines and sensors. The light comes in and is filtered so that it can be properly computed and analyzed by the computer allowing it to “perceive” what it is measuring. These energy measurements are then calculated to take a real time measurement of the oriented space time structure. [ 1 ]
3D Gaussian filters are used to extract orientation measurements. They were chosen due to their ability to capture a broad spectrum and easy and efficient computations. [ 2 ]
The use of these vision systems can then be used in smart room , human interface and surveillance applications. The computations used can tell more than the standalone frame that most perceived motion devices such as a television frame. The objects captured by these devices would tell the velocity and energy of an object and its direction in relation to space and time. This also allows for better tracking ability and recognition. [ 3 ]
This article related to sensors is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Oriented_energy_filters |
The orienting response ( OR ), also called orienting reflex , is an organism's immediate response to a change in its environment, when that change is not sudden enough to elicit the startle reflex . The phenomenon was first described by Russian physiologist Ivan Sechenov in his 1863 book Reflexes of the Brain , and the term ('ориентировочный рефлекс' in Russian) was coined by Ivan Pavlov , who also referred to it as the Shto takoye? (Что такое? or What is it? ) reflex. The orienting response is a reaction to novel or significant stimuli. In the 1950s the orienting response was studied systematically by the Russian scientist Evgeny Sokolov , who documented the phenomenon called " habituation ", referring to a gradual "familiarity effect" and reduction of the orienting response with repeated stimulus presentations. [ 1 ]
Researchers have found a number of physiological mechanisms associated with OR, including changes in phasic and tonic skin conductance response (SCR), electroencephalogram (EEG), and heart rate following a novel or significant stimulus. These observations all occur within seconds of stimulus introduction. [ 2 ] In particular, EEG studies of OR have corresponded particularly with the P300 wave and P3a component of the OR-related event-related potential (ERP). [ 3 ]
Current understanding of the localization of OR in the brain is still unclear. In one study using fMRI and SCR, researchers found novel visual stimuli associated with SCR responses typical of an OR also corresponded to activation in the hippocampus , anterior cingulate gyrus , and ventromedial prefrontal cortex . These regions are also believed to be largely responsible for emotion, decision making, and memory. Increases in cerebellar and extrastriate cortex were also recorded, which are significantly implicated in visual perception and processing. [ 4 ]
When an individual encounters a novel environmental stimulus, such as a bright flash of light or a sudden loud noise, they will pay attention to it even before identifying it. This orienting reflex seems to be present early in development, as babies will turn their head toward an environmental change ( Nelson Cowan , 1995). From an evolutionary perspective, this mechanism is useful in reacting quickly to events that call for immediate action.
Sokolov's investigation of OR was primarily motivated in understanding habituation. Provided the first introduction of a novel stimulus, defined in Sokolovian terms as any change from the "currently active neuronal model" (what the individual is currently focused on), results in OR. However, with repeated introduction of the same stimulus, the orienting response will decrease in intensity and eventually cease. [ 1 ] When novel stimuli have an associated contextual significance, repeated stimulus will still result in a sequentially decreasing OR, though at a modified rate of decay. [ 2 ]
The orienting response is believed to play an integral role in preference formation. When faced with deciding between two options, subjects in studies by Simion & Shimojo were shown to choose the items they preferentially orient their gaze toward. This gaze can occur while the stimulus is present or after it has been removed, the latter causing gaze to be fixated at the point in which the stimulus had been present. Gaze bias ceases following a decision, suggesting that gaze bias is the cause of preference and not its effect. Noting this postulated causal link with the irrelevance of a stimulus presence, it is argued that gaze orientation supports decision-making mechanisms in inducing a preferential bias. [ 5 ]
Both novelty and significance of a stimulation are implicated in the generation of an orienting response. Specifically, the emotional significance of a stimulus, defined by its level of pleasantness, can affect the intensity of the orienting response toward focusing attention on a subject. Studies showed that during exposure to neutral and emotionally significant novel images, both pleasant and unpleasant images produced higher skin conductance readings than neutral images. With repeated stimulation, all skin conductance readings diminished relative to novel introduction, though with emotionally significant content diminishing more slowly. Conversely, studies observing cardiac deceleration during novel stimuli introduction showed significantly more deceleration for unpleasant stimuli compared to pleasant and neutral stimuli. These findings suggest that OR represents a combination of responses that act in tandem to a common stimulus. More importantly, the differences between emotionally charged and neutral stimuli demonstrates the influence of emotion in orienting attention, despite novelty. [ 2 ]
The orienting response has been posited as being stimulated by bilateral stimulation, and being the active ingredient in Eye movement desensitization and reprocessing (EMDR) therapy . [ 6 ]
In his 2007 book The Assault on Reason , Al Gore posited that watching television affects the orienting response, an effect similar to vicarious traumatization .
6. Sokolov E N, Spinks J A, Naatanen R, Lyytinen H (2002) The Orienting Response In Information Processing. Lawrence Erlbaum Associates, Publishers. Mahwah, New Jersey. London. | https://en.wikipedia.org/wiki/Orienting_response |
An orifice plate is a device used for measuring flow rate, reducing pressure or restricting flow (in the latter two cases it is often called a restriction plate ).
An orifice plate is a thin plate with a hole in it, which is usually placed in a pipe. When a fluid (whether liquid or gaseous) passes through the orifice, its pressure builds up slightly upstream of the orifice [ 1 ] but as the fluid is forced to converge to pass through the hole, the velocity increases and the fluid pressure decreases. A little downstream of the orifice the flow reaches its point of maximum convergence, the vena contracta (see drawing to the right) where the velocity reaches its maximum and the pressure reaches its minimum. Beyond that, the flow expands, the velocity falls and the pressure increases. By measuring the difference in fluid pressure across tappings upstream and downstream of the plate, the flow rate can be obtained from Bernoulli's equation using coefficients established from extensive research. [ 2 ]
In general, the mass flow rate q m {\displaystyle q_{m}} measured in kg/s across an orifice can be described as [ 3 ]
where
The volume flow rate q v {\displaystyle q_{v}} measured in m 3 /s is [ 3 ]
The overall pressure loss in the pipe due to an orifice plate is lower than the measured differential pressure, typically by a factor of 1 − β 1.9 {\displaystyle 1-\beta ^{1.9}} . [ 4 ]
Orifice plates are most commonly used to measure flow rates in pipes, when the fluid is single-phase (rather than being a mixture of gases and liquids, or of liquids and solids) and well-mixed, the flow is continuous rather than pulsating, the fluid occupies the entire pipe (precluding silt or trapped gas), the flow profile is even and well-developed and the fluid and flow rate meet certain other conditions. Under these circumstances and when the orifice plate is constructed and installed according to appropriate standards, the flow rate can easily be determined using published formulae based on substantial research and published in industry, national and international standards. [ 5 ]
An orifice plate is called a calibrated orifice if it has been calibrated with an appropriate fluid flow and a traceable flow measurement device.
Plates are commonly made with sharp-edged circular orifices and installed concentric with the pipe and with pressure tappings at one of three standard pairs of distances upstream and downstream of the plate; these types are covered by ISO 5167 and other major standards. There are many other possibilities. The edges may be rounded or conical, the plate may have an orifice the same size as the pipe except for a segment at top or bottom which is obstructed, the orifice may be installed eccentric to the pipe, and the pressure tappings may be at other positions. Variations on these possibilities are covered in various standards and handbooks. Each combination gives rise to different coefficients of discharge which can be predicted so long as various conditions are met, conditions which differ from one type to another. [ 5 ]
Once the orifice plate is designed and installed, the flow rate can often be indicated with an acceptably low uncertainty simply by taking the square root of the differential pressure across the orifice's pressure tappings and applying an appropriate constant.
Orifice plates are also used to reduce pressure or restrict flow, in which case they are often called restriction plates. [ 6 ] [ 7 ]
There are three standard positions for pressure tappings (also called taps), commonly named as follows:
These types are covered by ISO 5167 and other major standards. Other types include
The measured differential pressure differs for each combination and so the coefficient of discharge used in flow calculations depends partly on the tapping positions.
The simplest installations use single tappings upstream and downstream, but in some circumstances these may be unreliable; they might be blocked by solids or gas-bubbles, or the flow profile might be uneven so that the pressures at the tappings are higher or lower than the average in those planes. In these situations multiple tappings can be used, arranged circumferentially around the pipe and joined by a piezometer ring, or (in the case of corner taps) annular slots running completely round the internal circumference of the orifice carrier.
Standards and handbooks are mainly concerned with sharp-edged thin plates. In these, the leading edge is sharp and free of burrs and the cylindrical section of the orifice is short, either because the entire plate is thin or because the downstream edge of the plate is bevelled. Exceptions include the quarter-circle or quadrant-edge orifice, which has a fully rounded leading edge and no cylindrical section, and the conical inlet or conical entrance plate which has a bevelled leading edge and a very short cylindrical section. The orifices are normally concentric with the pipe (the eccentric orifice is a specific exception) and circular (except in the specific case of the segmental or chord orifice, in which the plate obstructs just a segment of the pipe). Standards and handbooks stipulate that the upstream surface of the plate is particularly flat and smooth. Sometimes a small drain or vent hole is drilled through the plate where it meets the pipe, to allow condensate or gas bubbles to pass along the pipe.
Standards and handbooks stipulate a well-developed flow profile; velocities will be lower at the pipe wall than in the centre but not eccentric or jetting. Similarly the flow downstream of the plate must be unobstructed, otherwise the downstream pressure will be affected. To achieve this, the pipe must be acceptably circular, smooth and straight for stipulated distances. Sometimes when it is impossible to provide enough straight pipe, flow conditioners such as tube bundles or plates with multiple holes are inserted into the pipe to straighten and develop the flow profile, but even these require a further length of straight pipe before the orifice itself. Some standards and handbooks also provide for flows from or into large spaces rather than pipes, stipulating that the region before or after the plate is free of obstruction and abnormalities in the flow.
By assuming steady-state, incompressible (constant fluid density), inviscid , laminar flow in a horizontal pipe (no change in elevation) with negligible frictional losses, Bernoulli's equation (which expresses the conservation of energy of an incompressible fluid parcel as it moves between two points on the same streamline) can be rewritten without the gravitational potential energy term and reduced to:
p 1 + 1 2 ⋅ ρ ⋅ V 1 ′ 2 = p 2 + 1 2 ⋅ ρ ⋅ V 2 ′ 2 {\displaystyle p_{1}+{\frac {1}{2}}\cdot \rho \cdot V_{1}^{'^{2}}=p_{2}+{\frac {1}{2}}\cdot \rho \cdot V_{2}^{'^{2}}}
or:
p 1 − p 2 = 1 2 ⋅ ρ ⋅ V 2 ′ 2 − 1 2 ⋅ ρ ⋅ V 1 ′ 2 {\displaystyle p_{1}-p_{2}={\frac {1}{2}}\cdot \rho \cdot V_{2}^{'^{2}}-{\frac {1}{2}}\cdot \rho \cdot V_{1}^{'^{2}}}
By continuity equation:
q v ′ = A 1 ⋅ V 1 ′ = A 2 ⋅ V 2 ′ {\displaystyle q_{v}^{'}=A_{1}\cdot V_{1}^{'}=A_{2}\cdot V_{2}^{'}} or V 1 ′ = q v ′ / A 1 {\displaystyle V_{1}^{'}=q_{v}^{'}/A_{1}} and V 2 ′ = q v ′ / A 2 {\displaystyle V_{2}^{'}=q_{v}^{'}/A_{2}} :
p 1 − p 2 = 1 2 ⋅ ρ ⋅ ( q v ′ A 2 ) 2 − 1 2 ⋅ ρ ⋅ ( q v ′ A 1 ) 2 {\displaystyle p_{1}-p_{2}={\frac {1}{2}}\cdot \rho \cdot {\bigg (}{\frac {q_{v}^{'}}{A_{2}}}{\bigg )}^{2}-{\frac {1}{2}}\cdot \rho \cdot {\bigg (}{\frac {q_{v}^{'}}{A_{1}}}{\bigg )}^{2}}
Solving for q v ′ {\displaystyle q_{v}^{'}} :
q v ′ = A 2 2 ( p 1 − p 2 ) / ρ 1 − ( A 2 / A 1 ) 2 {\displaystyle q_{v}^{'}=A_{2}\;{\sqrt {\frac {2\;(p_{1}-p_{2})/\rho }{1-(A_{2}/A_{1})^{2}}}}}
and:
q v ′ = A 2 1 1 − ( d / D ) 4 2 ( p 1 − p 2 ) / ρ {\displaystyle q_{v}^{'}=A_{2}\;{\sqrt {\frac {1}{1-(d/D)^{4}}}}\;{\sqrt {2\;(p_{1}-p_{2})/\rho }}}
The above expression for q v ′ {\displaystyle q_{v}^{'}} gives the theoretical volume flow rate. Introducing the beta factor β = d / D {\displaystyle \beta =d/D} as well as the discharge coefficient C d {\displaystyle C_{d}} :
q v = C d A 2 1 1 − β 4 2 ( p 1 − p 2 ) / ρ {\displaystyle q_{v}=C_{d}\;A_{2}\;{\sqrt {\frac {1}{1-\beta ^{4}}}}\;{\sqrt {2\;(p_{1}-p_{2})/\rho }}}
And finally introducing the meter coefficient C {\displaystyle C} which is defined as C = C d 1 − β 4 {\displaystyle C={\frac {C_{d}}{\sqrt {1-\beta ^{4}}}}} to obtain the final equation for the volumetric flow of the fluid through the orifice which accounts for irreversible losses:
( 1 ) q v = C A 2 2 ( p 1 − p 2 ) / ρ {\displaystyle (1)\qquad q_{v}=C\;A_{2}\;{\sqrt {2\;(p_{1}-p_{2})/\rho }}}
Multiplying by the density of the fluid to obtain the equation for the mass flow rate at any section in the pipe: [ 8 ] [ 9 ] [ 10 ] [ 11 ]
( 2 ) q m = ρ q v = C A 2 2 ρ ( p 1 − p 2 ) {\displaystyle (2)\qquad q_{m}=\rho \;q_{v}=C\;A_{2}\;{\sqrt {2\;\rho \;(p_{1}-p_{2})}}}
Deriving the above equations used the cross-section of the orifice opening and is not as realistic as using the minimum cross-section at the vena contracta . In addition, frictional losses may not be negligible and viscosity and turbulence effects may be present. For that reason, the coefficient of discharge C d {\displaystyle C_{d}} is introduced. Methods exist for determining the coefficient of discharge as a function of the Reynolds number . [ 9 ]
The parameter 1 1 − β 4 {\displaystyle {\frac {1}{\sqrt {1-\beta ^{4}}}}} is often referred to as the velocity of approach factor [ 8 ] and multiplying the coefficient of discharge by that parameter (as was done above) produces the flow coefficient C {\displaystyle C} . Methods also exist for determining the flow coefficient as a function of the beta function β {\displaystyle \beta } and the location of the downstream pressure sensing tap. For rough approximations, the flow coefficient may be assumed to be between 0.60 and 0.75. For a first approximation, a flow coefficient of 0.62 can be used as this approximates to fully developed flow.
An orifice only works well when supplied with a fully developed flow profile. This is achieved by a long upstream length (20 to 40 pipe diameters, depending on Reynolds number) or the use of a flow conditioner. Orifice plates are small and inexpensive but do not recover the pressure drop as well as a venturi , nozzle, or venturi-nozzle does. Venturis also require much less straight pipe upstream. A venturi meter is more efficient, but usually more expensive and less accurate (unless calibrated in a laboratory) than an orifice plate.
In general, equation (2) is applicable only for incompressible flows. It can be modified by introducing the expansibility factor, (also called the expansion factor) ϵ {\displaystyle \epsilon } to account for the compressibility of gasses.
q m = ρ 1 q v , 1 = C ϵ A 2 2 ρ 1 ( p 1 − p 2 ) {\displaystyle q_{m}=\rho _{1}\;q_{v,1}=C\;\epsilon \;A_{2}\;{\sqrt {2\;\rho _{1}\;(p_{1}-p_{2})}}}
ϵ {\displaystyle \epsilon } is 1.0 for incompressible fluids and it can be calculated for compressible gases [ 9 ] using empirically determined formulae as shown below in computation .
For smaller values of β (such as restriction plates with β less than 0.25 and discharge from tanks), if the fluid is compressible, the rate of flow depends on whether the flow has become choked. If it is, then the flow may be calculated as shown at choked flow (although the flow of real gases through thin-plate orifices never becomes fully choked [ a ] [ 13 ] By using a mechanical energy balance, compressible fluid flow in un-choked conditions may be calculated as: [ 10 ] [ 11 ] [ 14 ]
q m = C A 2 2 ρ 1 p 1 ( γ γ − 1 ) [ ( p 2 / p 1 ) 2 / γ − ( p 2 / p 1 ) ( γ + 1 ) / γ ] {\displaystyle q_{m}=C\;A_{2}\;{\sqrt {2\;\rho _{1}\;p_{1}\;{\bigg (}{\frac {\gamma }{\gamma -1}}{\bigg )}{\bigg [}(p_{2}/p_{1})^{2/\gamma }-(p_{2}/p_{1})^{(\gamma +1)/\gamma }{\bigg ]}}}}
and
q v = q m ρ 1 {\displaystyle q_{v}={\frac {q_{m}}{\rho _{1}}}}
Under choked flow conditions, the fluid flow rate becomes: [ 10 ]
q m = C A 2 γ ρ 1 p 1 ( 2 γ + 1 ) γ + 1 γ − 1 {\displaystyle q_{m}=C\;A_{2}\;{\sqrt {\gamma \;\rho _{1}\;p_{1}\;{\bigg (}{\frac {2}{\gamma +1}}{\bigg )}^{\frac {\gamma +1}{\gamma -1}}}}}
or
q v = C A 2 γ p 1 ρ 1 ( 2 γ + 1 ) γ + 1 γ − 1 {\displaystyle q_{v}=C\;A_{2}\;{\sqrt {\gamma \;{\frac {p_{1}}{\rho _{1}}}\;{\bigg (}{\frac {2}{\gamma +1}}{\bigg )}^{\frac {\gamma +1}{\gamma -1}}}}}
Flow rates through an orifice plate can be calculated without specifically calibrating the individual flowmeter so long as the construction and installation of the device complies with the stipulations of the relevant standard or handbook. The calculation takes account of the fluid and fluid conditions, the pipe size, the orifice size and the measured differential pressure; it also takes account of the coefficient of discharge of the orifice plate, which depends upon the orifice type and the positions of the pressure tappings. With local pressure tappings (corner, flange and D+D/2), sharp-edged orifices have coefficients around 0.6 to 0.63, [ 15 ] while the coefficients for conical entrance plates are in the range 0.73 to 0.734 and for quarter-circle plates 0.77 to 0.85. [ 5 ] The coefficients of sharp-edged orifices vary more with fluids and flow rates than the coefficients of conical-entrance and quarter-circle plates, especially at low flows and high viscosities.
For compressible flows such as flows of gases or steam, an expansibility factor or expansion factor is also calculated. This factor is primarily a function of the ratio of the measured differential pressure to the fluid pressure and so can vary significantly as the flow rate varies, especially at high differential pressures and low static pressures.
The equations provided in American and European national and industry standards and the various coefficients used to differ from each other even to the extent of using different combinations of correction factors, but many are now closely aligned and give identical results; in particular, they use the same Reader-Harris/Gallagher (1998) equation for the coefficient of discharge for sharp-edged orifice plates. The equations below largely follow the notation of the international standard ISO 5167 and use SI units. [ 3 ] [ 16 ]
Volume flow rate:
Mass flow rate:
Coefficient of discharge for sharp-edged orifice plates with corner, flange or D and D/2 tappings and no drain or vent hole (Reader-Harris/Gallagher equation):
Expansibility factor, also called expansion factor, for sharp-edged orifice plates with corner, flange or D and D/2 tappings:
The overall pressure loss caused by an orifice plate is less than the differential pressure measured across tappings near the plate. For sharp-edged plates such as corner, flange or D and D/2 tappings, it can be approximated by the equation
or | https://en.wikipedia.org/wiki/Orifice_plate |
In mathematics , the origin of a Euclidean space is a special point , usually denoted by the letter O , used as a fixed point of reference for the geometry of the surrounding space.
In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the same answer. This allows one to pick an origin point that makes the mathematics as simple as possible, often by taking advantage of some kind of geometric symmetry .
In a Cartesian coordinate system , the origin is the point where the axes of the system intersect. [ 1 ] The origin divides each of these axes into two halves, a positive and a negative semiaxis. [ 2 ] Points can then be located with reference to the origin by giving their numerical coordinates —that is, the positions of their projections along each axis, either in the positive or negative direction. The coordinates of the origin are always all zero, for example (0,0) in two dimensions and (0,0,0) in three. [ 1 ]
In a polar coordinate system , the origin may also be called the pole. It does not itself have well-defined polar coordinates, because the polar coordinates of a point include the angle made by the positive x -axis and the ray from the origin to the point, and this ray is not well-defined for the origin itself. [ 3 ]
In Euclidean geometry , the origin may be chosen freely as any convenient point of reference. [ 4 ]
The origin of the complex plane can be referred as the point where real axis and imaginary axis intersect each other. In other words, it is the complex number zero . [ 5 ] | https://en.wikipedia.org/wiki/Origin_(mathematics) |
Fluorine is relatively rare in the universe compared to other elements of nearby atomic weight . On Earth , fluorine is essentially found only in mineral compounds because of its reactivity. The main commercial source, fluorite , is a common mineral.
At 400 ppb, fluorine is estimated to be the 24th most common element in the universe. It is comparably rare for a light element (elements tend to be more common the lighter they are). All of the elements from atomic number 6 (carbon) to atomic number 12 (magnesium) are hundreds or thousands of times more common than fluorine except for 11 (sodium). One science writer described fluorine as a "shack amongst mansions" in terms of abundance. [ 2 ] Fluorine is so rare because it is not a product of the usual nuclear fusion processes in stars. And any created fluorine within stars is rapidly eliminated through strong nuclear fusion reactions—either with hydrogen to form oxygen and helium, or with helium to make neon and hydrogen. [ 2 ] [ 3 ] The presence of fluorine at all—outside of temporary existence in stars—is somewhat of a mystery because of the need to escape these fluorine-destroying reactions. [ 2 ] [ 4 ]
Three theoretical solutions to the mystery exist: In type II supernovae , atoms of neon could be hit by neutrinos during the explosion and converted to fluorine. In Wolf-Rayet stars (blue stars over 40 times heavier than the Sun), a strong solar wind could blow the fluorine out of the star before hydrogen or helium could destroy it. Finally, in asymptotic giant branch (a type of red giant) stars, fusion reactions occur in pulses and convection could lift fluorine out of the inner star. Only the red giant hypothesis has supporting evidence from observations, fluorine cations have been found in planetary nebulae. [ 2 ] [ 4 ]
In space, fluorine commonly combines with hydrogen to form hydrogen fluoride. (This compound has been suggested as a tracer to enable tracking reservoirs of hydrogen in the universe.) [ 5 ] In addition to HF, monatomic fluorine has been observed in the interstellar medium . [ 6 ] [ 7 ] Fluorine cations have been seen in planetary nebulae and in stars, including the Sun. [ 8 ]
Fluorine is the thirteenth most common element in Earth's crust, comprising between 600 and 700 ppm of the crust by mass. Because of its reactivity, it is essentially only found in compounds.
Three minerals exist that are industrially relevant sources of fluorine: fluorite , fluorapatite , and cryolite . [ 9 ] [ 10 ]
Fluorite (CaF 2 ), also called fluorspar, is the main source of commercial fluorine. Fluorite is a colorful mineral associated with hydrothermal deposits. It is common and found worldwide. China supplies more than half of the world's demand and Mexico is the second-largest producer in the world. [ citation needed ]
The United States produced most of the world's fluorite in the early 20th century, but its last mine, in Illinois, shut down in 1995. Canada also exited production in the 1990s. The United Kingdom has declining fluorite mining and has been a net importer since the 1980s. [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ]
Fluorapatite (Ca 5 (PO 4 ) 3 F) is mined along with other apatites for its phosphate content and is used mostly for production of fertilizers. Most of the Earth's fluorine is bound in this mineral, but because the percentage within the mineral is low (3.5%), the fluorine is discarded as waste. Only in the United States is there significant recovery. There, the hexafluorosilicates produced as byproducts are used to supply water fluoridation. [ 10 ]
Cryolite (Na 3 AlF 6 ) is the least abundant of the three major fluorine-containing minerals, but is a concentrated source of fluorine. It was formerly used directly in aluminium production. However, the main commercial mine, on the west coast of Greenland, closed in 1987. [ 10 ]
Several other minerals, such as the gemstone topaz , contain fluoride. Fluoride is not significant in seawater or brines, unlike the other halides , because the alkaline earth fluorides precipitate out of water. [ 10 ] Commercially insignificant quantities of organofluorines have been observed in volcanic eruptions and in geothermal springs. Their ultimate origin (from biological sources or geological formation) is unclear. [ 15 ]
The possibility of small amounts of gaseous fluorine within crystals has been debated for many years. One form of fluorite, antozonite , has a smell suggestive of fluorine when crushed. The mineral also has a dark black color, perhaps from free calcium (not bonded to fluoride). In 2012, a study reported detection of trace quantities (0.04% by weight) of diatomic fluorine in antozonite. It was suggested that radiation from small amounts of uranium within the crystals had caused the free fluorine defects . [ 16 ] | https://en.wikipedia.org/wiki/Origin_and_occurrence_of_fluorine |
An origin myth is a type of myth that explains the beginnings of a natural or social aspect of the world. Creation myths are a type of origin myth narrating the formation of the universe. However, numerous cultures have stories that take place after the initial origin. These stories aim to explain the origins of natural phenomena or human institutions within an already existing world. In Greco-Roman scholarship, the terms founding myth or etiological myth (from Ancient Greek : αἴτιον aition 'cause') are occasionally used to describe a myth that clarifies an origin, particularly how an object or custom came into existence.
In modern political discourse the terms "founding myth", "foundational myth", etc. are often used as critical references to official or widely accepted narratives about the origins or early history of a nation, a society, a culture, etc. [ 1 ] [ 2 ]
Origin myths are narratives that explain how a particular reality came into existence. [ 3 ] They often serve to justify the established order by attributing its establishment to sacred forces [ 3 ] (see § Social function ). The line between cosmogonic myths which describe the origin of the world and origin myths is not always clear. A myth about the origin of a specific part of the world assumes the existence of the world itself, which often relies on a cosmogonic myth. [ 3 ] Therefore, origin myths can be seen as expanding upon and building upon their cultures' cosmogonic myths. In traditional cultures, it is common for the recitation of an origin myth to be preceded by the recitation of a cosmogonic myth. [ 4 ]
Within academic circles, the term myth is often used specifically to refer to origin and cosmogonic myths. Folklorists, for example, reserve the term myth for stories that describe creation. Stories that do not primarily focus on origins are categorized as legend or folk tale , which are distinct from myths according to folklorists. [ 5 ] Mircea Eliade , a historian, argues that in many traditional cultures, almost every sacred story can be considered an origin myth. Traditional societies often pattern their behavior after sacred events and view their lives as a cyclical return to a mythical age. As a result, nearly every sacred story portrays events that establish a new framework for human behavior, making them essentially stories of creation. [ 6 ]
An origin myth often functions to justify the current state of affairs. In traditional cultures, the entities and forces described in origin myths are often considered sacred. Thus, by attributing the state of the universe to the actions of these entities and forces, origin myths give the current order an aura of sacredness: "[M]yths reveal that the World, man, and life have a supernatural origin and history, and that this history is significant, precious, and exemplary". [ 7 ] Many cultures instill the expectation that people take mythical gods and heroes as their role models , imitating their deeds and upholding the customs they established:
When the missionary and ethnologist C. Strehlow asked the Australian Arunta why they performed certain ceremonies, the answer was always: "Because the ancestors so commanded it." The Kai of New Guinea refused to change their way of living and working, and they explained: "It was thus that the Nemu (the Mythical Ancestors) did, and we do likewise." Asked the reason for a particular detail in a ceremony, a Navaho chanter answered: "Because the Holy People did it that way in the first place." We find exactly the same justification in the prayer that accompanies a primitive Tibetan ritual: "As it has been handed down from the beginning of the earth’s creation, so must we sacrifice. … As our ancestors in ancient times did—so do we now." [ 8 ]
Founding myths unite people and tend to include mystical events along the way to make "founders" seem more desirable and heroic. Ruling monarchs or aristocracies may allege descent from mythical founders, gods or heroes in order to legitimate their control. For example, Julius Caesar and his relatives claimed Aeneas (and through Aeneas, the goddess Venus ) as an ancestor.
A founding myth or etiological myth (Greek aition ) explains either:
Beginning in prehistorical times, many civilizations and kingdoms adopted some version of a heroic model national origin myth, including the Hittites and Zhou dynasty in the Bronze Age; the Scythians , Wusun , Romans and Goguryeo in antiquity ; Turks and Mongols during the Middle Ages; and the Dzungar Khanate in the early modern period . [ 10 ]
In the founding myth of the Zhou dynasty in China, Lady Yuan makes a ritual sacrifice to conceive, then becomes pregnant after stepping into the footprint of the King of Heaven. She gives birth to a son, Hou Ji , whom she leaves alone in dangerous places where he is protected by sheep, cattle, birds, and woodcutters. Convinced that he is a supernatural being, she takes him back and raises him. When he grows to adulthood, he takes the position of Master of Horses in the court of Emperor Yao , and becomes successful at growing grains, gourds and beans. According to the legend, he becomes founder of the Zhou dynasty after overthrowing the evil ruler of Shang. [ 11 ]
Like other civilizations, the Scythians also claimed descent from the son of the god of heaven. One day, the daughter of the god of the Dnieper River stole a young man's horses while he was herding his cattle , and forced him to lie with her before returning them. From this union, she conceived three sons, giving them their father's greatbow when they came of age. The son who could draw the bow would become king. All tried, but only the youngest was successful. On his attempt, three golden objects fell from the sky: a plow and yoke, a sword, and a cup. When the eldest two tried to pick them up, fire prevented them. After this, it was decided the youngest son, Scythes, would become king, and his people would be known as Scythians. [ 11 ]
The Torah (or Pentateuch, as biblical scholars sometimes call it) is the collective name for the first five books of the Bible: Genesis , Exodus , Leviticus , Numbers , and Deuteronomy . It forms the charter myth of Israel, the story of the people's origins and the foundations of their culture and institutions, and it is a fundamental principle of Judaism that the relationship between God and his chosen people was set out on Mount Sinai through the Torah.
A founding myth may serve as the primary exemplum , as the myth of Ixion was the original Greek example of a murderer rendered unclean by his crime, who needed cleansing ( catharsis ) of his impurity.
Founding myths feature prominently in Greek mythology . "Ancient Greek rituals were bound to prominent local groups and hence to specific localities", Walter Burkert has observed, [ 12 ] "i.e., the sanctuaries and altars that had been set up for all time". Thus Greek and Hebrew founding myths established the special relationship between a deity and local people, who traced their origins from a hero and authenticated their ancestral rights through the founding myth. Greek founding myths often embody a justification for the ancient overturning of an older, archaic order, reformulating a historical event anchored in the social and natural world to valorize current community practices, creating symbolic narratives of "collective importance" [ 13 ] enriched with metaphor to account for traditional chronologies, and constructing an etiology considered to be plausible among those with a cultural investment. [ 14 ]
In the Greek view, the mythic past had deep roots in historic time, its legends treated as facts, as Carlo Brillante has noted, [ 15 ] its heroic protagonists seen as links between the "age of origins" and the mortal, everyday world that succeeded it. A modern translator of Apollonius of Rhodes ' Argonautica has noted, of the many aitia embedded as digressions in that Hellenistic epic, that "crucial to social stability had to be the function of myths in providing explanations, authorization or empowerment for the present in terms of origins: this could apply, not only to foundations or charter myths and genealogical trees (thus supporting family or territorial claims) but also to personal moral choices." [ 16 ] In the period after Alexander the Great expanded the Hellenistic world, Greek poetry— Callimachus wrote a whole work simply titled Aitia —is replete with founding myths. Simon Goldhill employs the metaphor of sedimentation in describing Apollonius' laying down of layers "where each object, cult, ritual, name, may be opened... into a narrative of origination, and where each narrative, each event, may lead to a cult, ritual, name, monument." [ 17 ]
A notable example is the myth of the foundation of Rome—the tale of Romulus and Remus , which Virgil in turn broadens in his Aeneid with the odyssey of Aeneas and his razing of Lavinium , and his son Iulus 's later relocation and rule of the famous twins' birthplace Alba Longa , and their descent from his royal line, thus fitting perfectly into the already established canon of events. Similarly, the Old Testament's story of the Exodus serves as the founding myth for the community of Israel, telling how God delivered the Israelites from slavery and how they therefore belonged to him through the Covenant of Mount Sinai . [ 18 ]
During the Middle Ages, founding myths of the medieval communes of northern Italy manifested the increasing self-confidence of the urban population and the will to find a Roman origin, however tenuous and legendary. In 13th-century Padua , when each commune looked for a Roman founder – and if one was not available, invented one—a legend had been current in the city, attributing its foundation to the Trojan Antenor . [ 19 ] | https://en.wikipedia.org/wiki/Origin_myth |
Original antigenic sin , also known as antigenic imprinting , the Hoskins effect , [ 1 ] immunological imprinting , [ 2 ] or primary addiction [ 3 ] is the propensity of the immune system to preferentially use immunological memory based on a previous infection when a second slightly different version of that foreign pathogen (e.g. a virus or bacterium ) is encountered. This leaves the immune system "trapped" by the first response it has made to each antigen , and unable to mount potentially more effective responses during subsequent infections. Antibodies or T-cells induced during infections with the first variant of the pathogen are subject to repertoire freeze, a form of original antigenic sin.
The phenomenon has been described in relation to influenza virus , SARS-CoV-2 , [ 2 ] dengue fever , human immunodeficiency virus (HIV) [ 4 ] and to several other viruses. [ 5 ]
This phenomenon was first described in 1960 by Thomas Francis Jr. in the article "On the Doctrine of Original Antigenic Sin". [ 6 ] [ 7 ] It is named by analogy to the Christian theological concept of original sin . According to Francis as cited by Richard Krause : [ 7 ]
The antibody of childhood is largely a response to dominant antigen of the virus causing the first type A influenza infection of the lifetime. [...] The imprint established by the original virus infection governs the antibody response thereafter. This we have called the Doctrine of the Original Antigenic Sin.
During a primary infection , long-lived memory B cells are generated, which remain in the body and protect from subsequent infections. These memory B cells respond to specific epitopes on the surface of viral proteins to produce antigen-specific antibodies and can respond to infection much faster than naive B cells can to novel antigens. This effect lessens time needed to clear subsequent infections.
Between primary and secondary infections or following vaccination , a virus may undergo antigenic drift , in which the viral surface proteins (the epitopes) change through natural mutation. This allows the virus to escape the immune system. The altered virus preferentially reactivates previously activated high-affinity memory B cells and spurs antibody production. However, the antibodies produced generally ineffectively bind to the altered epitopes. In addition, these antibodies inhibit activation of naive B cells that could make more effective antibodies to the second virus. This leads to a less effective immune response and recurrent infections may take longer to clear. [ 8 ]
Original antigenic sin has important implications for vaccine development . [ 9 ] In dengue fever , for example, once a response against one serotype has been established, it is unlikely that vaccination against a second will be effective. This implies that balanced responses against all four virus serotypes must be established with the first vaccine dose. [ 10 ]
Activation of naive B cells that recognize novel epitopes may be attenuated with repeated infection with variant influenza viruses. [ 11 ] However, the impact of antigenic sin on protection has not been well established and appears to differ with each infectious agent vaccine, geographic location, and age. [ 8 ] Research done in 2011 found reduced antibody responses to the 2009 pandemic H1N1 influenza vaccine in individuals who had been vaccinated against the seasonal A/Brisbane/59/2007 (H1N1) within the previous three months. [ 9 ]
The relative ineffectiveness of the bivalent booster against the SARS-CoV-2 Omicron variant in patients who had previously received COVID-19 vaccines has been attributed to immunological imprinting. [ 12 ]
A similar phenomenon has been described in cytotoxic T cells (CTL). [ 13 ] It has been demonstrated that during a second infection by a different strain of dengue virus, the CTLs prefer to release cytokines instead of causing cell lysis . As a result, the production of these cytokines is thought to increase vascular permeability and exacerbate damage to endothelial cells, resulting in dengue hemorrhagic fever . [ 14 ]
Several groups have attempted to design vaccines for HIV and hepatitis C based on induction of CTL response. The finding that the CTL response may be biased by original antigenic sin may help to explain the limited effectiveness of these vaccines. Viruses like HIV are highly variable and undergo mutation frequently; due to original antigenic sin, HIV infection induced by viruses that express slightly different epitopes (than those in a viral vaccine) might fail to be controlled by the vaccine. It has been hypothesized that: if original antigenic sin is a common phenomenon, a naively designed single-component vaccine could conceivably make an infection even worse than if no vaccination at all had occurred. The hypothesized mechanism is that the immune response would be "trapped" in a less effective response. Therefore, a recommendation was made for vaccines with multiple components or that target conserved epitopes. [ 13 ] | https://en.wikipedia.org/wiki/Original_antigenic_sin |
An original net animation ( ONA ), known in Japan as web anime ( ウェブアニメ , webu anime ) , is an anime that is directly released onto the Internet . [ 1 ] [ 2 ] ONAs may also have been aired on television if they were first directly released on the Internet. The name mirrors original video animation , a term that has been used in the anime industry for straight-to-video animation since the early 1980s.
A growing number of trailers and preview episodes of new anime have been released as ONA. For example, the anime movie of Megumi can be considered an ONA. ONAs have the tendency to be shorter than traditional anime titles, sometimes running only a few minutes. [ 3 ] There are many examples of an original net animation, such as Hetalia: Axis Powers , which only last a few minutes per episode. But while that was true for the beginning of the 2010s, this began to change in the second half of the decade as full series began to be licensed exclusively for streaming services like Netflix , Amazon Prime Video , and Disney+ .
The majority of the production of animation in Japan is made for television or for other audio-visual formats, which include ONAs that can be viewed on television, mobile devices or computers. [ 4 ]
As broadband Internet bandwidth began to increase in speed and availability, delivering high-quality online video over the Internet became a reality. In the early 2000s, the Japanese anime industry began broadcasting original net animations (ONA) on the Internet. [ 5 ] Early examples of ONA series include Infinite Ryvius: Illusion (2000), [ 6 ] Ajimu (2001), [ 7 ] and Mahou Yuugi (2001). [ 5 ] | https://en.wikipedia.org/wiki/Original_net_animation |
The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a shorter version of the proof, published as an article in 1930, titled "The completeness of the axioms of the functional calculus of logic" (in German)) is not easy to read today; it uses concepts and formalisms that are no longer used and terminology that is often obscure. The version given below attempts to represent all the steps in the proof and all the important ideas faithfully, while restating the proof in the modern language of mathematical logic . This outline should not be considered a rigorous proof of the theorem.
We work with first-order predicate calculus . Our languages allow constant, function and relation symbols. Structures consist of (non-empty) domains and interpretations of the relevant symbols as constant members, functions or relations over that domain.
We assume classical logic (as opposed to intuitionistic logic for example).
We fix some axiomatization (i.e. a syntax-based, machine-manageable proof system) of the predicate calculus: logical axioms and rules of inference. Any of the several well-known equivalent axiomatizations will do. Gödel's original proof assumed the Hilbert-Ackermann proof system .
We assume without proof all the basic well-known results about our formalism that we need, such as the normal form theorem or the soundness theorem .
We axiomatize predicate calculus without equality (sometimes confusingly called without identity ), i.e. there are no special axioms expressing the properties of (object) equality as a special relation symbol. After the basic form of the theorem has been proved, it will be easy to extend it to the case of predicate calculus with equality .
In the following, we state two equivalent forms of the theorem, and show their equivalence.
Later, we prove the theorem. This is done in the following steps:
This is the most basic form of the completeness theorem. We immediately restate it in a form more convenient for our purposes:
When we say "all structures", it is important to specify that the structures involved are classical (Tarskian) interpretations I, where I = <U,F> (U is a non-empty (possibly infinite) set of objects, whereas F is a set of functions from expressions of the interpreted symbolism into U). [By contrast, so-called "free logics" allow possibly empty sets for U. For more regarding free logics, see the work of Karel Lambert.]
" φ is refutable" means by definition "¬ φ is provable".
If Theorem 1 holds, and φ is not satisfiable in any structure, then ¬φ is valid in all structures and therefore provable, thus φ is refutable and Theorem 2 holds. If on the other hand Theorem 2 holds and φ is valid in all structures, then ¬φ is not satisfiable in any structure and therefore refutable; then ¬¬φ is provable and then so is φ, thus Theorem 1 holds.
We approach the proof of Theorem 2 by successively restricting the class of all formulas φ for which we need to prove "φ is either refutable or satisfiable". At the beginning we need to prove this for all possible formulas φ in our language. However, suppose that for every formula φ there is some formula ψ taken from a more restricted class of formulas C , such that "ψ is either refutable or satisfiable" → "φ is either refutable or satisfiable". Then, once this claim (expressed in the previous sentence) is proved, it will suffice to prove "φ is either refutable or satisfiable" only for φ's belonging to the class C . If φ is provably equivalent to ψ ( i.e. , ( φ ≡ ψ ) is provable), then it is indeed the case that "ψ is either refutable or satisfiable" → " φ is either refutable or satisfiable" (the soundness theorem is needed to show this).
There are standard techniques for rewriting an arbitrary formula into one that does not use function or constant symbols, at the cost of introducing additional quantifiers; we will therefore assume that all formulas are free of such symbols. Gödel's paper uses a version of first-order predicate calculus that has no function or constant symbols to begin with.
Next we consider a generic formula φ (which no longer uses function or constant symbols) and apply the prenex form theorem to find a formula ψ in normal form such that φ ≡ ψ ( ψ being in normal form means that all the quantifiers in ψ , if there are any, are found at the very beginning of ψ ). It follows now that we need only prove Theorem 2 for formulas φ in normal form.
Next, we eliminate all free variables from φ by quantifying them existentially: if, say, x 1 ... x n are free in φ , we form ψ = ∃ x 1 ⋯ ∃ x n φ {\displaystyle \psi =\exists x_{1}\cdots \exists x_{n}\varphi } . If ψ is satisfiable in a structure M , then certainly so is φ and if ψ is refutable, then ¬ ψ = ∀ x 1 ⋯ ∀ x n ¬ φ {\displaystyle \neg \psi =\forall x_{1}\cdots \forall x_{n}\neg \varphi } is provable, and then so is ¬ φ , thus φ is refutable. We see that we can restrict φ to be a sentence , that is, a formula with no free variables.
Finally, we would like, for reasons of technical convenience, that the prefix of φ (that is, the string of quantifiers at the beginning of φ , which is in normal form) begin with a universal quantifier and end with an existential quantifier. To achieve this for a generic φ (subject to restrictions we have already proved), we take some one-place relation symbol F unused in φ , and two new variables y and z .. If φ = (P)Φ , where (P) stands for the prefix of φ and Φ for the matrix (the remaining, quantifier-free part of φ ) we form ψ = ∀ y ( P ) ∃ z ( Φ ∧ [ F ( y ) ∨ ¬ F ( z ) ] ) {\displaystyle \psi =\forall y(P)\exists z(\Phi \wedge [F(y)\vee \neg F(z)])} . Since ∀ y ∃ z ( F ( y ) ∨ ¬ F ( z ) ) {\displaystyle \forall y\exists z(F(y)\vee \neg F(z))} is clearly provable, it is easy to see that φ = ψ {\displaystyle \varphi =\psi } is provable.
Our generic formula φ now is a sentence, in normal form, and its prefix starts with a universal quantifier and ends with an existential quantifier. Let us call the class of all such formulas R . We are faced with proving that every formula in R is either refutable or satisfiable. Given our formula φ, we group strings of quantifiers of one kind together in blocks:
We define the degree of φ {\displaystyle \varphi } to be the number of universal quantifier blocks, separated by existential quantifier blocks as shown above, in the prefix of φ {\displaystyle \varphi } . The following lemma, which Gödel adapted from Skolem's proof of the Löwenheim–Skolem theorem , lets us sharply reduce the complexity of the generic formula φ {\displaystyle \varphi } we need to prove the theorem for:
Lemma . Let k ≥ 1. If every formula in R of degree k is either refutable or satisfiable, then so is every formula in R of degree k + 1.
Proof. Let φ be a formula of degree k + 1; then we can write it as
where (P) is the remainder of the prefix of φ {\displaystyle \varphi } (it is thus of degree k – 1) and ψ {\displaystyle \psi } is the quantifier-free matrix of φ {\displaystyle \varphi } . x , y , u and v denote here tuples of variables rather than single variables; e.g. ( ∀ x ) {\displaystyle (\forall x)} really stands for ∀ x 1 ∀ x 2 ⋯ ∀ x n {\displaystyle \forall x_{1}\forall x_{2}\cdots \forall x_{n}} where x 1 … x n {\displaystyle x_{1}\ldots x_{n}} are some distinct variables.
Let now x' and y' be tuples of previously unused variables of the same length as x and y respectively, and let Q be a previously unused relation symbol that takes as many arguments as the sum of lengths of x and y ; we consider the formula
Clearly, Φ → φ {\displaystyle \Phi \rightarrow \varphi } is provable.
Now since the string of quantifiers ( ∀ u ) ( ∃ v ) ( P ) {\displaystyle (\forall u)(\exists v)(P)} does not contain variables from x or y , the following equivalence is easily provable with the help of whatever formalism we're using:
And since these two formulas are equivalent, if we replace the first with the second inside Φ, we obtain the formula Φ' such that Φ≡Φ':
Now Φ' has the form ( S ) ρ ∧ ( S ′ ) ρ ′ {\displaystyle (S)\rho \wedge (S')\rho '} , where (S) and (S') are some quantifier strings, ρ and ρ' are quantifier-free, and, furthermore , no variable of (S) occurs in ρ' and no variable of (S') occurs in ρ. Under such conditions every formula of the form ( T ) ( ρ ∧ ρ ′ ) {\displaystyle (T)(\rho \wedge \rho ')} , where (T) is a string of quantifiers containing all quantifiers in (S) and (S') interleaved among themselves in any fashion, but maintaining the relative order inside (S) and (S'), will be equivalent to the original formula Φ'(this is yet another basic result in first-order predicate calculus that we rely on). To wit, we form Ψ as follows:
and we have Φ ′ ≡ Ψ {\displaystyle \Phi '\equiv \Psi } .
Now Ψ {\displaystyle \Psi } is a formula of degree k and therefore by assumption either refutable or satisfiable.
If Ψ {\displaystyle \Psi } is satisfiable in a structure M , then, considering Ψ ≡ Φ ′ ≡ Φ ∧ Φ → φ {\displaystyle \Psi \equiv \Phi '\equiv \Phi \wedge \Phi \rightarrow \varphi } , we see that φ {\displaystyle \varphi } is satisfiable as well.
If Ψ {\displaystyle \Psi } is refutable, then so is Φ {\displaystyle \Phi } , which is equivalent to it; thus ¬ Φ {\displaystyle \neg \Phi } is provable.
Now we can replace all occurrences of Q inside the provable formula ¬ Φ {\displaystyle \neg \Phi } by some other formula dependent on the same variables, and we will still get a provable formula.
( This is yet another basic result of first-order predicate calculus. Depending on the particular formalism adopted for the calculus, it may be seen as a simple application of a "functional substitution" rule of inference, as in Gödel's paper, or it may be proved by considering the formal proof of ¬ Φ {\displaystyle \neg \Phi } , replacing in it all occurrences of Q by some other formula with the same free variables, and noting that all logical axioms in the formal proof remain logical axioms after the substitution, and all rules of inference still apply in the same way. )
In this particular case, we replace Q(x',y') in ¬ Φ {\displaystyle \neg \Phi } with the formula ( ∀ u ) ( ∃ v ) ( P ) ψ ( x , y ∣ x ′ , y ′ ) {\displaystyle (\forall u)(\exists v)(P)\psi (x,y\mid x',y')} . Here (x,y | x',y') means that instead of ψ we are writing a different formula, in which x and y are replaced with x' and y'. Q(x,y) is simply replaced by ( ∀ u ) ( ∃ v ) ( P ) ψ {\displaystyle (\forall u)(\exists v)(P)\psi } .
¬ Φ {\displaystyle \neg \Phi } then becomes
and this formula is provable; since the part under negation and after the ∧ {\displaystyle \wedge } sign is obviously provable, and the part under negation and before the ∧ {\displaystyle \wedge } sign is obviously φ, just with x and y replaced by x' and y' , we see that ¬ φ {\displaystyle \neg \varphi } is provable, and φ is refutable. We have proved that φ is either satisfiable or refutable, and this concludes the proof of the Lemma .
Notice that we could not have used ( ∀ u ) ( ∃ v ) ( P ) ψ ( x , y ∣ x ′ , y ′ ) {\displaystyle (\forall u)(\exists v)(P)\psi (x,y\mid x',y')} instead of Q(x',y') from the beginning, because Ψ {\displaystyle \Psi } would not have been a well-formed formula in that case. This is why we cannot naively use the argument appearing at the comment that precedes the proof.
As shown by the Lemma above, we only need to prove our theorem for formulas φ in R of degree 1. φ cannot be of degree 0, since formulas in R have no free variables and don't use constant symbols. So the formula φ has the general form:
Now we define an ordering of the k - tuples of natural numbers as follows: ( x 1 … x k ) < ( y 1 … y k ) {\displaystyle (x_{1}\ldots x_{k})<(y_{1}\ldots y_{k})} should hold if either Σ k ( x 1 … x k ) < Σ k ( y 1 … y k ) {\displaystyle \Sigma _{k}(x_{1}\ldots x_{k})<\Sigma _{k}(y_{1}\ldots y_{k})} , or Σ k ( x 1 … x k ) = Σ k ( y 1 … y k ) {\displaystyle \Sigma _{k}(x_{1}\ldots x_{k})=\Sigma _{k}(y_{1}\ldots y_{k})} , and ( x 1 … x k ) {\displaystyle (x_{1}\ldots x_{k})} precedes ( y 1 . . . y k ) {\displaystyle (y_{1}...y_{k})} in lexicographic order . [Here Σ k ( x 1 … x k ) {\displaystyle \Sigma _{k}(x_{1}\ldots x_{k})} denotes the sum of the terms of the tuple.] Denote the nth tuple in this order by ( a 1 n … a k n ) {\displaystyle (a_{1}^{n}\ldots a_{k}^{n})} .
Set the formula B n {\displaystyle B_{n}} as φ ( z a 1 n … z a k n , z ( n − 1 ) m + 2 , z ( n − 1 ) m + 3 … z n m + 1 ) {\displaystyle \varphi (z_{a_{1}^{n}}\ldots z_{a_{k}^{n}},z_{(n-1)m+2},z_{(n-1)m+3}\ldots z_{nm+1})} . Then put D n {\displaystyle D_{n}} as
Lemma : For every n , φ → D n {\displaystyle \varphi \rightarrow D_{n}} .
Proof : By induction on n ; we have D n ⇐ D n − 1 ∧ ( ∀ z 1 … z ( n − 1 ) m + 1 ) ( ∃ z ( n − 1 ) m + 2 … z n m + 1 ) B n ⇐ D n − 1 ∧ ( ∀ z a 1 n … z a k n ) ( ∃ y 1 … y m ) φ ( z a 1 n … z a k n , y 1 … y m ) {\displaystyle D_{n}\Leftarrow D_{n-1}\wedge (\forall z_{1}\ldots z_{(n-1)m+1})(\exists z_{(n-1)m+2}\ldots z_{nm+1})B_{n}\Leftarrow D_{n-1}\wedge (\forall z_{a_{1}^{n}}\ldots z_{a_{k}^{n}})(\exists y_{1}\ldots y_{m})\varphi (z_{a_{1}^{n}}\ldots z_{a_{k}^{n}},y_{1}\ldots y_{m})} , where the latter implication holds by variable substitution, since the ordering of the tuples is such that ( ∀ k ) ( a 1 n … a k n ) < ( n − 1 ) m + 2 {\displaystyle (\forall k)(a_{1}^{n}\ldots a_{k}^{n})<(n-1)m+2} . But the last formula is equivalent to D n − 1 ∧ {\displaystyle D_{n-1}\wedge } φ.
For the base case, D 1 ≡ ( ∃ z 1 … z m + 1 ) φ ( z a 1 1 … z a k 1 , z 2 , z 3 … z m + 1 ) ≡ ( ∃ z 1 … z m + 1 ) φ ( z 1 … z 1 , z 2 , z 3 … z m + 1 ) {\displaystyle D_{1}\equiv (\exists z_{1}\ldots z_{m+1})\varphi (z_{a_{1}^{1}}\ldots z_{a_{k}^{1}},z_{2},z_{3}\ldots z_{m+1})\equiv (\exists z_{1}\ldots z_{m+1})\varphi (z_{1}\ldots z_{1},z_{2},z_{3}\ldots z_{m+1})} is obviously a corollary of φ as well. So the Lemma is proven.
Now if D n {\displaystyle D_{n}} is refutable for some n , it follows that φ is refutable. On the other hand, suppose that D n {\displaystyle D_{n}} is not refutable for any n . Then for each n there is some way of assigning truth values to the distinct subpropositions E h {\displaystyle E_{h}} (ordered by their first appearance in D n {\displaystyle D_{n}} ; "distinct" here means either distinct predicates, or distinct bound variables) in B k {\displaystyle B_{k}} , such that D n {\displaystyle D_{n}} will be true when each proposition is evaluated in this fashion. This follows from the completeness of the underlying propositional logic .
We will now show that there is such an assignment of truth values to E h {\displaystyle E_{h}} , so that all D n {\displaystyle D_{n}} will be true: The E h {\displaystyle E_{h}} appear in the same order in every D n {\displaystyle D_{n}} ; we will inductively define a general assignment to them by a sort of "majority vote": Since there are infinitely many assignments (one for each D n {\displaystyle D_{n}} ) affecting E 1 {\displaystyle E_{1}} , either infinitely many make E 1 {\displaystyle E_{1}} true, or infinitely many make it false and only finitely many make it true. In the former case, we choose E 1 {\displaystyle E_{1}} to be true in general; in the latter we take it to be false in general. Then from the infinitely many n for which E 1 {\displaystyle E_{1}} through E h − 1 {\displaystyle E_{h-1}} are assigned the same truth value as in the general assignment, we pick a general assignment to E h {\displaystyle E_{h}} in the same fashion.
This general assignment must lead to every one of the B k {\displaystyle B_{k}} and D k {\displaystyle D_{k}} being true, since if one of the B k {\displaystyle B_{k}} were false under the general assignment, D n {\displaystyle D_{n}} would also be false for every n > k . But this contradicts the fact that for the finite collection of general E h {\displaystyle E_{h}} assignments appearing in D k {\displaystyle D_{k}} , there are infinitely many n where the assignment making D n {\displaystyle D_{n}} true matches the general assignment.
From this general assignment, which makes all of the D k {\displaystyle D_{k}} true, we construct an interpretation of the language's predicates that makes φ true. The universe of the model will be the natural numbers . Each i-ary predicate Ψ {\displaystyle \Psi } should be true of the naturals ( u 1 … u i ) {\displaystyle (u_{1}\ldots u_{i})} precisely when the proposition Ψ ( z u 1 … z u i ) {\displaystyle \Psi (z_{u_{1}}\ldots z_{u_{i}})} is either true in the general assignment, or not assigned by it (because it never appears in any of the D k {\displaystyle D_{k}} ).
In this model, each of the formulas ( ∃ y 1 … y m ) φ ( a 1 n … a k n , y 1 . . . y m ) {\displaystyle (\exists y_{1}\ldots y_{m})\varphi (a_{1}^{n}\ldots a_{k}^{n},y_{1}...y_{m})} is true by construction. But this implies that φ itself is true in the model, since the a n {\displaystyle a^{n}} range over all possible k-tuples of natural numbers. So φ is satisfiable, and we are done.
We may write each B i as Φ( x 1 ... x k , y 1 ... y m ) for some x s, which we may call "first arguments" and y s that we may call "last arguments".
Take B 1 for example. Its "last arguments" are z 2 , z 3 ... z m +1 , and for every possible combination of k of these variables there is some j so that they appear as "first arguments" in B j . Thus for large enough n 1 , D n 1 has the property that the "last arguments" of B 1 appear, in every possible combinations of k of them, as "first arguments" in other B j s within D n . For every B i there is a D n i with the corresponding property.
Therefore, in a model that satisfies all the D n s, there are objects corresponding to z 1 , z 2 ... and each combination of k of these appear as "first arguments" in some B j , meaning that for every k of these objects z p 1 ... z p k there are z q 1 ... z q m , which makes Φ( z p 1 ... z p k , z q 1 ... z q m ) satisfied. By taking a submodel with only these z 1 , z 2 ... objects, we have a model satisfying φ .
Gödel reduced a formula containing instances of the equality predicate to ones without it in an extended language. His method involves replacing a formula φ containing some instances of equality with the formula
Here A … Z {\displaystyle A\ldots Z} denote the predicates appearing in φ (with k … m {\displaystyle k\ldots m} their respective arities), and φ' is the formula φ with all occurrences of equality replaced with the new predicate Eq . If this new formula is refutable, the original φ was as well; the same is true of satisfiability, since we may take a quotient of satisfying model of the new formula by the equivalence relation representing Eq . This quotient is well-defined with respect to the other predicates, and therefore will satisfy the original formula φ.
Gödel also considered the case where there are a countably infinite collection of formulas. Using the same reductions as above, he was able to consider only those cases where each formula is of degree 1 and contains no uses of equality. For a countable collection of formulas φ i {\displaystyle \varphi ^{i}} of degree 1, we may define B k i {\displaystyle B_{k}^{i}} as above; then define D k {\displaystyle D_{k}} to be the closure of B 1 1 … B k 1 , … , B 1 k … B k k {\displaystyle B_{1}^{1}\ldots B_{k}^{1},\ldots ,B_{1}^{k}\ldots B_{k}^{k}} . The remainder of the proof then went through as before.
When there is an uncountably infinite collection of formulas, the Axiom of Choice (or at least some weak form of it) is needed. Using the full AC, one can well-order the formulas, and prove the uncountable case with the same argument as the countable one, except with transfinite induction . Other approaches can be used to prove that the completeness theorem in this case is equivalent to the Boolean prime ideal theorem , a weak form of AC. | https://en.wikipedia.org/wiki/Original_proof_of_Gödel's_completeness_theorem |
Origination of Organismal Form: Beyond the Gene in Developmental and Evolutionary Biology is an anthology published in 2003 edited by Gerd B. Müller and Stuart A. Newman . The book is the outcome of the 4th Altenberg Workshop in Theoretical Biology on "Origins of Organismal Form: Beyond the Gene Paradigm", hosted in 1999 at the Konrad Lorenz Institute for Evolution and Cognition Research . [ 1 ] [ 2 ] It has been cited over 200 times [ 3 ] and has a major influence on extended evolutionary synthesis research.
The book explores the multiple factors that may have been responsible for the origination of biological form in multicellular life. These biological forms include limbs , segmented structures, and different body symmetries.
It explores why the basic body plans of nearly all multicellular life arose in the relatively short time span of the Cambrian Explosion . The authors focus on physical factors ( structuralism ) other than changes in an organism's genome that may have caused multicellular life to form new structures. These physical factors include differential adhesion of cells and feedback oscillations between cells.
The book also presents recent experimental results that examine how the same embryonic tissues or tumor cells can be coaxed into forming dramatically different structures under different environmental conditions.
One of the goals of the book is to stimulate research that may lead to a more comprehensive theory of evolution . It is frequently cited as foundational to the development of the extended evolutionary synthesis . [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/Origination_of_Organismal_Form |
Origins Space Telescope ( Origins ) is a concept study for a far-infrared survey space telescope mission. [ 1 ] A preliminary concept in pre-formulation, it was presented to the United States Decadal Survey in 2019 for a possible selection to NASA's large strategic science missions . Origins would provide an array of new tools for studying star formation and the energetics and physical state of the interstellar medium within the Milky Way using infrared radiation and new spectroscopic capabilities. [ 2 ]
Study groups, primarily composed of international community members, prioritized the science identification and science drivers of the mission architecture. [ 3 ] [ 4 ] The study groups drew upon input from the international astronomical community; such a large mission will need international participation and support to make it a reality. [ 5 ]
In 2016, NASA began considering four different space telescopes for the Large strategic science missions ; [ 6 ] they are the Habitable Exoplanet Imaging Mission (HabEx), Large Ultraviolet Optical Infrared Surveyor (LUVOIR), Origins Space Telescope ( Origins ), and Lynx X-ray Observatory . In 2019, the four teams turned in their final reports to the National Academy of Sciences , whose independent Astronomy and Astrophysics Decadal Survey report advises NASA on which mission should take top priority. If funded, Origins would launch in approximately 2035. [ 6 ]
The Roadmap envisaged a mid- to far- infrared space telescope (contrasting with the near- to mid-infrared James Webb Space Telescope ) with a large gain in sensitivity over the Herschel Space Observatory (a previous far-infrared telescope), and better angular resolution with at least a four-order of magnitude sensitivity improvement over Herschel. [ 3 ] The mission development relies on the identification of primary science drivers to establish the technical requirements for the observatory. The workgroups have identified these baseline science topics:
Early and preliminary goals for the Origins Space Telescope mission include the study of water transport as both ice and gas from the interstellar medium to the inner regions of planet-forming disks, from interstellar clouds , to protoplanetary disks , to Earth itself—in order to understand the abundance and availability of water for habitable planets . [ 8 ] In the Solar System , it will chart the role of comets in delivering water to the early Earth by tracing their molecular heredity of deuterium/hydrogen ratio. [ 8 ]
The Origins Space Telescope would perform astrometry and astrophysics in the mid- to far-infrared range using a telescope with an aperture of 9.1 m (concept 1) or 5.9 m (concept 2). [ 8 ] [ 9 ] The telescope will require cryocooler systems to actively cool detectors at ~50 mK and the telescope optics at ~4 K . [ 8 ] It will attain sensitivities 100–1000 times greater than any previous far-infrared telescope. [ 8 ]
Targeting exoplanet observations in the 3.3–25 μm wavelength range, it will measure the temperatures and search for basic chemical ingredients for life in the atmospheres of small, warm planets at habitable temperatures (~300 K (27 °C)) and measure their atmospheric composition. This may be accomplished by a combination of transit spectroscopy and direct coronagraphic imaging. Important atmospheric diagnostics include spectral bands of ammonia ( NH 4 , a unique tracer of nitrogen), the 9 μm ozone line ( ozone , O 3 is a key biosignature ), the 15 μm CO 2 band ( carbon dioxide is an important greenhouse gas ), and many water wavelength bands. [ 8 ]
Its spectrographs will enable 3D surveys of the sky that will discover and characterize the most distant galaxies, Milky-Way, exoplanets, and the outer reaches of the Solar System. [ 9 ]
Based on the final report, [ 10 ] three instruments are required, plus a fourth optional upscope: [ 8 ] [ 1 ] | https://en.wikipedia.org/wiki/Origins_Space_Telescope |
Origins of Life and Evolution of Biospheres is a peer-reviewed scientific journal established in 1968 covering astrobiology and origins of life research. It is the official journal of the International Astrobiology Society (previously known as the International Society for the Study of the Origin of Life). The journal's scope includes research on the origin, evolution, distribution, and future of life on Earth and beyond. Some examples of areas of interest are: prebiotic chemistry and the nature of Earth's early environment, self-replicating and self-organizing systems, the RNA world hypothesis and of other possible precursor systems, and the problem of the origin of the genetic code . According to the Journal Citation Reports , the journal has a 2022 impact factor of 2.0. [ 1 ]
In January 2024, the journal was renamed Discover Life and became gold open access . [ 2 ]
The journal is abstracted and indexed in the following databases: | https://en.wikipedia.org/wiki/Origins_of_Life_and_Evolution_of_Biospheres |
Orimulsion is a registered trademark name for a bitumen -based fuel that was developed for industrial use by Intevep, the Research and Development Affiliate of Petroleos de Venezuela SA (PDVSA), following earlier collaboration on oil emulsions with BP .
Like coal and oil, bitumen occurs naturally and is obtained from the world's largest deposit in the Orinoco Belt in Venezuela . The deposit is estimated to be more than 1,300 billion barrels (190 billion m 3 ) of bitumen, an amount approximately equivalent to the world's estimated proven oil reserves . [ 1 ] [ 2 ]
Raw bitumen has an extremely high viscosity and specific gravity between 8 and 10 API gravity at ambient temperatures , making it unsuitable for direct use in conventional power stations. Orimulsion is produced by mixing the bitumen with approximately 30% fresh water and a small amount of surfactant . The resulting mixture behaves similarly to fuel oil . Recently, an alcohol -based surfactant has replaced the original phenol -based version, improving the transport properties of the fuel and eliminating the health concerns associated with the phenol group of surfactants.
As a fuel for electricity generation, Orimulsion has a number of attractive characteristics: [ 3 ]
While Orimulsion is little different to fuel oil in relation to environmental impacts when burnt, being similarly susceptible to pollution mitigation techniques, it is more problematic in spill situations. [ 4 ] If a spill occurs during shipping over water, the Orimulsion mixture de-emulsifies, causing the bitumen to separate and no longer remain in suspension.
Orimulsion is classified as a non-Newtonian fluid , and if its temperature drops below 30 °C , it undergoes a process referred to as 'setting' [ further explanation needed ] . Once set, it becomes extremely difficult to pump, and restarting operations or restoring the flow through the pipeline becomes impossible.
Orimulsion is currently used as a commercial boiler fuel in power plants worldwide, including countries such as Japan , Italy [ 5 ] and China . Its usage was previously more widespread, and there was an increasing demand for it. However, following the Venezuelan general strike of 2002–03 , many engineers from PDVSA were dismissed. Since Orimulsion had been highly regarded by these engineers, it lost favor among key political leaders. [ dubious – discuss ] Consequently, the Venezuelan government has been attempting to gradually phase out the Orimulsion program, except for its sales to China . The Venezuelan government maintains close ties with China, similar to its relationship with Cuba . As a result, China continues to receive supplies of Orimulsion, while the rest of the world either had their supply terminated or is still in the process of winding down. Despite these developments, Orimulsion still holds great potential for domestic consumption. [ citation needed ]
Another reason given by current PDVSA management is that with rising crude oil prices, it has been found that mixing or diluting Orinoco bitumen (extra-heavy oil) with a lighter crude oil can make this blend more profitable as a crude oil on the world market than by selling it as Orimulsion. An example of this is the popular Merey blend (Orinoco bitumen and Mesa crude oil). ConocoPhillips along with PDVSA operate the Merey Sweeny 58,000-barrel-per-day (9,200 m 3 /d) (bpd) delayed coker, vacuum tower and related facilities at ConocoPhillips' refinery in Sweeny, Texas, U.S.A. for processing and upgrading heavy sour Merey crude oil. [ 6 ]
Air pollutant control technology that is commonly available can limit emissions from Orimulsion to levels considered " Best Available Control Technology ", as defined by the United States Environmental Protection Agency . [ 7 ] | https://en.wikipedia.org/wiki/Orimulsion |
Orion is a system-on-a-chip manufactured by Marvell Technology Group and used in network-attached storage . Based on the ARMv5TE architecture , it has on-chip support for Ethernet , SATA and USB , and is used in hardware made by Hewlett-Packard and D-Link among others. [ 1 ] It is supported by the Lenny release of Debian GNU/Linux . [ 2 ]
This computer hardware article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orion_(system-on-a-chip) |
The Orka -class submarine is a future submarine class currently planned for the Royal Netherlands Navy (RNLN). [ 6 ] The submarines will replace the aging Walrus class . [ 7 ] [ 8 ] They will be the first submarines of the RNLN that are built at a foreign shipyard. [ 9 ] As of 2024 they are planned to enter service in 2035. [ 10 ]
In 2013 the Royal Netherlands Navy (RNLN) started the preparation process for the replacement of the Walrus -class submarines . [ 11 ] [ 12 ] That same year the Dutch Minister of Defence had signed letters of intent with both Norway and Germany for the development of new submarines, while there had also been talks with Norway about a Future Submarine Co-Operation. [ 13 ] Plans were announced by Dutch Minister of Defence , Jeanine Hennis-Plasschaert , in November 2014 to replace the Walrus -class submarines with four new submarines in 2025. [ 14 ] Later that year it was announced that the Netherlands would continue cooperating with Norway on the procurement of new submarines, but cooperation with Germany would not continue as a result of difference in urgency. [ 15 ] In 2015 a vision for the future of the Royal Netherlands Navy Submarine Service was sent by the Minister of Defence to the Tweede Kamer which underlined the need for new submarines and international cooperation. [ 16 ] [ 17 ] Meanwhile Dutch shipbuilder Damen had announced in January that it will work together with Saab to design and build submarines. [ 18 ] [ 19 ] Other companies, such as the French Naval Group and German ThyssenKrupp Marine Systems (TKMS), had also shown interest in building new submarines that could replace the Walrus -class. [ 20 ] The A-letter, which officially starts the replacement program, was at first expected to be sent to the Tweede Kamer in 2015, and later in April 2016. [ 21 ] [ 22 ] While no letter was sent during this period, talks and discussions continued about what kind of submarines were needed, the amount and international cooperation. [ 23 ] [ 24 ] In June 2016 the A-letter was finally sent and revealed four requirements that the potentially new submarines would need to meet. [ 25 ] [ 26 ] At the same time it was also announced that in the next phase of the replacement program research needs to be done on how these requirements can be fulfilled. [ 25 ] During this research four specific options will considered: expeditionary submarines, coastal submarines, submarine drones or other systems (and thus no submarines will be tendered). [ 27 ]
By 2017, there was still no political agreement on the quantity or type of new submarines to be ordered; nor the tasks they were expected to perform. However, it seems certain that they will be replaced, since the alleged Russian threat was regarded as an incentive to invest in a new class. The Minister of Defence, however, delayed the replacement by two years, until 2027. Roughly, there are two groups in the Dutch parliament – one in favor of replacing the Walrus class by an equally capable class of large, expeditionary, diesel-electric submarine, and the other in favor of choosing a cheaper solution of smaller diesel-electrics, similar to Swedish and German submarines. It is unknown where the new boats will be built; since the Dutch RDM shipyard (the only Dutch yard capable of building submarines) is no longer in operation. The Defensienota (Defense policy for the coming years) of March 2018 revealed that the Dutch government is still planning to replace the Walrus -class submarines, [ 28 ] with an allocated budget of more than 2.5 billion euros for the new submarines. Additional information on how to proceed with the replacement was expected at the end of 2018, when the Dutch Minister of Defence, Ank Bijleveld , was to send a so-called B-letter to the Dutch parliament. [ 28 ] Minister Bijleveld also underlined in an interview that the new submarines should have the same niche capabilities as the current Walrus -class submarines: the ability to operate and gather intelligence in both shallow water close to the coast and in deep water in the ocean. [ 29 ] In December 2019 the B-letter was sent to the Dutch parliament. [ 30 ] In mid-2021 it was indicated that the revised plan was to take a decision on the replacement type in 2022 and to have the first vessel in service by 2028, with the first two boats to be in service by 2031. [ 31 ] However, by October 2021 it was reported that this timeline was no longer feasible. Instead, the Dutch Ministry of Defence signalled that the envisaged dates would have to be "substantially adjusted", likely impacting the originally proposed in-service dates for the first submarines. [ 32 ] In April 2022 it was announced that the revised schedule for construction of the new replacement boats would likely see the first two vessels entering service in the 2034 to 2037 timeframe. [ 33 ] [ 34 ] As a result the two oldest Walrus -class submarines will be decommissioned and used for spare parts to keep the two youngest boats longer in service. [ 35 ] The goal is to keep two boats operational and prevent a capability gap. [ 36 ]
On 16 November 2022 the next phase in the program was started when DMO delivered the request for quotation (RfQ) to the three remaining yards. [ 37 ] [ 38 ] The proposals had to be submitted before 28 July 2023 with a final decision being made by the navy in late 2023 or early 2024. [ 39 ] [ 40 ]
The Ministry of Defence has shortlisted three bidders: [ 41 ] [ 42 ]
Spain's Navantia 's S-80 was not accepted as a contender following the B-letter in 2019. [ 52 ] In 2022 the Spanish Ministry of Defence sent a letter to the Dutch DMO for Navantia to be allowed to put in an offer following a RfQ sent to the remaining contenders, in which some of the requirements have changed. It is rumoured that the request was denied by DMO. [ 53 ]
On 15 March 2024 State Secretary for Defence Christophe van der Maat officially announced that Naval Group had been selected as the winning bid. [ 54 ] [ 55 ] [ 56 ] The first two submarines will be delivered within ten years after the contract has been signed. [ 54 ] [ 55 ] [ 56 ] Prior to this announcement, the winner was already leaked to several media outlets, which caused political backlash for choosing a foreign yard over a Dutch one. [ 57 ] In April 2024, it was announced which ten Dutch companies and two knowledge institutions will be involved in the construction of the Orka class submarines. [ 58 ]
On 10 September 2024 the Netherlands and Naval Group signed an industrial cooperation agreement (ICA). [ 59 ] [ 60 ] [ 61 ] This binding agreement ensures that Naval Group and the Dutch defense and maritime industries will collaborate on the Orka -class submarines. [ 62 ] [ 63 ] It will also result in orders for the Dutch industry that will have a total worth of approximately one billion euros. [ 64 ] [ 65 ] That same month, on 30 September 2024, the Delivery Agreement for the Replacement Netherlands Submarine Capability (RNSC) programme was also signed between the Dutch Ministry of Defence and Naval Group. [ 66 ] [ 67 ] [ 68 ] The signing of this agreement marks the start of the replacement program. [ 9 ] [ 69 ]
The submarines will be equipped with a Thales sonar suite, which will include bow, flank, and obstacle avoidance sonars, an underwater voice communication system, an intercept array, a passive towed-array sonar, and signal processing racks. [ 70 ] [ 71 ] The sensors in this sonar suite will be derived from the sensors that are installed in the systems equipping the French nuclear submarines of the Suffren -class . [ 72 ] Meanwhile, the passive towed-array sonar will make use of OptiArray technology from the Dutch company Optics11 . [ 73 ] [ 74 ]
The names of the new submarines were announced by Van der Maat. [ 75 ] The class will be known as the Orka class, with the subs named Orka (Orca), Zwaardvis (Swordfish), Barracuda (Barracuda) and Tijgerhaai (Tiger shark). [ 76 ] | https://en.wikipedia.org/wiki/Orka-class_submarine |
94103
66612
ENSG00000172057
ENSMUSG00000038150
Q8N138
Q9CPZ6
NM_139280 NM_001320801 NM_001320802 NM_001320803 NM_016471
NM_025661
NP_001307730 NP_001307731 NP_001307732 NP_644809
NP_079937
ORMDL sphingolipid biosynthesis regulator 3 is a protein that in humans is encoded by the ORMDL3 gene . [ 5 ] Variants affecting the expression of this gene are associated with asthma in childhood. [ 6 ] Transgenic mice which overexpress human ORMDL3 have increased levels of IgE . This correlated with increased numbers of macrophages , neutrophils , eosinophils , CD4 + and enhanced Th2 cytokine levels in the lung tissue. [ 7 ]
The ORMDL family, whose name stands for ORM1 ( Saccharomyces cerevisiae )–like genes, [ 8 ] consists of three members (ORMDL1-3) which are localised in the membrane of the endoplasmic reticulum (ER). [ 9 ] All three human ORMDL genes encode 153 amino acid products. [ 9 ] The genes ORMDL1 , ORMDL2 and ORMDL3 are located on human chromosomes 2q32, 12q13.2 and 17q21, respectively. [ 8 ]
ORMDL3 negatively regulates de novo sphingolipid synthesis through interaction with serine palmitoyltransferase (SPT), [ 9 ] [ 10 ] but it may be present in relative excess of SPT physiologically, as ORMDL3 overexpression does not significantly reduce cellular sphingolipid biosynthesis . [ 11 ] ORMDL3 also has a role in regulating Ca 2+ levels in the endoplasmic reticulum. [ 12 ] The ER is very important for generation, signaling function and storage of intracellular Ca 2+ . There are channels , which control the exit of Ca 2+ from the ER into the cytoplasm and also pumps (sarco-endoplasmic reticulum Ca 2+ ATPase or SERCA ) which return Ca 2+ back to the ER. [ 13 ] Dysregulation of Ca 2+ has the key role in several pathological conditions like dysfunction of SERCA, asthma , [ 14 ] and Alzheimer's . [ 15 ]
Mutations in ORMDL3 are associated with inflammatory diseases like Crohn's disease , type 1 diabetes , [ 16 ] and rheumatoid arthritis . [ 17 ]
This article on a gene on human chromosome 17 is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ormdl_sphingolipid_biosynthesis_regulator_3 |
Orme's law is a rule of thumb to assist modelers when they design an electric power system for their radio-controlled model . Orme's law simply recommends the use of one NiMH rechargeable battery cell for every 35 square inches (230 cm 2 ) of wing area for sport planes. One cell for every 50 square inches (320 cm 2 ) of wing area for trainers. [ 1 ] When using LiPo cells with higher voltage, the number of cells is cut in half, since a LiPo cell has double the voltage.
This rule is the work of Matthew Orme, [ 2 ] who used to manage the sales of Aveox's line of motors to the hobby market, and later developed a small high performance line of brushless motors at RazorMotors. [ 3 ] Matt wanted to come up with a simpler way to recommend systems to the many people who ask him for advice powering their models. Brushless motors are very versatile and it can be hard for newcomers to decide which system they should use.
The main purpose was to demonstrate to the modeler that the electric motor was not the source of power like an internal combustion engine. With an IC engine, a particular sized engine will have a particular power output. Typically a model airplane manufacturer will recommend a 2-cycle glow plug motor by its size (typically .40-.60 cubic inch for the average sized plane) Since electric motors operate over a much wider range, there was no good way to recommend an electric motor for a plane.
Orme's law makes it clear that the battery pack is the power source, and it determines the available power, not the electric motor. Once the power requirements of any particular airplane model have been determined, an electric motor can be chosen to match the power source. i.e., a 10 cell NiMh battery pack produces approximately 1 volt per cell under load. At 30 amps, that translates to .4 HP.
Matt Orme's rule makes system selection easy. Orme's law assumes that the hobbyist will be using 1700 to 2000 mAH cells and will prop for 4 minutes of flight, or 30 amps. 2000 mAH = 2 amp hours or 120 amp minutes, hence the 4-minute flight time (120 amp-minutes /30 amps) at full throttle, with increasing flight times at reduced throttle settings.
Applying the rule using a hobbyist's Citabria Pro electric conversion, which has 560 square inches (3,600 cm 2 ) of wing area, it needs exactly 16 cells according to Orme's law. Before Orme's law, much more work was needed to design the power for the system. | https://en.wikipedia.org/wiki/Orme's_law |
An ornamental animal is an animal kept for display or curiosity, often in a park . A wide range of mammals, birds and fish have been kept as ornamental animals. Ornamental animals have often formed the basis of introduced populations, sometimes with negative ecological effects, but a history of being kept as ornamental animals has also preserved breeds, types and even species which have become rare or extinct elsewhere.
This article does not cover animals kept in zoos , wildfowl collections or aquaria .
Ornamental animals have been kept for many centuries in several cultures.
Some ornamental animals have escaped from captivity and have formed feral populations.
A number of animals have been protected from local or worldwide extinction by being kept as ornamental animals.
The following are breeds or species whose history has included a significant period as ornamental animals, either globally or in particular regions (animals kept primarily in modern zoos, aquaria or waterfowl collections are not included):
Birds' ornamental value derives in part from their feather coloration. [ 2 ] Feather colors are often produced by carotenoids . [ 2 ] | https://en.wikipedia.org/wiki/Ornamental_animal |
Ornithology , from Ancient Greek ὄρνις ( órnis ), meaning "bird", and -logy from λόγος ( lógos ), meaning "study", is a branch of zoology dedicated to the study of birds . [ 1 ] Several aspects of ornithology differ from related disciplines, due partly to the high visibility and the aesthetic appeal of birds. [ 2 ] It has also been an area with a large contribution made by amateurs in terms of time, resources, and financial support. Studies on birds have helped develop key concepts in biology including evolution, behaviour and ecology such as the definition of species , the process of speciation , instinct , learning , ecological niches , guilds , insular biogeography , phylogeography , and conservation . [ 3 ]
While early ornithology was principally concerned with descriptions and distributions of species, ornithologists today seek answers to very specific questions, often using birds as models to test hypotheses or predictions based on theories. Most modern biological theories apply across life forms, and the number of scientists who identify themselves as "ornithologists" has therefore declined. [ 4 ] A wide range of tools and techniques are used in ornithology, both inside the laboratory and out in the field, and innovations are constantly made. Most biologists who recognise themselves as "ornithologists" study specific biology research areas, such as anatomy , physiology , taxonomy ( phylogenetics ), ecology , or behaviour . [ 5 ]
The word "ornithology" comes from the late 16th-century Latin ornithologia meaning "bird science" from the Greek ὄρνις ornis ("bird") and λόγος logos ("theory, science, thought"). [ 6 ]
The history of ornithology largely reflects the trends in the history of biology , as well as many other scientific disciplines, including ecology , anatomy , physiology , paleontology , and more recently, molecular biology. Trends include the move from mere descriptions to the identification of patterns, thus towards elucidating the processes that produce these patterns.
Humans have had an observational relationship with birds since prehistory , with some stone-age drawings being amongst the oldest indications of an interest in birds. [ 7 ] [ 8 ] Birds were perhaps important as food sources, and bones of as many as 80 species have been found in excavations of early Stone Age settlements. [ 9 ] [ 10 ] [ 11 ] Water bird and seabird remains have also been found in shell mounds on the island of Oronsay off the coast of Scotland . [ 7 ]
Cultures around the world have rich vocabularies related to birds. [ 12 ] Traditional bird names are often based on detailed knowledge of the behaviour, with many names being onomatopoeic , and still in use. [ 13 ] Traditional knowledge may also involve the use of birds in folk medicine [ 14 ] and knowledge of these practices are passed on through oral traditions (see ethnoornithology ). [ 15 ] [ 16 ] Hunting of wild birds as well as their domestication would have required considerable knowledge of their habits. Poultry farming and falconry were practised from early times in many parts of the world. Artificial incubation of poultry was practised in China around 246 BC and around at least 400 BC in Egypt. [ 17 ] The Egyptians also made use of birds in their hieroglyphic scripts, many of which, though stylized, are still identifiable to species. [ 18 ]
Early written records provide valuable information on the past distributions of species. For instance, Xenophon records the abundance of the ostrich in Assyria (Anabasis, i. 5); this subspecies from Asia Minor is extinct and all extant ostrich races are today restricted to Africa . Other old writings such as the Vedas (1500–800 BC) demonstrate the careful observation of avian life histories and include the earliest reference to the habit of brood parasitism by the Asian koel ( Eudynamys scolopaceus ). [ 19 ] Like writing, the early art of China, Japan, Persia, and India also demonstrate knowledge, with examples of scientifically accurate bird illustrations. [ 20 ]
Aristotle in 350 BC in his History of animals [ 21 ] noted the habit of bird migration , moulting, egg laying, and lifespans, as well as compiling a list of 170 different bird species. However, he also introduced and propagated several myths, such as the idea that swallows hibernated in winter, although he noted that cranes migrated from the steppes of Scythia to the marshes at the headwaters of the Nile . The idea of swallow hibernation became so well established that even as late as in 1878, Elliott Coues could list as many as 182 contemporary publications dealing with the hibernation of swallows and little published evidence to contradict the theory. [ 22 ] [ 23 ] Similar misconceptions existed regarding the breeding of barnacle geese . Their nests had not been seen, and they were believed to grow by transformations of goose barnacles , an idea that became prevalent from around the 11th century and noted by Bishop Giraldus Cambrensis ( Gerald of Wales ) in Topographia Hiberniae (1187). [ 24 ] Around 77 AD, Pliny the Elder described birds, among other creatures, in his Historia Naturalis . [ 25 ]
The earliest record of falconry comes from the reign of Sargon II (722–705 BC) in Assyria . Falconry is thought to have made its entry to Europe only after AD 400, brought in from the east after invasions by the Huns and Alans . Starting from the eighth century, numerous Arabic works on the subject and general ornithology were written, as well as translations of the works of ancient writers from Greek and Syriac . In the 12th and 13th centuries, crusades and conquest had subjugated Islamic territories in southern Italy, central Spain, and the Levant under European rule, and for the first time translations into Latin of the great works of Arabic and Greek scholars were made with the help of Jewish and Muslim scholars, especially in Toledo , which had fallen into Christian hands in 1085 and whose libraries had escaped destruction. Michael Scotus from Scotland made a Latin translation of Aristotle's work on animals from Arabic here around 1215, which was disseminated widely and was the first time in a millennium that this foundational text on zoology became available to Europeans. Falconry was popular in the Norman court in Sicily, and a number of works on the subject were written in Palermo . Emperor Frederick II of Hohenstaufen (1194–1250) learned about an falconry during his youth in Sicily and later built up a menagerie and sponsored translations of Arabic texts, among which the popular Arabic work known as the Liber Moaminus by an unknown author which was translated into Latin by Theodore of Antioch from Syria in 1240–1241 as the De Scientia Venandi per Aves , and also Michael Scotus (who had removed to Palermo) translated Ibn Sīnā 's Kitāb al-Ḥayawān of 1027 for the Emperor, a commentary and scientific update of Aristotle's work which was part of Ibn Sīnā's massive Kitāb al-Šifāʾ . Frederick II eventually wrote his own treatise on falconry, the De arte venandi cum avibus , in which he related his ornithological observations and the results of the hunts and experiments his court enjoyed performing. [ 26 ] [ 27 ]
Several early German and French scholars compiled old works and conducted new research on birds. These included Guillaume Rondelet , who described his observations in the Mediterranean, and Pierre Belon , who described the fish and birds that he had seen in France and the Levant. Belon's Book of Birds (1555) is a folio volume with descriptions of some 200 species. His comparison of the skeleton of humans and birds is considered as a landmark in comparative anatomy . [ 28 ] Volcher Coiter (1534–1576), a Dutch anatomist, made detailed studies of the internal structures of birds and produced a classification of birds, De Differentiis Avium (around 1572), that was based on structure and habits. [ 29 ] Konrad Gesner wrote the Vogelbuch and Icones avium omnium around 1557. Like Gesner, Ulisse Aldrovandi , an encyclopedic naturalist, began a 14-volume natural history with three volumes on birds, entitled ornithologiae hoc est de avibus historiae libri XII , which was published from 1599 to 1603. Aldrovandi showed great interest in plants and animals, and his work included 3000 drawings of fruits, flowers, plants, and animals, published in 363 volumes. His Ornithology alone covers 2000 pages and included such aspects as the chicken and poultry techniques. He used a number of traits including behaviour, particularly bathing and dusting, to classify bird groups. [ 30 ] [ 31 ] [ 32 ]
William Turner 's Historia Avium ( History of Birds ), published at Cologne in 1544, was an early ornithological work from England. He noted the commonness of kites in English cities where they snatched food out of the hands of children. He included folk beliefs such as those of anglers. Anglers believed that the osprey emptied their fishponds and would kill them, mixing the flesh of the osprey into their fish bait. Turner's work reflected the violent times in which he lived, and stands in contrast to later works such as Gilbert White 's 1789 The Natural History and Antiquities of Selborne that were written in a tranquil era. [ 28 ] [ 34 ]
In the 17th century, Francis Willughby (1635–1672) and John Ray (1627–1705) created the first major system of bird classification that was based on function and morphology rather than on form or behaviour. Willughby's Ornithologiae libri tres (1676) completed by John Ray is sometimes considered to mark the beginning of scientific ornithology. Ray also worked on Ornithologia , which was published posthumously in 1713 as Synopsis methodica avium et piscium . [ 35 ] The earliest list of British birds, Pinax Rerum Naturalium Britannicarum , was written by Christopher Merrett in 1667, but authors such as John Ray considered it of little value. [ 36 ] Ray did, however, value the expertise of the naturalist Sir Thomas Browne (1605–82), who not only answered his queries on ornithological identification and nomenclature, but also those of Willoughby and Merrett in letter correspondence. Browne himself in his lifetime kept an eagle, owl, cormorant, bittern, and ostrich, penned a tract on falconry, and introduced the words "incubation" and "oviparous" into the English language. [ 37 ] [ 38 ]
Towards the late 18th century, Mathurin Jacques Brisson (1723–1806) and Comte de Buffon (1707–1788) began new works on birds. Brisson produced a six-volume work Ornithologie in 1760 and Buffon's included nine volumes (volumes 16–24) on birds Histoire naturelle des oiseaux (1770–1785) in his work on science Histoire naturelle générale et particulière (1749–1804). Jacob Temminck sponsored François Le Vaillant [1753–1824] to collect bird specimens in Southern Africa and Le Vaillant's six-volume Histoire naturelle des oiseaux d'Afrique (1796–1808) included many non-African birds. His other bird books produced in collaboration with the artist Barraband are considered among the most valuable illustrated guides ever produced. Louis Pierre Vieillot (1748–1831) spent 10 years studying North American birds and wrote the Histoire naturelle des oiseaux de l'Amerique septentrionale (1807–1808?). Vieillot pioneered in the use of life histories and habits in classification. [ 39 ] Alexander Wilson composed a nine-volume work, American Ornithology , published 1808–1814, which is the first such record of North American birds, significantly antedating Audubon. In the early 19th century, Lewis and Clark studied and identified many birds in the western United States. John James Audubon , born in 1785, observed and painted birds in France and later in the Ohio and Mississippi valleys. From 1827 to 1838, Audubon published The Birds of America , which was engraved by Robert Havell Sr. and his son Robert Havell Jr. Containing 435 engravings, it is often regarded as the greatest ornithological work in history.
The emergence of ornithology as a scientific discipline began in the 18th century, when Mark Catesby published his two-volume Natural History of Carolina, Florida, and the Bahama Islands , a landmark work which included 220 hand-painted engravings and was the basis for many of the species Carl Linnaeus described in the 1758 Systema Naturae . Linnaeus' work revolutionised bird taxonomy by assigning every species a binomial name , categorising them into different genera. However, ornithology did not emerge as a specialised science until the Victorian era—with the popularization of natural history, and the collection of natural objects such as bird eggs and skins. [ 40 ] [ 41 ] This specialization led to the formation in Britain of the British Ornithologists' Union in 1858. In 1859, the members founded its journal The Ibis . The sudden spurt in ornithology was also due in part to colonialism . At 100 years later, in 1959, R. E. Moreau noted that ornithology in this period was preoccupied with the geographical distributions of various species of birds. [ 42 ]
No doubt the preoccupation with widely extended geographical ornithology, was fostered by the immensity of the areas over which British rule or influence stretched during the 19th century and for some time afterwards.
The bird collectors of the Victorian era observed the variations in bird forms and habits across geographic regions, noting local specialization and variation in widespread species. The collections of museums and private collectors grew with contributions from various parts of the world. The naming of species with binomials and the organization of birds into groups based on their similarities became the main work of museum specialists. The variations in widespread birds across geographical regions caused the introduction of trinomial names.
The search for patterns in the variations of birds was attempted by many. Friedrich Wilhelm Joseph Schelling (1775–1854), his student Johann Baptist von Spix (1781–1826), and several others believed that a hidden and innate mathematical order existed in the forms of birds. They believed that a "natural" classification was available and superior to "artificial" ones. A particularly popular idea was the Quinarian system popularised by Nicholas Aylward Vigors (1785–1840), William Sharp Macleay (1792–1865), William Swainson , and others. The idea was that nature followed a "rule of five" with five groups nested hierarchically. Some had attempted a rule of four, but Johann Jakob Kaup (1803–1873) insisted that the number five was special, noting that other natural entities such as the senses also came in fives. He followed this idea and demonstrated his view of the order within the crow family. Where he failed to find five genera, he left a blank insisting that a new genus would be found to fill these gaps. These ideas were replaced by more complex "maps" of affinities in works by Hugh Edwin Strickland and Alfred Russel Wallace . [ 44 ] [ 45 ] A major advance was made by Max Fürbringer in 1888, who established a comprehensive phylogeny of birds based on anatomy, morphology, distribution, and biology. This was developed further by Hans Gadow and others. [ 46 ] [ 47 ]
The Galapagos finches were especially influential in the development of Charles Darwin 's theory of evolution. His contemporary Alfred Russel Wallace also noted these variations and the geographical separations between different forms leading to the study of biogeography . Wallace was influenced by the work of Philip Lutley Sclater on the distribution patterns of birds. [ 48 ]
For Darwin, the problem was how species arose from a common ancestor, but he did not attempt to find rules for delineation of species. The species problem was tackled by the ornithologist Ernst Mayr , who was able to demonstrate that geographical isolation and the accumulation of genetic differences led to the splitting of species . [ 49 ] [ 50 ]
Early ornithologists were preoccupied with matters of species identification. Only systematics counted as true science and field studies were considered inferior through much of the 19th century. [ 51 ] In 1901, Robert Ridgway wrote in the introduction to The Birds of North and Middle America that:
There are two essentially different kinds of ornithology: systematic or scientific, and popular. The former deals with the structure and classification of birds, their synonymies, and technical descriptions. The latter treats of their habits, songs, nesting, and other facts pertaining to their life histories.
This early idea that the study of living birds was merely recreation held sway until ecological theories became the predominant focus of ornithological studies. [ 3 ] [ 42 ] The study of birds in their habitats was particularly advanced in Germany with bird ringing stations established as early as 1903. By the 1920s, the Journal für Ornithologie included many papers on the behaviour, ecology, anatomy, and physiology, many written by Erwin Stresemann . Stresemann changed the editorial policy of the journal, leading both to a unification of field and laboratory studies and a shift of research from museums to universities. [ 51 ] Ornithology in the United States continued to be dominated by museum studies of morphological variations, species identities, and geographic distributions, until it was influenced by Stresemann's student Ernst Mayr . [ 52 ] In Britain, some of the earliest ornithological works that used the word ecology appeared in 1915. [ 53 ] The Ibis , however, resisted the introduction of these new methods of study, and no paper on ecology appeared until 1943. [ 42 ] The work of David Lack on population ecology was pioneering. Newer quantitative approaches were introduced for the study of ecology and behaviour, and this was not readily accepted. For instance, Claud Ticehurst wrote:
Sometimes it seems that elaborate plans and statistics are made to prove what is commonplace knowledge to the mere collector, such as that hunting parties often travel more or less in circles.
David Lack's studies on population ecology sought to find the processes involved in the regulation of population based on the evolution of optimal clutch sizes. He concluded that population was regulated primarily by density-dependent controls , and also suggested that natural selection produces life-history traits that maximize the fitness of individuals. Others, such as Wynne-Edwards , interpreted population regulation as a mechanism that aided the "species" rather than individuals . This led to widespread and sometimes bitter debate on what constituted the "unit of selection". [ 49 ] Lack also pioneered the use of many new tools for ornithological research, including the idea of using radar to study bird migration. [ 54 ]
Birds were also widely used in studies of the niche hypothesis and Georgii Gause 's competitive exclusion principle. Work on resource partitioning and the structuring of bird communities through competition were made by Robert MacArthur . Patterns of biodiversity also became a topic of interest. Work on the relationship of the number of species to area and its application in the study of island biogeography was pioneered by E. O. Wilson and Robert MacArthur . [ 49 ] These studies led to the development of the discipline of landscape ecology .
John Hurrell Crook studied the behaviour of weaverbirds and demonstrated the links between ecological conditions, behaviour, and social systems. [ 49 ] [ 55 ] [ 56 ] Principles from economics were introduced to the study of biology by Jerram L. Brown in his work on explaining territorial behaviour. This led to more studies of behaviour that made use of cost-benefit analyses . [ 57 ] The rising interest in sociobiology also led to a spurt of bird studies in this area. [ 49 ] [ 58 ]
The study of imprinting behaviour in ducks and geese by Konrad Lorenz and the studies of instinct in herring gulls by Nicolaas Tinbergen led to the establishment of the field of ethology . The study of learning became an area of interest and the study of bird songs has been a model for studies in neuroethology. The study of hormones and physiology in the control of behaviour has also been aided by bird models. These have helped in finding the proximate causes of circadian and seasonal cycles. Studies on migration have attempted to answer questions on the evolution of migration, orientation, and navigation. [ 49 ]
The growth of genetics and the rise of molecular biology led to the application of the gene-centered view of evolution to explain avian phenomena. Studies on kinship and altruism, such as helpers , became of particular interest. The idea of inclusive fitness was used to interpret observations on behaviour and life history, and birds were widely used models for testing hypotheses based on theories postulated by W. D. Hamilton and others. [ 49 ]
The new tools of molecular biology changed the study of bird systematics, which changed from being based on phenotype to the underlying genotype . The use of techniques such as DNA–DNA hybridization to study evolutionary relationships was pioneered by Charles Sibley and Jon Edward Ahlquist , resulting in what is called the Sibley–Ahlquist taxonomy . These early techniques have been replaced by newer ones based on mitochondrial DNA sequences and molecular phylogenetics approaches that make use of computational procedures for sequence alignment , construction of phylogenetic trees , and calibration of molecular clocks to infer evolutionary relationships. [ 59 ] [ 60 ] Molecular techniques are also widely used in studies of avian population biology and ecology. [ 61 ]
The use of field glasses or telescopes for bird observation began in the 1820s and 1830s, with pioneers such as J. Dovaston (who also pioneered in the use of bird feeders), but instruction manuals did not begin to insist on the use of optical aids such as "a first-class telescope" or "field glass" until the 1880s. [ 62 ] [ 63 ]
The rise of field guides for the identification of birds was another major innovation. The early guides such as Thomas Bewick's two-volume guide and William Yarrell's three-volume guide were cumbersome, and mainly focused on identifying specimens in the hand. The earliest of the new generation of field guides was prepared by Florence Merriam , sister of Clinton Hart Merriam , the mammalogist. This was published in 1887 in a series Hints to Audubon Workers: Fifty Birds and How to Know Them in Grinnell's Audubon Magazine . [ 52 ] These were followed by new field guides, [ 64 ] from the pioneering illustrated handbooks of Frank Chapman to the classic Field Guide to the Birds by Roger Tory Peterson in 1934, to Birds of the West Indies published in 1936 by Dr. James Bond - the same who inspired the amateur ornithologist Ian Fleming in naming his famous literary spy . [ 65 ]
The interest in birdwatching grew in popularity in many parts of the world, and the possibility for amateurs to contribute to biological studies was soon realized. As early as 1916, Julian Huxley wrote a two-part article in The Auk , noting the tensions between amateurs and professionals, and suggested the possibility that the "vast army of bird lovers and bird watchers could begin providing the data scientists needed to address the fundamental problems of biology." [ 66 ] [ 67 ] The amateur ornithologist Harold F. Mayfield noted that the field was also funded by non-professionals. He noted that in 1975, 12% of the papers in American ornithology journals were written by persons who were not employed in biology related work. [ 68 ]
Organizations were started in many countries, and these grew rapidly in membership, most notable among them being the Royal Society for the Protection of Birds (RSPB) in Britain and the Audubon Society in the US, which started in 1885. Both these organizations were started with the primary objective of conservation. The RSPB, born in 1889, grew from a small Croydon -based group of women, including Eliza Phillips , Etta Lemon , Catherine Hall and Hannah Poland . Calling themselves the "Fur, Fin, and Feather Folk", the group met regularly and took a pledge "to refrain from wearing the feathers of any birds not killed for the purpose of food, the ostrich only exempted." The organization did not allow men as members initially, avenging a policy of the British Ornithologists' Union to keep out women. [ 40 ] Unlike the RSPB, which was primarily conservation oriented, the British Trust for Ornithology was started in 1933 with the aim of advancing ornithological research. Members were often involved in collaborative ornithological projects. These projects have resulted in atlases which detail the distribution of bird species across Britain. [ 4 ] In Canada, citizen scientist Elsie Cassels studied migratory birds and was involved in establishing Gaetz Lakes bird sanctuary. [ 69 ] In the United States, the Breeding Bird Surveys , conducted by the United States Geological Survey , have also produced atlases with information on breeding densities and changes in the density and distribution over time. Other volunteer collaborative ornithology projects were subsequently established in other parts of the world. [ 70 ]
The tools and techniques of ornithology are varied, and new inventions and approaches are quickly incorporated. The techniques may be broadly dealt under the categories of those that are applicable to specimens and those that are used in the field, but the classification is rough and many analysis techniques are usable both in the laboratory and field or may require a combination of field and laboratory techniques.
The earliest approaches to modern bird study involved the collection of eggs, a practice known as oology . While collecting became a pastime for many amateurs, the labels associated with these early egg collections made them unreliable for the serious study of bird breeding. To preserve eggs, a tiny hole was made and the contents extracted. This technique became standard with the invention of the blow drill around 1830. [ 40 ] Egg collection is no longer popular; however, historic museum collections have been of value in determining the effects of pesticides such as DDT on physiology. [ 71 ] [ 72 ] Museum bird collections continue to act as a resource for taxonomic studies. [ 73 ]
The use of bird skins to document species has been a standard part of systematic ornithology. Bird skins are prepared by retaining the key bones of the wings, legs, and skull along with the skin and feathers. In the past, they were treated with arsenic to prevent fungal and insect (mostly dermestid ) attack. Arsenic, being toxic, was replaced by less-toxic borax . Amateur and professional collectors became familiar with these skinning techniques and started sending in their skins to museums, some of them from distant locations. This led to the formation of huge collections of bird skins in museums in Europe and North America. Many private collections were also formed. These became references for comparison of species, and the ornithologists at these museums were able to compare species from different locations, often places that they themselves never visited. Morphometrics of these skins, particularly the lengths of the tarsus, bill, tail, and wing became important in the descriptions of bird species. These skin collections have been used in more recent times for studies on molecular phylogenetics by the extraction of ancient DNA . The importance of type specimens in the description of species make skin collections a vital resource for systematic ornithology. However, with the rise of molecular techniques, establishing the taxonomic status of new discoveries, such as the Bulo Burti boubou ( Laniarius liberatus , no longer a valid species) and the Bugun liocichla ( Liocichla bugunorum ), using blood, DNA and feather samples as the holotype material, has now become possible.
Other methods of preservation include the storage of specimens in spirit. Such wet specimens have special value in physiological and anatomical study, apart from providing better quality of DNA for molecular studies. [ 74 ] Freeze drying of specimens is another technique that has the advantage of preserving stomach contents and anatomy, although it tends to shrink, making it less reliable for morphometrics. [ 75 ] [ 76 ]
The study of birds in the field was helped enormously by improvements in optics. Photography made it possible to document birds in the field with great accuracy. High-power spotting scopes today allow observers to detect minute morphological differences that were earlier possible only by examination of the specimen "in the hand". [ 77 ]
The capture and marking of birds enable detailed studies of life history. Techniques for capturing birds are varied and include the use of bird liming for perching birds, mist nets for woodland birds, cannon netting for open-area flocking birds, the bal-chatri trap for raptors, [ 78 ] decoys and funnel traps for water birds. [ 79 ] [ 80 ]
The bird in the hand may be examined and measurements can be made, including standard lengths and weights. Feather moult and skull ossification provide indications of age and health. Sex can be determined by examination of anatomy in some sexually nondimorphic species. Blood samples may be drawn to determine hormonal conditions in studies of physiology, identify DNA markers for studying genetics and kinship in studies of breeding biology and phylogeography. Blood may also be used to identify pathogens and arthropod-borne viruses . Ectoparasites may be collected for studies of coevolution and zoonoses . [ 81 ] In many cryptic species, measurements (such as the relative lengths of wing feathers in warblers) are vital in establishing identity.
Captured birds are often marked for future recognition. Rings or bands provide long-lasting identification, but require capture for the information on them to be read. Field-identifiable marks such as coloured bands, wing tags, or dyes enable short-term studies where individual identification is required. Mark and recapture techniques make demographic studies possible. Ringing has traditionally been used in the study of migration. In recent times, satellite transmitters provide the ability to track migrating birds in near-real time. [ 82 ]
Techniques for estimating population density include point counts , transects , and territory mapping. Observations are made in the field using carefully designed protocols and the data may be analysed to estimate bird diversity, relative abundance, or absolute population densities. [ 83 ] These methods may be used repeatedly over large timespans to monitor changes in the environment. [ 84 ] Camera traps have been found to be a useful tool for the detection and documentation of elusive species, nest predators and in the quantitative analysis of frugivory, seed dispersal and behaviour. [ 85 ] [ 86 ]
Many aspects of bird biology are difficult to study in the field. These include the study of behavioural and physiological changes that require a long duration of access to the bird. Nondestructive samples of blood or feathers taken during field studies may be studied in the laboratory. For instance, the variation in the ratios of stable hydrogen isotopes across latitudes makes establishing the origins of migrant birds possible using mass spectrometric analysis of feather samples. [ 87 ] These techniques can be used in combination with other techniques such as ringing. [ 88 ]
The first attenuated vaccine developed by Louis Pasteur , for fowl cholera, was tested on poultry in 1878. [ 89 ] Anti-malarials were tested on birds which harbour avian-malarias. [ 90 ] Poultry continues to be used as a model for many studies in non-mammalian immunology. [ 91 ]
Studies in bird behaviour include the use of tamed and trained birds in captivity. Studies on bird intelligence and song learning have been largely laboratory-based. Field researchers may make use of a wide range of techniques such as the use of dummy owls to elicit mobbing behaviour, and dummy males or the use of call playback to elicit territorial behaviour and thereby to establish the boundaries of bird territories. [ 92 ]
Studies of bird migration including aspects of navigation, orientation, and physiology are often studied using captive birds in special cages that record their activities. The Emlen funnel , for instance, makes use of a cage with an inkpad at the centre and a conical floor where the ink marks can be counted to identify the direction in which the bird attempts to fly. The funnel can have a transparent top and visible cues such as the direction of sunlight may be controlled using mirrors or the positions of the stars simulated in a planetarium . [ 93 ]
The entire genome of the domestic fowl ( Gallus gallus ) was sequenced in 2004, and was followed in 2008 by the genome of the zebra finch ( Taeniopygia guttata ). [ 94 ] Such whole-genome sequencing projects allow for studies on evolutionary processes involved in speciation . [ 95 ] Associations between the expression of genes and behaviour may be studied using candidate genes. Variations in the exploratory behaviour of great tits ( Parus major ) have been found to be linked with a gene orthologous to the human gene DRD4 (Dopamine receptor D4) which is known to be associated with novelty-seeking behaviour. [ 96 ] The role of gene expression in developmental differences and morphological variations have been studied in Darwin's finches . The difference in the expression of Bmp4 have been shown to be associated with changes in the growth and shape of the beak. [ 97 ] [ 98 ]
The chicken has long been a model organism for studying vertebrate developmental biology . As the embryo is readily accessible, its development can be easily followed (unlike mice ). This also allows the use of electroporation for studying the effect of adding or silencing a gene. Other tools for perturbing their genetic makeup are chicken embryonic stem cells and viral vectors . [ 99 ]
With the widespread interest in birds, use of a large number of people to work on collaborative ornithological projects that cover large geographic scales has been possible. [ 100 ] [ 101 ] These citizen science projects include nationwide projects such as the Christmas Bird Count , [ 102 ] Backyard Bird Count, [ 103 ] the North American Breeding Bird Survey , the Canadian EPOQ [ 104 ] or regional projects such as the Asian Waterfowl Census and Spring Alive in Europe. These projects help to identify distributions of birds, their population densities and changes over time, arrival and departure dates of migration, breeding seasonality, and even population genetics. [ 105 ] The results of many of these projects are published as bird atlases . Studies of migration using bird ringing or colour marking often involve the cooperation of people and organizations in different countries. [ 106 ]
Wild birds impact many human activities, while domesticated birds are important sources of eggs, meat, feathers, and other products. Applied and economic ornithology aim to reduce the ill effects of problem birds and enhance gains from beneficial species.
The role of some species of birds as pests has been well known, particularly in agriculture. Granivorous birds such as the queleas in Africa are among the most numerous birds in the world, and foraging flocks can cause devastation. [ 107 ] [ 108 ] Many insectivorous birds are also noted as beneficial in agriculture. Many early studies on the benefits or damages caused by birds in fields were made by analysis of stomach contents and observation of feeding behaviour. [ 109 ] Modern studies aimed at managing birds in agriculture make use of a wide range of principles from ecology. [ 110 ] Intensive aquaculture has brought humans into conflict with fish-eating birds such as cormorants . [ 111 ]
Large flocks of pigeons and starlings in cities are often considered as a nuisance, and techniques to reduce their populations or their impacts are constantly innovated. [ 112 ] [ 113 ] Birds are also of medical importance, and their role as carriers of human diseases such as Japanese encephalitis , West Nile virus , and influenza H5N1 have been widely recognized. [ 114 ] [ 115 ] Bird strikes and the damage they cause in aviation are of particularly great importance, due to the fatal consequences and the level of economic losses caused. The airline industry incurs worldwide damages of an estimated US$1.2 billion each year. [ 116 ]
Many species of birds have been driven to extinction by human activities. Being conspicuous elements of the ecosystem, they have been considered as indicators of ecological health. [ 117 ] They have also helped in gathering support for habitat conservation . [ 118 ] Bird conservation requires specialized knowledge in aspects of biology and ecology, and may require the use of very location-specific approaches. Ornithologists contribute to conservation biology by studying the ecology of birds in the wild and identifying the key threats and ways of enhancing the survival of species. [ 119 ] Critically endangered species such as the California condor have had to be captured and bred in captivity. Such ex situ conservation measures may be followed by reintroduction of the species into the wild. [ 120 ] | https://en.wikipedia.org/wiki/Ornithology |
In statistical mechanics the Ornstein–Zernike ( OZ ) equation is an integral equation introduced [ 1 ] by Leonard Ornstein and Frits Zernike that relates different correlation functions with each other. Together with a closure relation, it is used to compute the structure factor and thermodynamic state functions of amorphous matter like liquids or colloids.
The OZ equation has practical importance as a foundation for approximations for computing the pair correlation function of molecules or ions in liquids, or of colloidal particles. The pair correlation function is related via Fourier transform to the static structure factor , which can be determined experimentally using X-ray diffraction or neutron diffraction .
The OZ equation relates the pair correlation function to the direct correlation function . The direct correlation function is only used in connection with the OZ equation, which can actually be seen as its definition. [ 2 ]
Besides the OZ equation, other methods for the computation of the pair correlation function include the virial expansion at low densities, and the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy . Any of these methods must be combined with a physical approximation: truncation in the case of the virial expansion, a closure relation for OZ or BBGKY.
To keep notation simple, we only consider homogeneous fluids. Thus the pair correlation function only depends on distance, and therefore is also called the radial distribution function . It can be written
where the first equality comes from homogeneity, the second from isotropy , and the equivalences introduce new notation.
It is convenient to define the total correlation function as:
which expresses the influence of molecule 1 on molecule 2 at distance r 12 {\displaystyle \,r_{12}\,} . The OZ equation
h ( 12 ) = c ( 12 ) + ρ ∫ d 3 r 3 c ( 13 ) h ( 32 ) {\displaystyle h(12)\;=\;c(12)\;+\;\rho \,\int {\text{d}}^{3}\mathbf {r} _{3}\,c(13)\,h(32)}
splits this influence into two contributions, a direct and indirect one. The direct contribution defines the direct correlation function , c ( r ) . {\displaystyle c(r).} The indirect part is due to the influence of molecule 1 on a third, labeled molecule 3, which in turn affects molecule 2, directly and indirectly. This indirect effect is weighted by the density and averaged over all the possible positions of molecule 3.
By eliminating the indirect influence, c ( r ) {\displaystyle \,c(r)\,} is shorter-ranged than h ( r ) {\displaystyle h(r)} and can be more easily modelled and approximated. The radius of c ( r ) {\displaystyle \,c(r)\,} is determined by the radius of intermolecular forces, whereas the radius of h ( r ) {\displaystyle \,h(r)\,} is of the order of the correlation length . [ 3 ]
The integral in the OZ equation is a convolution . Therefore, the OZ equation can be resolved by Fourier transform.
If we denote the Fourier transforms of h ( r ) {\displaystyle h(\mathbf {r} )} and c ( r ) {\displaystyle c(\mathbf {r} )} by h ^ ( k ) {\displaystyle {\hat {h}}(\mathbf {k} )} and c ^ ( k ) {\displaystyle {\hat {c}}(\mathbf {k} )} , respectively, and use the convolution theorem , we obtain
which yields
As both functions, h {\displaystyle \,h\,} and c {\displaystyle \,c\,} , are unknown, one needs an additional equation, known as a closure relation. While the OZ equation is purely formal, the closure must introduce some physically motivated approximation.
In the low-density limit, the pair correlation function is given by the Boltzmann factor ,
with β = 1 / k B T {\displaystyle \beta =1/k_{\text{B}}T} and with the pair potential u ( r ) {\displaystyle u(r)} . [ 4 ]
Closure relations for higher densities modify this simple relation in different ways. The best known closure approximations are: [ 5 ] [ 6 ]
The latter two interpolate in different ways between the former two, and thereby achieve a satisfactory description of particles that have a hard core and attractive forces. | https://en.wikipedia.org/wiki/Ornstein–Zernike_equation |
OroraTech is a German aerospace start-up company providing wildfire monitoring by employing nanosatellites . It was founded in 2018 as a university spin-off at the Technical University of Munich (TUM) . The headquarters are in Munich , Germany. [ 1 ] In June 2023, OroraTech joined the Copernicus Programme of the European Space Agency . [ 2 ]
OroraTech's key idea had been developed during the MOVE-II CubeSat project and WARR at the TUM. Starting as a spin-off in January 2017, the company was incorporated as Orbital Oracle Technologies GmbH (short: OroraTech ) in September 2018. [ 3 ] Since OroraTech's technology is based on academic research at the TUM, TUM professors Ulrich Walter , a former astronaut , and Alexander W. Koch act as advisors to the company. [ 4 ]
Wildfire detection using infrared sensors in space had been proposed as a technology since the 1990s. [ 5 ] [ 6 ] Technological advances, notably sunk space launch cost , enabled non-state actors to enter the market. As such, OroraTech operates a software platform for the detection and monitoring of wildfires based on measuring thermal- infrared radiation from space. The company is using data from existing satellites and develops their own constellation of 3-U CubeSats with thermal-infrared cameras to further improve temporal and spatial resolution of fire detection.
The software platform generates various overlays on base maps to visualize fire risk and fire detections. At the current stage, the platform uses data from twelve satellites in polar and geostationary orbits, including such by NASA , ESA , and EUMETSAT . [ 7 ] In early 2020, the platform had around 100 active users. [ 8 ]
The satellite technology is based on research from the MOVE-II project at the Chair of Astronautics (LRT) at the TUM. During the project, a 1-Unit CubeSat was launched with SpaceX in December 2018. [ 9 ] OroraTech's first nanosatellite, based on the original CubeSat, was developed to reach 10 cm x 10 cm x 34 cm in size, [ 10 ] weighing around 1.2 kg, [ 1 ] and it was launched on 13 January 2022 as part of SpaceX 's Transporter-3 rideshare mission. [ 11 ] The satellite features an uncooled thermal-infrared imager for space applications, [ 12 ] and GPU -accelerated on-orbit processing to reduce downlink latency and bandwidth for quicker wildfire alert dissemination, making it particularly efficient in tackling the issue of detecting wildfires in late afternoon images. [ 13 ] [ 11 ]
As of June 2022, the company plans to put its next eight satellites into orbit by the end of 2023, aiming for a detection time of 30 minutes. [ 11 ] A second satellite, once again hosted on a Lemur-2 cubesat platform, was launched on 12 June 2023 on a Falcon 9 Block 5 rocket as part of SpaceX Transporter-8 rideshare mission. [ 14 ]
The technology is used by Wildfire Services in British Columbia (Canada) and New South Wales (Australia) for wildfire detection and wildfire suppression . [ 15 ] International media used images from OroraTech's wildfire service for coverage of the 2020 wildfire season in California, [ 16 ] Oregon, [ 17 ] British Columbia, [ 18 ] and Siberia. [ 19 ] | https://en.wikipedia.org/wiki/OroraTech |
Orosomucoid ( ORM ) or alpha-1-acid glycoprotein ( α 1 AGp , [ 1 ] AGP or AAG ) is an acute phase protein found in plasma . Orosomucoid was discovered over 70 years ago and belongs to the lipocalin protein family. [ 2 ] There are two isoforms of AGP, referred to as AGP1 and AGP2. [ 2 ] It is an alpha-globulin glycoprotein and is modulated by two polymorphic genes. It is synthesized primarily in hepatocytes and has a normal plasma concentration between 0.6–1.2 mg/mL (1–3% plasma protein). [ 3 ] Recent research has shown that under certain physiological conditions, brain and adipose tissue can also synthesize this protein. [ 2 ] Plasma levels of AGP are affected by pregnancy , burns, certain drugs, and certain diseases, particularly HIV . [ 3 ] APG also plays an important role in inflammation and pharmacokinetics, acting as a major transport protein in the blood stream. [ 4 ] [ 5 ]
Orosomucoid is a highly glycosylated protein having a molecular weight of 34–54 kDa, with nearly 45% of its mass in carbohydrate sidechains. [ 6 ] The isoforms AGP1 and AGP2 are encoded by the ORM1 and ORM2 genes on chromosome 9, and differ by only 22 amino acids [ 2 ] This results in a slightly smaller beta-barrel in AGP2. [ 7 ] The structural differences between AGP 1 and 2 allow for Alpha 1-acid glycoprotein to bind to a wider variety of ligands, broadening AGP's functional
range. [ 2 ] These chains contribute significantly to molecular stability and interaction potential with other molecules, including significant drugs. [ 8 ] During systemic inflammation AGP concentration increases and its glycosylation pattern changes, generating various glycoforms with distinct — sometimes even opposing — biological activities. [ 4 ] One study shows that at least 5 different functions can be linked to changes in the heteroglycan side chains. [ 9 ] These side chain can be bi-, tri-, or tetra antennary, which contribute to the strength of binding to the ligand. [ 9 ] It has been proven that during acute inflammation there is an increase of AGP glycoforms with biantennary units, this is a type I glycosylation change. [ 9 ] In chronic inflammatory conditions, AGP often exhibits a reduction in glycoforms containing biantennary heteroglycans, this is a type II glycosylation shift. [ 9 ] Similar changes in glycosylation patterns have also been observed during pregnancy, estrogen therapy, and liver injury. [ 9 ]
The tertiary structure of AGP, determined via X-ray crystallography (PDB ID: 3KQ0), reveals a characteristic beta-barrel fold. Visualization using ChimeraX has provided valuable insights into its conformation and binding pockets. [ 7 ]
AGP is involved in immune regulation and regulates many inflammation-related processes, including white blood cell activity and pathogen binding. [ 4 ] One example of how Human AGP has been shown to regulate immunie response is by inhibition of the proliferative response of peripheral blood lymphocytes by phytohemagglutinin (PHA) stimulation. [ 7 ] These immunomodulatory effects are reversible and may be due to conformational changes on lymphocyte surfaces or interactions with protein kinases. [ 7 ] Overall, AGP is considered protective against the harmful consequences of prolonged inflammation. [ 4 ]
A study was conducted to compare the different glycosylation sites from patients with acute versus chronic inflammation. [ 10 ] The blood serum of patients with acute inflammation showed an increase in bi-antennary and decrease in tri- and tetra-antennary structures, and an increases in alpha1,3-fucosylation, at most glycosylation sites on AGP. [ 10 ] In the blood serum of patients with chronic inflammation, higher concentrations of tri-antennary alpha1,3-fucosylation at sites 3 and 4 and tetra-antennary alpha1,3-fucosylation at sites 3, 4 and 5 were detected. [ 10 ] In different pathophysiological state (inflammation, rheumatoid arthritis , cancer) alterations of Asn-linked glycans have been reported. [ 10 ]
A major established function of ORM is to act as a carrier, especially for basic and neutrally charged lipophilic compounds. In medicine, it is known as the primary carrier of basic (positively charged) drugs (whereas albumin carries acidic (negatively charged) and neutral drugs), steroids , and protease inhibitors . [ 3 ] [ 11 ] According to Zsila and Iwao, AGP significantly influences the pharmacokinetic affects of many therapeutic drugs due to its strong ligand-binding capabilities. [ 8 ] Being an acidic protein, AGP primarily binds to basic (positively charged) drugs, but it can also bind neutral or acidic molecules in some cases. [ 2 ] Glycosylation, particularly fucosylation, appears to impact this drug-binding affinity. [ 2 ]
A notable example is AGP's high binding affinity for 7-hydroxystaurosporine, an anti-cancer drug. [ 12 ] AGP limits the drug's effectiveness in humans but not in rats or cattle. [ 12 ] Other drugs with strong AGP binding includes but is not limited to the following: Warfarin , Pinometostat, Aripiprazole , Imatinib , Voriconazole , ONO-2160, Brigatinib . [ 12 ]
AGP's plasma levels vary in different medical conditions. It tends to increase in obstructive jaundice and decrease in hepatocellular jaundice and intestinal infections. It has also been identified as a circulating biomarker useful for estimating the five-year risk of all-cause mortality, along with albumin, VLDL particle size, and citrate. [ 7 ]
It has been proven that aging causes a small decrease in plasma albumin levels; but tends to not show any change in alpha-1-acid glycoprotein presents in the blood plasma. The effect of any changes on drug protein binding and drug delivery appear to be minimal. [ 13 ] In studies where plasma albumin and alpha-1-acid glycoprotein are monitored for individuals between 20–90 years old, there was a significant decrease in the concentrations of albumin while the concentration of AGP largely remained unchanged [ 14 ]
AGP shows a complex interaction with thyroid homeostasis: AGP in low concentrations was observed to stimulate the thyrotropin (TSH) receptor and intracellular accumulation of cyclic AMP . High AGP concentrations, however, inhibited TSH signalling. [ 15 ] [ 16 ] This specific function of AGP still remains largely unknown and under researched.
Alpha-1-acid glycoprotein has been identified as one of four potentially useful circulating biomarkers for estimating the five-year risk of all-cause mortality (the other three are albumin , very low-density lipoprotein particle size, and citrate ). [ 17 ] Studies have shown that Alpha 1-acid glycoprotein is an independent predictor death while hospitalized. [ 18 ] In a study of 433 patients, from ages 73–92, and all admitted in a rehabilitation department for geriatric medicine the study collected base line alpha 1-acid glycoproteins at baseline and then at discharge or death. [ 18 ] This study showed that in the population of discharged patients their baseline alpha 1-acid glycoprotein levels where higher than those who's stay ended with death (1691 +/* 69 mg/l versus 1340 +/- 456 mg/l). [ 18 ] | https://en.wikipedia.org/wiki/Orosomucoid |
Orotidine 5'-monophosphate ( OMP ), also known as orotidylic acid , is a pyrimidine nucleotide [ 1 ] which is the last intermediate in the biosynthesis of uridine monophosphate . [ 2 ] OMP is formed from orotate and phosphoribosyl pyrophosphate by the enzyme orotate phosphoribosyltransferase .
In humans, the enzyme UMP synthase converts OMP into uridine 5'- monophosphate . [ 2 ] If UMP synthase is defective, orotic aciduria can result. [ 2 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orotidine_5'-monophosphate |
An orphan drug is a pharmaceutical agent that is developed to treat certain rare medical conditions. An orphan drug would not be profitable to produce without government assistance, due to the small population of patients affected by the conditions. The conditions that orphan drugs are used to treat are referred to as orphan diseases . The assignment of orphan status to a disease and to drugs developed to treat it is a matter of public policy that depends on the legislation (if there is any) of the country.
Designation of a drug as an orphan drug has yielded medical breakthroughs that might not otherwise have been achieved, due to the economics of drug research and development . [ 1 ] Examples of this can be that in the U.S. and the EU, it is easier to gain marketing approval for an orphan drug. There may be other financial incentives, such as an extended period of exclusivity, during which the producer has sole rights to market the drug. All are intended to encourage development of drugs which would otherwise lack sufficient profit motive to attract corporate research budgets and personnel. [ 2 ] [ 3 ]
According to the US Food and Drug Administration (FDA), an orphan drug is defined as one "intended for the treatment, prevention or diagnosis of a rare disease or condition, which is one that affects less than 200,000 persons in the US" (which equates to approximately 6 cases per 10,000 population) "or meets cost recovery provisions of the act". [ 4 ] [ 5 ]
In the European Union (EU), the European Medicines Agency (EMA) defines a drug as "orphan" if it is intended for the diagnosis, prevention or treatment of a life-threatening or chronically and seriously debilitating condition affecting not more than 5 in 10,000 EU people. [ 6 ] EMA also qualifies a drug as orphan if – without incentives – it would be unlikely that marketing the drug in the EU would generate sufficient benefit for the affected people and for the drug manufacturer to justify the investment. [ 6 ]
In Japan, drugs and medical devices are given the designation as an orphan drug or device based on the Act of Securing Quality, Efficacy, Safety of Pharmaceuticals, Medical Devices, Regenerative or Cellular Therapy Products, Gene Therapy Products, and Cosmetics if they are intended for use in less than 50,000 patients in Japan for which there is a high medical need. [ 7 ]
As of 2014 [update] , there were 281 marketed orphan drugs and more than 400 orphan-designated drugs in clinical trials. More than 60% of orphan drugs were biologics . The U.S. dominated development of orphan drugs, with more than 300 trials, followed by Europe. Cancer treatment was the indication in more than 30% of orphan drug trials. [ 8 ]
According to Thomson Reuters in their 2012 publication "The Economic Power of Orphan Drugs", there has been increased investment in orphan drug research and development, partly due to the U.S. Orphan Drug Act of 1983 (ODA) and similar acts in other regions of the world driven by "high-profile philanthropic funding". [ 9 ] [ 10 ]
According to Drug Discovery Today , the years 2001 to 2011 were the "most productive period in the history of orphan drug development, in terms of average annual orphan drug designations and orphan drug approvals". [ 10 ] : 660 For the same decade the compound annual growth rate (CAGR) of the orphan drugs was an "impressive 25.8%, compared to only 20.1% for a matched control group of non-orphan drugs". [ 9 ] : 6 By 2012, the market for orphan drugs was worth US$637 million, compared with US$638 million for a control group of non-orphan drugs. [ 9 ]
By 2012,
the revenue-generating potential of orphan drugs [was] as great as for non-orphan drugs, even though patient populations for rare diseases are significantly smaller. Moreover, we suggest that orphan drugs have greater profitability when considered in the full context of developmental drivers, including government financial incentives, smaller clinical trial sizes, shorter clinical trial times and higher rates of regulatory success.
According to a 2014 report, the orphan drug market has become increasingly lucrative for a number of reasons. The cost of clinical trials for orphan drugs is substantially lower than for other diseases because trial sizes are naturally much smaller than for more diseases with larger numbers of patients. Small clinical trials and minimal competition place orphan agents at an advantage in regulatory review. [ 2 ]
Tax incentives reduce the cost of development. On average the cost per patient for orphan drugs is "six times that of non-orphan drugs, a clear indication of their pricing power". The cost of per-person outlays are large and are expected to increase with wider use of public subsidies. [ 2 ]
The 2014 Orphan Drug report stated that the percentage of orphan drug sales as part of all prescription drug sales had been increasing at a rapid rate. The report projected a total of US$176 billion by 2020. [ 2 ] Although orphan disease populations are the smallest, the cost of per-patient outlays among them are the largest and are expected to increase as more people with rare diseases become eligible for subsidies – in the U.S., for example, through the Affordable Care Act . [ 2 ]
Orphan drugs generally follow the same regulatory development path as any other pharmaceutical product, in which testing focuses on pharmacokinetics and pharmacodynamics , dosing , stability, safety and efficacy. However, some statistical burdens are lessened to maintain development momentum. For example, orphan drug regulations generally acknowledge the fact that it may not be possible to test 1,000 patients in a phase III clinical trial if fewer than that number are affected by the disease.
Government intervention on behalf of orphan drug development takes several forms:
A 2015 study of "34 key Canadian stakeholders, including drug regulators, funders, scientists, policy experts, pharmaceutical industry representatives, and patient advocates" investigated factors behind the pharmaceutical industry growing interest in "niche markets" such as orphan drugs. [ 11 ]
The Orphan Drug Act (ODA) of January 1983, passed in the United States , with lobbying from the National Organization for Rare Disorders and many other organizations, [ 12 ] is meant to encourage pharmaceutical companies to develop drugs for diseases that have a small market. [ 13 ] Under the ODA drugs, vaccines, and diagnostic agents would qualify for orphan status if they were intended to treat a disease affecting fewer than 200,000 American citizens. Under the ODA orphan drug sponsors qualify for seven-year FDA-administered market Orphan Drug Exclusivity (ODE), "tax credits of up to 50% of R&D costs, R&D grants, waived FDA fees, protocol assistance [ 10 ] : 660 and may get clinical trial tax incentives . [ 13 ]
In the U.S., orphan drug designation means that the sponsor qualifies for certain benefits, but it does not mean the drug is safe, effective or legal.
In 2002, the Rare Diseases Act was signed into law. It amended the Public Health Service Act to establish the Office of Rare Diseases . It also increased funding for the development of treatments for people with rare diseases . [ 14 ]
In 2000, the European Union (EU) enacted similar legislation, Regulation(EC) No 141/2000, which refers to drugs developed to treat rare diseases to as "orphan medicinal products". The EU's definition of an orphan condition is broader than that of the US, in that it also covers some tropical diseases that are primarily found in developing nations. [ 15 ] Orphan drug status granted by the European Commission gives marketing exclusivity in the EU for 10 years after approval. [ 16 ] The EU's legislation is administered by the Committee on Orphan Medicinal Products of the European Medicines Agency (EMA).
In late 2007 the FDA and EMA agreed to use a common application process for both agencies to make it easier for manufacturers to apply for orphan drug status but, while continuing two separate approval processes. [ 17 ]
Legislation has been implemented by Japan, Singapore, and Australia that offers subsidies and other incentives to encourage the development of drugs that treat orphan diseases. [ 18 ]
Under the ODA and EU legislation, many orphan drugs have been developed, including drugs to treat glioma , multiple myeloma , cystic fibrosis , phenylketonuria , snake venom poisoning, and idiopathic thrombocytopenic purpura . [ citation needed ] [ 19 ]
The Pharmaceutical Executive opines, that the "ODA is nearly universally acknowledged to be a success". [ 1 ]
Before the US Congress enacted the ODA in 1983, only 38 drugs were approved in the US specifically to treat orphan diseases. [ 3 ] In the US, from January 1983 to June 2004, 249 orphan drugs received marketing authorization and 1,129 received different orphan drug designations, compared to fewer than ten such products in the decade prior to 1983. From 1983 until May 2010, the FDA approved 353 orphan drugs and granted orphan designations to 2,116 compounds. As of 2010, 200 of the roughly 7,000 officially designated orphan diseases have become treatable. [ 1 ]
Critics have questioned whether orphan drug legislation was the real cause of this increase, claiming that many of the new drugs were for disorders which were already being researched anyway, and would have had drugs developed regardless of the legislation, and whether the ODA has truly stimulated the production of non-profitable drugs; the act also has been criticised for allowing some pharmaceutical companies to make a large profit off drugs which have a small market but sell for a high price. [ 13 ]
While the European Medicines Agency grants orphan drugs market access in all member states, in practice, they only reach the market when a member state decides that its national health system will reimburse for the drug. For example, in 2008, 44 orphan drugs reached the market in the Netherlands, 35 in Belgium, and 28 in Sweden, while in 2007, 35 such drugs reached the market in France and 23 in Italy. [ 20 ]
Though not technically an orphan disease, research and development into the treatment for AIDS has been heavily linked to the Orphan Drug Act . In the beginning of the AIDS epidemic the lack of treatment for the disease was often accredited to a believed lack of commercial base for a medication linked to HIV infection. This encouraged the FDA to use the Orphan Drug Act to help bolster research in this field, and by 1995 13 of the 19 drugs approved by the FDA to treat AIDS had received orphan drug designation, with 10 receiving marketing rights. These are in addition to the 70 designated orphan drugs designed to treat other HIV related illnesses. [ 21 ]
In the 1980s, people with cystic fibrosis rarely lived beyond their early teens. Drugs like Pulmozyme and tobramycin , both developed with aid from the ODA, revolutionized treatment for cystic fibrosis patients by significantly improving their quality of life and extending their life expectancies. Now, cystic fibrosis patients often survive into their thirties and some into their fifties. [ 14 ]
The 1985 Nobel Prize for medicine went to two researchers for their work related to familial hypercholesterolemia , which causes large and rapid increases in cholesterol levels. Their research led to the development of statin drugs which are now commonly used to treat high cholesterol. [ 18 ]
Penicillamine was developed to treat Wilson's disease , a rare hereditary disease that can lead to a fatal accumulation of copper in the body. This drug was later found to be effective in treating arthritis . [ 18 ] Bis-choline tetrathiomolybdate is currently under investigation as a therapy against Wilson's disease.
In 2017, FDA granted RT001 orphan drug designation in the treatment of phospholipase 2G6 -associated neurodegeneration ( PLAN ). [ 22 ]
The FDA granted Patisiran (Onpattro) orphan drug status and breakthrough therapy designation due to its novel mechanism involving RNA therapy to block the production of an abnormal form of transthyretin. Patisiran received full FDA approval in 2018 [ 23 ] and its RNA lipid nanoparticle drug delivery system was later used in the Pfizer–BioNTech COVID-19 vaccine and Moderna RNA vaccines.
The Center for Orphan Drug Research at the University of Minnesota College of Pharmacy helps small companies with insufficient in-house expertise and resources in drug synthesis, formulation, pharmacometrics, and bio-analysis. [ 24 ] The Keck Graduate Institute Center for Rare Disease Therapies (CRDT) in Claremont, California, supports projects to revive potential orphan drugs whose development has stalled by identifying barriers to commercialization, such as problems with formulation and bio-processing. [ 24 ]
Numerous advocacy groups such as the National Organization for Rare Disorders , Global Genes Project , Children's Rare Disease Network, Abetalipoproteinemia Collaboration Foundation, Zellweger Baby Support Network, and the Friedreich's Ataxia Research Alliance have been founded in order to advocate on behalf of patients with rare diseases with a particular emphasis on diseases that affect children. [ 1 ]
According to a 2015 report published by EvaluatePharma, the economics of orphan drugs mirrors the economics of the pharmaceutical market as a whole but has a few very large differences. [ 25 ] The market for orphan drugs is by definition very small, but while the customer base is drastically smaller the cost of research and development is very much the same as for non orphan drugs. This, the producers have claimed, causes them to charge extremely high amounts for treatment, sometimes as high as $700,000 a year, as in the case of Spinraza (Biogen), FDA approved in December 2016 for spinal muscular atrophy, [ 26 ] placing a large amount of stress on insurance companies and patients. An analysis of 12 orphan drugs that were approved in the US between 1990 and 2000 estimated a price reduction of on average 50% upon loss of marketing exclusivity, with a range of price reductions from 14% to 95%. [ 27 ]
Governments have implemented steps to reduce high research and development cost with subsidies and other forms of financial assistance. The largest assistance are tax breaks which can be as high as 50% of research and development costs. [ 28 ] Orphan drug manufacturers are also able to take advantage of the small customer base to cut cost on clinical trials due to the small number of cases to have smaller trials which reduces cost. These smaller clinical trials also allow orphan drugs to move to market faster as the average time to receive FDA approval for an orphan drug is 10 months compared to 13 months for non-orphan drugs. This is especially true in the market for cancer drugs, as a 2011 study found that between 2004 and 2010 orphan drug trials were more likely to be smaller and less randomized than their non-orphan counterparts, but still had a higher FDA approval rate, with 15 orphan cancer drugs being approved, while only 12 non-orphan drugs were approved. [ 29 ] This allows manufactures to get cost to the point that it is economically feasible to produce these treatments. [ 28 ] The subsidies can total up to $30 million per fiscal year in the United States alone. [ citation needed ]
By 2015, industry analysts and academic researchers agreed, that the sky-high price of orphan drugs, such as eculizumab , was not related to research, development and manufacturing costs. Their price is arbitrary and they have become more profitable than traditional medicines. [ 30 ]
Public resources went into understanding the molecular basis of the disease, public resources went into the technology to make antibodies and finally, Alexion, to their credit, kind of picked up the pieces.
By 2007 the use of economic evaluation methods regarding public-funding of orphan drugs, using estimates of the incremental cost-effectiveness, for example, became more established internationally. [ 31 ] The QALY has often been used in cost-utility analysis to calculate the ratio of cost to QALYs saved for a particular health care intervention. [ 32 ] [ 33 ] By 2008 the National Institute for Health and Care Excellence (NICE) in England and Wales, for example, operated with a threshold range of £20,000–30,000 per quality-adjusted life year (QALY). [ 34 ] By 2005 doubts were raised about the use of economic evaluations in orphan drugs. [ 31 ] By 2008 most of the orphan drugs appraised had cost-effectiveness thresholds "well in excess of the 'accepted' level and would not be reimbursed according to conventional criteria". [ 34 ] As early as 2005 McCabe et al. argued [ 35 ] [ 36 ] that rarity should not have a premium and orphan drugs should be treated like other pharmaceuticals in general. [ 35 ] [ 36 ] Drummond et al. [ 36 ] argued that the social value of health technologies should also be included in the assessment along with the estimation of the incremental cost-effectiveness ratio.
The very large incentives given to pharmaceutical companies to produce orphan drugs have led to the impression that the financial support afforded to make these drugs possible is akin to abuse. [ 37 ] Because drugs can be used to treat multiple conditions, companies can take drugs that were filed with their government agency as orphan drugs to receive financial assistance, and then market it to a wide population to increase their profit margin . For example AstraZeneca 's cholesterol drug Crestor was filed as a treatment for the rare disease pediatric familial hypercholesterolemia . After the drug was approved for orphan drug designation, and AstraZeneca had received tax breaks and other advantages, AstraZeneca later applied and received FDA approval for the drug to be used to treat cholesterol in all diabetics. [ 18 ]
The UK's National Institute for Health and Care Excellence (NICE) can pay from £100,000 to £300,000 per QALY ( Quality Adjusted Life Year ) for treatments of "very rare conditions". This is compared to under £20,000 for non-orphan drugs. [ 38 ]
In 2015, NICE held consultations with "patient groups, the Department of Health, companies, learned societies, charities and researchers" regarding the appraisal of medicines and other technologies. There was a call for more research into new processes, including: [ 39 ]
the model of pharmaceutical research and development, the expectations that companies and patient groups have about how risk and reward is shared between the industry and a publicly funded NHS, and in the arrangements for commissioning expensive new treatments. | https://en.wikipedia.org/wiki/Orphan_drug |
An orphan virus is a virus that is not associated with a disease but may possess pathogenicity . [ 1 ]
Some orphan viruses include adeno-associated virus ( Parvoviridae ), human herpesvirus 7 ( Herpesviridae ), human foamy virus ( Retroviridae ), Human Reovirus ( Reoviridae ), hepatitis G ( Flaviviridae ), and TT virus ( Anelloviridae ). [ citation needed ]
Gilbert Dalldorf, a pathologist who showed that Coxsackie viruses paralyze mice but not humans, indicated that the term ‘orphan’ was created "in a moment of conviviality" by a group of virologists. [ 2 ]
Many enteroviruses are referred to as ECHO, enteric cytopathic human orphan viruses , because they were originally not associated with any disease. Even though many of them are associated with severe diseases, the name ECHO still continues to be used. [ citation needed ]
This virus -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orphan_virus |
Orphan wells in Alberta, Canada are inactive oil or gas well sites that have no solvent owner that can be held legally or financially accountable for the decommissioning and reclamation obligations to ensure public safety and to address environmental liabilities. [ 2 ] [ 3 ] [ 4 ]
The 100% industry-funded Alberta Energy Regulator (AER)—the sole regulator of the province's energy sector—manages licensing and enforcement related to the full lifecycle of oil and gas wells based on Alberta Environment Ministry requirements, including orphaned and abandoned wells . [ 5 ] [ 6 ] [ 7 ] Oil and gas licensees are liable for the responsible and safe closure and clean-up of their oil and gas well sites under the Polluter Pays Principle (PPP) [ 8 ] as a legal asset retirement obligation (ARO). [ 5 ] [ 6 ] [ 9 ] [ 10 ] An operator's liability for surface reclamation issues continues for 25 years following the issuance of a site reclamation certificate. There is also a lifelong liability in case of contamination. [ 11 ] [ 12 ]
Once the current environmental legislation was in place, and the industry-led and industry-funded Orphan Wells Association (OWA), was established in 2002, some orphan wells became the OWA's responsibility. [ 13 ] OWA's Inventory does not include legacy wells [ 14 ] which are more complex, time-intensive and costly to remediate. [ 15 ] Following the 2014 downturn in the global price of oil, there was a "tsunami" of orphaned wells, facilities, and pipelines resulting from bankruptcies. [ 16 ]
As of March 2023, oil and gas companies owe rural municipalities $268 million in unpaid taxes; [ 17 ] they owe landowners "tens of millions in unpaid lease payments". [ 18 ] Original owners of what are now orphan wells "failed to fulfill their responsibility for costly end-of-life decommissioning and restoration work"; some sold these wells "strategically to insolvent operators". [ 18 ] Landowners suffer both "environmental and economic consequences" of having these wells on their property. [ 18 ] OWA funding is underfunded by at least several hundred million. [ 18 ] The total estimate for cleaning up all existing sites is as much as $260 billion. Remediation is paid for through federal and provincial bailouts, a PPP violation. [ 18 ]
In 2017, of the estimated 450,000 AER oil and gas registered wells [ b ] in the province, 150,000 were no longer producing but were not remediated, [ 21 ] and 92,000 were inactive with no set value. [ 22 ] A 2021 Alberta Liabilities Disclosure Project report, "The Big Clean", that accessed AER data through a Freedom of Information (FOIP) request, estimated that Alberta had 300,000 unreclaimed wells and that it would cost from $40 to $70 billion to clean them up. [ 23 ] [ 24 ] This cost estimate does not include unreclaimed pipelines and pumping stations. [ 23 ] The ALDP, an independent, nonpartisan research organization that provides "government-level data" on liabilities related to the oil and gas industry in Alberta, seeks solutions to—what they describe as—a "growing liabilities crisis". [ 23 ] [ 24 ]
Unreclaimed wells are inactive wells that may be orphaned or legally-licensed. Some unreclaimed wells may have been sealed off, while some have begun or completed remediation or reclamation of the well site. Under current AER regulations, it is legal for operators to leave well reclamation suspended indefinitely, this is not the case in some oil producing states, such as North Dakota. [ 25 ] [ 26 ] Daryl Bennett, who represents landowners through both My Landman Group and Action Surface Rights "in disputes involving resource companies", [ 27 ] said that there were 170,000 unreclaimed sites that require cleaning. [ 28 ] These unreclaimed wells were licensed by the province to oil and gas operators under Alberta's mineral rights provision, by which landowners only have surface—not below the surface mineral rights—and have no right of refusal to prevent a well being drilled on their property. [ 22 ] [ 27 ] [ 29 ] [ 30 ] When the wells were producing, landowners benefitted, as operators pay an annual fee to lease and access the site. When operators go bankrupt or simply cannot be relocated, landowners are left with these aging wells with no recourse. By 2001, there were about 59,000 farms with at least one well on their property. [ 31 ] By 2023, wells and pumpjacks dot the landscape across much of rural Alberta with a well for almost every 1.4 km 2 (0.54 sq mi). [ 25 ] [ 26 ] [ 32 ]
In 2019, the Intergovernmental Panel on Climate Change (IPCC) warned that methane gas leakage from abandoned oil and gas wells represented a serious risk to climate change and recommended the monitoring of these wells. [ 33 ] Canada began to monitor methane leakage from abandoned wells at that time. [ 13 ] [ 33 ]
It is uncertain how many of the roughly 300,000 inactive wells belong to the various classifications that describe oil and gas wells in Alberta. The oil and gas industry refer to wells that have been sealed as "abandoned", [ 1 ] or to be exact, "responsibly abandoned". [ 34 ] The Narwhal says that this has led to "countless confusing headlines." [ 1 ] There are numerous inactive well sites that are neither sealed nor officially designated as orphans by AER. [ 34 ] The annual inventory of the OWA does not include orphaned wells that AER has identified but not transitioned into orphan status. The OWA is also not responsible for wells that were orphaned prior to its establishment in 2002. These wells are the responsibility of the regulatory and ministerial bodies, the AER and the Department of Energy. [ 14 ] [ 15 ] A 2021 Office of the Auditor General (OAG) report said that the regulator and ministry failed to prioritize sites and rejected responsibility for funding and cleaning well sites "even when evidence showed otherwise." [ 35 ]
The January 2022 Parliamentary Budget Office (PB0) report on the cost of cleaning Canada's orphan oil and gas wells said that, in spite of the 1.7 billion federal money provided during the pandemic, the cost of cleaning up orphan well sites nationally will require funding sources from industry, the provinces, and the federal government. [ 36 ] By January 2022, Alberta had given about 50% of the allocated funding to viable energy companies, not companies "with an acute financial risk ." [ 37 ]
The CAPP says that most of their member companies pay taxes and clean up their own wells [ 17 ] and that the bankruptcies—one of the prime factors in the increase in orphan wells. [ 16 ] were the result of the "lagging effects of this multi-year downturn for the oil and gas sector." [ 17 ] The increase in the number of insolvencies and wells with no solvent owner was the result of the "largest oil price declines in modern history" in 2014 to 2016 and the longest decline in oil prices since the 1980s. [ 38 ]
As of 2022, most orphan wells were still not remediated. Farmers and ranchers suffer both "environmental and economic consequences" as the wells on their land, which are licensed as active, are not. [ 18 ] They face decades-long challenges including land devaluation because of orphan wells, and contamination, and loss of compensation from bankrupt companies. [ 11 ] [ 27 ] [ 39 ] Insolvent operators owe landowners "tens of millions" in unpaid surface rights lease payments, and/or transfer costs, such as taxes onto the landowners. [ 11 ] [ 18 ] [ 27 ] [ 40 ] [ 41 ] These delinquent operators owe municipalities $268 million in unpaid taxes [ 28 ] Rural Municipalities of Alberta (RMA) says this represents an increase of 261%, since 2018—despite industry recording multi-billions in profits. [ 17 ] [ 29 ] [ 42 ] This will result in service cuts or tax increases at the municipal level. [ 17 ] The level of unpaid taxes reported in was "unprecedented" and presented a "unique challenge that has not been experienced by municipalities in Alberta before." [ 41 ]
Starting in March 2022, the industry experienced the "largest 23-month increase in energy prices since the 1973 oil price" [ 42 ] following the Russian invasion of Ukraine . [ 42 ] The increase in the price of oil resulting record profits for Canadian oil companies, with some of them earning billions. [ 29 ] [ 42 ] In Alberta, Canadian Natural Resources, Cenovus Energy , Paramount Resources and Whitecap Resources earned a combined net income approximately $5 billion in the fourth quarter alone of the fiscal year 2022. [ 28 ]
The OWA funding is "grossly inadequate" by at least several hundred million. [ 18 ] The total estimate for cleaning up all existing sites is as much as $260 billion. Taxpayers have paid the difference through federal and provincial bailouts in the form of grants and loans, a PPP violation. [ 18 ]
Concerns have been raised about the "murky practice" of offloading liabilities strategically to smaller, junior operators with insufficient funds that are likely to face future insolvency. [ 11 ] [ 18 ] This practice allows original owners of what are now orphan wells to avoid paying for costly end-of-life decommissioning and restoration work for which they were responsible. Many of these wells become orphan wells. [ 18 ] In this way, companies misuse the bankruptcy process to keep their valuable assets. [ 11 ] The OWA says as owners shirk their responsibility the collective becomes responsible for the liabilities. [ 11 ] Fifty percent of the delinquent wells are owned by small companies that have insufficient finances but are still able to produce and collect revenue. [ 28 ] There is a direct correlation between these abandoned wells' environmental liabilities, unpaid taxes, and unpaid surface payments to landowners.
The AER has the authority to enforce the rules. [ 28 ] The RMA says that the AER "props" up small companies to avoid increasing the already concerning number of orphan wells which results primarily from bankruptcies. [ 28 ] The AER says that it is the RMA's role to collect taxes. [ 28 ] A lawyer representing Action Surface Rights, a landowners group, Christine Laing, called on the AER to use the power it has more often and in a timely fashion to "protect the public interest". [ 43 ]
The International Institute for Sustainable Development (IISD), which was established in 1990 during the premiership of Brian Mulroney as part of Canada's contribution to the 2002 Rio Earth Summit , drew attention to ways in which Canadian producers have failed on ESG issues. [ 18 ]
The province's oldest inactive well has been dormant and unreclaimed since June 30, 1918. [ 44 ]
Some of the legacy sites were in operation in the 1920s or earlier, and have no known operator and no "financial security to cover the cleanup costs." [ 45 ]
Canada's oil production in 1946 was only 21,000 barrels (3,300 m 3 ) of oil per day. By 1956, Alberta was producing 400,000 barrels (64,000 m 3 ) per day. [ 48 ] [ 49 ]
In 2012, the OWA only had 14 classified orphan wells; in 2013 there were 74; in 2014 there were 162; in 2015 there were 705; [ 51 ] in 2024 there were 2,647. [ 52 ]
The average cost of reclamation/remediation (R/R) site services in 2015 was $180,000 per site and range from $20,000 to $1 million. [ 51 ] This provides work during downturns in the oil industry. [ 51 ]
Prior to 2017, the energy industry paid $15 million a year into the Orphan Fund Levy. It doubled to $30 million in 2017. [ 53 ]
Between 1955 and 2017, approximately 580,000 wells were drilled in Canada, according to a Natural Resources Canada (NRC) report on wellbore integrity in the oil and gas industry in Canada. Of these, 400,000 were in Alberta and the NRC anticipated that there would be 100,000s more drilled. [ 47 ]
The New Democratic Party (NDP) provincial government began consulting with the energy industry in 2017 to "introduce new rules that might limit a multi-billion-dollar public liability for reclaiming about 80,000 inactive wells around Alberta." [ 6 ]
The C.D. Howe Institute report estimated that the social cost of orphan wells, including those incurred by financially insolvent firms, could be more than $8.6 billion. [ 54 ]
In 2017, the federal government provided Alberta with a one-time grant of $30 million for "decommissioning and reclamation" [ 55 ] which the province used to "cover the interest on a $235 million repayable loan". [ 56 ] [ 57 ]
As of 2018, 37.8% of all inactive wells—89,217—had been inactive for up to 5 years; 29.8% had been inactive for 5 to 10 years; 16% from 10 to 15 years; 8.2% from 15 to 20 years; 3.9% from 20 to 25 years; and 4.5% had been inactive for over 25 years. [ 44 ]
Based on the OWA's 2018 data, at the current level of the orphan well inventory, the cost of well abandonment and reclamation of their inventory of orphan wells was expected to be around $611 million. [ 58 ] However, this estimate of $611 million does not include potential orphan wells. In this context, potential candidates include wells owned by financially insolvent firms and nearly insolvent firms. [ 54 ]
The cost of abandonment and remediation per well can be estimated from reviewing the OWA's annual report; those costs are estimated to be $61,000 and $20,000 per well respectively. [ 59 ]
Of the 440,000 wells drilled in the province, approximately 22,000 were leaking as of 2019. [ 47 ]
As part of Alberta's Area-Based Closure program (ABC), which represented 70% of the provinces remediation activity, the oil and gas industry spent approximately $340 million on clean up. [ 60 ]
The federal government provided a grant of $1.2 billion through the COVID-19 Economic Response Plan announced in 2020. [ 61 ] Using the federal grant, in 2020, the province funded the Alberta Site Rehabilitation Program (ASRP) with $1 million in provincial loans. [ 57 ] The oil and gas industry paid almost the same amount on clean up—$363—as they did in 2019, in spite of the federal grant.
As of 2020, there were about 97,000 inactive wells that were not properly closed and another 71,000 abandoned wells requiring clean-up, according to a University of Calgary Policy School article. [ 39 ] [ 62 ]
The January 2022 Parliamentary Budget Officer (PB0) report on the cost of cleaning Canada's orphan oil and gas wells, estimated that it would cost $361 million just to clean traditional orphan wells nationally, which does not include the cost of oil sands operations. [ 4 ]
More than 50% of Alberta's wells are not producing oil or gas, yet they have not been cleaned up. [ 39 ] [ 63 ]
The OWA spent $161.5 million in the fiscal year 2021/2022 on decommissioning wells, pipelines, and facilities. [ 64 ] In 2021/22 42% of this total went going towards well decommissioning, 30% towards site reclamation, 13% to facilities decommissioning, and 5% to pipeline decommissioning. [ 64 ]
The oil and gas sector provided 22% of the Government of Alberta's total estimated revenue for the fiscal year 2021/22. Since 2012, the Alberta government has received $66 billion from the sector. [ 19 ]
AER reported that, as of July 2022, there were about 170,000 abandoned wells in the province that are the responsibility of the licensees for all abandonment and reclamation costs. This represents 37% of all the wells in Alberta. [ 65 ]
The January 2022 Parliamentary Budget Officer (PB0) report on the cost of cleaning Canada's orphan oil and gas wells, estimated that it would cost $361 million just to clean traditional orphan wells nationally, which does not include the cost of oil sands operations. [ 4 ] By 2025, the forecast is $1.1 billion in clean up costs for orphan wells. [ 36 ]
According to AER, as of December 2022, of the 463,000 oil and gas wells in Alberta, 33.7% or 156,031 were active and 28% or 129,640 were reclaimed. There were 172,236 wells that were either abandoned or inactive—19% or 88,433 were abandoned and 18.1% or 83,803 were inactive. [ 50 ]
There are thousands of oil and gas well in municipalities and on landowners properties that require plugging or reclamation and have no solvent owner, but have not yet transitioned to orphan status. They represent environmental and public safety liabilities but are not designated as orphaned by AER and are not being addressed. Liabilities and taxes for these wells become the responsibility of municipalities and landowners depending on where the wells are located. The 2023 OWA Inventory included only 3,114 orphan sites for which it was responsible. [ 14 ]
In contrast to Texas, where private property owners own both the mineral and surface rights, in Alberta, landowners only own surface rights, and they do not have the right of refusal to prevent extraction companies from operating wells on their private property. [ 22 ] [ 27 ] [ 29 ] [ 30 ] Many of the orphan wells are on private property owned by ranchers, farmers, and others. [ 27 ] By 2001, there were about 59,000 farm or ranch properties in the province that had at least one well on their property. [ 31 ] While the AER and CAPP were pleased with the 2019 Supreme Court ruling on orphan wells, landowners with orphan wells left by defunct energy companies, are concerned about the impact of the orphan wells on "crops, water and the environment". [ 43 ]
Bennett's group was invited by Alberta Energy Minister Peter Guthrie to a February 9, 2023 meeting on Premier's Smith proposed Liability Management Incentive Program. [ 28 ] [ 66 ] While Bennett acknowledged that it was "somewhat regrettable" that taxpayers would fund the LMIP, and oil companies would see their royalties reduced. [ 27 ]
Based on a survey in early January 2019, the Rural Municipalities of Alberta's (RMA) reported an "unprecedented" unpaid $81 million in property taxes from oil and gas companies that presented a "unique challenge that has not been experienced by municipalities in Alberta before." [ 41 ] According to RMA president, Paul McLauchlin, by 2023, the oil and gas industry owed $268 million in unpaid property taxes to towns and villages across Alberta. [ 17 ] [ 29 ] [ 67 ] In response to their concerns in 2021, Dale Nally , then Associate Minister of Natural Gas, said that the solution to unpaid taxes lies in the province helping the "battered" oil and gas industry so they can "pay their municipal taxes and contribute to the economy." [ 67 ]
The oil-industry led Orphan Well Association (OWA) is an independent, non-profit organization , that was established in 2002 [ 68 ] with a mandate to protect public safety and to manage the "environmental risks of oil and gas properties that do not have a legally or financially responsible party that can be held to account." [ 13 ] The OWA is responsible for orphan wells, pipelines, and facilities. [ 69 ]
Representatives from the Alberta provincial government, the AER and Alberta Environment and Parks (AEP), Canadian Association of Petroleum Producers (CAPP), and the Explorers and Producers Association of Canada (EPAC) serve on the OWA's board of directors. [ 2 ] Brad Herald is the Chair of the OWA and is also CAPP vice-president. [ 70 ]
The OWA manages the potential environmental and public safety risks that these orphaned properties represent. It also maintains an inventory, and oversees the decommissioning, remediation, and reclamation of these sites. [ 13 ] The OWA's mandate includes the management of the "decommissioning (abandonment) of upstream oil and gas 'orphan' wells, pipelines, facilities and the remediation and reclamation of their associated sites." [ 2 ]
The OWA is also responsible for orphaned pipelines and orphan facilities, which now includes the newly-established Large Facility Liability Management Program (LFP). [ 71 ] The LFP operates with separate financing from orphan wells and has its own levy set at $3 million a year. By 2022, its first project—decommissioning the Mazeppa Gas Plant pumping station facilities south of Calgary—was almost completed. [ 71 ] Critics say that the annual Orphan Wells Levy decided by the industry and set by AER is too low to cover the actual size of the problem. [ 24 ] [ 53 ] [ 72 ]
Because orphan wells are the entire responsibility of the oil and gas industry, they are also responsible for funding OWA's operations. Industry funding for the OWA includes an annual Orphan Wells Levy prescribed by the AER, in consultation with the Canadian Association of Petroleum Producers (CAPP) and Explorers and Producers Association of Canada (EPAC). CAPP's members produce about 80% of oil and gas in Canada. The levy is based on the "estimated cost of decommissioning and reclamation activities for the upcoming fiscal year". [ 53 ] Prior to 2017, the energy industry paid $15 million a year into the fund. It doubled to $30 million in 2017. For the fiscal year 2021/2022 it was set at $65 million. [ 53 ] Critics say that this levy is inadequate to cover the costs of the orphan wells clean up. [ 24 ]
As of 2022, the annual Orphan Fund Levy on oil and gas companies set by the industry-funded Alberta Energy Regulator (AER) is very low in relation to the OWA's responsibilities. [ 72 ] The OWA Levy is prescribed by the AER, in consultation with the Canadian Association of Petroleum Producers (CAPP) and Explorers and Producers Association of Canada (EPAC)—based on the "estimated cost of decommissioning and reclamation activities for the upcoming fiscal year". The 2021 levy was $65 million. [ 53 ]
OWA funding comes from a levy paid by the Alberta energy industry and collected by the AER. [ 15 ] [ 53 ] [ 56 ]
The OWA Inventory only includes orphan wells that have been designated as orphaned by the AER. [ 14 ]
Although the OWA is meant to be funded entirely by the oil and gas industry, it is also subsidized by the federal and provincial governments through grants and loans. [ 56 ] [ 57 ] [ 61 ]
The ballooning costs of decommissioning and reclamation were transferred from the oil and gas industry to the public which many see as corporate welfare and a PPP violation. [ 28 ] [ 73 ]
Federal grants include $30 million in 2017 and 1.2 billion dollars in 2020. [ 6 ] [ 21 ] [ 23 ] [ 56 ] [ 57 ]
In 2017, the Government of Canada provided Alberta with a one-time grant of $30 million for "activities associated with decommissioning and reclamation". [ 55 ] In that year, the provincial government used the federal funds to "cover the interest on a $235 million repayable loan" which the oil and gas industry will repay over the next nine years, to support the OWA's efforts. [ 56 ] [ 57 ]
As part of the federal government's COVID-19 Economic Response Plan, in April 2020, new financial aid was announced to help sustain employment in the energy sector that also served to respond to environmental concerns in provinces with orphan and inactive oil and gas wells. [ 61 ] Of the total $1.72 billion, up to $1.2 billion was available to the Alberta government and $200 million was made available in the form of a loan to the Orphan Wells Association. [ 61 ] By January 2022, Alberta had given about 50% of the allocated funding to viable energy companies, not companies "with an acute financial risk." [ 37 ]
In 2020, Alberta established the Alberta Site Rehabilitation Program (ASRP) through which applicants could apply for grants of up to $30,000. [ 74 ] The province also loaned the OWA $100-million for 1,000 environmental site assessments, as part of the process of decommissioning 800 to 1,000 orphan wells. [ 57 ] The loan was intended to "create 500 direct and indirect jobs in the oil services sector." [ 57 ] The loan was intended to enable the OWA to double its activity in 2020 to nearly 2,000 wells. [ 75 ]
In early February 2023, the Premier of Alberta introduced a controversial $100 million dollar Royalty Credit System as part of a new Liability Management Incentive Program (LMIP). [ 29 ] [ 66 ] [ 76 ] If fully enacted, it would provide individual oil and gas companies with royalty credits for cleaning their own well sites that have been inactive for two decades or more. [ 73 ] Alberta economist, Andrew Leach , said advocates for the oil industry were the original authors of the generous incentives-based royalty credit program, then called R-Star. [ 77 ] [ 78 ] According to a Scotiabank report, the incentive program "goes against the core capitalist principle that private companies should take full responsibility for the liabilities they willingly accept." [ 28 ] Their analysts cautioned that the program could result in the public viewing the oil and gas sector negatively. [ 28 ] The Scotiabank report said that "Canadian Natural Resources, Cenovus Energy, Paramount Resources and Whitecap Resources" would benefit most from the incentive program—their combined net income in fiscal year 2022 Q4 was almost $5 billion. [ 28 ] Mount Royal University professor, Duane Bratt, said that there was an element of "corporate welfare" in the program, but there was also the "corruption element"—in 2022, Smith—as paid lobbyist for dozens of Calgary companies in the Alberta Enterprise Group—had promoted "$20 billion of R-Star credits" [ 78 ] to then-energy minister Sonya Savage . [ 28 ] The piloting of RStar was in Minister Guthrie's mandate letter. [ 28 ] Critics include "[e]nvironmentalists, economists, landowners and analysts within Alberta Energy." [ 28 ] [ 66 ] [ 73 ] Some also question how this could apply to orphan wells as, by definition, there is no legal party to be incentivized. [ 73 ] [ 76 ] In a February 22 statement, Premier Smith said that Minister Guthrie's consultation process would take a number of months to complete. [ 76 ] [ 79 ]
Calgary-based Canadian Natural Resources is one of OWA's "largest single funders." [ 15 ] Canadian Natural, which "produces more than one million barrels of oil and gas per day, is also one of the most active at cleaning up." Of the 1,293 wells abandoned in 2018, the company "submitted 1,012 reclamation certificates." [ 15 ]
In Alberta, the sole regulator of the province's energy development—from a project's first application, licensing and production, through to its decommissioning, closure, and reclamation—is the 100% industry-funded corporation, the Alberta Energy Regulator (AER). The AER, which replaced the Energy Resources Conservation Board (ERCB) in 2013—following the passing of the Responsible Energy Development Act—operates at arm's length from the provincial government. [ 5 ] [ 9 ] AER regulations based on PPP, require energy companies to safely retire their inactive wells following provincial guidelines as a legal asset retirement obligation (ARO). [ 5 ] [ 6 ] [ 9 ] This includes the proper plugging of inactive wells as well as performing remediation to return the site to the condition it was in prior to extraction operations. [ 7 ]
AER wellbore licensing status includes abandoned, amended; cancelled; issued, re-entered, rec-certified; recexempt, rescinded; and suspension. [ 80 ]
Industry funding for the OWA includes an annual Orphan Wells Levy prescribed by the AER, in consultation with the Canadian Association of Petroleum Producers (CAPP) and Explorers and Producers Association of Canada (EPAC). It is based on the "estimated cost of decommissioning and reclamation activities for the upcoming fiscal year". [ 53 ]
In March 2014, AER took over Alberta Environment and Sustainable Resource Development's (ESRD) responsibilities to regulate reclamation and remediation activities resulting from fossil fuel extraction operations in Alberta. [ 12 ] AER's Directive 079 provides guidelines and regulations regarding surface development in municipalities that have abandoned wells. This includes identification of wells through the Subdivision and Development Regulation (SDR) and requirements to identify abandoned wells located near developments. Directive 079 also requires oil and gas companies to locate and test wells. [ 12 ]
On February 6, 2017, the Alberta Energy Regulator and the Alberta government revised Directive 67, which sets the "eligibility requirements for obtaining or continuing to hold a licence for energy development" in Alberta. [ 81 ] The new requirements came in to place in response to concerns about the "growing number of licensees abandoning wells in an unprofitable market in bankruptcy proceedings." [ 81 ] The changes gave AER the authority to refuse or grant licenses based on past behaviour, for example licensees with a "history, or a higher risk, of non-compliance". Previously, energy companies could get a license by paying a small down payment as long as they had an address, and some insurance. [ 82 ] Revised compliance rules cover operational, pipeline, and emission issues. [ 82 ]
The 2021 report submitted by Alberta's Office of the Auditor General (OAG), Doug Wylie, examined the provincial government's environmental liabilities and the roles of the Alberta Energy Regulator (AER) and Environment and Parks , now called Ministry of Environment and Protected Areas. [ 83 ] [ 84 ] Not all orphan and legacy wells are managed by the OWA. [ 45 ] The regulator and the ministry also manage legacy and orphan wells that existed prior to the enactment of environmental legislation in 2000. [ 45 ] The AER and the ministry—both under the jurisdiction of the government of Alberta—interpret their responsibilities differently. Each says the other has the responsibility to pay for and clean up oil and gas sites liabilities. [ 35 ] [ 84 ] This resulted in neither the regulatory nor the ministry taking "responsibility "for sites, even when evidence showed otherwise." [ 35 ] There was a lack of information on funding sources for cleaning up sites as well as a lack of up-to-date cost estimates, and site prioritization. [ 35 ] While regulatory AER staff maintained a list of legacy and orphan sites under its management, the list was not shared with AER's own financial staff until the list was uncovered through the OAG's audit. The list also included cost estimates with other similar sites. [ 84 ] [ 85 ]
Keith Wilson, who has been working with landowners on orphan wells for three decades, told The Narwhal in a 2018 interview that, "The [regulator's] system is not achieving anything. If anything, it's creating a false sense of comfort that this problem is being addressed—and we know it's not." [ 32 ]
Oil and gas companies that have profited from Alberta's energy revenue are liable for the responsible and safe closure and clean-up of their oil and gas well sites under the Polluter Pays Principle (PPP) as clearly defined by the Supreme Court of Canada (SCC) in 2003. [ 8 ]
Alberta's Environmental Law Centre (ELC) said that while the polluter pays principle appears to be simple and straightforward, its evolution, operationalization, and application in Alberta is complex, as it is often politically charged. [ 86 ]
As of, 2014, the EPEA "requires operators to conserve and reclaim specified land and get a reclamation certificate". [ 10 ] [ 12 ] [ 87 ]
The 1999 Canadian Environmental Protection Act , provided new powers for health and environmental protection. [ 88 ] The Environmental Protection and Enhancement Act (EPEA) enacted in 2000, is the only statute in Alberta that references the polluter pays principle directly. [ 87 ] The PPP is integrated in a variety of EPEA provisions but it does not have "an express statutory commitment to the principle." [ 87 ]
In their 2003 decision in Imperial Oil v Quebec , the SCC described the Polluter Pays Principle, saying that, in order to "encourage sustainable development, that principle assigns polluters the responsibility for remedying contamination for which they are responsible and imposes on them the direct and immediate costs of pollution." [ 8 ]
As of 2020, there were 97,920 wells that were "licensed as temporarily suspended" in Alberta. [ 62 ] [ 89 ] They were labelled as "zombie wells" by the New York Times . [ 62 ] Owners of inactive wells can choose to suspend operations indeterminately, without going through the costly process of decommissioning, remediation and reclamation. [ 4 ] [ 25 ] [ 26 ] Many suspended wells are orphaned, or simply deserted. They may still have oil, but are rarely recertified. [ 39 ] They are mainly on private property whose landowners have limited recourse for having them removed, maintaining the site, or collecting surface rights access fees. [ 89 ] Suspended wells have the highest risk of methane gas leaks, which increases with the age of the well. [ 90 ] Of all the inactive wells in Alberta, 29% —27,532 wells—have been suspended for more than a decade without being either "abandoned" or reactivated, as of March 25, 2021. [ 91 ] There is no limit on the amount of time an inactive well can remain suspended under existing AER regulations, even though the danger of leakage increases with the age of the well. The lack of a time limit favours well owners who can avoid paying $75,000 to $100,000 to reclaim a wellsite, by paying only several thousand a year in surface rights access and municipal taxes. It is a liability for the ranchers on whose lands the wells are left. These suspended, inactive, "zombie" wells have become a "hazardous threat to public safety." [ 62 ] [ 89 ] [ 92 ]
As of 2016, North Dakota—which shares a border with Alberta and also has a large oil sector—as of 2016, the state had no unfunded orphan or inactive well liabilities. [ 89 ] They learned the "hard lessons" following previous boom and bust cycles. Starting in 2001, as the number of orphan wells began to increase, the state enacted a use-it-or-lose-it policy. Operators are required to either pump oil or plug their wells. After a year of nonproduction, the state's industrial commission "calls the company's bond, levies fines and plugs the well itself." [ 89 ]
In contrast, in Alberta, owners of inactive wells can choose to suspend operations indeterminately, without going through the costly process of decommissioning, remediation and reclamation. [ 4 ] [ 25 ] [ 26 ] AER has set no time limit requirement on suspended wells. [ 4 ] [ 25 ] [ 26 ] A suspended well is only closed temporarily and may be reactivated. [ 39 ] These wells may also be relicensed by AER as "re-entered" if a new owner takes over the site. [ 80 ] The risk of leakage is higher in a suspended inactive well than in a well that the AER calls, "responsibly abandoned"—"rendered permanently incapable of flow and capped". [ 90 ] Suspended inactive older wells present the highest risk of leakage. [ 90 ] The risk of leakage in an inactive well increases with the amount of time it has been inactive without being properly closed down. [ 7 ] [ 39 ] Twenty-nine percent of all inactive wells in Alberta—27,532 wells—have been suspended for more than a decade without being either "abandoned" or reactivated, as of March 25, 2021. [ 91 ] AER's Directive 020: Well Abandonment deals with suspended wells. [ 93 ] [ 94 ]
Bankruptcies are prime factors in the increase in orphan wells. [ 16 ] In the last decade, companies have become insolvent because of the "multi-year downturn for the oil and gas sector." [ 17 ] This downturn or bust is part of the well-known cyclical nature of the oil and gas industry.
Historian David Finch, whose research focused on the oil industry in Western Canada, said that Alberta experienced three significant downturns in the oil industry since it first became commercially viable—the first in the 1960s; the second in the 1980s, and the third that started with the collapse of global oil prices in 2014. [ 95 ] Crude oil prices dropped to near ten-year low prices. [ 96 ] There were concerns that nearly a third of oil companies could go bankrupt. [ 97 ] It was the longest oil price decline since the 1980s. [ 38 ] That downturn resulted in what the CBC described in 2019 as a "tsunami" of orphaned oil and gas wells. [ 16 ] By 2017, there were "3,127 wells that need[ed] to be plugged or abandoned, and a further 1,553 sites that have been abandoned but still need[ed] to be reclaimed". [ 16 ]
Since the downturn in the oil industry in 2014, many companies became insolvent and went into receivership while holding costly liabilities, including abandoned wells. [ 98 ]
The media brought attention to four cases where bankruptcies threatened to increase the inventory of orphan wells: Redwater Energy, [ 1 ] Sequoia Resources, Trident Exploration, and Lexin Resources. [ 98 ] Trident Exploration's receivership in May 2019 resulted in 3,650 wells that no longer had a solvent owners, and the loss of 94 jobs. [ 99 ] Houston Oil & Gas entered receivership In November 2019, leaving behind 1,264 wells, 41 facilities and 251 pipelines. [ 99 ]
When Redwater entered receivership in 2015, ATB Financial —a provincial Crown corporation and financial service that lends money to oil and gas companies, including Redwater—went to court to recover its investments through Redwater's assets. [ 1 ] Redwater's bankruptcy trustee agreed that the banks and other creditors should collect first and any environmental liabilities, such as orphan wells, should get the leftovers. [ 1 ] When two lower courts agreed with the trustee in 2016 and 2016, both the OWA and AER appealed their decisions before the Supreme Court of Canada. The SCC overturned the lower court decisions in Orphan Well Association v. Grant Thornton Ltd. (Redwater) . [ 1 ] This benchmark ruling led to changes in the way in which bankruptcies were handled when orphan wells were at stake. [ 1 ] Prior to the 2019 SCC ruling, bankrupt energy companies were able to avoid paying for their abandoned wells. [ 100 ] The SCC clarified that in the case of a bankruptcy, a company's first priority is to fulfil its environmental obligations—not as a debt—but as a duty to "citizens and communities." [ 101 ]
A International Institute for Sustainable Development (IISD) report said that many of the orphan well sites were sold "strategically to insolvent operators". [ 18 ] These owners avoid PPP responsibilities which included paying the hefty price of "end-of-life decommissioning and restoration work". Citing the case of the insolvent Bellatrix Exploration Ltd, which sold its unwanted wells to a numbered shell company—also under threat of insolvency—a 2021 Financial Post article also said that this "murky practice" of misusing the bankruptcy process to get rid of liabilities while keeping valuable assets is raising concerns. The OWA says as owners shirk their responsibility the collective becomes responsible for the liabilities. [ 11 ]
Fifty percent of the delinquent wells are owned by small junior companies that have insufficient finances but are still able to produce and collect revenue. [ 28 ] The RMA says that the AER "props" up small companies to avoid increasing the already concerning number of orphan wells which results primarily from bankruptcies. [ 28 ] The AER says that it is the RMA's role to collect taxes. [ 28 ] A lawyer representing Action Surface Rights, a landowners group, Christine Laing, called on the AER to use the power it has more often and in a timely fashion to "protect the public interest". [ 43 ] Cases, such as Lexin and Sequoia, shed light on the complexity and opacity of ownership groups. It also drew attention to the way in which AER licensed, and ATB Financial provided loans, to small limited liability companies that had insufficient financing. This allowed them to take on risky legacy wells, then declare bankruptcy and avoid paying for clean up. [ 6 ] [ 40 ]
While Lexin is described in the media as a small Calgary-based limited liability company, its ownership group is MFC Resource Partnership of fifty-one companies—including Canadian Natural Resources Ltd., ExxonMobil Canada , and Husky Energy —who are also responsible for Levin's ARO. [ 102 ] AER had begun to receive concerns submitted by Lexin's Mazeppa Gas Plant employees in early 2016. These were forwarded to Occupational Health and Safety. [ 40 ] In February 2017, in response to concerns about public safety, environmental and financial risks, AER suspended Lexin's 1,600 or more licenses in a rare enforcement action—the largest suspension AER ever made. [ 40 ] According to the Post , fifty-one companies, including Canadian Natural Resources Ltd., ExxonMobil Canada , and Husky Energy , who own some of Lexin Resources Ltd. assets, may share the responsibility for Lexin's AROs. [ 102 ] Lexin had said that it would not be able to maintain its sour gas wells as of mid-February. [ 40 ] The enforcement effectively placed Lexin in receivership with these wells and the Mazeppa Gas Plant being added to OWA's Inventory of orphan wells. [ 40 ] AER sued Lexin to "recover money it is allegedly owed" saying that, "It is not open for a licensee, when times get tough, to transfer the burdens associated with holding AER licenses to the AER and/or the OWA." [ 103 ] About 50% of the newly orphaned wells were the result of 2017 MFC/Lexin 1,400 wells OWA transfer. [ 54 ]
Two years after purchasing 2,300 well licences in 2016 from Perpetual Energy Inc., Sequoia Resources entered receivership. [ 104 ] [ 105 ] Its liabilities including 4,000 wells, pipelines and other facilities". [ 104 ] [ 105 ] Then veteran AER CEO Jim Ellis, admitted in a public statement that the Sequoia "situation has exposed a gap in the system" that needed to be fixed. [ 105 ] [ 106 ] Sequoia's owners took Perpetual to court in an attempt to unwind the original 2016 sale—the first time such an attempt was made by a bankruptcy trustee in the province. Were it to succeed it would increase risks to oil and gas companies buying and selling assets. [ 107 ]
In 2021, in response to the concerns filed by he OWA, CNRL, Sunoco, and dozens of landowners, in an "unusual step" AER called for a public hearing on Shell's application to transfer hundreds of its oil well licenses to a junior player with questionable. [ 108 ] Landowners said that Shell was "shirking" its responsibilities by transferring dozens of wells to Pieridae, a small company that might not be able to cover the cost of cleaning up wells. [ 22 ] [ 108 ] In a 2020 BNN Bloomberg interview, a lawyer for landowners said that unlike CNRL and Sunoco, who take responsibility for their end-of-life wells, other major companies have been known to repackage liability wells with producing wells to sell to junior companies, with limited financial means. [ 22 ] Premier Smith compared this to 2008 repackaged mortgages. [ 77 ]
Gas contamination from both active and orphaned wells, particularly hydrogen sulfide and methane , is increasingly attracting attention from Alberta government and the public. [ c ]
In addition to fugitive gas emissions , shallow aquifers can also be contaminated by gas, causing very serious issues. Groundwater contamination can be caused by casing leaks—such as integrity failures —of which orphaned wells are susceptible. [ 109 ] [ 110 ] However, because orphaned well-induced groundwater contamination is not reported annually, statistical data was not available as of 2018. In comparison, gas emissions are more easily monitored and tracked by operators. Despite the lack of groundwater contamination data, gas emission data collected by AER from oil and gas industry may potentially reflect areas of groundwater contamination.
In the 1980s, Alberta's Energy Resources Conservation Board (ERCB)—the AER's precursor—warned of the dangers of fugitive gas emissions in 4,500 out of the 90,000 oil and gas wells in the province. [ 111 ] The ERCB raised concerns of the increase in orphan wells in the 1980s and of the significant risks of GM in terms of contaminating useable groundwater. [ 111 ]
The Energy Resources Conservation Board (ERCB) first identified surface casing vent flow (SCVF) and gas migration (GM) issues as a "significant concern" in the Lloydminster, Alberta area in the 1980s. [ 111 ] The ERCB said that 5% of the approximately 90,000 wells or 4,500 wells in the province had SCVF and that 150 wells had GM. [ 111 ] In the 1980s, GM concerns included an increase in the number of orphan wells and the "protection of useable groundwater." [ 111 ]
In 2014, new regulation directed industry to "locate and test" any abandoned wells that were close to houses, airports, businesses, etc. that may pose a risk due to gas leakage. The resulting 33-page 2016 AER unpublished study showed that of the estimated 170,000 abandoned wells in Alberta, up to 3,400 posed a health risk. [ 113 ] Of the 335 abandoned urban wells studied, there were 36 that were leaking and nine of these posed a risk to those who lived nearby. [ 113 ] Most were in Medicine Hat, a city that now owns and operates 4,000 gas wells. The city's history is tied to the natural gas boom in the early 1900s which left many abandoned wells. [ 113 ]
In 2019, Intergovernmental Panel on Climate Change (IPCC) scientists warned that methane gas leakage from abandoned oil and gas wells were a serious contributing factor in climate change. [ 33 ] The IPCC recommended that United Nations member countries track and publish methane leakage from abandoned oil and gas wells as this represented a "global warming risk." [ 33 ] By 2020, only Canada and the United States had begun to monitor methane leakage from abandoned wells. [ 33 ] Over a period of two decades, in terms of global warming potential (GWP), methane has 80 times the "heat-trapping power" carbon dioxide (CO 2 ). [ 62 ] According to the International Energy Agency (IEA)'s "Global Methane Tracker 2022", if all countries adopted well-known and effective methane reduction policy measures using existing technologies, it would decrease global methane emissions from the oil and gas sector by 50%. [ 114 ]
According to a 2015 conference presentation, the primary factors that should be considered in the evaluation of gas emissions from oil and gas wells are cementing, [ 115 ] drilling orientation, geological conditions, well age, and reservoir depth. [ 116 ] [ 117 ] They reported on three types of wellbore leakage—8% of leaks were related to surface casing vent flow (SCVF) and gas migration (GM); 2% were the result of failures in the casing, and 2% were due to failures in the abandonment plugs. [ 117 ]
SCVF and Gas Migration are two commonly recognized gas contamination mechanisms. [ 118 ] SCVF is defined as the flow of gas and/or liquid along the surface casing / casing annulus . [ 118 ] [ 119 ] [ 120 ] [ 121 ] GM is defined as a flow of gas that is detectable at the outer surface of the outermost casing string usually occurring at very shallow reservoir layers. [ 118 ] [ 119 ] [ 120 ] According to recent statistics from the Alberta Energy Regulator (AER) , a total of 617 billion m 3 of methane was released into atmosphere through venting (GM and SCVF) and flaring in Alberta during 2016, which has been constantly decreasing since 2012. Among the total emitted gas, 81 million m 3 originated from 9,972 unrepaired wells by GM and SCVF. [ 122 ] Historically, there are 18,829 repaired and unrepaired wells reported with SCVF, GM, or both in Alberta, with 7.0% of them being inactive (9,530 wells suspended and orphaned). [ 122 ] Wells with reported gas migration issues within Alberta are shown by Bachu in 2017. [ 116 ]
Most of the thermal wells are orphaned oil or gas wells. A study from the International Journal of Greenhouse Gas Control concluded that gas migration mainly occurs within the central-northeastern part of the province, focusing around the Edmonton , Cold Lake , and Lloydminster areas. [ 116 ] This observation is in agreement with the total gas flaring and venting conditions reported by the Alberta Energy Regulator (AER) . [ 122 ]
After oil wells become depleted, their depth and size make them good candidates for extraction of geothermal energy . The prospect of geothermal conversion of depleted wells is attractive for several reasons including potential recovery of abandonment costs, reduced consumption of non-renewable energy , [ 123 ] and elimination of geothermal drilling costs—a significant component in geothermal projects. [ 124 ] Several studies propose the conversion of existing wells into double pipe heat exchangers through the installation of an insulated pipe inside the well for fluid circulation. [ 125 ]
Across the province, a general northwestern trend of increasing geothermal gradient is commonly recognized with geothermal gradients ranging between 10 °C/km and 55 °C/km. [ 126 ] [ 127 ] [ 128 ]
The controlling factors for this broad geothermal range in Alberta are poorly understood. Two main reasons have been proposed up to date to explain the observed patterns.
The bottom hole temperatures (BHT) of wells within reasonable proximity to Albertan communities are, at best, sufficient for heating. Communities on the western side of Alberta are more likely to benefit from geothermal conversion for direct heat purposes . Previous projects in the United States have shown that temperatures around 80 °C are feasible for direct heating of institutions and district heating. [ 124 ] Another study also reported the use of a low-temperature geothermal well in China for heating within its proximity. [ 130 ]
There was a recent push by the US Department of Energy to investigate the feasibility of Deep Direct-Use (DDU) of low temperature geothermal resources. [ 131 ]
Critics blame the self-regulating nature of energy industry and its close relationship with provincial regulatory bodies for the lack of enforcement of existing regulations which allows oil and gas companies to avoid paying for the clean up. [ 39 ] [ 40 ] [ 53 ] Others say it is a lack of political will to be more proactive in establishing public policies that would remediate the situation. Suggested solutions to the orphaned and abandoned well crisis, include ensuring that there is enough funding attached to each wellsite for its cleanup paid by those who profited from oil and gas revenue for decades, [ 78 ] and enforcing a "use-it-or-lose-it policy as is the case in the neighbouring oil-producing state, North Dakota. [ 89 ]
On March 23, 2023 Alberta auditor general, Doug Wylie, published another report critical of the United Conservative Party 's (UCP) neglect of orphan wells and other oil patch liabilities in the province. [ 132 ] The report said that even though the number of inactive wells increased every year since 2000—except for the year that the federal government provided $1.2 billion dollars—operators still have no timelines for site remediation. [ 132 ] Two major issues have not been dealt with—"so-called 'legacy sites' and "inadequate security collected". [ 132 ] Current AER liability management processes to mitigate risks "associated with closure of oil and gas infrastructure" are not "well-designed" and are not effective. [ 132 ] Martin Olszynski, a University of Calgary resource law professor said the audit shows that this is more than mere "bureaucratic incompetence"; it reveals that the AER has been "captured" by the oil and gas industry. He said the UCP has refused "to do anything that might cost the industry money". [ 132 ] Kathleen Ganley the official opposition energy critic, said that the UCP has failed to protect taxpayers and is damaging the reputation of Alberta's energy industry's reputation. [ 132 ]
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Orpiment , also known as ″ yellow arsenic blende ″ is a deep-colored, orange-yellow arsenic sulfide mineral with formula As 2 S 3 . It is found in volcanic fumaroles , low-temperature hydrothermal veins, and hot springs and may be formed through sublimation .
Orpiment takes its name from the Latin auripigmentum ( aurum , "gold" + pigmentum , " pigment "), due to its deep-yellow color. Orpiment once was widely used in artworks, medicine, and other applications. Because of its toxicity and instability, its usage has declined.
The Latin auripigmentum ( aurum , "gold" + pigmentum , " pigment ") referred both to its deep-yellow color and to the historical belief that it was thought to contain gold. The Latin term was used by Pliny in the first century CE. [ citation needed ]
The Greek for orpiment was arsenikon , deriving from the Greek word arsenikos , meaning "male", from the belief that metals were of different sexes. This Greek term was used by Theophrastus in the fourth century BC. [ 5 ]
The Chinese term for orpiment is Ci-Huang (in Pinyin), meaning "female yellow". [ 6 ]
The Persian for orpiment is zarnikh , deriving from the word " zar" , the Persian for gold. [ citation needed ]
Orpiment is a common monoclinic arsenic sulfide mineral. It has a Mohs hardness of 1.5 to 2 and a specific gravity of 3.49. It melts at 300 °C (570 °F) to 325 °C (620 °F). Optically, it is biaxial (−) with refractive indices of a = 2.4, b = 2.81, g = 3.02.
Orpiment is a type of lemon-yellow to golden- or brownish-yellow crystal commonly found in foliated columnar or fibrous aggregates, may alternatively be botryoidal or reniform, granular or powdery, and, rarely, as prismatic crystals . [ 7 ] Used as a pigment, orpiment's color is often described as a lemon- or canary-yellow , and occasionally as a golden- or brownish-yellow.
In the Munsell color system , "orpiment" is designated "brilliant yellow", Munsell notation 4.4Y 8.7 /8.9. [ 8 ]
Orpiment and realgar are closely related minerals and are often categorized in the same group. They are both arsenic sulfides and belong to the monoclinic crystal system . They are found in the same deposits and can form in the same geologic environments. As a result, orpiment and realgar share similar physical properties and histories of use by humans. [ 7 ]
In Chinese, the names for orpiment and realgar are Ci-Huang and Xiong-Huang , respectively meaning "female yellow" and "male yellow". Their names symbolize their close natural conjunction, both physically in terms of their occurrence and properties and culturally in Chinese traditions.
Orpiment and realgar can be distinguished by their different visual characteristics. While orpiment typically has a vibrant golden-yellow color, realgar, in contrast, normally has an orange or reddish hue. [ 6 ]
Yellow orpiment (As 2 S 3 ) degrades into arsenic oxides . Because of their solubility in water, arsenic oxides readily migrate to the surrounding environment. In painted works using orpiment, migrating, degraded arsenic oxides are often detectable throughout the multi-layered paint system. This widespread arsenic migration has consequences for the conservation of orpiment as a pigment in works of art. [ 9 ]
Orpiment is also sensitive to light exposure, decaying into a friable white arsenic trioxide over time. Similarly, on ancient, orpiment-coated manuscript paper in Nepal, orpiment used to deter insects has often turned white over time. [ citation needed ]
Because of orpiment's solubility and instability as a pigment, preventing the degradation of orpiment may need to be prioritized in art conservation. Proper conservation methods should minimize exposure to strong light. Such methods should emphasize humidity control and avoid the use of water-based cleaning agents. [ 9 ]
Orpiment has historically been used in artworks in many locales in the Eastern Hemisphere . It was one of the few clear, bright-yellow pigments available to artists until the 19th century.
In Egypt, lumps of orpiment pigment have been found in a fourteenth-century BC tomb. [ 10 ] In China, orpiment is known to have been used to color Chinese lacquer , despite no written sources mentioning this. Orpiment has also been identified on Central Asian wall paintings from the sixth to the thirteenth centuries [ specify ] . [ 11 ] In a traditional Thai painting technique, still in use today, yellow ink for writing and drawing on black paper manuscripts is made using orpiment. [ 12 ]
Medieval European artists imported orpiment from Asia Minor. [ citation needed ] Orpiment has been identified on Norwegian wooden altar frontals , polychrome sculptures, and folk art objects, including a crucifix . It was also used in twelfth- to sixteenth-century Eastern Orthodox icons from Bulgaria, Russia, and the former Yugoslavia . In Venice , records show that orpiment was purchased for a Romanian prince in 1600. European use of orpiment was uncommon until the nineteenth century, during which it saw use as a pigment in Impressionist paintings. [ 5 ]
In the Medieval Norwegian church of Tingelstad , orpiment was used in painting the altar frontal . [ citation needed ]
Orpiment was commonly combined with indigo dye to make a dark, rich green. [ citation needed ] In the Wilton Diptych (c 1395-9), this green pigment was used in egg tempera on the left panel for the green cloak of Edmund the Martyr . [ citation needed ]
Renaissance artists such as Raphael also used orpiment as a yellow pigment. In Raphael's Sistine Madonna from 1513–14, orpiment is used to achieve yellow on the clothing of the figures and in the background. [ 13 ]
Tintoretto 's Portrait of Vincenzo Morosini from about 1575–80 uses the pigment in its details. Orpiment is used to replicate the gold embroidery on Morosini 's embroidered stole and to highlight the fur of the spotted ferret on his chest. [ 5 ] : 49
Orpiment was one of the few clear, bright-yellow pigments available to artists until the 19th century. Its extreme toxicity and incompatibility with other, common, pigments, including lead and copper -based substances such as verdigris and azurite , meant that its use as a pigment ended when cadmium yellows , chromium yellows and organic aniline dye -based colors were introduced during the 19th century. [ 14 ]
Orpiment was traded in the Roman Empire and was used as a medicine in China , even though it is very toxic. It has been used as fly poison [ 15 ] and to tip arrows with poison . [ 16 ] Because of its striking color, it was of interest to alchemists , both in China and Europe, searching for a way to make gold. It also has been found in the wall decorations of Tutankhamun 's tomb and ancient Egyptian scrolls, and on the walls of the Taj Mahal . [ 17 ] For centuries, orpiment was ground down and used as a pigment in painting and for sealing wax , and was even used in ancient China as a correction fluid . [ 18 ] Orpiment is mentioned in the 17th century by Robert Hooke in Micrographia for the manufacture of small shot . [ 19 ] Scientists like Richard Adolf Zsigmondy and Hermann Ambronn puzzled jointly over the amorphous form of As 2 S 3 , "orpiment glass", as early as 1904. [ 20 ]
Orpiment is used in the production of infrared -transmitting glass, oil cloth , linoleum , semiconductors , photoconductors , pigments, and fireworks . Mixed with two parts of slaked lime (calcium hydroxide), orpiment is still commonly used in rural India as a depilatory . It is used in the tanning industry to remove hair from hides.
Orpiment has been used as bookends . In 2023, the UK Office for Product Safety and Standards recalled 40 pieces sold by TK Maxx between June and October 2022, due to the mineral's toxicity. [ 21 ] [ 22 ] | https://en.wikipedia.org/wiki/Orpiment |
An orrery is a mechanical model of the Solar System that illustrates or predicts the relative positions and motions of the planets and moons , usually according to the heliocentric model . It may also represent the relative sizes of these bodies; however, since accurate scaling is often not practical due to the actual large ratio differences, it may use a scaled-down approximation. The Greeks had working planetaria , but the first modern example was produced c. 1712 by John Rowley. [ 1 ] He named it "orrery" [ 2 ] for his patron Charles Boyle, 4th Earl of Orrery (in County Cork , Ireland). The plaque on it reads "Orrery invented by Graham 1700 improved by Rowley and presented by him to John [sic] Earl of Orrery after whom it was named at the suggestion of Richard Steele ." [ 3 ] [ 4 ]
Orreries are typically driven by a clockwork mechanism with a globe representing the Sun at the centre, and with a planet at the end of each of a series of arms.
The Antikythera mechanism , discovered in 1901 in a wreck off the Greek island of Antikythera in the Mediterranean Sea, exhibited the diurnal motions of the Sun , Moon , and the five planets known to the ancient Greeks . It has been dated between 205 to 87 BC. [ 5 ] [ 6 ] [ 7 ] The mechanism is considered one of the first orreries. [ 8 ] It was geocentric and used as a mechanical calculator to calculate astronomical positions.
Cicero , the Roman philosopher and politician writing in the first century BC, has references describing planetary mechanical models. According to him, the Greek polymaths Thales [ 9 ] and Posidonius [ 10 ] both constructed a device modeling celestial motion.
In 1348, Giovanni Dondi built the first known clock driven mechanism of the system. It displays the ecliptic position of the Moon, Sun, Mercury , Venus , Mars , Jupiter and Saturn according to the complicated geocentric Ptolemaic planetary theories. [ 11 ] [ 12 ] The clock itself is lost, but Dondi left a complete description of its astronomic gear trains .
As late as 1650, P. Schirleus built a geocentric planetarium with the Sun as a planet, and with Mercury and Venus revolving around the Sun as its moons . [ 13 ]
At the court of William IV, Landgrave of Hesse-Kassel two complicated astronomic clocks were built in 1561 and 1563–1568. These use four sides to show the ecliptical positions of the Sun, Mercury, Venus, Mars, Jupiter, Saturn, the Moon, Sun and Dragon (Nodes of the Moon) according to Ptolemy , a calendar, the sunrise and sunset, and an automated celestial sphere with an animated Sun symbol which, for the first time on a celestial globe, shows the real position of the Sun, including the equation of time . [ 14 ] [ 15 ] The clocks are now on display in Kassel at the Astronomisch-Physikalisches Kabinett and in Dresden at the Mathematisch-Physikalischer Salon .
In De revolutionibus orbium coelestium , published in Nuremberg in 1543, Nicolaus Copernicus challenged the Western teaching of a geocentric universe in which the Sun revolved daily around the Earth . He observed that some Greek philosophers such as Aristarchus of Samos had proposed a heliocentric universe. This simplified the apparent epicyclic motions of the planets, making it feasible to represent the planets' paths as simple circles. This could be modeled by the use of gears. Tycho Brahe 's improved instruments made precise observations of the skies (1576–1601), and from these Johannes Kepler (1621) deduced that planets orbited the Sun in ellipses . In 1687 Isaac Newton explained the cause of elliptic motion in his theory of gravitation . [ 16 ]
There is an orrery built by clock makers George Graham and Thomas Tompion dated c. 1710 in the History of Science Museum, Oxford . [ 17 ] Graham gave the first model, or its design, to the celebrated instrument maker John Rowley of London to make a copy for Prince Eugene of Savoy . Rowley was commissioned to make another copy for his patron Charles Boyle, 4th Earl of Orrery , from which the device took its name in English. [ 18 ] [ 19 ] This model was presented to Charles' son John, later the 5th Earl of Cork and 5th Earl of Orrery . Independently, Christiaan Huygens published in 1703 details of a heliocentric planetary machine which he had built while living in Paris between 1665 and 1681. He calculated the gear trains needed to represent a year of 365.242 days, and used that to produce the cycles of the principal planets. [ 13 ]
Joseph Wright 's painting A Philosopher giving a Lecture on the Orrery ( c. 1766 ), which hangs in the Derby Museum and Art Gallery , depicts a group listening to a lecture by a natural philosopher . The Sun in a brass orrery provides the only light in the room. The orrery depicted in the painting has rings, which give it an appearance similar to that of an armillary sphere . The demonstration was thereby able to depict eclipses . [ 20 ]
To put this in chronological context, in 1762 John Harrison 's marine chronometer first enabled accurate measurement of longitude . In 1766, astronomer Johann Daniel Titius first demonstrated that the mean distance of each planet from the Sun could be represented by the following progression:
4 + 0 10 , 4 + 3 10 , 4 + 6 10 , 4 + 12 10 , 4 + 24 10 , . . . {\displaystyle {\frac {4+0}{10}},{\frac {4+3}{10}},{\frac {4+6}{10}},{\frac {4+12}{10}},{\frac {4+24}{10}},...}
That is, 0.4, 0.7, 1.0, 1.6, 2.8, ... The numbers refer to astronomical units , the mean distance between Sun and Earth, which is 1.496 × 10 8 km (93 × 10 6 miles). The Derby Orrery does not show mean distance, but demonstrated the relative planetary movements.
The Eisinga Planetarium was built from 1774 to 1781 by Eise Eisinga in his home in Franeker , in the Netherlands. It displays the planets across the width of a room's ceiling, and has been in operation almost continually since it was created. [ 21 ] This orrery is a planetarium in both senses of the word: a complex machine showing planetary orbits, and a theatre for depicting the planets' movement. Eisinga house was bought by the Dutch Royal family who gave him a pension.
In 1764, Benjamin Martin devised a new type of planetary model, in which the planets were carried on brass arms leading from a series of concentric or coaxial tubes. With this construction it was difficult to make the planets revolve, and to get the moons to turn around the planets. Martin suggested that the conventional orrery should consist of three parts: the planetarium where the planets revolved around the Sun, the tellurion (also tellurian or tellurium ) which showed the inclined axis of the Earth and how it revolved around the Sun, and the lunarium which showed the eccentric rotations of the Moon around the Earth. In one orrery, these three motions could be mounted on a common table, separately using the central spindle as a prime mover. [ 8 ]
All orreries are planetariums . The term orrery has only existed since 1714. A grand orrery is one that includes the outer planets known at the time of its construction. The word planetarium has shifted meaning, and now usually refers to hemispherical theatres in which images of the night sky are projected onto an overhead surface. Orreries can range widely in size from hand-held to room-sized. An orrery is used to demonstrate the motion of the planets, while a mechanical device used to predict eclipses and transits is called an astrarium .
An orrery should properly include the Sun, the Earth and the Moon (plus optionally other planets). A model that only includes the Earth, the Moon, and the Sun is called a tellurion or tellurium, and one which only includes the Earth and the Moon is a lunarium . A jovilabe is a model of Jupiter and its moons. [ 22 ]
‡ A negative figure indicates retrograde rotation.
A planetarium will show the orbital period of each planet and the rotation rate , as shown in the table above. A tellurion will show the Earth with the Moon revolving around the Sun. It will use the angle of inclination of the equator from the table above to show how it rotates around its own axis. It will show the Earth's Moon, rotating around the Earth. [ 23 ] A lunarium is designed to show the complex motions of the Moon as it revolves around the Earth.
Orreries are usually not built to scale . Human orreries, where humans move about as the planets, have also been constructed, but most are temporary. There is a permanent human orrery at Armagh Observatory in Northern Ireland , which has the six ancient planets, Ceres , and comets Halley and Encke . Uranus and beyond are also shown, but in a fairly limited way. [ 24 ] Another is at Sky's the Limit Observatory and Nature Center in Twentynine Palms, California ; it is a true to scale (20 billion to one), true to position (accurate to within four days) human orrery. The first four planets are relatively close to one another, but the next four require a certain amount of hiking in order to visit them. [ 25 ] A census of all permanent human orreries has been initiated by the French group F-HOU with a new effort to study their impact for education in schools. [ 26 ] A map of known human orreries is available. [ 27 ]
A normal mechanical clock could be used to produce an extremely simple orrery to demonstrate the principle, with the Sun in the centre, Earth on the minute hand and Jupiter on the hour hand; Earth would make 12 revolutions around the Sun for every 1 revolution of Jupiter. As Jupiter's actual year is 11.86 Earth years long, the model would lose accuracy rapidly.
Many planetariums have a projection orrery , which projects onto the dome of the planetarium a Sun with either dots or small images of the planets. These usually are limited to the planets from Mercury to Saturn, although some include Uranus. The light sources for the planets are projected onto mirrors which are geared to a motor which drives the images on the dome. Typically the Earth will circle the Sun in one minute, while the other planets will complete an orbit in time periods proportional to their actual motion. Thus Venus, which takes 224.7 days to orbit the Sun, will take 37 seconds to complete an orbit on an orrery, and Jupiter will take 11 minutes, 52 seconds.
Some planetariums have taken advantage of this to use orreries to simulate planets and their moons. Thus Mercury orbits the Sun in 0.24 of an Earth year, while Phobos and Deimos orbit Mars in a similar 4:1 time ratio. Planetarium operators wishing to show this have placed a red cap on the Sun (to make it resemble Mars) and turned off all the planets but Mercury and Earth. Similar approximations can be used to show Pluto and its five moons.
Shoemaker John Fulton of Fenwick, Ayrshire , built three between 1823 and 1833. The last is in Glasgow's Kelvingrove Art Gallery and Museum .
The Eisinga Planetarium built by a wool carder named Eise Eisinga in his own living room, in the small city of Franeker in Friesland , is in fact an orrery. It was constructed between 1774 and 1781. The base of the model faces down from the ceiling of the room, with most of the mechanical works in the space above the ceiling. It is driven by a pendulum clock, which has 9 weights or ponds. The planets move around the model in real time. [ 28 ]
An innovative concept is to have people play the role of the moving planets and other Solar System objects. Such a model, called a human orrery, has been laid out at the Armagh Observatory. [ 24 ]
In 2024, the LEGO Group commercially produced an orrery of the Sun, Earth, and Moon. The model is assembled exclusively from LEGO elements and reproduces solar and lunar orbits, as well Earth's rotation about a tilted axis. [ 29 ] | https://en.wikipedia.org/wiki/Orrery |
The Orr–Sommerfeld equation , in fluid dynamics , is an eigenvalue equation describing the linear two-dimensional modes of disturbance to a viscous parallel flow. The solution to the Navier–Stokes equations for a parallel, laminar flow can become unstable if certain conditions on the flow are satisfied, and the Orr–Sommerfeld equation determines precisely what the conditions for hydrodynamic stability are.
The equation is named after William McFadden Orr and Arnold Sommerfeld , who derived it at the beginning of the 20th century.
The equation is derived by solving a linearized version of the Navier–Stokes equation for the perturbation velocity field
where ( U ( z ) , 0 , 0 ) {\displaystyle (U(z),0,0)} is the unperturbed or basic flow. The perturbation velocity has the wave -like solution u ′ ∝ exp ( i α ( x − c t ) ) {\displaystyle \mathbf {u} '\propto \exp(i\alpha (x-ct))} (real part understood). Using this knowledge, and the streamfunction representation for the flow, the following dimensional form of the Orr–Sommerfeld equation is obtained:
where μ {\displaystyle \mu } is the dynamic viscosity of the fluid, ρ {\displaystyle \rho } is its density , and φ {\displaystyle \varphi } is the potential or stream function. In the case of zero viscosity ( μ = 0 {\displaystyle \mu =0} ), the equation reduces to Rayleigh's equation . The equation can be written in non-dimensional form by measuring velocities according to a scale set by some characteristic velocity U 0 {\displaystyle U_{0}} , and by measuring lengths according to channel depth h {\displaystyle h} . Then the equation takes the form
where
is the Reynolds number of the base flow. The relevant boundary conditions are the no-slip boundary conditions at the channel top and bottom z = z 1 {\displaystyle z=z_{1}} and z = z 2 {\displaystyle z=z_{2}} ,
Or:
The eigenvalue parameter of the problem is c {\displaystyle c} and the eigenvector is φ {\displaystyle \varphi } . If the imaginary part of the wave speed c {\displaystyle c} is positive, then the base flow is unstable, and the small perturbation introduced to the system is amplified in time.
The equation can also be derived for three-dimensional disturbances of the form
with u ′ ∝ exp ( i α ( x − c t ) + i β t ) {\displaystyle \mathbf {u} '\propto \exp(i\alpha (x-ct)+i\beta t)} (real part understood). Any solution to the three-dimensional equation can be mapped back to a more unstable (lower Reynolds number) solution of the two-dimensional equation above due to Squire's theorem . It is therefore sufficient to study only two-dimensional disturbances when dealing with the linear stability of a parallel flow.
For all but the simplest of velocity profiles U {\displaystyle U} , numerical or asymptotic methods are required to calculate solutions. Some typical flow profiles are discussed below. In general, the spectrum of the equation is discrete and infinite for a bounded flow, while for unbounded flows (such as boundary-layer flow), the spectrum contains both continuous and discrete parts. [ 1 ]
For plane Poiseuille flow , it has been shown that the flow is unstable (i.e. one or more eigenvalues c {\displaystyle c} has a positive imaginary part) for some α {\displaystyle \alpha } when R e > R e c = 5772.22 {\displaystyle Re>Re_{c}=5772.22} and the neutrally stable mode at R e = R e c {\displaystyle Re=Re_{c}} having α c = 1.02056 {\displaystyle \alpha _{c}=1.02056} , c r = 0.264002 {\displaystyle c_{r}=0.264002} . [ 2 ] To see the stability properties of the system, it is customary to plot a dispersion curve, that is, a plot of the growth rate Im ( α c ) {\displaystyle {\text{Im}}(\alpha {c})} as a function of the wavenumber α {\displaystyle \alpha } .
The first figure shows the spectrum of the Orr–Sommerfeld equation at the critical values listed above. This is a plot of the eigenvalues (in the form λ = − i α c {\displaystyle \lambda =-i\alpha {c}} ) in the complex plane . The rightmost eigenvalue is the most unstable one. At the critical values of Reynolds number and wavenumber , the rightmost eigenvalue is exactly zero. For higher (lower) values of Reynolds number, the rightmost eigenvalue shifts into the positive (negative) half of the complex plane. Then, a fuller picture of the stability properties is given by a plot exhibiting the functional dependence of this eigenvalue; this is shown in the second figure. The third figure shows the neutral stability curve which divides the ( R e , α ) {\displaystyle (Re,\alpha )} -plane into the region where the flow is linearly stable and the region where the flow is linearly unstable.
On the other hand, the spectrum of eigenvalues for Couette flow indicates stability, at all Reynolds numbers. [ 3 ] However, in experiments, Couette flow is found to be unstable to small, but finite, perturbations for which the linear theory, and the Orr–Sommerfeld equation do not apply. It has been argued that the non-normality of the eigenvalue problem associated with Couette (and indeed, Poiseuille) flow might explain that observed instability. [ 4 ] That is, the eigenfunctions of the Orr–Sommerfeld operator are complete but non-orthogonal. Then, the energy of the disturbance contains contributions from all eigenfunctions of the Orr–Sommerfeld equation. Even if the energy associated with each eigenvalue considered separately is decaying exponentially in time (as predicted by the Orr–Sommerfeld analysis for the Couette flow), the cross terms arising from the non-orthogonality of the eigenvalues can increase transiently. Thus, the total energy increases transiently (before tending asymptotically to zero). The argument is that if the magnitude of this transient growth is sufficiently large, it destabilizes the laminar flow, however this argument has not been universally accepted. [ 5 ]
A nonlinear theory explaining transition, [ 6 ] [ 7 ] has also been proposed. Although that theory does include linear transient growth, the focus is on 3D nonlinear processes that are strongly suspected to underlie transition to turbulence in shear flows. The theory has led to the construction of so-called complete 3D steady states, traveling waves and time-periodic solutions of the Navier-Stokes equations that capture many of the key features of transition and coherent structures observed in the near wall region of turbulent shear flows. [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] Even though "solution" usually implies the existence of an analytical result, it is common practice in fluid mechanics to refer to numerical results as "solutions" - regardless of whether the approximated solutions satisfy the Navier-Stokes equations in a mathematically satisfactory way or not. It is postulated that transition to turbulence involves the dynamic state of the fluid evolving from one solution to the next. The theory is thus predicated upon the actual existence of such solutions (many of which have yet to be observed in a physical experimental setup). This relaxation on the requirement of exact solutions allows a great deal of flexibility, since exact solutions are extremely difficult to obtain (contrary to numerical solutions), at the expense of rigor and (possibly) correctness. Thus, even though not as rigorous as previous approaches to transition, it has gained immense popularity.
An extension of the Orr–Sommerfeld equation to the flow in porous media has been recently suggested. [ 14 ]
For Couette flow, it is possible to make mathematical progress in the solution of the Orr–Sommerfeld equation. In this section, a demonstration of this method is given for the case of free-surface flow, that is, when the upper lid of the channel is replaced by a free surface. Note first of all that it is necessary to modify upper boundary conditions to take account of the free surface. In non-dimensional form, these conditions now read
φ = d φ d z = 0 , {\displaystyle \varphi ={d\varphi \over dz}=0,} at z = 0 {\displaystyle z=0} ,
d 2 φ d z 2 + α 2 φ = 0 {\displaystyle {\frac {d^{2}\varphi }{dz^{2}}}+\alpha ^{2}\varphi =0} , Ω ≡ d 3 φ d z 3 + i α R e [ ( c − U ( z 2 = 1 ) ) d φ d z + φ ] − i α R e ( 1 F r + α 2 W e ) φ c − U ( z 2 = 1 ) = 0 , {\displaystyle \Omega \equiv {\frac {d^{3}\varphi }{dz^{3}}}+i\alpha Re\left[\left(c-U\left(z_{2}=1\right)\right){\frac {d\varphi }{dz}}+\varphi \right]-i\alpha Re\left({\frac {1}{Fr}}+{\frac {\alpha ^{2}}{We}}\right){\frac {\varphi }{c-U\left(z_{2}=1\right)}}=0,} at z = 1 {\displaystyle \,z=1} .
The first free-surface condition is the statement of continuity of tangential stress, while the second condition relates the normal stress to the surface tension. Here
are the Froude and Weber numbers respectively.
For Couette flow U ( z ) = z {\displaystyle U\left(z\right)=z} , the four linearly independent solutions to the non-dimensional Orr–Sommerfeld equation are, [ 15 ]
where A i ( ⋅ ) {\displaystyle Ai\left(\cdot \right)} is the Airy function of the first kind. Substitution of the superposition solution φ = ∑ i = 1 4 c i χ i ( z ) {\displaystyle \varphi =\sum _{i=1}^{4}c_{i}\chi _{i}\left(z\right)} into the four boundary conditions gives four equations in the four unknown constants c i {\displaystyle c_{i}} . For the equations to have a non-trivial solution, the determinant condition
| χ 1 ( 0 ) χ 2 ( 0 ) χ 3 ( 0 ) χ 4 ( 0 ) χ 1 ′ ( 0 ) χ 2 ′ ( 0 ) χ 3 ′ ( 0 ) χ 4 ′ ( 0 ) Ω 1 ( 1 ) Ω 2 ( 1 ) Ω 3 ( 1 ) Ω 4 ( 1 ) χ 1 ″ ( 1 ) + α 2 χ 1 ( 1 ) χ 2 ″ ( 1 ) + α 2 χ 2 ( 1 ) χ 3 ″ ( 1 ) + α 2 χ 3 ( 1 ) χ 4 ″ ( 1 ) + α 2 χ 4 ( 1 ) | = 0 {\displaystyle \left|{\begin{array}{cccc}\chi _{1}\left(0\right)&\chi _{2}\left(0\right)&\chi _{3}\left(0\right)&\chi _{4}\left(0\right)\\\chi _{1}'\left(0\right)&\chi _{2}'\left(0\right)&\chi _{3}'\left(0\right)&\chi _{4}'\left(0\right)\\\Omega _{1}\left(1\right)&\Omega _{2}\left(1\right)&\Omega _{3}\left(1\right)&\Omega _{4}\left(1\right)\\\chi _{1}''\left(1\right)+\alpha ^{2}\chi _{1}\left(1\right)&\chi _{2}''\left(1\right)+\alpha ^{2}\chi _{2}\left(1\right)&\chi _{3}''\left(1\right)+\alpha ^{2}\chi _{3}\left(1\right)&\chi _{4}''\left(1\right)+\alpha ^{2}\chi _{4}\left(1\right)\end{array}}\right|=0}
must be satisfied. This is a single equation in the unknown c , which can be solved numerically or by asymptotic methods. It can be shown that for a range of wavenumbers α {\displaystyle \alpha } and for sufficiently large Reynolds numbers, the growth rate α c i {\displaystyle \alpha c_{\text{i}}} is positive. | https://en.wikipedia.org/wiki/Orr–Sommerfeld_equation |
In geometry , an orthant [ 1 ] or hyperoctant [ 2 ] is the analogue in n -dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions.
In general an orthant in n -dimensions can be considered the intersection of n mutually orthogonal half-spaces . By independent selections of half-space signs, there are 2 n orthants in n -dimensional space.
More specifically, a closed orthant in R n is a subset defined by constraining each Cartesian coordinate to be nonnegative or nonpositive. Such a subset is defined by a system of inequalities:
where each ε i is +1 or −1.
Similarly, an open orthant in R n is a subset defined by a system of strict inequalities
where each ε i is +1 or −1.
By dimension:
John Conway and Neil Sloane defined the term n - orthoplex from orthant complex as a regular polytope in n -dimensions with 2 n simplex facets , one per orthant. [ 3 ]
The nonnegative orthant is the generalization of the first quadrant to n -dimensions and is important in many constrained optimization problems. | https://en.wikipedia.org/wiki/Orthant |
ortho -Carborane is the organoboron compound with the formula C 2 B 10 H 12 . The prefix ortho is derived from ortho . It is the most prominent carborane . This derivative has been considered for a wide range of applications from heat-resistant polymers to medical applications. It is a colorless solid that melts, without decomposition, at 320 °C
The cluster has C 2v symmetry. [ 1 ]
Ortho-carborane is prepared by the addition of acetylenes to decaborane(14) . Modern syntheses involve two stages, the first involving generation of an adduct of decaborane: [ 2 ] [ 3 ]
In the second stage, the alkyne is installed as the source of two carbon vertices: [ 3 ]
Substituted acetylenes can be employed more conveniently than acetylene gas. For example bis(acetoxymethyl)acetylene adds to the decarborane readily.
The organic substituents are removed by ester hydrolysis followed by oxidation: [ 2 ]
Upon heating to 420 °C, it rearranges to form the meta isomer. The para isomer is produced by heating to temperatures above 600 °C.
ortho-Carborane undergoes 2e- reduction when treated with a solution of lithium in ammonia. The result is the nido cluster 7,9-[C 2 B 10 H 12 ] 2- . In the dianion, the carbon vertices are not adjacent. The same cluster is produced by reduction of meta-carborane. Oxidation of the resulting 7,9-[C 2 B 10 H 12 ] 2- gives ortho-carborane. [ 4 ]
Treatment with organolithium reagents gives the dilithio derivative. [ 5 ]
This dilithiated compound reacts with a variety of electrophiles, e.g. chlorophosphines, chlorosilanes, and sulfur. [ 6 ]
Base degradation of ortho carborane gives the anionic 11-vertex derivative, precursor to dicarbollide complexes: [ 7 ]
Dicarbollides (C 2 B 8 H 11 2- ) function as ligands for transition metals and f-elements. [ 8 ] The dianion forms sandwich compounds , bis(dicarbollides). Dicarbollides, being strong electron donors, stabilize higher oxidation states, e.g. Ni(IV).
The CH vertices of closo -dicarbadodecaboranes undergo deprotonation upon treatment with organolithium reagents: [ 9 ]
These dilithiated compounds react with a variety of electrophiles, e.g. chlorophosphines, chlorosilanes, and sulfur. [ 10 ] Many of the same compounds can be produced by hydroboration of alkynes:
ortho-Carborane can be converted to highly reactive carborynes with the formula B 10 C 2 H 10 .
Unlike the hydrogens on the carbon vertices, the hydrogens on the boron vertices are not acidic and do not react with strong bases. This is because boron is not as electronegative as carbon and thus the polarity of the B—H bonds is relatively low. Substitution at the boron vertices is still possible using halogenating agents through electrophilic substitution or photochemical reactions. [ 11 ]
For example, the boron vertices at the 9 and 12 positions opposite to the carbon vertices can be iodinated using iodine and a catalytic amount of AlCl 3 while in refluxing dichloromethane. [ 12 ]
Exohedral halogenation leads to an increase in the electron withdrawing effect of the carborane which increases the acidity of the C—H bonds especially when the halogens are located at the 9, and 12 positions. [ 13 ] Per-halogenation is also possible and when increasing the number of halide atoms, the π backdonation ability of the halide decreases allowing for the formation of intramolecular halide-halide noncovalent bonds. [ 14 ]
Iodinated derivatives of carborane can be further modified to access boron alkylated products via a cross coupling reaction. This can be done by treating the halogenated carborane with a Grignard reagent in the presence of a phosphine palladium complex. The bromo and chloro compounds do not react under the same conditions. [ 15 ]
Upon treatment of ortho-carboranes with organolithium reagents such as n-Butyllithium, the CH vertices of the carborane cage can be deprotonated, affording the dilithiated ortho-carborane cage. Taking advantage of this more active carbon-lithium bond, the metalated carborane cages can then be treated with copper(I) chloride while in organic solvents, resulting in a copper-mediated carbon-carbon coupling reaction of the carborane cages. The copper salt is needed to avoid unwanted carbon-boron and boron-boron coupling reactions. The reaction mixture is allowed to stir at room temperature for two days, forming a copper-metalated carborane cage. Finally, the mixture is treated with 3M hydrochloric acid to quench the reaction process. The crude product is then purified via column chromatography and affords one half-equivalent of the carbon-carbon linked dimer of the original ortho-carborane in high yields. Worth noting is the effect of donating solvents on the yields of the reactions, as yields in solvents such as tetrahydrofuran and diethyl ether afford product in greatly decreased yields. [ 16 ]
The preparation of closo-dicarbadodecaboranes was reported independently by groups at Olin Corporation and the Reaction Motors Division of Thiokol Chemical Corporation working under the U.S. Air Force and published in 1963. These groups demonstrated the high stability in air of 1,2-closo-dodecaborane and related compounds, presented a general synthesis, described the transformation of substituents without destroying the carborane cluster, and demonstrated the ortho to meta isomerization. [ 17 ] | https://en.wikipedia.org/wiki/Ortho-Carborane |
OrthoDB [ 1 ] [ 2 ] [ 3 ] [ 4 ] presents a catalog of orthologous protein-coding genes across vertebrates , arthropods , fungi , plants , and bacteria . Orthology refers to the last common ancestor of the species under consideration, and thus OrthoDB explicitly delineates orthologs at each major radiation along the species phylogeny. The database of orthologs presents available protein descriptors, together with Gene Ontology and InterPro attributes, which serve to provide general descriptive annotations of the orthologous groups, and facilitate comprehensive orthology database querying. OrthoDB also provides computed evolutionary traits of orthologs, such as gene duplicability and loss profiles, divergence rates, sibling groups, and gene intron-exon architectures.
In comparative genomics , the importance of scale cannot be underestimated. As gene orthology delineation requires specific expertise and considerable computational resources, scale is something that individual non-specialist research groups cannot accomplish on their own. This challenging task is achieved by OrthoDB , with very comprehensive sets of species and several unique features such as the extensive functional and evolutionary annotations of orthologous groups, with the integration of many useful links to other world-leading databases that focus on capturing information about gene function. No genome can exist as a useful data source without extensive comparative analyses with other genomes – OrthoDB provides a critically important resource for comparative genomics for the entire community of researchers from those interested in grand evolutionary questions to those focused on the specific biological functions of individual genes.
Orthology is defined relative to the last common ancestor of the species being considered, thereby determining the hierarchical nature of orthologous classifications. This is explicitly addressed in OrthoDB by application of the orthology delineation procedure at each major radiation point of the considered phylogeny. The OrthoDB implementation employs a Best-Reciprocal-Hit (BRH) clustering algorithm based on all-against-all Smith–Waterman protein sequence comparisons. Gene set pre-processing selects the longest protein-coding transcript of alternatively spliced genes and of very similar gene copies. The procedure triangulates BRHs to progressively build the clusters and requires an overall minimum sequence alignment overlap to avoid domain walking. These core clusters are further expanded to include all more closely related within-species in-paralogs, and the previously identified very similar gene copies.
The database contains some 600 eukaryotic species and more than 3600 bacteria [ 1 ] sourced from Ensembl , UniProt , NCBI , FlyBase , and several other databases. The ever-increasing sampling of sequenced genomes brings a clearer account of the majority of gene genealogies that will facilitate informed hypotheses of gene function in newly sequenced genomes.
Examples of studies that have employed data from OrthoDB include comparative analyses of gene repertoire evolution , [ 5 ] [ 6 ] comparisons of fruit fly and mosquito developmental genes , [ 7 ] analyses of bloodmeal- or infection-induced changes in gene expression in mosquitoes , [ 8 ] [ 9 ] [ 10 ] analysis of the evolution of mammalian milk production , [ 11 ] and mosquito gene and genome evolution . [ 12 ] Others studies citing OrthoDB can be found at PubMed and Google Scholar .
OrthoDB has performed consistently well in benchmarking assessments alongside other orthology delineation procedures. Results were compared to reference trees for three well-conserved protein families, [ 13 ] and to a larger set of curated protein families. [ 14 ]
B enchmarking sets of U niversal Si ngle- C opy O rthologs [ 15 ] - Orthologous groups are selected from OrthoDB for the root-level classifications of arthropods, vertebrates, metazoans, fungi, and other major clades. Groups are required to contain single-copy orthologs in at least 90% of the species (in others they may be lost or duplicated), and the missing species cannot all be from the same clade. Species with frequent losses or duplications are removed from the selection unless they hold a key position in the phylogeny. BUSCOs are therefore expected to be found as single-copy orthologs in any newly sequenced genome from the appropriate phylogenetic clade, and can be used to analyse newly sequenced genomes to assess their relative completeness. The BUSCO assessment tool and datasets (accessible here ) are being widely used in many genomics projects, with most journal editors now requiring such quality assessments before accepting new genome publications. | https://en.wikipedia.org/wiki/OrthoDB |
OrthoFinder is a command-line software tool for comparative genomics . [ 1 ] [ 2 ] OrthoFinder determines the correspondence between genes in different organisms (also known as orthology analysis). This correspondence provides a framework for understanding the evolution of life on Earth, and enables the extrapolation and transfer of biological knowledge between organisms.
OrthoFinder takes FASTA files of protein sequences as input (one per species) and as output provides:
As of August 2021, the tool has been referenced by more than 1500 published studies. [ 3 ] | https://en.wikipedia.org/wiki/OrthoFinder |
In organic chemistry , ortho acids are organic , hypothetical chemical compounds having the structure R−C(OH) 3 (R = alkyl or aryl ). [ 1 ]
Ortho acids themselves are unstable and cannot be isolated. However, ortho esters can be synthesized by the Pinner reaction , in which nitriles react with alcohols under acid catalysis:
Historically the prefixes " hypo -", " per -", " ortho -", " meta- ", and " pyro -" were used to distinguish between different oxyacids of the same element, of these ortho acid is the most highly oxidised or hydroxylated . For example, dehydration of orthoperiodic acid gives metaperiodic acid . Such naming conventions are now obsolete; however, various traditional names containing these prefixes have been retained in IUPAC nomenclature , namely:
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Ortho effect is an organic chemistry phenomenon where the presence of a chemical group at the at ortho position or the 1 and 2 position of a phenyl ring , relative to the carboxylic compound changes the chemical properties of the compound. This is caused by steric effects and bonding interactions along with polar effects caused by the various substituents which are in a given molecule, resulting in changes in its chemical and physical properties. The ortho effect is associated with substituted benzene compounds.
There are three main ortho effects in substituted benzene compounds:
When a substituent group is located ortho position to the carboxyl group in a substituted benzoic acid compound, the compound becomes more acidic surpassing the unmodified benzoic acid.
Generally ortho-substituted benzoic acids are stronger acids than their meta and para isomers.
When ortho substitution occurs in benzoic acid, steric hindrance causes the carboxyl group to twist out of the plane of the benzene ring. The twisting inhibits the resonance of the carboxyl group with the phenyl ring, leading to increased acidity of the carboxyl group. This increased acidity contrasts with the reduced acidity caused by destabilizing cross-conjugation. The destabilizing cross-conjugation causes decreased acidity of benzoic acid compared to formic acid. [ 1 ] [ 2 ]
The table given below shows pKa values of various monosubstituted benzoic acids.
[ 1 ]
When any group is present at ortho position to an amide group (NH 2 ) in aniline then the basic character of that compound becomes weaker. For example, see the order of basicity of following substituted aniline:-
The protonation of substituted aniline is inhibited by steric hindrance. When protonated, the nitrogen in the amino group changes its orbital hybridization from sp 2 to sp 3 , becoming non-planar. This leads to steric hindrance between the ortho-substituted group and the hydrogen atom of the amino group, reducing the stability of the conjugate acid and consequently decreasing the pH of substituted aniline.
The ortho effect also occurs when a meta-directing group is positioned in a meta arrangement relative to an ortho–para-directing group, a new substituent introduced into the molecule tends to preferentially occupy the ortho position relative to the meta-directing group rather than the para position. Currently, there is no definitive explanation for the ortho effect, but it is hypothesized that there may be intramolecular assistance from the meta-directing group influencing the positioning of the incoming substituent. [ 3 ] For example, the electrophilic aromatic nitration of 1-methyl-3-nitrobenzene affords 4-methyl-1,2-dinitrobenzene and 1-methyl-2,3-dinitrobenzene in 60.1% and 28.4% yields, respectively. [ 4 ] In contrast, 2-methyl-1,4-dinitrobenzene (2c) is isolated in only 9.9% yield. [ 4 ] As witnessed in the above example, when a π-acceptor substituent (πAS) is meta to a π-donor substituent (πDS), the electrophilic aromatic nitration occurs ortho to the πAS rather than para.
Similar results were also observed on the nitration of 3-methylbenzoic acid in which 5-methyl-2-nitrobenzoic acid and 3-methyl-2-nitrobenzoic acid were obtained as the major compounds, whereas 3-methyl-4-nitrobenzoic acid was reported as a minor compound. [ 5 ] Also in nitration of the nitration of 3-bromobenzoic acid 5-bromo-2-nitrobenzoic acid (83%yield) was obtained as major product and 3-bromo-2-nitrobenzoic acid (13% yield) as minor. On an interesting note the potential isomer 3-bromo-4-nitrobenzoic acid was not detected. [ 6 ]
The ortho effect occurs in Diels-Alder reactions when the Z-substituted dienophiles react with 1-substituted butadienes to give 3,4-disubstituted cyclohexenes, independent of the nature of diene substituents. [ 7 ] | https://en.wikipedia.org/wiki/Ortho_effect |
In organic chemistry , an ortho ester is a functional group containing three alkoxy groups attached to one carbon atom, i.e. with the general formula RC(OR') 3 . Orthoesters may be considered as products of exhaustive alkylation of unstable orthocarboxylic acids and it is from these that the name 'ortho ester' is derived. An example is ethyl orthoacetate , CH 3 C(OCH 2 CH 3 ) 3 , more correctly known as 1,1,1-triethoxyethane. [ 1 ]
Ortho esters can be prepared by the Pinner reaction , in which nitriles react with alcohols in the presence of one equivalent of hydrogen chloride. The reaction proceeds by formation of imido ester hydrochloride :
Upon standing in the presence of excess alcohol, this intermediate converts to the ortho ester:
The reaction requires anhydrous conditions, [ 1 ] and ideally a nonpolar solvent. [ 2 ] : 6
Acid chlorides can also drive the reaction from the corresponding amide, e.g.: [ 3 ] : 154
Although a less common method, ortho esters were first produced by reaction of 1,1,1-trichloroalkanes with sodium alkoxide: [ 1 ]
Compounds with an adjacent hydrogen atom on R tend to undergo elimination instead. [ 2 ] : 12 Traditional esters can be converted to α,α‑dichloro ethers with phosphorus pentachloride . The resulting halogenated compounds undergo ether synthesis like the trichloroalkanes. [ 3 ] : 162
Carboxylic acids naturally form a trithio ortho ester when heated with a mercaptan of appropriate stoichiometry. [ 4 ] The resulting compound undergoes transesterification to a traditional orthoester in the presence of zinc chloride . [ 3 ] : 156 Traditional transesterification from a cheaper ortho ester is also possible. [ 3 ]
Ortho esters are readily hydrolyzed in mild aqueous acid to form esters :
For example, trimethyl orthoformate CH(OCH 3 ) 3 may be hydrolyzed (under acidic conditions) to methyl formate and methanol ; [ 5 ] and may be further hydrolyzed (under alkaline conditions) to salts of formic acid and methanol. [ 6 ]
The Johnson–Claisen rearrangement is the reaction of an allylic alcohol with an ortho ester containing a deprotonatable alpha carbon (e.g. triethyl orthoacetate ) to give a γ,δ-unsaturated ester . [ 7 ]
In the Bodroux–Chichibabin aldehyde synthesis an ortho ester reacts with a Grignard reagent to form an aldehyde ; this is an example of a formylation reaction .
Examples of orthoesters include the reagents trimethyl orthoformate and triethylorthoacetate . Another example is the bicyclic OBO protecting group (4-methyl-2,6,7-tri o xa- b icyclo[2.2.2] o ctan-1-yl) which is formed by the action of (3-methyloxetan-3-yl)methanol on activated carboxylic acids in the presence of Lewis acids. The group is base stable and can be cleaved in two steps under mild conditions, mildly acidic hydrolysis yields the ester of tris(hydroxymethyl)ethane which is then cleaved using e.g. an aqueous carbonate solution. [ 8 ]
The threefold symmetry of the cyclohexanehexol isomer scyllo -inositol (scyllitol) yields the triply-bridged orthoformate esters scyllitol orthoformate with an adamantane -like skeleton, and scyllitol bis-orthoformate with two fused adamantane-like skeletons. [ 9 ] | https://en.wikipedia.org/wiki/Ortho_ester |
Orthoacetic acid or ethane-1,1,1-triol is an hypothetical organic compound with formula C 2 H 6 O 3 or H 3 C-C(OH) 3 . It would be an ortho acid with the ethane backbone.
Orthoacetic acid is believed to be impossible to isolate, since it would readily decompose into acetic acid and water . It may have a fleeting existence in aqueous solutions of acetic acid. [ 2 ]
The three hydroxyls of CH 3 C(OH) 3 could be deprotonated, leading successively to CH 3 C(OH) 2 (O – ) ( dihydrogenorthoacetate ), CH 3 C(OH)(O – ) 2 ( hydrogenorthoacetate ), and finally CH 3 C(O – ) 3 ( orthoacetate ).
There are many stable organic compounds with the trivalent moiety H 3 CC(OR) 3 , which are formally esters of orthoacetic acid and called orthoacetates . They include trimethyl orthoacetate and triethyl orthoacetate , which are commercially available.
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In inorganic chemistry , an orthoborate is a polyatomic anion with formula [BO 3 ] 3− or a salt containing the anion; such as trisodium orthoborate (Na + ) 3 [BO 3 ] 3− . It is one of several boron oxyanions , or borates .
The name is also used in organic chemistry for the trivalent functional group B(O−) 3 , or any compound ( ester ) that contains it, such as triethyl orthoborate B(OC 2 H 5 ) 3 .
The orthoborate ion is known in the solid state, for example, in calcium orthoborate (Ca 2+ ) 3 ([BO 3 ] 3− ) 2 , [ 1 ] where it adopts a nearly trigonal planar structure. It is a structural analogue of the carbonate anion [CO 3 ] 2− , with which it is isoelectronic . Simple bonding theories point to the trigonal planar structure. In terms of valence bond theory , the bonds are formed by using sp 2 hybrid orbitals on boron.
Some compounds termed orthoborates do not necessarily contain the trigonal planar ion. For example, gadolinium orthoborate GdBO 3 contains the planar [BO 3 ] 3− ion only a high temperatures; otherwise it contains the polyborate anion [B 3 O 9 ] 9− . [ 2 ]
When orthoborate salts are dissolved in water, the anion converts mostly to boric acid B(OH) 3 and other hydrogen -containing borate anions, mainly tetrahydroxyborate [B(OH) 4 ] − . The reactions of orthoborate in solution are therefore mostly those of these compounds.
In particular, these reactions include the condensation of tetrahydroxoborate with cis - vicinal diols such as mannitol , sorbitol , glucose and glycerol , to form relatively stable anion esters. This reaction is used in analytic chemistry to determine the concentration of borate anions. | https://en.wikipedia.org/wiki/Orthoborate |
Orthocarbonic acid , carbon hydroxide , methanetetrol is the name given to a hypothetical compound with the chemical formula H 4 CO 4 or C(OH) 4 . Its molecular structure consists of a single carbon atom bonded to four hydroxyl groups. It would be therefore a fourfold alcohol . In theory it could lose four protons to give the hypothetical oxocarbon anion orthocarbonate CO 4− 4 , and is therefore considered an oxoacid of carbon.
Orthocarbonic acid is highly unstable. Calculations show that it decomposes into carbonic acid and water: [ 2 ] [ 3 ]
Orthocarbonic acid is one of the group of ortho acids that have the general structure of RC(OH) 3 . The term ortho acid is also used to refer to the most hydroxylated acid in a set of oxoacids .
Researchers predict that orthocarbonic acid is stable at high pressure; hence it may form in the interior of the ice giant planets Uranus and Neptune , where water and methane are common. [ 4 ]
By loss of one through four protons, orthocarbonic acid could yield four anions: H 3 CO − 4 (trihydrogen orthocarbonate), H 2 CO 2− 4 (dihydrogen orthocarbonate), HCO 3− 4 (hydrogen orthocarbonate), and CO 4− 4 (orthocarbonate).
Numerous salts of fully deprotonated CO 4− 4 , such as Ca 2 CO 4 (calcium orthocarbonate) or Sr 2 CO 4 (strontium orthocarbonate), have been synthesized under high pressure conditions and structurally characterized by X-ray diffraction. [ 5 ] [ 6 ] [ 7 ] Strontium orthocarbonate, Sr 2 CO 4 , is stable at atmospheric pressure. Orthocarbonate is tetrahedral in shape, and is isoelectronic to orthonitrate . The C-O distance is 1.41 Å . [ 8 ] Sr 3 (CO 4 )O is an oxide orthocarbonate (tristrontium orthocarbonate oxide), also stable at atmospheric pressure . [ 9 ]
The tetravalent moiety CO 4 is found in stable organic compounds ; they are formally esters of orthocarbonic acid, and therefore are called orthocarbonates . For example, tetraethoxymethane can be prepared by the reaction between chloropicrin and sodium ethoxide in ethanol . [ 10 ] Polyorthocarbonates are stable polymers that might have applications in absorbing organic solvents in waste treatment processes, [ 11 ] or in dental restorative materials . [ 12 ] The explosive trinitroethylorthocarbonate possesses an orthocarbonate core.
A linear polymer which can be described as a ( spiro ) orthocarbonate ester of pentaerythritol , whose formula could be written as [(−CH 2 ) 2 C(CH 2 −) 2 (−O) 2 C(O−) 2 ] n , was synthesized in 2002. [ 13 ]
The carbon atom in the spiro ester bis- catechol orthocarbonate was found to have tetrahedral bond geometry, contrasting with the square planar geometry of the silicon atom in the analogous orthosilicate ester. [ 14 ]
Orthocarbonates may exist in several conformers , that differ by the relative rotation of the C–O–C bridges. The conformation structures of some esters, such as tetraphenoxymethane , tetrakis(3,5-dimethyl-phenoxy)methane , and tetrakis(4-bromophenoxy)methane have been determined by X-ray diffraction . [ 15 ] | https://en.wikipedia.org/wiki/Orthocarbonic_acid |
In geometry , an orthocentric tetrahedron is a tetrahedron where all three pairs of opposite edges are perpendicular . It is also known as an orthogonal tetrahedron since orthogonal means perpendicular. It was first studied by Simon Lhuilier in 1782, and got the name orthocentric tetrahedron by G. de Longchamps in 1890. [ 1 ]
In an orthocentric tetrahedron the four altitudes are concurrent . This common point is called the tetrahedron orthocenter (a generalization of the orthocenter of a triangle). It has the property that it is the symmetric point of the center of the circumscribed sphere with respect to the centroid . [ 1 ] Hence the orthocenter coincides with the Monge point of the tetrahedron.
All tetrahedra can be inscribed in a parallelepiped . A tetrahedron is orthocentric if and only if its circumscribed parallelepiped is a rhombohedron . Indeed, in any tetrahedron, a pair of opposite edges is perpendicular if and only if the corresponding faces of the circumscribed parallelepiped are rhombi. If four faces of a parallelepiped are rhombi, then all edges have equal lengths and all six faces are rhombi; it follows that if two pairs of opposite edges in a tetrahedron are perpendicular, then so is the third pair, and the tetrahedron is orthocentric. [ 1 ]
A tetrahedron ABCD is orthocentric if and only if the sum of the squares of opposite edges is the same for the three pairs of opposite edges: [ 2 ] [ 3 ]
In fact, it is enough for only two pairs of opposite edges to satisfy this condition for the tetrahedron to be orthocentric.
Another necessary and sufficient condition for a tetrahedron to be orthocentric is that its three bimedians have equal length. [ 3 ]
The characterization regarding the edges implies that if only four of the six edges of an orthocentric tetrahedron are known, the remaining two can be calculated as long as they are not opposite to each other. Therefore the volume of an orthocentric tetrahedron can be expressed in terms of four edges a , b , c , d . The formula is [ 4 ]
where c and d are opposite edges, and s = 1 2 ( a + b + c ) {\displaystyle s={\tfrac {1}{2}}(a+b+c)} . | https://en.wikipedia.org/wiki/Orthocenter_(tetrahedron) |
The orthogonal Procrustes problem [ 1 ] is a matrix approximation problem in linear algebra . In its classical form, one is given two matrices A {\displaystyle A} and B {\displaystyle B} and asked to find an orthogonal matrix Ω {\displaystyle \Omega } which most closely maps A {\displaystyle A} to B {\displaystyle B} . [ 2 ] [ 3 ] Specifically, the orthogonal Procrustes problem is an optimization problem given by
minimize Ω ‖ Ω A − B ‖ F subject to Ω T Ω = I , {\displaystyle {\begin{aligned}{\underset {\Omega }{\text{minimize}}}\quad &\|\Omega A-B\|_{F}\\{\text{subject to}}\quad &\Omega ^{T}\Omega =I,\end{aligned}}}
where ‖ ⋅ ‖ F {\displaystyle \|\cdot \|_{F}} denotes the Frobenius norm . This is a special case of Wahba's problem (with identical weights; instead of considering two matrices, in Wahba's problem the columns of the matrices are considered as individual vectors). Another difference is that Wahba's problem tries to find a proper rotation matrix instead of just an orthogonal one.
The name Procrustes refers to a bandit from Greek mythology who made his victims fit his bed by either stretching their limbs or cutting them off.
This problem was originally solved by Peter Schönemann in a 1964 thesis, and shortly after appeared in the journal Psychometrika. [ 4 ]
This problem is equivalent to finding the nearest orthogonal matrix to a given matrix M = B A T {\displaystyle M=BA^{T}} , i.e. solving the closest orthogonal approximation problem
To find matrix R {\displaystyle R} , one uses the singular value decomposition (for which the entries of Σ {\displaystyle \Sigma } are non-negative)
to write
One proof depends on the basic properties of the Frobenius inner product that induces the Frobenius norm :
where R {\displaystyle R} is the solution for the optimal value of Ω {\displaystyle \Omega } that minimizes the norm squared | | Ω A − B ‖ F 2 {\displaystyle ||\Omega A-B\|_{F}^{2}} .
There are a number of related problems to the classical orthogonal Procrustes problem. One might generalize it by seeking the closest matrix in which the columns are orthogonal , but not necessarily orthonormal . [ 5 ]
Alternately, one might constrain it by only allowing rotation matrices (i.e. orthogonal matrices with determinant 1, also known as special orthogonal matrices ). In this case, one can write (using the above decomposition M = U Σ V T {\displaystyle M=U\Sigma V^{T}} )
where Σ ′ {\displaystyle \Sigma '\,\!} is a modified Σ {\displaystyle \Sigma \,\!} , with the smallest singular value replaced by det ( U V T ) {\displaystyle \det(UV^{T})} (+1 or -1), and the other singular values replaced by 1, so that the determinant of R is guaranteed to be positive. [ 6 ] For more information, see the Kabsch algorithm .
The unbalanced Procrustes problem concerns minimizing the norm of A U − B {\displaystyle AU-B} , where A ∈ R m × ℓ , U ∈ R ℓ × n {\displaystyle A\in \mathbb {R} ^{m\times \ell },U\in \mathbb {R} ^{\ell \times n}} , and B ∈ R m × n {\displaystyle B\in \mathbb {R} ^{m\times n}} , with m > ℓ ≥ n {\displaystyle m>\ell \geq n} , or alternately with complex valued matrices. This is a problem over the Stiefel manifold U ∈ U ( m , ℓ ) {\displaystyle U\in U(m,\ell )} , and has no currently known closed form. To distinguish, the standard Procrustes problem ( A ∈ R m × m {\displaystyle A\in \mathbb {R} ^{m\times m}} ) is referred to as the balanced problem in these contexts. | https://en.wikipedia.org/wiki/Orthogonal_Procrustes_problem |
In mathematics, an orthogonal array (more specifically, a fixed-level orthogonal array ) is a "table" (array) whose entries come from a fixed finite set of symbols (for example, {1,2,..., v }), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t - tuples of the symbols, formed by taking the entries in each row restricted to these columns, appear the same number of times. The number t is called the strength of the orthogonal array. Here are two examples:
The example at left is that of an orthogonal array with symbol set {1,2} and strength 2. Notice that the four ordered pairs (2-tuples) formed by the rows restricted to the first and third columns, namely (1,1), (2,1), (1,2) and (2,2), are all the possible ordered pairs of the two element set and each appears exactly once. The second and third columns would give, (1,1), (2,1), (2,2) and (1,2); again, all possible ordered pairs each appearing once. The same statement would hold had the first and second columns been used. This is thus an orthogonal array of strength two.
In the example on the right, [ 1 ] the rows restricted to the first three columns contain the 8 possible ordered triples consisting of 0's and 1's, each appearing once. The same holds for any other choice of three columns. Thus this is an orthogonal array of strength 3.
A mixed-level orthogonal array is one in which each column may have a different number of symbols. An example is given below.
Orthogonal arrays generalize, in a tabular form, the idea of mutually orthogonal Latin squares . These arrays have many connections to other combinatorial designs and have applications in the statistical design of experiments , coding theory , cryptography and various types of software testing .
For t ≤ k , an orthogonal array of type ( N, k, v, t ) – an OA( N, k, v, t ) for short – is an N × k array whose entries are chosen from a set X with v points (a v -set ) such that in every subset of t columns of the array, every t -tuple of points of X is repeated the same number of times. The number of repeats is usually denoted λ.
In many applications these parameters are given the following names:
The definition of strength leads to the parameter relation
An orthogonal array is simple if it does not contain any repeated rows. ( Sub arrays of t columns may have repeated rows, as in the OA(18, 7, 3, 2) example pictured in this section.)
An orthogonal array is linear if X is a finite field F q of order q ( q a prime power) and the rows of the array form a subspace of the vector space ( F q ) k . [ 2 ] The right-hand example in the introduction is linear over the field F 2 . Every linear orthogonal array is simple.
In a mixed-level orthogonal array, the symbols in the columns may be chosen from different sets having different numbers of points, as in the following example: [ 3 ]
This array has strength 2:
It may thus be denoted may be denoted OA(8, 5, 2 4 4 1 , 2), as is discussed below. The expression 2 4 4 1 indicates that four factors have 2 levels and one has 4 levels.
As in this example, there is no single ``index" or repetition number λ in a mixed-level orthogonal array of strength t : Each subarray of t columns can have a different λ.
The terms symmetric and asymmetric are sometimes used for fixed-level and mixed-level . Here symmetry refers to the property that all factors have the same number of levels, not to the "shape" of the array: a symmetric orthogonal array is almost never a symmetric matrix .
The notation OA( N, k, v, t ) is sometimes contracted so that one may, for example, write simply OA( k, v ), [ 4 ] as long as the text makes clear the unstated parameter values. In the other direction, it may be expanded for mixed-level arrays. Here one would write OA( N, k, v 1 ···v k , t ), where column i has v i levels. This notation is usually shortened when values v are repeated, so that one writes OA(8, 5, 2 4 4 1 , 2) for the example at the end of the last section, rather than OA(8, 5, 2·2·2·2·4, 2). In similar fashion, one may shorten OA( N, k, v, t ) to OA( N, v k , t ) for fixed-level arrays.
This OA notation does not explicitly include the index λ, but λ can be recovered from the other parameters via the relation N = λ v t . This is effective when the parameters all have specific numerical values, but less so when a class of orthogonal arrays is intended. For example, when indicating the class of arrays having strength t = 2 and index λ=1, the notation OA( N, k, v, 2 ) is insufficient to determine λ by itself. This is typically remedied by writing OA( v 2 , k, v, 2) instead. While notations that explicitly include the parameter λ do not have this problem, they cannot easily be extended to denote mixed-level arrays.
Some authors define an OA( N, k, v, t ) as being k × N rather than N × k . In such cases the strength of the array is defined in terms of a subset of t rows rather than columns.
Except for the prefix OA, the notation OA( N, k, v, t ) is the same as that introduced by Rao. [ 5 ] While this notation is very common, it not universal. Hedayat, Sloane and Stufken [ 6 ] recommend it as standard, but list eight alternatives found in the literature, and there are others. [ 8 ]
An example of an OA(16, 5, 4, 2); a strength 2, 4-level design of index 1 with 16 runs:
An example of an OA(27, 5, 3, 2) (written as its transpose for ease of viewing): [ 9 ]
This example has index λ = 3.
An array consisting of all k -tuples of a v -set, arranged so that the k -tuples are rows, automatically ( "trivially" ) has strength k , and so is an OA( v k , k, v, k ).
Any OA( N, k, v, k ) would be considered trivial since such arrays are easily constructed by simply listing all the k -tuples of the v -set λ times.
An OA( n 2 , 3, n , 2) is equivalent to a Latin square of order n . For k ≤ n +1, an OA( n 2 , k, n , 2) is equivalent to a set of k − 2 mutually orthogonal Latin squares of order n . Such index one, strength 2 orthogonal arrays are also known as Hyper-Graeco-Latin square designs in the statistical literature.
Let A be a strength 2, index 1 orthogonal array on an n -set of elements, identified with the set of natural numbers {1,..., n }. Choose and fix, in order, two columns of A , called the indexing columns . Because the strength is 2 and the index is 1, all ordered pairs ( i , j ) with 1 ≤ i , j ≤ n appear exactly once in the rows of the indexing columns. Here i and j will in turn index the rows and columns of a n × n square. Take any other column of A and fill the ( i , j ) cell of this square with the entry that is in this column of A and in the row of A whose indexing columns contain ( i , j ). The resulting square is a Latin square of order n . For example, consider this OA(9, 4, 3, 2):
By choosing columns 3 and 4 (in that order) as the indexing columns, the first column produces the Latin square
while the second column produces the Latin square
These two squares, moreover, are mutually orthogonal. In general, the Latin squares produced in this way from an orthogonal array will be orthogonal Latin squares, so the k − 2 columns other than the indexing columns will produce a set of k − 2 mutually orthogonal Latin squares .
This construction is completely reversible and so strength 2, index 1 orthogonal arrays can be constructed from sets of mutually orthogonal Latin squares. [ 10 ]
Orthogonal arrays provide a uniform way to describe these diverse objects which are of interest in the statistical design of experiments .
As mentioned in the previous section, a Latin square of order n can be thought of as an OA( n 2 , 3, n , 2). Actually, the orthogonal array can lead to six Latin squares since any ordered pair of distinct columns can be used as the indexing columns. However, these are all isotopic and are considered equivalent. For concreteness we shall always assume that the first two columns in their natural order are used as the indexing columns.
In the statistics literature, a Latin cube is a three-dimensional n × n × n matrix consisting of n layers, each having n rows and n columns such that the n distinct elements which appear are repeated n 2 times and arranged so that in each layer parallel to each of the three pairs of opposite faces of the cube all the n distinct elements appear and each is repeated exactly n times in that layer. [ 11 ]
Note that with this definition a layer of a Latin cube need not be a Latin square. In fact, no row, column or file (the cells of a particular position in the different layers) need be a permutation of the n symbols. [ 12 ]
A Latin cube of order n is equivalent to an OA( n 3 , 4 ,n , 2). [ 9 ]
Two Latin cubes of order n are orthogonal if, among the n 3 pairs of elements chosen from corresponding cells of the two cubes, each distinct ordered pair of the elements occurs exactly n times. A set of k − 3 mutually orthogonal Latin cubes of order n is equivalent to an OA( n 3 , k, n , 2). [ 9 ] An example of a pair of mutually orthogonal Latin cubes of order three was given as the OA(27, 5, 3, 2) in the Examples section above.
Unlike the case with Latin squares, in which there are no constraints, the indexing columns of the orthogonal array representation of a Latin cube must be selected so as to form an OA( n 3 , 3, n , 3).
An m -dimensional Latin hypercube of order n of the r th class is an n × n × ... × n m -dimensional matrix having n r distinct elements, each repeated n m − r times, and such that each element occurs exactly n m − r − 1 times in each of its m sets of n parallel ( m − 1)-dimensional linear subspaces (or "layers"). Two such Latin hypercubes of the same order n and class r with the property that, when one is superimposed on the other, every element of the one occurs exactly n m − 2 r times with every element of the other, are said to be orthogonal . [ 13 ]
A set of k − m mutually orthogonal m -dimensional Latin hypercubes of order n is equivalent to an OA( n m , k, n, 2), where the indexing columns form an OA( n m , m, n, m ).
The concepts of Latin squares and mutually orthogonal Latin squares were generalized to Latin cubes and hypercubes, and orthogonal Latin cubes and hypercubes by Kishen (1942) . [ 14 ] Rao (1946) generalized these results to arrays of strength t . The present notion of orthogonal array as a generalization of these ideas, due to legendary scientist C. R. Rao , appears in Rao (1947) , [ 15 ] with his generalization to mixed-level arrays appearing in 1973. [ 16 ]
Rao initially used the term "array" with no modifier, and defined it to mean simply a subset of all treatment combinations – a simple array. The possibility of non-simple arrays arose naturally when making treatment combinations the rows of a matrix. Hedayat, Sloane and Stufken [ 17 ] credit K. Bush [ 18 ] with the term "orthogonal array".
There exists an OA( 4λ, 4λ − 1, 2, 2) if and only if there exists a Hadamard matrix of order 4 λ . [ 19 ] To proceed in one direction, let H be a Hadamard matrix of order 4 m in standardized form (first row and column entries are all +1). Delete the first row and take the transpose to obtain the desired orthogonal array. [ 20 ] The following example illustrates this. (The reverse construction is similar.)
The order 8 standardized Hadamard matrix below (±1 entries indicated only by sign),
produces the OA(8, 7, 2, 2): [ 21 ]
Using columns 1, 2 and 4 as indexing columns, the remaining columns produce four mutually orthogonal Latin cubes of order 2.
Let C ⊆ ( F q ) n , be a linear code of dimension m with minimum distance d . Then C ⊥ (the orthogonal complement of the vector subspace C ) is a (linear) OA( q n-m , n, q, d − 1)
where λ = q n − m − d + 1 . [ 22 ]
Secret sharing (also called secret splitting ) consists of methods for distributing a secret amongst a group of participants, each of whom is allocated a share of the secret. The secret can be reconstructed only when a sufficient number of shares, of possibly different types, are combined; individual shares are of no use on their own. A secret sharing scheme is perfect if every collection of participants that does not meet the criteria for obtaining the secret, has no additional knowledge of what the secret is than does an individual with no share.
In one type of secret sharing scheme there is one dealer and n players . The dealer gives shares of a secret to the players, but only when specific conditions are fulfilled will the players be able to reconstruct the secret. The dealer accomplishes this by giving each player a share in such a way that any group of t (for threshold ) or more players can together reconstruct the secret but no group of fewer than t players can. Such a system is called a ( t , n )-threshold scheme.
An OA( v t , n+1, v, t ) may be used to construct a perfect ( t , n )-threshold scheme. [ 23 ]
A factorial experiment is a statistically structured experiment in which several factors (watering levels, antibiotics, fertilizers, etc.) are applied to each experimental unit at finitely many levels , which may be quantitative or qualitative. [ 24 ] In a full factorial experiment all combinations of levels of the factors need to be tested. In a fractional factorial design only a subset of treatment combinations are used.
An orthogonal array can be used to design a fractional factorial experiment. The columns represent the various factors and the entries are the levels at which the factors are observed. An experimental run is a row of the orthogonal array, that is, a specific combination of factor levels. The strength of the array determines the resolution of the fractional design. When using one of these designs, the treatment units and trial order should be randomized as much as the design allows. For example, one recommendation is that an appropriately sized orthogonal array be randomly selected from those available, and that the run order then be randomized.
Mixed-level designs occur naturally in the statistical setting.
Orthogonal arrays played a central role in the development of Taguchi methods by Genichi Taguchi , which took place during his visit to Indian Statistical Institute in the early 1950s. His methods were successfully applied and adopted by Japanese and Indian industries and subsequently were also embraced by US industry albeit with some reservations [ citation needed ] . Taguchi's catalog [ 25 ] contains both fixed- and mixed-level arrays.
Orthogonal array testing is a black box testing technique which is a systematic, statistical way of software testing . [ 26 ] [ 27 ] It is used when the number of inputs to the system is relatively small, but too large to allow for exhaustive testing of every possible input to the systems . [ 26 ] It is particularly effective in finding errors associated with faulty logic within computer software systems . [ 26 ] Orthogonal arrays can be applied in user interface testing, system testing , regression testing and performance testing .
The permutations of factor levels comprising a single treatment are so chosen that their responses are uncorrelated and hence each treatment gives a unique piece of information . The net effect of organizing the experiment in such treatments is that the same piece of information is gathered in the minimum number of experiments .
This article incorporates public domain material from the National Institute of Standards and Technology | https://en.wikipedia.org/wiki/Orthogonal_array |
In mathematics , particularly linear algebra , an orthogonal basis for an inner product space V {\displaystyle V} is a basis for V {\displaystyle V} whose vectors are mutually orthogonal . If the vectors of an orthogonal basis are normalized , the resulting basis is an orthonormal basis .
Any orthogonal basis can be used to define a system of orthogonal coordinates V . {\displaystyle V.} Orthogonal (not necessarily orthonormal) bases are important due to their appearance from curvilinear orthogonal coordinates in Euclidean spaces , as well as in Riemannian and pseudo-Riemannian manifolds.
In functional analysis , an orthogonal basis is any basis obtained from an orthonormal basis (or Hilbert basis) using multiplication by nonzero scalars .
The concept of an orthogonal basis is applicable to a vector space V {\displaystyle V} (over any field ) equipped with a symmetric bilinear form ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } , where orthogonality of two vectors v {\displaystyle v} and w {\displaystyle w} means ⟨ v , w ⟩ = 0 {\displaystyle \langle v,w\rangle =0} . For an orthogonal basis { e k } {\displaystyle \left\{e_{k}\right\}} : ⟨ e j , e k ⟩ = { q ( e k ) j = k 0 j ≠ k , {\displaystyle \langle e_{j},e_{k}\rangle ={\begin{cases}q(e_{k})&j=k\\0&j\neq k,\end{cases}}} where q {\displaystyle q} is a quadratic form associated with ⟨ ⋅ , ⋅ ⟩ : {\displaystyle \langle \cdot ,\cdot \rangle :} q ( v ) = ⟨ v , v ⟩ {\displaystyle q(v)=\langle v,v\rangle } (in an inner product space, q ( v ) = ‖ v ‖ 2 {\displaystyle q(v)=\Vert v\Vert ^{2}} ).
Hence for an orthogonal basis { e k } {\displaystyle \left\{e_{k}\right\}} , ⟨ v , w ⟩ = ∑ k q ( e k ) v k w k , {\displaystyle \langle v,w\rangle =\sum _{k}q(e_{k})v_{k}w_{k},} where v k {\displaystyle v_{k}} and w k {\displaystyle w_{k}} are components of v {\displaystyle v} and w {\displaystyle w} in the basis.
The concept of orthogonality may be extended to a vector space over any field of characteristic not 2 equipped with a quadratic form q ( v ) {\displaystyle q(v)} . Starting from the observation that, when the characteristic of the underlying field is not 2, the associated symmetric bilinear form ⟨ v , w ⟩ = 1 2 ( q ( v + w ) − q ( v ) − q ( w ) ) {\displaystyle \langle v,w\rangle ={\tfrac {1}{2}}(q(v+w)-q(v)-q(w))} allows vectors v {\displaystyle v} and w {\displaystyle w} to be defined as being orthogonal with respect to q {\displaystyle q} when q ( v + w ) − q ( v ) − q ( w ) = 0 {\displaystyle q(v+w)-q(v)-q(w)=0} . | https://en.wikipedia.org/wiki/Orthogonal_basis |
In geometry , two circles are said to be orthogonal if their respective tangent lines at the points of intersection are perpendicular (meet at a right angle ).
A straight line through a circle's center is orthogonal to it, and if straight lines are also considered as a kind of generalized circles , for instance in inversive geometry , then an orthogonal pair of lines or line and circle are orthogonal generalized circles.
In the conformal disk model of the hyperbolic plane , every geodesic is an arc of a generalized circle orthogonal to the circle of ideal points bounding the disk.
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orthogonal_circles |
In the mathematical fields of linear algebra and functional analysis , the orthogonal complement of a subspace W {\displaystyle W} of a vector space V {\displaystyle V} equipped with a bilinear form B {\displaystyle B} is the set W ⊥ {\displaystyle W^{\perp }} of all vectors in V {\displaystyle V} that are orthogonal to every vector in W {\displaystyle W} . Informally, it is called the perp , short for perpendicular complement . It is a subspace of V {\displaystyle V} .
Let V = ( R 5 , ⟨ ⋅ , ⋅ ⟩ ) {\displaystyle V=(\mathbb {R} ^{5},\langle \cdot ,\cdot \rangle )} be the vector space equipped with the usual dot product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } (thus making it an inner product space ), and let W = { u ∈ V : A x = u , x ∈ R 2 } , {\displaystyle W=\{\mathbf {u} \in V:\mathbf {A} x=\mathbf {u} ,\ x\in \mathbb {R} ^{2}\},} with A = ( 1 0 0 1 2 6 3 9 5 3 ) . {\displaystyle \mathbf {A} ={\begin{pmatrix}1&0\\0&1\\2&6\\3&9\\5&3\\\end{pmatrix}}.} then its orthogonal complement W ⊥ = { v ∈ V : ⟨ u , v ⟩ = 0 ∀ u ∈ W } {\displaystyle W^{\perp }=\{\mathbf {v} \in V:\langle \mathbf {u} ,\mathbf {v} \rangle =0\ \ \forall \ \mathbf {u} \in W\}} can also be defined as W ⊥ = { v ∈ V : A ~ y = v , y ∈ R 3 } , {\displaystyle W^{\perp }=\{\mathbf {v} \in V:\mathbf {\tilde {A}} y=\mathbf {v} ,\ y\in \mathbb {R} ^{3}\},} being A ~ = ( − 2 − 3 − 5 − 6 − 9 − 3 1 0 0 0 1 0 0 0 1 ) . {\displaystyle \mathbf {\tilde {A}} ={\begin{pmatrix}-2&-3&-5\\-6&-9&-3\\1&0&0\\0&1&0\\0&0&1\end{pmatrix}}.}
The fact that every column vector in A {\displaystyle \mathbf {A} } is orthogonal to every column vector in A ~ {\displaystyle \mathbf {\tilde {A}} } can be checked by direct computation. The fact that the spans of these vectors are orthogonal then follows by bilinearity of the dot product. Finally, the fact that these spaces are orthogonal complements follows from the dimension relationships given below.
Let V {\displaystyle V} be a vector space over a field F {\displaystyle \mathbb {F} } equipped with a bilinear form B . {\displaystyle B.} We define u {\displaystyle \mathbf {u} } to be left-orthogonal to v {\displaystyle \mathbf {v} } , and v {\displaystyle \mathbf {v} } to be right-orthogonal to u {\displaystyle \mathbf {u} } , when B ( u , v ) = 0. {\displaystyle B(\mathbf {u} ,\mathbf {v} )=0.} For a subset W {\displaystyle W} of V , {\displaystyle V,} define the left-orthogonal complement W ⊥ {\displaystyle W^{\perp }} to be W ⊥ = { x ∈ V : B ( x , y ) = 0 ∀ y ∈ W } . {\displaystyle W^{\perp }=\left\{\mathbf {x} \in V:B(\mathbf {x} ,\mathbf {y} )=0\ \ \forall \ \mathbf {y} \in W\right\}.}
There is a corresponding definition of the right-orthogonal complement. For a reflexive bilinear form , where B ( u , v ) = 0 ⟹ B ( v , u ) = 0 ∀ u , v ∈ V {\displaystyle B(\mathbf {u} ,\mathbf {v} )=0\implies B(\mathbf {v} ,\mathbf {u} )=0\ \ \forall \ \mathbf {u} ,\mathbf {v} \in V} , the left and right complements coincide. This will be the case if B {\displaystyle B} is a symmetric or an alternating form .
The definition extends to a bilinear form on a free module over a commutative ring , and to a sesquilinear form extended to include any free module over a commutative ring with conjugation . [ 1 ]
This section considers orthogonal complements in an inner product space H {\displaystyle H} . [ 2 ]
Two vectors x {\displaystyle \mathbf {x} } and y {\displaystyle \mathbf {y} } are called orthogonal if ⟨ x , y ⟩ = 0 {\displaystyle \langle \mathbf {x} ,\mathbf {y} \rangle =0} , which happens if and only if ‖ x ‖ ≤ ‖ x + s y ‖ ∀ {\displaystyle \|\mathbf {x} \|\leq \|\mathbf {x} +s\mathbf {y} \|\ \forall } scalars s {\displaystyle s} . [ 3 ]
If C {\displaystyle C} is any subset of an inner product space H {\displaystyle H} then its orthogonal complement in H {\displaystyle H} is the vector subspace C ⊥ : = { x ∈ H : ⟨ x , c ⟩ = 0 ∀ c ∈ C } = { x ∈ H : ⟨ c , x ⟩ = 0 ∀ c ∈ C } {\displaystyle {\begin{aligned}C^{\perp }:&=\{\mathbf {x} \in H:\langle \mathbf {x} ,\mathbf {c} \rangle =0\ \ \forall \ \mathbf {c} \in C\}\\&=\{\mathbf {x} \in H:\langle \mathbf {c} ,\mathbf {x} \rangle =0\ \ \forall \ \mathbf {c} \in C\}\end{aligned}}} which is always a closed subset (hence, a closed vector subspace) of H {\displaystyle H} [ 3 ] [ proof 1 ] that satisfies:
If C {\displaystyle C} is a vector subspace of an inner product space H {\displaystyle H} then C ⊥ = { x ∈ H : ‖ x ‖ ≤ ‖ x + c ‖ ∀ c ∈ C } . {\displaystyle C^{\bot }=\left\{\mathbf {x} \in H:\|\mathbf {x} \|\leq \|\mathbf {x} +\mathbf {c} \|\ \ \forall \ \mathbf {c} \in C\right\}.} If C {\displaystyle C} is a closed vector subspace of a Hilbert space H {\displaystyle H} then [ 3 ] H = C ⊕ C ⊥ and ( C ⊥ ) ⊥ = C {\displaystyle H=C\oplus C^{\bot }\qquad {\text{ and }}\qquad \left(C^{\bot }\right)^{\bot }=C} where H = C ⊕ C ⊥ {\displaystyle H=C\oplus C^{\bot }} is called the orthogonal decomposition of H {\displaystyle H} into C {\displaystyle C} and C ⊥ {\displaystyle C^{\bot }} and it indicates that C {\displaystyle C} is a complemented subspace of H {\displaystyle H} with complement C ⊥ . {\displaystyle C^{\bot }.}
The orthogonal complement is always closed in the metric topology. In finite-dimensional spaces, that is merely an instance of the fact that all subspaces of a vector space are closed. In infinite-dimensional Hilbert spaces , some subspaces are not closed, but all orthogonal complements are closed. If W {\displaystyle W} is a vector subspace of a Hilbert space the orthogonal complement of the orthogonal complement of W {\displaystyle W} is the closure of W , {\displaystyle W,} that is, ( W ⊥ ) ⊥ = W ¯ . {\displaystyle \left(W^{\bot }\right)^{\bot }={\overline {W}}.}
Some other useful properties that always hold are the following. Let H {\displaystyle H} be a Hilbert space and let X {\displaystyle X} and Y {\displaystyle Y} be linear subspaces. Then:
The orthogonal complement generalizes to the annihilator , and gives a Galois connection on subsets of the inner product space, with associated closure operator the topological closure of the span.
For a finite-dimensional inner product space of dimension n {\displaystyle n} , the orthogonal complement of a k {\displaystyle k} -dimensional subspace is an ( n − k ) {\displaystyle (n-k)} -dimensional subspace, and the double orthogonal complement is the original subspace: ( W ⊥ ) ⊥ = W . {\displaystyle \left(W^{\bot }\right)^{\bot }=W.}
If A ∈ M m n {\displaystyle \mathbf {A} \in \mathbb {M} _{mn}} , where R ( A ) {\displaystyle {\mathcal {R}}(\mathbf {A} )} , C ( A ) {\displaystyle {\mathcal {C}}(\mathbf {A} )} , and N ( A ) {\displaystyle {\mathcal {N}}(\mathbf {A} )} refer to the row space , column space , and null space of A {\displaystyle \mathbf {A} } (respectively), then [ 4 ] ( R ( A ) ) ⊥ = N ( A ) and ( C ( A ) ) ⊥ = N ( A T ) . {\displaystyle \left({\mathcal {R}}(\mathbf {A} )\right)^{\bot }={\mathcal {N}}(\mathbf {A} )\qquad {\text{ and }}\qquad \left({\mathcal {C}}(\mathbf {A} )\right)^{\bot }={\mathcal {N}}(\mathbf {A} ^{\operatorname {T} }).}
There is a natural analog of this notion in general Banach spaces . In this case one defines the orthogonal complement of W {\displaystyle W} to be a subspace of the dual of V {\displaystyle V} defined similarly as the annihilator W ⊥ = { x ∈ V ∗ : ∀ y ∈ W , x ( y ) = 0 } . {\displaystyle W^{\bot }=\left\{x\in V^{*}:\forall y\in W,x(y)=0\right\}.}
It is always a closed subspace of V ∗ {\displaystyle V^{*}} . There is also an analog of the double complement property. W ⊥ ⊥ {\displaystyle W^{\perp \perp }} is now a subspace of V ∗ ∗ {\displaystyle V^{**}} (which is not identical to V {\displaystyle V} ). However, the reflexive spaces have a natural isomorphism i {\displaystyle i} between V {\displaystyle V} and V ∗ ∗ {\displaystyle V^{**}} . In this case we have i W ¯ = W ⊥ ⊥ . {\displaystyle i{\overline {W}}=W^{\perp \perp }.}
This is a rather straightforward consequence of the Hahn–Banach theorem .
In special relativity the orthogonal complement is used to determine the simultaneous hyperplane at a point of a world line . The bilinear form η {\displaystyle \eta } used in Minkowski space determines a pseudo-Euclidean space of events. [ 5 ] The origin and all events on the light cone are self-orthogonal. When a time event and a space event evaluate to zero under the bilinear form, then they are hyperbolic-orthogonal . This terminology stems from the use of conjugate hyperbolas in the pseudo-Euclidean plane: conjugate diameters of these hyperbolas are hyperbolic-orthogonal. | https://en.wikipedia.org/wiki/Orthogonal_complement |
In linear algebra , an orthogonal diagonalization of a normal matrix (e.g. a symmetric matrix ) is a diagonalization by means of an orthogonal change of coordinates. [ 1 ]
The following is an orthogonal diagonalization algorithm that diagonalizes a quadratic form q ( x ) on R {\displaystyle \mathbb {R} } n by means of an orthogonal change of coordinates X = PY . [ 2 ]
Then X = PY is the required orthogonal change of coordinates, and the diagonal entries of P T A P {\displaystyle P^{T}AP} will be the eigenvalues λ 1 , … , λ n {\displaystyle \lambda _{1},\dots ,\lambda _{n}} which correspond to the columns of P .
This linear algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orthogonal_diagonalization |
In linear algebra , an orthogonal transformation is a linear transformation T : V → V on a real inner product space V , that preserves the inner product . That is, for each pair u , v of elements of V , we have [ 1 ]
Since the lengths of vectors and the angles between them are defined through the inner product, orthogonal transformations preserve lengths of vectors and angles between them. In particular, orthogonal transformations map orthonormal bases to orthonormal bases.
Orthogonal transformations are injective : if T v = 0 {\displaystyle Tv=0} then 0 = ⟨ T v , T v ⟩ = ⟨ v , v ⟩ {\displaystyle 0=\langle Tv,Tv\rangle =\langle v,v\rangle } , hence v = 0 {\displaystyle v=0} , so the kernel of T {\displaystyle T} is trivial.
Orthogonal transformations in two- or three- dimensional Euclidean space are stiff rotations , reflections , or combinations of a rotation and a reflection (also known as improper rotations ). Reflections are transformations that reverse the direction front to back, orthogonal to the mirror plane, like (real-world) mirrors do. The matrices corresponding to proper rotations (without reflection) have a determinant of +1. Transformations with reflection are represented by matrices with a determinant of −1. This allows the concept of rotation and reflection to be generalized to higher dimensions.
In finite-dimensional spaces, the matrix representation (with respect to an orthonormal basis ) of an orthogonal transformation is an orthogonal matrix . Its rows are mutually orthogonal vectors with unit norm, so that the rows constitute an orthonormal basis of V . The columns of the matrix form another orthonormal basis of V .
If an orthogonal transformation is invertible (which is always the case when V is finite-dimensional) then its inverse T − 1 {\displaystyle T^{-1}} is another orthogonal transformation identical to the transpose of T {\displaystyle T} : T − 1 = T T {\displaystyle T^{-1}=T^{\mathtt {T}}} .
Consider the inner-product space ( R 2 , ⟨ ⋅ , ⋅ ⟩ ) {\displaystyle (\mathbb {R} ^{2},\langle \cdot ,\cdot \rangle )} with the standard Euclidean inner product and standard basis. Then, the matrix transformation
is orthogonal. To see this, consider
Then,
The previous example can be extended to construct all orthogonal transformations. For example, the following matrices define orthogonal transformations on ( R 3 , ⟨ ⋅ , ⋅ ⟩ ) {\displaystyle (\mathbb {R} ^{3},\langle \cdot ,\cdot \rangle )} : | https://en.wikipedia.org/wiki/Orthogonal_transformation |
In mathematics , orthogonality is the generalization of the geometric notion of perpendicularity to linear algebra of bilinear forms .
Two elements u and v of a vector space with bilinear form B {\displaystyle B} are orthogonal when B ( u , v ) = 0 {\displaystyle B(\mathbf {u} ,\mathbf {v} )=0} . Depending on the bilinear form, the vector space may contain null vectors , non-zero self-orthogonal vectors, in which case perpendicularity is replaced with hyperbolic orthogonality .
In the case of function spaces , families of functions are used to form an orthogonal basis , such as in the contexts of orthogonal polynomials , orthogonal functions , and combinatorics .
In certain cases, the word normal is used to mean orthogonal , particularly in the geometric sense as in the normal to a surface . For example, the y -axis is normal to the curve y = x 2 {\displaystyle y=x^{2}} at the origin. However, normal may also refer to the magnitude of a vector. In particular, a set is called orthonormal (orthogonal plus normal) if it is an orthogonal set of unit vectors . As a result, use of the term normal to mean "orthogonal" is often avoided. The word "normal" also has a different meaning in probability and statistics .
A vector space with a bilinear form generalizes the case of an inner product. When the bilinear form applied to two vectors results in zero, then they are orthogonal . The case of a pseudo-Euclidean plane uses the term hyperbolic orthogonality . In the diagram, axes x′ and t′ are hyperbolic-orthogonal for any given ϕ {\displaystyle \phi } .
In Euclidean space , two vectors are orthogonal if and only if their dot product is zero, i.e. they make an angle of 90° ( π 2 {\textstyle {\frac {\pi }{2}}} radians ), or one of the vectors is zero. [ 4 ] Hence orthogonality of vectors is an extension of the concept of perpendicular vectors to spaces of any dimension.
The orthogonal complement of a subspace is the space of all vectors that are orthogonal to every vector in the subspace. In a three-dimensional Euclidean vector space, the orthogonal complement of a line through the origin is the plane through the origin perpendicular to it, and vice versa. [ 5 ]
Note that the geometric concept of two planes being perpendicular does not correspond to the orthogonal complement, since in three dimensions a pair of vectors, one from each of a pair of perpendicular planes, might meet at any angle.
In four-dimensional Euclidean space, the orthogonal complement of a line is a hyperplane and vice versa, and that of a plane is a plane. [ 5 ]
By using integral calculus , it is common to use the following to define the inner product of two functions f {\displaystyle f} and g {\displaystyle g} with respect to a nonnegative weight function w {\displaystyle w} over an interval [ a , b ] {\displaystyle [a,b]} :
In simple cases, w ( x ) = 1 {\displaystyle w(x)=1} .
We say that functions f {\displaystyle f} and g {\displaystyle g} are orthogonal if their inner product (equivalently, the value of this integral) is zero:
Orthogonality of two functions with respect to one inner product does not imply orthogonality with respect to another inner product.
We write the norm with respect to this inner product as
The members of a set of functions f i ∣ i ∈ N {\displaystyle {f_{i}\mid i\in \mathbb {N} }} are orthogonal with respect to w {\displaystyle w} on the interval [ a , b ] {\displaystyle [a,b]} if
The members of such a set of functions are orthonormal with respect to w {\displaystyle w} on the interval [ a , b ] {\displaystyle [a,b]} if
where
is the Kronecker delta .
In other words, every pair of them (excluding pairing of a function with itself) is orthogonal, and the norm of each is 1. See in particular the orthogonal polynomials .
Various polynomial sequences named for mathematicians of the past are sequences of orthogonal polynomials . In particular:
In combinatorics , two n × n {\displaystyle n\times n} Latin squares are said to be orthogonal if their superimposition yields all possible n 2 {\displaystyle n^{2}} combinations of entries. [ 6 ]
Two flat planes A {\displaystyle A} and B {\displaystyle B} of a Euclidean four-dimensional space are called completely orthogonal if and only if every line in A {\displaystyle A} is orthogonal to every line in B {\displaystyle B} . [ 7 ] In that case the planes A {\displaystyle A} and B {\displaystyle B} intersect at a single point O {\displaystyle O} , so that if a line in A {\displaystyle A} intersects with a line in B {\displaystyle B} , they intersect at O {\displaystyle O} . A {\displaystyle A} and B {\displaystyle B} are perpendicular and Clifford parallel .
In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a ( w , x , y , z ) {\displaystyle (w,x,y,z)} Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes ( x y , x z , y z ) {\displaystyle (xy,xz,yz)} that we have in 3 dimensions, and also 3 others ( w x , w y , w z ) {\displaystyle (wx,wy,wz)} . Each of the 6 orthogonal planes shares an axis with 4 of the others, and is completely orthogonal to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: x y {\displaystyle xy} and w z {\displaystyle wz} intersect only at the origin; x z {\displaystyle xz} and w y {\displaystyle wy} intersect only at the origin; y z {\displaystyle yz} and w x {\displaystyle wx} intersect only at the origin.
More generally, two flat subspaces S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} of dimensions M {\displaystyle M} and N {\displaystyle N} of a Euclidean space S {\displaystyle S} of at least M + N {\displaystyle M+N} dimensions are called completely orthogonal if every line in S 1 {\displaystyle S_{1}} is orthogonal to every line in S 2 {\displaystyle S_{2}} . If dim ( S ) = M + N {\displaystyle \dim(S)=M+N} then S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} intersect at a single point O {\displaystyle O} . If dim ( S ) > M + N {\displaystyle \dim(S)>M+N} then S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} may or may not intersect. If dim ( S ) = M + N {\displaystyle \dim(S)=M+N} then a line in S 1 {\displaystyle S_{1}} and a line in S 2 {\displaystyle S_{2}} may or may not intersect; if they intersect then they intersect at O {\displaystyle O} . [ 8 ] | https://en.wikipedia.org/wiki/Orthogonality_(mathematics) |
Orthographic projection (also orthogonal projection and analemma ) [ a ] is a means of representing three-dimensional objects in two dimensions . Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane , [ 2 ] resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection , which is a parallel projection in which the projection lines are not orthogonal to the projection plane.
The term orthographic sometimes means a technique in multiview projection in which principal axes or the planes of the subject are also parallel with the projection plane to create the primary views . [ 2 ] If the principal planes or axes of an object in an orthographic projection are not parallel with the projection plane, the depiction is called axonometric or an auxiliary views . ( Axonometric projection is synonymous with parallel projection .) Sub-types of primary views include plans , elevations , and sections ; sub-types of auxiliary views include isometric , dimetric , and trimetric projections .
A lens that provides an orthographic projection is an object-space telecentric lens .
A simple orthographic projection onto the plane z = 0 can be defined by the following matrix:
For each point v = ( v x , v y , v z ), the transformed point Pv would be
Often, it is more useful to use homogeneous coordinates . The transformation above can be represented for homogeneous coordinates as
For each homogeneous vector v = ( v x , v y , v z , 1), the transformed vector Pv would be
In computer graphics , one of the most common matrices used for orthographic projection can be defined by a 6-tuple , ( left , right , bottom , top , near , far ), which defines the clipping planes. These planes form a box with the minimum corner at ( left , bottom , - near ) and the maximum corner at ( right , top , - far ). [ 3 ]
The box is translated so that its center is at the origin, then it is scaled to the unit cube which is defined by having a minimum corner at (−1,−1,−1) and a maximum corner at (1,1,1).
The orthographic transform can be given by the following matrix:
which can be given as a scaling S followed by a translation T of the form
The inversion of the projection matrix P −1 , which can be used as the unprojection matrix is defined:
P − 1 = [ right − left 2 0 0 left + right 2 0 top − bottom 2 0 top + bottom 2 0 0 far − near − 2 − far + near 2 0 0 0 1 ] {\displaystyle P^{-1}={\begin{bmatrix}{\frac {{\text{right}}-{\text{left}}}{2}}&0&0&{\frac {{\text{left}}+{\text{right}}}{2}}\\0&{\frac {{\text{top}}-{\text{bottom}}}{2}}&0&{\frac {{\text{top}}+{\text{bottom}}}{2}}\\0&0&{\frac {{\text{far}}-{\text{near}}}{-2}}&-{\frac {{\text{far}}+{\text{near}}}{2}}\\0&0&0&1\end{bmatrix}}}
Three sub-types of orthographic projection are isometric projection , dimetric projection , and trimetric projection , depending on the exact angle at which the view deviates from the orthogonal. [ 2 ] [ 4 ] Typically in axonometric drawing, as in other types of pictorials, one axis of space is shown to be vertical.
In isometric projection , the most commonly used form of axonometric projection in engineering drawing, [ 5 ] the direction of viewing is such that the three axes of space appear equally foreshortened , and there is a common angle of 120° between them. As the distortion caused by foreshortening is uniform, the proportionality between lengths is preserved, and the axes share a common scale; this eases one's ability to take measurements directly from the drawing. Another advantage is that 120° angles are easily constructed using only a compass and straightedge .
In dimetric projection , the direction of viewing is such that two of the three axes of space appear equally foreshortened, of which the attendant scale and angles of presentation are determined according to the angle of viewing; the scale of the third direction is determined separately.
In trimetric projection , the direction of viewing is such that all of the three axes of space appear unequally foreshortened. The scale along each of the three axes and the angles among them are determined separately as dictated by the angle of viewing. Trimetric perspective is seldom used in technical drawings. [ 4 ]
In multiview projection , up to six pictures of an object are produced, called primary views , with each projection plane parallel to one of the coordinate axes of the object. The views are positioned relative to each other according to either of two schemes: first-angle or third-angle projection. In each, the appearances of views may be thought of as being projected onto planes that form a six-sided box around the object. Although six different sides can be drawn, usually three views of a drawing give enough information to make a three-dimensional object. These views are known as front view (also elevation ), top view (also plan ) and end view (also section ). When the plane or axis of the object depicted is not parallel to the projection plane, and where multiple sides of an object are visible in the same image, it is called an auxiliary view . Thus isometric projection , dimetric projection and trimetric projection would be considered auxiliary views in multiview projection. A typical characteristic of multiview projection is that one axis of space is usually displayed as vertical.
An orthographic projection map is a map projection of cartography . Like the stereographic projection and gnomonic projection , orthographic projection is a perspective (or azimuthal) projection , in which the sphere is projected onto a tangent plane or secant plane . The point of perspective for the orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from outer space , where the horizon is a great circle . The shapes and areas are distorted , particularly near the edges. [ 6 ] [ 7 ]
The orthographic projection has been known since antiquity, with its cartographic uses being well documented. Hipparchus used the projection in the 2nd century BC to determine the places of star-rise and star-set. In about 14 BC, Roman engineer Marcus Vitruvius Pollio used the projection to construct sundials and to compute sun positions. [ 7 ]
Vitruvius also seems to have devised the term orthographic – from the Greek orthos ("straight") and graphē ("drawing") – for the projection. However, the name analemma , which also meant a sundial showing latitude and longitude, was the common name until François d'Aguilon of Antwerp promoted its present name in 1613. [ 7 ]
The earliest surviving maps on the projection appear as woodcut drawings of terrestrial globes of 1509 (anonymous), 1533 and 1551 (Johannes Schöner), and 1524 and 1551 (Apian). [ 7 ] | https://en.wikipedia.org/wiki/Orthographic_projection |
OMA ( Orthologous MAtrix ) is a database of orthologs extracted from available complete genomes . [ 1 ] [ 2 ] The orthology predictions of OMA are available in several forms:
This Biological database -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orthologous_MAtrix |
An orthomode transducer ( OMT ) is a waveguide component that is commonly referred to as a polarisation duplexer . Orthomode is a contraction of orthogonal mode . Orthomode transducers serve either to combine or to separate two orthogonally polarized microwave signal paths. [ 1 ] One of the paths forms the uplink , which is transmitted over the same waveguide as the received signal path, or downlink path. Such a device may be part of a very small aperture terminal (VSAT) antenna feed or a terrestrial microwave radio feed; for example, OMTs are often used with a feed horn to isolate orthogonal polarizations of a signal and to transfer transmit and receive signals to different ports. [ 2 ]
For VSAT modems the transmission and reception paths are at 90° to each other, or in other words, the signals are orthogonally polarized with respect to each other. This orthogonal shift between the two signal paths provides approximately an isolation of 40 dB in the K u band and K a band radio frequency bands.
Hence this device serves in an essential role as the junction element of the outdoor unit (ODU) of a VSAT modem. It protects the receiver front-end element (the low-noise block downconverter , LNB) from burn-out by the power of the output signal generated by the block up converter (BUC). The BUC is also connected to the feed horn through a wave guide port of the OMT junction device.
Orthomode transducers are used in dual-polarized VSATs, in sparsely populated areas, radar antennas , radiometers , and communications links. They are usually connected to the antenna's down converter or LNB and to the high-power amplifier (HPA), attached to a transmitting antenna .
When the transmitted and received radio signal to and from the antenna have two different polarizations (horizontal and vertical), they are said to be orthogonal . This means that the modulation planes of the two radio signal waves are at 90 degrees to each other. The OMT device is used to separate two equal frequency signals, but different polarizations, of high and low signal power. Protective separation is essential as the transmitter unit would seriously damage the very sensitive low micro-voltage (μV), front-end receiver amplifier unit at the antenna.
The transmission signal of the up-link, of relatively high power (1, 2, or 5 watts for common VSAT equipment) originating from BUC and the very low power received signal power (in the order of μV) coming from the antenna to the LNB receiver unit, in this case are at an angle of 90° relative to each other, are both coupled together at the feed-horn focal-point of the parabolic antenna. The device that unites both up-link and down-link paths, which are at 90° to each other is the OMT.
In the VSAT K u band of operation case, a typical OMT provides a -40 dB isolation between each of the connected radio ports to the feed horn that faces the parabolic dish reflector (-40 dB means that only 0.01% of the transmitter's output power is cross-fed into the receiver's wave guide port). The port facing the parabolic reflector of the antenna is a circular polarizing port so that horizontal and vertical polarity coupling of inbound and outbound radio signal is easily achieved.
The 40 dB isolation provides essential protection to the very sensitive receiver amplifier against burn out from the relatively high-power signal of the transmitter unit. Further isolation may be obtained by means of selective radio frequency filtering to achieve an isolation of -100 dB (-100 dB means that only a 10 −10 fraction of the transmitter's output power is cross-fed into the wave guide port of the receiver).
The second image demonstrates two types of outdoor units, a 1-watt Hughes unit and a composite configuration of a 2-watt BUC/OMT/LNB Andrew, Swedish Microwave units.
The following images show a Portenseigne & Hirschmann K u band configuration, that highlights the horizontal the vertical, and circular polarized wave-guide ports that join to the feed-horn, the LNB or BUC elements of an outdoor unit.
An ortho-mode transducer is also a component commonly found on high capacity terrestrial microwave radio links. In this arrangement, two parabolic reflector dishes operate in a point to point microwave radio path (4 GHz to 85 GHz) with four radios, two mounted on each end. On each dish a T-shaped ortho-mode transducer is mounted at the rear of the feed, separating the signal from the feed into two separate radios, one operating in the horizontal polarity, and the other in the vertical polarity. This arrangement is used to increase the aggregate data throughput between two dishes on a point to point microwave path, or for fault-tolerance redundancy. Certain types of outdoor microwave radios have integrated orthomode transducers and operate in both polarities from a single radio unit, performing cross-polarization interference cancellation ( XPIC ) within the radio unit itself.
Alternatively, the orthomode transducer may be built into the antenna, and allow connection of separate radios, or separate ports of the same radio, to the antenna.
An ortho-mode transducer can be modelled as a 4-port device, 2 of these (H and V) representing the single-polarization ports and the remaining (h, v) embodied by the degenerate modes in the dual-polarized port.
The scattering parameters can be gathered in a 4×4 scattering matrix S {\displaystyle {\boldsymbol {S}}} , which is symmetrical for a reciprocal OMT (i.e. not including circulators , isolators or active components ), thus leaving 10 independent terms for a general lossy device:
S = [ S H H S H V S H h S H v S H V S V V S V h S V v S H h S V h S h h S h v S H v S V v S h v S v v ] {\displaystyle {\boldsymbol {S}}={\begin{bmatrix}S_{HH}&S_{HV}&S_{Hh}&S_{Hv}\\S_{HV}&S_{VV}&S_{Vh}&S_{Vv}\\S_{Hh}&S_{Vh}&S_{hh}&S_{hv}\\S_{Hv}&S_{Vv}&S_{hv}&S_{vv}\end{bmatrix}}}
Of these:
An ideal OMT exhibits perfect matching (null terms on the diagonal), unitary direct transmission terms and infinite XPD and isolation (null corresponding scattering parameters):
S = [ 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 ] {\displaystyle {\boldsymbol {S}}={\begin{bmatrix}0&0&1&0\\0&0&0&1\\1&0&0&0\\0&1&0&0\end{bmatrix}}}
Characterization of a manufactured OMT (considered the device under test, DUT) is usually a delicate matter for both mechanical and theoretical reasons.
Conceptually, if an ideal OMT is available as part of the measurement setup, often named "golden sample", its dual-polarized port can be connected to its counterpart on the DUT, resulting in a 4-port equivalent device with 4 single-polarization ports. The ideal OMT splits the two polarizations at the dual-polarized port into two standard single-polarized ports and such arrangement allows the direct measurement of all the scattering parameters of the DUT (either by using a 4-port vector network analyzer (VNA) or a 2-port one with 2 single-polarized loads used in several combinations).
Such ideal setup is only prone to mechanical uncertainties related to the physical placement and alignment of the dual-polarized ports. A simple misalignment angle ϵ {\displaystyle \epsilon } introduces an artificial path from each polarization to the opposite proportional to sin ϵ {\displaystyle \sin {\epsilon }} . The phasorial combination of the leakage S V h {\displaystyle S_{Vh}} (or S H v {\displaystyle S_{Hv}} ) due to the XPDs of DUT and this artificial loss sin ϵ {\displaystyle \sin {\epsilon }} is the actual external measured quantity. If, by proper phase recombination, the two contributions tend to cancel each other, the actual measured XPD can increase to infinity (possible only if | S V h | = | sin ϵ | {\displaystyle |S_{Vh}|=|\sin \epsilon |} ), thus resulting in a huge estimation error.
Depending on the expected XPD of the DUT, mechanical countermeasures should be introduced to guarantee that the artificial measurement uncertainty can be neglected.
Any deviation from this ideal setup, however, introduces errors and uncertainties.
If a dual-polarization matched load is available in place of the ideal OMT, this allows 2×2 measurements from the single-polarization ports, yielding only 2 of the reflection terms ( S H H {\displaystyle S_{HH}} and S H H {\displaystyle S_{HH}} ) and one IPI ( S H V {\displaystyle S_{HV}} ). Other measurements aimed at gaining estimations of the other scattering parameters of the DUT involve the dual-polarized port and require additional components, such as dual-polarized to single-polarized transitions or tapers, which are often not matched on at least one of the two polarizations: this creates undesired reflections which propagate through the OMT and combine at the VNA ports thus preventing direct measurements. These issues add to mechanical factors and enhance uncertainties in the measurement procedure.
Due to the increasing demand for high-capacity data links, the exploitation of dual-polarization has fostered research in design and characterization of OMTs to overcome the practical difficulties. The literature concerning OMT modelling and practical characterization consists of works both by academic organizations such as the National Research Council (Italy) , [ 3 ] Marche Polytechnic University and European Space Agency [ 4 ] and likewise by industrial teams such as CommScope [ 5 ] and Siae Microelettronica [ 6 ] with immediate impact on products for modern dual-polarized telecommunication systems, for instance in terrestrial microwave backhauling . | https://en.wikipedia.org/wiki/Orthomode_transducer |
In abstract algebra , an orthomorphism is a certain kind of mapping from a group into itself. Let G be a group, and let θ be a permutation of G . Then θ is an orthomorphism of G if the mapping f defined by f ( x ) = x −1 θ ( x ) is also a permutation of G . A permutation φ of G is a complete mapping if the mapping g defined by g ( x ) = xφ ( x ) is also a permutation of G . [ 1 ] Orthomorphisms and complete mappings are closely related. [ 2 ]
This abstract algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orthomorphism |
An orthonormal function system (ONS) is an orthonormal basis in a vector space of functions . [ 1 ]
This linear algebra -related article is a stub . You can help Wikipedia by expanding it .
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Orthonormal_function_system |
In linear algebra , two vectors in an inner product space are orthonormal if they are orthogonal unit vectors . A unit vector means that the vector has a length of 1, which is also known as normalized. Orthogonal means that the vectors are all perpendicular to each other. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal basis .
The construction of orthogonality of vectors is motivated by a desire to extend the intuitive notion of perpendicular vectors to higher-dimensional spaces. In the Cartesian plane , two vectors are said to be perpendicular if the angle between them is 90° (i.e. if they form a right angle ). This definition can be formalized in Cartesian space by defining the dot product and specifying that two vectors in the plane are orthogonal if their dot product is zero.
Similarly, the construction of the norm of a vector is motivated by a desire to extend the intuitive notion of the length of a vector to higher-dimensional spaces. In Cartesian space, the norm of a vector is the square root of the vector dotted with itself. That is,
Many important results in linear algebra deal with collections of two or more orthogonal vectors. But often, it is easier to deal with vectors of unit length . That is, it often simplifies things to only consider vectors whose norm equals 1. The notion of restricting orthogonal pairs of vectors to only those of unit length is important enough to be given a special name. Two vectors which are orthogonal and of length 1 are said to be orthonormal .
What does a pair of orthonormal vectors in 2-D Euclidean space look like?
Let u = (x 1 , y 1 ) and v = (x 2 , y 2 ).
Consider the restrictions on x 1 , x 2 , y 1 , y 2 required to make u and v form an orthonormal pair.
Expanding these terms gives 3 equations:
Converting from Cartesian to polar coordinates , and considering Equation ( 2 ) {\displaystyle (2)} and Equation ( 3 ) {\displaystyle (3)} immediately gives the result r 1 = r 2 = 1. In other words, requiring the vectors be of unit length restricts the vectors to lie on the unit circle .
After substitution, Equation ( 1 ) {\displaystyle (1)} becomes cos θ 1 cos θ 2 + sin θ 1 sin θ 2 = 0 {\displaystyle \cos \theta _{1}\cos \theta _{2}+\sin \theta _{1}\sin \theta _{2}=0} . Rearranging gives tan θ 1 = − cot θ 2 {\displaystyle \tan \theta _{1}=-\cot \theta _{2}} . Using a trigonometric identity to convert the cotangent term gives
It is clear that in the plane, orthonormal vectors are simply radii of the unit circle whose difference in angles equals 90°.
Let V {\displaystyle {\mathcal {V}}} be an inner-product space . A set of vectors
is called orthonormal if and only if
where δ i j {\displaystyle \delta _{ij}\,} is the Kronecker delta and ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is the inner product defined over V {\displaystyle {\mathcal {V}}} .
Orthonormal sets are not especially significant on their own. However, they display certain features that make them fundamental in exploring the notion of diagonalizability of certain operators on vector spaces.
Orthonormal sets have certain very appealing properties, which make them particularly easy to work with.
Proof of the Gram-Schmidt theorem is constructive , and discussed at length elsewhere. The Gram-Schmidt theorem, together with the axiom of choice , guarantees that every vector space admits an orthonormal basis. This is possibly the most significant use of orthonormality, as this fact permits operators on inner-product spaces to be discussed in terms of their action on the space's orthonormal basis vectors. What results is a deep relationship between the diagonalizability of an operator and how it acts on the orthonormal basis vectors. This relationship is characterized by the Spectral Theorem .
The standard basis for the coordinate space F n is
Any two vectors e i , e j where i≠j are orthogonal, and all vectors are clearly of unit length. So { e 1 , e 2 ,..., e n } forms an orthonormal basis.
When referring to real -valued functions , usually the L² inner product is assumed unless otherwise stated. Two functions ϕ ( x ) {\displaystyle \phi (x)} and ψ ( x ) {\displaystyle \psi (x)} are orthonormal over the interval [ a , b ] {\displaystyle [a,b]} if
The Fourier series is a method of expressing a periodic function in terms of sinusoidal basis functions.
Taking C [−π,π] to be the space of all real-valued functions continuous on the interval [−π,π] and taking the inner product to be
it can be shown that
forms an orthonormal set.
However, this is of little consequence, because C [−π,π] is infinite-dimensional, and a finite set of vectors cannot span it. But, removing the restriction that n be finite makes the set dense in C [−π,π] and therefore an orthonormal basis of C [−π,π]. | https://en.wikipedia.org/wiki/Orthonormality |
In material science and solid mechanics , orthotropic materials have material properties at a particular point which differ along three orthogonal axes, where each axis has twofold rotational symmetry . These directional differences in strength can be quantified with Hankinson's equation .
They are a subset of anisotropic materials , because their properties change when measured from different directions.
A familiar example of an orthotropic material is wood . In wood, one can define three mutually perpendicular directions at each point in which the properties are different. It is most stiff (and strong) along the grain (axial direction), because most cellulose fibrils are aligned that way. It is usually least stiff in the radial direction (between the growth rings), and is intermediate in the circumferential direction. This anisotropy was provided by evolution, as it best enables the tree to remain upright.
Because the preferred coordinate system is cylindrical-polar, this type of orthotropy is also called polar orthotropy .
Another example of an orthotropic material is sheet metal formed by squeezing thick sections of metal between heavy rollers. This flattens and stretches its grain structure . As a result, the material becomes anisotropic — its properties differ between the direction it was rolled in and each of the two transverse directions. This method is used to advantage in structural steel beams, and in aluminium aircraft skins.
If orthotropic properties vary between points inside an object, it possesses both orthotropy and inhomogeneity . This suggests that orthotropy is the property of a point within an object rather than for the object as a whole (unless the object is homogeneous). The associated planes of symmetry are also defined for a small region around a point and do not necessarily have to be identical to the planes of symmetry of the whole object.
Orthotropic materials are a subset of anisotropic materials ; their properties depend on the direction in which they are measured. Orthotropic materials have three planes/axes of symmetry. An isotropic material, in contrast, has the same properties in every direction. It can be proved that a material having two planes of symmetry must have a third one. Isotropic materials have an infinite number of planes of symmetry.
Transversely isotropic materials are special orthotropic materials that have one axis of symmetry (any other pair of axes that are perpendicular to the main one and orthogonal among themselves are also axes of symmetry). One common example of transversely isotropic material with one axis of symmetry is a polymer reinforced by parallel glass or graphite fibers. The strength and stiffness of such a composite material will usually be greater in a direction parallel to the fibers than in the transverse direction, and the thickness direction usually has properties similar to the transverse direction. Another example would be a biological membrane, in which the properties in the plane of the membrane will be different from those in the perpendicular direction. Orthotropic material properties have been shown to provide a more accurate representation of bone's elastic symmetry and can also give information about the three-dimensional directionality of bone's tissue-level material properties. [ 1 ]
It is important to keep in mind that a material which is anisotropic on one length scale may be isotropic on another (usually larger) length scale. For instance, most metals are polycrystalline with very small grains . Each of the individual grains may be anisotropic, but if the material as a whole comprises many randomly oriented grains, then its measured mechanical properties will be an average of the properties over all possible orientations of the individual grains.
Material behavior is represented in physical theories by constitutive relations . A large class of physical behaviors can be represented by linear material models that take the form of a second-order tensor . The material tensor provides a relation between two vectors and can be written as
where d , f {\displaystyle \mathbf {d} ,\mathbf {f} } are two vectors representing physical quantities and K {\displaystyle {\boldsymbol {K}}} is the second-order material tensor. If we express the above equation in terms of components with respect to an orthonormal coordinate system , we can write
Summation over repeated indices has been assumed in the above relation. In matrix form we have
Examples of physical problems that fit the above template are listed in the table below. [ 2 ]
The material matrix K _ _ {\displaystyle {\underline {\underline {\boldsymbol {K}}}}} has a symmetry with respect to a given orthogonal transformation ( A {\displaystyle {\boldsymbol {A}}} ) if it does not change when subjected to that transformation.
For invariance of the material properties under such a transformation we require
Hence the condition for material symmetry is (using the definition of an orthogonal transformation)
Orthogonal transformations can be represented in Cartesian coordinates by a 3 × 3 {\displaystyle 3\times 3} matrix A _ _ {\displaystyle {\underline {\underline {\boldsymbol {A}}}}} given by
Therefore, the symmetry condition can be written in matrix form as
An orthotropic material has three orthogonal symmetry planes . If we choose an orthonormal coordinate system such that the axes coincide with the normals to the three symmetry planes, the transformation matrices are
It can be shown that if the matrix K _ _ {\displaystyle {\underline {\underline {\boldsymbol {K}}}}} for a material is invariant under reflection about two orthogonal planes then it is also invariant under reflection about the third orthogonal plane.
Consider the reflection A 3 _ _ {\displaystyle {\underline {\underline {{\boldsymbol {A}}_{3}}}}} about the 1 − 2 {\displaystyle 1-2\,} plane. Then we have
The above relation implies that K 13 = K 23 = K 31 = K 32 = 0 {\displaystyle K_{13}=K_{23}=K_{31}=K_{32}=0} . Next consider a reflection A 2 _ _ {\displaystyle {\underline {\underline {{\boldsymbol {A}}_{2}}}}} about the 1 − 3 {\displaystyle 1-3\,} plane. We then have
That implies that K 12 = K 21 = 0 {\displaystyle K_{12}=K_{21}=0} . Therefore, the material properties of an orthotropic material are described by the matrix
In linear elasticity , the relation between stress and strain depend on the type of material under consideration. This relation is known as Hooke's law . For anisotropic materials Hooke's law can be written as [ 3 ]
where σ {\displaystyle {\boldsymbol {\sigma }}} is the stress tensor , ε {\displaystyle {\boldsymbol {\varepsilon }}} is the strain tensor, and c {\displaystyle {\mathsf {c}}} is the elastic stiffness tensor . If the tensors in the above expression are described in terms of components with respect to an orthonormal coordinate system we can write
where summation has been assumed over repeated indices. Since the stress and strain tensors are symmetric , and since the stress-strain relation in linear elasticity can be derived from a strain energy density function , the following symmetries hold for linear elastic materials
Because of the above symmetries, the stress-strain relation for linear elastic materials can be expressed in matrix form as
An alternative representation in Voigt notation is
or
The stiffness matrix C _ _ {\displaystyle {\underline {\underline {\mathsf {C}}}}} in the above relation satisfies point symmetry . [ 4 ]
The stiffness matrix C _ _ {\displaystyle {\underline {\underline {\mathsf {C}}}}} satisfies a given symmetry condition if it does not change when subjected to the corresponding orthogonal transformation . The orthogonal transformation may represent symmetry with respect to a point , an axis , or a plane . Orthogonal transformations in linear elasticity include rotations and reflections, but not shape changing transformations and can be represented, in orthonormal coordinates, by a 3 × 3 {\displaystyle 3\times 3} matrix A _ _ {\displaystyle {\underline {\underline {\mathbf {A} }}}} given by
In Voigt notation, the transformation matrix for the stress tensor can be expressed as a 6 × 6 {\displaystyle 6\times 6} matrix A σ _ _ {\displaystyle {\underline {\underline {{\mathsf {A}}_{\sigma }}}}} given by [ 4 ]
The transformation for the strain tensor has a slightly different form because of the choice of notation. This transformation matrix is
It can be shown that A ε _ _ T = A σ _ _ − 1 {\displaystyle {\underline {\underline {{\mathsf {A}}_{\varepsilon }}}}^{T}={\underline {\underline {{\mathsf {A}}_{\sigma }}}}^{-1}} .
The elastic properties of a continuum are invariant under an orthogonal transformation A _ _ {\displaystyle {\underline {\underline {\mathbf {A} }}}} if and only if [ 4 ]
An orthotropic elastic material has three orthogonal symmetry planes . If we choose an orthonormal coordinate system such that the axes coincide with the normals to the three symmetry planes, the transformation matrices are
We can show that if the matrix C _ _ {\displaystyle {\underline {\underline {\mathsf {C}}}}} for a linear elastic material is invariant under reflection about two orthogonal planes then it is also invariant under reflection about the third orthogonal plane.
If we consider the reflection A 3 _ _ {\displaystyle {\underline {\underline {\mathbf {A} _{3}}}}} about the 1 − 2 {\displaystyle 1-2\,} plane, then we have
Then the requirement C _ _ = A ε _ _ T C _ _ A ε _ _ {\displaystyle {\underline {\underline {\mathsf {C}}}}={\underline {\underline {{\mathsf {A}}_{\varepsilon }}}}^{T}~{\underline {\underline {\mathsf {C}}}}~{\underline {\underline {{\mathsf {A}}_{\varepsilon }}}}} implies that [ 4 ]
The above requirement can be satisfied only if
Let us next consider the reflection A 2 _ _ {\displaystyle {\underline {\underline {\mathbf {A} _{2}}}}} about the 1 − 3 {\displaystyle 1-3\,} plane. In that case
Using the invariance condition again, we get the additional requirement that
No further information can be obtained because the reflection about third symmetry plane is not independent of reflections about the planes that we have already considered. Therefore, the stiffness matrix of an orthotropic linear elastic material can be written as
The inverse of this matrix is commonly written as [ 5 ]
where E i {\displaystyle {E}_{\rm {i}}\,} is the Young's modulus along axis i {\displaystyle i} , G i j {\displaystyle G_{\rm {ij}}\,} is the shear modulus in direction j {\displaystyle j} on the plane whose normal is in direction i {\displaystyle i} , and ν i j {\displaystyle \nu _{\rm {ij}}\,} is the Poisson's ratio that corresponds to a contraction in direction j {\displaystyle j} when an extension is applied in direction i {\displaystyle i} .
The strain-stress relation for orthotropic linear elastic materials can be written in Voigt notation as
where the compliance matrix S _ _ {\displaystyle {\underline {\underline {\mathsf {S}}}}} is given by
The compliance matrix is symmetric and must be positive definite for the strain energy density to be positive. This implies from Sylvester's criterion that all the principal minors of the matrix are positive, [ 6 ] i.e.,
where S k _ _ {\displaystyle {\underline {\underline {{\mathsf {S}}_{k}}}}} is the k × k {\displaystyle k\times k} principal submatrix of S _ _ {\displaystyle {\underline {\underline {\mathsf {S}}}}} .
Then,
We can show that this set of conditions implies that [ 7 ]
or
However, no similar lower bounds can be placed on the values of the Poisson's ratios ν i j {\displaystyle \nu _{ij}} . [ 6 ] | https://en.wikipedia.org/wiki/Orthotropic_material |
An Ortman key is a coupling device used to secure two adjacent cylindrical segments of a pressure vessel common in tactical rocket motors . An Ortman key is made of elongated rectangular metal bar stock, such as steel , and is inserted into juxtaposed annular grooves around the circumference of the mating parts. The Ortman key assembly is used in high-pressure applications where packaging, strength and mass are important.
The Edmund key is a common variant of the Ortman key which is similar except has a feature added to the end of the key to aid in extraction of the key from the assembly. | https://en.wikipedia.org/wiki/Ortman_key |
Oryx—The International Journal of Conservation is a peer-reviewed academic journal of conservation science and practice, published bimonthly by Cambridge University Press on behalf of Fauna & Flora International .
The journal publishes material on biodiversity conservation , conservation policy and sustainable use, and the interaction of these subjects with social, economic and political issues. It is interdisciplinary and has a particular interest in material that has the potential to improve conservation management and practice, supports the publishing and communication aspirations of conservation researchers and practitioners worldwide and helps build capacity for conservation. Besides research Articles and Short Communications, Oryx regularly publishes Reviews, Forum Articles, Book Reviews and Letters, and every issue includes a selection of international conservation news.
The journal provides a free Writing for Conservation guide to help researchers communicate their message through well-crafted text and graphics.
The journal was established in 1904 as Journal of the Society for the Preservation of the Wild Fauna of the Empire , and is currently edited by Martin Fisher . The name changed to Journal of the Society for the Preservation of the Fauna of the Empire , and the publication acquired its current name in 1950.
This article about an environment journal is a stub . You can help Wikipedia by expanding it .
See tips for writing articles about academic journals . Further suggestions might be found on the article's talk page . | https://en.wikipedia.org/wiki/Oryx_(journal) |
Osmium tetrabromide is the inorganic compound with the formula OsBr 4 . A black solid, this compound can be produced by heating osmium tetrachloride and bromine under pressure.
As determined by X-ray crystallography , osmium tetrabromide is an inorganic polymer. It is isomorphous with platinum tetrabromide and technetium tetrachloride . As such, osmium is in octahedral coordination. Each osmium center bonds to four doubly bridging bromide ligands and two mutually cis terminal bromide ligands. [ 1 ]
OsBr 3 is the only other binary osmium bromide is that has been crystallized. [ 2 ] | https://en.wikipedia.org/wiki/OsBr4 |
Osmium(III) chloride is an inorganic chemical compound of osmium metal and chlorine with the chemical formula OsCl 3 . [ 1 ] [ 2 ]
Osmium(III) chloride can be made by a reaction of chlorine with osmium:
It can also be made by heating of osmium(IV) chloride :
Osmium(III) chloride forms black-brown crystals. [ 3 ]
Osmium(III) chloride forms a hydrate of the composition OsCl 3 ·3H 2 O with dark green crystals. [ 4 ]
Osmium(III) chloride hydrate is used as a precursor material for the production of dichlorodihydridoosmium complex compounds and other compounds. [ 5 ]
It is the precursor to a variety of arene complexes. [ 6 ] | https://en.wikipedia.org/wiki/OsCl3 |
Osmium(IV) chloride or osmium tetrachloride is the inorganic compound composed of osmium and chlorine with the empirical formula OsCl 4 . It exists in two polymorphs (crystalline forms). The compound is used to prepare other osmium complexes.
It was first reported in 1909 as the product of chlorination of osmium metal. [ 1 ] This route affords the high temperature polymorph: [ 2 ]
This reddish-black polymorph is orthorhombic and adopts a structure in which osmium centres are octahedrally coordinated, sharing opposite edges of the OsCl 6 octahedra to form a chain. [ 3 ] A brown, apparently cubic polymorph forms upon reduction of osmium tetroxide with thionyl chloride : [ 4 ]
Osmium tetraoxide dissolves in hydrochloric acid to give the hexachloroosmate anion: | https://en.wikipedia.org/wiki/OsCl4 |
Osmium hexafluoride , also osmium(VI) fluoride , (OsF 6 ) is a compound of osmium and fluorine , and one of the seventeen known binary hexafluorides .
Osmium hexafluoride is made by a direct reaction of osmium metal exposed to an excess of elemental fluorine gas at 300 °C.
Osmium hexafluoride is a yellow crystalline solid that melts at 33.4 °C and boils at 47.5 °C. [ 1 ] The solid structure measured at −140 °C is orthorhombic space group Pnma . Lattice parameters are a = 9.387 Å , b = 8.543 Å, and c = 4.944 Å. There are four formula units (in this case, discrete molecules) per unit cell , giving a density of 5.09 g·cm −3 . [ 2 ]
The OsF 6 molecule itself (the form important for the liquid or gas phase) has octahedral molecular geometry , which has point group ( O h ). The Os–F bond length is 1.827 Å. [ 2 ]
Partial hydrolysis of OsF 6 produces OsOF 4 . [ 4 ] | https://en.wikipedia.org/wiki/OsF6 |
Osmium dioxide is an inorganic compound with the formula OsO 2 . It exists as brown to black crystalline powder, but single crystals are golden and exhibit metallic conductivity. The compound crystallizes in the rutile structural motif, i.e. the connectivity is very similar to that in the mineral rutile.
OsO 2 can be obtained by the reaction of osmium with a variety of oxidizing agents, including, sodium chlorate , osmium tetroxide , and nitric oxide at about 600 °C. [ 2 ] [ 3 ] Using chemical transport , one can obtain large crystals of OsO 2 , sized up to 7x5x3 mm 3 . Single crystals show metallic resistivity of ~15 μΩ cm. A typical transport agent is O 2 via the reversible formation of volatile OsO 4 : [ 4 ]
OsO 2 does not dissolve in water, but is attacked by dilute hydrochloric acid . [ 5 ] [ 6 ] The crystals have rutile structure. [ 7 ] Unlike osmium tetroxide , OsO 2 is not toxic. [ 8 ] | https://en.wikipedia.org/wiki/OsO2 |
Osmium tetroxide (also osmium(VIII) oxide ) is the chemical compound with the formula OsO 4 . The compound is noteworthy for its many uses, despite its toxicity and the rarity of osmium . It also has a number of unusual properties, one being that the solid is volatile . The compound is colourless, but most samples appear yellow. [ 6 ] This is most likely due to the presence of the impurity OsO 2 , which is yellow-brown in colour. [ 7 ] In biology, its property of binding to lipids has made it a widely used stain in electron microscopy.
Osmium(VIII) oxide forms monoclinic crystals. [ 4 ] [ 8 ] It has a characteristic acrid chlorine -like odor. The element name osmium is derived from osme , Greek for odor . OsO 4 is volatile: it sublimes at room temperature . It is soluble in a wide range of organic solvents. It is moderately soluble in water, with which it reacts reversibly to form osmic acid (see below). [ 9 ] Pure osmium(VIII) oxide is probably colourless; [ 10 ] it has been suggested that its yellow hue is attributable due to osmium dioxide (OsO 2 ) impurities. [ 11 ] The osmium tetroxide molecule is tetrahedral and therefore nonpolar. This nonpolarity helps OsO 4 penetrate charged cell membranes.
The osmium of OsO 4 has an oxidation number of VIII; however, the metal does not possess a corresponding 8+ charge as the bonding in the compound is largely covalent in character (the ionization energy required to produce a formal 8+ charge also far exceeds the energies available in normal chemical reactions). The osmium atom exhibits double bonds to the four oxide ligands , resulting in a 16 electron complex . OsO 4 is isoelectronic with permanganate and chromate ions.
OsO 4 is formed slowly when osmium powder reacts with O 2 at ambient temperature. Reaction of bulk solid requires heating to 400 °C. [ 12 ]
Alkenes add to OsO 4 to give diolate species that hydrolyze to cis -diols. The net process is called dihydroxylation. This proceeds via a [3 + 2] cycloaddition reaction between the OsO 4 and alkene to form an intermediate osmate ester that rapidly hydrolyses to yield the vicinal diol . As the oxygen atoms are added in a concerted step, the resulting stereochemistry is cis .
OsO 4 is expensive and highly toxic, making it an unappealing reagent to use in stoichiometric amounts. However, its reactions are made catalytic by adding reoxidants to reoxidise the Os(VI) by-product back to Os(VIII). Typical reagents include H 2 O 2 ( Milas hydroxylation ), N-methylmorpholine N-oxide ( Upjohn dihydroxylation ) and K 3 Fe(CN) 6 /water. These reoxidants do not react with the alkenes on their own. Other osmium compounds can be used as catalysts, including osmate(VI) salts ([OsO 2 (OH) 4 )] 2− , and osmium trichloride hydrate (OsCl 3 · x H 2 O). These species oxidise to osmium(VIII) in the presence of such oxidants. [ 13 ]
Lewis bases such as tertiary amines and pyridines increase the rate of dihydroxylation. This "ligand-acceleration" arises via the formation of adduct OsO 4 L, which adds more rapidly to the alkene. If the amine is chiral, then the dihydroxylation can proceed with enantioselectivity (see Sharpless asymmetric dihydroxylation ). [ 14 ] OsO 4 does not react with most carbohydrates. [ 15 ]
The process can be extended to give two aldehydes in the Lemieux–Johnson oxidation , which uses periodate to achieve diol cleavage and to regenerate the catalytic loading of OsO 4 . This process is equivalent to that of ozonolysis .
OsO 4 is a Lewis acid and a mild oxidant. It reacts with alkaline aqueous solution to give the perosmate anion OsO 4 (OH) 2− 2 . [ 17 ] This species is easily reduced to osmate anion, OsO 2 (OH) 2− 4 .
When the Lewis base is an amine , adducts are also formed. Thus OsO 4 can be stored in the form of osmeth , in which OsO 4 is complexed with hexamine . Osmeth can be dissolved in tetrahydrofuran (THF) and diluted in an aqueous buffer solution to make a dilute (0.25%) working solution of OsO 4 . [ 18 ]
With tert-BuNH 2 , the imido derivative is produced:
Similarly, with NH 3 one obtains the nitrido complex :
The [Os(N)O 3 ] − anion is isoelectronic and isostructural with OsO 4 .
OsO 4 is very soluble in tert-butyl alcohol . In solution, it is readily reduced by hydrogen to osmium metal. The suspended osmium metal can be used to catalytically hydrogenate a wide variety of organic chemicals containing double or triple bonds.
OsO 4 undergoes "reductive carbonylation" with carbon monoxide in methanol at 400 K and 200 sbar to produce the triangular cluster Os 3 (CO) 12 :
Osmium forms several oxofluorides, all of which are very sensitive to moisture.
Purple cis -OsO 2 F 4 forms at 77 K in an anhydrous HF solution: [ 19 ]
OsO 4 also reacts with F 2 to form yellow OsO 3 F 2 : [ 20 ]
OsO 4 reacts with one equivalent of [Me 4 N]F at 298 K and 2 equivalents at 253 K: [ 12 ]
In organic synthesis OsO 4 is widely used to oxidize alkenes to the vicinal diols, adding two hydroxyl groups at the same side ( syn addition ). See reaction and mechanism above. This reaction has been made both catalytic ( Upjohn dihydroxylation ) and asymmetric ( Sharpless asymmetric dihydroxylation ).
Osmium(VIII) oxide is also used in catalytic amounts in the Sharpless oxyamination to give vicinal amino-alcohols.
In combination with sodium periodate , OsO 4 is used for the oxidative cleavage of alkenes ( Lemieux-Johnson oxidation ) when the periodate serves both to cleave the diol formed by dihydroxylation, and to reoxidize the OsO 3 back to OsO 4 . The net transformation is identical to that produced by ozonolysis . Below an example from the total synthesis of Isosteviol. [ 21 ]
OsO 4 is a widely used staining agent used in transmission electron microscopy (TEM) to provide contrast to the image. [ 22 ] This staining method may also be known in the literature as the OTO [ 23 ] [ 24 ] (osmium-thiocarbohydrazide-osmium) method, or osmium impregnation [ 25 ] technique or simply as osmium staining. As a lipid stain, it is also useful in scanning electron microscopy (SEM) as an alternative to sputter coating . It embeds a heavy metal directly into cell membranes, creating a high electron scattering rate without the need for coating the membrane with a layer of metal, which can obscure details of the cell membrane. In the staining of the plasma membrane , osmium(VIII) oxide binds phospholipid head regions, thus creating contrast with the neighbouring protoplasm (cytoplasm). Additionally, osmium(VIII) oxide is also used for fixing biological samples in conjunction with HgCl 2 . Its rapid killing abilities are used to quickly kill live specimens such as protozoa. OsO 4 stabilizes many proteins by transforming them into gels without destroying structural features. Tissue proteins that are stabilized by OsO 4 are not coagulated by alcohols during dehydration. [ 15 ] Osmium(VIII) oxide is also used as a stain for lipids in optical microscopy. [ 26 ] OsO 4 also stains the human cornea (see safety considerations ).
It is also used to stain copolymers preferentially, the best known example being block copolymers where one phase can be stained so as to show the microstructure of the material. For example, styrene-butadiene block copolymers have a central polybutadiene chain with polystyrene end caps. When treated with OsO 4 , the butadiene matrix reacts preferentially and so absorbs the oxide. The presence of a heavy metal is sufficient to block the electron beam, so the polystyrene domains are seen clearly in thin films in TEM .
OsO 4 is an intermediate in the extraction of osmium from its ores. Osmium-containing residues are treated with sodium peroxide (Na 2 O 2 ) forming Na 2 [OsO 4 (OH) 2 ], which is soluble. When exposed to chlorine , this salt gives OsO 4 . In the final stages of refining, crude OsO 4 is dissolved in alcoholic NaOH forming Na 2 [OsO 2 (OH) 4 ], which, when treated with NH 4 Cl , to give (NH 4 ) 4 [OsO 2 Cl 2 ]. This salt is reduced under hydrogen to give osmium. [ 9 ]
OsO 4 allowed for the confirmation of the soccer ball model of buckminsterfullerene , a 60-atom carbon allotrope . The adduct , formed from a derivative of OsO 4 , was C 60 (OsO 4 )(4- tert - butyl pyridine ) 2 . The adduct broke the fullerene's symmetry, allowing for crystallization and confirmation of the structure of C 60 by X-ray crystallography . [ 27 ]
The only known clinical use of osmium tetroxide is for the treatment of arthritis. [ 28 ] The lack of reports of long-term side effects from the local administration of osmium tetroxide (OsO 4 ) suggest that osmium itself can be biocompatible , though this depends on the osmium compound administered.
OsO 4 will irreversibly stain the human cornea , which can lead to blindness. The permissible exposure limit for osmium(VIII) oxide (8 hour time-weighted average) is 2 μg/m 3 . [ 8 ] Osmium(VIII) oxide can penetrate plastics and food packaging, and therefore must be stored in glass under refrigeration. [ 15 ] | https://en.wikipedia.org/wiki/OsO4 |
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