text stringlengths 11 320k | source stringlengths 26 161 |
|---|---|
Since quaternion algebra is division ring , then module over quaternion algebra is called vector space. Because quaternion algebra is non-commutative, we distinguish left and right vector spaces. In left vector space, linear composition of vectors v {\displaystyle v} and w {\displaystyle w} has form a v + b w {\displaystyle av+bw} where a {\displaystyle a} , b ∈ H {\displaystyle b\in H} . In right vector space, linear composition of vectors v {\displaystyle v} and w {\displaystyle w} has form v a + w b {\displaystyle va+wb} .
If quaternionic vector space has finite dimension n {\displaystyle n} , then it is isomorphic to direct sum H n {\displaystyle H^{n}} of n {\displaystyle n} copies of quaternion algebra H {\displaystyle H} . In such case we can use basis which has form
In left quaternionic vector space H n {\displaystyle H^{n}} we use componentwise sum of vectors and product of vector over scalar
In right quaternionic vector space H n {\displaystyle H^{n}} we use componentwise sum of vectors and product of vector over scalar
This linear algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Quaternionic_vector_space |
In quantum computing , a qubit ( / ˈ k juː b ɪ t / ) or quantum bit is a basic unit of quantum information —the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system , one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two spin states (left-handed and the right-handed circular polarization) can also be measured as horizontal and vertical linear polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of multiple states simultaneously, a property that is fundamental to quantum mechanics and quantum computing .
The coining of the term qubit is attributed to Benjamin Schumacher . [ 1 ] In the acknowledgments of his 1995 paper, Schumacher states that the term qubit was created in jest during a conversation with William Wootters .
A binary digit , characterized as 0 or 1, is used to represent information in classical computers. When averaged over both of its states (0,1), a binary digit can represent up to one bit of information content , where a bit is the basic unit of information . However, in this article, the word bit is synonymous with a binary digit.
In classical computer technologies, a processed bit is implemented by one of two levels of low direct current voltage , and whilst switching from one of these two levels to the other, a so-called "forbidden zone" between two logic levels must be passed as fast as possible, as electrical voltage cannot change from one level to another instantly.
There are two possible outcomes for the measurement of a qubit—usually taken to have the value "0" and "1", like a bit. However, whereas the state of a bit can only be binary (either 0 or 1), the general state of a qubit according to quantum mechanics can arbitrarily be a coherent superposition of all computable states simultaneously. [ 2 ] Moreover, whereas a measurement of a classical bit would not disturb its state, a measurement of a qubit would destroy its coherence and irrevocably disturb the superposition state. It is possible to fully encode one bit in one qubit. However, a qubit can hold more information, e.g., up to two bits using superdense coding .
A bit is always completely in either one of its two states, and a set of n bits (e.g. a processor register or some bit array) can only hold a single of its 2 n possible states at any time. A quantum state can be in a superposition state, which means that the qubit can have non-zero probability amplitude in both its states simultaneously (popularly expressed as "it can be in both states simultaneously"). A qubit requires two complex numbers to describe its two probability amplitudes, and these two complex numbers can together be viewed as a 2-dimensional complex vector , which is called a quantum state vector , or superposition state vector. Alternatively and equivalently, the value stored in a qubit can be described as a single point in a 2-dimensional complex coordinate space .
Furthermore, a set of n bits can be represented by n binary digits, simply by concatenating the representations of each of the bits, whereas a set of n qubits, which is also called a register , requires 2 n complex numbers to describe its superposition state vector. [ 3 ] [ 4 ] : 7–17 [ 2 ] : 13–17 This is because the n qubits are not independent from one another and therefore the register cannot be described by breaking it down and describing the individual qubits.
In quantum mechanics, the general quantum state of a qubit can be represented by a linear superposition of its two orthonormal basis states (or basis vectors ). These vectors are usually denoted as | 0 ⟩ = [ 1 0 ] {\displaystyle |0\rangle ={\bigl [}{\begin{smallmatrix}1\\0\end{smallmatrix}}{\bigr ]}} and | 1 ⟩ = [ 0 1 ] {\displaystyle |1\rangle ={\bigl [}{\begin{smallmatrix}0\\1\end{smallmatrix}}{\bigr ]}} . They are written in the conventional Dirac —or "bra–ket" —notation; the | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } are pronounced "ket 0" and "ket 1", respectively. These two orthonormal basis states, { | 0 ⟩ , | 1 ⟩ } {\displaystyle \{|0\rangle ,|1\rangle \}} , together called the computational basis, are said to span the two-dimensional linear vector (Hilbert) space of the qubit. [ 5 ]
Qubit basis states can also be combined to form product basis states. A set of qubits taken together is called a quantum register . For example, two qubits could be represented in a four-dimensional linear vector space spanned by the following product basis states:
| 00 ⟩ = [ 1 0 0 0 ] {\displaystyle |00\rangle ={\biggl [}{\begin{smallmatrix}1\\0\\0\\0\end{smallmatrix}}{\biggr ]}} , | 01 ⟩ = [ 0 1 0 0 ] {\displaystyle |01\rangle ={\biggl [}{\begin{smallmatrix}0\\1\\0\\0\end{smallmatrix}}{\biggr ]}} , | 10 ⟩ = [ 0 0 1 0 ] {\displaystyle |10\rangle ={\biggl [}{\begin{smallmatrix}0\\0\\1\\0\end{smallmatrix}}{\biggr ]}} , and | 11 ⟩ = [ 0 0 0 1 ] {\displaystyle |11\rangle ={\biggl [}{\begin{smallmatrix}0\\0\\0\\1\end{smallmatrix}}{\biggr ]}} .
In general, n qubits are represented by a superposition state vector in 2 n dimensional Hilbert space. [ 5 ]
A pure qubit state is a coherent superposition of the basis states. This means that a single qubit ( ψ {\displaystyle \psi } ) can be described by a linear combination of | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } :
where α and β are the probability amplitudes , and are both complex numbers . When we measure this qubit in the standard basis, according to the Born rule , the probability of outcome | 0 ⟩ {\displaystyle |0\rangle } with value "0" is | α | 2 {\displaystyle |\alpha |^{2}} and the probability of outcome | 1 ⟩ {\displaystyle |1\rangle } with value "1" is | β | 2 {\displaystyle |\beta |^{2}} . Because the absolute squares of the amplitudes equate to probabilities, it follows that α {\displaystyle \alpha } and β {\displaystyle \beta } must be constrained according to the second axiom of probability theory by the equation [ 4 ]
The probability amplitudes, α {\displaystyle \alpha } and β {\displaystyle \beta } , encode more than just the probabilities of the outcomes of a measurement; the relative phase between α {\displaystyle \alpha } and β {\displaystyle \beta } is for example responsible for quantum interference , as seen in the double-slit experiment .
It might, at first sight, seem that there should be four degrees of freedom in | ψ ⟩ = α | 0 ⟩ + β | 1 ⟩ {\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle \,} , as α {\displaystyle \alpha } and β {\displaystyle \beta } are complex numbers with two degrees of freedom each. However, one degree of freedom is removed by the normalization constraint | α | 2 + | β | 2 = 1 . This means, with a suitable change of coordinates, one can eliminate one of the degrees of freedom. One possible choice is that of Hopf coordinates :
Additionally, for a single qubit the global phase of the state e i δ {\displaystyle e^{i\delta }} has no physically observable consequences, [ a ] so we can arbitrarily choose α to be real (or β in the case that α is zero), leaving just two degrees of freedom:
where e i φ {\displaystyle e^{i\varphi }} is the physically significant relative phase . [ 7 ] [ b ]
The possible quantum states for a single qubit can be visualised using a Bloch sphere (see picture). Represented on such a 2-sphere , a classical bit could only be at the "North Pole" or the "South Pole", in the locations where | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } are respectively. This particular choice of the polar axis is arbitrary, however. The rest of the surface of the Bloch sphere is inaccessible to a classical bit, but a pure qubit state can be represented by any point on the surface. For example, the pure qubit state ( | 0 ⟩ + | 1 ⟩ ) / 2 {\displaystyle (|0\rangle +|1\rangle )/{\sqrt {2}}} would lie on the equator of the sphere at the positive X-axis. In the classical limit , a qubit, which can have quantum states anywhere on the Bloch sphere, reduces to the classical bit, which can be found only at either poles.
The surface of the Bloch sphere is a two-dimensional space , which represents the observable state space of the pure qubit states. This state space has two local degrees of freedom, which can be represented by the two angles φ {\displaystyle \varphi } and θ {\displaystyle \theta } .
A pure state is fully specified by a single ket, | ψ ⟩ = α | 0 ⟩ + β | 1 ⟩ , {\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle ,\,} a coherent superposition, represented by a point on the surface of the Bloch sphere as described above. Coherence is essential for a qubit to be in a superposition state. With interactions, quantum noise and decoherence , it is possible to put the qubit in a mixed state , a statistical combination or "incoherent mixture" of different pure states. Mixed states can be represented by points inside the Bloch sphere (or in the Bloch ball). A mixed qubit state has three degrees of freedom: the angles φ {\displaystyle \varphi } and θ {\displaystyle \theta } , as well as the length r {\displaystyle r} of the vector that represents the mixed state.
Quantum error correction can be used to maintain the purity of qubits.
There are various kinds of physical operations that can be performed on qubits.
An important distinguishing feature between qubits and classical bits is that multiple qubits can exhibit quantum entanglement ; the qubit itself is an exhibition of quantum entanglement. In this case, quantum entanglement is a local or nonlocal property of two or more qubits that allows a set of qubits to express higher correlation than is possible in classical systems.
The simplest system to display quantum entanglement is the system of two qubits. Consider, for example, two entangled qubits in the | Φ + ⟩ {\displaystyle |\Phi ^{+}\rangle } Bell state :
In this state, called an equal superposition , there are equal probabilities of measuring either product state | 00 ⟩ {\displaystyle |00\rangle } or | 11 ⟩ {\displaystyle |11\rangle } , as | 1 / 2 | 2 = 1 / 2 {\displaystyle |1/{\sqrt {2}}|^{2}=1/2} . In other words, there is no way to tell if the first qubit has value "0" or "1" and likewise for the second qubit.
Imagine that these two entangled qubits are separated, with one each given to Alice and Bob. Alice makes a measurement of her qubit, obtaining—with equal probabilities—either | 0 ⟩ {\displaystyle |0\rangle } or | 1 ⟩ {\displaystyle |1\rangle } , i.e., she can now tell if her qubit has value "0" or "1". Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice. For example, if she measures a | 0 ⟩ {\displaystyle |0\rangle } , Bob must measure the same, as | 00 ⟩ {\displaystyle |00\rangle } is the only state where Alice's qubit is a | 0 ⟩ {\displaystyle |0\rangle } . In short, for these two entangled qubits, whatever Alice measures, so would Bob, with perfect correlation, in any basis, however far apart they may be and even though both can not tell if their qubit has value "0" or "1"—a most surprising circumstance that cannot be explained by classical physics.
Controlled gates act on 2 or more qubits, where one or more qubits act as a control for some specified operation. In particular, the controlled NOT gate (CNOT or CX) acts on 2 qubits, and performs the NOT operation on the second qubit only when the first qubit is | 1 ⟩ {\displaystyle |1\rangle } , and otherwise leaves it unchanged. With respect to the unentangled product basis { | 00 ⟩ {\displaystyle \{|00\rangle } , | 01 ⟩ {\displaystyle |01\rangle } , | 10 ⟩ {\displaystyle |10\rangle } , | 11 ⟩ } {\displaystyle |11\rangle \}} , it maps the basis states as follows:
A common application of the CNOT gate is to maximally entangle two qubits into the | Φ + ⟩ {\displaystyle |\Phi ^{+}\rangle } Bell state . To construct | Φ + ⟩ {\displaystyle |\Phi ^{+}\rangle } , the inputs A (control) and B (target) to the CNOT gate are:
1 2 ( | 0 ⟩ + | 1 ⟩ ) A {\displaystyle {\frac {1}{\sqrt {2}}}(|0\rangle +|1\rangle )_{A}} ⊗ {\displaystyle \otimes } | 0 ⟩ B {\displaystyle |0\rangle _{B}} = 1 2 {\displaystyle {\frac {1}{\sqrt {2}}}} ( | 00 ⟩ + | 10 ⟩ ) {\displaystyle (|00\rangle +|10\rangle )} .
After applying CNOT, the output is the | Φ + ⟩ {\displaystyle |\Phi ^{+}\rangle } Bell State: 1 2 ( | 00 ⟩ + | 11 ⟩ ) {\displaystyle {\frac {1}{\sqrt {2}}}(|00\rangle +|11\rangle )} .
The | Φ + ⟩ {\displaystyle |\Phi ^{+}\rangle } Bell state forms part of the setup of the superdense coding , quantum teleportation , and entangled quantum cryptography algorithms.
Quantum entanglement also allows multiple states (such as the Bell state mentioned above) to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum computation that cannot be done efficiently on a classical computer. Many of the successes of quantum computation and communication, such as quantum teleportation and superdense coding, make use of entanglement, suggesting that entanglement is a resource that is unique to quantum computation. [ 8 ] A major hurdle facing quantum computing, as of 2018, in its quest to surpass classical digital computing, is noise in quantum gates that limits the size of quantum circuits that can be executed reliably. [ 9 ]
A number of qubits taken together is a qubit register . Quantum computers perform calculations by manipulating qubits within a register.
The term qudit denotes the unit of quantum information that can be realized in suitable d -level quantum systems. [ 10 ] A qubit register that can be measured to N states is identical to an N -level qudit. A rarely used [ 11 ] synonym for qudit is quNit , [ 12 ] since both d and N are frequently used to denote the dimension of a quantum system.
Qudits are similar to the integer types in classical computing, and may be mapped to (or realized by) arrays of qubits. Qudits where the d -level system is not an exponent of 2 cannot be mapped to arrays of qubits. It is for example possible to have 5-level qudits.
In 2017, scientists at the National Institute of Scientific Research constructed a pair of qudits with 10 different states each, giving more computational power than 6 qubits. [ 13 ]
In 2022, researchers at the University of Innsbruck succeeded in developing a universal qudit quantum processor with trapped ions. [ 14 ] In the same year, researchers at Tsinghua University 's Center for Quantum Information implemented the dual-type qubit scheme in trapped ion quantum computers using the same ion species. [ 15 ] In 2025, the Innsbruck team managed to simulate two-dimensional lattice gauge theories on their qudit quantum computer. [ 16 ]
Also in 2022, researchers at the University of California, Berkeley developed a technique to dynamically control the cross-Kerr interactions between fixed-frequency qutrits, achieving high two-qutrit gate fidelities. [ 17 ] This was followed by a demonstration of extensible control of superconducting qudits up to d = 4 {\displaystyle d=4} in 2024 based on programmable two-photon interactions. [ 18 ]
Similar to the qubit, the qutrit is the unit of quantum information that can be realized in suitable 3-level quantum systems. This is analogous to the unit of classical information trit of ternary computers . [ 19 ] Besides the advantage associated with the enlarged computational space, the third qutrit level can be exploited to implement efficient compilation of multi-qubit gates. [ 18 ] [ 20 ] [ 21 ]
Any two-level quantum-mechanical system can be used as a qubit. Multilevel systems can be used as well, if they possess two states that can be effectively decoupled from the rest (e.g., the ground state and first excited state of a nonlinear oscillator). There are various proposals. Several physical implementations that approximate two-level systems to various degrees have been successfully realized. Similarly to a classical bit, where the state of a transistor in a processor, the magnetization of a surface in a hard disk , and the presence of current in a cable can all be used to represent bits in the same computer, an eventual quantum computer is likely to use various combinations of qubits in its design.
All physical implementations are affected by noise. The so-called T 1 lifetime and T 2 dephasing time are a time to characterize the physical implementation and represent their sensitivity to noise. A higher time does not necessarily mean that one or the other qubit is better suited for quantum computing because gate times and fidelities need to be considered, too.
Different applications like quantum sensing , quantum computing and quantum communication use different implementations of qubits to suit their application.
The following is an incomplete list of physical implementations of qubits, and the choices of basis are by convention only.
In 2008 a team of scientists from the U.K. and U.S. reported the first relatively long (1.75 seconds) and coherent transfer of a superposition state in an electron spin "processing" qubit to a nuclear spin "memory" qubit. [ 24 ] This event can be considered the first relatively consistent quantum data storage, a vital step towards the development of quantum computing . In 2013, a modification of similar systems (using charged rather than neutral donors) has dramatically extended this time, to 3 hours at very low temperatures and 39 minutes at room temperature. [ 25 ] Room temperature preparation of a qubit based on electron spins instead of nuclear spin was also demonstrated by a team of scientists from Switzerland and Australia. [ 26 ] An increased coherence of qubits is being explored by researchers who are testing the limitations of a Ge hole spin-orbit qubit structure. [ 27 ] | https://en.wikipedia.org/wiki/Qubit |
The Qubit fluorometer is a laboratory instrument developed and distributed by Invitrogen , which is now a part of Thermo Fisher . It is used for the quantification of DNA , RNA , and protein . [ 1 ] [ 2 ] [ 3 ] [ 4 ]
The Qubit fluorometer method is to use fluorescent dyes to determine the concentration of either nucleic acids or proteins in a sample. Specialized fluorescent dyes bind specifically to the substances of interest. A spectrophotometer is used in this method to measure the natural absorbance of light at 260 nm (for DNA and RNA) or 280 nm (for proteins). [ 5 ] [ 6 ] [ 7 ] [ 8 ]
The Qubit assays (formerly known as Quant-iT) were previously developed and manufactured by Molecular Probes (now part of Life Technologies ). Each dye is specialized for one type of molecule (DNA, RNA, or protein). These dyes exhibit extremely low fluorescence until bound to their target molecule. Upon binding to DNA, the dye molecules assume a more rigid shape and increase in fluorescence by several orders of magnitude, most likely due to intercalation between the bases. [ 9 ] [ 10 ]
The Qubit fluorometer, a device designed to measure fluorescence signals from samples, operates by correlating these signals with known concentrations of probes. This process enables it to transform the fluorescence data into a quantified concentration measurement. The device uses this established relationship to accurately determine the concentration of a sample.
A specific instance of this technology is the Qubit 2.0 fluorometer, which is often used in conjunction with the "dsDNA BR Assay Kit." This kit, along with others in the Qubit quantification system, incorporates dyes. These dyes are sensitive to different biomolecules and their concentrations. In this context, "ds" denotes double-stranded and "ss" signifies single-stranded DNA, indicating the specific types of DNA that the dyes can detect.
The second generation, the Qubit 2.0 Fluorometer, was released in 2010, and the 3rd generation as Qubit 3.0 in 2014. The newest version is the 4th generation Qubit 4, introduced in 2017. | https://en.wikipedia.org/wiki/Qubit_fluorometer |
In computer science , a queap is a priority queue data structure . The data structure allows insertions and deletions of arbitrary elements, as well as retrieval of the highest-priority element. Each deletion takes amortized time logarithmic in the number of items that have been in the structure for a longer time than the removed item. Insertions take constant amortized time.
The data structure consists of a doubly linked list and a 2–4 tree data structure, each modified to keep track of its minimum-priority element. The basic operation of the structure is to keep newly inserted elements in the doubly linked list, until a deletion would remove one of the list items, at which point they are all moved into the 2–4 tree. The 2–4 tree stores its elements in insertion order, rather than the more conventional priority-sorted order.
Both the data structure and its name were devised by John Iacono and Stefan Langerman . [ 1 ]
A queap is a priority queue that inserts elements in O (1) amortized time, and removes the minimum element in O (log( k + 2)) if there are k items that have been in the heap for a longer time than the element to be extracted. The queap has a property called the queueish property: the time to search for element x is O(lg q ( x )) where q ( x ) is equal to n − 1 − w ( x ) and w ( x ) is the number of distinct items that has been accessed by operations such as searching, inserting, or deleting. q ( x ) is defined as how many elements have not been accessed since x 's last access. Indeed, the queueish property is the complement of the splay tree working set property: the time to search for element x is O (lg w ( x )).
A queap can be represented by two data structures: a doubly linked list and a modified version of 2–4 tree. The doubly linked list, L , is used for a series of insert and locate-min operations. The queap keeps a pointer to the minimum element stored in the list. To add element x to list l , the element x is added to the end of the list and a bit variable in element x is set to one. This operation is done to determine if the element is either in the list or in a 2–4 tree.
A 2–4 tree is used when a delete operation occurs. If the item x is already in tree T , the item is removed using the 2–4 tree delete operation. Otherwise, the item x is in list L (done by checking if the bit variable is set). All the elements stored in list L are then added to the 2–4 tree, setting the bit variable of each element to zero. x is then removed from T .
A queap uses only the 2–4 tree structure properties, not a search tree. The modified 2–4 tree structure is as follows. Suppose list L has the following set of elements: x 1 , x 2 , x 3 , … , x k {\displaystyle x_{1},x_{2},x_{3},\dots ,x_{k}} . When the deletion operation is invoked, the set of elements stored in L is then added to the leaves of the 2–4 tree in that order, proceeded by a dummy leaf containing an infinite key. Each internal node of T has a pointer h v {\displaystyle h_{v}} , which points to the smallest item in subtree v . Each internal node on path P from the root to x 0 {\displaystyle x_{0}} has a pointer c v {\displaystyle c_{v}} , which points to the smallest key in T − T v − { r } {\displaystyle T-T_{v}-\{r\}} . The h v {\displaystyle h_{v}} pointers of each internal node on path P are ignored. The queap has a pointer to c x 0 {\displaystyle c_{x_{0}}} , which points to the smallest element in T .
An application of queaps includes a unique set of high priority events and extraction of the highest priority event for processing.
Let minL be a pointer that points to the minimum element in the doubly linked list L , c x 0 {\displaystyle c_{x_{0}}} be the minimum element stored in the 2–4 tree, T , k be the number of elements stored in T , and n be the total number of elements stored in queap Q . The operations are as follows:
New(Q): Initializes a new empty queap.
Insert(Q, x): Add the element x to queap Q .
Minimum(Q): Retrieve a pointer to the smallest element from queap Q .
Delete(Q, x): Remove element x from queap Q .
DeleteMin(Q): Delete and return the smallest element from queap Q .
CleanUp(Q): Delete all the elements in list L and tree T .
The running time is analyzed using the amortized analysis . The potential function for queap Q will be ϕ ( Q ) = c | L | {\displaystyle \phi (Q)=c|L|} where Q = ( T , L ) {\displaystyle Q=(T,L)} .
Insert(Q, x): The cost of the operation is O(1) . The size of list L grows by one, the potential increases by some constant c .
Minimum(Q): The operation does not alter the data structure so the amortized cost is equal to its actual cost, O(1).
Delete(Q, x): There are two cases.
If x is in tree T , then the amortized cost is not modified. The delete operation is O(1) amortized 2–4 tree. Since x was removed from the tree, h v {\displaystyle h_{v}} and c v {\displaystyle c_{v}} pointers may need updating. At most, there will be O ( l g q ( x ) ) {\displaystyle O(lgq(x))} updates.
If x is in list L , then all the elements from L are inserted in T . This has a cost of a | L | {\displaystyle a|L|} of some constant a , amortized over the 2–4 tree. After inserting and updating the h v {\displaystyle h_{v}} and c v {\displaystyle c_{v}} pointers, the total time spent is bounded by 2 a | L | {\displaystyle 2a|L|} . The second operation is to delete x from T , and to walk on the path from x to x 0 {\displaystyle x_{0}} , correcting h v {\displaystyle h_{v}} and c v {\displaystyle c_{v}} values. The time is spent at most 2 a | L | + O ( l g q ( x ) ) {\displaystyle 2a|L|+O(lgq(x))} . If c > 2 a {\displaystyle c>2a} , then the amortized cost will be O ( l g q ( x ) ) {\displaystyle O(lgq(x))} . Delete(Q, x): is the addition of the amortized cost of Minimum(Q) and Delete(Q, x) , which is O ( l g q ( x ) ) {\displaystyle O(lgq(x))} .
A small Java implementation of a queap: | https://en.wikipedia.org/wiki/Queap |
Queen's Metal , an alloy of nine parts [ 1 ] tin and one each of antimony , lead , and bismuth , is intermediate in hardness between pewter and britannia metal . It was developed by English pewtersmiths in the 16th century; [ 2 ] the recipe was initially a secret and was reserved for pieces made for the English royal family .
This article incorporates text from a publication now in the public domain : Wood, James , ed. (1907). " Queen's Metal ". The Nuttall Encyclopædia . London and New York: Frederick Warne.
This alloy-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Queen's_metal |
A queen post is a tension member in a truss that can span longer openings than a king post truss. A king post uses one central supporting post, whereas the queen post truss uses two. [ 1 ] Even though it is a tension member, rather than a compression member, they are commonly still called a post . A queen post is often confused with a queen strut, one of two compression members in roof framing which do not form a truss in the engineering sense. [ 2 ]
The double punch truss appeared in Central Europe during the Renaissance . [ 3 ]
A queen-post bridge has two uprights, placed about one-third of the way from each end of the truss. They are connected across the top by a beam and use a diagonal brace between the outer edges. The central square between the two verticals is either unbraced (on shorter spans), or has one or two diagonal braces for rigidity. A single diagonal reaches between opposite corners; two diagonal braces may either reach from the bottom of each upright post to the center of the upper beam, or form a corner-to-corner "X" inside the square. [ 4 ]
This architectural element –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Queen_post |
The Wood Reference Collection is a Queensland Government scientific collection based in Queensland , Australia . It is the oldest xylotheque (also known as a xylarium) of authenticated wood specimens in Australia and the third largest in the nation. [ 1 ] It consists of 21 separate collections of wood block samples, including 17 international collections, and a glass slide collection of timber microstructure sections. [ 2 ] Together, they provide a comprehensive reference collection of anatomical characteristics for Queensland timbers, and some national and international timbers. [ 2 ]
The Wood Reference Collection supports activities integral to the:
The Wood Reference Collection was first established in the 1880's as a legacy of Australia sending wood samples to international exhibitions to promote their timber exports. The Wood Reference Collection is the only xylarium in Australia still in use for the identification of wood specimens. It is also the only public collection for the accurate identification of processed wood. The services of the collection are open for government and the public (on a fee-for-service basis), helping to ascertain the provenance of any processed wood piece, including furniture, cultural products or architecture, among others. In Queensland, the expertise connected to the collection is regularly used for insurance investigations, forensic examination and to assure compliance with trade and import laws.
The collection includes: [ 2 ]
The Wood Reference Collection is a unique collection of mainly Queensland timbers assembled by government botanists collecting plant materials since the 1880s. [ 3 ] Once a tree has been removed from its environment and the wood has been processed, it can often be hard to identify the provenance or age of a specific piece. The wood blocks and microscope samples held at the Wood Reference Collection are invaluable as the provenance of a specific piece can influence how its value is determined.
In art history, the wood used by specific artists or furniture makers (for antiques) is often very characteristic. The frame of a painting or the type of wood used to make a stool can give crucial information when investigating whether an object is genuine or a replica.
Similarly, anthropological studies on cultural objects or forensic studies on weapons often benefit from wood identification services. [ 1 ] Specific cultures might have favoured specific wood types for ritual purposes, giving a clue as to the use of found objects. [ 1 ] The Queensland Police Service Ballistic Unit have used the collection to identify the type and origin of wooden firearm stocks, and archaeologists working on structures such as a heritage listed timber bridge in Beaudesert, Queensland , the Wickham Terrace Tower Mill ( The Old Windmill, Brisbane ), the Cato (1800 ship) (wrecked on the Wreck Reefs ) and many others have also benefitted from wood identification services. [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Queensland_Wood_Reference_Collection |
The Quelet reaction (also called the Blanc–Quelet reaction ) is an organic coupling reaction in which a phenolic ether reacts with an aliphatic aldehyde to generate an α-chloroalkyl derivative. [ 1 ] The Quelet reaction is an example of a larger class of reaction, electrophilic aromatic substitution . The reaction is named after its creator R. Quelet, who first reported the reaction in 1932, [ 2 ] and is similar to the Blanc chloromethylation process.
The reaction proceeds under strong acid catalysis using HCl; zinc(II) chloride may be used as a catalyst in instances where the ether is deactivated. [ 3 ] The reaction primarily yields para-substituted products; however it can also produce ortho-substituted compounds if the para site is blocked.
The mechanism [ 4 ] of the Quelet reaction is primarily categorized as a reaction in polar acid. First, the carbonyl is protonated forming a highly reactive protonated aldehyde that acts as the electrophile to the nucleophilic pi-bond of the aromatic ring. Next, the aromatic ring is reformed via E1 . Finally, the hydroxy group formed from the carbonyl oxygen is protonated a second time and leaves as a molecule of water, creating a carbocation that is attacked by the negatively charged chlorine ion.
The reaction requires a strong acid catalyst, but both Lewis acids and Brownsted-Lowry acids can be used in the Quelet reaction. [ 5 ] It has been noted that aqueous formaldehyde sometimes produces a better yield than paraformaldehyde . [ 4 ] The reaction was first reported using zinc(II) chloride, however the reaction has been noted to proceed in the absence of this catalyst in highly activated aromatic compounds. [ 1 ] If using an aromatic compound where the para-site is blocked, the reaction will add in the ortho-position (see example right).
Not all aromatic compounds can undergo Quelet reactions. For example, too highly halogenated aromatic compounds, aromatic compounds with nitro groups , and terphenyls cannot be used as reactants for Quelet reactions. [ 6 ] Even for compounds that can undergo Quelet reactions, there sometimes exists other reactions that produce the same products in higher yields. [ 7 ] The Quelet reaction can produce dangerous halomethyl ethers , gaseous and liquid compounds that are toxic to humans, and therefore is sometimes passed up for chloromethylations without these harmful byproducts. [ 8 ]
The Quelet reaction is an important step in the polymerization of aromatic monomers , such as styrene , PPO and PPEK. [ 5 ] These chloromethylated aromatic polymers are used in a diverse set of industries, such as fuel cells and membranes for drug delivery . [ 9 ] [ 10 ] | https://en.wikipedia.org/wiki/Quelet_reaction |
The quellung reaction , also called the Neufeld reaction , is a biochemical reaction in which antibodies bind to the bacterial capsule of Streptococcus pneumoniae , Klebsiella pneumoniae , Neisseria meningitidis , Bacillus anthracis , Haemophilus influenzae , [ 1 ] Escherichia coli , and Salmonella . The antibody reaction allows these species to be visualized under a microscope . If the reaction is positive, the capsule becomes opaque and appears to enlarge.
Quellung is the German word for "swelling" and describes the microscopic appearance of pneumococcal or other bacterial capsules after their polysaccharide antigen has combined with a specific antibody. The antibody usually comes from serum taken from an immunized laboratory animal. As a result of this combination, and precipitation of the large, complex molecule formed, the capsule appears to swell, because of increased surface tension, and its outlines become demarcated.
The pneumococcal quellung reaction was first described in 1902 by the scientist Fred Neufeld , and applied only to Streptococcus pneumoniae , both as microscopic capsular swelling and macroscopic agglutination (clumping visible with the naked eye). [ 2 ] It was initially an intellectual curiosity more than anything else, and could distinguish only the three pneumococcal serotypes known at that time. However, it acquired an important practical use with the advent of serum therapy to treat certain types of pneumococcal pneumonia in the 1920s because selection of the proper antiserum to treat an individual patient required correct identification of the infecting pneumococcal serotype, and the quellung reaction was the only method available to do this. Dr. Albert Sabin made modifications to Neufeld's technique so that it could be done more rapidly, [ 3 ] and other scientists expanded the technique to identify 29 additional serotypes. [ 4 ]
Application of Neufeld’s discoveries to other important areas of research came when Fred Griffith showed that pneumococci could transfer information to transform one serotype into another. [ 5 ] Oswald Avery , Colin MacLeod , and Maclyn McCarty later showed that the transforming factor was deoxyribonucleic acid, or DNA . [ 6 ]
Serum therapy for infectious diseases was displaced by antibiotics in the 1940s, but identification of specific serotypes remained important as the understanding of the epidemiology of pneumococcal infections still required their identification to determine where different serotypes spread, as well as the variable invasiveness of different serotypes. Understanding the prevalence of various serotypes was also critical to the development of pneumococcal vaccines to prevent invasive infections.
The quellung reaction has been used to identify the 93 known capsular serotypes of Streptococcus pneumoniae in diagnostic settings, but in recent years it has been challenged by the latex agglutination method , and further by molecular typing techniques such as the polymerase chain reaction , which detect DNA and therefore target genetic differences between serotypes. [ 7 ] Currently, there are 100 known capsular serotypes. [ 8 ] | https://en.wikipedia.org/wiki/Quellung_reaction |
A quench press is a machine that uses concentrated forces to hold an object as it is quenched. These types of quench facilities are used to quench large gears and other circular parts so that they remain circular. They are also used to quench saw blades and other flat or plate-shaped objects so that they remain flat. [ 1 ]
Quench presses are able to quench the part while it is being held because of the unique structure of the clamps holding the part. Clamps are slotted so that oil or water can flow through each slot and cool the part and the ribs of the clamps can hold the part in place. | https://en.wikipedia.org/wiki/Quench_press |
In chemistry , quenching refers to any process which decreases the fluorescent intensity of a given substance. A variety of processes can result in quenching, such as excited state reactions, energy transfer, complex -formation and collisions . As a consequence, quenching is often heavily dependent on pressure and temperature . Molecular oxygen , iodine ions and acrylamide [ 1 ] are common chemical quenchers. The chloride ion is a well known quencher for quinine fluorescence. [ 2 ] [ 3 ] [ 4 ] Quenching poses a problem for non-instant spectroscopic methods, such as laser-induced fluorescence .
Quenching is made use of in optode sensors; for instance the quenching effect of oxygen on certain ruthenium complexes allows the measurement of oxygen saturation in solution. Quenching is the basis for Förster resonance energy transfer (FRET) assays. [ 5 ] [ 6 ] [ 7 ] Quenching and dequenching upon interaction with a specific molecular biological target is the basis for activatable optical contrast agents for molecular imaging . [ 8 ] [ 9 ] Many dyes undergo self-quenching, which can decrease the brightness of protein-dye conjugates for fluorescence microscopy , [ 10 ] or can be harnessed in sensors of proteolysis . [ 11 ]
There are a few distinct mechanisms by which energy can be transferred non-radiatively (without absorption or emission of photons) between two dyes, a donor and an acceptor. Förster resonance energy transfer (FRET or FET) is a dynamic quenching mechanism because energy transfer occurs while the donor is in the excited state. FRET is based on classical dipole-dipole interactions between the transition dipoles of the donor and acceptor and is extremely dependent on the donor-acceptor distance, R , falling off at a rate of 1/ R 6 . FRET also depends on the donor-acceptor spectral overlap (see figure) and the relative orientation of the donor and acceptor transition dipole moments. FRET can typically occur over distances up to 100 Å.
Dexter (also known as Dexter exchange or collisional energy transfer, colloquially known as D exter E nergy T ransfer) is another dynamic quenching mechanism. [ 12 ] Dexter electron transfer is a short-range phenomenon that falls off exponentially with distance (proportional to e − kR where k is a constant that is the inverse of the sum of both van der Waals radius of the atom over 2 [ 13 ] ) and depends on spatial overlap of donor and quencher molecular orbitals. In most donor-fluorophore–quencher-acceptor situations, the Förster mechanism is more important than the Dexter mechanism. With both Förster and Dexter energy transfer, the shapes of the absorption and fluorescence spectra of the dyes are unchanged.
Dexter electron transfer can be significant between the dye and the solvent especially when hydrogen bonds are formed between them.
Exciplex (excited state complex) formation is a third dynamic quenching mechanism.
The remaining energy transfer mechanism is static quenching (also referred to as contact quenching). Static quenching can be a dominant mechanism for some reporter-quencher probes. Unlike dynamic quenching, static quenching occurs when the molecules form a complex in the ground state, i.e. before excitation occurs. The complex has its own unique properties, such as being nonfluorescent and having a unique absorption spectrum . Dye aggregation is often due to hydrophobic effects—the dye molecules stack together to minimize contact with water. Planar aromatic dyes that are matched for association through hydrophobic forces can enhance static quenching. High temperatures and addition of surfactants tend to disrupt ground state complex formation.
Collisional quenching occurs when the excited fluorophore experiences contact with an atom or molecule that can facilitate non-radiative transitions to the ground state. ... Excited-state molecule collides with quencher molecule and returns to ground state non-radiatively. | https://en.wikipedia.org/wiki/Quenching_(fluorescence) |
Quenching , in the context of pollution scrubbers , refers to the cooling of hot exhaust gas by water sprays before it enters the scrubber proper. Hot gases (those above ambient temperature) are often cooled to near the saturation level. If not cooled, the hot gas stream can evaporate a large portion of the scrubbing liquor, adversely affecting collection efficiency and damaging scrubber internal parts. If the gases entering the scrubber are too hot, some liquid droplets may evaporate before they have a chance to contact pollutants in the exhaust stream, and others may evaporate after contact, causing captured particles to become reentrained. In some cases, quenching can actually save money. Cooling the gases reduces the temperature and, therefore, the volume of gases, permitting the use of less expensive construction materials and a smaller scrubber vessel and fan.
A quenching system can be as simple as spraying liquid into the duct just preceding the main scrubbing vessel, or it can be a separate chamber (or tower) with its own spray system identical to a spray tower . Quenchers are designed using the same principles as scrubbers. Increasing the gas-liquid contact in them increases their operational efficiency.
Small liquid droplets cool the exhaust stream more quickly than large droplets because they evaporate more easily. Therefore, less liquid is required. However, in most scrubbing systems, approximately one-and-a-half to two and- a-half times the theoretical evaporation demand is required to ensure proper cooling. [ 1 ] Evaporation also depends on time; it does not occur instantaneously. Therefore, the quencher should be sized to allow for an adequate exhaust stream residence time. Normal residence times range from 0.15 to 0.25 seconds for gases under 540°C (1000°F) to 0.2 to 0.3 seconds for gases hotter than 540°C. [ 2 ]
Quenching with recirculated scrubber liquor could potentially reduce overall scrubber performance, since recycled liquid usually contains a high level of suspended and dissolved solids. As the liquid droplets evaporate, these solids could become re-entrained in the exhaust gas stream. To help reduce this problem, clean makeup water can be added directly to the quench system rather than adding all makeup water to a common sump . [ 3 ] | https://en.wikipedia.org/wiki/Quenching_(scrubber) |
Quentin Meillassoux ( / m eɪ . ə ˈ s uː / ; [ 2 ] French: [mɛjasu] ; born 26 October 1967) [ 3 ] is a French philosopher. He teaches at the Université Paris 1 Panthéon-Sorbonne .
Quentin Meillassoux is the son of the anthropologist Claude Meillassoux . He is a former student of the philosophers Bernard Bourgeois and Alain Badiou . He is married to the novelist and philosopher Gwenaëlle Aubry . [ 4 ]
Meillassoux's first book is After Finitude ( Après la finitude , 2006). Alain Badiou, Meillassoux's former teacher, wrote the foreword . [ 5 ] Badiou describes the work as introducing a new possibility for philosophy which is different from Immanuel Kant 's three alternatives of criticism , skepticism , and dogmatism . [ 6 ] The book was translated into English by Ray Brassier . Meillassoux is associated with the speculative realism movement.
In this book, Meillassoux argues that post-Kantian philosophy is dominated by what he calls " correlationism ", the theory that humans cannot exist without the world nor the world without humans. [ 7 ] In Meillassoux's view, this theory allows philosophy to avoid the problem of how to describe the world as it really is independent of human knowledge. He terms this reality independent of human knowledge as the "ancestral" realm. [ 8 ] Following the commitment to mathematics of his mentor Alain Badiou, Meillassoux claims that mathematics describes the primary qualities of things as opposed to their secondary qualities shown by perception .
Meillassoux argues that in place of the agnostic scepticism about the reality of cause and effect , there should be a radical certainty that there is no causality at all. Following the rejection of causality, Meillassoux says that it is absolutely necessary that the laws of nature be contingent. The world is a kind of hyper-chaos in which the principle of sufficient reason is not necessary although Meillassoux says that the principle of non-contradiction is necessary.
For these reasons, Meillassoux rejects Kant's Copernican Revolution in philosophy. Since Kant makes the world dependent on the conditions by which humans observe it, Meillassoux accuses Kant of a "Ptolemaic Counter-Revolution." Meillassoux clarified and revised some of the views published in After Finitude during his lectures at the Free University of Berlin in 2012. [ 9 ]
Several of Meillassoux's articles have appeared in English via the British philosophical journal Collapse , helping to spark interest in his work in the Anglophone world.
His unpublished dissertation L'inexistence divine (1997) is noted in After Finitude to be "forthcoming" in book form; [ 10 ] as of 2021, it had not yet been published. In Parrhesia , in 2016, an excerpt from Meillassoux's dissertation was translated by Nathan Brown, who noted in his introduction that "what is striking about the document... is the marked difference of its rhetorical strategies, its order of reasons, and its philosophical style" from After Finitude , counter to the general view that the latter merely constituted "a partial précis" of L'inexistence divine ; he notes further that the dissertation presents a "very different articulation of the Principle of Factiality" from that in After Finitude . [ 11 ] While Nathan Brown's translation uses the French text of the 1997 dissertation, in 2011 Graham Harman used a 2003 revision to offer a partial translation of Meillassoux's ongoing work of expanding the dissertation into a book.
In September 2011, Meillassoux's book on Stéphane Mallarmé was published in France under the title Le nombre et la sirène. Un déchiffrage du coup de dés de Mallarmé . [ 12 ] In this second book, he offers a detailed reading of Mallarmé's famous poem " Un coup de dés jamais n'abolira le hasard " ("A Throw of the Dice Will Never Abolish Chance"), in which he finds a numerical code at work in the text. [ 13 ] | https://en.wikipedia.org/wiki/Quentin_Meillassoux |
Quest Diagnostics Incorporated is an American clinical laboratory . A Fortune 500 company, Quest operates in the United States , Puerto Rico , Mexico , and Brazil . [ 3 ] Quest also maintains collaborative agreements with various hospitals and clinics across the globe. [ 4 ]
As of 2020, the company had approximately 48,000 employees, and it generated more than $7.7 billion in revenue in 2019. [ 5 ] [ 6 ] The company offers access to diagnostic testing services for cancer , cardiovascular disease , infectious disease, neurological disorders , COVID-19 , and employment and court-ordered drug testing . [ 7 ]
Originally founded as Metropolitan Pathology Laboratory, Inc. in 1967 by Paul A. Brown, MD , the clinical laboratory underwent a variety of name changes. [ 8 ] In 1969, the company's name changed to MetPath, Inc. [ 9 ] with headquarters in Teaneck, New Jersey . By 1982, MetPath was acquired by what was then known as Corning Glass Works [ 10 ] and was subsequently renamed Corning Clinical Laboratories. [ 11 ]
On December 31, 1996, Quest Diagnostics became an independent company as a spin-off from Corning . [ 11 ] [ 12 ] Kenneth W. Freeman was appointed as CEO during this transition. [ 13 ] [ 14 ] Over the next year, Quest acquired a clinical laboratory division of Branford, Connecticut –based Diagnostic Medical Laboratory, Inc. (DML). [ 15 ] Two years later in 1999, Quest added SmithKline Beecham Clinical Laboratories to their subsidiaries; [ 16 ] [ 17 ] which includes a joint venture ownership with CompuNet Clinical Laboratory. [ 18 ] The purchase of SmithKline Beecham also included the lab's medical sample transport airline ( ICAO : LBQ , call sign : LABQUEST ) originally founded in 1988. [ 19 ]
In 1997, Quest and Banner Health formed a joint venture creating the Arizona based Sonora Quest laboratory, a business unit of Laboratory Sciences of Arizona. [ 20 ] This entity represents the operations of Quest Diagnostics in the Arizona regional market.
From May 2004 to April 2012, Surya Mohapatra served as the company's President and CEO. In 2007 Quest acquired diagnostic testing equipment company AmeriPath. [ 21 ] In response to Mohapatra's resignation after eight years with Quest, former Philips Healthcare CEO Stephen Rusckowski was appointed. [ 22 ] Under Rusckowski, Quest Diagnostics teamed up with central New England's largest health care system, UMass Memorial Health Care , to purchase its clinical outreach laboratory. [ 23 ]
In 2016, Quest collaborated with Safeway to bring testing services to twelve of its stores in California, Maryland, Virginia, Texas and Colorado. [ 24 ]
By the end of 2017, Quest, in partnership with Walmart , incorporated laboratory testing in about 15 of their locations in Texas and Florida. [ 25 ]
In May 2018, the company announced it will become an in-network laboratory provider to UnitedHealthcare starting in 2019, providing access to 48 million plan members. [ 26 ]
In September 2018, Quest moved its headquarters from Madison, where it was located since 2007, to Secaucus, New Jersey . [ 27 ] [ 28 ]
In November 2018, Quest launched QuestDirect, a consumer-initiated testing service that allows patients to order health and wellness lab testing from home. [ 29 ] [ 30 ]
In March 2020, the company launched a COVID-19 testing service. [ 31 ] As of July 2020, Quest had performed more than 9.2 million COVID-19 molecular tests and 2.8 million serology tests. [ 32 ]
In April 2024, Quest has added a new blood screening to their AD-Detect product line. This test will analyze the blood for a specific Alzheimer's protein, pTau-217. [ 33 ]
In Febuaray 2025, Fresenius Medical Care announced via Helen Giza (CEO, Chair of the management board and acting CFO) that "under terms of a definitive acquisition agreement, Quest will acquire select assets of FME’s wholly owned Spectra Laboratories, a leading provider of renal-specific laboratory testing services in the U.S."
In addition, under a separate agreement, "Quest will provide comprehensive laboratory services related to end-stage kidney disease (ESKD) and specialized water testing for patients and providers served by dialysis centers operated by Fresenius Medical Care and its wholly owned and joint-venture partners in the United States." [ 34 ]
Quest Diagnostics set a record in April 2009 when it paid $302 million to the government to settle a Medicare fraud case alleging the company sold faulty medical testing kits. It was the largest qui tam ( whistleblower ) settlement paid by a medical lab for manufacturing and distributing a faulty product. [ 56 ] In May 2011, Quest paid $241 million to the state of California to settle a False Claims Act case that alleged the company had overcharged Medi-Cal , the state's Medicaid program, and provided illegal kickbacks as incentives for healthcare providers to use Quest labs. [ 57 ]
In 2018, Quest Diagnostics was among a number of US based labs linked to inaccuracies of over 200 women's cervical smear tests for CervicalCheck , Ireland 's national screening program. [ 58 ] [ 59 ] Audits of the testing performed by Quest (and another subcontractor Clinical Pathology Laboratories, Inc. of Austin Texas) showed a high rate of errors in analysis of samples which led to lawsuits [ 60 ] and a government inquiry. Quest and the Irish government continue to settle the resulting lawsuits. [ 61 ] [ 62 ]
On June 3, 2019, Quest announced that American Medical Collection Agency (AMCA), a billing collections service provider, had informed Quest Diagnostics that an unauthorized user had access to AMCA’s system containing personal information AMCA received from various entities, including from Quest. [ 63 ] AMCA provides billing collections services to Optum360, which in turn is a Quest contractor. [ 64 ] AMCA later went bankrupt after the breach. [ 65 ] | https://en.wikipedia.org/wiki/Quest_Diagnostics |
In telecommunications and computer engineering , the queuing delay is the time a job waits in a queue until it can be executed. It is a key component of network delay . In a switched network, queuing delay is the time between the completion of signaling by the call originator and the arrival of a ringing signal at the call receiver. Queuing delay may be caused by delays at the originating switch, intermediate switches, or the call receiver servicing switch. In a data network, queuing delay is the sum of the delays between the request for service and the establishment of a circuit to the called data terminal equipment (DTE). In a packet-switched network, queuing delay is the sum of the delays encountered by a packet between the time of insertion into the network and the time of delivery to the address. [ 1 ]
This term is most often used in reference to routers . When packets arrive at a router, they have to be processed and transmitted. A router can only process one packet at a time. If packets arrive faster than the router can process them (such as in a burst transmission ) the router puts them into the queue (also called the buffer ) until it can get around to transmitting them. Delay can also vary from packet to packet so averages and statistics are usually generated when measuring and evaluating queuing delay. [ 2 ]
As a queue begins to fill up due to traffic arriving faster than it can be processed, the amount of delay a packet experiences going through the queue increases. The speed at which the contents of a queue can be processed is a function of the transmission rate of the facility. This leads to the classic delay curve. The average delay any given packet is likely to experience is given by the formula 1/(μ-λ) where μ is the number of packets per second the facility can sustain and λ is the average rate at which packets are arriving to be serviced. [ 3 ] This formula can be used when no packets are dropped from the queue.
The maximum queuing delay is proportional to buffer size. The longer the line of packets waiting to be transmitted, the longer the average waiting time is. The router queue of packets waiting to be sent also introduces a potential cause of packet loss. Since the router has a finite amount of buffer memory to hold the queue, a router that receives packets at too high a rate may experience a full queue. In this case, the router has no other option than to simply discard excess packets.
When the transmission protocol uses the dropped-packets symptom of filled buffers to regulate its transmit rate, as the Internet's TCP does, bandwidth is fairly shared at near theoretical capacity with minimal network congestion delays. Absent this feedback mechanism the delays become both unpredictable and rise sharply, a symptom also seen as freeways approach capacity; metered onramps are the most effective solution there, just as TCP's self-regulation is the most effective solution when the traffic is packets instead of cars). This result is both hard to model mathematically and quite counterintuitive to people who lack experience with mathematics or real networks. Failing to drop packets, choosing instead to buffer an ever-increasing number of them, produces bufferbloat .
In Kendall's notation , the M/M/1/K queuing model, where K is the size of the buffer, may be used to analyze the queuing delay in a specific system. Kendall's notation should be used to calculate the queuing delay when packets are dropped from the queue. The M/M/1/K queuing model is the most basic and important queuing model for network analysis. [ 4 ]
This article incorporates public domain material from Federal Standard 1037C . General Services Administration . Archived from the original on 2022-01-22. (in support of MIL-STD-188 ). | https://en.wikipedia.org/wiki/Queuing_delay |
The QuickSilver project at Cornell University is an AFRL -funded effort to build a platform in support of a new generation of scalable, secure, reliable distributed computing applications able to "regenerate" themselves after failure.
Among the partners on this project are DARPA funding under the SRS program, the United States Air Force . Raytheon , Microsoft , IBM , and Amazon .
The principal investigators are Cornell Professors Kenneth P. Birman , Johannes Gehrke , and Paul Francis
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/QuickSilver_(project) |
The Quick Start Programme (also known as the QSP ) is a fund administered by the United Nations Environment Programme . By Resolution I/4 of the First Session of the International Conference on Chemicals Management, it has been granted the responsibility to act as the financial arm of the Strategic Approach to International Chemicals Management . [ 1 ]
The QSP now has become a fund of approximately US$123.2 million, [ 2 ] with an investment portfolio of 184 projects in 108 different countries, including 54 Least Developed Countries and Small Island Developing States . | https://en.wikipedia.org/wiki/Quick_Start_Programme |
A quick access recorder ( QAR ) is an airborne flight recorder designed to provide quick and easy access to raw flight data, [ 1 ] through means such as USB [ 2 ] or cellular network [ 3 ] connections and/or the use of standard flash memory cards . [ 2 ] QARs are typically used by airlines to improve flight safety and operational efficiency, usually in the scope of their flight operational quality assurance plans. [ 4 ] Like the aircraft's flight data recorder (FDR), a QAR receives its inputs from the Flight Data Acquisition Unit (FDAU), recording over 2000 flight parameters. [ 1 ] The QAR is also able to sample data at much higher rates than the FDR and, in some cases, for longer periods of time. Unlike the FDR, the QAR usually is not required by a national Civil Aviation Authority on commercial flights and is not designed to survive an accident. Despite this, some QARs have survived accidents and provided valuable information beyond what was recorded by the FDR. [ 5 ] [ page needed ]
The quick access recorder was pioneered by British European Airways (BEA) on its Hawker Siddeley Trident aircraft in the 1960s as a requirement to prove the safety of the aircraft's autoland system for certification of the autoland system by the Civil Aviation Authority (CAA). Quick access recorders are installed in all aircraft operated by BEA's successor airline, British Airways (BA). Data from the Penny & Giles quick access recorder of a BA Boeing 747-400 London - Bangkok flight in which the aircraft suffered un-commanded elevator movement and momentary elevator reversal caused Boeing to implement a change in the elevator servo valve design, a modification that was applied to all Boeing 747s in service, and suspicion of a similar original valve design arising from this BA data was subsequently used by the National Transportation Safety Board (NTSB) in the determining of the causes of the crashes of United Airlines Flight 585 and USAir Flight 427 . [ 6 ]
Earlier, data from a Trident's quick access recorder had provided the Air Accidents Investigation Branch (AAIB) with useful supplemental data over-and-above that of the aircraft's flight data recorder that helped the diagnosing of the cause of the 1972 British European Airways Flight 548 , the "Staines air disaster" where the Trident's leading edge droop flaps had been retracted too early and at too low an airspeed . | https://en.wikipedia.org/wiki/Quick_access_recorder |
To quiesce is to pause or alter a device or application to achieve a consistent state, usually in preparation for a backup or other maintenance.
In software applications that modify information stored on disk , this generally involves flushing any outstanding writes; see buffering . With telecom applications, this generally involves allowing existing callers to finish their call but preventing new calls from initiating.
Perhaps the best known support for this was incorporated into Microsoft Shadow Copies [ 1 ] which was introduced in Microsoft Windows Server 2003. For an application to be quiesced during the shadow copy process, it must register itself as a writer [ 2 ] and it is responsible for putting itself into a quiescent mode upon notification.
Various database and application vendors implement schemes to provide support for this feature including:
The dictionary definition of quiesce at Wiktionary | https://en.wikipedia.org/wiki/Quiesce |
The concept of quiet and loud aliens is used in the modelling of hypotheses for the prevalence of extraterrestrial intelligence , particularly in the context of the Fermi Paradox . Hypothetical "loud" aliens expand their sphere of influence rapidly in a highly detectable way; hypothetical "quiet" aliens are hard or impossible to detect. [ 1 ] A special type of loud alien civilizations are " grabby aliens " who also inhibit the development of other technological civilizations in their sphere of influence. [ 2 ]
This astrobiology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Quiet_and_loud_aliens |
Quil is a quantum instruction set architecture that first introduced a shared quantum/classical memory model. It was introduced by Robert Smith, Michael Curtis, and William Zeng in A Practical Quantum Instruction Set Architecture . [ 1 ] Many quantum algorithms (including quantum teleportation , quantum error correction , simulation, [ 2 ] [ 3 ] and optimization algorithms [ 4 ] ) require a shared memory architecture . Quil is being developed for the superconducting quantum processors developed by Rigetti Computing through the Forest quantum programming API . [ 5 ] [ 6 ] A Python library called pyQuil was introduced to develop Quil programs with higher level constructs. A Quil backend is also supported by other quantum programming environments. [ 7 ] [ 8 ]
In the paper presented by Smith, Curtis and Zeng, Quil specifies the instruction set for a Quantum Abstract Machine (QAM,) akin to a Turing machine, yet more practical for accomplishing "real-world" tasks. [ 1 ] The state of the QAM can be represented as a 6- tuple ( | Ψ ⟩ , C , G , G ′ , P , κ ) {\displaystyle (|\Psi \rangle ,C,G,G',P,\kappa )} where:
The semantics of the QAM are defined using tensor products of Hilbert spaces and the linear maps between them. [ 1 ]
Quil has support for defining possibly parametrized gates in matrix form (the language does not include a way to verify that the matrices are unitary , which is a necessary condition for the physical realizability of the defined gate) and their application on qubits. The language also supports macro -like definitions of possibly parametrized quantum circuits and their expansion, qubit measurement and recording of the outcome in classical memory, synchronization with classical computers with the WAIT instruction which pauses the execution of a Quil program until a classical program has ended its execution, conditional and unconditional branching , pragma support, as well as inclusion of files for use as libraries (a standard set of gates is provided as one of the libraries.)
Rigetti Computing developed a quantum virtual machine in Common Lisp that simulates the defined Quantum Abstract Machine on a classical computer and is capable of the parsing and execution of Quil programs with possibly remote execution via HTTP. [ 9 ]
The following example demonstrates the classical control flow needed to do quantum teleportation of the qubit in register 2 to register 1: [ 10 ] [ 11 ]
Examples of the implementations of the quantum Fourier transform and the variational quantum Eigensolver are given in the paper. | https://en.wikipedia.org/wiki/Quil_(instruction_set_architecture) |
In algebra , Quillen's lemma states that an endomorphism of a simple module over the enveloping algebra of a finite-dimensional Lie algebra over a field k is algebraic over k . In contrast to a version of Schur's lemma due to Dixmier, it does not require k to be uncountable . Quillen 's original short proof uses generic flatness .
This algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Quillen's_lemma |
In topology , a branch of mathematics , Quillen's Theorem A gives a sufficient condition for the classifying spaces of two categories to be homotopy equivalent. Quillen's Theorem B gives a sufficient condition for a square consisting of classifying spaces of categories to be homotopy Cartesian . The two theorems play central roles in Quillen's Q-construction in algebraic K-theory and are named after Daniel Quillen .
The precise statements of the theorems are as follows. [ 1 ]
Quillen's Theorem A — If f : C → D {\displaystyle f:C\to D} is a functor such that the classifying space B ( d ↓ f ) {\displaystyle B(d\downarrow f)} of the comma category d ↓ f {\displaystyle d\downarrow f} is contractible for any object d in D , then f induces a homotopy equivalence B C → B D {\displaystyle BC\to BD} .
Quillen's Theorem B — If f : C → D {\displaystyle f:C\to D} is a functor that induces a homotopy equivalence B ( d ′ ↓ f ) → B ( d ↓ f ) {\displaystyle B(d'\downarrow f)\to B(d\downarrow f)} for any morphism d → d ′ {\displaystyle d\to d'} in D , then there is an induced long exact sequence:
In general, the homotopy fiber of B f : B C → B D {\displaystyle Bf:BC\to BD} is not naturally the classifying space of a category: there is no natural category F f {\displaystyle Ff} such that F B f = B F f {\displaystyle FBf=BFf} . Theorem B constructs F f {\displaystyle Ff} in a case when f {\displaystyle f} is especially nice.
This topology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Quillen's_theorems_A_and_B |
In the area of mathematics known as K-theory , the Quillen spectral sequence , also called the Brown–Gersten–Quillen or BGQ spectral sequence (named after Kenneth Brown , Stephen Gersten , and Daniel Quillen ), is a spectral sequence converging to the sheaf cohomology of a type of topological space that occurs in algebraic geometry. [ 1 ] [ 2 ] It is used in calculating the homotopy properties of a simplicial group .
This algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Quillen_spectral_sequence |
In mathematics , the Quillen–Lichtenbaum conjecture is a conjecture relating étale cohomology to algebraic K-theory introduced by Quillen (1975 , p. 175), who was inspired by earlier conjectures of Lichtenbaum (1973) . Kahn (1997) and Rognes & Weibel (2000) proved the Quillen–Lichtenbaum conjecture at the prime 2 for some number fields . Voevodsky , using some important results of Markus Rost , proved the Bloch–Kato conjecture , which implies the Quillen–Lichtenbaum conjecture for all primes.
The conjecture in Quillen's original form states that if A is a finitely-generated algebra over the integers and l is prime, then there is a spectral sequence analogous to the Atiyah–Hirzebruch spectral sequence , starting at
and abutting to
for − p − q > 1 + dim A .
Assuming the Quillen–Lichtenbaum conjecture and the Vandiver conjecture , the K -groups of the integers, K n ( Z ), are given by:
where c k / d k is the Bernoulli number B 2 k / k in lowest terms and n is 4 k − 1 or 4 k − 2 ( Weibel 2005 ). | https://en.wikipedia.org/wiki/Quillen–Lichtenbaum_conjecture |
Quinaldine red (pronounced / ˈ k w ɪ n əl d iː n / , abbreviated QR) [ 3 ] is a dark green–red or black solid that does not dissolve easily in water (it is partly miscible). [ 4 ] In addition to being used as colored indicator, quinaldine red is also used as a fluorescence probe and an agent in bleaching.
Quinaldine red is an indicator that turns from colorless to red between a pH of 1.0–2.2. [ 5 ] The image below shows what color quinaldine red would appear as in a given pH.
It is a cationic molecule that undergoes oxidation at different levels of pH. [ 3 ] The rate of oxidation of Quinaldine red is in the first order with respect to the concentration of the oxidizing agent. [ 3 ] Other factors that increases the rate of oxidation includes increasing pH and increased sodium carbonate concentration. The reaction rate eventually levels off due to the maximum formation of the product within the oxidation process.
Quinaldine red also has the ability to fluoresce . Free quinaldine red does not fluoresce in solution when it is not bound to anything, making quinaldine red only visible by fluorescence when it is bound to something. Quinaldine red can exhibit fluorescence when it is bound to nucleic acids , which then emit radiation between 580-650 nm. [ 6 ] Maximum fluorescence of QR is detected from 557 nm to 607 nm. QR and the nucleic acids react quickly under room temperature, and the resulting QR-nucleic acid complex is able to fluorescence. However, fluorescent activity decrease as time goes on. Maximum fluorescence between QR and DNA is found within the pH range of 3.2-3.6, with the optimum being a pH 3.5. The amount of fluorescence seen with the use of QR is linearly related to the concentrations of DNA or RNA.
QR is synthesized by a condensation reaction between the methyl group of 1-ethyl-2-methylquinolinium iodide and the carbonyl of para -dimethylaminobenzaldehyde . [ 7 ] [ full citation needed ]
QR has many uses as a fluorescent probe. The use of QR as a probe is relatively safe, inexpensive, and a sensitive method compared with other fluorescence probes like ethidium bromide or dimeric cyanine dyes. [ 6 ] QR is also an ideal fluorescent probe because substrates of interest, such as antibodies, can be detected within a 0.3nM detection limit without the use of radiolabeled or fluorescently labeled oligonucleotides , which are the DNA components. In other words, quinaldine red is preferred tag since its binding increases the fluorescence without extra tags being needed. [ 8 ]
The dye's ability to bind to proteins makes it a great tag. Once bound to a protein, fluorescent signals are emitted which allow the strength of QR binding to the protein to be determined. Using this technique allows for many dynamic interactions to be understood. [ 9 ] Another variation to detecting the QR probes is by measuring the fluorescence via a spectrofluorometer . This allows the concentration of the QR-substance (could be a protein or nucleic acids) to be measured. This also indirectly allows the binding ability of QR to the substance to be measured. Using this technique gives an emission wavelength of 520/160 nm. [ 10 ]
QR's ability to bind to substrates and fluoresce can be further utilized to determine the location of a substrate with the use of Raman spectroscopy and the electronic absorption spectra . For example, when a cell is not energized, a cell will not take up QR. When a cell is energized, aggregations of red substrate can be found within a cell, and this can be detected with Raman spectroscopy [ 11 ]
In addition to being used as a fluorescent probe, QR can also be used as an agent in bleaching. When exposed to intensive rays such as X-rays , gamma rays , and electron beams , the dye is able to photobleach a substance. In the case of dental bleaching , a laser is the source of intensive rays. QR is dissolved in a mixture of water, ethanol , isopropyl alcohol , glycerol , and other solvents and is placed on the teeth. In the presence of oxygen, the QR and carrier particles solution uses its sensitivity to light energy to ultimately bleach teeth, making them whiter. [ 12 ]
Quinaldine red is also used as an indicator in experiments. In an assay for inorganic and organic phosphates, QR proved to be a better indicator due to a low blank and its color stability. [ 13 ] When being used as an indicator, a color change is involved in order to indicate a change in the pH. For example, in a solution containing inorganic phosphate and ammonium molybdate in sulfuric acid , a reaction could occur where the two substances react forming a phosphomolybdate complex ion, or no reaction could occur. In this case, if pale pink mixture of quinaldine red turns to a colorless solution, this indicates the presence of a free phosphate. If the solution turns a dark red, that indicates the phosphomolybdate complex ion has formed. By using QR as an indicator in this manner, enzymatic activities can be monitored. [ 14 ] | https://en.wikipedia.org/wiki/Quinaldine_red |
Quinapril , sold under the brand name Accupril [ 2 ] by the Pfizer corporation, is a medication used to treat high blood pressure (hypertension), heart failure , and diabetic kidney disease . [ 1 ] [ 3 ] It is a first line treatment for high blood pressure. [ 3 ] It is taken by mouth . [ 1 ] [ 3 ]
Common side effects include headaches, dizziness, feeling tired, and cough. [ 3 ] Serious side effects may include liver problems, low blood pressure , angioedema , kidney problems , and high blood potassium . [ 3 ] Use in pregnancy and breastfeeding is not recommended. [ 4 ] It is among a class of drugs called ACE inhibitors and works by decreasing renin-angiotensin-aldosterone system activity. [ 3 ]
Quinapril was patented in 1980 and came into medical use in 1989. [ 5 ] It is available as a generic medication . [ 6 ] In 2020, it was the 253rd most commonly prescribed medication in the United States, with more than 1 million prescriptions. [ 7 ] [ 8 ]
Quinapril is indicated for the treatment of high blood pressure ( hypertension ) and as adjunctive therapy in the management of heart failure . [ 1 ] It may be used for the treatment of hypertension by itself or in combination with thiazide diuretics , and with diuretics and digoxin for heart failure. [ 1 ]
Contraindications include: [ 9 ]
Side effects of Quinapril [ 9 ] include dizziness, cough, vomiting, upset stomach, angioedema , and fatigue .
Quinapril inhibits angiotensin converting enzyme , an enzyme which catalyses the formation of angiotensin II from its precursor, angiotensin I . Angiotensin II is a powerful vasoconstrictor and increases blood pressure through a variety of mechanisms. Due to reduced angiotensin production, plasma concentrations of aldosterone are also reduced, resulting in increased excretion of sodium in the urine and increased concentrations of potassium in the blood.
In April of 2022, Pfizer voluntarily recalled five batches of the drug because of the presence of a nitrosamine , N-Nitroso-quinapril. Testing found that the amount of nitrosamines was above the acceptable daily intake level (all humans are exposed to nitrosamines up to a certain daily level by cured and grilled meats, water, dairy products, and vegetables) set by the U.S.'s Food and Drug Administration (FDA). Though long-term ingestion of N-Nitroso-quinapril potentially might cause cancer in some individuals, there is not believed to be an imminent risk of harm. [ 10 ] [ 11 ] | https://en.wikipedia.org/wiki/Quinapril |
The quinarian system was a method of zoological classification which was popular in the mid 19th century, especially among British naturalists. It was largely developed by the entomologist William Sharp Macleay in 1819. [ 1 ] The system was further promoted in the works of Nicholas Aylward Vigors , William Swainson and Johann Jakob Kaup . Swainson's work on ornithology gave wide publicity to the idea. The system had opponents even before the publication of Charles Darwin 's On the Origin of Species (1859), which paved the way for evolutionary trees. [ 2 ]
Quinarianism gets its name from the emphasis on the number five: it proposed that all taxa are divisible into five subgroups, and if fewer than five subgroups were known, quinarians believed that a missing subgroup remained to be found. [ 2 ]
Presumably this arose as a chance observation of some accidental analogies between different groups, but it was erected into a guiding principle by the quinarians. It became increasingly elaborate, proposing that each group of five classes could be arranged in a circle, with those closer together having greater affinities. Typically they were depicted with relatively advanced groups at the top, and supposedly degenerate forms towards the bottom. Each circle could touch or overlap with adjacent circles; the equivalent overlapping of actual groups in nature was called osculation.
Another aspect of the system was the identification of analogies across groups: [ 3 ]
[W]e shall consider that to be a natural system which endeavours to explain the multifarious relations which one object bears to another, not simply in their direct affinity, by which they follow each other like the links of a vast chain, but in their more remote relations [analogies], whereby they typify or represent other objects totally distinct in structure and organization from themselves
Quinarianism was not widely popular outside the United Kingdom (some followers like William Hincks persisted in Canada [ 5 ] ); it became unfashionable by the 1840s, during which time more complex "maps" were made by Hugh Edwin Strickland and Alfred Russel Wallace . Strickland and others specifically rejected the use of relations of "analogy" in constructing natural classifications. [ 6 ] These systems were eventually discarded in favour of principles of genuinely natural classification, namely based on evolutionary relationship. [ 2 ] [ 7 ] | https://en.wikipedia.org/wiki/Quinarian_system |
The quinhydrone electrode may be used to measure the hydrogen ion concentration ( pH ) of a solution containing an acidic substance. [ 1 ] [ 2 ]
Quinones form a quinhydrone cocrystal by formation of hydrogen bonding between ρ-quinone and ρ-hydroquinone. [ 3 ] An equimolar mixture of ρ-quinones and ρ-hydroquinone in contact with an inert metallic electrode, such as antimony , forms what is known as a quinhydrone electrode. Such devices can be used to measure the pH of solutions. [ 4 ] Quinhydrone electrodes provide fast response times and high accuracy. However, it can only measure pH in the range of 1 to 9 and the solution must not contain a strong oxidizing or reducing agent .
A platinum wire electrode is immersed in a saturated aqueous solution of quinhydrone , in which there is the following equilibrium
The potential difference between the platinum electrode and a reference electrode is dependent on the activity , a H + {\displaystyle a_{H^{+}}} , of hydrogen ions in the solution.
The quinhydrone electrode provides an alternative to the most commonly used glass electrode . [ 5 ] however, it is not reliable above pH 8 (at 298 K) and cannot be used with solutions that contain a strong oxidizing or reducing agent. [ 1 ]
This electrochemistry -related article is a stub . You can help Wikipedia by expanding it .
This article about analytical chemistry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Quinhydrone_electrode |
The total synthesis of quinine , a naturally-occurring antimalarial drug, was developed over a 150-year period. The development of synthetic quinine is considered a milestone in organic chemistry although it has never been produced industrially as a substitute for natural occurring quinine. The subject has also been attended with some controversy: Gilbert Stork published the first stereoselective total synthesis of quinine in 2001, meanwhile shedding doubt on the earlier claim by Robert Burns Woodward and William Doering in 1944, claiming that the final steps required to convert their last synthetic intermediate, quinotoxine, into quinine would not have worked had Woodward and Doering attempted to perform the experiment. A 2001 editorial published in Chemical & Engineering News sided with Stork, but the controversy was eventually laid to rest once and for all when Robert Williams and coworkers successfully repeated Woodward's proposed conversion of quinotoxine to quinine in 2007. [ 1 ]
The aromatic component of the quinine molecule is a quinoline with a methoxy substituent. The amine component has a quinuclidine skeleton and the methylene bridge in between the two components has a hydroxyl group. The substituent at the 3 position is a vinyl group . The molecule is optically active with five stereogenic centers (the N1 and C4 constituting a single asymmetric unit), making synthesis potentially difficult because it is one of 16 stereoisomers .
The Stork quinine synthesis starts from chiral ( S )-4-vinylbutyrolactone 1 . The compound is obtained by chiral resolution and in fact, in the subsequent steps all stereogenic centers are put in place by chiral induction : the sequence does not contain asymmetric steps.
The lactone is ring-opened with diethylamine to amide 2 and its hydroxyl group is protected as a tert -butyldimethyl silyl ether (TBS) in 3 . The C5 and C6 atoms are added as tert -butyldiphenylsilyl (TBDPS) protected iodoethanol in a nucleophilic substitution of acidic C4 with lithium diisopropylamide (LDA) at −78 °C to 4 with correct stereochemistry. Removal of the silyl protecting group with p -toluenesulfonic acid to alcohol 4b and ring-closure by azeotropic distillation returns the compound to lactone 5 (direct alkylation of 1 met with undisclosed problems).
The lactone is then reduced to the lactol 5b with diisobutylaluminum hydride and its liberated aldehyde reacts in a Wittig reaction with methoxymethylenetriphenylphosphine (delivering the C8 atom) to form enol ether 6 . The hydroxyl group is replaced in a Mitsunobu reaction by an azide group with diphenylphosphoryl azide in 7 and acid hydrolysis yields the azido aldehyde 8 .
The methyl group in 6-methoxy-4-methylquinoline 9 is sufficiently acidic for nucleophilic addition of its anion (by reaction with LDA ) to the aldehyde group in 8 to form 10 as a mixture of epimers . This is of no consequence for stereocontrol because in the next step the alcohol is oxidized in a Swern oxidation to ketone 11 . A Staudinger reaction with triphenylphosphine closes the ring between the ketone and the azide to the tetrahydropyridine 12 . The imine group in this compound is reduced to the amine 13 with sodium borohydride with the correct stereospecificity . The silyl protecting group is removed with hydrogen fluoride to alcohol 14 and then activated as a mesyl leaving group by reaction with mesyl chloride in pyridine which enables the third ring closure to 15 . In the final step the C9 hydroxyl group was introduced by oxidation with sodium hydride , dimethylsulfoxide and oxygen with quinine to epiquinine ratio of 14:1.
The 1944 Woodward–Doering synthesis starts from 7-hydroxyisoquinoline 3 for the quinuclidine skeleton which is somewhat counter intuitive because one goes from a stable heterocyclic aromatic system to a completely saturated bicyclic ring. This compound (already known since 1895) is prepared in two steps.
The first reaction step is condensation reaction of 3-hydroxybenzaldehyde 1 with (formally) the di acetal of aminoacetaldehyde to the imine 2 and the second reaction step is cyclization in concentrated sulfuric acid . Isoquinoline 3 is then alkylated in another condensation by formaldehyde and piperidine and the product is isolated as the sodium salt of 4 .
Hydrogenation at 220 °C for 10 hours in methanol with sodium methoxide liberates the piperidine group and leaving the methyl group in 5 with already all carbon and nitrogen atoms accounted for. A second hydrogenation takes place with Adams catalyst in acetic acid to tetrahydroisoquinoline 6 . Further hydrogenation does not take place until the amino group is acylated with acetic anhydride in methanol but by then 7 is again hydrogenated with Raney nickel in ethanol at 150 °C under high pressure to decahydroisoquinoline 8 . The mixture of cis and trans isomers is then oxidized by chromic acid in acetic acid to the ketone 9 . Only the cis isomer crystallizes and used in the next reaction step, a ring opening with the alkyl nitrite ethyl nitrite with sodium ethoxide in ethanol to 10 with a newly formed carboxylic ester group and an oxime group. The oxime group is hydrogenated to the amine 11 with platinum in acetic acid and alkylation with iodomethane gives the quaternary ammonium salt 12 and subsequently the betaine 13 after reaction with silver oxide .
Quinine's vinyl group is then constructed by Hofmann elimination with sodium hydroxide in water at 140 °C. This process is accompanied by hydrolysis of both the ester and the amide group but it is not the free amine that is isolated but the urea 14 by reaction with potassium cyanate . In the next step the carboxylic acid group is esterified with ethanol and the urea group replaced with a benzoyl group. The final step is a Claisen condensation of 15 with ethyl quininate 16 , which after acidic workup yields racemic quinotoxine 17 . The desired enantiomer is obtained by chiral resolution with the chiral dibenzoyl ester of Tartaric acid . The conversion of this compound to quinine is based on the Rabe–Kindler chemistry discussed in the timelime. | https://en.wikipedia.org/wiki/Quinine_total_synthesis |
Quinone-interacting membrane-bound oxidoreductase is a membrane-bound protein complex present in the electron transport chain of sulfate reducers (e.g. Desulfovibrio species) and some sulfur oxidizers .
It was first described by Pires et al. (2003). [ 1 ]
This oxidoreductase article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Quinone-interacting_membrane-bound_oxidoreductase |
A quinone methide is a type of conjugated organic compound that contain a cyclohexadiene with a carbonyl and an exocyclic methylidene or extended alkene unit. It is analogous to a quinone , but having one of the double bonded oxygens replaced with a carbon. The carbonyl and methylidene are usually oriented either ortho or para to each other. There are some examples of transient synthetic meta quinone methides.
Quinone methides are cross-conjugated rather than aromatic . Nucleophilic addition at the exo-cyclic double bond will result in rearomatisation, making such reactions highly favourable. As a result, quinone methides are excellent, electrophilic Michael acceptors , react quickly with nucleophiles and can be easily reduced. They are able to act as radical scavengers via a similar process, a behaviour exploited by certain polymerisation inhibitors . Quinone methides are more polar than quinones, and therefore more chemically reactive . Simple unhindered quinone methides are short lived reactive intermediates that are not stable enough to be isolated under normal circumstances, they will trimerise in the absence of nucleophiles. [ 1 ] Sterically hindered quinone methides can be sufficiently stable to be isolated, with some examples being commercially available.
Quinone methides are often prepared by oxidation of the corresponding ortho or para cresol .
Quinone methides can be produced in aqueous solution by photochemical dehydration of o-hydroxybenzyl alcohols (i.e. salicyl alcohol ).
Quinones methides are commonly invoked in biochemistry , but are rarely observed as long-lived intermediates.
Quinone methide itself arises by the degradation of tyrosine , leading ultimately to p - cresol . [ 2 ] Various quinone methides are directly involved in the process of lignification (creation of complex lignin polymers ) in plants. [ 3 ]
Quinone methides have been implicated as the ultimate cytotoxins responsible for the effects of such agents as antitumor drugs, antibiotics , and DNA alkylators . [ 4 ] Oxidation to a reactive quinone methide is the mechanistic basis of many phenolic anti-cancer drugs.
Celastrol is a triterpenoid quinone methide isolated from Tripterygium wilfordii (Thunder of God vine) and Celastrus regelii that exhibits antioxidant (15 times the potency of α-tocopherol), [ 6 ] anti-inflammatory, [ 7 ] anticancer, [ 8 ] [ 9 ] [ 10 ] [ 11 ] and insecticidal [ 12 ] activities.
Pristimerin, the methyl ester of celasterol, is a triterpenoid quinone methide isolated from Maytenus heterophylla that displays antitumor and antiviral [ 13 ] activities. Pristimerin has also been found to have a contraceptive effect due to its inhibiting effect on the calcium channel of sperm (CatSper). [ 14 ]
Taxodone and its oxidized rearrangement product, taxodione, are diterpenoid quinone methides found in Taxodium distichum (bald cypress), Rosmarinus officinalis (rosemary), several Salvia species and other plants, that display anticancer , [ 15 ] [ 16 ] [ 17 ] antibacterial , [ 18 ] [ 19 ] [ 20 ] antioxidant , [ 21 ] antifungal , [ 22 ] insecticide , [ 23 ] and antifeedant [ 24 ] activities.
Maytenoquinone, an isomer of taxodione, is a biologically active quinone methide found in Maytenus dispermus . [ 25 ]
Kendomycin is an antitumor antibacterial quinone methide macrolide first isolated from the bacterium Streptomyces violaceoruber . [ 26 ] It has potent activity as an endothelin receptor antagonist and anti- osteoporosis agent. [ 27 ]
Elansolid A3 is a quinone methide from the bacterium Chitinophaga sancti that displays antibiotic activity. [ 28 ] Antibacterial quinone methides, 20-epi-isoiguesterinol, 6-oxoisoiguesterin, isoiguesterin and isoiguesterinol were found in Salacia madagascariensis . [ 29 ] Quinone methides tingenone and netzahualcoyonol were isolated from Salacia petenensis . [ 30 ] Nortriterpenoid quinone methide amazoquinone and (7S, 8S)-7-hydroxy-7,8-dihydro-tingenone were isolated from Maytenus amazonica . [ 31 ] An antimicrobial quinone methide, 15 alpha-hydroxypristimerin, was isolated from a South American medicinal plant, Maytenus scutioides . [ 32 ]
A quinone dimethide (or "xylylene") is a compound with the formula C 6 H 4 (=CH 2 ) 2 . Thus they are related to quinone mono methides (the topic of this article) by replacing the keto group with methylidene . A well studied example is tetracyanoquinodimethane . | https://en.wikipedia.org/wiki/Quinone_methide |
In mathematics , a quintic function is a function of the form
where a , b , c , d , e and f are members of a field , typically the rational numbers , the real numbers or the complex numbers , and a is nonzero. In other words, a quintic function is defined by a polynomial of degree five.
Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum. The derivative of a quintic function is a quartic function .
Setting g ( x ) = 0 and assuming a ≠ 0 produces a quintic equation of the form:
Solving quintic equations in terms of radicals ( n th roots) was a major problem in algebra from the 16th century, when cubic and quartic equations were solved, until the first half of the 19th century, when the impossibility of such a general solution was proved with the Abel–Ruffini theorem .
Finding the roots (zeros) of a given polynomial has been a prominent mathematical problem.
Solving linear , quadratic , cubic and quartic equations in terms of radicals and elementary arithmetic operations on the coefficients can always be done, no matter whether the roots are rational or irrational, real or complex; there are formulas that yield the required solutions. However, there is no algebraic expression (that is, in terms of radicals) for the solutions of general quintic equations over the rationals; this statement is known as the Abel–Ruffini theorem , first asserted in 1799 and completely proven in 1824. This result also holds for equations of higher degree. An example of a quintic whose roots cannot be expressed in terms of radicals is x 5 − x + 1 = 0 .
Numerical approximations of quintics roots can be computed with root-finding algorithms for polynomials . Although some quintics may be solved in terms of radicals, the solution is generally too complicated to be used in practice.
Some quintic equations can be solved in terms of radicals. These include the quintic equations defined by a polynomial that is reducible , such as x 5 − x 4 − x + 1 = ( x 2 + 1)( x + 1)( x − 1) 2 . For example, it has been shown [ 1 ] that
has solutions in radicals if and only if it has an integer solution or r is one of ±15, ±22440, or ±2759640, in which cases the polynomial is reducible.
As solving reducible quintic equations reduces immediately to solving polynomials of lower degree, only irreducible quintic equations are considered in the remainder of this section, and the term "quintic" will refer only to irreducible quintics. A solvable quintic is thus an irreducible quintic polynomial whose roots may be expressed in terms of radicals.
To characterize solvable quintics, and more generally solvable polynomials of higher degree, Évariste Galois developed techniques which gave rise to group theory and Galois theory . Applying these techniques, Arthur Cayley found a general criterion for determining whether any given quintic is solvable. [ 2 ] This criterion is the following. [ 3 ]
Given the equation
the Tschirnhaus transformation x = y − b / 5 a , which depresses the quintic (that is, removes the term of degree four), gives the equation
where
Both quintics are solvable by radicals if and only if either they are factorisable in equations of lower degrees with rational coefficients or the polynomial P 2 − 1024 z Δ , named Cayley's resolvent , has a rational root in z , where
and
Cayley's result allows us to test if a quintic is solvable. If it is the case, finding its roots is a more difficult problem, which consists of expressing the roots in terms of radicals involving the coefficients of the quintic and the rational root of Cayley's resolvent.
In 1888, George Paxton Young described how to solve a solvable quintic equation, without providing an explicit formula; [ 4 ] in 2004, Daniel Lazard wrote out a three-page formula. [ 5 ]
There are several parametric representations of solvable quintics of the form x 5 + ax + b = 0 , called the Bring–Jerrard form .
During the second half of the 19th century, John Stuart Glashan, George Paxton Young, and Carl Runge gave such a parameterization: an irreducible quintic with rational coefficients in Bring–Jerrard form
is solvable if and only if either a = 0 or it may be written
where μ and ν are rational.
In 1994, Blair Spearman and Kenneth S. Williams gave an alternative,
The relationship between the 1885 and 1994 parameterizations can be seen by defining the expression
where a = 5 4 ν + 3 ν 2 + 1 {\displaystyle a=5{\tfrac {4\nu +3}{\nu ^{2}+1}}} . Using the negative case of the square root yields, after scaling variables, the first parametrization while the positive case gives the second.
The substitution c = − m ℓ 5 , {\displaystyle c=-{\tfrac {m}{\ell ^{5}}},} e = 1 ℓ {\displaystyle e={\tfrac {1}{\ell }}} in the Spearman–Williams parameterization allows one to not exclude the special case a = 0 , giving the following result:
If a and b are rational numbers, the equation x 5 + ax + b = 0 is solvable by radicals if either its left-hand side is a product of polynomials of degree less than 5 with rational coefficients or there exist two rational numbers ℓ and m such that
A polynomial equation is solvable by radicals if its Galois group is a solvable group . In the case of irreducible quintics, the Galois group is a subgroup of the symmetric group S 5 of all permutations of a five element set, which is solvable if and only if it is a subgroup of the group F 5 , of order 20 , generated by the cyclic permutations (1 2 3 4 5) and (1 2 4 3) .
If the quintic is solvable, one of the solutions may be represented by an algebraic expression involving a fifth root and at most two square roots, generally nested . The other solutions may then be obtained either by changing the fifth root or by multiplying all the occurrences of the fifth root by the same power of a primitive 5th root of unity , such as
In fact, all four primitive fifth roots of unity may be obtained by changing the signs of the square roots appropriately; namely, the expression
where α , β ∈ { − 1 , 1 } {\displaystyle \alpha ,\beta \in \{-1,1\}} , yields the four distinct primitive fifth roots of unity.
It follows that one may need four different square roots for writing all the roots of a solvable quintic. Even for the first root that involves at most two square roots, the expression of the solutions in terms of radicals is usually highly complicated. However, when no square root is needed, the form of the first solution may be rather simple, as for the equation x 5 − 5 x 4 + 30 x 3 − 50 x 2 + 55 x − 21 = 0 , for which the only real solution is
An example of a more complicated (although small enough to be written here) solution is the unique real root of x 5 − 5 x + 12 = 0 . Let a = √ 2 φ −1 , b = √ 2 φ , and c = 4 √ 5 , where φ = 1+ √ 5 / 2 is the golden ratio . Then the only real solution x = −1.84208... is given by
or, equivalently, by
where the y i are the four roots of the quartic equation
More generally, if an equation P ( x ) = 0 of prime degree p with rational coefficients is solvable in radicals, then one can define an auxiliary equation Q ( y ) = 0 of degree p − 1 , also with rational coefficients, such that each root of P is the sum of p -th roots of the roots of Q . These p -th roots were introduced by Joseph-Louis Lagrange , and their products by p are commonly called Lagrange resolvents . The computation of Q and its roots can be used to solve P ( x ) = 0 . However these p -th roots may not be computed independently (this would provide p p −1 roots instead of p ). Thus a correct solution needs to express all these p -roots in term of one of them. Galois theory shows that this is always theoretically possible, even if the resulting formula may be too large to be of any use.
It is possible that some of the roots of Q are rational (as in the first example of this section) or some are zero. In these cases, the formula for the roots is much simpler, as for the solvable de Moivre quintic
where the auxiliary equation has two zero roots and reduces, by factoring them out, to the quadratic equation
such that the five roots of the de Moivre quintic are given by
where y i is any root of the auxiliary quadratic equation and ω is any of the four primitive 5th roots of unity . This can be easily generalized to construct a solvable septic and other odd degrees, not necessarily prime.
There are infinitely many solvable quintics in Bring–Jerrard form which have been parameterized in a preceding section.
Up to the scaling of the variable, there are exactly five solvable quintics of the shape x 5 + a x 2 + b {\displaystyle x^{5}+ax^{2}+b} , which are [ 6 ] (where s is a scaling factor):
Paxton Young (1888) gave a number of examples of solvable quintics:
An infinite sequence of solvable quintics may be constructed, whose roots are sums of n th roots of unity , with n = 10 k + 1 being a prime number :
There are also two parameterized families of solvable quintics:
The Kondo–Brumer quintic,
and the family depending on the parameters a , ℓ , m {\displaystyle a,\ell ,m}
where
Analogously to cubic equations , there are solvable quintics which have five real roots all of whose solutions in radicals involve roots of complex numbers. This is casus irreducibilis for the quintic, which is discussed in Dummit. [ 7 ] : p.17 Indeed, if an irreducible quintic has all roots real, no root can be expressed purely in terms of real radicals (as is true for all polynomial degrees that are not powers of 2).
About 1835, Jerrard demonstrated that quintics can be solved by using ultraradicals (also known as Bring radicals), the unique real root of t 5 + t − a = 0 for real numbers a . In 1858, Charles Hermite showed that the Bring radical could be characterized in terms of the Jacobi theta functions and their associated elliptic modular functions , using an approach similar to the more familiar approach of solving cubic equations by means of trigonometric functions . At around the same time, Leopold Kronecker , using group theory , developed a simpler way of deriving Hermite's result, as had Francesco Brioschi . Later, Felix Klein came up with a method that relates the symmetries of the icosahedron , Galois theory , and the elliptic modular functions that are featured in Hermite's solution, giving an explanation for why they should appear at all, and developed his own solution in terms of generalized hypergeometric functions . [ 8 ] Similar phenomena occur in degree 7 ( septic equations ) and 11 , as studied by Klein and discussed in Icosahedral symmetry § Related geometries .
A Tschirnhaus transformation , which may be computed by solving a quartic equation , reduces the general quintic equation of the form
to the Bring–Jerrard normal form x 5 − x + t = 0 .
The roots of this equation cannot be expressed by radicals. However, in 1858, Charles Hermite published the first known solution of this equation in terms of elliptic functions . [ 9 ] At around the same time Francesco Brioschi [ 10 ] and Leopold Kronecker [ 11 ] came upon equivalent solutions.
See Bring radical for details on these solutions and some related ones.
Solving for the locations of the Lagrangian points of an astronomical orbit in which the masses of both objects are non-negligible involves solving a quintic.
More precisely, the locations of L 2 and L 1 are the solutions to the following equations, where the gravitational forces of two masses on a third (for example, Sun and Earth on satellites such as Gaia and the James Webb Space Telescope at L 2 and SOHO at L 1 ) provide the satellite's centripetal force necessary to be in a synchronous orbit with Earth around the Sun:
The ± sign corresponds to L 2 and L 1 , respectively; G is the gravitational constant , ω the angular velocity , r the distance of the satellite to Earth, R the distance Sun to Earth (that is, the semi-major axis of Earth's orbit), and m , M E , and M S are the respective masses of satellite, Earth , and Sun .
Using Kepler's Third Law ω 2 = 4 π 2 P 2 = G ( M S + M E ) R 3 {\displaystyle \omega ^{2}={\frac {4\pi ^{2}}{P^{2}}}={\frac {G(M_{S}+M_{E})}{R^{3}}}} and rearranging all terms yields the quintic
with:
Solving these two quintics yields r = 1.501 × 10 9 m for L 2 and r = 1.491 × 10 9 m for L 1 . The Sun–Earth Lagrangian points L 2 and L 1 are usually given as 1.5 million km from Earth.
If the mass of the smaller object ( M E ) is much smaller than the mass of the larger object ( M S ), then the quintic equation can be greatly reduced and L 1 and L 2 are at approximately the radius of the Hill sphere , given by:
That also yields r = 1.5 × 10 9 m for satellites at L 1 and L 2 in the Sun-Earth system. | https://en.wikipedia.org/wiki/Quintic_function |
A quintuple bond in chemistry is an unusual type of chemical bond , first reported in 2005 for a dichromium compound. Single bonds , double bonds , and triple bonds are commonplace in chemistry. Quadruple bonds are rarer and are currently known only among the transition metals, especially for Cr , Mo , W , and Re , e.g. [Mo 2 Cl 8 ] 4− and [Re 2 Cl 8 ] 2− . In a quintuple bond, ten electrons participate in bonding between the two metal centers, allocated as σ 2 π 4 δ 4 .
In some cases of high-order bonds between metal atoms, the metal-metal bonding is facilitated by ligands that link the two metal centers and reduce the interatomic distance. By contrast, the chromium dimer with quintuple bonding is stabilized by a bulky terphenyl (2,6-[(2,6-diisopropyl)phenyl]phenyl) ligands . The species is stable up to 200 °C. [ 1 ] [ 2 ] The chromium–chromium quintuple bond has been analyzed with multireference ab initio and DFT methods, [ 3 ] which were also used to elucidate the role of the terphenyl ligand, in which the flanking aryls were shown to interact very weakly with the chromium atoms, causing only a small weakening of the quintuple bond. [ 4 ] A 2007 theoretical study identified two global minima for quintuple bonded RMMR compounds: a trans -bent molecular geometry and surprisingly another trans -bent geometry with the R substituent in a bridging position. [ 5 ]
In 2005, a quintuple bond was postulated to exist in the hypothetical uranium molecule U 2 based on computational chemistry . [ 6 ] [ 7 ] Diuranium compounds are rare, but do exist; for example, the U 2 Cl 2− 8 anion.
In 2007 the shortest-ever metal–metal bond (180.28 pm) was reported to exist also in a compound containing a quintuple chromium-chromium bond with diazadiene bridging ligands. [ 8 ] Other metal–metal quintuple bond containing complexes that have been reported include quintuply bonded dichromium with [6-(2,4,6-triisopropylphenyl)pyridin-2-yl](2,4,6-trimethylphenyl)amine bridging ligands [ 9 ] and a dichromium complex with amidinate bridging ligands. [ 10 ]
Synthesis of quintuple bonds is usually achieved through reduction of a dimetal species using potassium graphite . This adds valence electrons to the metal centers, giving them the needed number of electrons to participate in quintuple bonding. Below is a figure of a typical quintuple bond synthesis.
In 2009 a dimolybdenum compound with a quintuple bond and two di amido bridging ligands was reported with a Mo–Mo bond length of 202 pm. [ 11 ] The compound was synthesised starting from potassium octachlorodimolybdate (which already contains a Mo 2 quadruple bond) and a lithium amidinate, followed by reduction with potassium graphite:
As stated above, metal–metal quintuple bonds have a σ 2 π 4 δ 4 configuration. Among the five bonds present between the metal centers, one is a sigma bond , two are pi bonds , and two are delta bonds . The σ-bond is the result of mixing between the d z 2 orbital on each metal center. The first π-bond comes from mixing of the d yz orbitals from each metal while the other π-bond comes from the d xz orbitals on each metal mixing. Finally the δ-bonds come from mixing of the d xy orbitals as well as mixing between the d x 2 − y 2 orbitals from each metal.
Molecular orbital calculations have elucidated the relative energies of the orbitals created by these bonding interactions. As shown in the figure below, the lowest energy orbitals are the π bonding orbitals followed by the σ bonding orbital. The next highest are the δ bonding orbitals which represent the HOMO . Because the 10 valence electrons of the metals are used to fill these first 5 orbitals, the next highest orbital becomes the LUMO which is the δ* antibonding orbital. Though the π and δ orbitals are represented as being degenerate , they in fact are not. This is because the model shown here is a simplification and that hybridization of s, p, and d orbitals is believed to take place, causing a change in the orbital energy levels. [ citation needed ]
Quintuple bond lengths are heavily dependent on the ligands bound to the metal centers. Nearly all complexes containing a metal–metal quintuple bond have bidentate bridging ligands, and even those that do not, such as the terphenyl complex mentioned earlier, have some bridging characteristic to it through metal– ipso -carbon interactions.
The bidentate ligand can act as a sort of tweezer in that in order for chelation to occur the metal atoms must move closer together, thereby shortening the quintuple bond length. The two ways in which to obtain shorter metal–metal distances is to either reduce the distance between the chelating atoms in the ligand by changing the structure, or by using steric effects to force a conformational change in the ligand that bends the molecule in a way that forces the chelating atoms closer together. An example of the latter is shown below:
The above example shows the ligand used in the dimolybdenum complex shown earlier. When the carbon between the two nitrogens in the ligand has a hydrogen bound to it, the steric repulsion is small. However, when the hydrogen is replaced with a much more bulky phenyl ring the steric repulsion increases dramatically and the ligand "bows" which causes a change in the orientation of the lone pairs of electrons on the nitrogen atoms. These lone pairs are what is responsible for forming bonds with the metal centers so forcing them to move closer together also forces the metal centers to be positioned closer together. Thus, decreasing the length of the quintuple bond. In the case where this ligand is bound to quintuply bonded dimolybdenum the quintuple bond length goes from 201.87 pm to 201.57 pm when the hydrogen in replaced with a phenyl group. Similar results have also been demonstrated in dichromium quintuple bond complexes as well. [ 12 ]
Efforts continue to prepare shorter quintuple bonds. [ 13 ] [ 14 ]
Quintuple-bonded dichromium complexes appear to act like magnesium to produce Grignard reagents . [ 15 ] | https://en.wikipedia.org/wiki/Quintuple_bond |
In mathematics the Watson quintuple product identity is an infinite product identity introduced by Watson ( 1929 ) and rediscovered by Bailey (1951) and Gordon (1961) . It is analogous to the Jacobi triple product identity , and is the Macdonald identity for a certain non-reduced affine root system . It is related to Euler's pentagonal number theorem . | https://en.wikipedia.org/wiki/Quintuple_product_identity |
Quipu ( / ˈ k iː p uː / KEE -poo ), also spelled khipu , are record keeping devices fashioned from knotted cords. They were historically used by various cultures in the central Andes of South America, most prominently by the Inca Empire . [ 1 ]
A quipu usually consists of cotton or camelid fiber cords, and contains categorized information based on dimensions like color, order and number. [ 2 ] The Inca, in particular, used knots tied in a decimal positional system to store numbers and other values in quipu cords. Depending on its use and the amount of information it stored, a given quipu may have anywhere from a few to several thousand cords.
Objects which can unambiguously be identified as quipus first appear in the archaeological record during 1st millennium CE, [ 3 ] likely attributable to the Wari Empire . [ 4 ] [ 5 ] Quipus subsequently played a key part in the administration of the Kingdom of Cusco of the 13th to 15th centuries, and later of the Inca Empire (1438–1533), flourishing across the Andes from c. 1100 to 1532. Inca administration used quipus extensively for a variety of uses: monitoring tax obligations, collecting census records, keeping calendrical information, military organization, [ 6 ] and potentially for recording simple and stereotyped historical "annales". [ 2 ]
It is not known exactly how many intact quipus still remain and where, as many were deposited in ancient mausoleums [ 3 ] or later destroyed by the Spanish. However, a recent survey of both museum and private collection inventories places the total number of known extant pre-Columbian quipus at just under 1,400. [ 7 ]
After the Spanish conquest of the Inca Empire , quipus were slowly replaced by European writing and numeral systems. Many quipus were identified as idolatrous and destroyed, but some Spaniards promoted the adaptation of the quipu recording system to the needs of the colonial administration, and some priests advocated the use of quipus for ecclesiastical purposes. [ 8 ] Today, quipus continue to serve as important items in several modern Andean villages. [ 9 ]
Various other cultures have used knotted strings, unrelated to South American quipu, to record information—these include, but are not limited to, Chinese knotting , and practiced by Tibetans , Japanese , and Polynesians . [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ]
The word Quipu is derived from a Quechua word meaning 'knot' or 'to knot'. [ 15 ] The terms quipu and khipu are simply spelling variations on the same word. Quipu is the traditional spelling based on the Spanish orthography , while khipu reflects the recent Quechuan and Aymaran spelling shift . Khipu (pronounced [ˈkʰɪpʊ] , plural: khipukuna ) comes from Cusco Quechua , while many other Quechua varieties use the term kipu . Currently, the hispanicized spelling of quipu is the form most commonly used in both Spanish and English. [ 16 ]
"The khipu were knotted-string devices that were used for recording both statistical and narrative information, most notably by the Inca but also by other peoples of the central Andes from pre-Incaic times, through the colonial and republican eras, and even – in a considerably transformed and attenuated form – down to the present day."
Quipus held information, decipherable by officials called quipucamayocs , classified in various categories, narrated from the most important to the least important category, according to color, number, and order. [ 2 ]
To date, most of the information recorded on the quipus studied by researchers consists of numbers in a decimal system, [ 18 ] such as "Indian chiefs ascertain[ing] which province had lost more than another and balanc[ing] the losses between them" after the Spanish invasion. [ 19 ] In the early years of the Spanish conquest of Peru , Spanish officials often relied on the quipus to settle disputes over local tribute payments or goods production. Quipucamayocs ( Quechua khipu kamayuq "khipu specialist", plural: khipu kamayuqkuna ) could be summoned to court, where their bookkeeping was recognised as valid documentation of past payments.
Some knots — as well as other features, such as color, fiber type, cord attachments, etc. — are thought to represent non-numeric information, which has not been deciphered. It is generally thought that the system did not include phonetic symbols analogous to letters of the alphabet. However, Gary Urton has suggested that the quipus used a binary system which could record phonological or logographic data. [ 20 ] According to Martti Pärssinen, quipucamayocs would learn specific oral texts , which in relation to the basic information contained in quipu , and pictorial representations, often painted on quiru vessels, similar to aztec pictograms , related simple "episodes". [ 2 ]
In 2011, a potential match between a Spanish colonial document and six colonial-era quipus from the same region was identified. [ 3 ] Researchers believe this possible quipu -document match is the strongest Rosetta Stone -like connection currently known, which could offer key clues needed to unlock the full extent of the quipu code. Subsequent studies have built on the proposed quipu -document connection, suggesting that the binary manner by which cords can be attached to the main body of the six quipus may encode moiety affiliation, [ 21 ] [ 22 ] and, more recently, uncovering detailed Andean social structures encoded within the six quipus . [ 23 ]
The lack of a clear link between any indigenous Andean languages and the quipus has historically led to the supposition that quipus are not a glottographic writing system and have no phonetic referent. [ 24 ] Frank Salomon, at the University of Wisconsin, has argued that quipus are actually a semasiographic language, a system of representative symbols – such as music notation or numerals – that relay information but are not directly related to the speech sounds of a particular language, [ 25 ] like ideograms and proto-writing .
Sabine Hyland claims to have made the first phonetic decipherment through her analysis of epistolary quipus from San Juan de Collata, Peru , challenging the assumption that quipus do not represent information phonetically. [ 26 ] However, the quipus in question date to the colonial period and are believed to have been exchanged during an 18th-century rebellion against the Spanish government, suggesting that their encoding may have been influenced by the introduction of European writing systems. With the help of local leaders, Hyland argues that the names of the two ayllus , or family lineages, who received and sent the quipus can be translated using phonetic references to the animal fibers and colors of the relevant quipu cords. [ 27 ] [ 28 ]
While Spanish colonial chroniclers, such as Inca Garcilaso de la Vega , hinted at the numerical system of quipus , it is Leslie Leland Locke who is often credited with first demonstrating that many quipus encode numbers using a base-10 positional notation. [ 29 ] [ 30 ] Starting in the late 1960's and building on Locke's foundational work, Marcia Ascher and Robert Ascher analyzed several hundred quipus , revealing that most of the information recorded by quipu knots is numerical and can be systematically interpreted.
Most q uipus use three main types of knots: simple overhand knots ; "long knots", consisting of an overhand knot with one or more additional turns ; and figure-eight knots . The Aschers’ also identified a fourth, and less common, type of knot—a figure-eight knot with an extra twist—which they refer to as an "EE" knot. On a given quipu cord, knots are grouped into clusters. Each cluster is tied at specific registers, or lengths, along the cord. These knot clusters represent digits in a base-10 number system. [ 31 ] The units, or "ones" position is commonly tied at the bottom of a cord, followed by a space above it, then the "tens" position, then another space, then hundreds position, and so on. In other words:
For example, if 4s represents four simple knots, 3L represents a long knot with three turns, E represents a figure-eight knot, and X represents a space:
Since the ones position on quipu cords are shown in a distinctive way (i.e., using long knots and figure-eight knots), it is usually clear where a number ends. Thus, it is possible that a single quipu cord could contain several numbers. For example:
The "reading" of quipu knots as numbers in the way outlined above is bolstered by the fortunate fact that quipus regularly contain sums in systematic ways. [ 29 ] [ 30 ] [ 32 ] For instance, a cord may contain the sum of the next n cords, with this relationship being repeated throughout the quipu . In other cases, there are even cords which contain sums of sums. Such a relationship would be highly improbable if quipu knot values were being incorrectly interpreted.
Some data items are not numbers but what Ascher and Ascher call number labels . [ 1 ] They are still composed of digits, but the resulting number seems to be used as a code, much as we use numbers to identify individuals, places, or things. For example, Carrie J. Brezine decoded that a particular three-number label at the beginning of some quipus may refer to Puruchuco , similar to a ZIP code . [ 33 ]
Some have argued that far more than numeric information is present and that quipus are a writing system . This would be an especially important discovery as there is no surviving record of written Quechua predating the Spanish invasion . Possible reasons for this apparent absence of a written language include destruction by the Spanish of all written records, or the successful concealment by the Inca peoples of those records. Making the matter even more complex, the Inca 'kept separate "khipu" for each province, on which a pendant string recorded the number of people belonging to each category.' [ 34 ] This creates yet another step in the process of decryption in addition to the Spanish attempts at eradicating the system. [ 35 ] Historians Edward Hyams and George Ordish believe quipus were recording devices, similar to musical notation, in that the notes on the page present basic information, and the performer would then bring those details to life. [ 36 ]
In 2003, while checking the geometric signs that appear on drawings of Inca dresses from the First New Chronicle and Good Government , written by Felipe Guaman Poma de Ayala in 1615, William Burns Glynn found a pattern that seems to decipher some words from quipus by matching knots to colors of strings.
The August 12, 2005, edition of the journal Science includes a report titled "Khipu Accounting in Ancient Peru" by anthropologist Gary Urton and mathematician Carrie J. Brezine. Their work may represent the first identification of a quipu element for a non-numeric concept, a sequence of three figure-eight knots at the start of a quipu that seems to be a unique signifier. It could be a toponym for the city of Puruchuco (near Lima ), or the name of the quipu keeper who made it, or its subject matter, or even a time designator. [ 37 ]
Beynon-Davies considers quipus as a sign system and develops an interpretation of their physical structure in terms of the concept of a data system . [ 38 ]
Khipu kamayuqkuna (knot makers/keepers, i.e., the former Inca record keepers) supplied colonial administrators with a variety and quantity of information pertaining to censuses, tribute, ritual and calendrical organization, genealogies, and other such matters from Inca times. Performing a number of statistical tests for quipu sample VA 42527, one study led by Alberto Sáez-Rodríguez discovered that the distribution and patterning of S- and Z-knots can organize the information system from a real star map of the Pleiades cluster. [ 39 ]
Laura Minelli, a professor of pre-Columbian studies at the University of Bologna , has discovered something which she believed to be a seventeenth-century Jesuit manuscript that describes literary quipus , titled Historia et Rudimenta Linguae Piruanorum . This manuscript consists of nine folios with Spanish, Latin , and ciphered Italian texts. Owned by the family of Neapolitan historian Clara Miccinelli, the manuscript also includes a wool quipu fragment. Miccinelli believes that the text was written by two Italian Jesuit missionaries, Joan Antonio Cumis and Giovanni Anello Oliva, around 1610–1638, and Blas Valera , a mestizo Jesuit sometime before 1618. Along with the details of reading literary quipus , the documents also discuss the events and people of the Spanish conquest of Peru . According to Cumis, since so many quipus were burned by the Spanish, very few remained for him to analyze. As related in the manuscript, the word Pacha Kamaq , the Inca deity of earth and time, was used many times in these quipus , where the syllables were represented by symbols formed in the knots. Following the analysis of the use of "Pacha Kamaq", the manuscript offers a list of many words present in quipus . [ 40 ] However, both Bruce Mannheim, the director of the Center for Latin American Studies at the University of Michigan , and Colgate University 's Gary Urton, question its origin and authenticity. These documents seem to be inspired freely by a 1751 writing of Raimondo di Sangro, Prince of Sansevero . [ 41 ] [ 42 ] [ 43 ]
Claims of the earliest quipu, or possible proto- quipu, comes from the Late Preceramic (c. 3000–1800 BCE) site of Caral , [ 44 ] [ 45 ] though this claim has yet to be thoroughly evaluated. A more plausible candidate for the earliest known precursor to quipus may be the wrapped batons found at the site of Cerrillos from the Late Paracas Period (c. 350–200 BCE). [ 46 ]
The first undisputed evidence of quipu technology dates back to the Middle Horizon (c. 600–1000 CE), [ 47 ] with these early quipus being used by the Wari Empire . Differing slightly from their Inca successors, extant Wari quipu specimens tend to be smaller, have brightly colored thread wrapped cords, and its own system of knots which scholars do not fully understand. [ 4 ] [ 5 ]
Quipucamayocs (Quechua khipu kamayuq , "khipu-authority"), the accountants of Tawantin Suyu , created and deciphered the quipu knots. Quipucamayocs could carry out basic arithmetic operations, such as addition, subtraction, multiplication, and division. They kept track of mita , a form of taxation . The quipucamayocs also tracked the type of labor being performed, maintained a record of economic output , and ran a census that counted everyone from infants to "old blind men over 80". The system was also used to keep track of the calendar. According to Guaman Poma, quipucamayocs could "read" the quipus with their eyes closed. [ 41 ]
Quipucamayocs were from a class of people, "males, fifty to sixty", [ 48 ] and were not the only members of Inca society to use quipus . Inca historians used quipus when telling the Spanish about Tawantin Suyu history (whether they only recorded important numbers or actually contained the story itself is unknown). Members of the ruling class were usually taught to read quipus in the Inca equivalent of a university, the yachay wasi (literally, "house of teaching"), in the third year of schooling, for the higher classes who would eventually become the bureaucracy. [ 49 ]
In 1532, the Spanish Empire 's conquest of the Andean region began, with several Spanish conquerors making note of the existence of quipus in their written records about the invasion. The earliest known example comes from Hernando Pizarro , the brother of the Spanish military leader Francisco Pizarro , who recorded an encounter that he and his men had in 1533 as they traveled along the royal road from the highlands to the central coast. [ 50 ] It was during this journey that they encountered several quipu keepers, later relating that these keepers "untied some of the knots which they had in the deposits section [of the khipu], and they [re-]tied them in another section [of the khipu]." [ 51 ] [ 52 ] [ 53 ] [ 54 ]
Christian officials of the Third Council of Lima banned and ordered the burning of some q uipus in 1583 because they were used to record offerings to non-Christian gods and were therefore considered idolatrous objects and an obstacle to religious conversion. [ 9 ]
The quipu system operated as both a method of calculation and social organization, regulating regional governance and land use. [ 55 ] While evidence for the latter is still under the critical eye of scholars around the world, the very fact that they are kept to this day without any confirmed level of fluent literacy in the system is testament to its historical 'moral authority.' [ 56 ] Today, "khipu" is regarded as a powerful symbol of heritage, only 'unfurled' and handled by 'pairs of [contemporary] dignitaries,' as the system and its 'construction embed' modern 'cultural knowledge.' [ 56 ] Ceremonies in which they are 'curated, even though they can no longer be read,' is even further support for the case of societal honor and significance associated with the quipu . [ 56 ] Even today, 'the knotted cords must be present and displayed when village officers leave or begin service, and draping the cords over the incoming office holders instantiates the moral and political authority of the past.' [ 56 ] These examples are indicative of how the quipu system was not only fundamental mathematically and linguistically for the original Inca, but also for cultural preservation of the original empire's descendants.
Anthropologists and archaeologists carrying out research in Peru have highlighted two known cases where quipus have continued to be used by contemporary communities, albeit as ritual items seen as "communal patrimony" rather than as devices for recording information. [ 57 ] The quipu system, being the useful method of social management it was for the Inca, is also a link to the Cuzco census, as it was one of the primary methods of population calculation. [ 58 ] This also has allowed historians and anthropologists to understand both the census and the "decimal hierarchy" system the Inca used, and that they were actually 'initiated together,' due to the fact that they were 'conceptually so closely linked.' [ 58 ]
In 1994, the American cultural anthropologist Frank Salomon conducted a study in the Peruvian village of Tupicocha, where quipus are still an important part of the social life of the village. [ 59 ] As of 1994, this was the only known village where quipus with a structure similar to pre-Columbian quipus were still used for official local government record-keeping and functions, although the villagers did not associate their quipus with Inca artifacts. [ 60 ]
The villagers of San Cristóbal de Rapaz (known as Rapacinos), located in the Province of Oyón , keep a quipu in an old ceremonial building, the Kaha Wayi , that is itself surrounded by a walled architectural complex. Also within the complex is a disused communal storehouse, known as the Pasa Qullqa , which was formerly used to protect and redistribute the local crops, and some Rapacinos believe that the quipu was once a record of this process of collecting and redistributing food. The entire complex was important to the villagers, being "the seat of traditional control over land use, and the centre of communication with the deified mountains who control weather". [ 57 ]
In 2004, the archaeologist Renata Peeters (of the UCL Institute of Archaeology in London) and the cultural anthropologist Frank Salomon (of the University of Wisconsin ) undertook a project to conserve both the quipus in Rapaz and the building that it was in, due to their increasingly poor condition. [ 61 ]
The remote village of Jucul, Peru, has kept quipus in the attic of its colonial church for centuries, only recently being discovered by outsiders in 2024. [ 62 ] These quipus are closely related to those of San Cristóbal de Rapaz, which is near by. [ 63 ]
In 1912, Leslie Leland Locke published "The Ancient Quipu, A Peruvian Knot Record," American Anthropologist, New Series I4 (1912) 325–332. [ 29 ] This was the first work to show how the Inca (Inka) Empire and its predecessor societies used the quipu for mathematical and accounting records in the decimal system.
The archaeologist Gary Urton noted in his 2003 book Signs of the Inka Khipu that he estimated "from my own studies and from the published works of other scholars that there are about 600 extant quipu in public and private collections around the world." [ 64 ]
According to the Khipu Database Project [ 65 ] undertaken by Harvard University professor Gary Urton and his colleague Carrie Brezine, 751 quipus have been reported to exist across the globe. [ failed verification ] Their whereabouts range from Europe to North and South America . Most are housed in museums outside of their native countries, but some reside in their native locations under the care of the descendants of those who made the knot records. A table of the largest collections is shown below.
While patrimonial quipu collections have not been accounted for in this database, their numbers are likely to be unknown. One prominent patrimonial collection held by the Rapazians of Rapaz, Peru, was recently researched by University of Wisconsin–Madison professor, Frank Salomon. [ 71 ]
Quipus are made of fibers , either spun and plied thread such as wool or hair from alpaca , llama , guanaco or vicuña , though are also commonly made of cellulose like cotton . Archaeological evidence has also shown that, in some cases, finely carved wood was used as a supplemental base to which the color-coded cords could be attached. [ 72 ] The knotted strings of quipus were often made with an "elaborate system of knotted cords, dyed in various colors, the significance of which was known to the magistrates ". [ 73 ] Fading of color , natural or dyed, cannot be reversed, and may indicate further damage to the fibers. Colors can darken if damaged by dust or by certain dyes and mordants . [ 74 ] Quipus have been found with adornments, such dried potatoes and beans, attached to the cords, and these non-textile materials may require additional preservation measures. [ 75 ]
Quipus are now preserved using techniques that aim to minimize their future degradation. Museums , archives and special collections have adopted preservation guidelines from textile practices. [ 76 ]
Environmental controls are used to monitor and control temperature , humidity and light exposure of storage areas. As with all textiles, cool, clean, dry and dark environments are most suitable. The heating, ventilating and air conditioning, or HVAC systems, of buildings that house quipu knot records are usually automatically regulated. Relative humidity should be 60% or lower, with low temperatures, as high temperatures can damage the fibres and make them brittle. Damp conditions and high humidity can damage protein-rich material. Textiles suffer damage from ultraviolet (UV) light, which can include fading and weakening of the fibrous material. When quipus are on display, their exposure to ambient conditions is usually minimized and closely monitored. [ 74 ] [ 77 ]
Despite best efforts, damage can occur during storage, or be from the result of earlier conservation efforts. [ 78 ] The more accessible the items are during storage, the greater the chance of early detection. [ 77 ] Storing quipus horizontally on boards covered with a neutral pH paper (paper that is neither acid or alkaline ) to prevent potential acid transfer is a preservation technique that extends the life of a collection. The fibers can be abraded by rubbing against each other or, for those attached to sticks or rods, by their own weight if held in an upright position. Extensive handling of quipus can also increase the risk of further damage. [ 79 ]
Quipus are also closely monitored for mold , as well as insects and their larvae . As with all textiles, these are major problems. Fumigation may not be recommended for fiber textiles displaying mold or insect infestations , although it is common practice for ridding paper of mold and insects.
Conservators in the field of library science have the skills to handle a variety of situations. Even though some quipus have hundreds of cords, each cord should be assessed and treated individually. Quipu cords can be "mechanically cleaned with brushes, small tools and light vacuuming". [ 80 ] Just as the application of fungicides is not recommended to rid quipus of mold, neither is the use of solvents to clean them.
Even when people have tried to preserve quipus , corrective care may still be required. If quipus are to be conserved close to their place of origin, local camelid or wool fibres in natural colors can be obtained and used to mend breaks and splits in the cords. [ 80 ] Rosa Choque Gonzales and Rosalia Choque Gonzales, conservators from southern Peru, worked to conserve the Rapaz patrimonial quipus in the Andean village of Rapaz, Peru. These quipus had undergone repair in the past, so this conservator team used new local camelid and wool fibers to spin around the area under repair in a similar fashion to the earlier repairs found on the quipu . [ 80 ]
When Gary Urton, professor of Anthropology at Harvard, was asked "Are they [ quipus ] fragile?", he answered, "some of them are, and you can't touch them – they would break or turn into dust. Many are quite well preserved, and you can actually study them without doing them any harm. Of course, any time you touch an ancient fabric like that, you're doing some damage, but these strings are generally quite durable." [ 81 ]
Ruth Shady , a Peruvian archeologist , has discovered a quipu or perhaps proto-quipu believed to be around 5,000 years old in the coastal city of Caral . It was in quite good condition, with "brown cotton strings wound around thin sticks", along with "a series of offerings, including mysterious fiber balls of different sizes wrapped in 'nets' and pristine reed baskets. Piles of raw cotton – uncombed and containing seeds, though turned a dirty brown by the ages – and a ball of cotton thread" were also found preserved. The good condition of these articles can be attributed to the arid climate of Caral. [ 82 ] | https://en.wikipedia.org/wiki/Quipu |
Quorn is a brand of meat substitute products. Quorn originated in the UK and is sold primarily in Europe, but is available in 11 countries. The brand is owned by parent company Monde Nissin . [ 1 ]
Quorn is sold as both a cooking ingredient and as a meat substitute used in a range of prepackaged meals .
Though all Quorn products are vegetarian , not all are vegan . All Quorn foods contain mycoprotein as an ingredient, which is derived from the Fusarium venenatum fungus. [ 2 ] In most Quorn products, the fungus culture is dried and mixed with egg white , which acts as a binder, and then is adjusted in texture and pressed into various forms. The vegan formulation uses potato protein as a binder instead of egg white. [ 3 ]
Quorn was launched in 1985 by Marlow Foods, a joint venture between Rank Hovis McDougall (RHM) and Imperial Chemical Industries (ICI). [ 4 ]
Microbial biomass is produced commercially as single-cell protein (SCP) for human food or animal feed and as viable yeast cells for the baking industry. The industrial production of bakers' yeast started in the early 1900s, and yeast biomass was used as human food in Germany during World War I . The development of large-scale processes for the production of microbial biomass as a source of commercial protein began in earnest in the late 1960s.
Several of the processes investigated did not come to fruition owing to political and economic problems, but the establishment of the ICI Pruteen process for the production of bacterial SCP for animal feed was a milestone in the development of the fermentation industry. [ 5 ] This process used continuous culture on a large scale 1,500 m 3 (53,000 cu ft). The economics of the production of SCP as animal feed were marginal, which eventually led to the discontinuation of the Pruteen process.
The technical expertise gained from the Pruteen process assisted ICI in collaborating with company Rank Hovis McDougall on a process for the production of fungal biomass for human food. A continuous fermentation process for the production of Fusarium venenatum biomass (marketed as Quorn) was developed using a 40 m 3 (1,400 cu ft) air-lift fermenter. [ 6 ] [ 7 ]
During the 1960s, it was predicted that by the 1980s there would be a shortage of protein-rich foods. [ 8 ] [ 9 ]
The filamentous fungus, Fusarium venenatum , was discovered in a soil sample in 1967. [ 10 ] In 1985, RHM was given permission to sell mycoprotein for human consumption after a ten-year evaluation programme. [ 11 ] [ 12 ]
The brand Quorn was first marketed in 1985 by Marlow Foods (named after Rank Hovis McDougall's headquarters in Marlow, Buckinghamshire ), a joint venture between RHM and Imperial Chemical Industries (ICI), which provided a fermenter left vacant from their abandoned single-cell feed programme. [ 13 ] The two partners invested in patents for growing and processing the fungus, and other intellectual properties in the brand. [ citation needed ] The name of the product was taken from a trademark owned by RHM. This trademark was previously used for a range of instant food packets named after the Quorn Hunt , which in turn derives from the Leicestershire village of Quorn . [ 14 ] [ 15 ]
Quorn entered distribution in the UK in 1993, and it was introduced to other parts of Europe in the 1990s, and to North America in 2002. [ 16 ]
The initial advertising campaign for Quorn featured sports personalities, including footballer Ryan Giggs , rugby player Will Carling , and Olympic runner Sally Gunnell . In 2013, the company appointed Mo Farah as its ambassador in a marketing push for fitness. [ 17 ] [ 18 ] [ 19 ]
Quorn is sold in ready-to-cook forms, such as cubes and a form resembling minced meat . The company later introduced a range of chilled vegetarian meals, including pizzas, lasagne, cottage pie, and products resembling sliced meat, hot dogs, and burgers. [ 20 ] By 2005, Quorn enjoyed around 60% of the meat-replacement food market in the UK, with annual sales of around £95 million. [ 9 ] [ 21 ] By 2006, it was available in stores in the UK; Europe (Belgium, Denmark, Ireland, Netherlands, Sweden and Switzerland); and North America (Canada and United States). Since June 2010, it has been available in Australia. [ 22 ] [ 23 ] In May 2012, Quorn Foods opened the German website quorn.de to relaunch Quorn in Germany.
After its producer switched to using free-range eggs as an ingredient, the Vegetarian Society gave the product its seal of approval. [ 24 ]
In 2004, McDonald's introduced a Quorn-branded burger bearing the seal of approval of the Vegetarian Society. [ 25 ] [ 26 ] However, as of 2009, the Quorn burgers were no longer available at any McDonald's restaurant in the UK, and the McPlant was made using Beyond Meat . In 2011, Quorn Foods launched a vegan burger into the United States market, using potato protein as a binder instead of egg albumen, to confer vegan status. [ 27 ] According to Quorn's website, by 2020, a number of Quorn items were available in United States markets, many of which are vegan. They also have gluten-free options.
As of 2014, it was reported that most consumers of Quorn are meat eaters rather than vegetarians . [ 28 ] As of 2018, the market for Quorn products was said to be increasing worldwide and the company expects further growth. [ 29 ] [ 30 ] However, six years on parent Monde Nissin is bleeding heavily on its investments on Quorn to the total tune so far of 40 billion Philippine pesos (equivalent to US$690 million). [ 31 ]
Originally conceived in 1985 and owned by Marlow Foods, a joint venture between Rank Hovis McDougall (RHM) and Imperial Chemical Industries (ICI), RHM exited the business in 1990 by selling its shares to ICI. When ICI spun off its biological products divisions from the core chemical business in 1993, Marlow Foods became a part of the newly formed Zeneca group, later AstraZeneca .
In 2003, AstraZeneca sold Marlow Foods, including the Quorn business and associated trademarks and patents, to Montagu Private Equity for £72m. Montagu sold the business on to Premier Foods in 2005 for £172m. [ 21 ]
In 2011, Premier Foods sold Quorn to Exponent Private Equity and Intermediate Capital Group for £205 million . [ 32 ] [ 33 ] In 2015, the owners put the company up for sale via a business auction process. Attracting bidders including Danone , Kerry Group , McCain Foods and Nomad Foods , it was sold to Monde Nissin Corporation headquartered in the Philippines for £550m ($831m). [ 34 ] [ 35 ]
Quorn is made from the soil mould Fusarium venenatum strain PTA-2684 (previously misidentified as the parasitic mould Fusarium graminearum [ 40 ] ).
The fungus is grown in continually oxygenated water in large, otherwise sterile fermentation tanks. Glucose and fixed nitrogen are added as a food for the fungus, as are vitamins and minerals to improve the food value of the product. The resulting mycoprotein is then extracted and heat-treated to remove excess levels of RNA . Previous attempts to produce such fermented protein foodstuffs were thwarted by excessive levels of DNA or RNA; without the heat treatment, purines , found in nucleic acids , are metabolised by humans to produce uric acid , which can lead to gout . [ 41 ]
The product is dried and mixed with egg albumen , which acts as a binder. It is then textured, giving it some of the grained character of meat, and pressed into a mince resembling ground beef; forms resembling chicken breasts, meatballs, and turkey roasts; or chunks resembling diced chicken breast. In these forms, Quorn has a varying colour and a mild flavour resembling the imitated meat product, and is suitable for use as a replacement for meat in many dishes, such as stews and casseroles.
The final Quorn product is high in protein and dietary fibre and is low in saturated fat . It contains less dietary iron than most meats and the manufacturers have not released much information about additives they use to make Quorn resemble meat. Quorn is considered acceptable in small amounts for babies over nine months old, but should be introduced gradually. The high fibre and low food energy content is better for adults than babies and too much fibre can cause flatulence. The salt content should be checked before giving Quorn to babies, since the salt content varies among products. [ 42 ] [ 43 ]
The carbon footprint of Quorn Frozen Mince in the UK is claimed to be at least 80% less than that of beef. [ 44 ]
Quorn for the UK and European market is produced at Marlow's headquarters in Stokesley , North Yorkshire and at nearby Billingham in Stockton-on-Tees . [ 45 ]
After Quorn's 2002 debut in the United States, the Center for Science in the Public Interest (CSPI) disputed the original labeling of Quorn as a "mushroom based" product, since Fusarium venenatum is not a mushroom (rather, it is a microfungus ). [ 46 ] The sale of Quorn was opposed by the American Mushroom Institute , and rival Gardenburger , which filed complaints with advertising and trading-standards watchdogs in Europe and the US, stating Quorn's 'mushroom based' claim was deceptive. [ 46 ] [ 47 ]
CSPI claimed that Quorn could cause allergic reactions and should be removed from stores. CSPI claimed in 2003 that it "sickens 4.5% of eaters". [ 48 ] The manufacturer (Marlow Foods) disputed the figure, claiming that only 0.0007% (1 in 146,000) suffer adverse reactions and that the strain of fungus it uses does not produce toxins. [ 48 ] Leslie Bonci, professor of nutrition at the University of Pittsburgh , described CSPI's claims as "overblown". [ 49 ] Wendy Preiser, Gardenburger's vice president of marketing, said the company feared that Quorn's labels would cause suspicion about all meat-free products. [ 50 ] [ 49 ]
The UK's Advertising Standards Authority was concerned that Marlow's marketing of Quorn as "mushroom in origin" was "misleading consumers". Marlow Foods were asked either to delete the claim or modify it to identify its fungal origin. [ 51 ]
Quorn formerly used battery eggs in some of its production processes, a practice opposed on ethical grounds by many vegetarians. Working with the Vegetarian Society, which initially did not approve Quorn's products, Marlow began phasing out battery eggs in 2000, [ 52 ] and by 2004 all of their UK products were free of battery eggs, earning the Vegetarian Society's seal of approval. [ 24 ]
An asthma attack in 2003 was linked to Quorn. Tests showed Quorn to be the only food to which the patient had an allergic reaction. A spokesperson for the Food Standards Agency stated that an allergy was not surprising, due to the high protein content. [ 53 ] Former FSA director Jon Bell responded in defence of Quorn, stating that several commonly consumed foods and food ingredients, such as soya , have a much higher intolerance level than Quorn. Adverse reactions were reported for 1 in 146,000 people who ate Quorn, compared to 1 in 35 who ate shellfish and 1 in 350 who ate soya. [ 53 ] [ 54 ]
In the European Union, patents expire after 20 years from their filing date. Since the first patent application was filed in 1985, [ 55 ] the mycoprotein patents had already expired in 2010 in all European Union countries. Now anyone can legally produce mycoprotein products using the previously patented processes. However, they would have to use other brand names as Marlow Foods maintains ownership of the Quorn brand name. On 14 March 2011, CEO Kevin Brennan said in an interview: "Some patents surrounding the core technology have expired, but the product uses a peculiar fermentation method, and we have 30-plus years' experience in perfecting this on site to produce the product better and at a lower cost. Huge related costs include £30m cost for a fermentation tower and related equipment, so you can't simply look at a patent and say 'there you go'." [ 56 ]
In late 2011, the first vegan Quorn product was released, called the Quorn Vegan Burger, [ 57 ] available initially only in the United States. Following strong sales of the product and increasing demand from the UK market, Quorn began development of a line of vegan products for the UK market, as well as reducing its use of eggs overall, using 3.5 million fewer eggs since 2010. [ 58 ] The first range of vegan Quorn in the UK included eight products and was launched in October 2015. [ 59 ]
In January 2019, Quorn produced the filling for a vegan sausage roll sold by UK bakery chain Greggs . [ 60 ] The product was consistently sold out, and was identified by the chain as a major contributor to increasing profits and a record share price . [ 61 ] [ 62 ] In January 2020, Greggs released a Quorn-based vegan "steak bake". [ 63 ] | https://en.wikipedia.org/wiki/Quorn |
In biology , quorum sensing or quorum signaling ( QS ) [ 1 ] is the process of cell-to-cell communication [ 2 ] that allows bacteria to detect and respond to cell population density by gene regulation , typically as a means of acclimating to environmental disadvantages. [ 3 ]
Quorum sensing is a type of cellular signaling , and can be more specifically considered a type of paracrine signaling . However, it also contains traits of autocrine signaling : a cell produces both an autoinducer molecule and the receptor for the autoinducer. [ 3 ] As one example, quorum sensing enables bacteria to restrict the expression of specific genes to the high cell densities at which the resulting phenotypes will be most beneficial, especially for phenotypes that would be ineffective at low cell densities and therefore too energetically costly to express. [ 4 ]
Many species of bacteria use quorum sensing to coordinate gene expression according to the density of their local population. In a similar fashion, some social insects use quorum sensing to determine where to nest. Quorum sensing in pathogenic bacteria activates host immune signaling and prolongs host survival, by limiting the bacterial intake of nutrients, such as tryptophan , which further is converted to serotonin . [ 5 ] As such, quorum sensing allows a commensal interaction between host and pathogenic bacteria. [ 5 ] Quorum sensing may also be useful for cancer cell communications. [ 6 ]
In addition to its function in biological systems, quorum sensing has several useful applications for computing and robotics. In general, quorum sensing can function as a decision-making process in any decentralized system in which the components have: (a) a means of assessing the number of other components they interact with and (b) a standard response once a threshold of the number of components is detected.
The first observations of an autoinducer-controlled phenotype in bacteria were reported in 1970, by Kenneth Nealson, Terry Platt, and J. Woodland Hastings , [ 7 ] who observed what they described as a conditioning of the medium in which they had grown the bioluminescent marine bacterium Aliivibrio fischeri . [ 8 ] These bacteria did not synthesize luciferase —and therefore did not luminesce—in freshly inoculated culture but only after the bacterial population had increased significantly.
In a series of publications from 1998 to 2001, Bonnie Bassler showed that quorum sensing is not just an isolated mechanism in Aliivibrio fischeri , but is used ubiquitously across bacteria to communicate. [ 9 ] [ 10 ] This advance demonstrated that bacteria are capable of carrying out complex, collective behaviors. [ 11 ] [ 12 ]
Because Nealson, Platt, and Hastings attributed the conditioning of the growth medium to the growing population of cells itself, they referred to the phenomenon as autoinduction. [ 7 ] [ 13 ] [ 8 ]
In 1994, after study of the phenomenon had expanded into several additional bacteria, Stephen Winans did not believe the word autoinduction fully characterized the true process so, in a review article coauthored with W. Claiborne Fuqua and E. Peter Greenberg, [ 14 ] he introduced the term quorum sensing . Its use also avoided confusion between the terms autoinduction and autoregulation . The new term was not stumbled onto, but rather created through trial and error. Among the alternatives that Winans had created and considered were gridlockins , communiolins , and quoromones . [ 15 ]
Some of the best-known examples of quorum sensing come from studies of bacteria . Bacteria use quorum sensing to regulate certain phenotype expressions, which in turn, coordinate their behaviors. Some common phenotypes include biofilm formation, virulence factor expression, and motility . Certain bacteria are able to use quorum sensing to regulate bioluminescence , nitrogen fixation and sporulation . [ 16 ]
The quorum-sensing function is based on the local density of the bacterial population in the immediate environment. [ 17 ] It can occur within a single bacterial species, as well as between diverse species. Both gram-positive and gram-negative bacteria use quorum sensing, but there are some major differences in their mechanisms. [ 18 ]
For the bacteria to use quorum sensing constitutively, they must possess three abilities: secretion of a signaling molecule, secretion of an autoinducer (to detect the change in concentration of signaling molecules), and regulation of gene transcription as a response. [ 16 ] This process is highly dependent on the diffusion mechanism of the signaling molecules. QS signaling molecules are usually secreted at a low level by individual bacteria. At low cell density, the molecules may just diffuse away. At high cell density, the local concentration of signaling molecules may exceed its threshold level, and trigger changes in gene expression. [ 18 ]
Gram-positive bacteria use autoinducing peptides (AIP) as their autoinducers. [ 19 ]
When gram-positive bacteria detect high concentration of AIPs in their environment, that happens by way of AIPs binding to a receptor to activate a kinase . The kinase phosphorylates a transcription factor , which regulates gene transcription. This is called a two-component system .
Another possible mechanism is that AIP is transported into the cytosol , and binds directly to a transcription factor to initiate or inhibit transcription. [ 19 ]
Gram-negative bacteria produce N-acyl homoserine lactones (AHL) as their signaling molecule. [ 19 ] Usually AHLs do not need additional processing, and bind directly to transcription factors to regulate gene expression. [ 18 ]
Some gram-negative bacteria may use the two-component system as well. [ 19 ]
The bioluminescent bacterium Aliivibrio fischeri is the first organism in which QS was observed. It lives as a mutualistic symbiont in the photophore (or light-producing organ) of the Hawaiian bobtail squid . When A. fischeri cells are free-living (or planktonic ), the autoinducer is at low concentration, and, thus, cells do not show luminescence. However, when the population reaches the threshold in the photophore (about 10 11 cells/ml), transcription of luciferase is induced, leading to bioluminescence .
In A. fischeri , bioluminescence is regulated by AHLs (N-acyl-homoserine lactones) which is a product of the LuxI gene whose transcription is regulated by the LuxR activator. LuxR works only when AHLs binds to the LuxR.
Curvibacter sp. is a gram-negative curved rod-formed bacterium which is the main colonizer of the epithelial cell surfaces of the early branching metazoan Hydra vulgaris . [ 20 ] [ 21 ] Sequencing the complete genome uncovered a circular chromosome (4.37 Mb), a plasmid (16.5 kb), and two operons coding each for an AHL (N-acyl-homoserine lactone) synthase ( curI1 and curI2 ) and an AHL receptor ( curR1 and curR2 ). [ 21 ] Moreover, a study showed that these host associated Curvibacter bacteria produce a broad spectrum of AHL, explaining the presence of those operons. [ 21 ] As mentioned before, AHL are the quorum sensing molecules of gram-negative bacteria, which means Curvibacter has a quorum sensing activity.
Even though their function in host-microbe interaction is largely unknown, Curvibacter quorum-sensing signals are relevant for host-microbe interactions. [ 21 ] Indeed, due to the oxidoreductase activity of Hydra , there is a modification of AHL signalling molecules (3-oxo-homoserine lactone into 3-hydroxy-homoserine lactone) which leads to a different host-microbe interaction. On one hand, a phenotypic switch of the colonizer Curvibacter takes place. The most likely explanation is that the binding of 3-oxo-HSL and 3-hydroxy-HSL causes different conformational changes in the AHL receptors curR1 and curR2 . As a result, there is a different DNA-binding motif affinity and thereby different target genes are activated. [ 21 ] On the other hand, this switch modifies its ability to colonize the epithelial cell surfaces of Hydra vulgaris . [ 21 ] Indeed, one explanation is that with a 3-oxo-HSL quorum-sensing signal, there is an up-regulation of flagellar assembly. Yet, flagellin , the main protein component of flagella, can act as an immunomodulator and activate the innate immune response in Hydra . Therefore, bacteria have less chance to evade the immune system and to colonize host tissues. [ 21 ] Another explanation is that 3-hydroxy-HSL induces carbon metabolism and fatty acid degradation genes in Hydra . This allows the bacterial metabolism to adjust itself to the host growth conditions, which is essential for the colonization of the ectodermal mucus layer of Hydrae . [ 21 ]
Enterococcus faecalis is an opportunistic, gram-positive bacteria that forms biofilm in glass. This process is also known as forming a biofilm in vitro. The presence of (Esp), a certain cell surface protein, aids the formation of a biofilm by E. faecalis . [ 22 ]
The ability of E. faecalis to form biofilms contributes to its capacity to survive in extreme environments, and facilitates its involvement in persistent bacterial infection, particularly in the case of multi-drug resistant strains. [ 23 ] Biofilm formation in E. faecalis is associated with DNA release, and such release has emerged as a fundamental aspect of biofilm formation. [ 23 ] Conjugative plasmid DNA transfer in E. faecalis is enhanced by the release of peptide sex pheromones . [ 24 ]
In the gram-negative bacterium Escherichia coli , cell division may be partially regulated by AI-2 -mediated quorum sensing. This species uses AI-2, which is produced and processed by the lsr operon . Part of it encodes an ABC transporter , which imports AI-2 into the cells during the early stationary (latent) phase of growth. AI-2 is then phosphorylated by the LsrK kinase , and the newly produced phospho-AI-2 can be either internalized or used to suppress LsrR, a repressor of the lsr operon (thereby activating the operon). Transcription of the lsr operon is also thought to be inhibited by dihydroxyacetone phosphate (DHAP) through its competitive binding to LsrR. Glyceraldehyde 3-phosphate has also been shown to inhibit the lsr operon through cAMP -CAPK-mediated inhibition. This explains why, when grown with glucose , E. coli will lose the ability to internalize AI-2 (because of catabolite repression ). When grown normally, AI-2 presence is transient.
E. coli and Salmonella enterica do not produce AHL signals commonly found in other gram-negative bacteria. However, they have a receptor that detects AHLs from other bacteria and change their gene expression in accordance with the presence of other "quorate" populations of gram-negative bacteria. [ 25 ] AHL quorum sensing regulates a wide range of genes through cell density. Other species of bacteria produce AHLs that Escherichia and Salmonella can detect. E. coli and Salmonella produce a receptor like protein (SdiA) allowing the amino acid sequence that is similar to AHL show AHLs can be found in the bovine rumen and E. coli responds to AHLs taken out of the bovine rumen. Most animals do not have AHL in their gastrointestinal tracts. [ 26 ]
Salmonella encodes a LuxR homolog, SdiA, but does not encode an AHL synthase. SdiA detects AHLs produced by other species of bacteria including Aeromonas hydrophila , Hafnia alvei , and Yersinia enterocolitica . [ 27 ] When AHL is detected, SdiA regulates the rck operon on the Salmonella virulence plasmid ( pefI-srgD-srgA-srgB-rck-srgC ) and a single gene horizontal acquisition in the chromosome srgE . [ 28 ] [ 29 ] Salmonella does not detect AHL when passing through the gastrointestinal tracts of several animal species, suggesting that the normal microbiota does not produce AHLs. However, SdiA does become activated when Salmonella transits through turtles colonized with Aeromonas hydrophila or mice infected with Yersinia enterocolitica . [ 30 ] [ 31 ] Therefore, Salmonella appears to use SdiA to detect the AHL production of other pathogens rather than the normal gut flora.
Myxococcus is a genus of gram-negative bacterium in the Myxococcacae family. Myxococcus xanthus specifically, a bacillus myxobacteria species within Myxococcae , grows in the upper layers of soil. This bacterium is known for its unique utilization of quorum sensing practices to hunt.
The bacterium uniquely survives not on sugars, but lipids created by the degradation of macromolecules lysed by the species. It hunts and feeds through a density-regulated method of predation that is "the regulation of gene expression in response to cell density." [ 32 ] The pilus propelled microorganism moves with the use of both S- and A- (or gliding) motility, which provide transportation across a dynamic range of different surfaces. [ 33 ] M. xanthus 's A-motility is most effective in the presence of a single or low number of cells, allowing the bacteria to glide in high agar concentrations. The S-motility, or social motility, is controlled by the process of quorum sensing and is only effective when cells are within one cell length of a neighbor. [ 34 ] Although the precise specifics of M. xanthus 's communication methods for quorum sensing are not well understood, the bacteria mediate the process by using both C-signal and A-factor. The A-factor molecule, produced by M. xanthus , must reach a set concentration to initiate aggregation for hunting. [ 35 ] The C-signal concentration, on the other hand, plays a role in fruiting body production.
The species is known for its ability to use quorum sensing to hunt in special packs with thousands of individual cells, lending to M. xanthus 's name "the wolf packs." M. xanthus is inclined to behave in a multicellular fashion. In the presence of many cells, it uses these "wolf packs" to form "highly structured biofilms that include tentacle-like packs of surface-gliding cell groups, synchronized rippling waves of oscillating cells and massive spore-filled aggregates that protrude upwards from the substratum to form fruiting bodies." [ 36 ] [ 32 ] On the fringes of this film, individual cells can be observed "gliding across the surface, but the majority of cells are observed in large tendril-shaped groups" using S-motility. [ 32 ]
Staphylococcus aureus is a type of pathogen that causes infection to the skin and soft tissue and can lead to a variety of more severe diseases such as osteomyelitis, pneumonia, and endocarditis. S. aureus uses biofilms in order to increase its chances of survival by becoming resistant to antibiotics. Biofilms help S. aureus become up to 1500 times more resistant to antibiofilm agents, which try to break down biofilms formed by S. aureus . [ 37 ]
Each year Streptococcus pneumoniae kills more than a million people, even though vaccines are available. [ 38 ] A complex quorum sensing system has evolved in S. pneumoniae that regulates bacteriocin production. This system also enables entry into the competent state essential for natural genetic transformation . [ 39 ] In naturally competent S. pneumoniae the competent state is not a constitutive property. However competence can be induced by a peptide pheromone by means of a quorum-sensing mechanism. [ 40 ] When the competent state is induced, this causes release of DNA from a sub-fraction of the S. pneumoniae population, probably by cell lysis. Then most of the S. pneumoniae cells that have been induced to competence become recipients and take up the DNA released by the donors. [ 40 ] Thus it appears that natural transformation in S. pneumoniae is a natural adaptive process for promoting genetic recombination , a process that resembles sexual reproduction in higher organisms. [ 40 ]
The environmental bacterium and opportunistic pathogen Pseudomonas aeruginosa uses quorum sensing to coordinate the formation of biofilm , swarming motility , exopolysaccharide production, virulence, and cell aggregation. [ 41 ] These bacteria can grow within a host without harming it until they reach a threshold concentration. Then they become aggressive, developing to the point at which their numbers are sufficient to overcome the host's immune system , and form a biofilm , leading to disease within the host as the biofilm is a protective layer encasing the bacterial population. [ citation needed ] The relative ease of growth, handling, and genetic manipulation of P. aeruginosa has lent much research effort to the quorum sensing circuits of this relatively common bacterium. Quorum sensing in P. aeruginosa typically encompasses two complete AHL synthase-receptor circuits, LasI-LasR and RhlI-RhlR, as well as the orphan receptor-regulator QscR, which is also activated by the LasI-generated signal. [ 42 ] Together, the multiple AHL quorum sensing circuits of P. aeruginosa influence regulation of hundreds of genes.
Another form of gene regulation that allows the bacteria to rapidly adapt to surrounding changes is through environmental signaling. Recent studies have discovered that anaerobiosis can significantly impact the major regulatory circuit of quorum sensing. This important link between quorum sensing and anaerobiosis has a significant impact on the production of virulence factors of this organism . [ 43 ] There is hope among some humans that the therapeutic enzymatic degradation of the signaling molecules will be possible when treating illness caused by biofilms, and prevent the formation of such biofilms and possibly weaken established biofilms. Disrupting the signaling process in this way is called quorum sensing inhibition . [ 44 ]
It has recently been found that Acinetobacter sp. also show quorum sensing activity. This bacterium, an emerging pathogen, produces AHLs. [ 45 ] Acinetobacter sp. shows both quorum sensing and quorum quenching activity. It produces AHLs and can also degrade the AHL molecules. [ 45 ]
This bacterium was previously considered a fish pathogen, but it has recently emerged as a human pathogen. [ 46 ] Aeromonas sp. have been isolated from various infected sites from patients (bile, blood, peritoneal fluid, pus, stool and urine). All isolates produced the two principal AHLs, N-butanoylhomoserine lactone (C4-HSL) and N-hexanoyl homoserine lactone (C6-HSL). It has been documented that Aeromonas sobria has produced C6-HSL and two additional AHLs with N-acyl side chain longer than C6. [ 47 ]
The YenR and YenI proteins produced by the gammaproteobacterium Yersinia enterocolitica are similar to Aliivibrio fischeri LuxR and LuxI. [ 48 ] [ 49 ] YenR activates the expression of a small non-coding RNA , YenS. YenS inhibits YenI expression and acylhomoserine lactone production. [ 50 ] YenR/YenI/YenS are involved in the control of swimming and swarming motility. [ 49 ] [ 50 ]
V. cholerae is a bacterial pathogen that causes cholera , a disease associated with severe contagious diarrhea that affects millions of people worldwide. V. cholerae is capable of strong communication between cells, and this process is referred to as quorum-sensing. [ 51 ] [ 52 ] In the small intestine, the absence of oxygen and exposure to host-produced bile salts , influence V. cholerae quorum sensing function and thus its pathogenicity. [ 53 ] Quorum sensing appears to contribute to natural genetic transformation , a process that involves the uptake of V. cholerae extracellular DNA by ( competent ) V. cholerae cells. [ 54 ]
Three-dimensional structures of proteins involved in quorum sensing were first published in 2001, when the crystal structures of three LuxS orthologs were determined by X-ray crystallography . [ 55 ] In 2002, the crystal structure of the receptor LuxP of Vibrio harveyi with its inducer AI-2 (which is one of the few biomolecules containing boron ) bound to it was also determined. [ 56 ] Many bacterial species, including E. coli , an enteric bacterium and model organism for gram-negative bacteria, produce AI-2. A comparative genomic and phylogenetic analysis of 138 genomes of bacteria, archaea , and eukaryotes found that "the LuxS enzyme required for AI-2 synthesis is widespread in bacteria, while the periplasmic binding protein LuxP is present only in Vibrio strains," leading to the conclusion that either "other organisms may use components different from the AI-2 signal transduction system of Vibrio strains to sense the signal of AI-2 or they do not have such a quorum sensing system at all." [ 57 ] Vibrio species utilize Qrr RNAs , small non-coding RNAs, that are activated by these autoinducers to target cell density master regulators. Farnesol is used by the fungus Candida albicans as a quorum sensing molecule that inhibits filamentation . [ 58 ]
A database of quorum-sensing peptides is available under the name Quorumpeps. [ 59 ] [ 60 ]
Certain bacteria can produce enzymes called lactonases that can target and inactivate AHLs.
Researchers have developed novel molecules which block the signalling receptors of bacteria ("Quorum quenching"). mBTL is a compound that has been shown to inhibit quorum sensing and decrease the amount of cell death by a significant amount. [ 61 ] Additionally, researchers are also examining the role of natural compounds (such as caffeine ) as potential quorum sensing inhibitors. [ 62 ] Research in this area has been promising and could lead to the development of natural compounds as effective therapeutics.
The majority of quorum sensing systems that fall under the "two-gene" (an autoinducer synthase coupled with a receptor molecule) paradigm as defined by the Vibrio fischeri system occur in the gram-negative Pseudomonadota . A comparison between the Pseudomonadota phylogeny as generated by 16S ribosomal RNA sequences and phylogenies of LuxI-, LuxR-, or LuxS-homologs shows a notably high level of global similarity. Overall, the quorum sensing genes seem to have diverged along with the Pseudomonadota phylum as a whole. This indicates that these quorum sensing systems are quite ancient, and arose very early in the Pseudomonadota lineage. [ 63 ] [ 64 ]
LuxI and LuxR have coevolved through a long history of horizontal gene transfer (HGT) events. An early study reconciling their gene trees with the rRNA tree suggested frequent HGT events for both LuxI and LuxR, indicating that they are horizontally transferred together and coevolve due to their functional dependency. [ 63 ] Similarly, in QS systems in bacteria associated with Populus deltoides , the gene trees for luxI and luxR show high topological similarity, indicating coevolution of cognate pairs. [ 65 ] In addition to horizontal transfer of complete LuxI/LuxR-type QS systems, many Proteobacteria genomes exhibit an excess of LuxR genes or cases with only LuxR but not LuxI, acquired from different sources via HGT. [ 65 ] Due to the frequent transfer of functional pairs of homologs (i.e., LuxI/LuxR-type systems from multiple independent sources), it is possible that the regulatory hierarchy formed by the LuxI/LuxR and RhlR-RhlI systems is a result of sequential integration of circuits obtained from different sources, due to interactions between multiple homologs. [ 63 ] Interestingly, LuxI genes have likely undergone horizontal gene transfer from Proteobacteria to other lineages, as they have been detected in Nitrospira lineage II. [ 66 ]
In quorum sensing genes of Gammaproteobacteria , which includes Pseudomonas aeruginosa and Escherichia coli , the LuxI/LuxR genes form a functional pair, with LuxI as the auto-inducer synthase and LuxR as the receptor. Gammaproteobacteria are unique in possessing quorum sensing genes, which, although functionally similar to the LuxI/LuxR genes, have a markedly divergent sequence. [ 64 ] This family of quorum-sensing homologs may have arisen in the Gammaproteobacteria ancestor, although the cause of their extreme sequence divergence yet maintenance of functional similarity has yet to be explained. In addition, species that employ multiple discrete quorum sensing systems are almost all members of the Gammaproteobacteria, and evidence of horizontal transfer of quorum sensing genes is most evident in this class. [ 63 ] [ 64 ]
Next to the potential antimicrobial functionality, quorum-sensing derived molecules, especially the peptides, are being investigated for their use in other therapeutic domains as well, including immunology, central nervous system disorders and oncology. Quorum-sensing peptides have been demonstrated to interact with cancer cells, as well as to permeate the blood–brain barrier reaching the brain parenchyma. [ 67 ] [ 68 ] [ 69 ]
Quorum sensing (QS) is used by bacteria to form biofilms. Quorum sensing is used by bacteria to form biofilms because the process determines if the minimum number of bacteria necessary for biofilm formation are present. The criteria to form a biofilm is dependent on a certain density of bacteria rather than a certain number of bacteria being present. When aggregated in high enough densities, some bacteria may form biofilms to protect themselves from biotic or abiotic threats. [ 70 ] Quorum sensing is used by both Gram-positive and Gram-negative bacteria because it aids cellular reproduction. Once in a biofilm, bacteria can communicate with other bacteria of the same species. Bacteria can also communicate with other species of bacteria. This communication is enabled through autoinducers used by the bacteria. [ 17 ]
Additionally, certain responses can be generated by the host organism in response to the certain bacterial autoinducers. Despite the fact that specific bacterial quorum sensing systems are different, for example the target genes, signal relay mechanisms, and chemical signals used between bacteria, the ability to coordinate gene expression for a specific species of bacteria remains the same. This ability alludes to the larger idea that bacteria have potential to become a multicellular bacterial body. [ 17 ]
Secondly, biofilms may also serve to transport nutrients into the microbial community or transport toxins out by means of channels that permeate the extracellular polymeric matrix (like cellulose) that holds the cells together. Finally, biofilms are an ideal environment for horizontal gene transfer through either conjugation or environmental DNA (eDNA) that exists in the biofilm matrix. [ 70 ]
The process of biofilm development is often triggered by environmental signals, and bacteria are proven to require flagella to successfully approach a surface, adhere to it, and form the biofilm. [ 70 ] As cells either replicate or aggregate in a location, the concentration of autoinducers outside of the cells increases until a critical mass threshold is reached. At this point, it is energetically unfavorable for intracellular autoinducers to leave the cell and they bind to receptors and trigger a signaling cascade to initiate gene expression and begin secreting an extracellular polysaccharide to encase themselves inside. [ 71 ]
One modern method of preventing biofilm development without the use of antibiotics is with anti-QS substances, such ( naringenin , taxifolin , etc.) that can be utilized as alternative form of therapy against bacterial virulence. [ 72 ]
Methanosaeta harundinacea 6Ac, a methanogenic archaeon, produces carboxylated acyl homoserine lactone compounds that facilitate the transition from growth as short cells to growth as filaments. [ 73 ]
A mechanism involving arbitrium has recently been described in bacteriophages infecting several Bacillus species. [ 74 ] [ 75 ] The viruses communicate with each other to ascertain their own density compared to potential hosts. They use this information to decide whether to enter a lytic or lysogenic life-cycle. [ 76 ] This decision is crucial as it affects their replication strategy and potential to spread within the host population, optimizing their survival and proliferation under varying environmental conditions. This communication mechanism enables a coordinated infection strategy, significantly enhancing the efficiency of phage proliferation. By synchronizing their life cycles, bacteriophages can maximize their impact on the host population, potentially leading to more effective control of bacterial densities.
QS is important to plant-pathogen interactions, and their study has also contributed to the QS field more generally. [ 77 ] [ 8 ] The first X-ray crystallography results for some of the key proteins were those of Pantoea stewartii subsp. stewartii in maize/corn [ 78 ] [ 8 ] and Agrobacterium tumefaciens , a crop pathogen with a wider range of hosts. [ 79 ] [ 80 ] [ 8 ] These interactions are facilitated by quorum-sensing molecules and play a major role in maintaining the pathogenicity of bacteria towards other hosts, such as humans. This mechanism can be understood by looking at the effects of N-Acyl homoserine lactone (AHL), one of the quorum sensing-signaling molecules in gram-negative bacteria , on plants. The model organism used is Arabidopsis thaliana . [ 81 ] Further insights reveal that AHLs influence plant immune responses and can alter plant hormone levels, thereby affecting plant growth and susceptibility to infection. Understanding these dynamics is crucial for developing innovative strategies to combat plant diseases and improve agricultural productivity. Researchers have also noted that certain plants can degrade these signaling molecules, potentially as a defensive strategy to disrupt bacterial communication. This interplay between bacterial signaling and plant responses suggests a complex co-evolutionary relationship that could be exploited to enhance crop resistance to bacterial pathogens.
The role of AHLs having long carbon-chains (C12, C14), which have an unknown receptor mechanism, is less well understood than AHLs having short carbon-chains (C4, C6, C8), which are perceived by the G protein-coupled receptor . A phenomenon called "AHL priming", which is a dependent signalling pathway, enhanced our knowledge of long-chain AHLs. The role of quorum-sensing molecules was better explained according to three categories: host physiology–based impact of quorum sensing molecules; ecological effects; and cellular signaling. Calcium signalling and calmodulin have a large role in short-chain AHLs' response in Arabidopsis . Research was also conducted on barley and the crop called yam bean ( Pachyrhizus erosus ) that reveals the AHLs determining the detoxification enzymes called GST were found less in yam bean. [ 82 ]
Quorum sensing-based regulatory systems are necessary to plant-disease-causing bacteria. Looking towards developing new strategies based on plant-associated microbiomes, the aim of further study is to improve the quantity and quality of the food supply. Further research into this inter-kingdom communication also enhances the possibility of learning about quorum sensing in humans. [ 83 ] This exploration could open new avenues for managing microbial communities in agricultural settings, potentially leading to the development of more sustainable farming practices that leverage natural microbial processes to boost crop resilience and productivity.
Social insect colonies are an excellent example of a decentralized system , because no individual is in charge of directing or making decisions for the colony. Several groups of social insects have been shown to use quorum sensing in a process that resembles collective decision-making.
Colonies of the ant Temnothorax albipennis nest in small crevices between rocks. When the rocks shift and the nest is broken up, these ants must quickly choose a new nest to move into. During the first phase of the decision-making process, a small portion of the workers leave the destroyed nest and search for new crevices. When one of these scout ants finds a potential nest, she assesses the quality of the crevice based on a variety of factors including the size of the interior, the number of openings (based on light level), and the presence or absence of dead ants. [ 84 ] [ 85 ] The worker then returns to the destroyed nest, where she waits for a short period before recruiting other workers to follow her to the nest that she has found, using a process called tandem running . The waiting period is inversely related to the quality of the site; for instance, a worker that has found a poor site will wait longer than a worker that encountered a good site. [ 86 ] As the new recruits visit the potential nest site and make their own assessment of its quality, the number of ants visiting the crevice increases. During this stage, ants may be visiting many different potential nests. However, because of the differences in the waiting period, the number of ants in the best nest will tend to increase at the greatest rate. Eventually, the ants in this nest will sense that the rate at which they encounter other ants has exceeded a particular threshold, indicating that the quorum number has been reached. [ 87 ] Once the ants sense a quorum, they return to the destroyed nest and begin rapidly carrying the brood, queen, and fellow workers to the new nest. Scouts that are still tandem-running to other potential sites are also recruited to the new nest, and the entire colony moves. Thus, although no single worker may have visited and compared all of the available options, quorum sensing enables the colony as a whole to quickly make good decisions about where to move.
Honey bees ( Apis mellifera ) also use quorum sensing to make decisions about new nest sites. Large colonies reproduce through a process called swarming , in which the queen leaves the hive with a portion of the workers to form a new nest elsewhere. After leaving the nest, the workers form a swarm that hangs from a branch or overhanging structure. This swarm persists during the decision-making phase until a new nest site is chosen.
The quorum sensing process in honey bees is similar to the method used by Temnothorax ants in several ways. A small portion of the workers leave the swarm to search out new nest sites, and each worker assesses the quality of the cavity it finds. The worker then returns to the swarm and recruits other workers to her cavity using the honey bee waggle dance . However, instead of using a time delay, the number of dance repetitions the worker performs is dependent on the quality of the site. Workers that found poor nests stop dancing sooner, and can, therefore, be recruited to the better sites. Once the visitors to a new site sense that a quorum number (usually 10–20 bees) has been reached, they return to the swarm and begin using a new recruitment method called piping. This vibration signal causes the swarm to take off and fly to the new nest location. In an experimental test, this decision-making process enabled honey bee swarms to choose the best nest site in four out of five trials. [ 88 ] [ 89 ]
Quorum sensing can function as a collective decision-making process in fish schools . A quorum response has been defined as "a steep increase in the probability of group members performing a given behaviour once a threshold minimum number of their group mates already performing that behaviour is exceeded". [ 90 ] A recent investigation showed that small groups of fish used consensus decision-making when deciding which fish model to follow. The fish did this by a simple quorum rule such that individuals watched the decisions of others before making their own decisions. This technique generally resulted in the 'correct' decision but occasionally cascaded into the 'incorrect' decision. In addition, as the group size increased, the fish made more accurate decisions in following the more attractive fish model. [ 91 ] Consensus decision-making, a form of collective intelligence , thus effectively uses information from multiple sources to generally reach the correct conclusion. Such behaviour has also been demonstrated in the shoaling behaviour of threespine sticklebacks . [ 90 ]
Quorum quenching is the process of preventing quorum sensing by disrupting signalling. [ 92 ] This is achieved by inactivating signalling enzymes, by introducing molecules that mimic signalling molecules and block their receptors, by degrading signalling molecules themselves, or by a modification of the quorum sensing signals due to an enzyme activity. [ 21 ] [ 92 ] [ 93 ] [ 94 ]
Closantel and triclosan are known inhibitors of quorum sensing enzymes. [ 95 ] Closantel induces aggregation of the histidine kinase sensor in two-component signalling. The latter disrupts the synthesis of a class of signalling molecules known as N -acyl homoserine lactones (AHLs) by blocking the enoyl-acyl carrier protein (ACP) reductase . [ 95 ] [ 96 ]
Two groups of well-known mimicking molecules include halogenated furanones , which mimic AHL molecules, and synthetic Al peptides (AIPs), which mimic naturally occurring AIPs. These groups inhibit receptors from binding substrate or decrease the concentration of receptors in the cell. [ 95 ] Furanones have also been found to act on AHL-dependant transcriptional activity, whereby the half life of the autoinducer -binding LuxR protein is significantly shortened. [ 97 ]
Recently, a well-studied quorum quenching bacterial strain (KM1S) was isolated and its AHL degradation kinetics were studied using rapid resolution liquid chromatography (RRLC). [ 98 ] RRLC efficiently separates components of a mixture to a high degree of sensitivity, based on their affinities for different liquid phases. [ 99 ] It was found that the genome of this strain encoded an inactivation enzyme with distinct motifs targeting the degradation of AHLs. [ 98 ]
As mentioned before, N-acyl-homoserine lactones (AHL) are the quorum sensing signaling molecules of the gram-negative bacteria . However, these molecules may have different functional groups on their acyl chain, and also a different length of acyl chain. Therefore, there exist many different AHL signaling molecules, for example, 3-oxododecanoyl-L-homoserine lactone (3OC12-HSL) or 3-hydroxydodecanoyl-L-homoserine lactone (3OHC12-HSL). The modification of those quorum sensing (QS) signaling molecules is another sort of quorum quenching. This can be carried out by an oxidoreductase activity. [ 21 ] As an example, we will discuss the interaction between a host, Hydra vulgaris , and the main colonizer of its epithelial cell surfaces, Curvibacter spp. Those bacteria produce 3-oxo-HSL quorum sensing molecules. [ 21 ] However, the oxidoreductase activity of the polyp Hydra is able to modify the 3-oxo-HSL into their 3-hydroxy-HSL counterparts. [ 21 ] We can characterize this as quorum quenching since there is an interference with quorum sensing molecules. In this case, the outcomes differ from simple QS inactivation: the host modification results in a phenotypic switch of Curvibacter , which modifies its ability to colonize the epithelial cell surfaces of H. vulgaris . [ 21 ]
Applications of quorum quenching that have been exploited by humans include the use of AHL-degrading bacteria in aquacultures to limit the spread of diseases in aquatic populations of fish, mollusks and crustaceans. [ 100 ] This technique has also been translated to agriculture, to restrict the spread of pathogenic bacteria that use quorum sensing in plants. [ 100 ] [ 101 ] Anti- biofouling is another process that exploits quorum quenching bacteria to mediate the dissociation of unwanted biofilms aggregating on wet surfaces, such as medical devices, transportation infrastructure and water systems. [ 100 ] [ 102 ] Quorum quenching is recently studied for the control of fouling and emerging contaminants in electro membrane bioreactors (eMBRs) for the advanced treatment of wastewater. [ 103 ] Extracts of several traditional medicinal herbs display quorum quenching activity, and have potential antibacterial applications. [ 104 ] [ 105 ]
Quorum sensing has been engineered using synthetic biological circuits in different systems. Examples include rewiring the AHL components to toxic genes to control population size in bacteria; [ 106 ] and constructing an auxin-based system to control population density in mammalian cells. [ 107 ] Synthetic quorum sensing circuits have been proposed to enable applications like controlling biofilms [ 108 ] or enabling drug delivery. [ 109 ] Quorum sensing based genetic circuits have been used to convert AI-2 signals to AI-1 and then subsequently use the AI-1 signal to alter bacterial growth rate, thereby changing the composition of a consortium. [ 110 ]
Remarkable advancements have been and are continuing to be made in recent years in our understanding of synthetic biology in terms of endocrine and paracrine signaling mechanisms, and the myriad of modes by which bacteria record domestic and foreign cell numbers. [ 111 ] The modulation of gene expression in response to oscillations in cell-population density is thanks to the QS techniques regulating bacterial communication natural and artificial cultures. It is also clear that intra- and inter-species cell–cell communication occurs and is regulated by quorum sensing systems. Further, there is mounting data demonstrating that autoinducer signals elicit specific responses from eukaryotic hosts.
Quorum sensing can be a useful tool for improving the function of self-organizing networks such as the SECOAS (Self-Organizing Collegiate Sensor) environmental monitoring system. In this system, individual nodes sense that there is a population of other nodes with similar data to report. The population then nominates just one node to report the data, resulting in power savings. [ 112 ] Ad hoc wireless networks can also benefit from quorum sensing, by allowing the system to detect and respond to network conditions. [ 113 ]
Quorum sensing can also be used to coordinate the behavior of autonomous robot swarms. Using a process similar to that used by Temnothorax ants, robots can make rapid group decisions without the direction of a controller. [ 114 ]
Despite recent advancements, the true nature of these back-and-forth conversations remains a mystery, and further rigorous research targeting inter- and intra- species communication is still necessary to maximize knowledge of quorum sensing and its potential to improve research and treatments of cancer and bacterial diseases. The code to understanding these complex bacterial languages is to decipher the impact of the words. [ 111 ] | https://en.wikipedia.org/wiki/Quorum_sensing |
In arithmetic , a quotient (from Latin : quotiens 'how many times', pronounced / ˈ k w oʊ ʃ ən t / ) is a quantity produced by the division of two numbers. [ 1 ] The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division ) [ 2 ] or a fraction or ratio (in the case of a general division ). For example, when dividing 20 (the dividend ) by 3 (the divisor ), the quotient is 6 (with a remainder of 2) in the first sense and 6 + 2 3 = 6.66... {\displaystyle 6+{\tfrac {2}{3}}=6.66...} (a repeating decimal ) in the second sense.
In metrology ( International System of Quantities and the International System of Units ), "quotient" refers to the general case with respect to the units of measurement of physical quantities . [ 3 ] [ 4 ] [ 5 ] Ratios is the special case for dimensionless quotients of two quantities of the same kind . [ 3 ] [ 6 ] Quotients with a non-trivial dimension and compound units , especially when the divisor is a duration (e.g., " per second "), are known as rates . [ 7 ] For example, density (mass divided by volume, in units of kg/m 3 ) is said to be a "quotient", whereas mass fraction (mass divided by mass, in kg/kg or in percent) is a "ratio". [ 8 ] Specific quantities are intensive quantities resulting from the quotient of a physical quantity by mass, volume, or other measures of the system "size". [ 3 ]
The quotient is most frequently encountered as two numbers, or two variables, divided by a horizontal line. The words "dividend" and "divisor" refer to each individual part, while the word "quotient" refers to the whole.
1 2 ← dividend or numerator ← divisor or denominator } ← quotient {\displaystyle {\dfrac {1}{2}}\quad {\begin{aligned}&\leftarrow {\text{dividend or numerator}}\\&\leftarrow {\text{divisor or denominator}}\end{aligned}}{\Biggr \}}\leftarrow {\text{quotient}}}
The quotient is also less commonly defined as the greatest whole number of times a divisor may be subtracted from a dividend—before making the remainder negative. For example, the divisor 3 may be subtracted up to 6 times from the dividend 20, before the remainder becomes negative:
while
In this sense, a quotient is the integer part of the ratio of two numbers. [ 9 ]
A rational number can be defined as the quotient of two integers (as long as the denominator is non-zero).
A more detailed definition goes as follows: [ 10 ]
Or more formally:
The existence of irrational numbers —numbers that are not a quotient of two integers—was first discovered in geometry, in such things as the ratio of the diagonal to the side in a square. [ 11 ]
Outside of arithmetic, many branches of mathematics have borrowed the word "quotient" to describe structures built by breaking larger structures into pieces. Given a set with an equivalence relation defined on it, a " quotient set " may be created which contains those equivalence classes as elements. A quotient group may be formed by breaking a group into a number of similar cosets , while a quotient space may be formed in a similar process by breaking a vector space into a number of similar linear subspaces . | https://en.wikipedia.org/wiki/Quotient |
In calculus , the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let h ( x ) = f ( x ) g ( x ) {\displaystyle h(x)={\frac {f(x)}{g(x)}}} , where both f and g are differentiable and g ( x ) ≠ 0. {\displaystyle g(x)\neq 0.} The quotient rule states that the derivative of h ( x ) is
It is provable in many ways by using other derivative rules .
Given h ( x ) = e x x 2 {\displaystyle h(x)={\frac {e^{x}}{x^{2}}}} , let f ( x ) = e x , g ( x ) = x 2 {\displaystyle f(x)=e^{x},g(x)=x^{2}} , then using the quotient rule: d d x ( e x x 2 ) = ( d d x e x ) ( x 2 ) − ( e x ) ( d d x x 2 ) ( x 2 ) 2 = ( e x ) ( x 2 ) − ( e x ) ( 2 x ) x 4 = x 2 e x − 2 x e x x 4 = x e x − 2 e x x 3 = e x ( x − 2 ) x 3 . {\displaystyle {\begin{aligned}{\frac {d}{dx}}\left({\frac {e^{x}}{x^{2}}}\right)&={\frac {\left({\frac {d}{dx}}e^{x}\right)(x^{2})-(e^{x})\left({\frac {d}{dx}}x^{2}\right)}{(x^{2})^{2}}}\\&={\frac {(e^{x})(x^{2})-(e^{x})(2x)}{x^{4}}}\\&={\frac {x^{2}e^{x}-2xe^{x}}{x^{4}}}\\&={\frac {xe^{x}-2e^{x}}{x^{3}}}\\&={\frac {e^{x}(x-2)}{x^{3}}}.\end{aligned}}}
The quotient rule can be used to find the derivative of tan x = sin x cos x {\displaystyle \tan x={\frac {\sin x}{\cos x}}} as follows: d d x tan x = d d x ( sin x cos x ) = ( d d x sin x ) ( cos x ) − ( sin x ) ( d d x cos x ) cos 2 x = ( cos x ) ( cos x ) − ( sin x ) ( − sin x ) cos 2 x = cos 2 x + sin 2 x cos 2 x = 1 cos 2 x = sec 2 x . {\displaystyle {\begin{aligned}{\frac {d}{dx}}\tan x&={\frac {d}{dx}}\left({\frac {\sin x}{\cos x}}\right)\\&={\frac {\left({\frac {d}{dx}}\sin x\right)(\cos x)-(\sin x)\left({\frac {d}{dx}}\cos x\right)}{\cos ^{2}x}}\\&={\frac {(\cos x)(\cos x)-(\sin x)(-\sin x)}{\cos ^{2}x}}\\&={\frac {\cos ^{2}x+\sin ^{2}x}{\cos ^{2}x}}\\&={\frac {1}{\cos ^{2}x}}=\sec ^{2}x.\end{aligned}}}
The reciprocal rule is a special case of the quotient rule in which the numerator f ( x ) = 1 {\displaystyle f(x)=1} . Applying the quotient rule gives h ′ ( x ) = d d x [ 1 g ( x ) ] = 0 ⋅ g ( x ) − 1 ⋅ g ′ ( x ) g ( x ) 2 = − g ′ ( x ) g ( x ) 2 . {\displaystyle h'(x)={\frac {d}{dx}}\left[{\frac {1}{g(x)}}\right]={\frac {0\cdot g(x)-1\cdot g'(x)}{g(x)^{2}}}={\frac {-g'(x)}{g(x)^{2}}}.}
Utilizing the chain rule yields the same result.
Let h ( x ) = f ( x ) g ( x ) . {\displaystyle h(x)={\frac {f(x)}{g(x)}}.} Applying the definition of the derivative and properties of limits gives the following proof, with the term f ( x ) g ( x ) {\displaystyle f(x)g(x)} added and subtracted to allow splitting and factoring in subsequent steps without affecting the value: h ′ ( x ) = lim k → 0 h ( x + k ) − h ( x ) k = lim k → 0 f ( x + k ) g ( x + k ) − f ( x ) g ( x ) k = lim k → 0 f ( x + k ) g ( x ) − f ( x ) g ( x + k ) k ⋅ g ( x ) g ( x + k ) = lim k → 0 f ( x + k ) g ( x ) − f ( x ) g ( x + k ) k ⋅ lim k → 0 1 g ( x ) g ( x + k ) = lim k → 0 [ f ( x + k ) g ( x ) − f ( x ) g ( x ) + f ( x ) g ( x ) − f ( x ) g ( x + k ) k ] ⋅ 1 [ g ( x ) ] 2 = [ lim k → 0 f ( x + k ) g ( x ) − f ( x ) g ( x ) k − lim k → 0 f ( x ) g ( x + k ) − f ( x ) g ( x ) k ] ⋅ 1 [ g ( x ) ] 2 = [ lim k → 0 f ( x + k ) − f ( x ) k ⋅ g ( x ) − f ( x ) ⋅ lim k → 0 g ( x + k ) − g ( x ) k ] ⋅ 1 [ g ( x ) ] 2 = f ′ ( x ) g ( x ) − f ( x ) g ′ ( x ) [ g ( x ) ] 2 . {\displaystyle {\begin{aligned}h'(x)&=\lim _{k\to 0}{\frac {h(x+k)-h(x)}{k}}\\&=\lim _{k\to 0}{\frac {{\frac {f(x+k)}{g(x+k)}}-{\frac {f(x)}{g(x)}}}{k}}\\&=\lim _{k\to 0}{\frac {f(x+k)g(x)-f(x)g(x+k)}{k\cdot g(x)g(x+k)}}\\&=\lim _{k\to 0}{\frac {f(x+k)g(x)-f(x)g(x+k)}{k}}\cdot \lim _{k\to 0}{\frac {1}{g(x)g(x+k)}}\\&=\lim _{k\to 0}\left[{\frac {f(x+k)g(x)-f(x)g(x)+f(x)g(x)-f(x)g(x+k)}{k}}\right]\cdot {\frac {1}{[g(x)]^{2}}}\\&=\left[\lim _{k\to 0}{\frac {f(x+k)g(x)-f(x)g(x)}{k}}-\lim _{k\to 0}{\frac {f(x)g(x+k)-f(x)g(x)}{k}}\right]\cdot {\frac {1}{[g(x)]^{2}}}\\&=\left[\lim _{k\to 0}{\frac {f(x+k)-f(x)}{k}}\cdot g(x)-f(x)\cdot \lim _{k\to 0}{\frac {g(x+k)-g(x)}{k}}\right]\cdot {\frac {1}{[g(x)]^{2}}}\\&={\frac {f'(x)g(x)-f(x)g'(x)}{[g(x)]^{2}}}.\end{aligned}}} The limit evaluation lim k → 0 1 g ( x + k ) g ( x ) = 1 [ g ( x ) ] 2 {\displaystyle \lim _{k\to 0}{\frac {1}{g(x+k)g(x)}}={\frac {1}{[g(x)]^{2}}}} is justified by the differentiability of g ( x ) {\displaystyle g(x)} , implying continuity, which can be expressed as lim k → 0 g ( x + k ) = g ( x ) {\displaystyle \lim _{k\to 0}g(x+k)=g(x)} .
Let h ( x ) = f ( x ) g ( x ) , {\displaystyle h(x)={\frac {f(x)}{g(x)}},} so that f ( x ) = g ( x ) h ( x ) . {\displaystyle f(x)=g(x)h(x).}
The product rule then gives f ′ ( x ) = g ′ ( x ) h ( x ) + g ( x ) h ′ ( x ) . {\displaystyle f'(x)=g'(x)h(x)+g(x)h'(x).}
Solving for h ′ ( x ) {\displaystyle h'(x)} and substituting back for h ( x ) {\displaystyle h(x)} gives: h ′ ( x ) = f ′ ( x ) − g ′ ( x ) h ( x ) g ( x ) = f ′ ( x ) − g ′ ( x ) ⋅ f ( x ) g ( x ) g ( x ) = f ′ ( x ) g ( x ) − f ( x ) g ′ ( x ) [ g ( x ) ] 2 . {\displaystyle {\begin{aligned}h'(x)&={\frac {f'(x)-g'(x)h(x)}{g(x)}}\\&={\frac {f'(x)-g'(x)\cdot {\frac {f(x)}{g(x)}}}{g(x)}}\\&={\frac {f'(x)g(x)-f(x)g'(x)}{[g(x)]^{2}}}.\end{aligned}}}
Let h ( x ) = f ( x ) g ( x ) = f ( x ) ⋅ 1 g ( x ) . {\displaystyle h(x)={\frac {f(x)}{g(x)}}=f(x)\cdot {\frac {1}{g(x)}}.}
Then the product rule gives h ′ ( x ) = f ′ ( x ) ⋅ 1 g ( x ) + f ( x ) ⋅ d d x [ 1 g ( x ) ] . {\displaystyle h'(x)=f'(x)\cdot {\frac {1}{g(x)}}+f(x)\cdot {\frac {d}{dx}}\left[{\frac {1}{g(x)}}\right].}
To evaluate the derivative in the second term, apply the reciprocal rule , or the power rule along with the chain rule : d d x [ 1 g ( x ) ] = − 1 g ( x ) 2 ⋅ g ′ ( x ) = − g ′ ( x ) g ( x ) 2 . {\displaystyle {\frac {d}{dx}}\left[{\frac {1}{g(x)}}\right]=-{\frac {1}{g(x)^{2}}}\cdot g'(x)={\frac {-g'(x)}{g(x)^{2}}}.}
Substituting the result into the expression gives h ′ ( x ) = f ′ ( x ) ⋅ 1 g ( x ) + f ( x ) ⋅ [ − g ′ ( x ) g ( x ) 2 ] = f ′ ( x ) g ( x ) − f ( x ) g ′ ( x ) g ( x ) 2 = g ( x ) g ( x ) ⋅ f ′ ( x ) g ( x ) − f ( x ) g ′ ( x ) g ( x ) 2 = f ′ ( x ) g ( x ) − f ( x ) g ′ ( x ) g ( x ) 2 . {\displaystyle {\begin{aligned}h'(x)&=f'(x)\cdot {\frac {1}{g(x)}}+f(x)\cdot \left[{\frac {-g'(x)}{g(x)^{2}}}\right]\\&={\frac {f'(x)}{g(x)}}-{\frac {f(x)g'(x)}{g(x)^{2}}}\\&={\frac {g(x)}{g(x)}}\cdot {\frac {f'(x)}{g(x)}}-{\frac {f(x)g'(x)}{g(x)^{2}}}\\&={\frac {f'(x)g(x)-f(x)g'(x)}{g(x)^{2}}}.\end{aligned}}}
Let h ( x ) = f ( x ) g ( x ) . {\displaystyle h(x)={\frac {f(x)}{g(x)}}.} Taking the absolute value and natural logarithm of both sides of the equation gives ln | h ( x ) | = ln | f ( x ) g ( x ) | {\displaystyle \ln |h(x)|=\ln \left|{\frac {f(x)}{g(x)}}\right|}
Applying properties of the absolute value and logarithms, ln | h ( x ) | = ln | f ( x ) | − ln | g ( x ) | {\displaystyle \ln |h(x)|=\ln |f(x)|-\ln |g(x)|}
Taking the logarithmic derivative of both sides, h ′ ( x ) h ( x ) = f ′ ( x ) f ( x ) − g ′ ( x ) g ( x ) {\displaystyle {\frac {h'(x)}{h(x)}}={\frac {f'(x)}{f(x)}}-{\frac {g'(x)}{g(x)}}}
Solving for h ′ ( x ) {\displaystyle h'(x)} and substituting back f ( x ) g ( x ) {\displaystyle {\tfrac {f(x)}{g(x)}}} for h ( x ) {\displaystyle h(x)} gives: h ′ ( x ) = h ( x ) [ f ′ ( x ) f ( x ) − g ′ ( x ) g ( x ) ] = f ( x ) g ( x ) [ f ′ ( x ) f ( x ) − g ′ ( x ) g ( x ) ] = f ′ ( x ) g ( x ) − f ( x ) g ′ ( x ) g ( x ) 2 = f ′ ( x ) g ( x ) − f ( x ) g ′ ( x ) g ( x ) 2 . {\displaystyle {\begin{aligned}h'(x)&=h(x)\left[{\frac {f'(x)}{f(x)}}-{\frac {g'(x)}{g(x)}}\right]\\&={\frac {f(x)}{g(x)}}\left[{\frac {f'(x)}{f(x)}}-{\frac {g'(x)}{g(x)}}\right]\\&={\frac {f'(x)}{g(x)}}-{\frac {f(x)g'(x)}{g(x)^{2}}}\\&={\frac {f'(x)g(x)-f(x)g'(x)}{g(x)^{2}}}.\end{aligned}}}
Taking the absolute value of the functions is necessary for the logarithmic differentiation of functions that may have negative values, as logarithms are only real-valued for positive arguments. This works because d d x ( ln | u | ) = u ′ u {\displaystyle {\tfrac {d}{dx}}(\ln |u|)={\tfrac {u'}{u}}} , which justifies taking the absolute value of the functions for logarithmic differentiation.
Implicit differentiation can be used to compute the n th derivative of a quotient (partially in terms of its first n − 1 derivatives). For example, differentiating f = g h {\displaystyle f=gh} twice (resulting in f ″ = g ″ h + 2 g ′ h ′ + g h ″ {\displaystyle f''=g''h+2g'h'+gh''} ) and then solving for h ″ {\displaystyle h''} yields h ″ = ( f g ) ″ = f ″ − g ″ h − 2 g ′ h ′ g . {\displaystyle h''=\left({\frac {f}{g}}\right)''={\frac {f''-g''h-2g'h'}{g}}.} | https://en.wikipedia.org/wiki/Quotient_rule |
In linear algebra , the quotient of a vector space V {\displaystyle V} by a subspace N {\displaystyle N} is a vector space obtained by "collapsing" N {\displaystyle N} to zero. The space obtained is called a quotient space and is denoted V / N {\displaystyle V/N} (read " V {\displaystyle V} mod N {\displaystyle N} " or " V {\displaystyle V} by N {\displaystyle N} ").
Formally, the construction is as follows. [ 1 ] Let V {\displaystyle V} be a vector space over a field K {\displaystyle \mathbb {K} } , and let N {\displaystyle N} be a subspace of V {\displaystyle V} . We define an equivalence relation ∼ {\displaystyle \sim } on V {\displaystyle V} by stating that x ∼ y {\displaystyle x\sim y} iff x − y ∈ N {\displaystyle x-y\in N} . That is, x {\displaystyle x} is related to y {\displaystyle y} if and only if one can be obtained from the other by adding an element of N {\displaystyle N} . This definition implies that any element of N {\displaystyle N} is related to the zero vector; more precisely, all the vectors in N {\displaystyle N} get mapped into the equivalence class of the zero vector.
The equivalence class – or, in this case, the coset – of x {\displaystyle x} is defined as
and is often denoted using the shorthand [ x ] = x + N {\displaystyle [x]=x+N} .
The quotient space V / N {\displaystyle V/N} is then defined as V / ∼ {\displaystyle V/_{\sim }} , the set of all equivalence classes induced by ∼ {\displaystyle \sim } on V {\displaystyle V} . Scalar multiplication and addition are defined on the equivalence classes by [ 2 ] [ 3 ]
It is not hard to check that these operations are well-defined (i.e. do not depend on the choice of representatives ). These operations turn the quotient space V / N {\displaystyle V/N} into a vector space over K {\displaystyle \mathbb {K} } with N {\displaystyle N} being the zero class, [ 0 ] {\displaystyle [0]} .
The mapping that associates to v ∈ V {\displaystyle v\in V} the equivalence class [ v ] {\displaystyle [v]} is known as the quotient map .
Alternatively phrased, the quotient space V / N {\displaystyle V/N} is the set of all affine subsets of V {\displaystyle V} which are parallel to N {\displaystyle N} . [ 4 ]
Let X = R 2 be the standard Cartesian plane , and let Y be a line through the origin in X . Then the quotient space X / Y can be identified with the space of all lines in X which are parallel to Y . That is to say that, the elements of the set X / Y are lines in X parallel to Y . Note that the points along any one such line will satisfy the equivalence relation because their difference vectors belong to Y . This gives a way to visualize quotient spaces geometrically. (By re-parameterising these lines, the quotient space can more conventionally be represented as the space of all points along a line through the origin that is not parallel to Y . Similarly, the quotient space for R 3 by a line through the origin can again be represented as the set of all co-parallel lines, or alternatively be represented as the vector space consisting of a plane which only intersects the line at the origin.)
Another example is the quotient of R n by the subspace spanned by the first m standard basis vectors . The space R n consists of all n -tuples of real numbers ( x 1 , ..., x n ) . The subspace, identified with R m , consists of all n -tuples such that the last n − m entries are zero: ( x 1 , ..., x m , 0, 0, ..., 0) . Two vectors of R n are in the same equivalence class modulo the subspace if and only if they are identical in the last n − m coordinates. The quotient space R n / R m is isomorphic to R n − m in an obvious manner.
Let P 3 ( R ) {\displaystyle {\mathcal {P}}_{3}(\mathbb {R} )} be the vector space of all cubic polynomials over the real numbers. Then P 3 ( R ) / ⟨ x 2 ⟩ {\displaystyle {\mathcal {P}}_{3}(\mathbb {R} )/\langle x^{2}\rangle } is a quotient space, where each element is the set corresponding to polynomials that differ by a quadratic term only. For example, one element of the quotient space is { x 3 + a x 2 − 2 x + 3 : a ∈ R } {\displaystyle \{x^{3}+ax^{2}-2x+3:a\in \mathbb {R} \}} , while another element of the quotient space is { a x 2 + 2.7 x : a ∈ R } {\displaystyle \{ax^{2}+2.7x:a\in \mathbb {R} \}} .
More generally, if V is an (internal) direct sum of subspaces U and W,
then the quotient space V / U is naturally isomorphic to W . [ 5 ]
An important example of a functional quotient space is an L p space .
There is a natural epimorphism from V to the quotient space V / U given by sending x to its equivalence class [ x ]. The kernel (or nullspace) of this epimorphism is the subspace U . This relationship is neatly summarized by the short exact sequence
If U is a subspace of V , the dimension of V / U is called the codimension of U in V . Since a basis of V may be constructed from a basis A of U and a basis B of V / U by adding a representative of each element of B to A , the dimension of V is the sum of the dimensions of U and V / U . If V is finite-dimensional , it follows that the codimension of U in V is the difference between the dimensions of V and U : [ 6 ] [ 7 ]
Let T : V → W be a linear operator . The kernel of T , denoted ker( T ), is the set of all x in V such that Tx = 0. The kernel is a subspace of V . The first isomorphism theorem for vector spaces says that the quotient space V /ker( T ) is isomorphic to the image of V in W . An immediate corollary , for finite-dimensional spaces, is the rank–nullity theorem : the dimension of V is equal to the dimension of the kernel (the nullity of T ) plus the dimension of the image (the rank of T ).
The cokernel of a linear operator T : V → W is defined to be the quotient space W /im( T ).
If X is a Banach space and M is a closed subspace of X , then the quotient X / M is again a Banach space. The quotient space is already endowed with a vector space structure by the construction of the previous section. We define a norm on X / M by
Let C [0,1] denote the Banach space of continuous real-valued functions on the interval [0,1] with the sup norm . Denote the subspace of all functions f ∈ C [0,1] with f (0) = 0 by M . Then the equivalence class of some function g is determined by its value at 0, and the quotient space C [0,1]/ M is isomorphic to R .
If X is a Hilbert space , then the quotient space X / M is isomorphic to the orthogonal complement of M .
The quotient of a locally convex space by a closed subspace is again locally convex. [ 8 ] Indeed, suppose that X is locally convex so that the topology on X is generated by a family of seminorms { p α | α ∈ A } where A is an index set. Let M be a closed subspace, and define seminorms q α on X / M by
Then X / M is a locally convex space, and the topology on it is the quotient topology .
If, furthermore, X is metrizable , then so is X / M . If X is a Fréchet space , then so is X / M . [ 9 ] | https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra) |
In arithmetic , quotition and partition are two ways of viewing fractions and division . In quotitive division one asks "how many parts are there?" while in partitive division one asks "what is the size of each part?"
In general, a quotient Q = N / D , {\displaystyle Q=N/D,} where Q , N , and D are integers or rational numbers , can be conceived of in either of 2 ways:
For example, the quotient 6 / 2 = 3 {\displaystyle 6/2=3} can be conceived of as representing either of the decompositions:
6 = 2 + 2 + 2 ⏟ 3 parts = 3 + 3 ⏟ 2 parts . {\displaystyle 6=\underbrace {2+2+2} _{\text{3 parts}}=\underbrace {3+3} _{\text{2 parts}}.}
In the rational number system used in elementary mathematics, the numerical answer is always the same no matter which way you put it, as a consequence of the commutativity of multiplication .
Thought of quotitively, a division problem can be solved by repeatedly subtracting groups of the size of the divisor. [ 1 ] For instance, suppose each egg carton fits 12 eggs, and the problem is to find how many cartons are needed to fit 36 eggs in total. Groups of 12 eggs at a time can be separated from the main pile until none are left, 3 groups:
36 eggs − 12 eggs − 12 eggs − 12 eggs ⏟ 3 groups = 0 ⟹ 36 12 = 3. {\displaystyle 36{\text{ eggs}}{}-{}\!\!\!\ \ \underbrace {12{\text{ eggs}}-12{\text{ eggs}}-12{\text{ eggs}}} _{3{\text{ groups}}}=0\implies {\frac {36}{12}}=3.}
If the last group is a remainder smaller than the divisor, it can be thought of as forming an additional smaller group. For example, if 45 eggs are to be put into 12-egg cartons, then after the first 3 cartons have been filled there are 9 eggs remaining, which only partially fill the 4th carton. The answer to the question "How many cartons are needed to fit 45 eggs?" is 4 cartons, since 45 12 = 3 + 9 12 {\textstyle {\frac {45}{12}}=3+{\frac {9}{12}}} rounds up to 4.
Quotition is the concept of division most used in measurement . For example, measuring the length of a table using a measuring tape involves comparing the table to the markings on the tape. This is conceptually equivalent to dividing the length of the table by a unit of length, the distance between markings.
Thought of partitively, a division problem might be solved by sorting the initial quantity into a specific number of groups by adding items to each group in turn. For instance, a deck of 52 playing cards could be divided among 4 players by dealing the cards to into 4 piles one at a time, eventually yielding piles of 13 cards each.
If there is a remainder in solving a partition problem, the parts will end up with unequal sizes. For example, if 52 cards are dealt out to 5 players, then 3 of the players will receive 10 cards each, and 2 of the players will receive 11 cards each, since 52 5 = 10 + 2 5 {\textstyle {\frac {52}{5}}=10+{\frac {2}{5}}} .
This mathematics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Quotition_and_partition |
QuteMol is an open-source , interactive, molecular visualization system that was based on advanced rendering techniques that make possible to have for the first time a set of innovative visualization modalities in an interactive real-time application. [ 1 ] QuteMol was the first system to use the capabilities of GPUs through OpenGL shaders to offer an array of innovative visual effects. QuteMol visualization techniques are aimed at improving clarity and an easier understanding of the 3D shape and structure of large molecules or complex proteins. [ 2 ]
In 2021 the IEEE Visualization Conference awarded the paper introducing QuteMol with the Test of Time Award to testify that " contents are still vibrant and useful today and have had a major impact and influence within and beyond the visualization community ." [ 3 ]
Features available in QuteMol include: [ 4 ]
Notably after many years since the last release QuteMol is still used in the molecular visualization community as can be testified by searching on google scholar for papers citing explicitly the tool or the paper for creating high quality images of molecules. [ 5 ]
This article about molecular modelling software is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/QuteMol |
A qutrit (or quantum trit ) is a unit of quantum information that is realized by a 3-level quantum system, that may be in a superposition of three mutually orthogonal quantum states . [ 1 ]
The qutrit is analogous to the classical radix -3 trit , just as the qubit , a quantum system described by a superposition of two orthogonal states, is analogous to the classical radix-2 bit .
There is ongoing work to develop quantum computers using qutrits [ 2 ] [ 3 ] [ 4 ] and qudits in general. [ 5 ] [ 6 ] [ 7 ]
A qutrit has three orthonormal basis states or vectors , often denoted | 0 ⟩ {\displaystyle |0\rangle } , | 1 ⟩ {\displaystyle |1\rangle } , and | 2 ⟩ {\displaystyle |2\rangle } in Dirac or bra–ket notation .
These are used to describe the qutrit as a superposition state vector in the form of a linear combination of the three orthonormal basis states:
where the coefficients are complex probability amplitudes , such that the sum of their squares is unity (normalization):
The qubit 's orthonormal basis states { | 0 ⟩ , | 1 ⟩ } {\displaystyle \{|0\rangle ,|1\rangle \}} span the two-dimensional complex Hilbert space H 2 {\displaystyle H_{2}} , corresponding to spin-up and spin-down of a spin-1/2 particle. Qutrits require a Hilbert space of higher dimension, namely the three-dimensional H 3 {\displaystyle H_{3}} spanned by the qutrit's basis { | 0 ⟩ , | 1 ⟩ , | 2 ⟩ } {\displaystyle \{|0\rangle ,|1\rangle ,|2\rangle \}} , [ 8 ] which can be realized by a three-level quantum system.
An n -qutrit register can represent 3 n different states simultaneously, i.e., a superposition state vector in 3 n -dimensional complex Hilbert space. [ 9 ]
Qutrits have several peculiar features when used for storing quantum information. For example, they are more robust to decoherence under certain environmental interactions. [ 10 ] In reality, manipulating qutrits directly might be tricky, and one way to do that is by using an entanglement with a qubit . [ 11 ]
The quantum logic gates operating on single qutrits are 3 × 3 {\displaystyle 3\times 3} unitary matrices and gates that act on registers of n {\displaystyle n} qutrits are 3 n × 3 n {\displaystyle 3^{n}\times 3^{n}} unitary matrices (the elements of the unitary groups U(3) and U(3 n ) respectively). [ 12 ]
The rotation operator gates [ a ] for SU(3) are Rot ( Θ 1 , Θ 2 , … , Θ 8 ) = exp ( − i ∑ a = 1 8 Θ a λ a 2 ) {\displaystyle \operatorname {Rot} (\Theta _{1},\Theta _{2},\dots ,\Theta _{8})=\exp \left(-i\sum _{a=1}^{8}\Theta _{a}{\frac {\lambda _{a}}{2}}\right)} , where λ a {\displaystyle \lambda _{a}} is the a ' th Gell-Mann matrix , and Θ a {\displaystyle \Theta _{a}} is a real value. The Lie algebra of the matrix exponential is provided here . The same rotation operators are used for gluon interactions, where the three basis states are the three colors ( | 0 ⟩ = red , | 1 ⟩ = green , | 2 ⟩ = blue {\displaystyle |0\rangle ={\text{red}},|1\rangle ={\text{green}},|2\rangle ={\text{blue}}} ) of the strong interaction . [ 13 ] [ 14 ] [ b ]
The global phase shift gate for the qutrit [ c ] is Ph ( δ ) = [ e i δ 0 0 0 e i δ 0 0 0 e i δ ] = exp ( i δ I ) = e i δ I {\displaystyle \operatorname {Ph} (\delta )={\begin{bmatrix}e^{i\delta }&0&0\\0&e^{i\delta }&0\\0&0&e^{i\delta }\end{bmatrix}}=\exp \left(i\delta I\right)=e^{i\delta }I} where the phase factor e i δ {\displaystyle e^{i\delta }} is called the global phase .
This phase gate performs the mapping | Ψ ⟩ ↦ e i δ | Ψ ⟩ {\displaystyle |\Psi \rangle \mapsto e^{i\delta }|\Psi \rangle } and together with the 8 rotation operators is capable of expressing any single-qutrit gate in U(3) , as a series circuit of at most 9 gates. | https://en.wikipedia.org/wiki/Qutrit |
In projective geometry , Qvist's theorem , named after the Finnish mathematician Bertil Qvist [ de ] , is a statement on ovals in finite projective planes . Standard examples of ovals are non-degenerate (projective) conic sections . The theorem gives an answer to the question How many tangents to an oval can pass through a point in a finite projective plane? The answer depends essentially upon the order (number of points on a line −1) of the plane.
When | l ∩ Ω | = 0 the line l is an exterior line (or passant ), [ 1 ] if | l ∩ Ω | = 1 a tangent line and if | l ∩ Ω | = 2 the line is a secant line .
For finite planes (i.e. the set of points is finite) we have a more convenient characterization: [ 2 ]
Let Ω be an oval in a finite projective plane of order n .
(a) Let t R be the tangent to Ω at point R and let P 1 , ... , P n be the remaining points of this line. For each i , the lines through P i partition Ω into sets of cardinality 2 or 1 or 0. Since the number | Ω | = n + 1 is even, for any point P i , there must exist at least one more tangent through that point. The total number of tangents is n + 1 , hence, there are exactly two tangents through each P i , t R and one other. Thus, for any point P not in oval Ω , if P is on any tangent to Ω it is on exactly two tangents.
(b) Let s be a secant, s ∩ Ω = { P 0 , P 1 } and s = { P 0 , P 1 ,..., P n }. Because | Ω | = n + 1 is odd, through any P i , i = 2,...,n , there passes at least one tangent t i . The total number of tangents is n + 1 . Hence, through any point P i for i = 2,..., n there is exactly one tangent. If N is the point of intersection of two tangents, no secant can pass through N . Because n + 1 , the number of tangents, is also the number of lines through any point, any line through N is a tangent.
Using inhomogeneous coordinates over a field K , | K | = n even, the set
the projective closure of the parabola y = x 2 , is an oval with the point N = (0) as nucleus (see image), i.e., any line y = c , with c ∈ K , is a tangent.
One easily checks the following essential property of a hyperoval:
This property provides a simple means of constructing additional ovals from a given oval.
For a projective plane over a finite field K , | K | = n even and n > 4 , the set | https://en.wikipedia.org/wiki/Qvist's_theorem |
The QWERTY effect (or qwerty effect ) emphasizes ways that modern keyboard layouts have influenced human language, [ 1 ] naming preferences [ 2 ] and behavior. [ 3 ] [ 4 ]
One area this affects is how words are perceived in terms of positive vs. negative association. For example, Jasmin and Casasanto (2012) found that words that contain more right-hand letters are perceived more positively than those with more left-hand letters, and that this phenomenon affects both real and nonsense words for speakers across multiple European languages. [ 5 ] Garcia and Strohmaier (2016) find this effect applies both when text is interpreted and when text is composed. [ 6 ]
This phenomenon applies even to personal names, such that Casasanto et al. (2014) find evidence that the QWERTY layout is influencing the choice of children's names in the United States. [ 7 ]
The Wubi effect references the same process of influence driven by autocomplete , Chinese input methods for computers (such as the Wubi method ), and real time input suggestions from search engines based on current events. [ 8 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Qwerty_effect |
R&D Dynamics is a Connecticut -based aerospace and energy company involves in research, design, development, and production of turbomachinery that does not use oil and is energy efficient. [ 1 ] [ 2 ]
It was founded in 1990 by Dr. Giri Agrawal while he was working in Garrett Air Research and Hamilton Standard . Dr. Agrawal received the George Mead Medal for his air bearing development work. [ 3 ] [ 4 ] [ 5 ]
R&D Dynamics selected by Airbus UpNext to supply fuel cell compressors. [ 6 ] [ 7 ] [ 8 ] [ 9 ] | https://en.wikipedia.org/wiki/R&D_Dynamics_Corporation |
R-407C is a mixture of hydrofluorocarbons used as a refrigerant . It is a zeotropic blend of difluoromethane (R-32), pentafluoroethane (R-125), and 1,1,1,2-tetrafluoroethane (R-134a). Difluoromethane serves to provide the heat capacity, pentafluoroethane decreases flammability, tetrafluoroethane reduces pressure. [ 1 ] R-407C cylinders are colored burnt orange .
This refrigerant is intended as a replacement for R-22 in existing refrigerators. [ 2 ] R-22 production will be phased out by 2020 as per the Montreal Protocol as the chlorine in R-22 can lead to ozone depletion. [ 3 ] As the components in R-407C lack chlorine it does not contribute significantly to ozone depletion in the stratosphere. Despite improved environmental impact with respect to ozone depletion, R-407C still has a calculated 100-year global warming potential of 1774, [ 4 ] only slightly lower than calculated value of 1960 for the R-22 refrigerant it replaces. [ 5 ] The use of R-407C and other high GWP hydrofluorocarbon refrigerants is being phased out worldwide in accordance with the Kigali Amendment to the Montreal Protocol. Its use was barred for many applications in the United States on 1 January 2025 with near-complete phaseout planned by 1 January 2028. [ 6 ]
This article about a hydrocarbon is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/R-407C |
R-410A is a refrigerant fluid used in air conditioning and heat pump applications. It is a zeotropic but near- azeotropic mixture of difluoromethane (CH 2 F 2 , called R-32) and pentafluoroethane (CHF 2 CF 3 , called R-125). R-410A is sold under the trademarked names AZ-20, EcoFluor R410, Forane 410A, Genetron R410A, Puron, and Suva 410A.
On December 27, 2020, the United States Congress passed the American Innovation and Manufacturing (AIM) Act, which directs US Environmental Protection Agency (EPA) to phase down production and consumption of hydrofluorocarbons (HFCs). [ 1 ] [ 2 ] The AIM act was passed because HFCs have high global warming potential . Rules developed under the AIM Act require HFC production and consumption to be reduced by 85% from 2022 to 2036. [ 3 ] R-410A will be restricted by this Act because it contains the HFC R-125. Other refrigerants with lower global warming potential will replace R-410A in most applications, just as R-410A replaced the earlier ozone-depleting refrigerant, R-22. [ 4 ]
R-410A was invented and patented by Allied Signal (later Honeywell ) in 1991. [ 5 ] Other producers around the world have been licensed to manufacture and sell R-410A. [ 6 ] R-410A was successfully commercialized in the air conditioning segment by a combined effort of Carrier Corporation , Emerson Climate Technologies, Inc. , Copeland Scroll Compressors (a division of Emerson Electric Company ), and Allied Signal . Carrier Corporation was the first company to introduce an R-410A-based residential air conditioning unit into the market in 1996 and holds the trademark "Puron". [ 7 ]
In accordance with terms and agreement reached in the Montreal Protocol (The Montreal Protocol on Substances That Deplete the Ozone Layer), the United States Environmental Protection Agency mandated that production or import of R-22 along with other hydrochlorofluorocarbons (HCFCs) be phased out in the United States. In the EU and the US, R-22 could not be used in the manufacture of new air conditioning or similar units after 1 January 2010. [ 8 ] In other parts of the world, the phase-out date varied from country to country.
Since 1 January 2020, the production and importation of R-22 has been banned in the US; the only available sources of R-22 include that which has been stockpiled or recovered from existing devices. [ 8 ]
By 2020, most newly manufactured window air conditioners and mini split air conditioners in the United States used refrigerant R-410A. [ 9 ] Further, R-410A had largely replaced R-22 as the preferred refrigerant for use in residential and commercial air conditioners in Japan and Europe, as well as the United States. [ 8 ]
Unlike alkyl halide refrigerants that contain bromine or chlorine, R-410A (which contains only fluorine) does not contribute to ozone depletion and therefore became more widely used as ozone-depleting refrigerants like R-22 were phased out. However, like methane , R-410A has a global warming potential (GWP) that is appreciably worse than CO 2 (GWP = 1) for the time it persists. R-410A is a mixture of 50% HFC-32 and 50% HFC-125. HFC-32 has a 4.9 year lifetime and a 100-year GWP of 675 and HFC-125 has a 29-year lifetime and a 100-year GWP of 3500. [ 10 ] [ 11 ] The combination has an effective GWP of 2088, higher than that of R-22 (100-year GWP = 1810), and an atmospheric lifetime of nearly 30 years compared with the 12-year lifetime of R-22. [ 12 ] [ 13 ]
Since R-410A allows for higher SEER ratings than an R-22 system by reducing power consumption, the overall impact on global warming of R-410A systems can, in some cases, be lower than that of R-22 systems due to reduced greenhouse gas emissions from power plants. [ 11 ] This assumes that the atmospheric leakage will be sufficiently managed. [ 14 ] Under the assumption that preventing ozone depletion is more important in the short term than GWP reduction, R-410A is preferable to R-22. [ 11 ]
The phase-down mandated by the AIM Act will lead to R-410A's replacement by other refrigerants beginning in 2022. Alternative refrigerants are available, including hydrofluoroolefins , R-454B (a zeotropic blend of R-32 and R-1234yf ), hydrocarbons (such as propane R-290 and isobutane R-600A ), and even carbon dioxide ( R-744 , GWP = 1). [ 4 ] [ 15 ] [ 16 ] [ 17 ] The alternative refrigerants have much lower global warming potential than R-410A. Some alternatives have mild or moderate flammability, operate in higher pressure ranges, or require specialized compressor lubricants and seals.
R-410A is an A1 class non-flammable substance according to ISO 817 & ASHRAE 34. One of its components, R-32, is mildly flammable (AL2), and the other, R-125, is an A1 class substance that suppresses the flammability of R32.
Thermophysical properties - Properties of refrigerant R410a
R-410A cannot be used in R-22 service equipment because of higher operating pressures (approximately 40 to 70% higher). Parts designed specifically for R-410A must be used. R-410A systems thus require service personnel to use different tools, equipment, safety standards, and techniques to manage the higher pressure. Equipment manufacturers were aware of these differences and required the certification of professionals installing R-410A systems. In addition, the AC&R Safety Coalition was created to help educate professionals about R-410A systems.
R-410A cylinders were once [ when? ] colored rose , but they now [ when? ] bear a standard light gray color. [ 21 ] [ 22 ]
While R-410A has negligible fractionation potential, it cannot be ignored when charging. | https://en.wikipedia.org/wiki/R-410A |
R-454B , also known by the trademarked names Opteon XL41 , Solstice 454B , and Puron Advance, is a zeotropic blend of 68.9 percent difluoromethane (R-32), a hydrofluorocarbon , and 31.1 percent 2,3,3,3-tetrafluoropropene (R-1234yf), a hydrofluoroolefin . [ 1 ] Because of its reduced global warming potential (GWP), R-454B is intended to be an alternative to refrigerant R-410A in new equipment. [ 2 ] [ 3 ] [ 4 ] R-454B has a GWP of 466, which is 78 percent lower than R-410A's GWP of 2088. [ 2 ]
R-454B is non-toxic and mildly flammable, with an ASHRAE safety classification of A2L. In the United States, it is expected to be packaged in a container that is red or has a red band on the shoulder or top. [ 2 ] [ 5 ] [ 6 ]
The refrigeration industry has been seeking replacements for R-410A because of its high global warming potential. R-454B, formerly known as DL-5A, has been selected by several manufacturers. [ 4 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ]
R-454B was developed at and is manufactured by Chemours . Carrier first announced introduction of R-454B in ducted residential and light commercial packaged refrigeration and air conditioning products in 2018, with R-454B-based products launches starting in 2023. [ 11 ]
R-454B is not the only blend of R-32 and R-1234yf to be proposed as a refrigerant. Other blends include R-454A (35 percent R-32, 65 percent R-1234yf) and R-454C (21.5 percent R-32, 78.5 percent R1234yf). There are also several blends that include a third component. [ 1 ] | https://en.wikipedia.org/wiki/R-454B |
In organic chemistry , an aldehyde ( / ˈ æ l d ɪ h aɪ d / ) (lat. al cohol dehyd rogenatum, [ 1 ] dehydrogenated alcohol ) is an organic compound containing a functional group with the structure R−CH=O . [ 2 ] The functional group itself (without the "R" side chain ) can be referred to as an aldehyde but can also be classified as a formyl group . Aldehydes are a common motif in many chemicals important in technology and biology. [ 3 ] [ 4 ]
Aldehyde molecules have a central carbon atom that is connected by a double bond to oxygen, a single bond to hydrogen and another single bond to a third substituent, which is carbon or, in the case of formaldehyde, hydrogen. The central carbon is often described as being sp 2 - hybridized . The aldehyde group is somewhat polar . The C=O bond length is about 120–122 picometers . [ 5 ]
Aldehydes have properties that are diverse and that depend on the remainder of the molecule. Smaller aldehydes such as formaldehyde and acetaldehyde are soluble in water, and the volatile aldehydes have pungent odors.
Aldehydes can be identified by spectroscopic methods. Using IR spectroscopy , they display a strong ν CO band near 1700 cm −1 . In their 1 H NMR spectra, the formyl hydrogen center absorbs near δ H 9.5 to 10, which is a distinctive part of the spectrum. This signal shows the characteristic coupling to any protons on the α carbon with a small coupling constant typically less than 3.0 Hz. The 13 C NMR spectra of aldehydes and ketones gives a suppressed (weak) but distinctive signal at δ C 190 to 205.
Important aldehydes and related compounds. The aldehyde group (or formyl group ) is colored red. From the left: (1) formaldehyde and (2) its trimer 1,3,5-trioxane , (3) acetaldehyde and (4) its enol vinyl alcohol , (5) glucose (pyranose form as α- D -glucopyranose), (6) the flavorant cinnamaldehyde , (7) retinal , which forms with opsins photoreceptors , and (8) the vitamin pyridoxal .
Traces of many aldehydes are found in essential oils and often contribute to their pleasant odours, including cinnamaldehyde , cilantro , and vanillin . Possibly due to the high reactivity of the formyl group, aldehydes are not commonly found in organic "building block" molecules, such as amino acids, nucleic acids, and lipids. However, most sugars are derivatives of aldehydes. These aldoses exist as hemiacetals , a sort of masked form of the parent aldehyde. For example, in aqueous solution only a tiny fraction of glucose exists as the aldehyde.
Of the several methods for preparing aldehydes, [ 3 ] one dominant technology is hydroformylation . [ 6 ] Hydroformylation is conducted on a very large scale for diverse aldehydes. It involves treatment of the alkene with a mixture of hydrogen gas and carbon monoxide in the presence of a metal catalyst. Illustrative is the generation of butyraldehyde by hydroformylation of propylene :
One complication with this process is the formation of isomers, such as isobutyraldehyde:
The largest operations involve methanol and ethanol respectively to formaldehyde and acetaldehyde , which are produced on multimillion ton scale annually. Other large scale aldehydes are produced by autoxidation of hydrocarbons: benzaldehyde from toluene , acrolein from propylene , and methacrolein from isobutene . [ 7 ] [ 8 ] In the Wacker process , oxidation of ethylene to acetaldehyde in the presence of copper and palladium catalysts, is also used. " Green " and cheap oxygen (or air) is the oxidant of choice.
Laboratories may instead apply a wide variety of specialized oxidizing agents , which are often consumed stoichiometrically. chromium(VI) reagents are popular . Oxidation can be achieved by heating the alcohol with an acidified solution of potassium dichromate . In this case, excess dichromate will further oxidize the aldehyde to a carboxylic acid , so either the aldehyde is distilled out as it forms (if volatile ) or milder reagents such as PCC are used. [ 9 ]
A variety of reagent systems achieve aldehydes under chromium-free conditions. One such are the hypervalent organoiodine compounds (i.e., IBX acid , Dess–Martin periodinane ), although these often also oxidize the α position . A Lux-Flood acid will activate other pre-oxidized substrates: various sulfoxides (e.g. the Swern oxidation ), or amine oxides (e.g., the Ganem oxidation ). Sterically-hindered nitroxyls (i.e., TEMPO ) can catalyze aldehyde formation with a cheaper oxidant .
Alternatively, vicinal diols or their oxidized sequelae ( acyloins or α-hydroxy acids ) can be oxidized with cleavage to two aldehydes or an aldehyde and carbon dioxide . [ 10 ] [ 11 ]
Aldehydes participate in many reactions. [ 3 ] From the industrial perspective, important reactions are:
Because of resonance stabilization of the conjugate base, an α-hydrogen in an aldehyde is weakly acidic with a p K a near 17. Note, however, this is much more acidic than an alkane or ether hydrogen, which has p K a near 50 approximately, and is even more acidic than a ketone α-hydrogen which has p K a near 20. This acidification of the α-hydrogen in aldehyde is attributed to:
The formyl proton itself does not readily undergo deprotonation.
Aldehydes (except those without an alpha carbon, or without protons on the alpha carbon, such as formaldehyde and benzaldehyde) can exist in either the keto or the enol tautomer . Keto–enol tautomerism is catalyzed by either acid or base. In neutral solution, the enol is the minority tautomer, reversing several times per second. [ 16 ] But it becomes the dominant tautomer in strong acid or base solutions, and enolized aldehydes undergo nucleophilic attack at the α position . [ 17 ] [ 18 ]
The formyl group can be readily reduced to a primary alcohol ( −CH 2 OH ). Typically this conversion is accomplished by catalytic hydrogenation either directly or by transfer hydrogenation . Stoichiometric reductions are also popular, as can be effected with sodium borohydride .
The formyl group readily oxidizes to the corresponding carboxyl group ( −COOH ). The preferred oxidant in industry is oxygen or air. In the laboratory, popular oxidizing agents include potassium permanganate , nitric acid , chromium(VI) oxide , and chromic acid . The combination of manganese dioxide , cyanide , acetic acid and methanol will convert the aldehyde to a methyl ester . [ 3 ]
Another oxidation reaction is the basis of the silver-mirror test . In this test, an aldehyde is treated with Tollens' reagent , which is prepared by adding a drop of sodium hydroxide solution into silver nitrate solution to give a precipitate of silver(I) oxide, and then adding just enough dilute ammonia solution to redissolve the precipitate in aqueous ammonia to produce [Ag(NH 3 ) 2 ] + complex. This reagent converts aldehydes to carboxylic acids without attacking carbon–carbon double bonds. The name silver-mirror test arises because this reaction produces a precipitate of silver, whose presence can be used to test for the presence of an aldehyde.
A further oxidation reaction involves Fehling's reagent as a test. The Cu 2+ complex ions are reduced to a red-brick-coloured Cu 2 O precipitate.
If the aldehyde cannot form an enolate (e.g., benzaldehyde ), addition of strong base induces the Cannizzaro reaction . This reaction results in disproportionation , producing a mixture of alcohol and carboxylic acid.
Nucleophiles add readily to the carbonyl group. In the product, the carbonyl carbon becomes sp 3 -hybridized, being bonded to the nucleophile, and the oxygen center becomes protonated:
In many cases, a water molecule is removed after the addition takes place; in this case, the reaction is classed as an addition – elimination or addition – condensation reaction . There are many variations of nucleophilic addition reactions.
In the acetalisation reaction, under acidic or basic conditions, an alcohol adds to the carbonyl group and a proton is transferred to form a hemiacetal . Under acidic conditions, the hemiacetal and the alcohol can further react to form an acetal and water. Simple hemiacetals are usually unstable, although cyclic ones such as glucose can be stable. Acetals are stable, but revert to the aldehyde in the presence of acid. Aldehydes can react with water to form hydrates , R−CH(OH) 2 . These diols are stable when strong electron withdrawing groups are present, as in chloral hydrate . The mechanism of formation is identical to hemiacetal formation.
Another aldehyde molecule can also act as the nucleophile to give polymeric or oligomeric acetals called paraldehydes.
In alkylimino-de-oxo-bisubstitution , a primary or secondary amine adds to the carbonyl group and a proton is transferred from the nitrogen to the oxygen atom to create a carbinolamine . In the case of a primary amine, a water molecule can be eliminated from the carbinolamine intermediate to yield an imine or its trimer, a hexahydrotriazine This reaction is catalyzed by acid. Hydroxylamine ( NH 2 OH ) can also add to the carbonyl group. After the elimination of water, this results in an oxime . An ammonia derivative of the form H 2 NNR 2 such as hydrazine ( H 2 NNH 2 ) or 2,4-dinitrophenylhydrazine can also be the nucleophile and after the elimination of water, resulting in the formation of a hydrazone , which are usually orange crystalline solids. This reaction forms the basis of a test for aldehydes and ketones . [ 19 ]
The cyano group in HCN can add to the carbonyl group to form cyanohydrins , R−CH(OH)CN . In this reaction the CN − ion is the nucleophile that attacks the partially positive carbon atom of the carbonyl group . The mechanism involves a pair of electrons from the carbonyl-group double bond transferring to the oxygen atom, leaving it single-bonded to carbon and giving the oxygen atom a negative charge. This intermediate ion rapidly reacts with H + , such as from the HCN molecule, to form the alcohol group of the cyanohydrin.
Organometallic compounds , such as organolithium reagents , Grignard reagents , or acetylides , undergo nucleophilic addition reactions, yielding a substituted alcohol group. Related reactions include organostannane additions , Barbier reactions , and the Nozaki–Hiyama–Kishi reaction .
In the aldol reaction , the metal enolates of ketones , esters , amides , and carboxylic acids add to aldehydes to form β-hydroxycarbonyl compounds ( aldols ). Acid or base-catalyzed dehydration then leads to α,β-unsaturated carbonyl compounds. The combination of these two steps is known as the aldol condensation .
The Prins reaction occurs when a nucleophilic alkene or alkyne reacts with an aldehyde as electrophile. The product of the Prins reaction varies with reaction conditions and substrates employed.
Aldehydes characteristically form "addition compounds" with bisulfites :
This reaction is used as a test for aldehydes and is useful for separation or purification of aldehydes. [ 19 ] [ 20 ]
A dialdehyde is an organic chemical compound with two aldehyde groups. The nomenclature of dialdehydes have the ending -dial or sometimes -dialdehyde . Short aliphatic dialdehydes are sometimes named after the diacid from which they can be derived. An example is butanedial , which is also called succinaldehyde (from succinic acid ).
Some aldehydes are substrates for aldehyde dehydrogenase enzymes which metabolize aldehydes in the body. There are toxicities associated with some aldehydes that are related to neurodegenerative disease, heart disease , and some types of cancer . [ 21 ]
Of all aldehydes, formaldehyde is produced on the largest scale, about 6 000 000 tons per year . It is mainly used in the production of resins when combined with urea , melamine , and phenol (e.g., Bakelite ). It is a precursor to methylene diphenyl diisocyanate ("MDI"), a precursor to polyurethanes . [ 8 ] The second main aldehyde is butyraldehyde , of which about 2 500 000 tons per year are prepared by hydroformylation . It is the principal precursor to 2-ethylhexanol , which is used as a plasticizer . [ 22 ] Acetaldehyde once was a dominating product, but production levels have declined to less than 1 000 000 tons per year because it mainly served as a precursor to acetic acid , which is now prepared by carbonylation of methanol . Many other aldehydes find commercial applications, often as precursors to alcohols, the so-called oxo alcohols , which are used in detergents. Some aldehydes are produced only on a small scale (less than 1000 tons per year) and are used as ingredients in flavours and perfumes such as Chanel No. 5 . These include cinnamaldehyde and its derivatives, citral , and lilial .
The common names for aldehydes do not strictly follow official guidelines, such as those recommended by IUPAC , but these rules are useful. IUPAC prescribes the following nomenclature for aldehydes: [ 23 ] [ 24 ] [ 25 ]
The word aldehyde was coined by Justus von Liebig as a contraction of the Latin al cohol dehyd rogenatus (dehydrogenated alcohol). [ 26 ] [ 27 ] In the past, aldehydes were sometimes named after the corresponding alcohols , for example, vinous aldehyde for acetaldehyde . ( Vinous is from Latin vinum "wine", the traditional source of ethanol , cognate with vinyl .)
The term formyl group is derived from the Latin word formica "ant". This word can be recognized in the simplest aldehyde, formaldehyde , and in the simplest carboxylic acid, formic acid . | https://en.wikipedia.org/wiki/R-CHO |
In organic chemistry , a nitrile is any organic compound that has a − C ≡ N functional group . The name of the compound is composed of a base, which includes the carbon of the −C≡N , suffixed with "nitrile", so for example CH 3 CH 2 C≡N is called " propionitrile " (or propanenitrile). [ 1 ] The prefix cyano - is used interchangeably with the term nitrile in industrial literature. Nitriles are found in many useful compounds, including methyl cyanoacrylate , used in super glue , and nitrile rubber , a nitrile-containing polymer used in latex-free laboratory and medical gloves . Nitrile rubber is also widely used as automotive and other seals since it is resistant to fuels and oils. Organic compounds containing multiple nitrile groups are known as cyanocarbons .
Inorganic compounds containing the −C≡N group are not called nitriles, but cyanides instead. [ 2 ] Though both nitriles and cyanides can be derived from cyanide salts, most nitriles are not nearly as toxic.
The N−C−C geometry is linear in nitriles, reflecting the sp hybridization of the triply bonded carbon. The C−N distance is short at 1.16 Å , consistent with a triple bond . [ 3 ] Nitriles are polar, as indicated by high dipole moments. As liquids, they have high relative permittivities , often in the 30s.
The first compound of the homolog row of nitriles, the nitrile of formic acid , hydrogen cyanide was first synthesized by C. W. Scheele in 1782. [ 4 ] [ 5 ] In 1811 J. L. Gay-Lussac was able to prepare the very toxic and volatile pure acid. [ 6 ] Around 1832 benzonitrile , the nitrile of benzoic acid , was prepared by Friedrich Wöhler and Justus von Liebig , but due to minimal yield of the synthesis neither physical nor chemical properties were determined nor a structure suggested. In 1834 Théophile-Jules Pelouze synthesized propionitrile , suggesting it to be an ether of propionic alcohol and hydrocyanic acid. [ 7 ] The synthesis of benzonitrile by Hermann Fehling in 1844 by heating ammonium benzoate was the first method yielding enough of the substance for chemical research.
Fehling determined the structure by comparing his results to the already known synthesis of hydrogen cyanide by heating ammonium formate . He coined the name "nitrile" for the newfound substance, which became the name for this group of compounds. [ 8 ]
Industrially, the main methods for producing nitriles are ammoxidation and hydrocyanation . Both routes are green in the sense that they do not generate stoichiometric amounts of salts.
In ammoxidation , a hydrocarbon is partially oxidized in the presence of ammonia . This conversion is practiced on a large scale for acrylonitrile : [ 9 ]
In the production of acrylonitrile, a side product is acetonitrile . On an industrial scale, several derivatives of benzonitrile , phthalonitrile , as well as Isobutyronitrile are prepared by ammoxidation. The process is catalysed by metal oxides and is assumed to proceed via the imine.
Hydrocyanation is an industrial method for producing nitriles from hydrogen cyanide and alkenes. The process requires homogeneous catalysts . An example of hydrocyanation is the production of adiponitrile , a precursor to nylon-6,6 from 1,3-butadiene :
Two salt metathesis reactions are popular for laboratory scale reactions. In the Kolbe nitrile synthesis , alkyl halides undergo nucleophilic aliphatic substitution with alkali metal cyanides . Aryl nitriles are prepared in the Rosenmund-von Braun synthesis .
In general, metal cyanides combine with alkyl halides to give a mixture of the nitrile and the isonitrile , although appropriate choice of counterion and temperature can minimize the latter. An alkyl sulfate obviates the problem entirely, particularly in nonaqueous conditions (the Pelouze synthesis). [ 5 ]
The cyanohydrins are a special class of nitriles. Classically they result from the addition of alkali metal cyanides to aldehydes in the cyanohydrin reaction . Because of the polarity of the organic carbonyl, this reaction requires no catalyst, unlike the hydrocyanation of alkenes. O-Silyl cyanohydrins are generated by the addition trimethylsilyl cyanide in the presence of a catalyst (silylcyanation). Cyanohydrins are also prepared by transcyanohydrin reactions starting, for example, with acetone cyanohydrin as a source of HCN. [ 10 ]
Nitriles can be prepared by the dehydration of primary amides . Common reagents for this include phosphorus pentoxide ( P 2 O 5 ) [ 11 ] and thionyl chloride ( SOCl 2 ). [ 12 ] In a related dehydration, secondary amides give nitriles by the von Braun amide degradation . In this case, one C-N bond is cleaved.
Numerous traditional methods exist for nitrile preparation by amine oxidation. [ 13 ] Common methods include the use of potassium persulfate , [ 14 ] Trichloroisocyanuric acid , [ 15 ] or anodic electrosynthesis . [ 16 ] In addition, several selective methods have been developed in the last decades for electrochemical processes. [ 17 ]
The conversion of aldehydes to nitriles via aldoximes is a popular laboratory route. Aldehydes react readily with hydroxylamine salts, sometimes at temperatures as low as ambient, to give aldoximes. These can be dehydrated to nitriles by simple heating, [ 18 ] although a wide range of reagents may assist with this, including triethylamine / sulfur dioxide , zeolites , or sulfuryl chloride . The related hydroxylamine-O-sulfonic acid reacts similarly. [ 19 ]
In specialised cases the Van Leusen reaction can be used. Biocatalysts such as aliphatic aldoxime dehydratase are also effective.
Aromatic nitriles are often prepared in the laboratory from the aniline via diazonium compounds . This is the Sandmeyer reaction . It requires transition metal cyanides. [ 20 ]
Nitrile groups in organic compounds can undergo a variety of reactions depending on the reactants or conditions. A nitrile group can be hydrolyzed, reduced, or ejected from a molecule as a cyanide ion.
The hydrolysis of nitriles RCN proceeds in the distinct steps under acid or base treatment to first give carboxamides RC(O)NH 2 and then carboxylic acids RC(O)OH . The hydrolysis of nitriles to carboxylic acids is efficient. In acid or base, the balanced equations are as follows:
Strictly speaking, these reactions are mediated (as opposed to catalyzed ) by acid or base, since one equivalent of the acid or base is consumed to form the ammonium or carboxylate salt, respectively.
Kinetic studies show that the second-order rate constant for hydroxide-ion catalyzed hydrolysis of acetonitrile to acetamide is 1.6 × 10 −6 M −1 s −1 , which is slower than the hydrolysis of the amide to the carboxylate (7.4 × 10 −5 M −1 s −1 ). Thus, the base hydrolysis route will afford the carboxylate (or the amide contaminated with the carboxylate). On the other hand, the acid catalyzed reactions requires a careful control of the temperature and of the ratio of reagents in order to avoid the formation of polymers, which is promoted by the exothermic character of the hydrolysis. [ 28 ] The classical procedure to convert a nitrile to the corresponding primary amide calls for adding the nitrile to cold concentrated sulfuric acid . [ 29 ] The further conversion to the carboxylic acid is disfavored by the low temperature and low concentration of water.
Two families of enzymes catalyze the hydrolysis of nitriles. Nitrilases hydrolyze nitriles to carboxylic acids:
Nitrile hydratases are metalloenzymes that hydrolyze nitriles to amides.
These enzymes are used commercially to produce acrylamide .
The "anhydrous hydration" of nitriles to amides has been demonstrated using an oxime as water source: [ 30 ]
Nitriles are susceptible to hydrogenation over diverse metal catalysts. The reaction can afford either the primary amine ( RCH 2 NH 2 ) or the tertiary amine ( (RCH 2 ) 3 N ), depending on conditions. [ 31 ] In conventional organic reductions , nitrile is reduced by treatment with lithium aluminium hydride to the amine. Reduction to the imine followed by hydrolysis to the aldehyde takes place in the Stephen aldehyde synthesis , which uses stannous chloride in acid.
Alkyl nitriles are sufficiently acidic to undergo deprotonation of the C-H bond adjacent to the C≡N group. [ 32 ] [ 33 ] Strong bases are required, such as lithium diisopropylamide and butyl lithium . The product is referred to as a nitrile anion . These carbanions alkylate a wide variety of electrophiles. Key to the exceptional nucleophilicity is the small steric demand of the C≡N unit combined with its inductive stabilization. These features make nitriles ideal for creating new carbon-carbon bonds in sterically demanding environments.
The carbon center of a nitrile is electrophilic , hence it is susceptible to nucleophilic addition reactions:
Nitriles are precursors to transition metal nitrile complexes , which are reagents and catalysts. Examples include tetrakis(acetonitrile)copper(I) hexafluorophosphate ( [Cu(MeCN) 4 ] + ) and bis(benzonitrile)palladium dichloride ( PdCl 2 (PhCN) 2 ). [ 40 ]
Cyanamides are N -cyano compounds with general structure R 1 R 2 N−C≡N and related to the parent cyanamide . [ 41 ]
Nitrile oxides have the chemical formula RCNO . Their general structure is R−C≡N + −O − . The R stands for any group (typically organyl , e.g., acetonitrile oxide CH 3 −C≡N + −O − , hydrogen in the case of fulminic acid H−C≡N + −O − , or halogen (e.g., chlorine fulminate Cl−C≡N + −O − ). [ 42 ] : 1187–1192
Nitrile oxides are quite different from nitriles: they are highly reactive 1,3-dipoles , and cannot be synthesized from the direct oxidation of nitriles. [ 43 ] Instead, they can be synthesised by nitroalkane dehydration, oxime dehydrogenation, [ 44 ] : 934–936 or halooxime elimination in base. [ 45 ] They are used in 1,3-dipolar cycloadditions , [ 42 ] : 1187–1192 such as to isoxazoles . [ 44 ] : 1201–1202 They undergo type 1 dyotropic rearrangement to isocyanates . [ 42 ] : 1700
The heavier nitrile sulfides are extremely reactive and rare, but temporarily form during the thermolysis of oxathiazolones . They react similarly to nitrile oxides. [ 46 ]
Nitriles occur naturally in a diverse set of plant and animal sources. Over 120 naturally occurring nitriles have been isolated from terrestrial and marine sources. Nitriles are commonly encountered in fruit pits, especially almonds, and during cooking of Brassica crops (such as cabbage, Brussels sprouts, and cauliflower), which release nitriles through hydrolysis. Mandelonitrile , a cyanohydrin produced by ingesting almonds or some fruit pits, releases hydrogen cyanide and is responsible for the toxicity of cyanogenic glycosides. [ 47 ]
Over 30 nitrile-containing pharmaceuticals are currently marketed for a diverse variety of medicinal indications with more than 20 additional nitrile-containing leads in clinical development. The types of pharmaceuticals containing nitriles are diverse, from vildagliptin , an antidiabetic drug, to anastrozole , which is the gold standard in treating breast cancer. In many instances the nitrile mimics functionality present in substrates for enzymes, whereas in other cases the nitrile increases water solubility or decreases susceptibility to oxidative metabolism in the liver. [ 48 ] The nitrile functional group is found in several drugs. | https://en.wikipedia.org/wiki/R-CN |
In organic chemistry , an amide , [ 1 ] [ 2 ] [ 3 ] also known as an organic amide or a carboxamide , is a compound with the general formula R−C(=O)−NR′R″ , where R, R', and R″ represent any group, typically organyl groups or hydrogen atoms. [ 4 ] [ 5 ] The amide group is called a peptide bond when it is part of the main chain of a protein , and an isopeptide bond when it occurs in a side chain , as in asparagine and glutamine . It can be viewed as a derivative of a carboxylic acid ( R−C(=O)−OH ) with the hydroxyl group ( −OH ) replaced by an amino group ( −NR′R″ ); or, equivalently, an acyl (alkanoyl) group ( R−C(=O)− ) joined to an amino group.
Common of amides are formamide ( H−C(=O)−NH 2 ), acetamide ( H 3 C−C(=O)−NH 2 ), benzamide ( C 6 H 5 −C(=O)−NH 2 ), and dimethylformamide ( H−C(=O)−N(−CH 3 ) 2 ). Some uncommon examples of amides are N -chloroacetamide ( H 3 C−C(=O)−NH−Cl ) and chloroformamide ( Cl−C(=O)−NH 2 ).
Amides are qualified as primary , secondary , and tertiary according to the number of acyl groups bounded to the nitrogen atom. [ 5 ] [ 6 ]
The core −C(=O)−(N) of amides is called the amide group (specifically, carboxamide group ).
In the usual nomenclature, one adds the term "amide" to the stem of the parent acid's name. For instance, the amide derived from acetic acid is named acetamide (CH 3 CONH 2 ). IUPAC recommends ethanamide , but this and related formal names are rarely encountered. When the amide is derived from a primary or secondary amine, the substituents on nitrogen are indicated first in the name. Thus, the amide formed from dimethylamine and acetic acid is N , N -dimethylacetamide (CH 3 CONMe 2 , where Me = CH 3 ). Usually even this name is simplified to dimethylacetamide . Cyclic amides are called lactams ; they are necessarily secondary or tertiary amides. [ 5 ] [ 7 ]
Amides are pervasive in nature and technology. Proteins and important plastics like nylons , aramids , Twaron , and Kevlar are polymers whose units are connected by amide groups ( polyamides ); these linkages are easily formed, confer structural rigidity, and resist hydrolysis . Amides include many other important biological compounds, as well as many drugs like paracetamol , penicillin and LSD . [ 8 ] Low-molecular-weight amides, such as dimethylformamide, are common solvents.
The lone pair of electrons on the nitrogen atom is delocalized into the Carbonyl group , thus forming a partial double bond between nitrogen and carbon. In fact the O, C and N atoms have molecular orbitals occupied by delocalized electrons , forming a conjugated system . Consequently, the three bonds of the nitrogen in amides is not pyramidal (as in the amines ) but planar. This planar restriction prevents rotations about the N linkage and thus has important consequences for the mechanical properties of bulk material of such molecules, and also for the configurational properties of macromolecules built by such bonds. The inability to rotate distinguishes amide groups from ester groups which allow rotation and thus create more flexible bulk material.
The C-C(O)NR 2 core of amides is planar. The C=O distance is shorter than the C-N distance by almost 10%. The structure of an amide can be described also as a resonance between two alternative structures: neutral (A) and zwitterionic (B).
It is estimated that for acetamide , structure A makes a 62% contribution to the structure, while structure B makes a 28% contribution (these figures do not sum to 100% because there are additional less-important resonance forms that are not depicted above). There is also a hydrogen bond present between the hydrogen and nitrogen atoms in the active groups. [ 10 ] Resonance is largely prevented in the very strained quinuclidone .
In their IR spectra, amides exhibit a moderately intense ν CO band near 1650 cm −1 . The energy of this band is about 60 cm −1 lower than for the ν CO of esters and ketones. This difference reflects the contribution of the zwitterionic resonance structure.
Compared to amines , amides are very weak bases . While the conjugate acid of an amine has a p K a of about 9.5, the conjugate acid of an amide has a p K a around −0.5. Therefore, compared to amines, amides do not have acid–base properties that are as noticeable in water . This relative lack of basicity is explained by the withdrawing of electrons from the amine by the carbonyl. On the other hand, amides are much stronger bases than carboxylic acids , esters , aldehydes , and ketones (their conjugate acids' p K a s are between −6 and −10).
The proton of a primary or secondary amide does not dissociate readily; its p K a is usually well above 15. Conversely, under extremely acidic conditions, the carbonyl oxygen can become protonated with a p K a of roughly −1. It is not only because of the positive charge on the nitrogen but also because of the negative charge on the oxygen gained through resonance.
Because of the greater electronegativity of oxygen than nitrogen, the carbonyl (C=O) is a stronger dipole than the N–C dipole. The presence of a C=O dipole and, to a lesser extent a N–C dipole, allows amides to act as H-bond acceptors. In primary and secondary amides, the presence of N–H dipoles allows amides to function as H-bond donors as well. Thus amides can participate in hydrogen bonding with water and other protic solvents; the oxygen atom can accept hydrogen bonds from water and the N–H hydrogen atoms can donate H-bonds. As a result of interactions such as these, the water solubility of amides is greater than that of corresponding hydrocarbons. These hydrogen bonds also have an important role in the secondary structure of proteins.
The solubilities of amides and esters are roughly comparable. Typically amides are less soluble than comparable amines and carboxylic acids since these compounds can both donate and accept hydrogen bonds. Tertiary amides, with the important exception of N , N -dimethylformamide , exhibit low solubility in water.
Amides do not readily participate in nucleophilic substitution reactions. Amides are stable to water, and are roughly 100 times more stable towards hydrolysis than esters. [ citation needed ] Amides can, however, be hydrolyzed to carboxylic acids in the presence of acid or base. The stability of amide bonds has biological implications, since the amino acids that make up proteins are linked with amide bonds. Amide bonds are resistant enough to hydrolysis to maintain protein structure in aqueous environments but are susceptible to catalyzed hydrolysis. [ citation needed ]
Primary and secondary amides do not react usefully with carbon nucleophiles. Instead, Grignard reagents and organolithiums deprotonate an amide N-H bond. Tertiary amides do not experience this problem, and react with carbon nucleophiles to give ketones ; the amide anion (NR 2 − ) is a very strong base and thus a very poor leaving group, so nucleophilic attack only occurs once. When reacted with carbon nucleophiles, N , N -dimethylformamide (DMF) can be used to introduce a formyl group. [ 11 ]
Here, phenyllithium 1 attacks the carbonyl group of DMF 2 , giving tetrahedral intermediate 3 . Because the dimethylamide anion is a poor leaving group, the intermediate does not collapse and another nucleophilic addition does not occur. Upon acidic workup, the alkoxide is protonated to give 4 , then the amine is protonated to give 5 . Elimination of a neutral molecule of dimethylamine and loss of a proton give benzaldehyde, 6 .
Amides hydrolyse in hot alkali as well as in strong acidic conditions. Acidic conditions yield the carboxylic acid and the ammonium ion while basic hydrolysis yield the carboxylate ion and ammonia. The protonation of the initially generated amine under acidic conditions and the deprotonation of the initially generated carboxylic acid under basic conditions render these processes non-catalytic and irreversible. Electrophiles other than protons react with the carbonyl oxygen. This step often precedes hydrolysis, which is catalyzed by both Brønsted acids and Lewis acids . Peptidase enzymes and some synthetic catalysts often operate by attachment of electrophiles to the carbonyl oxygen.
Amides are usually prepared by coupling a carboxylic acid with an amine . The direct reaction generally requires high temperatures to drive off the water:
Esters are far superior [ further explanation needed ] substrates relative to carboxylic acids. [ 14 ] [ 15 ] [ 16 ] [ better source needed ]
Further "activating" both acid chlorides ( Schotten-Baumann reaction ) and anhydrides ( Lumière–Barbier method ) react with amines to give amides:
Peptide synthesis use coupling agents such as HATU , HOBt , or PyBOP . [ 17 ]
The hydrolysis of nitriles is conducted on an industrial scale to produce fatty amides. [ 18 ] Laboratory procedures are also available. [ 19 ]
Many specialized methods also yield amides. [ 20 ] A variety of reagents, e.g. tris(2,2,2-trifluoroethyl) borate have been developed for specialized applications. [ 21 ] [ 22 ] | https://en.wikipedia.org/wiki/R-CONH2 |
In organic chemistry , an amide , [ 1 ] [ 2 ] [ 3 ] also known as an organic amide or a carboxamide , is a compound with the general formula R−C(=O)−NR′R″ , where R, R', and R″ represent any group, typically organyl groups or hydrogen atoms. [ 4 ] [ 5 ] The amide group is called a peptide bond when it is part of the main chain of a protein , and an isopeptide bond when it occurs in a side chain , as in asparagine and glutamine . It can be viewed as a derivative of a carboxylic acid ( R−C(=O)−OH ) with the hydroxyl group ( −OH ) replaced by an amino group ( −NR′R″ ); or, equivalently, an acyl (alkanoyl) group ( R−C(=O)− ) joined to an amino group.
Common of amides are formamide ( H−C(=O)−NH 2 ), acetamide ( H 3 C−C(=O)−NH 2 ), benzamide ( C 6 H 5 −C(=O)−NH 2 ), and dimethylformamide ( H−C(=O)−N(−CH 3 ) 2 ). Some uncommon examples of amides are N -chloroacetamide ( H 3 C−C(=O)−NH−Cl ) and chloroformamide ( Cl−C(=O)−NH 2 ).
Amides are qualified as primary , secondary , and tertiary according to the number of acyl groups bounded to the nitrogen atom. [ 5 ] [ 6 ]
The core −C(=O)−(N) of amides is called the amide group (specifically, carboxamide group ).
In the usual nomenclature, one adds the term "amide" to the stem of the parent acid's name. For instance, the amide derived from acetic acid is named acetamide (CH 3 CONH 2 ). IUPAC recommends ethanamide , but this and related formal names are rarely encountered. When the amide is derived from a primary or secondary amine, the substituents on nitrogen are indicated first in the name. Thus, the amide formed from dimethylamine and acetic acid is N , N -dimethylacetamide (CH 3 CONMe 2 , where Me = CH 3 ). Usually even this name is simplified to dimethylacetamide . Cyclic amides are called lactams ; they are necessarily secondary or tertiary amides. [ 5 ] [ 7 ]
Amides are pervasive in nature and technology. Proteins and important plastics like nylons , aramids , Twaron , and Kevlar are polymers whose units are connected by amide groups ( polyamides ); these linkages are easily formed, confer structural rigidity, and resist hydrolysis . Amides include many other important biological compounds, as well as many drugs like paracetamol , penicillin and LSD . [ 8 ] Low-molecular-weight amides, such as dimethylformamide, are common solvents.
The lone pair of electrons on the nitrogen atom is delocalized into the Carbonyl group , thus forming a partial double bond between nitrogen and carbon. In fact the O, C and N atoms have molecular orbitals occupied by delocalized electrons , forming a conjugated system . Consequently, the three bonds of the nitrogen in amides is not pyramidal (as in the amines ) but planar. This planar restriction prevents rotations about the N linkage and thus has important consequences for the mechanical properties of bulk material of such molecules, and also for the configurational properties of macromolecules built by such bonds. The inability to rotate distinguishes amide groups from ester groups which allow rotation and thus create more flexible bulk material.
The C-C(O)NR 2 core of amides is planar. The C=O distance is shorter than the C-N distance by almost 10%. The structure of an amide can be described also as a resonance between two alternative structures: neutral (A) and zwitterionic (B).
It is estimated that for acetamide , structure A makes a 62% contribution to the structure, while structure B makes a 28% contribution (these figures do not sum to 100% because there are additional less-important resonance forms that are not depicted above). There is also a hydrogen bond present between the hydrogen and nitrogen atoms in the active groups. [ 10 ] Resonance is largely prevented in the very strained quinuclidone .
In their IR spectra, amides exhibit a moderately intense ν CO band near 1650 cm −1 . The energy of this band is about 60 cm −1 lower than for the ν CO of esters and ketones. This difference reflects the contribution of the zwitterionic resonance structure.
Compared to amines , amides are very weak bases . While the conjugate acid of an amine has a p K a of about 9.5, the conjugate acid of an amide has a p K a around −0.5. Therefore, compared to amines, amides do not have acid–base properties that are as noticeable in water . This relative lack of basicity is explained by the withdrawing of electrons from the amine by the carbonyl. On the other hand, amides are much stronger bases than carboxylic acids , esters , aldehydes , and ketones (their conjugate acids' p K a s are between −6 and −10).
The proton of a primary or secondary amide does not dissociate readily; its p K a is usually well above 15. Conversely, under extremely acidic conditions, the carbonyl oxygen can become protonated with a p K a of roughly −1. It is not only because of the positive charge on the nitrogen but also because of the negative charge on the oxygen gained through resonance.
Because of the greater electronegativity of oxygen than nitrogen, the carbonyl (C=O) is a stronger dipole than the N–C dipole. The presence of a C=O dipole and, to a lesser extent a N–C dipole, allows amides to act as H-bond acceptors. In primary and secondary amides, the presence of N–H dipoles allows amides to function as H-bond donors as well. Thus amides can participate in hydrogen bonding with water and other protic solvents; the oxygen atom can accept hydrogen bonds from water and the N–H hydrogen atoms can donate H-bonds. As a result of interactions such as these, the water solubility of amides is greater than that of corresponding hydrocarbons. These hydrogen bonds also have an important role in the secondary structure of proteins.
The solubilities of amides and esters are roughly comparable. Typically amides are less soluble than comparable amines and carboxylic acids since these compounds can both donate and accept hydrogen bonds. Tertiary amides, with the important exception of N , N -dimethylformamide , exhibit low solubility in water.
Amides do not readily participate in nucleophilic substitution reactions. Amides are stable to water, and are roughly 100 times more stable towards hydrolysis than esters. [ citation needed ] Amides can, however, be hydrolyzed to carboxylic acids in the presence of acid or base. The stability of amide bonds has biological implications, since the amino acids that make up proteins are linked with amide bonds. Amide bonds are resistant enough to hydrolysis to maintain protein structure in aqueous environments but are susceptible to catalyzed hydrolysis. [ citation needed ]
Primary and secondary amides do not react usefully with carbon nucleophiles. Instead, Grignard reagents and organolithiums deprotonate an amide N-H bond. Tertiary amides do not experience this problem, and react with carbon nucleophiles to give ketones ; the amide anion (NR 2 − ) is a very strong base and thus a very poor leaving group, so nucleophilic attack only occurs once. When reacted with carbon nucleophiles, N , N -dimethylformamide (DMF) can be used to introduce a formyl group. [ 11 ]
Here, phenyllithium 1 attacks the carbonyl group of DMF 2 , giving tetrahedral intermediate 3 . Because the dimethylamide anion is a poor leaving group, the intermediate does not collapse and another nucleophilic addition does not occur. Upon acidic workup, the alkoxide is protonated to give 4 , then the amine is protonated to give 5 . Elimination of a neutral molecule of dimethylamine and loss of a proton give benzaldehyde, 6 .
Amides hydrolyse in hot alkali as well as in strong acidic conditions. Acidic conditions yield the carboxylic acid and the ammonium ion while basic hydrolysis yield the carboxylate ion and ammonia. The protonation of the initially generated amine under acidic conditions and the deprotonation of the initially generated carboxylic acid under basic conditions render these processes non-catalytic and irreversible. Electrophiles other than protons react with the carbonyl oxygen. This step often precedes hydrolysis, which is catalyzed by both Brønsted acids and Lewis acids . Peptidase enzymes and some synthetic catalysts often operate by attachment of electrophiles to the carbonyl oxygen.
Amides are usually prepared by coupling a carboxylic acid with an amine . The direct reaction generally requires high temperatures to drive off the water:
Esters are far superior [ further explanation needed ] substrates relative to carboxylic acids. [ 14 ] [ 15 ] [ 16 ] [ better source needed ]
Further "activating" both acid chlorides ( Schotten-Baumann reaction ) and anhydrides ( Lumière–Barbier method ) react with amines to give amides:
Peptide synthesis use coupling agents such as HATU , HOBt , or PyBOP . [ 17 ]
The hydrolysis of nitriles is conducted on an industrial scale to produce fatty amides. [ 18 ] Laboratory procedures are also available. [ 19 ]
Many specialized methods also yield amides. [ 20 ] A variety of reagents, e.g. tris(2,2,2-trifluoroethyl) borate have been developed for specialized applications. [ 21 ] [ 22 ] | https://en.wikipedia.org/wiki/R-CONHR |
In organic chemistry , an amide , [ 1 ] [ 2 ] [ 3 ] also known as an organic amide or a carboxamide , is a compound with the general formula R−C(=O)−NR′R″ , where R, R', and R″ represent any group, typically organyl groups or hydrogen atoms. [ 4 ] [ 5 ] The amide group is called a peptide bond when it is part of the main chain of a protein , and an isopeptide bond when it occurs in a side chain , as in asparagine and glutamine . It can be viewed as a derivative of a carboxylic acid ( R−C(=O)−OH ) with the hydroxyl group ( −OH ) replaced by an amino group ( −NR′R″ ); or, equivalently, an acyl (alkanoyl) group ( R−C(=O)− ) joined to an amino group.
Common of amides are formamide ( H−C(=O)−NH 2 ), acetamide ( H 3 C−C(=O)−NH 2 ), benzamide ( C 6 H 5 −C(=O)−NH 2 ), and dimethylformamide ( H−C(=O)−N(−CH 3 ) 2 ). Some uncommon examples of amides are N -chloroacetamide ( H 3 C−C(=O)−NH−Cl ) and chloroformamide ( Cl−C(=O)−NH 2 ).
Amides are qualified as primary , secondary , and tertiary according to the number of acyl groups bounded to the nitrogen atom. [ 5 ] [ 6 ]
The core −C(=O)−(N) of amides is called the amide group (specifically, carboxamide group ).
In the usual nomenclature, one adds the term "amide" to the stem of the parent acid's name. For instance, the amide derived from acetic acid is named acetamide (CH 3 CONH 2 ). IUPAC recommends ethanamide , but this and related formal names are rarely encountered. When the amide is derived from a primary or secondary amine, the substituents on nitrogen are indicated first in the name. Thus, the amide formed from dimethylamine and acetic acid is N , N -dimethylacetamide (CH 3 CONMe 2 , where Me = CH 3 ). Usually even this name is simplified to dimethylacetamide . Cyclic amides are called lactams ; they are necessarily secondary or tertiary amides. [ 5 ] [ 7 ]
Amides are pervasive in nature and technology. Proteins and important plastics like nylons , aramids , Twaron , and Kevlar are polymers whose units are connected by amide groups ( polyamides ); these linkages are easily formed, confer structural rigidity, and resist hydrolysis . Amides include many other important biological compounds, as well as many drugs like paracetamol , penicillin and LSD . [ 8 ] Low-molecular-weight amides, such as dimethylformamide, are common solvents.
The lone pair of electrons on the nitrogen atom is delocalized into the Carbonyl group , thus forming a partial double bond between nitrogen and carbon. In fact the O, C and N atoms have molecular orbitals occupied by delocalized electrons , forming a conjugated system . Consequently, the three bonds of the nitrogen in amides is not pyramidal (as in the amines ) but planar. This planar restriction prevents rotations about the N linkage and thus has important consequences for the mechanical properties of bulk material of such molecules, and also for the configurational properties of macromolecules built by such bonds. The inability to rotate distinguishes amide groups from ester groups which allow rotation and thus create more flexible bulk material.
The C-C(O)NR 2 core of amides is planar. The C=O distance is shorter than the C-N distance by almost 10%. The structure of an amide can be described also as a resonance between two alternative structures: neutral (A) and zwitterionic (B).
It is estimated that for acetamide , structure A makes a 62% contribution to the structure, while structure B makes a 28% contribution (these figures do not sum to 100% because there are additional less-important resonance forms that are not depicted above). There is also a hydrogen bond present between the hydrogen and nitrogen atoms in the active groups. [ 10 ] Resonance is largely prevented in the very strained quinuclidone .
In their IR spectra, amides exhibit a moderately intense ν CO band near 1650 cm −1 . The energy of this band is about 60 cm −1 lower than for the ν CO of esters and ketones. This difference reflects the contribution of the zwitterionic resonance structure.
Compared to amines , amides are very weak bases . While the conjugate acid of an amine has a p K a of about 9.5, the conjugate acid of an amide has a p K a around −0.5. Therefore, compared to amines, amides do not have acid–base properties that are as noticeable in water . This relative lack of basicity is explained by the withdrawing of electrons from the amine by the carbonyl. On the other hand, amides are much stronger bases than carboxylic acids , esters , aldehydes , and ketones (their conjugate acids' p K a s are between −6 and −10).
The proton of a primary or secondary amide does not dissociate readily; its p K a is usually well above 15. Conversely, under extremely acidic conditions, the carbonyl oxygen can become protonated with a p K a of roughly −1. It is not only because of the positive charge on the nitrogen but also because of the negative charge on the oxygen gained through resonance.
Because of the greater electronegativity of oxygen than nitrogen, the carbonyl (C=O) is a stronger dipole than the N–C dipole. The presence of a C=O dipole and, to a lesser extent a N–C dipole, allows amides to act as H-bond acceptors. In primary and secondary amides, the presence of N–H dipoles allows amides to function as H-bond donors as well. Thus amides can participate in hydrogen bonding with water and other protic solvents; the oxygen atom can accept hydrogen bonds from water and the N–H hydrogen atoms can donate H-bonds. As a result of interactions such as these, the water solubility of amides is greater than that of corresponding hydrocarbons. These hydrogen bonds also have an important role in the secondary structure of proteins.
The solubilities of amides and esters are roughly comparable. Typically amides are less soluble than comparable amines and carboxylic acids since these compounds can both donate and accept hydrogen bonds. Tertiary amides, with the important exception of N , N -dimethylformamide , exhibit low solubility in water.
Amides do not readily participate in nucleophilic substitution reactions. Amides are stable to water, and are roughly 100 times more stable towards hydrolysis than esters. [ citation needed ] Amides can, however, be hydrolyzed to carboxylic acids in the presence of acid or base. The stability of amide bonds has biological implications, since the amino acids that make up proteins are linked with amide bonds. Amide bonds are resistant enough to hydrolysis to maintain protein structure in aqueous environments but are susceptible to catalyzed hydrolysis. [ citation needed ]
Primary and secondary amides do not react usefully with carbon nucleophiles. Instead, Grignard reagents and organolithiums deprotonate an amide N-H bond. Tertiary amides do not experience this problem, and react with carbon nucleophiles to give ketones ; the amide anion (NR 2 − ) is a very strong base and thus a very poor leaving group, so nucleophilic attack only occurs once. When reacted with carbon nucleophiles, N , N -dimethylformamide (DMF) can be used to introduce a formyl group. [ 11 ]
Here, phenyllithium 1 attacks the carbonyl group of DMF 2 , giving tetrahedral intermediate 3 . Because the dimethylamide anion is a poor leaving group, the intermediate does not collapse and another nucleophilic addition does not occur. Upon acidic workup, the alkoxide is protonated to give 4 , then the amine is protonated to give 5 . Elimination of a neutral molecule of dimethylamine and loss of a proton give benzaldehyde, 6 .
Amides hydrolyse in hot alkali as well as in strong acidic conditions. Acidic conditions yield the carboxylic acid and the ammonium ion while basic hydrolysis yield the carboxylate ion and ammonia. The protonation of the initially generated amine under acidic conditions and the deprotonation of the initially generated carboxylic acid under basic conditions render these processes non-catalytic and irreversible. Electrophiles other than protons react with the carbonyl oxygen. This step often precedes hydrolysis, which is catalyzed by both Brønsted acids and Lewis acids . Peptidase enzymes and some synthetic catalysts often operate by attachment of electrophiles to the carbonyl oxygen.
Amides are usually prepared by coupling a carboxylic acid with an amine . The direct reaction generally requires high temperatures to drive off the water:
Esters are far superior [ further explanation needed ] substrates relative to carboxylic acids. [ 14 ] [ 15 ] [ 16 ] [ better source needed ]
Further "activating" both acid chlorides ( Schotten-Baumann reaction ) and anhydrides ( Lumière–Barbier method ) react with amines to give amides:
Peptide synthesis use coupling agents such as HATU , HOBt , or PyBOP . [ 17 ]
The hydrolysis of nitriles is conducted on an industrial scale to produce fatty amides. [ 18 ] Laboratory procedures are also available. [ 19 ]
Many specialized methods also yield amides. [ 20 ] A variety of reagents, e.g. tris(2,2,2-trifluoroethyl) borate have been developed for specialized applications. [ 21 ] [ 22 ] | https://en.wikipedia.org/wiki/R-CONR2 |
In chemistry , an ester is a compound derived from an acid (either organic or inorganic) in which the hydrogen atom (H) of at least one acidic hydroxyl group ( −OH ) of that acid is replaced by an organyl group (R ′ ). [ 1 ] These compounds contain a distinctive functional group . Analogues derived from oxygen replaced by other chalcogens belong to the ester category as well. [ 1 ] According to some authors, organyl derivatives of acidic hydrogen of other acids are esters as well (e.g. amides ), but not according to the IUPAC . [ 1 ]
Glycerides are fatty acid esters of glycerol ; they are important in biology, being one of the main classes of lipids and comprising the bulk of animal fats and vegetable oils . Lactones are cyclic carboxylic esters; naturally occurring lactones are mainly 5- and 6-membered ring lactones. Lactones contribute to the aroma of fruits, butter, cheese, vegetables like celery and other foods.
Esters can be formed from oxoacids (e.g. esters of acetic acid , carbonic acid , sulfuric acid , phosphoric acid , nitric acid , xanthic acid ), but also from acids that do not contain oxygen (e.g. esters of thiocyanic acid and trithiocarbonic acid ). An example of an ester formation is the substitution reaction between a carboxylic acid ( R−C(=O)−OH ) and an alcohol ( R'−OH ), forming an ester ( R−C(=O)−O−R' ), where R stands for any group (typically hydrogen or organyl) and R ′ stands for organyl group.
Organyl esters of carboxylic acids typically have a pleasant smell; those of low molecular weight are commonly used as fragrances and are found in essential oils and pheromones . They perform as high-grade solvents for a broad array of plastics , plasticizers , resins , and lacquers , [ 2 ] and are one of the largest classes of synthetic lubricants on the commercial market. [ 3 ] Polyesters are important plastics, with monomers linked by ester moieties . Esters of phosphoric acid form the backbone of DNA molecules. Esters of nitric acid , such as nitroglycerin , are known for their explosive properties.
There are compounds in which an acidic hydrogen of acids mentioned in this article are not replaced by an organyl, but by some other group. According to some authors, those compounds are esters as well, especially when the first carbon atom of the organyl group replacing acidic hydrogen, is replaced by another atom from the group 14 elements ( Si , Ge , Sn , Pb ); for example, according to them, trimethylstannyl acetate (or trimethyltin acetate) CH 3 COOSn(CH 3 ) 3 is a trimethylstannyl ester of acetic acid , and dibutyltin dilaurate (CH 3 (CH 2 ) 10 COO) 2 Sn((CH 2 ) 3 CH 3 ) 2 is a dibutylstannylene ester of lauric acid , and the Phillips catalyst CrO 2 (OSi(OCH 3 ) 3 ) 2 is a trimethoxysilyl ester of chromic acid ( H 2 CrO 4 ). [ 4 ] [ 5 ]
The word ester was coined in 1848 by a German chemist Leopold Gmelin , [ 6 ] probably as a contraction of the German Essigäther , " acetic ether ".
The names of esters that are formed from an alcohol and an acid, are derived from the parent alcohol and the parent acid, where the latter may be organic or inorganic. Esters derived from the simplest carboxylic acids are commonly named according to the more traditional, so-called " trivial names " e.g. as formate, acetate, propionate, and butyrate, as opposed to the IUPAC nomenclature methanoate, ethanoate, propanoate, and butanoate. Esters derived from more complex carboxylic acids are, on the other hand, more frequently named using the systematic IUPAC name, based on the name for the acid followed by the suffix -oate . For example, the ester hexyl octanoate, also known under the trivial name hexyl caprylate , has the formula CH 3 (CH 2 ) 6 CO 2 (CH 2 ) 5 CH 3 .
The chemical formulas of organic esters formed from carboxylic acids and alcohols usually take the form RCO 2 R' or RCOOR', where R and R' are the organyl parts of the carboxylic acid and the alcohol, respectively, and R can be a hydrogen in the case of esters of formic acid . For example, butyl acetate (systematically butyl ethanoate), derived from butanol and acetic acid (systematically ethanoic acid) would be written CH 3 CO 2 (CH 2 ) 3 CH 3 . Alternative presentations are common including BuOAc and CH 3 COO(CH 2 ) 3 CH 3 .
Cyclic esters are called lactones , regardless of whether they are derived from an organic or inorganic acid. One example of an organic lactone is γ-valerolactone .
An uncommon class of esters are the orthoesters . One of them are the esters of orthocarboxylic acids. Those esters have the formula RC(OR′) 3 , where R stands for any group (organic or inorganic) and R ′ stands for organyl group. For example, triethyl orthoformate ( HC(OCH 2 CH 3 ) 3 ) is derived, in terms of its name (but not its synthesis) from esterification of orthoformic acid ( HC(OH) 3 ) with ethanol .
Esters can also be derived from inorganic acids.
Inorganic acids that exist as tautomers form two or more types of esters.
Some inorganic acids that are unstable or elusive form stable esters.
In principle, a part of metal and metalloid alkoxides , of which many hundreds are known, could be classified as esters of the corresponding acids (e.g., aluminium triethoxide ( Al(OCH 2 CH 3 ) 3 ) could be classified as an ester of aluminic acid which is aluminium hydroxide , tetraethyl orthosilicate ( Si(OCH 2 CH 3 ) 4 ) could be classified as an ester of orthosilicic acid , and titanium ethoxide ( Ti(OCH 2 CH 3 ) 4 ) could be classified as an ester of orthotitanic acid ).
Esters derived from carboxylic acids and alcohols contain a carbonyl group C=O, which is a divalent group at C atom, which gives rise to 120° C–C–O and O–C–O angles. Unlike amides , carboxylic acid esters are structurally flexible functional groups because rotation about the C–O–C bonds has a low barrier. Their flexibility and low polarity is manifested in their physical properties; they tend to be less rigid (lower melting point) and more volatile (lower boiling point) than the corresponding amides . [ 7 ] The p K a of the alpha-hydrogens on esters of carboxylic acids is around 25 (alpha-hydrogen is a hydrogen bound to the carbon adjacent to the carbonyl group (C=O) of carboxylate esters). [ 8 ]
Many carboxylic acid esters have the potential for conformational isomerism , but they tend to adopt an S - cis (or Z ) conformation rather than the S - trans (or E ) alternative, due to a combination of hyperconjugation and dipole minimization effects. The preference for the Z conformation is influenced by the nature of the substituents and solvent, if present. [ 9 ] [ 10 ] Lactones with small rings are restricted to the s -trans (i.e. E ) conformation due to their cyclic structure.
Esters derived from carboxylic acids and alcohols are more polar than ethers but less polar than alcohols. They participate in hydrogen bonds as hydrogen-bond acceptors, but cannot act as hydrogen-bond donors, unlike their parent alcohols. This ability to participate in hydrogen bonding confers some water-solubility. Because of their lack of hydrogen-bond-donating ability, esters do not self-associate. Consequently, esters are more volatile than carboxylic acids of similar molecular weight. [ 7 ]
Esters are generally identified by gas chromatography, taking advantage of their volatility. IR spectra for esters feature an intense sharp band in the range 1730–1750 cm −1 assigned to ν C=O . This peak changes depending on the functional groups attached to the carbonyl. For example, a benzene ring or double bond in conjunction with the carbonyl will bring the wavenumber down about 30 cm −1 .
Esters are widespread in nature and are widely used in industry. In nature, fats are, in general, triesters derived from glycerol and fatty acids . [ 12 ] Esters are responsible for the aroma of many fruits, including apples , durians , pears , bananas , pineapples , and strawberries . [ 13 ] Several billion kilograms of polyesters are produced industrially annually, important products being polyethylene terephthalate , acrylate esters , and cellulose acetate . [ 14 ]
Esterification is the general name for a chemical reaction in which two reactants (typically an alcohol and an acid) form an ester as the reaction product . Esters are common in organic chemistry and biological materials, and often have a pleasant characteristic, fruity odor. This leads to their extensive use in the fragrance and flavor industry. Ester bonds are also found in many polymers .
The classic synthesis is the Fischer esterification , which involves treating a carboxylic acid with an alcohol in the presence of a dehydrating agent:
The equilibrium constant for such reactions is about 5 for typical esters, e.g., ethyl acetate. [ 15 ] The reaction is slow in the absence of a catalyst. Sulfuric acid is a typical catalyst for this reaction. Many other acids are also used such as polymeric sulfonic acids . Since esterification is highly reversible, the yield of the ester can be improved using Le Chatelier's principle :
Reagents are known that drive the dehydration of mixtures of alcohols and carboxylic acids. One example is the Steglich esterification , which is a method of forming esters under mild conditions. The method is popular in peptide synthesis , where the substrates are sensitive to harsh conditions like high heat. DCC ( dicyclohexylcarbodiimide ) is used to activate the carboxylic acid to further reaction. 4-Dimethylaminopyridine (DMAP) is used as an acyl-transfer catalyst . [ 16 ]
Another method for the dehydration of mixtures of alcohols and carboxylic acids is the Mitsunobu reaction :
Carboxylic acids can be esterified using diazomethane :
Using this diazomethane, mixtures of carboxylic acids can be converted to their methyl esters in near quantitative yields, e.g., for analysis by gas chromatography . The method is useful in specialized organic synthetic operations but is considered too hazardous and expensive for large-scale applications.
Carboxylic acids are esterified by treatment with epoxides , giving β-hydroxyesters:
This reaction is employed in the production of vinyl ester resin from acrylic acid .
Alcohols react with acyl chlorides and acid anhydrides to give esters:
The reactions are irreversible simplifying work-up . Since acyl chlorides and acid anhydrides also react with water, anhydrous conditions are preferred. The analogous acylations of amines to give amides are less sensitive because amines are stronger nucleophiles and react more rapidly than does water. This method is employed only for laboratory-scale procedures, as it is expensive.
Trimethyloxonium tetrafluoroborate can be used for esterification of carboxylic acids under conditions where acid-catalyzed reactions are infeasible: [ 17 ]
Although rarely employed for esterifications, carboxylate salts (often generated in situ ) react with electrophilic alkylating agents , such as alkyl halides , to give esters. [ 14 ] [ 18 ] Anion availability can inhibit this reaction, which correspondingly benefits from phase transfer catalysts or such highly polar aprotic solvents as DMF . An additional iodide salt may, via the Finkelstein reaction , catalyze the reaction of a recalcitrant alkyl halide. Alternatively, salts of a coordinating metal, such as silver, may improve the reaction rate by easing halide elimination.
Transesterification , which involves changing one ester into another one, is widely practiced:
Like the hydrolysation, transesterification is catalysed by acids and bases. The reaction is widely used for degrading triglycerides , e.g. in the production of fatty acid esters and alcohols. Poly(ethylene terephthalate) is produced by the transesterification of dimethyl terephthalate and ethylene glycol: [ 14 ]
A subset of transesterification is the alcoholysis of diketene . This reaction affords 2-ketoesters. [ 14 ]
Alkenes undergo carboalkoxylation in the presence of metal carbonyl catalysts. Esters of propanoic acid are produced commercially by this method:
A preparation of methyl propionate is one illustrative example.
The carbonylation of methanol yields methyl formate , which is the main commercial source of formic acid . The reaction is catalyzed by sodium methoxide :
In hydroesterification , alkenes and alkynes insert into the O−H bond of carboxylic acids. Vinyl acetate is produced industrially by the addition of acetic acid to acetylene in the presence of zinc acetate catalysts: [ 19 ]
Vinyl acetate can also be produced by palladium -catalyzed reaction of ethylene, acetic acid , and oxygen :
Silicotungstic acid is used to manufacture ethyl acetate by the alkylation of acetic acid by ethylene:
The Tishchenko reaction involves disproportionation of an aldehyde in the presence of an anhydrous base to give an ester. Catalysts are aluminium alkoxides or sodium alkoxides. Benzaldehyde reacts with sodium benzyloxide (generated from sodium and benzyl alcohol ) to generate benzyl benzoate . [ 20 ] The method is used in the production of ethyl acetate from acetaldehyde . [ 14 ]
Esters are less reactive than acid halides and anhydrides. As with more reactive acyl derivatives, they can react with ammonia and primary and secondary amines to give amides, although this type of reaction is not often used, since acid halides give better yields.
Esters can be converted to other esters in a process known as transesterification . Transesterification can be either acid- or base-catalyzed, and involves the reaction of an ester with an alcohol. Unfortunately, because the leaving group is also an alcohol, the forward and reverse reactions will often occur at similar rates. Using a large excess of the reactant alcohol or removing the leaving group alcohol (e.g. via distillation ) will drive the forward reaction towards completion, in accordance with Le Chatelier's principle . [ 24 ]
Acid-catalyzed hydrolysis of esters is also an equilibrium process – essentially the reverse of the Fischer esterification reaction. Because an alcohol (which acts as the leaving group) and water (which acts as the nucleophile) have similar p K a values, the forward and reverse reactions compete with each other. As in transesterification, using a large excess of reactant (water) or removing one of the products (the alcohol) can promote the forward reaction.
Basic hydrolysis of esters, known as saponification , is not an equilibrium process; a full equivalent of base is consumed in the reaction, which produces one equivalent of alcohol and one equivalent of a carboxylate salt. The saponification of esters of fatty acids is an industrially important process, used in the production of soap. [ 24 ]
Esterification is a reversible reaction. Esters undergo hydrolysis under acidic and basic conditions. Under acidic conditions, the reaction is the reverse reaction of the Fischer esterification . Under basic conditions, hydroxide acts as a nucleophile, while an alkoxide is the leaving group. This reaction, saponification , is the basis of soap making.
The alkoxide group may also be displaced by stronger nucleophiles such as ammonia or primary or secondary amines to give amides (ammonolysis reaction):
This reaction is not usually reversible. Hydrazines and hydroxylamine can be used in place of amines. Esters can be converted to isocyanates through intermediate hydroxamic acids in the Lossen rearrangement .
Sources of carbon nucleophiles, e.g., Grignard reagents and organolithium compounds, add readily to the carbonyl.
Compared to ketones and aldehydes, esters are relatively resistant to reduction . The introduction of catalytic hydrogenation in the early part of the 20th century was a breakthrough; esters of fatty acids are hydrogenated to fatty alcohols .
A typical catalyst is copper chromite . Prior to the development of catalytic hydrogenation , esters were reduced on a large scale using the Bouveault–Blanc reduction . This method, which is largely obsolete, uses sodium in the presence of proton sources.
Especially for fine chemical syntheses, lithium aluminium hydride is used to reduce esters to two primary alcohols. The related reagent sodium borohydride is slow in this reaction. DIBAH reduces esters to aldehydes. [ 25 ]
Direct reduction to give the corresponding ether is difficult as the intermediate hemiacetal tends to decompose to give an alcohol and an aldehyde (which is rapidly reduced to give a second alcohol). The reaction can be achieved using triethylsilane with a variety of Lewis acids. [ 26 ] [ 27 ]
Esters can undergo a variety of reactions with carbon nucleophiles. They react with an excess of a Grignard reagent to give tertiary alcohols. Esters also react readily with enolates . In the Claisen condensation , an enolate of one ester ( 1 ) will attack the carbonyl group of another ester ( 2 ) to give tetrahedral intermediate 3 . The intermediate collapses, forcing out an alkoxide (R'O − ) and producing β-keto ester 4 .
Crossed Claisen condensations, in which the enolate and nucleophile are different esters, are also possible. An intramolecular Claisen condensation is called a Dieckmann condensation or Dieckmann cyclization, since it can be used to form rings. Esters can also undergo condensations with ketone and aldehyde enolates to give β-dicarbonyl compounds. [ 28 ] A specific example of this is the Baker–Venkataraman rearrangement , in which an aromatic ortho -acyloxy ketone undergoes an intramolecular nucleophilic acyl substitution and subsequent rearrangement to form an aromatic β-diketone. [ 29 ] The Chan rearrangement is another example of a rearrangement resulting from an intramolecular nucleophilic acyl substitution reaction.
Esters react with nucleophiles at the carbonyl carbon. [ 30 ] The carbonyl is weakly electrophilic but is attacked by strong nucleophiles (amines, alkoxides, hydride sources, organolithium compounds, etc.). The C–H bonds adjacent to the carbonyl are weakly acidic but undergo deprotonation with strong bases. This process is the one that usually initiates condensation reactions. The carbonyl oxygen in esters is weakly basic, less so than the carbonyl oxygen in amides due to resonance donation of an electron pair from nitrogen in amides, but forms adducts .
As for aldehydes , the hydrogen atoms on the carbon adjacent ("α to") the carboxyl group in esters are sufficiently acidic to undergo deprotonation, which in turn leads to a variety of useful reactions. Deprotonation requires relatively strong bases, such as alkoxides . Deprotonation gives a nucleophilic enolate , which can further react, e.g., the Claisen condensation and its intramolecular equivalent, the Dieckmann condensation . This conversion is exploited in the malonic ester synthesis , wherein the diester of malonic acid reacts with an electrophile (e.g., alkyl halide ), and is subsequently decarboxylated. Another variation is the Fráter–Seebach alkylation .
As a class, esters serve as protecting groups for carboxylic acids . Protecting a carboxylic acid is useful in peptide synthesis, to prevent self-reactions of the bifunctional amino acids . Methyl and ethyl esters are commonly available for many amino acids; the t -butyl ester tends to be more expensive. However, t -butyl esters are particularly useful because, under strongly acidic conditions, the t -butyl esters undergo elimination to give the carboxylic acid and isobutylene , simplifying work-up.
Many esters have distinctive fruit-like odors, and many occur naturally in the essential oils of plants. This has also led to their common use in artificial flavorings and fragrances which aim to mimic those odors. [ 32 ]
b. Ester oder sauerstoffsäure Aetherarten. Ethers du troisième genre. Viele mineralische und organische Sauerstoffsäuren treten mit einer Alkohol-Art unter Ausscheidung von Wasser zu neutralen flüchtigen ätherischen Verbindungen zusammen, welche man als gepaarte Verbindungen von Alkohol und Säuren-Wasser oder, nach der Radicaltheorie, als Salze betrachten kann, in welchen eine Säure mit einem Aether verbunden ist.
b. Ester or oxy-acid ethers. Ethers of the third type. Many mineral and organic acids containing oxygen combine with an alcohol upon elimination of water to [form] neutral, volatile ether compounds, which one can view as coupled compounds of alcohol and acid-water, or, according to the theory of radicals, as salts in which an acid is bonded with an ether. | https://en.wikipedia.org/wiki/R-COO-R |
In organic chemistry , a carboxylic acid is an organic acid that contains a carboxyl group ( −C(=O)−OH ) [ 1 ] attached to an R-group . The general formula of a carboxylic acid is often written as R−COOH or R−CO 2 H , sometimes as R−C(O)OH with R referring to an organyl group (e.g., alkyl , alkenyl , aryl ), or hydrogen , or other groups. Carboxylic acids occur widely. Important examples include the amino acids and fatty acids . Deprotonation of a carboxylic acid gives a carboxylate anion .
Carboxylic acids are commonly identified by their trivial names . They often have the suffix -ic acid . IUPAC -recommended names also exist; in this system, carboxylic acids have an -oic acid suffix. [ 2 ] For example, butyric acid ( CH 3 CH 2 CH 2 CO 2 H ) is butanoic acid by IUPAC guidelines. For nomenclature of complex molecules containing a carboxylic acid, the carboxyl can be considered position one of the parent chain even if there are other substituents , such as 3-chloropropanoic acid . Alternately, it can be named as a "carboxy" or "carboxylic acid" substituent on another parent structure, such as 2-carboxyfuran . [ citation needed ]
The carboxylate anion ( R−COO − or R−CO − 2 ) of a carboxylic acid is usually named with the suffix -ate , in keeping with the general pattern of -ic acid and -ate for a conjugate acid and its conjugate base, respectively. For example, the conjugate base of acetic acid is acetate . [ citation needed ]
Carbonic acid , which occurs in bicarbonate buffer systems in nature, is not generally classed as one of the carboxylic acids, despite that it has a moiety that looks like a COOH group. [ citation needed ]
Carboxylic acids are polar . Because they are both hydrogen-bond acceptors (the carbonyl −C(=O)− ) and hydrogen-bond donors (the hydroxyl −OH ), they also participate in hydrogen bonding . Together, the hydroxyl and carbonyl group form the functional group carboxyl. Carboxylic acids usually exist as dimers in nonpolar media due to their tendency to "self-associate". Smaller carboxylic acids (1 to 5 carbons) are soluble in water, whereas bigger carboxylic acids have limited solubility due to the increasing hydrophobic nature of the alkyl chain. These longer chain acids tend to be soluble in less-polar solvents such as ethers and alcohols. [ 3 ] Aqueous sodium hydroxide and carboxylic acids, even hydrophobic ones, react to yield water-soluble sodium salts. For example, enanthic acid has a low solubility in water (0.2 g/L), but its sodium salt is very soluble in water.
Carboxylic acids tend to have higher boiling points than water, because of their greater surface areas and their tendency to form stabilized dimers through hydrogen bonds . For boiling to occur, either the dimer bonds must be broken or the entire dimer arrangement must be vaporized, increasing the enthalpy of vaporization requirements significantly. [ citation needed ]
Carboxylic acids are Brønsted–Lowry acids because they are proton (H + ) donors. They are the most common type of organic acid . [ citation needed ]
Carboxylic acids are typically weak acids , meaning that they only partially dissociate into [H 3 O] + cations and R−CO − 2 anions in neutral aqueous solution. For example, at room temperature, in a 1- molar solution of acetic acid , only 0.001% of the acid are dissociated (i.e. 10 −5 moles out of 1 mol). Electron-withdrawing substituents such as trifluoromethyl ( −CF 3 ) give stronger acids (the p K a of acetic acid is 4.76 whereas trifluoroacetic acid, with a trifluoromethyl substituent , has a p K a of 0.23). Electron-donating substituents give weaker acids (the p K a of formic acid is 3.75 whereas acetic acid, with a methyl substituent , has a p K a of 4.76) [ citation needed ]
Deprotonation of carboxylic acids gives carboxylate anions; these are resonance stabilized , because the negative charge is delocalized over the two oxygen atoms, increasing the stability of the anion. Each of the carbon–oxygen bonds in the carboxylate anion has a partial double-bond character. The carbonyl carbon's partial positive charge is also weakened by the − 1 / 2 negative charges on the 2 oxygen atoms. [ citation needed ]
Carboxylic acids often have strong sour odours. Esters of carboxylic acids tend to have fruity, pleasant odours, and many are used in perfume . [ citation needed ]
Carboxylic acids are readily identified as such by infrared spectroscopy . They exhibit a sharp band associated with vibration of the C=O carbonyl bond ( ν C=O ) between 1680 and 1725 cm −1 . A characteristic ν O–H band appears as a broad peak in the 2500 to 3000 cm −1 region. [ 3 ] [ 6 ] By 1 H NMR spectrometry, the hydroxyl hydrogen appears in the 10–13 ppm region, although it is often either broadened or not observed owing to exchange with traces of water. [ citation needed ]
Many carboxylic acids are produced industrially on a large scale. They are also frequently found in nature. Esters of fatty acids are the main components of lipids and polyamides of aminocarboxylic acids are the main components of proteins . [ citation needed ]
Carboxylic acids are used in the production of polymers, pharmaceuticals, solvents, and food additives. Industrially important carboxylic acids include acetic acid (component of vinegar, precursor to solvents and coatings), acrylic and methacrylic acids (precursors to polymers, adhesives), adipic acid (polymers), citric acid (a flavor and preservative in food and beverages), ethylenediaminetetraacetic acid (chelating agent), fatty acids (coatings), maleic acid (polymers), propionic acid (food preservative), terephthalic acid (polymers). Important carboxylate salts are soaps. [ citation needed ]
In general, industrial routes to carboxylic acids differ from those used on a smaller scale because they require specialized equipment.
Preparative methods for small scale reactions for research or for production of fine chemicals often employ expensive consumable reagents.
Many reactions produce carboxylic acids but are used only in specific cases or are mainly of academic interest.
Carboxylic acids react with bases to form carboxylate salts, in which the hydrogen of the hydroxyl (–OH) group is replaced with a metal cation . For example, acetic acid found in vinegar reacts with sodium bicarbonate (baking soda) to form sodium acetate , carbon dioxide , and water: [ citation needed ]
Widely practiced reactions convert carboxylic acids into esters , amides , carboxylate salts , acid chlorides , and alcohols .
Their conversion to esters is widely used, e.g. in the production of polyesters . Likewise, carboxylic acids are converted into amides , but this conversion typically does not occur by direct reaction of the carboxylic acid and the amine. Instead esters are typical precursors to amides. The conversion of amino acids into peptides is a significant biochemical process that requires ATP . [ citation needed ]
Converting a carboxylic acid to an amide is possible, but not straightforward. Instead of acting as a nucleophile, an amine will react as a base in the presence of a carboxylic acid to give the ammonium carboxylate salt. Heating the salt to above 100 °C will drive off water and lead to the formation of the amide. This method of synthesizing amides is industrially important, and has laboratory applications as well. [ 10 ] In the presence of a strong acid catalyst, carboxylic acids can condense to form acid anhydrides. The condensation produces water, however, which can hydrolyze the anhydride back to the starting carboxylic acids. Thus, the formation of the anhydride via condensation is an equilibrium process. [ citation needed ]
Under acid-catalyzed conditions, carboxylic acids will react with alcohols to form esters via the Fischer esterification reaction, which is also an equilibrium process. Alternatively, diazomethane can be used to convert an acid to an ester. While esterification reactions with diazomethane often give quantitative yields, diazomethane is only useful for forming methyl esters. [ 10 ]
Like esters , most carboxylic acids can be reduced to alcohols by hydrogenation , or using hydride transferring agents such as lithium aluminium hydride . Strong alkyl transferring agents, such as organolithium compounds but not Grignard reagents , will reduce carboxylic acids to ketones along with transfer of the alkyl group. [ citation needed ]
The Vilsmaier reagent ( N , N -Dimethyl(chloromethylene)ammonium chloride; [ClHC=N + (CH 3 ) 2 ]Cl − ) is a highly chemoselective agent for carboxylic acid reduction. It selectively activates the carboxylic acid to give the carboxymethyleneammonium salt, which can be reduced by a mild reductant like lithium tris( t -butoxy)aluminum hydride to afford an aldehyde in a one pot procedure. This procedure is known to tolerate reactive carbonyl functionalities such as ketone as well as moderately reactive ester, olefin, nitrile, and halide moieties. [ 11 ]
The hydroxyl group on carboxylic acids may be replaced with a chlorine atom using thionyl chloride to give acyl chlorides . In nature, carboxylic acids are converted to thioesters . Thionyl chloride can be used to convert carboxylic acids to their corresponding acyl chlorides. First, carboxylic acid 1 attacks thionyl chloride, and chloride ion leaves. The resulting oxonium ion 2 is activated towards nucleophilic attack and has a good leaving group, setting it apart from a normal carboxylic acid. In the next step, 2 is attacked by chloride ion to give tetrahedral intermediate 3 , a chlorosulfite. The tetrahedral intermediate collapses with the loss of sulfur dioxide and chloride ion, giving protonated acyl chloride 4 . Chloride ion can remove the proton on the carbonyl group, giving the acyl chloride 5 with a loss of HCl .
Phosphorus(III) chloride (PCl 3 ) and phosphorus(V) chloride (PCl 5 ) will also convert carboxylic acids to acid chlorides, by a similar mechanism. One equivalent of PCl 3 can react with three equivalents of acid, producing one equivalent of H 3 PO 3 , or phosphorus acid , in addition to the desired acid chloride. PCl 5 reacts with carboxylic acids in a 1:1 ratio, and produces phosphorus(V) oxychloride (POCl 3 ) and hydrogen chloride (HCl) as byproducts. [ citation needed ]
Carboxylic acids react with Grignard reagents and organolithiums to form ketones. The first equivalent of nucleophile acts as a base and deprotonates the acid. A second equivalent will attack the carbonyl group to create a geminal alkoxide dianion, which is protonated upon workup to give the hydrate of a ketone. Because most ketone hydrates are unstable relative to their corresponding ketones, the equilibrium between the two is shifted heavily in favor of the ketone. For example, the equilibrium constant for the formation of acetone hydrate from acetone is only 0.002. The carboxylic group is the most acidic in organic compounds. [ 12 ]
The carboxyl radical , •COOH, only exists briefly. [ 13 ] The acid dissociation constant of •COOH has been measured using electron paramagnetic resonance spectroscopy. [ 14 ] The carboxyl group tends to dimerise to form oxalic acid . [ citation needed ] | https://en.wikipedia.org/wiki/R-COOH |
In organic chemistry , a nitrile is any organic compound that has a − C ≡ N functional group . The name of the compound is composed of a base, which includes the carbon of the −C≡N , suffixed with "nitrile", so for example CH 3 CH 2 C≡N is called " propionitrile " (or propanenitrile). [ 1 ] The prefix cyano - is used interchangeably with the term nitrile in industrial literature. Nitriles are found in many useful compounds, including methyl cyanoacrylate , used in super glue , and nitrile rubber , a nitrile-containing polymer used in latex-free laboratory and medical gloves . Nitrile rubber is also widely used as automotive and other seals since it is resistant to fuels and oils. Organic compounds containing multiple nitrile groups are known as cyanocarbons .
Inorganic compounds containing the −C≡N group are not called nitriles, but cyanides instead. [ 2 ] Though both nitriles and cyanides can be derived from cyanide salts, most nitriles are not nearly as toxic.
The N−C−C geometry is linear in nitriles, reflecting the sp hybridization of the triply bonded carbon. The C−N distance is short at 1.16 Å , consistent with a triple bond . [ 3 ] Nitriles are polar, as indicated by high dipole moments. As liquids, they have high relative permittivities , often in the 30s.
The first compound of the homolog row of nitriles, the nitrile of formic acid , hydrogen cyanide was first synthesized by C. W. Scheele in 1782. [ 4 ] [ 5 ] In 1811 J. L. Gay-Lussac was able to prepare the very toxic and volatile pure acid. [ 6 ] Around 1832 benzonitrile , the nitrile of benzoic acid , was prepared by Friedrich Wöhler and Justus von Liebig , but due to minimal yield of the synthesis neither physical nor chemical properties were determined nor a structure suggested. In 1834 Théophile-Jules Pelouze synthesized propionitrile , suggesting it to be an ether of propionic alcohol and hydrocyanic acid. [ 7 ] The synthesis of benzonitrile by Hermann Fehling in 1844 by heating ammonium benzoate was the first method yielding enough of the substance for chemical research.
Fehling determined the structure by comparing his results to the already known synthesis of hydrogen cyanide by heating ammonium formate . He coined the name "nitrile" for the newfound substance, which became the name for this group of compounds. [ 8 ]
Industrially, the main methods for producing nitriles are ammoxidation and hydrocyanation . Both routes are green in the sense that they do not generate stoichiometric amounts of salts.
In ammoxidation , a hydrocarbon is partially oxidized in the presence of ammonia . This conversion is practiced on a large scale for acrylonitrile : [ 9 ]
In the production of acrylonitrile, a side product is acetonitrile . On an industrial scale, several derivatives of benzonitrile , phthalonitrile , as well as Isobutyronitrile are prepared by ammoxidation. The process is catalysed by metal oxides and is assumed to proceed via the imine.
Hydrocyanation is an industrial method for producing nitriles from hydrogen cyanide and alkenes. The process requires homogeneous catalysts . An example of hydrocyanation is the production of adiponitrile , a precursor to nylon-6,6 from 1,3-butadiene :
Two salt metathesis reactions are popular for laboratory scale reactions. In the Kolbe nitrile synthesis , alkyl halides undergo nucleophilic aliphatic substitution with alkali metal cyanides . Aryl nitriles are prepared in the Rosenmund-von Braun synthesis .
In general, metal cyanides combine with alkyl halides to give a mixture of the nitrile and the isonitrile , although appropriate choice of counterion and temperature can minimize the latter. An alkyl sulfate obviates the problem entirely, particularly in nonaqueous conditions (the Pelouze synthesis). [ 5 ]
The cyanohydrins are a special class of nitriles. Classically they result from the addition of alkali metal cyanides to aldehydes in the cyanohydrin reaction . Because of the polarity of the organic carbonyl, this reaction requires no catalyst, unlike the hydrocyanation of alkenes. O-Silyl cyanohydrins are generated by the addition trimethylsilyl cyanide in the presence of a catalyst (silylcyanation). Cyanohydrins are also prepared by transcyanohydrin reactions starting, for example, with acetone cyanohydrin as a source of HCN. [ 10 ]
Nitriles can be prepared by the dehydration of primary amides . Common reagents for this include phosphorus pentoxide ( P 2 O 5 ) [ 11 ] and thionyl chloride ( SOCl 2 ). [ 12 ] In a related dehydration, secondary amides give nitriles by the von Braun amide degradation . In this case, one C-N bond is cleaved.
Numerous traditional methods exist for nitrile preparation by amine oxidation. [ 13 ] Common methods include the use of potassium persulfate , [ 14 ] Trichloroisocyanuric acid , [ 15 ] or anodic electrosynthesis . [ 16 ] In addition, several selective methods have been developed in the last decades for electrochemical processes. [ 17 ]
The conversion of aldehydes to nitriles via aldoximes is a popular laboratory route. Aldehydes react readily with hydroxylamine salts, sometimes at temperatures as low as ambient, to give aldoximes. These can be dehydrated to nitriles by simple heating, [ 18 ] although a wide range of reagents may assist with this, including triethylamine / sulfur dioxide , zeolites , or sulfuryl chloride . The related hydroxylamine-O-sulfonic acid reacts similarly. [ 19 ]
In specialised cases the Van Leusen reaction can be used. Biocatalysts such as aliphatic aldoxime dehydratase are also effective.
Aromatic nitriles are often prepared in the laboratory from the aniline via diazonium compounds . This is the Sandmeyer reaction . It requires transition metal cyanides. [ 20 ]
Nitrile groups in organic compounds can undergo a variety of reactions depending on the reactants or conditions. A nitrile group can be hydrolyzed, reduced, or ejected from a molecule as a cyanide ion.
The hydrolysis of nitriles RCN proceeds in the distinct steps under acid or base treatment to first give carboxamides RC(O)NH 2 and then carboxylic acids RC(O)OH . The hydrolysis of nitriles to carboxylic acids is efficient. In acid or base, the balanced equations are as follows:
Strictly speaking, these reactions are mediated (as opposed to catalyzed ) by acid or base, since one equivalent of the acid or base is consumed to form the ammonium or carboxylate salt, respectively.
Kinetic studies show that the second-order rate constant for hydroxide-ion catalyzed hydrolysis of acetonitrile to acetamide is 1.6 × 10 −6 M −1 s −1 , which is slower than the hydrolysis of the amide to the carboxylate (7.4 × 10 −5 M −1 s −1 ). Thus, the base hydrolysis route will afford the carboxylate (or the amide contaminated with the carboxylate). On the other hand, the acid catalyzed reactions requires a careful control of the temperature and of the ratio of reagents in order to avoid the formation of polymers, which is promoted by the exothermic character of the hydrolysis. [ 28 ] The classical procedure to convert a nitrile to the corresponding primary amide calls for adding the nitrile to cold concentrated sulfuric acid . [ 29 ] The further conversion to the carboxylic acid is disfavored by the low temperature and low concentration of water.
Two families of enzymes catalyze the hydrolysis of nitriles. Nitrilases hydrolyze nitriles to carboxylic acids:
Nitrile hydratases are metalloenzymes that hydrolyze nitriles to amides.
These enzymes are used commercially to produce acrylamide .
The "anhydrous hydration" of nitriles to amides has been demonstrated using an oxime as water source: [ 30 ]
Nitriles are susceptible to hydrogenation over diverse metal catalysts. The reaction can afford either the primary amine ( RCH 2 NH 2 ) or the tertiary amine ( (RCH 2 ) 3 N ), depending on conditions. [ 31 ] In conventional organic reductions , nitrile is reduced by treatment with lithium aluminium hydride to the amine. Reduction to the imine followed by hydrolysis to the aldehyde takes place in the Stephen aldehyde synthesis , which uses stannous chloride in acid.
Alkyl nitriles are sufficiently acidic to undergo deprotonation of the C-H bond adjacent to the C≡N group. [ 32 ] [ 33 ] Strong bases are required, such as lithium diisopropylamide and butyl lithium . The product is referred to as a nitrile anion . These carbanions alkylate a wide variety of electrophiles. Key to the exceptional nucleophilicity is the small steric demand of the C≡N unit combined with its inductive stabilization. These features make nitriles ideal for creating new carbon-carbon bonds in sterically demanding environments.
The carbon center of a nitrile is electrophilic , hence it is susceptible to nucleophilic addition reactions:
Nitriles are precursors to transition metal nitrile complexes , which are reagents and catalysts. Examples include tetrakis(acetonitrile)copper(I) hexafluorophosphate ( [Cu(MeCN) 4 ] + ) and bis(benzonitrile)palladium dichloride ( PdCl 2 (PhCN) 2 ). [ 40 ]
Cyanamides are N -cyano compounds with general structure R 1 R 2 N−C≡N and related to the parent cyanamide . [ 41 ]
Nitrile oxides have the chemical formula RCNO . Their general structure is R−C≡N + −O − . The R stands for any group (typically organyl , e.g., acetonitrile oxide CH 3 −C≡N + −O − , hydrogen in the case of fulminic acid H−C≡N + −O − , or halogen (e.g., chlorine fulminate Cl−C≡N + −O − ). [ 42 ] : 1187–1192
Nitrile oxides are quite different from nitriles: they are highly reactive 1,3-dipoles , and cannot be synthesized from the direct oxidation of nitriles. [ 43 ] Instead, they can be synthesised by nitroalkane dehydration, oxime dehydrogenation, [ 44 ] : 934–936 or halooxime elimination in base. [ 45 ] They are used in 1,3-dipolar cycloadditions , [ 42 ] : 1187–1192 such as to isoxazoles . [ 44 ] : 1201–1202 They undergo type 1 dyotropic rearrangement to isocyanates . [ 42 ] : 1700
The heavier nitrile sulfides are extremely reactive and rare, but temporarily form during the thermolysis of oxathiazolones . They react similarly to nitrile oxides. [ 46 ]
Nitriles occur naturally in a diverse set of plant and animal sources. Over 120 naturally occurring nitriles have been isolated from terrestrial and marine sources. Nitriles are commonly encountered in fruit pits, especially almonds, and during cooking of Brassica crops (such as cabbage, Brussels sprouts, and cauliflower), which release nitriles through hydrolysis. Mandelonitrile , a cyanohydrin produced by ingesting almonds or some fruit pits, releases hydrogen cyanide and is responsible for the toxicity of cyanogenic glycosides. [ 47 ]
Over 30 nitrile-containing pharmaceuticals are currently marketed for a diverse variety of medicinal indications with more than 20 additional nitrile-containing leads in clinical development. The types of pharmaceuticals containing nitriles are diverse, from vildagliptin , an antidiabetic drug, to anastrozole , which is the gold standard in treating breast cancer. In many instances the nitrile mimics functionality present in substrates for enzymes, whereas in other cases the nitrile increases water solubility or decreases susceptibility to oxidative metabolism in the liver. [ 48 ] The nitrile functional group is found in several drugs. | https://en.wikipedia.org/wiki/R-C≡N |
In organic chemistry , nitro compounds are organic compounds that contain one or more nitro functional groups ( −NO 2 ). The nitro group is one of the most common explosophores (functional group that makes a compound explosive) used globally. The nitro group is also strongly electron-withdrawing . Because of this property, C−H bonds alpha (adjacent) to the nitro group can be acidic. For similar reasons, the presence of nitro groups in aromatic compounds retards electrophilic aromatic substitution but facilitates nucleophilic aromatic substitution . Nitro groups are rarely found in nature. They are almost invariably produced by nitration reactions starting with nitric acid . [ 1 ]
Aromatic nitro compounds are typically synthesized by nitration. Nitration is achieved using a mixture of nitric acid and sulfuric acid , which produce the nitronium ion ( NO + 2 ), which is the electrophile:
The nitration product produced on the largest scale, by far, is nitrobenzene . Many explosives are produced by nitration including trinitrophenol (picric acid), trinitrotoluene (TNT), and trinitroresorcinol (styphnic acid). [ 3 ] Another but more specialized method for making aryl–NO 2 group starts from halogenated phenols, is the Zinke nitration .
Aliphatic nitro compounds can be synthesized by various methods; notable examples include:
In nucleophilic aliphatic substitution , sodium nitrite (NaNO 2 ) replaces an alkyl halide . In the so-called Ter Meer reaction (1876) named after Edmund ter Meer , [ 14 ] the reactant is a 1,1-halonitroalkane:
The reaction mechanism is proposed in which in the first slow step a proton is abstracted from nitroalkane 1 to a carbanion 2 followed by protonation to an aci-nitro 3 and finally nucleophilic displacement of chlorine based on an experimentally observed hydrogen kinetic isotope effect of 3.3. [ 15 ] When the same reactant is reacted with potassium hydroxide the reaction product is the 1,2-dinitro dimer. [ 16 ]
Chloramphenicol is a rare example of a naturally occurring nitro compound. At least some naturally occurring nitro groups arose by the oxidation of amino groups. [ 17 ] 2-Nitrophenol is an aggregation pheromone of ticks .
Examples of nitro compounds are rare in nature. 3-Nitropropionic acid found in fungi and plants ( Indigofera ). Nitropentadecene is a defense compound found in termites . Aristolochic acids are found in the flowering plant family Aristolochiaceae . Nitrophenylethane is found in Aniba canelilla . [ 18 ] Nitrophenylethane is also found in members of the Annonaceae , Lauraceae and Papaveraceae . [ 19 ]
Despite the occasional use in pharmaceuticals, the nitro group is associated with mutagenicity and genotoxicity and therefore is often regarded as a liability in the drug discovery process. [ 20 ]
Nitro compounds participate in several organic reactions , the most important being reduction of nitro compounds to the corresponding amines:
Virtually all aromatic amines (e.g. aniline ) are derived from nitroaromatics through such catalytic hydrogenation . A variation is formation of a dimethylaminoarene with palladium on carbon and formaldehyde : [ 21 ]
The α-carbon of nitroalkanes is somewhat acidic. The p K a values of nitromethane and 2-nitropropane are respectively 17.2 and 16.9 in dimethyl sulfoxide (DMSO) solution, suggesting an aqueous p K a of around 11. [ 22 ] In other words, these carbon acids can be deprotonated in aqueous solution. The conjugate base is called a nitronate , and behaves similar to an enolate . In the nitroaldol reaction , it adds directly to aldehydes , and, with enones , can serve as a Michael donor . Conversely, a nitroalkene reacts with enols as a Michael acceptor. [ 23 ] [ 24 ] Nitrosating a nitronate gives a nitrolic acid . [ 25 ]
Nitronates are also key intermediates in the Nef reaction : when exposed to acids or oxidants, a nitronate hydrolyzes to a carbonyl and azanone . [ 26 ]
Grignard reagents combine with nitro compounds to give a nitrone ; but a Grignard reagent with an α hydrogen will then add again to the nitrone to give a hydroxylamine salt. [ 27 ]
The Leimgruber–Batcho , Bartoli and Baeyer–Emmerling indole syntheses begin with aromatic nitro compounds. Indigo can be synthesized in a condensation reaction from ortho -nitrobenzaldehyde and acetone in strongly basic conditions in a reaction known as the Baeyer–Drewson indigo synthesis .
Many flavin -dependent enzymes are capable of oxidizing aliphatic nitro compounds to less-toxic aldehydes and ketones. Nitroalkane oxidase and 3-nitropropionate oxidase oxidize aliphatic nitro compounds exclusively, whereas other enzymes such as glucose oxidase have other physiological substrates. [ 28 ]
Explosive decomposition of organo nitro compounds are redox reactions, wherein both the oxidant (nitro group) and the fuel (hydrocarbon substituent) are bound within the same molecule. The explosion process generates heat by forming highly stable products including molecular nitrogen (N 2 ), carbon dioxide, and water. The explosive power of this redox reaction is enhanced because these stable products are gases at mild temperatures. Many contact explosives contain the nitro group. | https://en.wikipedia.org/wiki/R-NO2 |
In crystallography , the R-factor (sometimes called residual factor or reliability factor or the R-value or R Work ) is a measure of the disagreement between the crystallographic model and the experimental X-ray diffraction data - lower the R value lower is the disagreement or better is the agreement. In other words, it is a measure of how well the refined structure predicts the observed data. [ 1 ] The value is also sometimes called the discrepancy index , as it mathematically describes the difference between the experimental observations and the ideal calculated values. [ 2 ] It is defined by the following equation:
where F is the so-called structure factor and the sum extends over all the reflections of X-rays measured and their calculated counterparts respectively. The structure factor is closely related to the intensity of the reflection it describes:
The minimum possible value is zero, indicating perfect agreement between experimental observations and the structure factors predicted from the model. There is no theoretical maximum, but in practice, values are considerably less than one even for poor models, provided the model includes a suitable scale factor. Random experimental errors in the data contribute to R {\displaystyle R} even for a perfect model, and these have more leverage when the data are weak or few, such as for a low-resolution data set. Model inadequacies such as incorrect or missing parts and unmodeled disorder are the other main contributors to R {\displaystyle R} , making it useful to assess the progress and final result of a crystallographic model refinement. For large molecules, the R-factor usually ranges between 0.6 (when computed for a random model and against an experimental data set) and 0.2 (for example for a well refined macro-molecular model at a resolution of 2.5 Ångström). Small molecules (up to ca . 1000 atoms) usually form better-ordered crystals than large molecules, and thus it is possible to attain lower R-factors. In the Cambridge Structural Database of small-molecule structures, more than 95% of the 500,000+ crystals have an R-factor lower than 0.15, and 9.5% have an R-factor lower than 0.03.
Crystallographers also use the Free R-Factor ( R F r e e {\displaystyle R_{Free}} ) [ 3 ] to assess possible overmodeling of the data. R F r e e {\displaystyle R_{Free}} is computed according to the same formula given above, but on a small, random sample of data that are set aside for the purpose and never included in the refinement. R F r e e {\displaystyle R_{Free}} will always be greater than R {\displaystyle R} because the model is not fitted to the reflections that contribute to R F r e e {\displaystyle R_{Free}} , but the two statistics should be similar because a correct model should predict all the data with uniform accuracy. If the two statistics differ significantly then that indicates the model has been over-parameterized, so that to some extent it predicts not the ideal error-free data for the correct model, but rather the error-afflicted data actually observed.
The quantities R sym {\displaystyle R_{\text{sym}}} and R merge {\displaystyle R_{\text{merge}}} are similarly used to describe the internal agreement of measurements in a crystallographic data set.
This crystallography -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/R-factor_(crystallography) |
The term R-matrix has several meanings, depending on the field of study. Its original use has been to mathematically describe nuclear reactions . [ 1 ] In particular the general problem of nuclear reactions is to relate the values of the scattering or collision matrix elements (which in principle can be obtained from measurements) to the (slow) dynamics of nuclear structure . The R-matrix formalism describes the effects of the interaction of the nucleus with the outside world. Its interior is not specified, i.e. it is considered a "black box". The original formulations of the theory came from nuclear scientists Wigner , [ 2 ] [ 3 ] Eisenbud , Breit , [ 4 ] Blatt , Weisskopf , and others. [ 5 ] Related theories are U-matrix, S-matrix , by M-matrix , or T-matrix . [ 6 ]
The term R-matrix is used in connection with the Yang–Baxter equation , first introduced in the field of statistical mechanics in the works of J. B. McGuire in 1964 [ 7 ] and C. N. Yang in 1967 [ 8 ] and in the group algebra C [ S n ] {\displaystyle \mathbb {C} [S_{n}]} of the symmetric group in the work of A. A. Jucys in 1966. [ 9 ] The classical R-matrix arises in the definition of the classical Yang–Baxter equation. [ 10 ]
In quasitriangular Hopf algebra , the R-matrix is a solution of the Yang–Baxter equation .
The numerical modeling of diffraction gratings in optical science can be performed using the R-matrix propagation algorithm. [ 11 ]
There is a method in computational quantum mechanics for studying scattering known as the R-matrix. Using the original R-matrix theory as a basis, a method was developed for electron , positron and photon scattering by atoms . [ 12 ] This approach was later adapted for electron, positron and photon scattering by molecules . [ 13 ] [ 14 ] [ 15 ]
R-matrix method is used in UKRmol [ 16 ] and UKRmol+ [ 17 ] code suits. The user-friendly software Quantemol Electron Collisions (Quantemol-EC) and its predecessor Quantemol-N are based on UKRmol/UKRmol+ and employ MOLPRO package for electron configuration calculations. | https://en.wikipedia.org/wiki/R-matrix |
R-parity is a concept in particle physics . In the Minimal Supersymmetric Standard Model , baryon number and lepton number are no longer conserved by all of the renormalizable couplings in the theory. Since baryon number and lepton number conservation have been tested very precisely, these couplings need to be very small in order not to be in conflict with experimental data. R-parity is a Z 2 {\displaystyle \mathbb {Z} _{2}} symmetry acting on the Minimal Supersymmetric Standard Model (MSSM) fields that forbids these couplings and can be defined as [ 1 ]
or, equivalently, as
where s is spin , B is baryon number, and L is lepton number. All Standard Model particles have R-parity of +1 while supersymmetric particles have R-parity of −1.
Note that there are different forms of parity with different effects and principles, one should not confuse this parity with any other parity .
With R-parity being preserved, the lightest supersymmetric particle ( LSP ) cannot decay. This lightest particle (if it exists) may therefore account for the observed missing mass of the universe that is generally called dark matter . [ 2 ] In order to fit observations, it is assumed that this particle has a mass of 100 GeV/ c 2 to 1 TeV/ c 2 , is neutral and only interacts through weak interactions and gravitational interactions . It is often called a weakly interacting massive particle or WIMP.
Typically the dark matter candidate of the MSSM is a mixture of the electroweak gauginos and Higgsinos and is called a neutralino . In extensions to the MSSM it is possible to have a sneutrino be the dark matter candidate. Another possibility is the gravitino , which only interacts via gravitational interactions and does not require strict R-parity.
The renormalizable R-parity violating couplings of the MSSM are
The strongest constraint involving this coupling alone is from the non-observation of neutron–antineutron oscillations.
The strongest constraint involving this coupling alone is the violation universality of Fermi constant G F {\displaystyle G_{F}} in quark and leptonic charged current decays.
The strongest constraint involving this coupling alone is the violation universality of Fermi constant in leptonic charged current decays.
The strongest constraint involving this coupling alone is that it leads to a large neutrino mass.
While the constraints on single couplings are reasonably strong, if multiple couplings are combined together, they lead to proton decay . Thus there are further maximal bounds on values of the couplings from maximal bounds on proton decay rate.
Without baryon and lepton number being conserved and taking O ( 1 ) {\displaystyle {\mathcal {O}}(1)} couplings for the R-parity violating couplings, the proton can decay in approximately 10 −2 seconds or if minimal flavor violation is assumed the proton lifetime can be extended to 1 year. Since the proton lifetime is observed to be greater than 10 33 to 10 34 years (depending on the exact decay channel), this would highly disfavour the model. R-parity sets all of the renormalizable baryon and lepton number violating couplings to zero and the proton is stable at the renormalizable level and the lifetime of the proton is increased to 10 32 years and is nearly consistent with current observational data.
Because proton decay involves violating both lepton and baryon number simultaneously, no single renormalizable R-parity violating coupling leads to proton decay. This has motivated the study of R-parity violation where only one set of the R-parity violating couplings are non-zero which is sometimes called the single coupling dominance hypothesis.
A very attractive way to motivate R-parity is with a B − L continuous gauge symmetry which is spontaneously broken at a scale inaccessible to current experiments. A continuous U ( 1 ) B − L {\displaystyle U(1)_{B-L}} forbids renormalizable terms which violate B and L . [ 3 ] [ 4 ] [ 5 ] [ 6 ] If U ( 1 ) B − L {\displaystyle U(1)_{B-L}} is only broken by scalar vacuum expectation values (or other order parameters) that carry even integer values of 3( B − L ) , then there exist an exactly conserved discrete remnant subgroup which has the desired properties. [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] The crucial issue is to determine whether the sneutrino (the supersymmetric partner of neutrino), which is odd under R-parity, develops a vacuum expectation value. It can be shown, on phenomenological grounds, that this cannot happen in any theory where U ( 1 ) B − L {\displaystyle U(1)_{B-L}} is broken at a scale much above the electroweak one. This is true in any theory based on a large-scale seesaw mechanism . [ 12 ] As a consequence, in such theories R-parity remains exact at all energies.
This phenomenon can arise as an automatic symmetry in SO(10) grand unified theories . This natural occurrence of R-parity is possible because in SO(10) the Standard Model fermions arise from the 16 dimensional spinor representation , while the Higgs arises from a 10 dimensional vector representation. In order to make an SO(10) invariant coupling, one must have an even number of spinor fields (i.e. there is a spinor parity). After GUT symmetry breaking, this spinor parity descends into R-parity so long as no spinor fields were used to break the GUT symmetry. Explicit examples of such SO(10) theories have been constructed. [ 13 ] [ 14 ] | https://en.wikipedia.org/wiki/R-parity |
In nuclear astrophysics , the rapid neutron-capture process , also known as the r -process , is a set of nuclear reactions that is responsible for the creation of approximately half of the atomic nuclei heavier than iron , the "heavy elements", with the other half produced by the p-process and s -process . The r -process usually synthesizes the most neutron-rich stable isotopes of each heavy element. The r -process can typically synthesize the heaviest four isotopes of every heavy element; of these, the heavier two are called r-only nuclei because they are created exclusively via the r -process. Abundance peaks for the r -process occur near mass numbers A = 82 (elements Se, Br, and Kr), A = 130 (elements Te, I, and Xe) and A = 196 (elements Os, Ir, and Pt).
The r -process entails a succession of rapid neutron captures (hence the name) by one or more heavy seed nuclei , typically beginning with nuclei in the abundance peak centered on 56 Fe . The captures must be rapid in the sense that the nuclei must not have time to undergo radioactive decay (typically via β − decay) before another neutron arrives to be captured. This sequence can continue up to the limit of stability of the increasingly neutron-rich nuclei (the neutron drip line ) to physically retain neutrons as governed by the short range nuclear force. The r -process therefore must occur in locations where there exists a high density of free neutrons .
Early studies theorized that 10 24 free neutrons per cm 3 would be required, for temperatures of about 1 GK, in order to match the waiting points, at which no more neutrons can be captured, with the mass numbers of the abundance peaks for r -process nuclei. [ 1 ] This amounts to almost a gram of free neutrons in every cubic centimeter, an astonishing number requiring extreme locations. [ a ] Traditionally this suggested the material ejected from the reexpanded core of a core-collapse supernova , as part of supernova nucleosynthesis , [ 2 ] or decompression of neutron star matter thrown off by a binary neutron star merger in a kilonova . [ 3 ] The relative contribution of each of these sources to the astrophysical abundance of r -process elements is a matter of ongoing research as of 2018 [update] . [ 4 ]
A limited r -process-like series of neutron captures occurs to a minor extent in thermonuclear weapon explosions. These led to the discovery of the elements einsteinium (element 99) and fermium (element 100) in nuclear weapon fallout .
The r -process contrasts with the s -process , the other predominant mechanism for the production of heavy elements, which is nucleosynthesis by means of slow captures of neutrons. In general, isotopes involved in the s -process have half-lives long enough to enable their study in laboratory experiments, but this is not typically true for isotopes involved in the r -process. [ 5 ] The s -process primarily occurs within ordinary stars, particularly AGB stars , where the neutron flux is sufficient to cause neutron captures to recur every 10–100 years, much too slow for the r -process, which requires 100 captures per second. The s -process is secondary , meaning that it requires pre-existing heavy isotopes as seed nuclei to be converted into other heavy nuclei by a slow sequence of captures of free neutrons. The r -process scenarios create their own seed nuclei, so they might proceed in massive stars that contain no heavy seed nuclei. Taken together, the r - and s -processes account for almost the entire abundance of chemical elements heavier than iron. The historical challenge has been to locate physical settings appropriate to their time scales.
Following pioneering research into the Big Bang and the formation of helium in stars, an unknown process responsible for producing heavier elements found on Earth from hydrogen and helium was suspected to exist. One early attempt at explanation came from Subrahmanyan Chandrasekhar and Louis R. Henrich who postulated that elements were produced at temperatures between 6×10 9 and 8×10 9 K . Their theory accounted for elements up to chlorine , though there was no explanation for elements of atomic weight heavier than 40 amu at non-negligible abundances. [ 6 ] This became the foundation of a study by Fred Hoyle , who hypothesized that conditions in the core of collapsing stars would enable nucleosynthesis of the remainder of the elements via rapid capture of densely packed free neutrons. However, there remained unanswered questions about equilibrium in stars that was required to balance beta-decays and precisely account for abundances of elements that would be formed in such conditions. [ 6 ]
The need for a physical setting providing rapid neutron capture , which was known to almost certainly have a role in element formation, was also seen in a table of abundances of isotopes of heavy elements by Hans Suess and Harold Urey in 1956. [ 7 ] Their abundance table revealed larger than average abundances of natural isotopes containing magic numbers [ b ] of neutrons as well as abundance peaks about 10 amu lighter than stable nuclei containing magic numbers of neutrons which were also in abundance, suggesting that radioactive neutron-rich nuclei having the magic neutron numbers but roughly ten fewer protons were formed. These observations also implied that rapid neutron capture occurred faster than beta decay , and the resulting abundance peaks were caused by so-called waiting points at magic numbers. [ 1 ] [ c ] This process, rapid neutron capture by neutron-rich isotopes, became known as the r -process, whereas the s -process was named for its characteristic slow neutron capture. A table apportioning the heavy isotopes phenomenologically between s -process and r -process isotopes was published in 1957 in the B 2 FH review paper , [ 1 ] which named the r -process and outlined the physics that guides it. [ 8 ] Alastair G. W. Cameron also published a smaller study about the r -process in the same year. [ 9 ]
The stationary r -process as described by the B 2 FH paper was first demonstrated in a time-dependent calculation at Caltech by Phillip A. Seeger, William A. Fowler and Donald D. Clayton , [ 10 ] who found that no single temporal snapshot matched the solar r -process abundances, but, that when superposed, did achieve a successful characterization of the r -process abundance distribution. Shorter-time distributions emphasize abundances at atomic weights less than A = 140 , whereas longer-time distributions emphasized those at atomic weights greater than A = 140 . [ 11 ] Subsequent treatments of the r -process reinforced those temporal features. Seeger et al. were also able to construct more quantitative apportionment between s -process and r -process of the abundance table of heavy isotopes, thereby establishing a more reliable abundance curve for the r -process isotopes than B 2 FH had been able to define. Today, the r -process abundances are determined using their technique of subtracting the more reliable s -process isotopic abundances from the total isotopic abundances and attributing the remainder to r -process nucleosynthesis. [ 12 ] That r -process abundance curve (vs. atomic weight) has provided for many decades the target for theoretical computations of abundances synthesized by the physical r -process.
The creation of free neutrons by electron capture during the rapid collapse to high density of a supernova core along with quick assembly of some neutron-rich seed nuclei makes the r -process a primary nucleosynthesis process , a process that can occur even in a star initially of pure H and He. This in contrast to the B 2 FH designation which is a secondary process building on preexisting iron. Primary stellar nucleosynthesis begins earlier in the galaxy than does secondary nucleosynthesis. Alternatively the high density of neutrons within neutron stars would be available for rapid assembly into r -process nuclei if a collision were to eject portions of a neutron star, which then rapidly expands freed from confinement. That sequence could also begin earlier in galactic time than would s -process nucleosynthesis; so each scenario fits the earlier growth of r -process abundances in the galaxy. Each of these scenarios is the subject of active theoretical research.
Observational evidence of the early r -process enrichment of interstellar gas and of subsequent newly formed stars, as applied to the abundance evolution of the galaxy of stars, was first laid out by James W. Truran in 1981. [ 13 ] He and subsequent astronomers showed that the pattern of heavy-element abundances in the earliest metal-poor stars matched that of the shape of the solar r -process curve, as if the s -process component were missing. This was consistent with the hypothesis that the s -process had not yet begun to enrich interstellar gas when these young stars missing the s -process abundances were born from that gas, for it requires about 100 million years of galactic history for the s -process to get started whereas the r -process can begin after two million years. These s -process–poor, r -process–rich stellar compositions must have been born earlier than any s -process, showing that the r -process emerges from quickly evolving massive stars that become supernovae and leave neutron-star remnants that can merge with another neutron star. The primary nature of the early r -process thereby derives from observed abundance spectra in old stars [ 4 ] that had been born early, when the galactic metallicity was still small, but that nonetheless contain their complement of r -process nuclei.
Either interpretation, though generally supported by supernova experts, has yet to achieve a totally satisfactory calculation of r -process abundances because the overall problem is numerically formidable. However, existing results are supportive; in 2017, new data about the r -process was discovered when the LIGO and Virgo gravitational-wave observatories discovered a merger of two neutron stars ejecting r -process matter. [ 14 ] See Astrophysical sites below.
Noteworthy is that the r -process is responsible for our natural cohort of radioactive elements, such as uranium and thorium, as well as the most neutron-rich isotopes of each heavy element.
There are three natural candidate sites for r -process nucleosynthesis where the required conditions are thought to exist: low-mass supernovae , Type II supernovae , and neutron star mergers . [ 15 ]
Immediately after the severe compression of electrons in a Type II supernova, beta-minus decay is blocked. This is because the high electron density fills all available free electron states up to a Fermi energy which is greater than the energy of nuclear beta decay. However, nuclear capture of those free electrons still occurs, and causes increasing neutronization of matter. This results in an extremely high density of free neutrons which cannot decay, on the order of 10 24 neutrons per cm 3 , [ 1 ] and high temperatures . As this re-expands and cools, neutron capture by still-existing heavy nuclei occurs much faster than beta-minus decay . As a consequence, the r -process runs up along the neutron drip line and highly-unstable neutron-rich nuclei are created.
Three processes which affect the climbing of the neutron drip line are a notable decrease in the neutron-capture cross section in nuclei with closed neutron shells , the inhibiting process of photodisintegration , and the degree of nuclear stability in the heavy-isotope region. Neutron captures in r -process nucleosynthesis leads to the formation of neutron-rich, weakly bound nuclei with neutron separation energies as low as 2 MeV. [ 16 ] [ 1 ] At this stage, closed neutron shells at N = 50, 82, and 126 are reached, and neutron capture is temporarily paused. These so-called waiting points are characterized by increased binding energy relative to heavier isotopes, leading to low neutron capture cross sections and a buildup of semi-magic nuclei that are more stable toward beta decay. [ 17 ] In addition, nuclei beyond the shell closures are susceptible to quicker beta decay owing to their proximity to the drip line; for these nuclei, beta decay occurs before further neutron capture. [ 18 ] Waiting point nuclei are then allowed to beta decay toward stability before further neutron capture can occur, [ 1 ] resulting in a slowdown or freeze-out of the reaction. [ 17 ]
Decreasing nuclear stability terminates the r -process when its heaviest nuclei become unstable to spontaneous fission, when the total number of nucleons approaches 270. The fission barrier may be low enough before 270 such that neutron capture might induce fission instead of continuing up the neutron drip line. [ 19 ] After the neutron flux decreases, these highly unstable radioactive nuclei undergo a rapid succession of beta decays until they reach more stable, neutron-rich nuclei. [ 20 ] While the s -process creates an abundance of stable nuclei having closed neutron shells, the r -process, in neutron-rich predecessor nuclei, creates an abundance of radioactive nuclei about 10 amu below the s -process peaks. [ 21 ] These abundance peaks correspond to stable isobars produced from successive beta decays of waiting point nuclei having N = 50, 82, and 126—which are about 10 protons removed from the line of beta stability . [ 22 ]
The r -process also occurs in thermonuclear weapons, and was responsible for the initial discovery of neutron-rich almost stable isotopes of actinides like plutonium-244 and the new elements einsteinium and fermium (atomic numbers 99 and 100) in the 1950s. It has been suggested that multiple nuclear explosions would make it possible to reach the island of stability , as the affected nuclides (starting with uranium-238 as seed nuclei) would not have time to beta decay all the way to the quickly spontaneously fissioning nuclides at the line of beta stability before absorbing more neutrons in the next explosion, thus providing a chance to reach neutron-rich superheavy nuclides like copernicium -291 and -293 which may have half-lives of centuries or millennia. [ 23 ]
The most probable candidate site for the r -process has long been suggested to be core-collapse supernovae (spectral types Ib , Ic and II ), which may provide the necessary physical conditions for the r -process. However, the very low abundance of r -process nuclei in the interstellar gas limits the amount each can have ejected. It requires either that only a small fraction of supernovae eject r -process nuclei to the interstellar medium , or that each supernova ejects only a very small amount of r -process material. The ejected material must be relatively neutron-rich, a condition which has been difficult to achieve in models, [ 2 ] so that astrophysicists remain uneasy about their adequacy for successful r -process yields.
In 2017, new astronomical data about the r -process was discovered in data from the merger of two neutron stars . Using the gravitational wave data captured in GW170817 to identify the location of the merger, several teams [ 24 ] [ 25 ] [ 26 ] observed and studied optical data of the merger, finding spectroscopic evidence of r -process material thrown off by the merging neutron stars. The bulk of this material seems to consist of two types: hot blue masses of highly radioactive r -process matter of lower-mass-range heavy nuclei ( A < 140 such as strontium ) [ 27 ] and cooler red masses of higher mass-number r -process nuclei ( A > 140 ) rich in actinides (such as uranium , thorium , and californium ). When released from the huge internal pressure of the neutron star, these ejecta expand and form seed heavy nuclei that rapidly capture free neutrons, and radiate detected optical light for about a week. Such duration of luminosity would not be possible without heating by internal radioactive decay, which is provided by r -process nuclei near their waiting points. Two distinct mass regions ( A < 140 and A > 140 ) for the r -process yields have been known since the first time dependent calculations of the r -process. [ 10 ] Because of these spectroscopic features it has been argued that such nucleosynthesis in the Milky Way has been primarily ejecta from neutron-star mergers rather than from supernovae. [ 3 ]
These results offer a new possibility for clarifying six decades of uncertainty over the site of origin of r -process nuclei. Confirming relevance to the r -process is that it is radiogenic power from radioactive decay of r -process nuclei that maintains the visibility of these spun off r -process fragments. Otherwise they would dim quickly. Such alternative sites were first seriously proposed in 1974 [ 28 ] as decompressing neutron star matter. It was proposed such matter is ejected from neutron stars merging with black holes in compact binaries. In 1989 [ 29 ] (and 1999 [ 30 ] ) this scenario was extended to binary neutron star mergers (a binary star system of two neutron stars that collide). After preliminary identification of these sites, [ 31 ] the scenario was confirmed in GW170817 . Current astrophysical models suggest that a single neutron star merger event may have generated between 3 and 13 Earth masses of gold. [ 32 ] | https://en.wikipedia.org/wiki/R-process |
R-salt ( TNX , systematic name hexahydro-1,3,5-trinitroso-1,3,5-triazine ) is an explosive organic compound that has been used in terrorist attacks . [ 1 ] [ 2 ] It is a high explosive that is less sensitive than other compounds of similar availability. [ 2 ] It has a similar structure to RDX but with nitrosamine groups replacing the nitroamine groups of RDX. It is also found as a decomposition product of RDX in the environment, such as after RDX detonation. [ 3 ] This may be a potential environmental issue as a study concluded that TNX is toxic to earthworm Eisenia fetida . [ 4 ] R-salt is synthesized by nitrosation of hexamine . [ 2 ]
This explosives -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/R-salt |
The R -value is a measure of how well a two-dimensional barrier, such as a layer of insulation , a window or a complete wall or ceiling, resists the conductive [ 2 ] flow of heat, in the context of construction . [ 3 ] R-value is the temperature difference per unit of heat flux needed to sustain one unit of heat flux between the warmer surface and colder surface of a barrier under steady-state conditions. The measure is therefore equally relevant for lowering energy bills for heating in the winter, for cooling in the summer, and for general comfort.
The R-value is the building industry term [ 3 ] for thermal resistance "per unit area." [ 4 ] It is sometimes denoted RSI-value if the SI units are used. [ 5 ] An R-value can be given for a material (e.g., for polyethylene foam), or for an assembly of materials (e.g., a wall or a window). In the case of materials, it is often expressed in terms of R-value per metre. R-values are additive for layers of materials, and the higher the R-value the better the performance.
The U-factor or U-value is the overall heat transfer coefficient and can be found by taking the inverse of the R-value. It is a property that describes how well building elements conduct heat per unit area across a temperature gradient. [ 6 ] The elements are commonly assemblies of many layers of materials, such as those that make up the building envelope . It is expressed in watts per square metre kelvin. The higher the U-value, the lower the ability of the building envelope to resist heat transfer. A low U-value, or conversely a high R-value usually indicates high levels of insulation. They are useful as it is a way of predicting the composite behaviour of an entire building element rather than relying on the properties of individual materials.
This relates to the technical/constructional value. R val = Δ T ϕ q , {\displaystyle R_{\text{val}}={\frac {\Delta T}{\phi _{q}}},}
where:
The R-value per unit of a barrier's exposed surface area measures the absolute thermal resistance of the barrier. [ 7 ] R val A = R , {\displaystyle {\frac {R_{\text{val}}}{A}}=R,}
where:
Absolute thermal resistance , R {\displaystyle R} , quantifies the temperature difference per unit of heat flow rate needed to sustain one unit of heat flow rate. Confusion sometimes arises because some publications use the term thermal resistance for the temperature difference per unit of heat flux , but other publications use the term thermal resistance for the temperature difference per unit of heat flow rate. Further confusion arises because some publications use the character R to denote the temperature difference per unit of heat flux, but other publications use the character R to denote the temperature difference per unit of heat flow rate. This article uses the term absolute thermal resistance for the temperature difference per unit of heat flow rate and uses the term R-value for the temperature difference per unit of heat flux.
In any event, the greater the R-value, the greater the resistance, and so the better the thermal insulating properties of the barrier. R-values are used in describing the effectiveness of insulating material and in analysis of heat flow across assemblies (such as walls, roofs, and windows) under steady-state conditions. [ 7 ] Heat flow through a barrier is driven by temperature difference between two sides of the barrier, and the R-value quantifies how effectively the object resists this drive: [ 8 ] [ 9 ] The temperature difference divided by the R-value and then multiplied by the exposed surface area of the barrier gives the total rate of heat flow through the barrier, as measured in watts or in BTUs per hour. ϕ = Δ T ⋅ A R val , {\displaystyle \phi ={\frac {\Delta T\cdot A}{R_{\text{val}}}},}
where:
As long as the materials involved are dense solids in direct mutual contact, [ 10 ] R-values are additive; for example, the total R-value of a barrier composed of several layers of material is the sum of the R-values of the individual layers. [ 7 ] [ 11 ]
For example, in winter it might be 2 °C outside and 20 °C inside, making a temperature difference of 18 °C or 18 K. If the material has an R-value of 4, it will lose 0.25 W/(°C⋅m 2 ). With an area of 100 m 2 , the heat energy being lost is 0.25 W/(K⋅m 2 ) × 18 °C × 100 m 2 = 450 W. There will be other losses through the floor, windows, ventilation slots, etc. But for that material alone, 450 W is going out, and can be replaced with a 450 W heater inside, to maintain the inside temperature.
Note that the R-value is the building industry term [ 3 ] for what is in other contexts called " thermal resistance " "for a unit area." [ 4 ] It is sometimes denoted RSI-value if the SI (metric) units are used. [ 5 ] [ 12 ]
An R-value can be given for a material (e.g., for polyethylene foam), or for an assembly of materials (e.g., a wall or a window). In the case of materials, it is often expressed in terms of R-value per unit length (e.g., per inch of thickness). The latter can be misleading in the case of low-density building thermal insulations, for which R-values are not additive: their R-value per inch is not constant as the material gets thicker, but rather usually decreases. [ 10 ]
The units of an R-value (see below ) are usually not explicitly stated, and so it is important to determine from context which units are being used: an R-value expressed in I-P (inch-pound) units [ 13 ] is about 5.68 times larger than when expressed in SI units, [ 14 ] so that, for example, a window that is R-2 in I-P units has an RSI of 0.35 (since 2/5.68 = 0.35). For R-values there is no difference between US customary units and imperial units .
All of the following mean the same thing: "this is an R-2 window"; [ 15 ] "this is an R2 window"; [ 16 ] [ 5 ] "this window has an R-value of 2"; [ 15 ] "this is a window with R = 2" [ 17 ] (and similarly with RSI-values, which also include the possibility "this window provides RSI 0.35 of resistance to heat flow" [ 18 ] [ 5 ] ).
The more a material is intrinsically able to conduct heat, as given by its thermal conductivity , the lower its R-value. On the other hand, the thicker the material, the higher its R-value. Sometimes heat transfer processes other than conduction (namely, convection and radiation ) significantly contribute to heat transfer within the material. In such cases, it is useful to introduce an "apparent thermal conductivity", which captures the effects of all three kinds of processes, and to define the R-value more generally as the thickness of a sample divided by its apparent thermal conductivity . Some equations relating this generalized R-value, also known as the apparent R-value , to other quantities are: R val ′ = Δ x k ′ = 1 U val = Δ x ⋅ r ′ , {\displaystyle R_{\text{val}}^{\prime }={\frac {\Delta x}{k^{\prime }}}={\frac {1}{U_{\text{val}}}}=\Delta x\cdot r^{\prime },}
where:
An apparent R-value quantifies the physical quantity called thermal insulance .
However, this generalization comes at a price because R-values that include non-conductive processes may no longer be additive and may have significant temperature dependence. In particular, for a loose or porous material, the R-value per inch generally depends on the thickness, almost always so that it decreases with increasing thickness [ 10 ] ( polyisocyanurate (colloquially, polyiso ) being an exception; its R-value/inch increases with thickness [ 19 ] ). For similar reasons, the R-value per inch also depends on the temperature of the material, usually increasing with decreasing temperature (polyisocyanurate again being an exception); a nominally R-13 fiberglass batt may be R-14 at −12 °C (10 °F) and R-12 at 43 °C (109 °F). [ 20 ] Nevertheless, in construction it is common to treat R-values as independent of temperature. [ 21 ] Note that an R-value may not account for radiative or convective processes at the material's surface , which may be an important factor for some applications. [ citation needed ]
The R-value is the reciprocal of the thermal transmittance ( U-factor ) of a material or assembly. The U.S. construction industry prefers to use R-values, however, because they are additive and because bigger values mean better insulation, neither of which is true for U-factors. [ 3 ]
The U-factor or U-value is the overall heat transfer coefficient that describes how well a building element conducts heat or the rate of transfer of heat (in watts) through one square metre of a structure divided by the difference in temperature across the structure. [ 6 ] The elements are commonly assemblies of many layers of components such as those that make up walls/floors/roofs etc. It is expressed in watts per meter squared kelvin W/(m 2 ⋅K). This means that the higher the U-value the worse the thermal performance of the building envelope. A low U-value usually indicates high levels of insulation. They are useful as it is a way of predicting the composite behavior of an entire building element rather than relying on the properties of individual materials.
In most countries the properties of specific materials (such as insulation) are indicated by the thermal conductivity , sometimes called a k-value or lambda-value (lowercase λ). The thermal conductivity (k-value) is the ability of a material to conduct heat; hence, the lower the k-value, the better the material is for insulation. Expanded polystyrene (EPS) has a k-value of around 0.033 W/(m⋅K). [ 22 ] For comparison, phenolic foam insulation has a k-value of around 0.018 W/(m⋅K), [ 23 ] while wood varies anywhere from 0.15 to 0.75 W/(m⋅K), and steel has a k-value of approximately 50.0 W/(m⋅K). These figures vary from product to product, so the UK and EU have established a 90/90 standard which means that 90% of the product will conform to the stated k-value with a 90% confidence level so long as the figure quoted is stated as the 90/90 lambda-value.
U is the inverse of R [ 24 ] with SI units of W/(m 2 ⋅K) and U.S. units of BTU/(h⋅°F⋅ft 2 ) U = 1 R = Q ˙ A Δ T = k L , {\displaystyle U={\frac {1}{R}}={\frac {{\dot {Q}}_{A}}{\Delta T}}={\frac {k}{L}},}
where Q ˙ A {\displaystyle {\dot {Q}}_{A}} is the heat flux , Δ T {\displaystyle \Delta T} is the temperature difference across the material, k is the material's coefficient of thermal conductivity and L is its thickness. In some contexts, U is referred to as unit surface conductance. [ 25 ]
The term U-factor is usually used in the U.S. and Canada to express the heat flow through entire assemblies (such as roofs, walls, and windows [ 26 ] ). For example, energy codes such as ASHRAE 90.1 and the IECC prescribe U-values. However, R-value is widely used in practice to describe the thermal resistance of insulation products, layers, and most other parts of the building enclosure (walls, floors, roofs). Other areas of the world more commonly use U-value/U-factor for elements of the entire building enclosure including windows, doors, walls, roof, and ground slabs. [ 27 ]
The SI (metric) unit of R-value is kelvin square-metre per watt (K⋅m 2 /W or, equally, °C⋅m 2 /W),
whereas the I-P (inch-pound) unit is degree Fahrenheit square-foot hour per British thermal unit (°F⋅ft 2 ⋅h/BTU). [ 13 ]
For R-values there is no difference between U.S. and Imperial units , so the same I-P unit is used in both.
Some sources use "RSI" when referring to R-values in SI units. [ 5 ] [ 12 ]
R-values expressed in I-P units are approximately 5.68 times as large as R-values expressed in SI units. [ 14 ] For example, a window that is R-2 in the I-P system is about RSI 0.35, since 2/5.68 ≈ 0.35.
In countries where the SI system is generally in use, the R-values will also normally be given in SI units. This includes the United Kingdom, Australia, and New Zealand.
I-P values are commonly given in the United States and Canada, though in Canada normally both I-P and RSI values are listed. [ 28 ]
Because the units are usually not explicitly stated, one must decide from context which units are being used. In this regard, it helps to keep in mind that I-P R-values are 5.68 times larger than the corresponding SI R-values.
More precisely, [ 29 ] [ 30 ]
R-value (in I-P) ≈ RSI-value (in SI) × 5.678263 RSI-value (in SI) ≈ R-value (in I-P) × 0.1761102
The Australian Government explains that the required total R-values for the building fabric vary depending on climate zone. "Such materials include aerated concrete blocks, hollow expanded polystyrene blocks, straw bales and rendered extruded polystyrene sheets." [ 31 ]
In Germany, after the law Energieeinsparverordnung (EnEv) introduced in 2009 (October 10) regarding energy savings, all new buildings must demonstrate an ability to remain within certain boundaries of the U-value for each particular building material. Further, the EnEv describes the maximum coefficient for each new material if parts are replaced or added to standing structures. [ 32 ]
The U.S. Department of Energy has recommended R-values for given areas of the USA based on the general local energy costs for heating and cooling, as well as the climate of an area. There are four types of insulation: rolls and batts, loose-fill, rigid foam, and foam-in-place. Rolls and batts are typically flexible insulators that come in fibers, like fiberglass. Loose-fill insulation comes in loose fibers or pellets and should be blown into a space. Rigid foam is more expensive than fiber, but generally has a higher R-value per unit of thickness. Foam-in-place insulation can be blown into small areas to control air leaks, like those around windows, or can be used to insulate an entire house. [ 33 ]
Increasing the thickness of an insulating layer increases the thermal resistance. For example, doubling the thickness of fiberglass batting will double its R-value, perhaps from 2.0 m 2 ⋅K/W for 110 mm of thickness, up to 4.0 m 2 ⋅K/W for 220 mm of thickness. Heat transfer through an insulating layer is analogous to adding resistance to a series circuit with a fixed voltage. However, this holds only approximately because the effective thermal conductivity of some insulating materials depends on thickness. The addition of materials to enclose the insulation such as drywall and siding provides additional but typically much smaller R-value.
There are many factors that come into play when using R-values to compute heat loss for a particular wall. Manufacturer R-values apply only to properly installed insulation. Stuffing two layers of batting into the thickness intended for one layer will increase but not double the R-value (essentially, compressing a fiberglass batt decreases the R-value of the batt but increases the R-value per inch).
Another factor is that studs and windows provide a parallel heat conduction path that is unaffected by the insulation's R-value. The practical implication of this is that one could double the R-value of insulation installed between framing members and realize substantially less than a 50 percent reduction in heat loss. When installed between wall studs, even perfect wall insulation only eliminates conduction through the insulation but leaves unaffected the conductive heat loss through such materials as glass windows and studs. Insulation installed between the studs may reduce, but usually does not eliminate, heat losses due to air leakage through the building envelope. Installing a continuous layer of rigid foam insulation on the exterior side of the wall sheathing will interrupt thermal bridging through the studs while also reducing the rate of air leakage.
The R-value is a measure of an insulation sample's ability to reduce the rate of heat flow under specified test conditions. The primary mode of heat transfer impeded by insulation is conduction, but insulation also reduces heat loss by all three heat transfer modes: conduction, convection, and radiation. The primary heat loss across an uninsulated air-filled space is natural convection , which occurs because of changes in air density with temperature. Insulation greatly retards natural convection making conduction the primary mode of heat transfer. Porous insulations accomplish this by trapping air so that significant convective heat loss is eliminated, leaving only conduction and minor radiation transfer. The primary role of such insulation is to make the thermal conductivity of the insulation that of trapped, stagnant air. However this cannot be realized fully because the glass wool or foam needed to prevent convection increases the heat conduction compared to that of still air.
The minor radiative heat transfer is obtained by having many surfaces interrupting a "clear view" between the inner and outer surfaces of the insulation such as visible light is interrupted from passing through porous materials. Such multiple surfaces are abundant in batting and porous foam. Radiation is also minimized by low emissivity (highly reflective) exterior surfaces such as aluminum foil. Lower thermal conductivity, or higher R-values, can be achieved by replacing air with argon when practical such as within special closed-pore foam insulation because argon has a lower thermal conductivity than air.
Heat transfer through an insulating layer is analogous to electrical resistance . The heat transfers can be worked out by thinking of resistance in series with a fixed potential, except the resistances are thermal resistances and the potential is the difference in temperature from one side of the material to the other. The resistance of each material to heat transfer depends on the specific thermal resistance [R-value]/[unit thickness], which is a property of the material (see table below) and the thickness of that layer. A thermal barrier that is composed of several layers will have several thermal resistors in the analogous with circuits, each in series. Analogous to a set of resistors in parallel, a well insulated wall with a poorly insulated window will allow proportionally more of the heat to go through the (low-R) window, and additional insulation in the wall will only minimally improve the overall R-value. As such, the least well insulated section of a wall will play the largest role in heat transfer relative to its size, similar to the way most current flows through the lowest resistance resistor in a parallel array. Hence ensuring that windows, service breaks (around wires/pipes), doors, and other breaks in a wall are well sealed and insulated is often the most cost effective way to improve the insulation of a structure, once the walls are sufficiently insulated.
Like resistance in electrical circuits, increasing the physical length (for insulation, thickness) of a resistive element, such as graphite for example, increases the resistance linearly; double the thickness of a layer means double the R-value and half the heat transfer; quadruple, quarters; etc. In practice, this linear relationship does not always hold for compressible materials such as glass wool and cotton batting whose thermal properties change when compressed. So, for example, if one layer of fiberglass insulation in an attic provides R-20 thermal resistance, adding on a second layer will not necessarily double the thermal resistance because the first layer will be compressed by the weight of the second.
To find the average heat loss per unit area, simply divide the temperature difference by the R-value for the layer.
If the interior of a home is at 20 °C and the roof cavity is at 10 °C then the temperature difference is 10 °C (or 10 K). Assuming a ceiling insulated to RSI 2.0 (R = 2 m 2 ⋅K/W), energy will be lost at a rate of 10 K / (2 K⋅m 2 /W) = 5 watts for every square meter (W/m 2 ) of ceiling. The RSI-value used here is for the actual insulating layer (and not per unit thickness of insulation).
R-value should not be confused with the intrinsic property of thermal resistivity and its inverse, thermal conductivity . The SI unit of thermal resistivity is K⋅m/W. Thermal conductivity assumes that the heat transfer of the material is linearly related to its thickness.
In calculating the R-value of a multi-layered installation, the R-values of the individual layers are added: [ 34 ]
R-value (outside air film) + R-value (brick) + R-value (sheathing) + R-value (insulation) + R-value (plasterboard) + R-value (inside air film) = R-value (total) .
To account for other components in a wall such as framing, first calculate the U-value (= 1/R-value) of each component, then the area-weighted average U-value. An average R-value is 1/(average U-value). For example, if 10% of the area is 4 inches of softwood (R-value 5.6) and 90% is 2 inches of silica aerogel (R-value 20), the area-weighted U-value is 0.1/5.6 + 0.9/20 ≈ 0.0629 and the weighted R-value is 1/0.0629 ≈ 15.9.
Thermal conductivity is conventionally defined as the rate of thermal conduction through a material per unit area per unit thickness per unit temperature differential (Δ T ). The inverse of conductivity is resistivity (or R per unit thickness). Thermal conductance is the rate of heat flux through a unit area at the installed thickness and any given Δ T .
Experimentally, thermal conduction is measured by placing the material in contact between two conducting plates and measuring the energy flux required to maintain a certain temperature gradient.
For the most part, testing the R-value of insulation is done at a steady temperature, usually about 70 °F (21 °C) with no surrounding air movement. Since these are ideal conditions, the listed R-value for insulation will almost certainly be higher than it would be in actual use, because most situations with insulation are under different conditions
A definition of R-value based on apparent thermal conductivity has been proposed in document C168 published by the American Society for Testing and Materials. This describes heat being transferred by all three mechanisms—conduction, radiation, and convection.
Debate remains among representatives from different segments of the U.S. insulation industry during revision of the U.S. FTC's regulations about advertising R-values [ 35 ] illustrating the complexity of the issues.
There are weaknesses to using a single laboratory model to simultaneously assess the properties of a material to resist conducted, radiated, and convective heating. Surface temperature varies depending on the mode of heat transfer.
If we assume idealized heat transfer between the air on each side and the surface of the insulation, the surface temperature of the insulator would equal the air temperature on each side.
In response to thermal radiation, surface temperature depends on the thermal emissivity of the material. Low-emissivity surfaces such as shiny metal foil will reduce heat transfer by radiation.
Convection will alter the rate of heat transfer between the air and the surface of the insulator, depending on the flow characteristics of the air (or other fluid) in contact with it.
With multiple modes of heat transfer, the final surface temperature (and hence the observed energy flux and calculated R-value) will be dependent on the relative contributions of radiation, conduction, and convection, even though the total energy contribution remains the same.
This is an important consideration in building construction because heat energy arrives in different forms and proportions. The contribution of radiative and conductive heat sources also varies throughout the year and both are important contributors to thermal comfort
In the hot season, solar radiation predominates as the source of heat gain. According to the Stefan–Boltzmann law , radiative heat transfer is related to the fourth power of the absolute temperature (measured in kelvins : T [K] = T [°C] + 273.16). Therefore, such transfer is at its most significant when the objective is to cool (i.e. when solar radiation has produced very warm surfaces). On the other hand, the conductive and convective heat loss modes play a more significant role during the cooler months. At such lower ambient temperatures the traditional fibrous, plastic and cellulose insulations play by far the major role: the radiative heat transfer component is of far less importance, and the main contribution of the radiation barrier is in its superior air-tightness contribution.
In summary: claims for radiant barrier insulation are justifiable at high temperatures, typically when minimizing summer heat transfer; but these claims are not justifiable in traditional winter (keeping-warm) conditions.
Unlike bulk insulators, radiant barriers resist conducted heat poorly. Materials such as reflective foil have a high thermal conductivity and would function poorly as a conductive insulator. Radiant barriers retard heat transfer by two means: by reflecting radiant energy away from its irradiated surface and by reducing the emission of radiation from its opposite side.
The question of how to quantify performance of other systems such as radiant barriers has resulted in controversy and confusion in the building industry with the use of R-values or 'equivalent R-values' for products which have entirely different systems of inhibiting heat transfer. (In the U.S., the federal government's R-value rule establishes a legal definition for the R-value of a building material; the term 'equivalent R-value' has no legal definition and is therefore meaningless.) According to current standards, R-values are most reliably stated for bulk insulation materials. All of the products quoted at the end are examples of these.
Calculating the performance of radiant barriers is more complex. With a good radiant barrier in place, most heat flow is by convection, which depends on many factors other than the radiant barrier itself. Although radiant barriers have high reflectivity (and low emissivity ) over a range of electromagnetic spectra (including visible and UV light), their thermal advantages are mainly related to their emissivity in the infra-red range. Emissivity values [ 36 ] are the appropriate metric for radiant barriers. Their effectiveness when employed to resist heat gain in limited applications is established, [ 37 ] even though R-value does not adequately describe them.
While research is lacking on the long-term degradation of R-value in insulation, recent [ when? ] research indicates that the R-values of products may deteriorate over time. For instance, the compaction of loose-fill cellulose creates voids that reduce overall performance; this may be avoided by densely packing at initial installation. Some types of foam insulation, such as polyurethane and polyisocyanurate are blown into form with heavy gases such as chlorofluorocarbons (CFC) or hydrochlorofluorocarbons (HFCs). However, over time these gases diffuse out of the foam and are replaced by air, thus reducing the effective R-value of the product. There are other foams which do not change significantly with aging because they are blown with water or are open-cell and contain no trapped CFCs or HFCs (e.g., half-pound low-density foams). On certain brands, twenty-year tests have shown no shrinkage or reduction in insulating value. [ citation needed ]
This has led to controversy as how to rate the insulation of these products. Many manufacturers will rate the R-value at the time of manufacture; critics argue that a more fair assessment would be its settled value. [ citation needed ] The foam industry [ when? ] adopted the long-term thermal resistance (LTTR) method, [ 38 ] which rates the R-value based on a 15-year weighted average. However, the LTTR effectively provides only an eight-year aged R-value, short in the scale of a building that may have a lifespan of 50 to 100 years.
Research has been conducted by the U.S. Army Engineer Research and Development Center on the long-term degradation of insulating materials. Values on the degradation were obtained from short-term laboratory testing on materials exposed to various temperature and humidity conditions. Results indicate that moisture absorption and loss of blowing agent (in closed-cell spray polyurethane foam) were major causes of R-value loss. Fiberglass and extruded polystyrene retained over 97% of their initial R-values while, aerogels and closed-cell polyurethane saw a reduction of 15% and 27.5%, respectively. Results suggest an exponential decay law over time applies to R-values for closed-cell polyurethanes and aerogel blankets. [ 39 ]
Correct attention to air sealing measures and consideration of vapor transfer mechanisms are important for the optimal function of bulk insulators. Air infiltration can allow convective heat transfer or condensation formation, both of which may degrade the performance of an insulation.
One of the primary values of spray-foam insulation is its ability to create an airtight (and in some cases, watertight) seal directly against the substrate to reduce the undesirable effects of air leakage. Other construction technologies are also used to reduce or eliminate infiltration such as air sealing techniques.
The deterioration of R-values is especially a problem when defining the energy efficiency of an existing building. Especially in older or historic buildings the R-values defined before construction might be very different from the actual values. This greatly affects energy efficiency analysis. To obtain reliable data, R-values are therefore often determined via U-value measurements at the specific location (in situ). There are several potential methods to this, each with their specific trade-offs: thermography, multiple temperature measurements, and the heat flux method. [ 6 ]
Thermography is applied in the building sector to assess the quality of the thermal insulation of a room or building. By means of a thermographic camera thermal bridges and inhomogeneous insulation parts can be identified. However, it does not produce any quantitative data. This method can only be used to approximate the U-value or the inverse R-value.
This approach is based on three or more temperature measurements inside and outside of a building element. By synchronizing these measurements and making some basic assumptions, it is possible to calculate the heat flux indirectly, and thus deriving the U-value of a building element. The following requirements have to be fulfilled for reliable results:
The R-value of a building element can be determined by using a heat flux sensor in combination with two temperature sensors. [ 40 ] By measuring the heat that is flowing through a building element and combining this with the inside and outside temperature, it is possible to define the R-value precisely. A measurement that lasts at least 72 hours with a temperature difference of at least 5 °C is required for a reliable result according to ISO 9869 norms, but shorter measurement durations give a reliable indication of the R-value as well. The progress of the measurement can be viewed on the laptop via corresponding software and obtained data can be used for further calculations. Measuring devices for such heat flux measurements are offered by companies like FluxTeq, [ 41 ] Ahlborn, greenTEG and Hukseflux.
Placing the heat flux sensor on either the inside or outside surface of the building element allows one to determine the heat flux through the heat flux sensor as a representative value for the heat flux through the building element. The heat flux through the heat flux sensor is the rate of heat flow through the heat flux sensor divided by the surface area of the heat flux sensor . Placing the temperature sensors on the inside and outside surfaces of the building element allows one to determine the inside surface temperature, outside surface temperature, and the temperature difference between them. In some cases the heat flux sensor itself can serve as one of the temperature sensors. The R-value for the building element is the temperature difference between the two temperature sensors divided by the heat flux through the heat flux sensor . The mathematical formula is: R val = Δ T ϕ q = T o − T i q / A , {\displaystyle R_{\text{val}}={\frac {\Delta T}{\phi _{q}}}={\frac {T_{o}-T_{i}}{q/A}},}
where:
The U-value can be calculated as well by taking the reciprocal of the R-value. That is, U val = 1 R val . {\displaystyle U_{\text{val}}={\frac {1}{R_{\text{val}}}}.}
where U val {\displaystyle U_{\text{val}}} is the U-value ( W ⋅ m −2 ⋅ K −1 ).
The derived R-value and U-value may be accurate to the extent that the heat flux through the heat flux sensor equals the heat flux through the building element. Recording all of the available data allows one to study the dependence of the R-value and U-value on factors like the inside temperature, outside temperature, or position of the heat flux sensor . To the extent that all heat transfer processes (conduction, convection, and radiation) contribute to the measurements, the derived R-value represents an apparent R-value.
Vacuum insulated panels have the highest R-value, approximately R-45 (in U.S. units) per inch; aerogel has the next highest R-value (about R-10 to R-30 per inch), followed by polyurethane (PUR) and phenolic foam insulations with R-7 per inch. They are followed closely by polyisocyanurate (PIR) at R-5.8, graphite impregnated expanded polystyrene at R-5, and expanded polystyrene (EPS) at R-4 per inch. Loose cellulose, fibreglass (both blown and in batts), and rock wool (both blown and in batts) all possess an R-value of roughly R-2.5 to R-4 per inch.
Straw bales perform at about R-2.38 to 2.68 per inch, depending on orientation of the bales. [ 42 ] However, typical straw bale houses have very thick walls and thus are well insulated. Snow is roughly R-1 per inch. Brick has a very poor insulating ability at a mere R-0.2 per inch; however it does have a relatively good thermal mass .
Note that the above examples all use the U.S. (non-SI) definition for R-value.
This is a list of insulation materials used around the world.
Typical R-values are given for various materials and structures as approximations based on the average of available figures and are sorted by lowest value. R-value at 1 m gives R-values normalised to a 1 metre (3 ft 3 in) thickness and sorts by median value of the range.
When determining the overall thermal resistance of a building assembly such as a wall or roof, the insulating effect of the surface air film is added to the thermal resistance of the other materials. [ 64 ]
In practice the above surface values are used for floors, ceilings, and walls in a building, but are not accurate for enclosed air cavities, such as between panes of glass. The effective thermal resistance of an enclosed air cavity is strongly influenced by radiative heat transfer and distance between the two surfaces. See insulated glazing for a comparison of R-values for windows, with some effective R-values that include an air cavity.
Ask for the R-value tests from the manufacturer for your specific assembly.
The Federal Trade Commission (FTC) governs claims about R-values to protect consumers against deceptive and misleading advertising claims. It issued the R-value rule. [ 67 ]
The primary purpose of the rule is to ensure that the home insulation marketplace provides this essential pre-purchase information to the consumer. The information gives consumers an opportunity to compare relative insulating efficiencies, to select the product with the greatest efficiency and potential for energy savings, to make a cost-effective purchase and to consider the main variables limiting insulation effectiveness and realization of claimed energy savings.
The rule mandates that specific R-value information for home insulation products be disclosed in certain ads and at the point of sale. The purpose of the R-value disclosure requirement for advertising is to prevent consumers from being misled by certain claims which have a bearing on insulating value. At the point of transaction, some consumers will be able to get the requisite R-value information from the label on the insulation package. However, since the evidence shows that packages are often unavailable for inspection prior to purchase, no labeled information would be available to consumers in many instances. As a result, the Rule requires that a fact sheet be available to consumers for inspection before they make their purchase.
The R-value Rule specifies: [ 68 ]
You can list a range of R-value per inch. If you do, you must say exactly how much the R-value drops with greater thickness. You must also add this statement: "The R-value per inch of this insulation varies with thickness. The thicker the insulation, the lower the R-value per inch." | https://en.wikipedia.org/wiki/R-value_(insulation) |
Robert Bruce Hoadley (1933 – October 15, 2019) [ 1 ] was Professor Emeritus of Building and Construction Materials in the Department of Environmental Conservation at the University of Massachusetts Amherst . [ 2 ]
His main research interests were wood identification and dimensional changes due to wood-moisture relationships. He is known to the general public primarily as the author of popular books on the anatomy, properties and processing of wood, and for his work as a contributing editor and technical consultant for Fine Woodworking magazine. His expertise in wood identification has been utilized in analysis of antique furniture and art objects for Sotheby's [ 3 ] and major museums. [ 2 ]
His book Identifying Wood: Accurate results with simple tools is an accessible introduction to the topic, [ 4 ] and his Understanding Wood is a comprehensive treatment of wood technology. The first edition of this work sold over 130,000 copies. [ 5 ] | https://en.wikipedia.org/wiki/R._Bruce_Hoadley |
R. Bruce King is emeritus professor at the University of Georgia . [ 1 ] He has contributed to many areas of organometallic chemistry , including synthesis, spectroscopy, and theory. He is the author and editor of several monographs and book series. [ 2 ]
He received his Ph.D. in 1961 under the direction of F. Gordon A. Stone at Harvard for research on organocobalt and organoiron compounds . [ 4 ] He subsequently conducted studies on synthetic organometallic chemistry at DuPont and then at the Mellon Institute . His endeavors led to the first examples of diazonium complexes . [ 5 ] His contributions also include organophosphorus ligands.
Among his accolades, King was recognized by the American Chemical Society Awards in Pure Chemistry (1971) and in Inorganic Chemistry (1991).
This biographical article about an American chemist is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/R._Bruce_King |
R. J. Dwayne Miller FRSC FRS is a Canadian chemist and a professor at the University of Toronto . His focus is in physical chemistry and biophysics . He is most widely known for his work in ultrafast laser science , time-resolved spectroscopy , and
the development of new femtosecond electron sources . His research has enabled real-time observation of atomic motions in materials during chemical processes and has shed light on the structure-function correlation that underlies biology. [ 11 ]
Miller was born and raised in Winnipeg , Manitoba . [ 12 ] In 1978, he received a B.Sc. in chemistry and immunology at the University of Manitoba where Bryan R. Henry was his advisor. He completed his Ph.D. in chemistry at Stanford University in 1983 under the supervision of Michael D. Fayer . His thesis work focused on energy transport in model systems of photosynthesis and is titled Part I, Electronic excited state transport and trapping in disordered systems; Part II, Laser induced ultrasonics .
Following graduation, Miller gained a faculty position at the University of Rochester and immediately took a 12-month leave to do postdoctoral research in solid state physics as a NATO science fellow at the Laboratoire de Spectrometrie Physique (renamed to Laboratoire Interdisciplinaire de Physique in 2011 [ 13 ] ) at the Université Joseph Fourier in Grenoble , France under the direction of Hans Peter Trommsdorff and Robert Romenstain. [ 14 ] He returned to University of Rochester in 1984 as an assistant professor of chemistry. He was promoted to associate professor in 1988 and then full professor of chemistry and optics in 1992. In 1995, he moved back to Canada and relocated his research group to the departments of chemistry and physics at the University of Toronto. In 2006, he was appointed as a University Professor [ 15 ] and later as a Distinguished Faculty Research Chair.
From 2010-2014, R. J. D. Miller was the director of the Max Planck Group, Centre for Free Electron Laser Science/DESY, University of Hamburg. From 2014-2020, he was the co-founding director of Max Planck Institute for the Structure and Dynamics of Matter (MPSD) in Hamburg , Germany . [ 16 ]
In 2023, he was inducted as a fellow of the Royal Society [ 17 ] and has been a fellow of Royal Society of Canada and the Royal Society of Chemistry since 1999 and 2016, respectively. He is also a member of the Chemical Institute of Canada , Canadian Association of Physicists , American Physical Society , and Optical Society of America .
Beyond his scientific work, Miller is dedicated to the promotion of science education through outreach to school children. He founded and is a board member of Science Rendezvous , an annual science festival that aims to expose general public to science and technology. [ 18 ] | https://en.wikipedia.org/wiki/R._J._Dwayne_Miller |
Ramasubbu Sankararamakrishnan is an Indian computational biologist, bioinformatician and a professor at the Department of Biological Sciences and Bioengineering of the Indian Institute of Technology, Kanpur . He is known for his computational studies on membrane protein function. The Department of Biotechnology of the Government of India awarded him the National Bioscience Award for Career Development , one of the highest Indian science awards, for his contributions to biosciences in 2008.
R. Sankararamakrishnan, who completed his early college education at the Madurai Kamaraj University in 1986, did his doctoral studies at the Indian Institute of Science and after obtaining a PhD in 1992, he moved to the UK where he did his post-doctoral research in computational biology at the University of Oxford . [ 1 ] He had another stint of post-doctoral work at the University of Illinois, Urbana-Champaign and started his career in 1996 as an instructor (later assistant professor of research) at the Icahn School of Medicine at Mount Sinai . In April 2002, he returned to India to join the Indian Institute of Technology, Kanpur (IITK) as an assistant professor and serves as a professor at the Department of Biological Sciences and Bioengineering (BSBE). [ 2 ] Subsequently, he founded the Bioinformatics and Biomolecular Simulation Laboratory at IITK where he hosts several research scholars. [ 3 ] He also serves as a resource person for the Centre for Mathematical Biology of the Department of Science and Technology . [ 4 ]
Sankaramakrishnan's research is focused on mechanism of membrane protein function using computational approaches . [ 2 ] He is known to have carried out research on aquaporin genes in plants, Asx turns , molecular dynamic simulations of protein-protein interactions , GPCR peptide hormones as well as nonAUG start codons and AUG codons . [ 5 ] His studies have been documented by way of a number of articles [ 6 ] [ note 1 ] and ResearchGate , an online repository of scientific articles has listed 98 of them. [ 7 ] Besides, he has also contributed chapters to books published by others [ 8 ] and his articles have drawn many citations. [ 9 ] [ 10 ] [ 11 ] He is the co-author of MIPModDB , a database of structure models of Major intrinsic proteins . [ 12 ] He has also delivered invited or keynote speeches at various national and international seminars. [ 13 ] [ 14 ] [ 15 ]
Sankararamakrishnan is a member of the National Network for Mathematical and Computational Biology, [ 16 ] an agency funded by the Science and Engineering Research Board of the Government of India for promoting scientific research and advanced training in the discipline. [ 17 ] He is also a life member of the National Academy of Sciences, India , one of the three major Indian science academies. [ 18 ]
The Department of Biotechnology of the Government of India awarded him the National Bioscience Award for Career Development , one of the highest Indian science awards in 2008. [ 19 ] He has also held the Joy Gill Chair Professorship for Young Faculty and the U.S.V. Chair Professorship of the Indian Institute of Technology, Kanpur during 2007-2010 and 2011-2014 respectively. [ 2 ] | https://en.wikipedia.org/wiki/R._Sankararamakrishnan |
In chemistry , amines ( / ə ˈ m iː n , ˈ æ m iː n / , [ 1 ] [ 2 ] UK also / ˈ eɪ m iː n / [ 3 ] ) are compounds and functional groups that contain a basic nitrogen atom with a lone pair . Formally, amines are derivatives of ammonia ( NH 3 in which the bond angle between the nitrogen and hydrogen is 107°), wherein one or more hydrogen atoms have been replaced by a substituent such as an alkyl or aryl group [ 4 ] (these may respectively be called alkylamines and arylamines; amines in which both types of substituent are attached to one nitrogen atom may be called alkylarylamines). Important amines include amino acids , biogenic amines , trimethylamine , and aniline . Inorganic derivatives of ammonia are also called amines, such as monochloramine ( NClH 2 ). [ 5 ]
The substituent −NH 2 is called an amino group. [ 6 ]
The chemical notation for amines contains the letter "R", where "R" is not an element, but an "R-group", which in amines could be a single hydrogen or carbon atom, or could be a hydrocarbon chain.
Compounds with a nitrogen atom attached to a carbonyl group , thus having the structure R−C(=O)−NR′R″ , are called amides and have different chemical properties from amines.
Amines can be classified according to the nature and number of substituents on nitrogen . Aliphatic amines contain only H and alkyl substituents. Aromatic amines have the nitrogen atom connected to an aromatic ring.
Amines, alkyl and aryl alike, are organized into three subcategories (see table) based on the number of carbon atoms adjacent to the nitrogen (how many hydrogen atoms of the ammonia molecule are replaced by hydrocarbon groups): [ 6 ] [ 7 ]
A fourth subcategory is determined by the connectivity of the substituents attached to the nitrogen:
It is also possible to have four organic substituents on the nitrogen. These species are not amines but are quaternary ammonium cations and have a charged nitrogen center. Quaternary ammonium salts exist with many kinds of anions .
Amines are named in several ways. Typically, the compound is given the prefix "amino-" or the suffix "-amine". The prefix " N -" shows substitution on the nitrogen atom. An organic compound with multiple amino groups is called a diamine , triamine , tetraamine and so forth.
Lower amines are named with the suffix -amine .
Higher amines have the prefix amino as a functional group. IUPAC however does not recommend this convention, [ 8 ] but prefers the alkanamine form, e.g. butan-2-amine.
Hydrogen bonding significantly influences the properties of primary and secondary amines. For example, methyl and ethyl amines are gases under standard conditions, whereas the corresponding methyl and ethyl alcohols are liquids. Amines possess a characteristic ammonia smell, liquid amines have a distinctive "fishy" and foul smell.
The nitrogen atom features a lone electron pair that can bind H + to form an ammonium ion R 3 NH + . The lone electron pair is represented in this article by two dots above or next to the N. The water solubility of simple amines is enhanced by hydrogen bonding involving these lone electron pairs. Typically salts of ammonium compounds exhibit the following order of solubility in water: primary ammonium ( RNH + 3 ) > secondary ammonium ( R 2 NH + 2 ) > tertiary ammonium (R 3 NH + ). Small aliphatic amines display significant solubility in many solvents , whereas those with large substituents are lipophilic. Aromatic amines, such as aniline , have their lone pair electrons conjugated into the benzene ring, thus their tendency to engage in hydrogen bonding is diminished. Their boiling points are high and their solubility in water is low.
Typically the presence of an amine functional group is deduced by a combination of techniques, including mass spectrometry as well as NMR and IR spectroscopies. 1 H NMR signals for amines disappear upon treatment of the sample with D 2 O. In their infrared spectrum primary amines exhibit two N-H bands, whereas secondary amines exhibit only one. [ 6 ] In their IR spectra, primary and secondary amines exhibit distinctive N-H stretching bands near 3300 cm −1 . Somewhat less distinctive are the bands appearing below 1600 cm −1 , which are weaker and overlap with C-C and C-H modes. For the case of propyl amine , the H-N-H scissor mode appears near 1600 cm −1 , the C-N stretch near 1000 cm −1 , and the R 2 N-H bend near 810 cm −1 . [ 9 ]
Alkyl amines characteristically feature tetrahedral nitrogen centers. C-N-C and C-N-H angles approach the idealized angle of 109°. C-N distances are slightly shorter than C-C distances. The energy barrier for the nitrogen inversion of the stereocenter is about 7 kcal/mol for a trialkylamine. The interconversion has been compared to the inversion of an open umbrella into a strong wind.
Amines of the type NHRR' and NRR′R″ are chiral : the nitrogen center bears four substituents counting the lone pair. Because of the low barrier to inversion, amines of the type NHRR' cannot be obtained in optical purity. For chiral tertiary amines, NRR′R″ can only be resolved when the R, R', and R″ groups are constrained in cyclic structures such as N -substituted aziridines ( quaternary ammonium salts are resolvable).
In aromatic amines ("anilines"), nitrogen is often nearly planar owing to conjugation of the lone pair with the aryl substituent. The C-N distance is correspondingly shorter. In aniline, the C-N distance is the same as the C-C distances. [ 10 ]
Like ammonia, amines are bases . [ 11 ] Compared to alkali metal hydroxides, amines are weaker.
The basicity of amines depends on:
Owing to inductive effects, the basicity of an amine might be expected to increase with the number of alkyl groups on the amine. Correlations are complicated owing to the effects of solvation which are opposite the trends for inductive effects. Solvation effects also dominate the basicity of aromatic amines (anilines). For anilines, the lone pair of electrons on nitrogen delocalizes into the ring, resulting in decreased basicity. Substituents on the aromatic ring, and their positions relative to the amino group, also affect basicity as seen in the table.
Solvation significantly affects the basicity of amines. N-H groups strongly interact with water, especially in ammonium ions. Consequently, the basicity of ammonia is enhanced by 10 11 by solvation. The intrinsic basicity of amines, i.e. the situation where solvation is unimportant, has been evaluated in the gas phase. In the gas phase, amines exhibit the basicities predicted from the electron-releasing effects of the organic substituents. Thus tertiary amines are more basic than secondary amines, which are more basic than primary amines, and finally ammonia is least basic. The order of pK b 's (basicities in water) does not follow this order. Similarly aniline is more basic than ammonia in the gas phase, but ten thousand times less so in aqueous solution. [ 14 ]
In aprotic polar solvents such as DMSO , DMF , and acetonitrile the energy of solvation is not as high as in protic polar solvents like water and methanol. For this reason, the basicity of amines in these aprotic solvents is almost solely governed by the electronic effects.
Industrially significant alkyl amines are prepared from ammonia by alkylation with alcohols: [ 5 ]
Unlike the reaction of amines with alcohols the reaction of amines and ammonia with alkyl halides is used for synthesis in the laboratory:
In such reactions, which are more useful for alkyl iodides and bromides, the degree of alkylation is difficult to control such that one obtains mixtures of primary, secondary, and tertiary amines, as well as quaternary ammonium salts. [ 5 ]
Selectivity can be improved via the Delépine reaction , although this is rarely employed on an industrial scale. Selectivity is also assured in the Gabriel synthesis , which involves organohalide reacting with potassium phthalimide .
Aryl halides are much less reactive toward amines and for that reason are more controllable. A popular way to prepare aryl amines is the Buchwald-Hartwig reaction .
Disubstituted alkenes react with HCN in the presence of strong acids to give formamides, which can be decarbonylated. This method, the Ritter reaction , is used industrially to produce tertiary amines such as tert -octylamine . [ 5 ]
Hydroamination of alkenes is also widely practiced. The reaction is catalyzed by zeolite-based solid acids . [ 5 ]
Via the process of hydrogenation , unsaturated N-containing functional groups are reduced to amines using hydrogen in the presence of a nickel catalyst. Suitable groups include nitriles , azides , imines including oximes , amides, and nitro . In the case of nitriles, reactions are sensitive to acidic or alkaline conditions, which can cause hydrolysis of the −CN group. LiAlH 4 is more commonly employed for the reduction of these same groups on the laboratory scale.
Many amines are produced from aldehydes and ketones via reductive amination , which can either proceed catalytically or stoichiometrically.
Aniline ( C 6 H 5 NH 2 ) and its derivatives are prepared by reduction of the nitroaromatics. In industry, hydrogen is the preferred reductant, whereas, in the laboratory, tin and iron are often employed.
Many methods exist for the preparation of amines, many of these methods being rather specialized.
Aside from their basicity, the dominant reactivity of amines is their nucleophilicity . [ 16 ] Most primary amines are good ligands for metal ions to give coordination complexes . Amines are alkylated by alkyl halides. Acyl chlorides and acid anhydrides react with primary and secondary amines to form amides (the " Schotten–Baumann reaction ").
Similarly, with sulfonyl chlorides, one obtains sulfonamides . This transformation, known as the Hinsberg reaction , is a chemical test for the presence of amines.
Because amines are basic, they neutralize acids to form the corresponding ammonium salts R 3 NH + . When formed from carboxylic acids and primary and secondary amines, these salts thermally dehydrate to form the corresponding amides .
Amines undergo sulfamation upon treatment with sulfur trioxide or sources thereof:
Amines reacts with nitrous acid to give diazonium salts. The alkyl diazonium salts are of little importance because they are too unstable. The most important members are derivatives of aromatic amines such as aniline ("phenylamine") (A = aryl or naphthyl):
Anilines and naphthylamines form more stable diazonium salts, which can be isolated in the crystalline form. [ 17 ] Diazonium salts undergo a variety of useful transformations involving replacement of the N 2 group with anions. For example, cuprous cyanide gives the corresponding nitriles:
Aryldiazoniums couple with electron-rich aromatic compounds such as a phenol to form azo compounds . Such reactions are widely applied to the production of dyes. [ 18 ]
Imine formation is an important reaction. Primary amines react with ketones and aldehydes to form imines . In the case of formaldehyde (R' = H), these products typically exist as cyclic trimers : RNH 2 + R 2 ′ C = O ⟶ R 2 ′ C = NR + H 2 O {\displaystyle {\ce {RNH2 + R'_2C=O -> R'_2C=NR + H2O}}} Reduction of these imines gives secondary amines: R 2 ′ C = NR + H 2 ⟶ R 2 ′ CH − NHR {\displaystyle {\ce {R'_2C=NR + H2 -> R'_2CH-NHR}}}
Similarly, secondary amines react with ketones and aldehydes to form enamines : R 2 NH + R ′ ( R ″ CH 2 ) C = O ⟶ R ″ CH = C ( NR 2 ) R ′ + H 2 O {\displaystyle {\ce {R2NH + R'(R''CH2)C=O -> R''CH=C(NR2)R' + H2O}}}
Mercuric ions reversibly oxidize tertiary amines with an α hydrogen to iminium ions: [ 19 ] Hg 2 + + R 2 NCH 2 R ′ ↽ − − ⇀ Hg + [ R 2 N = CHR ′ ] + + H + {\displaystyle {\ce {Hg^2+ + R2NCH2R' <=> Hg + [R2N=CHR']+ + H+}}}
An overview of the reactions of amines is given below:
Amines are ubiquitous in biology. The breakdown of amino acids releases amines, famously in the case of decaying fish which smell of trimethylamine . Many neurotransmitters are amines, including epinephrine , norepinephrine , dopamine , serotonin , and histamine . Protonated amino groups ( –NH + 3 ) are the most common positively charged moieties in proteins , specifically in the amino acid lysine . [ 20 ] The anionic polymer DNA is typically bound to various amine-rich proteins. [ 21 ] Additionally, the terminal charged primary ammonium on lysine forms salt bridges with carboxylate groups of other amino acids in polypeptides , which is one of the primary influences on the three-dimensional structures of proteins. [ 22 ]
Hormones derived from the modification of amino acids are referred to as amine hormones. Typically, the original structure of the amino acid is modified such that a –COOH, or carboxyl, group is removed, whereas the –NH + 3 , or amine, group remains. Amine hormones are synthesized from the amino acids tryptophan or tyrosine . [ 23 ]
Primary aromatic amines are used as a starting material for the manufacture of azo dyes . It reacts with nitrous acid to form diazonium salt, which can undergo coupling reaction to form an azo compound. As azo-compounds are highly coloured, they are widely used in dyeing industries, such as:
Most drugs and drug candidates contain amine functional groups: [ 24 ]
Aqueous monoethanolamine (MEA), diglycolamine (DGA), diethanolamine (DEA), diisopropanolamine (DIPA) and methyldiethanolamine (MDEA) are widely used industrially for removing carbon dioxide (CO 2 ) and hydrogen sulfide (H 2 S) from natural gas and refinery process streams. They may also be used to remove CO 2 from combustion gases and flue gases and may have potential for abatement of greenhouse gases . Related processes are known as sweetening . [ 26 ]
Amines are often used as epoxy resin curing agents. [ 27 ] [ 28 ] These include dimethylethylamine , cyclohexylamine , and a variety of diamines such as 4,4-diaminodicyclohexylmethane. [ 5 ] Multifunctional amines such as tetraethylenepentamine and triethylenetetramine are also widely used in this capacity. [ 29 ] The reaction proceeds by the lone pair of electrons on the amine nitrogen attacking the outermost carbon on the oxirane ring of the epoxy resin. This relieves ring strain on the epoxide and is the driving force of the reaction. [ 30 ] Molecules with tertiary amine functionality are often used to accelerate the epoxy-amine curing reaction and include substances such as 2,4,6-Tris(dimethylaminomethyl)phenol . It has been stated that this is the most widely used room temperature accelerator for two-component epoxy resin systems. [ 31 ] [ 32 ]
Low molecular weight simple amines, such as ethylamine , are toxic with LD 50 between 100 and 1000 mg/kg. They are skin irritants, especially as some are easily absorbed through the skin. [ 5 ] Amines are a broad class of compounds, and more complex members of the class can be extremely bioactive, for example strychnine . | https://en.wikipedia.org/wiki/R2NH |
Rab27 is a member of the Rab subfamily of GTPases . Rab27 is post translationally modified by the addition of two geranylgeranyl groups on the two C-terminal cysteines .
Rab27 has two main isoforms : Rab27a and Rab27b. These are similar in primary composition, with 66% similarity between nucleotides. [ 1 ] Most of their differences originate from their C-terminal , which is responsible for interactions with proteins such as SPIREs . [ 1 ] [ 2 ] Thus, these isoforms play different roles in the regulation pathway of exocytosis. Throughout the process of exocytosis, Rab27a and Rab27b are found in different sections of the cell, with Rab27b found commonly in the TGN and Rab27a usually bound to multivesicular endosomes with CD63 present. [ 3 ]
Rab27 plays a key role in the regulation of exocytosis of vesicles in various cellular organelles. [ 4 ] Rab27 uses effectors to tether vesicles to itself and transport them to the plasma membrane, where they undergo fusion. [ 4 ] They ensure that vesicles attach correctly, in the proper orientation, at the dedicated site of fusion. However, fusion itself is started when effectors bind SNARE proteins that catalyze the start of exocytosis. [ 4 ]
Mutations that prevent the expression of Rab27 ('knock out' mutations) cause the hypopigmentation and immunodeficiency disorder known as type II Griscelli syndrome , while a decrease in Rab27 prenylation is thought to be involved in choroideremia .
The symptoms of type II Griscelli syndrome have shown that Rab27 is involved in melanosome transport in melanocytes and in cytotoxic killing activity in cytotoxic T lymphoblasts . In melanocytes Rab27 binds the melanosome. The melanosome is transported along the microtubule . Rab27 then recruits Slac2A and myosin Va, these enzymes are essential for the transfer of the melanosomes from the microtubules to actin filaments. The melanosomes can now continue on their path towards the cell periphery. If either Rab27, Slac2A or myosin Va are absent then the melanosomes remain in the perinuclear region of the cell. This disruption in pigmentation results in the hypopigmentation seen in the silvery hair colour of patients with Griscelli syndrome .
The Rab27a isoform might play a role in cancer. It contributes to the growth of cancerous tumors due to its promotion of chemokine and metalloproteinase secretions. [ 5 ] Because of the over-expression of Rab27a in tissues in the breasts, lungs, and pancreas, there may be a linkage between Rab27a presence and likelihood of cancer. [ 5 ] Additionally, the release of metalloproteinases results in the breakdown of the ECM , which releases many of the growth factors held within. [ 6 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RAB27 |
RADOM is a Bulgarian Liulin-type instruments -type spectrometry- dosimetry instrument, designed to precisely measure cosmic radiation around the Moon . It is installed on the Indian satellite Chandrayaan-1 . Another three instruments were deployed on the International Space Station . All Liulin-type instruments are designed and build by the Solar-Terrestrial Influences Laboratory at the Bulgarian Academy of Sciences . [ citation needed ]
Dachev, Yu.; Dimitrov, F.; Tomov, O.; Matviichuk, Y.; et al. (2011). "Liulin-type spectrometry-dosimetry instruments". Radiation Protection Dosimetry . 144 ( 1– 4). Oxford University Press : 675– 679. doi : 10.1093/rpd/ncq506 . ISSN 1742-3406 . PMID 21177270 .
This astronomy -related article is a stub . You can help Wikipedia by expanding it .
This Bulgaria -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RADOM-7 |
RAFM Company, Inc. of Brantford , Ontario is a producer of miniatures , reference materials, and board games. RAFM has produced games, reference materials, and their own lines of miniature figures in 15 mm, 20 mm, 25 mm, and 28 mm scales since 1977. Their games concern soldiers, adventurers and monsters inspired by both history and fiction. Their products are sold at gaming conventions, in hobby shops, and by mail order for use in role playing games, wargaming, dioramas, competitive painting, and collecting. The company is best known for its Baker Company (WW2 Rules & Miniatures 20mm), Charlie Company (Vietnam Rules & Miniatures 20mm), Death in the Dark (28mm Fantasy Board Game), RAFM historical miniatures, Call of Cthulhu miniatures, fantasy miniatures (featuring the Iron Lords line of 28mm figures), Space: 1889 figures, historical source materials, and pewter dice.
RAFM was founded in 1977 by a group of wargaming enthusiasts in Paris, Ontario to publish a set of miniature battles rules called The Universal Soldier: Wargame Rules for Ancient, Medieval and Pike and Shot (1977) by Patrick Jenkins, John Laing, Colin McClelland, and Paul Sharpe. [ citation needed ] Initially, RAFM focused on publications for historical gaming, particularly the wars of the 18th and 19th centuries. Like their contemporaries at Ral Partha Enterprises and Grenadier Models Inc. , the company turned their focus to the rapidly expanding market in fantasy games. Bob Murch began sculpting for RAFM in the early 1980s and remained their primary sculptor until he began Pulp Figures in 2002. The company started as a partnership among the principal owners until John Laing moved to England in 1987 and left the partnership. Jack Van Schaik has been the president and part-owner of the company since the beginning. In 1999, RAFM Company Inc. became a subsidiary of Van Schaik's Silver Fox Productions and the RAFM headquarters was moved to Brantford , Ontario . In addition to their own lines, RAFM was the long-time caster and Canadian distributor for Ral Partha Enterprises , Citadel Miniatures , and currently distribute figures of Reaper Miniatures of Denton, Texas .
RAFM's miniatures are typically unmarked and in order to be identified must be matched to pictures and descriptions in product catalogs. Catalogs were produced in 1986 Canada, [ 1 ] 1986 U.S., [ 2 ] 1987 Canada, [ 3 ] 1989–90 U.S., [ 4 ] 1994, [ 5 ] 1996 Update #1, [ 6 ] 2005, [ 7 ] 2006, [ 8 ] and 2009. [ 9 ]
RAFM was also the Canadian caster and distributor of Ral Partha Enterprises and Citadel Miniatures , carrying most of their lines. RAFM tended to preserve older manufacturer's codes. For example, when Ral Partha switched to all numeric product codes in early 1980, RAFM continued production with the originals. In the 1990s RAFM distributed Frei Korps 15 's Yellow Ribbon line of 15mm figures for the American Wild West (YR01-YR18), another series for the American Civil War (7000-7011). [ 5 ] A one time sculptor for RAFM, Bob Ridolfi's sculpts and others are licensed by Reaper Miniatures for distribution in Canada. RAFM also produced miniatures for GHQ and Martian Metals in the 1980s. Contracts were also signed with Dream Pod 9's Heavy Gear, Global Games and Palladium's Rifts.
Unless otherwise noted, RAFM's miniatures were designed by Bob Murch and produced in 25mm scale. Other sculptors included Murch's apprentice Stephen Koo, Carol Moyer, James Johnson, and Bill Schwarz who specializes in the engines and vehicles of war throughout history. In recent years the boss' sons James and Brock Van Schaik have become accomplished sculptors. | https://en.wikipedia.org/wiki/RAFM_Company |
10743
19377
ENSG00000108557
ENSMUSG00000062115
Q7Z5J4
Q61818
NM_030665 NM_017574 NM_152256
NM_001037764 NM_009021
NP_109590
NP_001032853 NP_033047
RAI1 is a transcription factor associated with Smith–Magenis syndrome when individuals have deletions of the gene and Potocki–Lupski syndrome when individuals have a duplication. It is known as retinoic acid induced 1 .
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RAI1 |
RAMP Simulation Software for Modelling Reliability, Availability and Maintainability (RAM) is a computer software application developed by WS Atkins specifically for the assessment of the reliability , availability , maintainability and productivity characteristics of complex systems that would otherwise prove too difficult, cost too much or take too long to study analytically. The name RAMP is an acronym standing for R eliability, A vailability and M aintainability of P rocess systems.
RAMP models reliability using failure probability distributions for system elements, as well as accounting for common mode failures . RAMP models availability using logistic repair delays caused by shortages of spare parts or manpower , and their associated resource conditions defined for system elements. RAMP models maintainability using repair probability distributions for system elements, as well as preventive maintenance data and fixed logistic delays between failure detection and repair commencement.
RAMP consists of two parts:
The RAMP Model Builder enables the user to create a block diagram describing the dependency of the process being modelled on the state of individual elements in the system.
Elements are the basic building blocks of a system modelled in RAMP and can have user-specified failure and repair characteristics in the form probability distributions, typically of Mean Time Between Failure (MTBF) and Mean Time To Repair (MTTR) values respectively, chosen from the following:
Elements can represent any part of a system from a specific failure mode of a minor component (e.g. isolation valve fails open) to major subsystems (e.g. compressor or power turbine failure) depending on the level and detail of the analysis required.
RAMP allows the user to define deterministic elements which are failure free and/or are unrepairable. These elements may be used to represent parameters of the process (e.g. purity of feedstock or production demand at a particular time) or where necessary in the modelling logic (e.g. to provide conversion factors).
Each element of the model has a user-defined process 'q value' representing a parameter of interest (e.g. mass flow, generation capacity etc.). Each element is considered to be either operating or not operating and has associated performance values q = Q or q = 0 respectively. The interpretation of each 'q value' in the model depends on the parameter of interest being modelled, which is typically chosen during the system analysis stage of model design.
Elements with interacting functionality can be organised into groups. Groups can be further combined (to any depth) to produce a Process Dependency Diagram (PDD) of the system, which is similar to a normal reliability block diagram (RBD) commonly used in reliability engineering , but also allows complex logical relationships between groups and elements to permit a more accurate representation of the process being modelled. The PDD should not be confused with a flow diagram since it describes dependency, not flow. For example, an element may appear in more than one position in the PDD if this is required to represent the true dependency of the process on that element. Groups may also be shown in full or may be compressed to allow the screen to show other areas to greater resolution.
Each group can be one of eleven group types, each with its own rule for combining 'q values' of elements and/or other groups within it to produce a 'q value' output. Groups thus define how the behaviour of each element affects the reliability, availability, maintainability and productivity of the system. The eleven group types are divided into two classes:
Five 'Flow' group types:
Six 'Logic' group types:
Three group types (Active Redundant, Standby Redundant and Time) are displayed in parallel configurations (vertically down the screen). All others are displayed in series configurations (horizontally across the screen).
Six group types (Buffer, Quotient, Conditionally Greater Than, Conditionally Less Than, Difference and Equality) contain exactly two components with 'q values' q1 and q2. All others contain two or more components with 'q values' q1, q2 to qn.
An element may be in one of five possible states and its 'q value' is determined by its state:
Occurrence of a state transition for an element is determined largely by the user-defined parameters for that element (i.e. its failure and repair distributions and any preventive maintenance cycles).
There is often a time delay between an element failing and the commencement of repair of the element. This may be caused by a lack of spare parts, the unavailability of manpower or the element cannot be repaired due to dependencies on other elements (e.g. a pump cannot be repaired because the isolating valve is defective and cannot be closed). In all of these cases, the element must be queued for repair. RAMP allows the user to define multiple resource conditions per element, all of which must be satisfied to allow a repair to be commenced. Each resource condition is one of five types:
Repair trades can be specified for the repair of any element, and they represent manpower in the form of a set of skilled maintenance workers with a particular trade. A repair trade can be used for the duration of an element repair (i.e. logistic delay plus a time value drawn from the element repair distribution). On completion of the repair, the Repair Trade becomes available to repair another element. the number of repairs which can be performed simultaneously for elements requiring a particular repair trade depends on the number of repair trade resources allocated and the number of that repair trade specified as a requirement for the repair.
If a spare part is required for an element repair, then the spare part is withdrawn from stock at the instant the repair commences (i.e. as soon as the element leaves the repair queue). The maximum number of spare parts of each type that may be held in stock is user-defined. The stock may either be replenished periodically at a user-defined time interval, or when the stock falls below a user-defined level, in which case RAMP allows a user-defined a time delay that must occur between reordering and the actual replenishment of the stock.
RAMP allows the user to specify that an element cannot be repaired until the 'q value' of a nominated group satisfies one of six conditions (>, ≥, <, ≤, =, ≠) relative to a user-defined non-negative real number repair constraint. These conditions may be used to model certain rules in a system (e.g. a pump cannot be repaired until a tank is empty).
Specifying a buffer level constraint means that preventive maintenance of an element can be restricted until the buffer level of a nominated buffer group satisfies one of six conditions (>, ≥, <, ≤, =, ≠) relative to a user-defined non-negative real number repair constraint. These conditions may be used to model certain rules in a system (e.g. it may be a requirement for maintenance of a submersible pump that the tank it is in should be empty before repair work commences).
RAMP allows the user to specify that an element cannot be repaired until the state of another nominated element satisfies one of six conditions (>, ≥, <, ≤, =, ≠) relative to a user-defined non-negative real number repair constraint.
Each element has user-defined parameters that can affect how it is repaired:
In addition, each element in a Standby Redundant group has more parameters that can affect how it is repaired:
RAMP allows the user to model preventive maintenance for each system element by cycles expressed using the three parameters 'up-time'. 'down-time' and 'down-time' start time. RAMP also has an option to toggle 'intelligent preventive maintenance' on each system element, which attempts to improve system performance by doing preventive maintenance when the element is already in 'down-time' for other reasons.
Common mode failures (CMFs) that cause a number of elements to fail at the same time (e.g. due to the occurrence of a fire or some other catastrophic event, or the failure of a power supply that provides power to several separately defined elements). RAMP allows the user to define CMFs by stating the set of affected elements and the frequency distribution for occurrences of the CMF. When a CMF occurs, any elements which are affected by that particular CMF are placed in the failed state and must be repaired, being queued for repair if necessary. Any elements failed by a CMF will be repaired according to the repair distribution defined for that element. Elements which are already being repaired, are in the repair queue, or are undergoing preventive maintenance remain unaffected by the occurrence of an associated CMF.
The criticality of an element is a measure of how much the element has affected the 'q value' (i.e. performance) of the group to which it belongs. Elements with a high criticality cause more 'down-time' or unavailability on average and are thus critical to the performance of the group. The criticality of an element may vary according to the level of the group (e.g. a motor failure may have a very high criticality for a group that contains failure modes for one pump, but a very low criticality for a group that contains several redundant pumps).
RAMP allows the user to set the time unit of interest, according to scale and fidelity considerations. The only requirement is that time units should be used consistently across a model to avoid misleading results. Time units are expressed in the following input data:
Elements that are assumed to have the same failure and repair characteristics and share a common pool of spare parts can be assigned the same user-defined element type (i.e. pump, motor, tank etc.). This allows for faster construction of complex systems containing many elements that are similar in function since the entry of element data does not need to be repeated for such elements.
Previously built systems can be imported as subsystems of the system currently displayed. This allows for faster construction of complex systems containing many subsystems since they can be constructed in parallel by multiple users before being imported into a common system.
The RAMP Model Processor mimics the system operating over the time period of interest - known in RAMP as a mission - by sampling failure and repair times from probability distributions (with probabilities drawn from a pseudo-random number generator ) and combining with other data defined in the RAMP Model Builder to determine state transition events for each element in the model. The simulation uses discrete events that are queued in chronological order with each event being processed in turn to determine the states and thus the 'q values' of every element in the model at that discrete point in time. Group combination rules are used to determine the 'q values' at successively higher levels of groups, culminating in 'q values' of the outermost groups that when averaged over the events of the simulation typically provide performance measures of the system, which are output in model results in terms of the chosen parameters of interest.
By running enough missions over the same time period of interest (different possible histories from the same starting point), RAMP can be used to generate statistically significant results that establish the likely distribution of the user-defined parameters of interest and thus objectively assess the system, with the confidence bands on the results dependent on the number of missions simulated. On the other hand, by running a mission length that is long in comparison with the failure frequencies and repair times, and simulating only one mission, RAMP can be used to establish the steady-state performance of the system.
RAMP was originally developed by Rex Thompson & Partners Ltd. in the mid-1980s as an availability simulation program, primarily used for plant and process modelling. [ 1 ] The ownership of RAMP was transferred to T.A. Group [ 2 ] upon its founding in January 1990, [ 3 ] and then to Fluor Corporation when it acquired T.A. Group in April 1996, [ 4 ] before passing to the Advantage Technical Consulting business of parent company Advantage Business Group Ltd., [ 5 ] formed in February 2001 by a management buy-out of the consulting and information technology businesses of Fluor Corporation, operating in the transport, defence, energy and manufacturing sectors. [ 6 ] RAMP is currently owned by Atkins following its acquisition of Advantage Business Group Ltd. in March 2007. [ 7 ] Extensive redevelopment by Atkins of the original RAMP application for DOS has produced a series of RAMP applications for the Microsoft Windows platform, with the RAMP Model Builder written in Visual Basic and the RAMP Model Processor written in FORTRAN .
Due to its inherent flexibility, RAMP is now used to optimise system design and support critical decision making in many sectors [ 8 ] RAMP provides the capability to model many factors that may affect a system such as changes in specification or procurement contracts, 'what if' studies, sensitivity analysis , equipment redundancy , equipment criticality , delayed failures, as well as allowing the generation of results that can be exported for failure mode, effects and criticality analysis ( FMECA ) and cost-benefit analysis . | https://en.wikipedia.org/wiki/RAMP_Simulation_Software_for_Modelling_Reliability,_Availability_and_Maintainability |
R epeat A ssociated N on-AUG translation, or RAN translation , is an irregular mode of mRNA translation that can occur in eukaryotic cells. [ 1 ] [ 2 ]
For the majority of eukaryotic messenger RNAs (mRNAs) , translation initiates from a methionine-encoding AUG start codon following the molecular processes of 'cap-binding' and 'scanning' by ribosomal pre-initiation complexes (PICs). In rare exceptions, such as translation by viral IRES -containing mRNAs, 'cap-binding' and/or 'scanning' are not required for initiation, although AUG is still typically used as the first codon. RAN translation is an exception to the canonical rules as it uses variable start site selection and initiates from a non-AUG codon, but may still depend on 'cap-binding' and 'scanning'. [ 3 ]
RAN translation produces a variety of dipeptide repeat proteins by translation of expanded hexanucleotide repeats present in an intron of the C9orf72 gene. The expansion of the hexanucleotide repeats and thus accumulation of dipeptide repeat proteins are thought to cause cellular toxicity that leads to neurodegeneration in ALS disease. [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] | https://en.wikipedia.org/wiki/RAN_translation |
RAP6 is the abbreviation for Rab5-activating protein 6 , a novel endosomal protein with a role in endocytosis . RAP6 was discovered by Alejandro Barbieri and his group of researchers (Christine Hunker, Adriana Galvis, Ivan Kruk, Hugo Giambini, Lina Torres and Maria Luisa Veisaga) working at Florida International University . [ 1 ]
This novel human protein has been reported to be involved in membrane trafficking. It has been shown that RAP6 has a guanine nucleotide exchange factor (GEF) activity specific to Rab5 and a GTPase activating protein (GAP) activity specific to RAS . [ 1 ]
The original GeneBank Identifications (GIs) have been published in the NCBI Nucleotide databases with GIs 77176718 and 77176720 . Since then, many names have been coined to the validated protein such as RabGEF1, GeneID: 27342 . [ 2 ] RAP6 belongs to the family of the GAPVD1, GeneID: 26130 | https://en.wikipedia.org/wiki/RAP6 |
RAPIEnet ( Real-time Automation Protocols for Industrial Ethernet ) was Korea 's first Ethernet international standard for real-time data transmission. It is an Ethernet-based industrial networking protocol, [ 1 ] developed in-house by LSIS offers real-time transmission and is registered as an international standard. [ 2 ] (IEC 61158-3-21: 2010, IEC 61158-4-21: 2010, IEC 61158-5-21: 2010, IEC 61158-6-21: 2010, IEC 61784-2: 2010, IEC 62439-7) | https://en.wikipedia.org/wiki/RAPIEnet |
The Radiological Research Accelerator Facility ( RARAF ), [ 1 ] located on the Columbia University Nevis Laboratories campus in Irvington , New York is a National Institute of Biomedical Imaging and Bioengineering biotechnology resource center (P41) [ 2 ] specializing in microbeam technology.
The facility is currently built around a 5MV Singletron, a particle accelerator similar to a Van de Graaff .
The RARAF microbeam can produce with high accuracy and precision:
RARAF was conceived by Victor P. Bond and Harald H. Rossi in the late 1960s . Their aim was to provide a source of monoenergetic neutrons designed and operated specifically for studies in radiation biology , dosimetry , and microdosimetry. The facility was built around the 4 MV Van de Graaff particle accelerator that originally served as the injector for the Cosmotron , a 2 GeV accelerator operated at Brookhaven National Laboratory (BNL) in the 1950s and 1960s.
RARAF operated at BNL from 1967 until 1980, when it was dismantled to make room for the ISABELLE project , a very large accelerator which was never completed. A new site for RARAF was found at the Nevis Laboratories of Columbia University where its cyclotron was being disassembled. The U.S. Department of Energy provided funds to move RARAF to Nevis Laboratories and reassemble it in a new multi-level facility constructed within the cyclotron building. The new RARAF has been routinely operating for research since mid-1984.
RARAF was one of the first three microbeam facilities [ 3 ] to be built, and it is the only original microbeam facility still in operation.
In 2006 the Van de Graaff was replaced by a 5 MV Singletron from High Voltage Engineering Europa (HVEE) in the Netherlands .
As an NIBIB biotechnology resource center, RARAF is dedicated to developing and improving microbeam technologies. Developments focus on adding and improving imaging techniques to the existing microbeam. Neutron and x-ray microbeams are also in development. Some examples of microbeam developments are listed below.
In order to focus charged particles in the RARAF microbeam, an electrostatic lens consisting of six quadrupole arranged in two triplets with each successive quadrupole rotated by 90° around its axis, is used. Each quadrupole triplet consists of 4 ceramic rods on which gold electrodes were plated. This design ensures alignment of the three quadrupoles in the triplet and allows a small pole-gap and better focusing properties.
Due to the nature of the RARAF microbeam, sub-cellular targets such as the cell nucleus or the cell cytoplasm have been possible for years. With a sub-micrometre diameter beam routinely available, additional targets within cellular systems are accessible. For instance, preliminary radiation experiments that target mitochondria have been conducted on small airway epithelial cells. [ 1 ]
During microbeam irradiation, cells to be irradiated are moved to the beam position using a high-speed high-resolution three-axis piezo-electric stage. [ 4 ] In order to further reduce targeting time, and making use of the fact that a focused microbeam, unlike a collimated one, is not restricted to a single location on the accelerator exit window, we have implemented a magnetic-coil-based fast deflector, placed between the two quadrupole triplets, that allows deflecting the beam to any position in the field of view of the microscope used to observe the cells during irradiation. Moving the beam to the cell position magnetically can be performed much faster than moving the stage. The deflector used in this system can move the beam to as many as 1000 separate locations per second—more than 5 times the speed of movement of the stage—dramatically reducing the irradiation time.
The RARAF microbeam is adding an x-ray microbeam using characteristic Kα x rays from Ti. The x rays will be generated using an electrostatic lens system to focus protons onto a thick Ti target. The x rays generated are demagnified using a zone plate. By using the already focused proton microbeam to generate characteristic x rays, it is possible to obtain a nearly monochromatic x-ray beam (very low bremsstrahlung yield) and a reasonably small x-ray source (~20 μm diameter), reducing the requirements on the zone plate.
There are considerable benefits in using soft x-ray microbeams for both mechanistic and risk estimation end-points. The higher spatial resolution achievable with modern state-of-the-art x-ray optics elements combined with the localized damage produced by the absorption of low energy photons (~1 keV) represents a unique tool to investigate the radio-sensitivity of sub-cellular and eventually sub-nuclear targets. Also, since low-energy x rays undergo very little scattering, by using x rays with an energy of ~5 keV it will be possible to irradiate with micrometre precision individual cells and/or parts of cells up to a few hundred micrometres deep inside a tissue sample in order to investigate the relevance of effects such as the bystander effect in 3-D structured cell systems.
RARAF is also a user facility for biologists interested in performing microbeam studies. The prominent theme of research undertaken using the RARAF microbeam is damage signal transduction, both within cells and between cells, which is of interest due in part to the discovery of the radiation-induced bystander effect . Early inter-cellular signal transduction studies were done with cells plated in 2D monolayers. More recently due to the significance of the extracellular environment and technological developments, studies involving 3D tissue systems, [ 5 ] [ 6 ] including living organisms, [ 7 ] have become more common.
RARAF is developing various microfluidic devices which add to the irradiation capabilities of the facility. The precision control and manipulation of fluids and biological materials afforded by microfluidics are ideal to interface with the microbeam. Additional microfluidic systems beyond those listed here are currently under development.
The Flow and Shoot microbeam system allows for controlled transport of cells through a microfluidic channel which intersects with the point and shoot microbeam. [ 8 ] A high speed camera allows for dynamic targeting of the flowing cells with flow rates of 1–10 mm/s, allowing for total throughput upwards of 100,000 cells per hour.
An optoelectronic tweezer platform has been interfaced with the RARAF microbeam. [ 9 ] This allows precision manipulation of cell position before, during, and after irradiation.
RARAF has implemented a microfluidic platform for the immobilization of Caenorhabditis elegans during microbeam irradiation. [ 10 ] The device avoids the use of anesthetics that might interfere with normal physiological processes by capturing the C. elegans worms in tapered microfluidic channels. It is possible to target specific regions of interest within C. elegans using this technology.
Broad beam irradiations are also possible. Particles with linear energy transfer (LET) between 10 and 200 keV/μm are available utilizing beams of protons, deuterons, helium-3, and helium-4 ions. Additionally, energetic and thermal neutrons and x rays can be used in broad beam irradiations.
RARAF has trained scientists at all levels: high school students, undergraduates, graduate students, post docs, and senior scientists. The lab estimates that about 45 scientists have received training in microbeam physics and or biology in the past 5 years.
RARAF is an active participant in the Columbia University Research Experience for Undergraduates program.
In addition, RARAF has become a de facto training center for developers of new microbeams. A virtual microbeam training course , complete with videos and handouts, is also available online. | https://en.wikipedia.org/wiki/RARAF |
The RAYDAC (for Ray theon D igital A utomatic C omputer) was a one-of-a-kind computer built by Raytheon . It was started in 1949 and finished in 1953. [ 1 ] [ 2 ] [ page needed ] It was installed at the Naval Air Missile Test Center at Point Mugu , California .
The RAYDAC used 5,200 vacuum tubes [ 3 ] and 18,000 crystal diodes . It had 1,152 words of memory (36 bits per word), using delay-line memory , with an access time of up to 305 microseconds . Its addition time was 38 microseconds, multiplication time was 240 microseconds, and division time was 375 microseconds. (These times exclude the memory-access time.) [ 4 ] [ self-published source ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RAYDAC |
The ratio average (RA) plot is an integer-based version of an MA plot for visualizing two-condition count data. Its distinctive arrow-like shape derives from the way it includes condition-unique (0, n ) or ( n ,0) points into the plot via an epsilon factor .
An RA plot , like its cousin, the MA plot , is a re-scaled and (45-degree) rotated version of a simple two-dimensional scatter plot of a versus b where a and b are equal-length vectors of positive measurements. This rescaling and rotation allows for better visibility and emphasis of important outliers points that vary between the two measurement conditions. [ 1 ] Essentially it is a plot of the log ratio [R] vs the average log [A] of each pairing of the elements of a and b . Unlike an MA plot, however, because the RA plot takes non-negative integer counts as input, it must employ work-arounds to include mathematically invisible points (such as points where one or both element(s) of the pair is zero).
If we modify our original a (or b ) vector via:
where
then R and A can be defined as:
R , like M , is plotted on the y -axis and represents a log (fold change) ratio between a and b . A is plotted on the x -axis and represents the average abundance for a coordinate pair. The RA plot provides a quick overview of the distribution and size of a dataset consisting of non-zero counts.
The acronym prefix "R.A." is sometimes pronounced as the one syllable word "ray" because of the plot's strong resemblance to a geometric ray . This characteristic arrow-like shape derives from two key features: on the right at the vector origin, a long asymptotic tail, and on the left (forming the arrow head) two (often dense) patches of condition-unique points.
Because a large portion of the pairs of a and b contain zeros in one or both conditions, they are impossible to plot as-is on a log scale. Other MA plotting functions artificially include these condition-unique points in the plot by spreading them vertically as a "smear" on the left or horizontally as a " rug " at the very top and bottom of the plot. In an RA plot, by contrast, the uniques are included via addition a small epsilon factor (between .1 and .5) which places them in a more statistically appropriate location in the plot.
Another problem with plotting this (or any) type of count data is overplotting which is solved in the RA plot by jittering the points out away from each other but no so far as to merge with other coordinates. The result of this feature is a patchwork-like appearance to the plot that fades away as the A increases.
The caroline CRAN R package contains the only known implementation of an RA plot. However, the meta-transcriptomics "manta" R package provides a wrapper around this RA plot implementation and is used for assessing fold change in transcription of genes (the points) while simultaneously visualizing each gene's taxonomic distributions as individual pie chart points. [ 2 ] | https://en.wikipedia.org/wiki/RA_plot |
The reflected binary code ( RBC ), also known as reflected binary ( RB ) or Gray code after Frank Gray , is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit).
For example, the representation of the decimal value "1" in binary would normally be " 001 ", and "2" would be " 010 ". In Gray code, these values are represented as " 001 " and " 011 ". That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two.
Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems. The use of Gray code in these devices helps simplify logic operations and reduce errors in practice. [ 3 ]
Many devices indicate position by closing and opening switches. If that device uses natural binary codes , positions 3 and 4 are next to each other but all three bits of the binary representation differ:
The problem with natural binary codes is that physical switches are not ideal: it is very unlikely that physical switches will change states exactly in synchrony. In the transition between the two states shown above, all three switches change state. In the brief period while all are changing, the switches will read some spurious position. Even without keybounce , the transition might look like 011 — 001 — 101 — 100 . When the switches appear to be in position 001 , the observer cannot tell if that is the "real" position 1, or a transitional state between two other positions. If the output feeds into a sequential system, possibly via combinational logic , then the sequential system may store a false value.
This problem can be solved by changing only one switch at a time, so there is never any ambiguity of position, resulting in codes assigning to each of a contiguous set of integers , or to each member of a circular list, a word of symbols such that no two code words are identical and each two adjacent code words differ by exactly one symbol. These codes are also known as unit-distance , [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] single-distance , single-step , monostrophic [ 9 ] [ 10 ] [ 7 ] [ 8 ] or syncopic codes , [ 9 ] in reference to the Hamming distance of 1 between adjacent codes.
In principle, there can be more than one such code for a given word length, but the term Gray code was first applied to a particular binary code for non-negative integers, the binary-reflected Gray code , or BRGC . Bell Labs researcher George R. Stibitz described such a code in a 1941 patent application, granted in 1943. [ 11 ] [ 12 ] [ 13 ] Frank Gray introduced the term reflected binary code in his 1947 patent application, remarking that the code had "as yet no recognized name". [ 14 ] He derived the name from the fact that it "may be built up from the conventional binary code by a sort of reflection process".
In the standard encoding of the Gray code the least significant bit follows a repetitive pattern of 2 on, 2 off (... 11001100 ...); the next digit a pattern of 4 on, 4 off; the i -th least significant bit a pattern of 2 i on 2 i off. The most significant digit is an exception to this: for an n -bit Gray code, the most significant digit follows the pattern 2 n −1 on, 2 n −1 off, which is the same (cyclic) sequence of values as for the second-most significant digit, but shifted forwards 2 n −2 places. The four-bit version of this is shown below:
For decimal 15 the code rolls over to decimal 0 with only one switch change. This is called the cyclic or adjacency property of the code. [ 15 ]
In modern digital communications , Gray codes play an important role in error correction . For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point. This makes the transmission system less susceptible to noise .
Despite the fact that Stibitz described this code [ 11 ] [ 12 ] [ 13 ] before Gray, the reflected binary code was later named after Gray by others who used it. Two different 1953 patent applications use "Gray code" as an alternative name for the "reflected binary code"; [ 16 ] [ 17 ] one of those also lists "minimum error code" and "cyclic permutation code" among the names. [ 17 ] A 1954 patent application refers to "the Bell Telephone Gray code". [ 18 ] Other names include "cyclic binary code", [ 12 ] "cyclic progression code", [ 19 ] [ 12 ] "cyclic permuting binary" [ 20 ] or "cyclic permuted binary" (CPB). [ 21 ] [ 22 ]
The Gray code is sometimes misattributed to 19th century electrical device inventor Elisha Gray . [ 13 ] [ 23 ] [ 24 ] [ 25 ]
Reflected binary codes were applied to mathematical puzzles before they became known to engineers.
The binary-reflected Gray code represents the underlying scheme of the classical Chinese rings puzzle , a sequential mechanical puzzle mechanism described by the French Louis Gros in 1872. [ 26 ] [ 13 ]
It can serve as a solution guide for the Towers of Hanoi problem, based on a game by the French Édouard Lucas in 1883. [ 27 ] [ 28 ] [ 29 ] [ 30 ] Similarly, the so-called Towers of Bucharest and Towers of Klagenfurt game configurations yield ternary and pentary Gray codes. [ 31 ]
Martin Gardner wrote a popular account of the Gray code in his August 1972 "Mathematical Games" column in Scientific American . [ 32 ]
The code also forms a Hamiltonian cycle on a hypercube , where each bit is seen as one dimension.
When the French engineer Émile Baudot changed from using a 6-unit (6-bit) code to 5-unit code for his printing telegraph system, in 1875 [ 33 ] or 1876, [ 34 ] [ 35 ] he ordered the alphabetic characters on his print wheel using a reflected binary code, and assigned the codes using only three of the bits to vowels. With vowels and consonants sorted in their alphabetical order, [ 36 ] [ 37 ] [ 38 ] and other symbols appropriately placed, the 5-bit character code has been recognized as a reflected binary code. [ 13 ] This code became known as Baudot code [ 39 ] and, with minor changes, was eventually adopted as International Telegraph Alphabet No. 1 (ITA1, CCITT-1) in 1932. [ 40 ] [ 41 ] [ 38 ]
About the same time, the German-Austrian Otto Schäffler [ de ] [ 42 ] demonstrated another printing telegraph in Vienna using a 5-bit reflected binary code for the same purpose, in 1874. [ 43 ] [ 13 ]
Frank Gray , who became famous for inventing the signaling method that came to be used for compatible color television, invented a method to convert analog signals to reflected binary code groups using vacuum tube -based apparatus. Filed in 1947, the method and apparatus were granted a patent in 1953, [ 14 ] and the name of Gray stuck to the codes. The " PCM tube " apparatus that Gray patented was made by Raymond W. Sears of Bell Labs, working with Gray and William M. Goodall, who credited Gray for the idea of the reflected binary code. [ 44 ]
Gray was most interested in using the codes to minimize errors in converting analog signals to digital; his codes are still used today for this purpose.
Gray codes are used in linear and rotary position encoders ( absolute encoders and quadrature encoders ) in preference to weighted binary encoding. This avoids the possibility that, when multiple bits change in the binary representation of a position, a misread will result from some of the bits changing before others.
For example, some rotary encoders provide a disk which has an electrically conductive Gray code pattern on concentric rings (tracks). Each track has a stationary metal spring contact that provides electrical contact to the conductive code pattern. Together, these contacts produce output signals in the form of a Gray code. Other encoders employ non-contact mechanisms based on optical or magnetic sensors to produce the Gray code output signals.
Regardless of the mechanism or precision of a moving encoder, position measurement error can occur at specific positions (at code boundaries) because the code may be changing at the exact moment it is read (sampled). A binary output code could cause significant position measurement errors because it is impossible to make all bits change at exactly the same time. If, at the moment the position is sampled, some bits have changed and others have not, the sampled position will be incorrect. In the case of absolute encoders, the indicated position may be far away from the actual position and, in the case of incremental encoders, this can corrupt position tracking.
In contrast, the Gray code used by position encoders ensures that the codes for any two consecutive positions will differ by only one bit and, consequently, only one bit can change at a time. In this case, the maximum position error will be small, indicating a position adjacent to the actual position.
Due to the Hamming distance properties of Gray codes, they are sometimes used in genetic algorithms . [ 15 ] They are very useful in this field, since mutations in the code allow for mostly incremental changes, but occasionally a single bit-change can cause a big leap and lead to new properties.
Gray codes are also used in labelling the axes of Karnaugh maps since 1953 [ 45 ] [ 46 ] [ 47 ] as well as in Händler circle graphs since 1958, [ 48 ] [ 49 ] [ 50 ] [ 51 ] both graphical methods for logic circuit minimization .
In modern digital communications , 1D- and 2D-Gray codes play an important role in error prevention before applying an error correction . For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point. This makes the transmission system less susceptible to noise .
Digital logic designers use Gray codes extensively for passing multi-bit count information between synchronous logic that operates at different clock frequencies. The logic is considered operating in different "clock domains". It is fundamental to the design of large chips that operate with many different clocking frequencies.
If a system has to cycle sequentially through all possible combinations of on-off states of some set of controls, and the changes of the controls require non-trivial expense (e.g. time, wear, human work), a Gray code minimizes the number of setting changes to just one change for each combination of states. An example would be testing a piping system for all combinations of settings of its manually operated valves.
A balanced Gray code can be constructed, [ 52 ] that flips every bit equally often. Since bit-flips are evenly distributed, this is optimal in the following way: balanced Gray codes minimize the maximal count of bit-flips for each digit.
George R. Stibitz utilized a reflected binary code in a binary pulse counting device in 1941 already. [ 11 ] [ 12 ] [ 13 ]
A typical use of Gray code counters is building a FIFO (first-in, first-out) data buffer that has read and write ports that exist in different clock domains. The input and output counters inside such a dual-port FIFO are often stored using Gray code to prevent invalid transient states from being captured when the count crosses clock domains. [ 53 ] The updated read and write pointers need to be passed between clock domains when they change, to be able to track FIFO empty and full status in each domain. Each bit of the pointers is sampled non-deterministically for this clock domain transfer. So for each bit, either the old value or the new value is propagated. Therefore, if more than one bit in the multi-bit pointer is changing at the sampling point, a "wrong" binary value (neither new nor old) can be propagated. By guaranteeing only one bit can be changing, Gray codes guarantee that the only possible sampled values are the new or old multi-bit value. Typically Gray codes of power-of-two length are used.
Sometimes digital buses in electronic systems are used to convey quantities that can only increase or decrease by one at a time, for example the output of an event counter which is being passed between clock domains or to a digital-to-analog converter. The advantage of Gray codes in these applications is that differences in the propagation delays of the many wires that represent the bits of the code cannot cause the received value to go through states that are out of the Gray code sequence. This is similar to the advantage of Gray codes in the construction of mechanical encoders, however the source of the Gray code is an electronic counter in this case. The counter itself must count in Gray code, or if the counter runs in binary then the output value from the counter must be reclocked after it has been converted to Gray code, because when a value is converted from binary to Gray code, [ nb 1 ] it is possible that differences in the arrival times of the binary data bits into the binary-to-Gray conversion circuit will mean that the code could go briefly through states that are wildly out of sequence. Adding a clocked register after the circuit that converts the count value to Gray code may introduce a clock cycle of latency, so counting directly in Gray code may be advantageous. [ 54 ]
To produce the next count value in a Gray-code counter, it is necessary to have some combinational logic that will increment the current count value that is stored. One way to increment a Gray code number is to convert it into ordinary binary code, [ 55 ] add one to it with a standard binary adder, and then convert the result back to Gray code. [ 56 ] Other methods of counting in Gray code are discussed in a report by Robert W. Doran , including taking the output from the first latches of the master-slave flip flops in a binary ripple counter. [ 57 ]
As the execution of program code typically causes an instruction memory access pattern of locally consecutive addresses, bus encodings using Gray code addressing instead of binary addressing can reduce the number of state changes of the address bits significantly, thereby reducing the CPU power consumption in some low-power designs. [ 58 ] [ 59 ]
The binary-reflected Gray code list for n bits can be generated recursively from the list for n − 1 bits by reflecting the list (i.e. listing the entries in reverse order), prefixing the entries in the original list with a binary 0 , prefixing the entries in the reflected list with a binary 1 , and then concatenating the original list with the reversed list. [ 13 ] For example, generating the n = 3 list from the n = 2 list:
The one-bit Gray code is G 1 = ( 0,1 ). This can be thought of as built recursively as above from a zero-bit Gray code G 0 = ( Λ ) consisting of a single entry of zero length. This iterative process of generating G n +1 from G n makes the following properties of the standard reflecting code clear:
These characteristics suggest a simple and fast method of translating a binary value into the corresponding Gray code. Each bit is inverted if the next higher bit of the input value is set to one. This can be performed in parallel by a bit-shift and exclusive-or operation if they are available: the n th Gray code is obtained by computing n ⊕ ⌊ n 2 ⌋ {\displaystyle n\oplus \left\lfloor {\tfrac {n}{2}}\right\rfloor } . Prepending a 0 bit leaves the order of the code words unchanged, prepending a 1 bit reverses the order of the code words. If the bits at position i {\displaystyle i} of codewords are inverted, the order of neighbouring blocks of 2 i {\displaystyle 2^{i}} codewords is reversed. For example, if bit 0 is inverted in a 3 bit codeword sequence, the order of two neighbouring codewords is reversed
If bit 1 is inverted, blocks of 2 codewords change order:
If bit 2 is inverted, blocks of 4 codewords reverse order:
Thus, performing an exclusive or on a bit b i {\displaystyle b_{i}} at position i {\displaystyle i} with the bit b i + 1 {\displaystyle b_{i+1}} at position i + 1 {\displaystyle i+1} leaves the order of codewords intact if b i + 1 = 0 {\displaystyle b_{i+1}={\mathtt {0}}} , and reverses the order of blocks of 2 i + 1 {\displaystyle 2^{i+1}} codewords if b i + 1 = 1 {\displaystyle b_{i+1}={\mathtt {1}}} . Now, this is exactly the same operation as the reflect-and-prefix method to generate the Gray code.
A similar method can be used to perform the reverse translation, but the computation of each bit depends on the computed value of the next higher bit so it cannot be performed in parallel. Assuming g i {\displaystyle g_{i}} is the i {\displaystyle i} th Gray-coded bit ( g 0 {\displaystyle g_{0}} being the most significant bit), and b i {\displaystyle b_{i}} is the i {\displaystyle i} th binary-coded bit ( b 0 {\displaystyle b_{0}} being the most-significant bit), the reverse translation can be given recursively: b 0 = g 0 {\displaystyle b_{0}=g_{0}} , and b i = g i ⊕ b i − 1 {\displaystyle b_{i}=g_{i}\oplus b_{i-1}} . Alternatively, decoding a Gray code into a binary number can be described as a prefix sum of the bits in the Gray code, where each individual summation operation in the prefix sum is performed modulo two.
To construct the binary-reflected Gray code iteratively, at step 0 start with the c o d e 0 = 0 {\displaystyle \mathrm {code} _{0}={\mathtt {0}}} , and at step i > 0 {\displaystyle i>0} find the bit position of the least significant 1 in the binary representation of i {\displaystyle i} and flip the bit at that position in the previous code c o d e i − 1 {\displaystyle \mathrm {code} _{i-1}} to get the next code c o d e i {\displaystyle \mathrm {code} _{i}} . The bit positions start 0, 1, 0, 2, 0, 1, 0, 3, ... [ nb 2 ] See find first set for efficient algorithms to compute these values.
The following functions in C convert between binary numbers and their associated Gray codes. While it may seem that Gray-to-binary conversion requires each bit to be handled one at a time, faster algorithms exist. [ 60 ] [ 55 ] [ nb 1 ]
On newer processors, the number of ALU instructions in the decoding step can be reduced by taking advantage of the CLMUL instruction set . If MASK is the constant binary string of ones ended with a single zero digit, then carryless multiplication of MASK with the grey encoding of x will always give either x or its bitwise negation.
In practice, "Gray code" almost always refers to a binary-reflected Gray code (BRGC). However, mathematicians have discovered other kinds of Gray codes. Like BRGCs, each consists of a list of words, where each word differs from the next in only one digit (each word has a Hamming distance of 1 from the next word).
It is possible to construct binary Gray codes with n bits with a length of less than 2 n , if the length is even. One possibility is to start with a balanced Gray code and remove pairs of values at either the beginning and the end, or in the middle. [ 61 ] OEIS sequence A290772 [ 62 ] gives the number of possible Gray sequences of length 2 n that include zero and use the minimum number of bits.
0 → 000 1 → 001 2 → 002 10 → 012 11 → 011 12 → 010 20 → 020 21 → 021 22 → 022 100 → 122 101 → 121 102 → 120 110 → 110 111 → 111 112 → 112 120 → 102 121 → 101 122 → 100 200 → 200 201 → 201 202 → 202 210 → 212 211 → 211 212 → 210 220 → 220 221 → 221
There are many specialized types of Gray codes other than the binary-reflected Gray code. One such type of Gray code is the n -ary Gray code , also known as a non-Boolean Gray code . As the name implies, this type of Gray code uses non- Boolean values in its encodings.
For example, a 3-ary ( ternary ) Gray code would use the values 0,1,2. [ 31 ] The ( n , k )- Gray code is the n -ary Gray code with k digits. [ 63 ] The sequence of elements in the (3, 2)-Gray code is: 00,01,02,12,11,10,20,21,22. The ( n , k )-Gray code may be constructed recursively, as the BRGC, or may be constructed iteratively . An algorithm to iteratively generate the ( N , k )-Gray code is presented (in C ):
There are other Gray code algorithms for ( n , k )-Gray codes. The ( n , k )-Gray code produced by the above algorithm is always cyclical; some algorithms, such as that by Guan, [ 63 ] lack this property when k is odd. On the other hand, while only one digit at a time changes with this method, it can change by wrapping (looping from n − 1 to 0). In Guan's algorithm, the count alternately rises and falls, so that the numeric difference between two Gray code digits is always one.
Gray codes are not uniquely defined, because a permutation of the columns of such a code is a Gray code too. The above procedure produces a code in which the lower the significance of a digit, the more often it changes, making it similar to normal counting methods.
See also Skew binary number system , a variant ternary number system where at most two digits change on each increment, as each increment can be done with at most one digit carry operation.
Although the binary reflected Gray code is useful in many scenarios, it is not optimal in certain cases because of a lack of "uniformity". [ 52 ] In balanced Gray codes , the number of changes in different coordinate positions are as close as possible. To make this more precise, let G be an R -ary complete Gray cycle having transition sequence ( δ k ) {\displaystyle (\delta _{k})} ; the transition counts ( spectrum ) of G are the collection of integers defined by
λ k = | { j ∈ Z R n : δ j = k } | , for k ∈ Z n {\displaystyle \lambda _{k}=|\{j\in \mathbb {Z} _{R^{n}}:\delta _{j}=k\}|\,,{\text{ for }}k\in \mathbb {Z} _{n}}
A Gray code is uniform or uniformly balanced if its transition counts are all equal, in which case we have λ k = R n n {\displaystyle \lambda _{k}={\tfrac {R^{n}}{n}}} for all k . Clearly, when R = 2 {\displaystyle R=2} , such codes exist only if n is a power of 2. [ 64 ] If n is not a power of 2, it is possible to construct well-balanced binary codes where the difference between two transition counts is at most 2; so that (combining both cases) every transition count is either 2 ⌊ 2 n 2 n ⌋ {\displaystyle 2\left\lfloor {\tfrac {2^{n}}{2n}}\right\rfloor } or 2 ⌈ 2 n 2 n ⌉ {\displaystyle 2\left\lceil {\tfrac {2^{n}}{2n}}\right\rceil } . [ 52 ] Gray codes can also be exponentially balanced if all of their transition counts are adjacent powers of two, and such codes exist for every power of two. [ 65 ]
For example, a balanced 4-bit Gray code has 16 transitions, which can be evenly distributed among all four positions (four transitions per position), making it uniformly balanced: [ 52 ]
whereas a balanced 5-bit Gray code has a total of 32 transitions, which cannot be evenly distributed among the positions. In this example, four positions have six transitions each, and one has eight: [ 52 ]
We will now show a construction [ 66 ] and implementation [ 67 ] for well-balanced binary Gray codes which allows us to generate an n -digit balanced Gray code for every n . The main principle is to inductively construct an ( n + 2)-digit Gray code G ′ {\displaystyle G'} given an n -digit Gray code G in such a way that the balanced property is preserved. To do this, we consider partitions of G = g 0 , … , g 2 n − 1 {\displaystyle G=g_{0},\ldots ,g_{2^{n}-1}} into an even number L of non-empty blocks of the form
{ g 0 } , { g 1 , … , g k 2 } , { g k 2 + 1 , … , g k 3 } , … , { g k L − 2 + 1 , … , g − 2 } , { g − 1 } {\displaystyle \left\{g_{0}\right\},\left\{g_{1},\ldots ,g_{k_{2}}\right\},\left\{g_{k_{2}+1},\ldots ,g_{k_{3}}\right\},\ldots ,\left\{g_{k_{L-2}+1},\ldots ,g_{-2}\right\},\left\{g_{-1}\right\}}
where k 1 = 0 {\displaystyle k_{1}=0} , k L − 1 = − 2 {\displaystyle k_{L-1}=-2} , and k L ≡ − 1 ( mod 2 n ) {\displaystyle k_{L}\equiv -1{\pmod {2^{n}}}} ). This partition induces an ( n + 2 ) {\displaystyle (n+2)} -digit Gray code given by
If we define the transition multiplicities
m i = | { j : δ k j = i , 1 ≤ j ≤ L } | {\displaystyle m_{i}=\left|\left\{j:\delta _{k_{j}}=i,1\leq j\leq L\right\}\right|}
to be the number of times the digit in position i changes between consecutive blocks in a partition, then for the ( n + 2)-digit Gray code induced by this partition the transition spectrum λ i ′ {\displaystyle \lambda '_{i}} is
λ i ′ = { 4 λ i − 2 m i , if 0 ≤ i < n L , otherwise {\displaystyle \lambda '_{i}={\begin{cases}4\lambda _{i}-2m_{i},&{\text{if }}0\leq i<n\\L,&{\text{ otherwise }}\end{cases}}}
The delicate part of this construction is to find an adequate partitioning of a balanced n -digit Gray code such that the code induced by it remains balanced, but for this only the transition multiplicities matter; joining two consecutive blocks over a digit i {\displaystyle i} transition and splitting another block at another digit i {\displaystyle i} transition produces a different Gray code with exactly the same transition spectrum λ i ′ {\displaystyle \lambda '_{i}} , so one may for example [ 65 ] designate the first m i {\displaystyle m_{i}} transitions at digit i {\displaystyle i} as those that fall between two blocks. Uniform codes can be found when R ≡ 0 ( mod 4 ) {\displaystyle R\equiv 0{\pmod {4}}} and R n ≡ 0 ( mod n ) {\displaystyle R^{n}\equiv 0{\pmod {n}}} , and this construction can be extended to the R -ary case as well. [ 66 ]
Long run (or maximum gap ) Gray codes maximize the distance between consecutive changes of digits in the same position. That is, the minimum run-length of any bit remains unchanged for as long as possible. [ 68 ]
Monotonic codes are useful in the theory of interconnection networks, especially for minimizing dilation for linear arrays of processors. [ 69 ] If we define the weight of a binary string to be the number of 1s in the string, then although we clearly cannot have a Gray code with strictly increasing weight, we may want to approximate this by having the code run through two adjacent weights before reaching the next one.
We can formalize the concept of monotone Gray codes as follows: consider the partition of the hypercube Q n = ( V n , E n ) {\displaystyle Q_{n}=(V_{n},E_{n})} into levels of vertices that have equal weight, i.e.
V n ( i ) = { v ∈ V n : v has weight i } {\displaystyle V_{n}(i)=\{v\in V_{n}:v{\text{ has weight }}i\}}
for 0 ≤ i ≤ n {\displaystyle 0\leq i\leq n} . These levels satisfy | V n ( i ) | = ( n i ) {\displaystyle |V_{n}(i)|=\textstyle {\binom {n}{i}}} . Let Q n ( i ) {\displaystyle Q_{n}(i)} be the subgraph of Q n {\displaystyle Q_{n}} induced by V n ( i ) ∪ V n ( i + 1 ) {\displaystyle V_{n}(i)\cup V_{n}(i+1)} , and let E n ( i ) {\displaystyle E_{n}(i)} be the edges in Q n ( i ) {\displaystyle Q_{n}(i)} . A monotonic Gray code is then a Hamiltonian path in Q n {\displaystyle Q_{n}} such that whenever δ 1 ∈ E n ( i ) {\displaystyle \delta _{1}\in E_{n}(i)} comes before δ 2 ∈ E n ( j ) {\displaystyle \delta _{2}\in E_{n}(j)} in the path, then i ≤ j {\displaystyle i\leq j} .
An elegant construction of monotonic n -digit Gray codes for any n is based on the idea of recursively building subpaths P n , j {\displaystyle P_{n,j}} of length 2 ( n j ) {\displaystyle 2\textstyle {\binom {n}{j}}} having edges in E n ( j ) {\displaystyle E_{n}(j)} . [ 69 ] We define P 1 , 0 = ( 0 , 1 ) {\displaystyle P_{1,0}=({\mathtt {0}},{\mathtt {1}})} , P n , j = ∅ {\displaystyle P_{n,j}=\emptyset } whenever j < 0 {\displaystyle j<0} or j ≥ n {\displaystyle j\geq n} , and
P n + 1 , j = 1 P n , j − 1 π n , 0 P n , j {\displaystyle P_{n+1,j}={\mathtt {1}}P_{n,j-1}^{\pi _{n}},{\mathtt {0}}P_{n,j}}
otherwise. Here, π n {\displaystyle \pi _{n}} is a suitably defined permutation and P π {\displaystyle P^{\pi }} refers to the path P with its coordinates permuted by π {\displaystyle \pi } . These paths give rise to two monotonic n -digit Gray codes G n ( 1 ) {\displaystyle G_{n}^{(1)}} and G n ( 2 ) {\displaystyle G_{n}^{(2)}} given by
G n ( 1 ) = P n , 0 P n , 1 R P n , 2 P n , 3 R ⋯ and G n ( 2 ) = P n , 0 R P n , 1 P n , 2 R P n , 3 ⋯ {\displaystyle G_{n}^{(1)}=P_{n,0}P_{n,1}^{R}P_{n,2}P_{n,3}^{R}\cdots {\text{ and }}G_{n}^{(2)}=P_{n,0}^{R}P_{n,1}P_{n,2}^{R}P_{n,3}\cdots }
The choice of π n {\displaystyle \pi _{n}} which ensures that these codes are indeed Gray codes turns out to be π n = E − 1 ( π n − 1 2 ) {\displaystyle \pi _{n}=E^{-1}\left(\pi _{n-1}^{2}\right)} . The first few values of P n , j {\displaystyle P_{n,j}} are shown in the table below.
These monotonic Gray codes can be efficiently implemented in such a way that each subsequent element can be generated in O ( n ) time. The algorithm is most easily described using coroutines .
Monotonic codes have an interesting connection to the Lovász conjecture , which states that every connected vertex-transitive graph contains a Hamiltonian path. The "middle-level" subgraph Q 2 n + 1 ( n ) {\displaystyle Q_{2n+1}(n)} is vertex-transitive (that is, its automorphism group is transitive, so that each vertex has the same "local environment" and cannot be differentiated from the others, since we can relabel the coordinates as well as the binary digits to obtain an automorphism ) and the problem of finding a Hamiltonian path in this subgraph is called the "middle-levels problem", which can provide insights into the more general conjecture. The question has been answered affirmatively for n ≤ 15 {\displaystyle n\leq 15} , and the preceding construction for monotonic codes ensures a Hamiltonian path of length at least 0.839 N , where N is the number of vertices in the middle-level subgraph. [ 70 ]
Another type of Gray code, the Beckett–Gray code , is named for Irish playwright Samuel Beckett , who was interested in symmetry . His play " Quad " features four actors and is divided into sixteen time periods. Each period ends with one of the four actors entering or leaving the stage. The play begins and ends with an empty stage, and Beckett wanted each subset of actors to appear on stage exactly once. [ 71 ] Clearly the set of actors currently on stage can be represented by a 4-bit binary Gray code. Beckett, however, placed an additional restriction on the script: he wished the actors to enter and exit so that the actor who had been on stage the longest would always be the one to exit. The actors could then be represented by a first in, first out queue , so that (of the actors onstage) the actor being dequeued is always the one who was enqueued first. [ 71 ] Beckett was unable to find a Beckett–Gray code for his play, and indeed, an exhaustive listing of all possible sequences reveals that no such code exists for n = 4. It is known today that such codes do exist for n = 2, 5, 6, 7, and 8, and do not exist for n = 3 or 4. An example of an 8-bit Beckett–Gray code can be found in Donald Knuth 's Art of Computer Programming . [ 13 ] According to Sawada and Wong, the search space for n = 6 can be explored in 15 hours, and more than 9500 solutions for the case n = 7 have been found. [ 72 ]
Snake-in-the-box codes, or snakes , are the sequences of nodes of induced paths in an n -dimensional hypercube graph , and coil-in-the-box codes, [ 73 ] or coils , are the sequences of nodes of induced cycles in a hypercube. Viewed as Gray codes, these sequences have the property of being able to detect any single-bit coding error. Codes of this type were first described by William H. Kautz in the late 1950s; [ 5 ] since then, there has been much research on finding the code with the largest possible number of codewords for a given hypercube dimension.
Yet another kind of Gray code is the single-track Gray code (STGC) developed by Norman B. Spedding [ 74 ] [ 75 ] and refined by Hiltgen, Paterson and Brandestini in Single-track Gray Codes (1996). [ 76 ] [ 77 ] The STGC is a cyclical list of P unique binary encodings of length n such that two consecutive words differ in exactly one position, and when the list is examined as a P × n matrix , each column is a cyclic shift of the first column. [ 78 ]
The name comes from their use with rotary encoders , where a number of tracks are being sensed by contacts, resulting for each in an output of 0 or 1 . To reduce noise due to different contacts not switching at exactly the same moment in time, one preferably sets up the tracks so that the data output by the contacts are in Gray code. To get high angular accuracy, one needs lots of contacts; in order to achieve at least 1° accuracy, one needs at least 360 distinct positions per revolution, which requires a minimum of 9 bits of data, and thus the same number of contacts.
If all contacts are placed at the same angular position, then 9 tracks are needed to get a standard BRGC with at least 1° accuracy. However, if the manufacturer moves a contact to a different angular position (but at the same distance from the center shaft), then the corresponding "ring pattern" needs to be rotated the same angle to give the same output. If the most significant bit (the inner ring in Figure 1) is rotated enough, it exactly matches the next ring out. Since both rings are then identical, the inner ring can be cut out, and the sensor for that ring moved to the remaining, identical ring (but offset at that angle from the other sensor on that ring). Those two sensors on a single ring make a quadrature encoder. That reduces the number of tracks for a "1° resolution" angular encoder to 8 tracks. Reducing the number of tracks still further cannot be done with BRGC.
For many years, Torsten Sillke [ 79 ] and other mathematicians believed that it was impossible to encode position on a single track such that consecutive positions differed at only a single sensor, except for the 2-sensor, 1-track quadrature encoder. So for applications where 8 tracks were too bulky, people used single-track incremental encoders (quadrature encoders) or 2-track "quadrature encoder + reference notch" encoders.
Norman B. Spedding, however, registered a patent in 1994 with several examples showing that it was possible. [ 74 ] Although it is not possible to distinguish 2 n positions with n sensors on a single track, it is possible to distinguish close to that many. Etzion and Paterson conjecture that when n is itself a power of 2, n sensors can distinguish at most 2 n − 2 n positions and that for prime n the limit is 2 n − 2 positions. [ 80 ] The authors went on to generate a 504-position single track code of length 9 which they believe is optimal. Since this number is larger than 2 8 = 256, more than 8 sensors are required by any code, although a BRGC could distinguish 512 positions with 9 sensors.
An STGC for P = 30 and n = 5 is reproduced here:
Each column is a cyclic shift of the first column, and from any row to the next row only one bit changes. [ 81 ] The single-track nature (like a code chain) is useful in the fabrication of these wheels (compared to BRGC), as only one track is needed, thus reducing their cost and size.
The Gray code nature is useful (compared to chain codes , also called De Bruijn sequences ), as only one sensor will change at any one time, so the uncertainty during a transition between two discrete states will only be plus or minus one unit of angular measurement the device is capable of resolving. [ 82 ]
Since this 30 degree example was added, there has been a lot of interest in examples with higher angular resolution. In 2008, Gary Williams, [ 83 ] [ user-generated source? ] based on previous work, [ 80 ] discovered a 9-bit single track Gray code that gives a 1 degree resolution. This Gray code was used to design an actual device which was published on the site Thingiverse . This device [ 84 ] was designed by etzenseep (Florian Bauer) in September 2022.
An STGC for P = 360 and n = 9 is reproduced here:
Two-dimensional Gray codes are used in communication to minimize the number of bit errors in quadrature amplitude modulation (QAM) adjacent points in the constellation . In a typical encoding the horizontal and vertical adjacent constellation points differ by a single bit, and diagonal adjacent points differ by 2 bits. [ 85 ]
Two-dimensional Gray codes also have uses in location identifications schemes, where the code would be applied to area maps such as a Mercator projection of the earth's surface and an appropriate cyclic two-dimensional distance function such as the Mannheim metric be used to calculate the distance between two encoded locations, thereby combining the characteristics of the Hamming distance with the cyclic continuation of a Mercator projection. [ 86 ]
If a subsection of a specific codevalue is extracted from that value, for example the last 3 bits of a 4-bit Gray code, the resulting code will be an "excess Gray code". This code shows the property of counting backwards in those extracted bits if the original value is further increased. Reason for this is that Gray-encoded values do not show the behaviour of overflow, known from classic binary encoding, when increasing past the "highest" value.
Example: The highest 3-bit Gray code, 7, is encoded as (0)100. Adding 1 results in number 8, encoded in Gray as 1100. The last 3 bits do not overflow and count backwards if you further increase the original 4 bit code.
When working with sensors that output multiple, Gray-encoded values in a serial fashion, one should therefore pay attention whether the sensor produces those multiple values encoded in 1 single Gray code or as separate ones, as otherwise the values might appear to be counting backwards when an "overflow" is expected.
The bijective mapping { 0 ↔ 00 , 1 ↔ 01 , 2 ↔ 11 , 3 ↔ 10 } establishes an isometry between the metric space over the finite field Z 2 2 {\displaystyle \mathbb {Z} _{2}^{2}} with the metric given by the Hamming distance and the metric space over the finite ring Z 4 {\displaystyle \mathbb {Z} _{4}} (the usual modular arithmetic ) with the metric given by the Lee distance . The mapping is suitably extended to an isometry of the Hamming spaces Z 2 2 m {\displaystyle \mathbb {Z} _{2}^{2m}} and Z 4 m {\displaystyle \mathbb {Z} _{4}^{m}} . Its importance lies in establishing a correspondence between various "good" but not necessarily linear codes as Gray-map images in Z 2 2 {\displaystyle \mathbb {Z} _{2}^{2}} of ring-linear codes from Z 4 {\displaystyle \mathbb {Z} _{4}} . [ 87 ] [ 88 ]
There are a number of binary codes similar to Gray codes, including:
The following binary-coded decimal (BCD) codes are Gray code variants as well: | https://en.wikipedia.org/wiki/RBC_(code) |
In organic chemistry , a nitrile is any organic compound that has a − C ≡ N functional group . The name of the compound is composed of a base, which includes the carbon of the −C≡N , suffixed with "nitrile", so for example CH 3 CH 2 C≡N is called " propionitrile " (or propanenitrile). [ 1 ] The prefix cyano - is used interchangeably with the term nitrile in industrial literature. Nitriles are found in many useful compounds, including methyl cyanoacrylate , used in super glue , and nitrile rubber , a nitrile-containing polymer used in latex-free laboratory and medical gloves . Nitrile rubber is also widely used as automotive and other seals since it is resistant to fuels and oils. Organic compounds containing multiple nitrile groups are known as cyanocarbons .
Inorganic compounds containing the −C≡N group are not called nitriles, but cyanides instead. [ 2 ] Though both nitriles and cyanides can be derived from cyanide salts, most nitriles are not nearly as toxic.
The N−C−C geometry is linear in nitriles, reflecting the sp hybridization of the triply bonded carbon. The C−N distance is short at 1.16 Å , consistent with a triple bond . [ 3 ] Nitriles are polar, as indicated by high dipole moments. As liquids, they have high relative permittivities , often in the 30s.
The first compound of the homolog row of nitriles, the nitrile of formic acid , hydrogen cyanide was first synthesized by C. W. Scheele in 1782. [ 4 ] [ 5 ] In 1811 J. L. Gay-Lussac was able to prepare the very toxic and volatile pure acid. [ 6 ] Around 1832 benzonitrile , the nitrile of benzoic acid , was prepared by Friedrich Wöhler and Justus von Liebig , but due to minimal yield of the synthesis neither physical nor chemical properties were determined nor a structure suggested. In 1834 Théophile-Jules Pelouze synthesized propionitrile , suggesting it to be an ether of propionic alcohol and hydrocyanic acid. [ 7 ] The synthesis of benzonitrile by Hermann Fehling in 1844 by heating ammonium benzoate was the first method yielding enough of the substance for chemical research.
Fehling determined the structure by comparing his results to the already known synthesis of hydrogen cyanide by heating ammonium formate . He coined the name "nitrile" for the newfound substance, which became the name for this group of compounds. [ 8 ]
Industrially, the main methods for producing nitriles are ammoxidation and hydrocyanation . Both routes are green in the sense that they do not generate stoichiometric amounts of salts.
In ammoxidation , a hydrocarbon is partially oxidized in the presence of ammonia . This conversion is practiced on a large scale for acrylonitrile : [ 9 ]
In the production of acrylonitrile, a side product is acetonitrile . On an industrial scale, several derivatives of benzonitrile , phthalonitrile , as well as Isobutyronitrile are prepared by ammoxidation. The process is catalysed by metal oxides and is assumed to proceed via the imine.
Hydrocyanation is an industrial method for producing nitriles from hydrogen cyanide and alkenes. The process requires homogeneous catalysts . An example of hydrocyanation is the production of adiponitrile , a precursor to nylon-6,6 from 1,3-butadiene :
Two salt metathesis reactions are popular for laboratory scale reactions. In the Kolbe nitrile synthesis , alkyl halides undergo nucleophilic aliphatic substitution with alkali metal cyanides . Aryl nitriles are prepared in the Rosenmund-von Braun synthesis .
In general, metal cyanides combine with alkyl halides to give a mixture of the nitrile and the isonitrile , although appropriate choice of counterion and temperature can minimize the latter. An alkyl sulfate obviates the problem entirely, particularly in nonaqueous conditions (the Pelouze synthesis). [ 5 ]
The cyanohydrins are a special class of nitriles. Classically they result from the addition of alkali metal cyanides to aldehydes in the cyanohydrin reaction . Because of the polarity of the organic carbonyl, this reaction requires no catalyst, unlike the hydrocyanation of alkenes. O-Silyl cyanohydrins are generated by the addition trimethylsilyl cyanide in the presence of a catalyst (silylcyanation). Cyanohydrins are also prepared by transcyanohydrin reactions starting, for example, with acetone cyanohydrin as a source of HCN. [ 10 ]
Nitriles can be prepared by the dehydration of primary amides . Common reagents for this include phosphorus pentoxide ( P 2 O 5 ) [ 11 ] and thionyl chloride ( SOCl 2 ). [ 12 ] In a related dehydration, secondary amides give nitriles by the von Braun amide degradation . In this case, one C-N bond is cleaved.
Numerous traditional methods exist for nitrile preparation by amine oxidation. [ 13 ] Common methods include the use of potassium persulfate , [ 14 ] Trichloroisocyanuric acid , [ 15 ] or anodic electrosynthesis . [ 16 ] In addition, several selective methods have been developed in the last decades for electrochemical processes. [ 17 ]
The conversion of aldehydes to nitriles via aldoximes is a popular laboratory route. Aldehydes react readily with hydroxylamine salts, sometimes at temperatures as low as ambient, to give aldoximes. These can be dehydrated to nitriles by simple heating, [ 18 ] although a wide range of reagents may assist with this, including triethylamine / sulfur dioxide , zeolites , or sulfuryl chloride . The related hydroxylamine-O-sulfonic acid reacts similarly. [ 19 ]
In specialised cases the Van Leusen reaction can be used. Biocatalysts such as aliphatic aldoxime dehydratase are also effective.
Aromatic nitriles are often prepared in the laboratory from the aniline via diazonium compounds . This is the Sandmeyer reaction . It requires transition metal cyanides. [ 20 ]
Nitrile groups in organic compounds can undergo a variety of reactions depending on the reactants or conditions. A nitrile group can be hydrolyzed, reduced, or ejected from a molecule as a cyanide ion.
The hydrolysis of nitriles RCN proceeds in the distinct steps under acid or base treatment to first give carboxamides RC(O)NH 2 and then carboxylic acids RC(O)OH . The hydrolysis of nitriles to carboxylic acids is efficient. In acid or base, the balanced equations are as follows:
Strictly speaking, these reactions are mediated (as opposed to catalyzed ) by acid or base, since one equivalent of the acid or base is consumed to form the ammonium or carboxylate salt, respectively.
Kinetic studies show that the second-order rate constant for hydroxide-ion catalyzed hydrolysis of acetonitrile to acetamide is 1.6 × 10 −6 M −1 s −1 , which is slower than the hydrolysis of the amide to the carboxylate (7.4 × 10 −5 M −1 s −1 ). Thus, the base hydrolysis route will afford the carboxylate (or the amide contaminated with the carboxylate). On the other hand, the acid catalyzed reactions requires a careful control of the temperature and of the ratio of reagents in order to avoid the formation of polymers, which is promoted by the exothermic character of the hydrolysis. [ 28 ] The classical procedure to convert a nitrile to the corresponding primary amide calls for adding the nitrile to cold concentrated sulfuric acid . [ 29 ] The further conversion to the carboxylic acid is disfavored by the low temperature and low concentration of water.
Two families of enzymes catalyze the hydrolysis of nitriles. Nitrilases hydrolyze nitriles to carboxylic acids:
Nitrile hydratases are metalloenzymes that hydrolyze nitriles to amides.
These enzymes are used commercially to produce acrylamide .
The "anhydrous hydration" of nitriles to amides has been demonstrated using an oxime as water source: [ 30 ]
Nitriles are susceptible to hydrogenation over diverse metal catalysts. The reaction can afford either the primary amine ( RCH 2 NH 2 ) or the tertiary amine ( (RCH 2 ) 3 N ), depending on conditions. [ 31 ] In conventional organic reductions , nitrile is reduced by treatment with lithium aluminium hydride to the amine. Reduction to the imine followed by hydrolysis to the aldehyde takes place in the Stephen aldehyde synthesis , which uses stannous chloride in acid.
Alkyl nitriles are sufficiently acidic to undergo deprotonation of the C-H bond adjacent to the C≡N group. [ 32 ] [ 33 ] Strong bases are required, such as lithium diisopropylamide and butyl lithium . The product is referred to as a nitrile anion . These carbanions alkylate a wide variety of electrophiles. Key to the exceptional nucleophilicity is the small steric demand of the C≡N unit combined with its inductive stabilization. These features make nitriles ideal for creating new carbon-carbon bonds in sterically demanding environments.
The carbon center of a nitrile is electrophilic , hence it is susceptible to nucleophilic addition reactions:
Nitriles are precursors to transition metal nitrile complexes , which are reagents and catalysts. Examples include tetrakis(acetonitrile)copper(I) hexafluorophosphate ( [Cu(MeCN) 4 ] + ) and bis(benzonitrile)palladium dichloride ( PdCl 2 (PhCN) 2 ). [ 40 ]
Cyanamides are N -cyano compounds with general structure R 1 R 2 N−C≡N and related to the parent cyanamide . [ 41 ]
Nitrile oxides have the chemical formula RCNO . Their general structure is R−C≡N + −O − . The R stands for any group (typically organyl , e.g., acetonitrile oxide CH 3 −C≡N + −O − , hydrogen in the case of fulminic acid H−C≡N + −O − , or halogen (e.g., chlorine fulminate Cl−C≡N + −O − ). [ 42 ] : 1187–1192
Nitrile oxides are quite different from nitriles: they are highly reactive 1,3-dipoles , and cannot be synthesized from the direct oxidation of nitriles. [ 43 ] Instead, they can be synthesised by nitroalkane dehydration, oxime dehydrogenation, [ 44 ] : 934–936 or halooxime elimination in base. [ 45 ] They are used in 1,3-dipolar cycloadditions , [ 42 ] : 1187–1192 such as to isoxazoles . [ 44 ] : 1201–1202 They undergo type 1 dyotropic rearrangement to isocyanates . [ 42 ] : 1700
The heavier nitrile sulfides are extremely reactive and rare, but temporarily form during the thermolysis of oxathiazolones . They react similarly to nitrile oxides. [ 46 ]
Nitriles occur naturally in a diverse set of plant and animal sources. Over 120 naturally occurring nitriles have been isolated from terrestrial and marine sources. Nitriles are commonly encountered in fruit pits, especially almonds, and during cooking of Brassica crops (such as cabbage, Brussels sprouts, and cauliflower), which release nitriles through hydrolysis. Mandelonitrile , a cyanohydrin produced by ingesting almonds or some fruit pits, releases hydrogen cyanide and is responsible for the toxicity of cyanogenic glycosides. [ 47 ]
Over 30 nitrile-containing pharmaceuticals are currently marketed for a diverse variety of medicinal indications with more than 20 additional nitrile-containing leads in clinical development. The types of pharmaceuticals containing nitriles are diverse, from vildagliptin , an antidiabetic drug, to anastrozole , which is the gold standard in treating breast cancer. In many instances the nitrile mimics functionality present in substrates for enzymes, whereas in other cases the nitrile increases water solubility or decreases susceptibility to oxidative metabolism in the liver. [ 48 ] The nitrile functional group is found in several drugs. | https://en.wikipedia.org/wiki/RC≡N |
RDKit is open-source toolkit for cheminformatics . It was developed by Greg Landrum with numerous additional contributions from the RDKit open source community. It has an application programming interface (API) for Python , Java , C++ , and C# . [ 1 ] | https://en.wikipedia.org/wiki/RDKit |
RDS03-94 , or RDS3-094 , is an atypical dopamine reuptake inhibitor that was derived from the wakefulness-promoting agent modafinil . [ 1 ] [ 2 ] [ 3 ] [ 4 ]
It has substantially higher affinity and potency in terms of dopamine transporter (DAT) inhibition than modafinil (K i = 39.4 nM vs. 8,160 nM) whilst retaining the atypical DAT blocker profile of modafinil. [ 1 ] [ 2 ] However, RDS03-94 also has high affinity for the sigma σ 1 receptor (K i = 2.19 nM). [ 2 ]
RDS03-94 shows some reversal of tetrabenazine -induced motivational deficits in animals and hence may have the capacity to produce pro-motivational effects. [ 5 ] [ 6 ] However, it appears to be less effective than certain other related agents, like JJC8-088 . [ 6 ] [ 5 ]
RDS03-94 is under development for the treatment of psychostimulant use disorder . [ 1 ] The drug was first described in the scientific literature in 2020. [ 1 ] [ 2 ]
This drug article relating to the nervous system is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RDS03-94 |
RDX ( Research Department Explosive or Royal Demolition Explosive ) or hexogen , [ 4 ] among other names, is an organic compound with the formula (CH 2 N 2 O 2 ) 3 . It is white, odorless, and tasteless, widely used as an explosive . [ 5 ] Chemically, it is classified as a nitroamine alongside HMX , which is a more energetic explosive than TNT . It was used widely in World War II and remains common in military applications .
RDX is often used in mixtures with other explosives and plasticizers or phlegmatizers (desensitizers); it is the explosive agent in C-4 plastic explosive and a key ingredient in Semtex . It is stable in storage and is considered one of the most energetic and brisant of the military high explosives , [ 2 ] with a relative effectiveness factor of 1.60.
RDX is also less commonly known as cyclonite , hexogen (particularly in Russian, French and German-influenced languages), T4 , and, chemically, as cyclotrimethylene trinitramine . [ 6 ] In the 1930s, the Royal Arsenal , Woolwich , started investigating cyclonite to use against German U-boats that were being built with thicker hulls. The goal was to develop an explosive more energetic than TNT . For security reasons, Britain termed cyclonite "Research Department Explosive" (R.D.X.). [ 7 ] The term RDX appeared in the United States in 1946. [ 8 ] The first public reference in the United Kingdom to the name RDX , or R.D.X. , to use the official title, appeared in 1948; its authors were the managing chemist, ROF Bridgwater , the chemical research and development department, Woolwich, and the director of Royal Ordnance Factories , Explosives. [ 9 ]
RDX was widely used during World War II , often in explosive mixtures with TNT such as Torpex , Composition B , Cyclotols, and H6. RDX was used in one of the first plastic explosives . The bouncing bomb depth charges used in the " Dambusters Raid " each contained 6,600 pounds (3,000 kg) of Torpex; [ 10 ] The Tallboy and Grand Slam bombs designed by Barnes Wallis also used Torpex.
RDX is believed to have been used in many bomb plots, including terrorist plots.
RDX is the base for a number of common military explosives:
Outside military applications, RDX is also used in controlled demolition to raze structures. [ 20 ] The demolition of the Jamestown Bridge in the U.S. state of Rhode Island was one instance where RDX shaped charges were used to remove the span. [ 21 ]
RDX is classified by chemists as a hexahydro-1,3,5-triazine derivative. In laboratory settings (industrial routes are described below separately) it is obtained by treating hexamine with white fuming nitric acid . [ 22 ]
This nitrolysis reaction also produces methylene dinitrate, ammonium nitrate , and water as by-products. The overall reaction is: [ 22 ]
The conventional cheap nitration agent, called "mixed acid", cannot be used for RDX synthesis because concentrated sulfuric acid conventionally used to stimulate the nitronium ion formation decomposes hexamine into formaldehyde and ammonia.
Modern syntheses employ hexahydro triacyl triazine as it avoids formation of HMX. [ 23 ]
RDX was used by both sides in World War II . The US produced about 15,000 long tons (15,000 t) per month during WWII and Germany about 7,100 tonnes (7,000 long tons) per month. [ 24 ] RDX had the major advantages of possessing greater explosive force than TNT and required no additional raw materials for its manufacture. Thus, it was also extensively used in World War I [ 24 ]
RDX was reported in 1898 by Georg Friedrich Henning (1863-1945), who obtained a German patent [ 25 ] for its manufacture by nitrolysis of hexamine ( hexamethylenetetramine ) with concentrated nitric acid. [ 26 ] In this patent, only the medical properties of RDX were mentioned. [ 26 ]
During WWI , Heinrich Brunswig (1865-1946) at the private military-industrial laboratory Zentralstelle für wissenschaftlich-technische Untersuchungen [ de ] (Center for Scientific-Technical Research) in Neubabelsberg studied the compound more closely and in June 1916 filed two patent applications, one for its use in smokeless propellants [ 27 ] and another for its use as an explosive, noting its excellent characteristics. [ 28 ] [ 29 ] The German military hadn't considered its adoption during the war due to the expense of production [ 30 ] but started investigating its use in 1920, referring to it as hexogen. [ 31 ]
Research and development findings were not published further until Edmund von Herz, [ 32 ] described as an Austrian and later a German citizen, rediscovered the explosive properties of RDX [ 30 ] and applied for an Austrian patent in 1919, obtaining a British one in 1921 [ 33 ] and an American one in 1922. [ 34 ] All patents described the synthesis of the compound by nitrating hexamethylenetetramine . [ 33 ] [ 34 ] The British patent claims included the manufacture of RDX by nitration, its use with or without other explosives, its use as a bursting charge and as an initiator. [ 33 ] The US patent claim was for the use of a hollow explosive device containing RDX and a detonator cap containing it. [ 34 ] Herz was also the first to identify the cyclic nature of the molecule. [ 30 ]
In the 1930s, Germany developed improved production methods. [ 31 ]
During World War II, Germany used the code names W Salt, SH Salt, K-method, the E-method, and the KA-method. These names represented the identities of the developers of the various chemical routes to RDX. The W-method was developed by Wolfram in 1934 and gave RDX the code name "W-Salz". It used sulfamic acid , formaldehyde, and nitric acid. [ 35 ] SH-Salz (SH salt) was from Schnurr, who developed a batch-process in 1937–38 based on nitrolysis of hexamine. [ 36 ] The K-method, from Knöffler, involved addition of ammonium nitrate to the hexamine/nitric acid process. [ 37 ] The E-method, developed by Ebele, proved to be identical to the Ross and Schiessler process described below. [ 38 ] The KA-method, also developed by Knöffler, turned out to be identical to the Bachmann process described below. [ 39 ]
The explosive shells fired by the MK 108 cannon and the warhead of the R4M rocket , both used in Luftwaffe fighter aircraft as offensive armament, both used hexogen as their explosive base. [ 40 ]
In the United Kingdom (UK), RDX was manufactured from 1933 by the research department in a pilot plant at the Royal Arsenal in Woolwich, London , a larger pilot plant being built at the RGPF Waltham Abbey just outside London in 1939. [ 41 ] [ 42 ] In 1939 a twin-unit industrial-scale plant was designed to be installed at a new 700-acre (280 ha) site, ROF Bridgwater , away from London and production of RDX started at Bridgwater on one unit in August 1941. [ 41 ] [ 43 ] The ROF Bridgwater plant brought in ammonia and methanol as raw materials: the methanol was converted to formaldehyde and some of the ammonia converted to nitric acid, which was concentrated for RDX production. [ 9 ] The rest of the ammonia was reacted with formaldehyde to produce hexamine. The hexamine plant was supplied by Imperial Chemical Industries . It incorporated some features based on data obtained from the United States (US). [ 9 ] RDX was produced by continually adding hexamine and concentrated nitric acid to a cooled mixture of hexamine and nitric acid in the nitrator. [ 9 ] The RDX was purified and processed for its intended use; recovery and reuse of some methanol and nitric acid also was carried out. [ 9 ] The hexamine-nitration and RDX purification plants were duplicated (i.e. twin-unit) to provide some insurance against loss of production due to fire, explosion, or air attack. [ 41 ]
The United Kingdom and British Empire were fighting without allies against Nazi Germany until the middle of 1941 and had to be self-sufficient . At that time (1941), the UK had the capacity to produce 70 long tons (71 t) (160,000 lb) of RDX per week; both Canada , an allied country and self-governing dominion within the British Empire, and the US were looked upon to supply ammunition and explosives, including RDX. [ 44 ] By 1942 the Royal Air Force 's annual requirement was forecast to be 52,000 long tons (53,000 t) of RDX, much of which came from North America (Canada and the US). [ 43 ]
A different method of production to the Woolwich process was found and used in Canada, possibly at the McGill University department of chemistry. This was based on reacting paraformaldehyde and ammonium nitrate in acetic anhydride . [ 45 ] A UK patent application was made by Robert Walter Schiessler (Pennsylvania State University) and James Hamilton Ross (McGill, Canada) in May 1942; the UK patent was issued in December 1947. [ 46 ] Gilman states that the same method of production had been independently discovered by Ebele in Germany prior to Schiessler and Ross, but that this was not known by the Allies. [ 26 ] [ 45 ] Urbański provides details of five methods of production, and he refers to this method as the (German) E-method. [ 38 ]
At the beginning of the 1940s, the major US explosive manufacturers, E. I. du Pont de Nemours & Company and Hercules , had several decades of experience of manufacturing trinitrotoluene (TNT) and had no wish to experiment with new explosives. US Army Ordnance held the same viewpoint and wanted to continue using TNT. [ 47 ] RDX had been tested by Picatinny Arsenal in 1929, and it was regarded as too expensive and too sensitive. [ 44 ] The Navy proposed to continue using ammonium picrate . [ 47 ] In contrast, the National Defense Research Committee (NDRC), who had visited The Royal Arsenal, Woolwich, thought new explosives were necessary. [ 47 ] James B. Conant , chairman of Division B, wished to involve academic research into this area. Conant therefore set up an experimental explosives research laboratory at the Bureau of Mines , Bruceton, Pennsylvania , using Office of Scientific Research and Development (OSRD) funding. [ 44 ]
In 1941, the UK's Tizard Mission visited the US Army and Navy departments and part of the information handed over included details of the "Woolwich" method of manufacture of RDX and its stabilisation by mixing it with beeswax . [ 44 ] The UK was asking that the US and Canada, combined, supply 220 short tons (200 t) (440,000 lb) of RDX per day. [ 44 ] A decision was taken by William H. P. Blandy , chief of the Bureau of Ordnance , to adopt RDX for use in mines and torpedoes . [ 44 ] Given the immediate need for RDX, the US Army Ordnance, at Blandy's request, built a plant that copied the equipment and process used at Woolwich. The result was the Wabash River Ordnance Works run by E. I. du Pont de Nemours & Company. [ 48 ] At that time, this works had the largest nitric acid plant in the world. [ 44 ] The Woolwich process was expensive: it needed 11 pounds (5.0 kg) of strong nitric acid for every pound of RDX produced. [ 49 ]
By early 1941, the NDRC was researching new processes. [ 49 ] The Woolwich or direct nitration process has at least two serious disadvantages: (1) it used large amounts of nitric acid and (2) at least one-half of the formaldehyde is lost. One mole of hexamethylenetetramine could produce at most one mole of RDX. [ 50 ] At least three laboratories with no previous explosive experience were instructed to develop better production methods for RDX; they were based at Cornell , Michigan , and Pennsylvania State universities. [ 44 ] [ a ] Werner Emmanuel Bachmann , from Michigan, successfully developed the "combination process" by combining the Ross and Schiessler process used in Canada (aka the German E-method) with direct nitration. [ 39 ] [ 44 ] The combination process required large quantities of acetic anhydride instead of nitric acid in the old British "Woolwich process". Ideally, the combination process could produce two moles of RDX from each mole of hexamethylenetetramine. [ 50 ]
The expanded production of RDX could not continue to rely on the use of natural beeswax to desensitize the explosive as in the original British composition (RDX/BWK-91/9). A substitute stabilizer based on petroleum was developed at the Bruceton Explosives Research Laboratory in Pennsylvania, with the resulting explosive designated Composition A-3. [ 44 ] [ 51 ]
The National Defence Research Committee (NDRC) instructed three companies to develop pilot plants. They were the Western Cartridge Company, E. I. du Pont de Nemours & Company, and Tennessee Eastman Company , part of Eastman Kodak. [ 44 ] At the Eastman Chemical Company (TEC), a leading manufacturer of acetic anhydride, Werner Emmanuel Bachmann developed a continuous-flow process for RDX utilizing an ammonium nitrate/nitric acid mixture as a nitrating agent in a medium of acetic acid and acetic anhydride. RDX was crucial to the war effort and the current batch-production process was too slow. In February 1942, TEC began producing small amounts of RDX at its Wexler Bend pilot plant, which led to the US government authorizing TEC to design and build Holston Ordnance Works (H.O.W.) in June 1942. By April 1943, RDX was being manufactured there. [ 52 ] At the end of 1944, the Holston plant and the Wabash River Ordnance Works , which used the Woolwich process, were producing 25,000 short tons (23,000 t) (50 million pounds) of Composition B per month. [ 53 ]
The Bachmann process yields both RDX and HMX , with the major product determined by the specific reaction conditions. [ 54 ]
The United Kingdom's intention in World War II was to use "desensitised" RDX. In the original Woolwich process, RDX was phlegmatized with beeswax, but later paraffin wax was used, based on the work carried out at Bruceton. In the event the UK was unable to obtain sufficient RDX to meet its needs, some of the shortfall was met by substituting amatol , a mixture of ammonium nitrate and TNT. [ 43 ]
Karl Dönitz was reputed to have claimed that "an aircraft can no more kill a U-boat than a crow can kill a mole ". [ 55 ] Nonetheless, by May 1942 Wellington bombers began to deploy depth charges containing Torpex , a mixture of RDX, TNT, and aluminium, which had up to 50 percent more destructive power than TNT-filled depth charges. [ 55 ] Considerable quantities of the RDX–TNT mixture were produced at the Holston Ordnance Works, with Tennessee Eastman developing an automated mixing and cooling process based around the use of stainless steel conveyor belts . [ 56 ]
A Semtex bomb was used in the Pan Am Flight 103 (known also as the Lockerbie) bombing in 1988. [ 57 ] A belt laden with 700 g (1.5 lb) of RDX explosives tucked under the dress of the assassin was used in the assassination of former Indian prime minister Rajiv Gandhi in 1991. [ 58 ] The 1993 Bombay bombings used RDX placed into several vehicles as bombs. RDX was the main component used for the 2006 Mumbai train bombings and the Jaipur bombings in 2008. [ 59 ] [ 60 ] It also is believed to be the explosive used in the 2010 Moscow Metro bombings . [ 61 ]
Traces of RDX were found on pieces of wreckage from 1999 Russian apartment bombings [ 62 ] [ 63 ] and 2004 Russian aircraft bombings . [ 64 ] FSB reports on the bombs used in the 1999 apartment bombings indicated that while RDX was not a part of the main charge, each bomb contained plastic explosive used as a booster charge . [ 65 ] [ 66 ]
Ahmed Ressam , the al-Qaeda Millennium Bomber , used a small quantity of RDX as one of the components in the bomb that he prepared to detonate in Los Angeles International Airport on New Year's Eve 1999–2000; the bomb could have produced a blast forty times greater than that of a devastating car bomb . [ 67 ] [ 68 ]
In July 2012, the Kenyan government arrested two Iranian nationals and charged them with illegal possession of 15 kilograms (33 pounds) of RDX. According to the Kenyan Police , the Iranians planned to use the RDX for "attacks on Israeli, US, UK and Saudi Arabian targets". [ 69 ]
RDX was used in the assassination of Lebanese Prime Minister Rafic Hariri on February 14, 2005. [ 70 ]
In the 2019 Pulwama attack in India, 250 kg of high-grade RDX was used by Jaish-e-Mohammed . The attack resulted in the deaths of 44 Central Reserve Police Force (CRPF) personnel as well as the attacker. [ 71 ]
Two letter bombs sent to journalists in Ecuador were disguised as USB flash drives which contained RDX that would detonate when plugged in. [ 72 ]
RDX has a high nitrogen content and a high oxygen to carbon ratio, (O:C ratio), both of which indicate its explosive potential for formation of N 2 and CO 2 .
RDX undergoes a deflagration to detonation transition (DDT) in confinement and certain circumstances. [ 73 ]
The velocity of detonation of RDX at a density of 1.80 g/cm 3 is 8750 m/s. [ 74 ] [ page needed ]
It starts to decompose at approximately 170 °C and melts at 204 °C. At room temperature , it is very stable. It burns rather than explodes. It detonates only with a detonator , being unaffected even by small arms fire. This property makes it a useful military explosive. It is less sensitive than pentaerythritol tetranitrate ( PETN ). Under normal conditions, RDX has a Figure of Insensitivity of exactly 80 (RDX defines the reference point). [ 75 ] [ page needed ]
RDX sublimes in vacuum , which restricts or prevents its use in some applications. [ 76 ]
RDX, when exploded in air, has about 1.5 times the explosive energy of TNT per unit weight and about 2.0 times per unit volume. [ 56 ] [ 77 ]
RDX is insoluble in water, with solubility 0.05975 g/L at temperature of 25 °C. [ 78 ]
The substance's toxicity has been studied for many years. [ 79 ] RDX has caused convulsions (seizures) in military field personnel ingesting it, and in munition workers inhaling its dust during manufacture. At least one fatality was attributed to RDX toxicity in a European munitions manufacturing plant. [ 80 ]
During the Vietnam War , at least 40 American soldiers were hospitalized with composition C-4 (which is 91% RDX) intoxication from December 1968 to December 1969. C-4 was frequently used by soldiers as a fuel to heat food, and the food was generally mixed by the same knife that was used to cut C-4 into small pieces prior to burning. Soldiers were exposed to C-4 either due to inhaling the fumes, or due to ingestion, made possible by many small particles adhering to the knife having been deposited into the cooked food. The symptom complex involved nausea, vomiting, generalized seizures, and prolonged postictal confusion and amnesia; which indicated toxic encephalopathy . [ 81 ]
Oral toxicity of RDX depends on its physical form; in rats, the LD50 was found to be 100 mg/kg for finely powdered RDX, and 300 mg/kg for coarse, granular RDX. [ 80 ] A case has been reported of a human child hospitalized in status epilepticus following the ingestion of 84.82 mg/kg dose of RDX (or 1.23 g for the patient's body weight of 14.5 kg) in the "plastic explosive" form. [ 82 ]
The substance has low to moderate toxicity with a possible human carcinogen classification. [ 83 ] [ 84 ] [ 85 ] Further research is ongoing, however, and this classification may be revised by the United States Environmental Protection Agency (EPA). [ 86 ] [ 87 ] Remediating RDX-contaminated water supplies has proven to be successful. [ 88 ] It is known to be a kidney toxin in humans and highly toxic to earthworms and plants, thus army testing ranges where RDX was used heavily may need to undergo environmental remediation. [ 89 ] Concerns have been raised by research published in late 2017 indicating that the issue has not been addressed correctly by U.S. officials. [ 90 ]
RDX has been used as a rodenticide because of its toxicity. [ 91 ]
RDX is degraded by the organisms in sewage sludge as well as the fungus Phanaerocheate chrysosporium . [ 92 ] Both wild and transgenic plants can phytoremediate explosives from soil and water. [ 93 ] [ 94 ] One by-product of the environmental decomposition is R-salt . [ 95 ]
FOX-7 is considered to be approximately a 1-to-1 replacement for RDX in almost all applications. [ 96 ] [ 97 ] | https://en.wikipedia.org/wiki/RDX |
rDock (previously RiboDock ) is an open-source molecular docking software that be used for docking small molecules against proteins and nucleic acids. It is primarily designed for high-throughput virtual screening and prediction of binding mode.
The development of rDock started in 1998 in RiboTargets (later Vernalis (R&D) Ltd ). [ 1 ] The software was originally called RiboDock. [ 2 ] The development went on until 2006 when the software was licensed to University of York for academic distribution and also maintenance.
Six years later, in 2012, Vernalis and University of York decided to release rDock as open-source software to allow its further development by the wider community. The version that was released as open source is developed and supported by University of Barcelona on SourceForge . [ 3 ] The development on SourceForge stalled after June 2014 and the repository is considered deprecated after the migration to GitHub . [ 4 ] [ 5 ]
A fork named RxDock continued the development of rDock from April 2019 until March 2022 on GitLab . [ 6 ] [ 7 ] [ 8 ] As of April 2022, the RxDock project development activity is very low. [ 9 ]
This scientific software article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RDock |
The authorisation procedure is one of the regulatory tools of the European regulation (EC) REACH n°1907/2006 aiming to ban the use of substances of very high concern ( SVHC ) included in the Annex XIV of REACH, so as to replace them with technically and economically feasible alternatives.
This process concerns manufacturers, importers and downstream users of substances. Only representatives of foreign manufacturers can also apply for an authorisation.
Authorisation today impacts many industries, including the aerospace , electronics , automotive , energy , and paint industries. Moreover, defence applications are not de facto exempted from the authorisation process. Member states must decide on a case by case basis whether a company can benefit or not from this procedure (outlined in article 2.3 of REACH).
The REACh [ 1 ] regulation relies on four main procedures: [ 2 ] registration, evaluation, restriction and authorisation of chemical substances .
EU Member States or the European Chemicals Agency , on request of the European Commission , can submit propositions to identify Substances of Very High Concern , based on the criteria laid down in article 57 of REACH:
This work is supported by Expert Groups of ECHA and the EU Member States [ 3 ] and is based on various criteria and screening methodologies in order to identify the most relevant SVHCs. [ 4 ]
Annex XIV is the last step of this prioritisation process. It lists SVHCs which exhibit a particularly high risk for human health or the environment (based on their inherent properties, quantities and uses) in order to forbid their use in the EU market.
Recommendations [ 5 ] to include SVHCs in the Annex XIV are made by ECHA and are debated by all relevant stakeholders (Member States, companies, NGOs, etc.). The final decision of inclusion of the substance into Annex XIV is taken by the European Commission.
When listed in Annex XIV of the REACh regulation, a substance is therefore assigned a “sunset date” after which its use will be banned, unless an Authorisation is granted for a definite period of time.
As of today (2022/03/02), 223 substances are listed on the Candidate List [ 6 ] and 54 substances (date 2022/03/02) are listed in the Annex XIV. [ 7 ] The candidate list is usually updated every 6 months and the Annex XIV is updated every 12 to 18 months.
The authorisation procedure is complex and concerns manufacturers , importers, downstream users and Only Representatives of substances [ 8 ] for which:
The banning of the use takes effect at the "Sunset date". As of this date, the use of the substance is only possible for companies which have been granted an authorisation or for those that have submitted their dossier before the Latest Application Date. The latter indeed benefit from a transitional period, pending the EU Commission final decision.
An exception is made for downstream users in the case where an upstream stakeholder, within the supply chain , has been granted an authorisation for this very substance and this very use. From this point of view, it is the supply chain of the substance that matters. For instance, subcontractors of authorised importers will not be covered if the Annex XIV substance they use is supplied via a supply chain for which no authorisation application has been made or granted.
Finally, downstream users that do not need to apply for an authorisation nevertheless have the obligation to notify their use(s) to ECHA (art. 66 of REACH) and check the compliance of their risk management measures.
Concerned companies are thus invited to take measures as soon as a substance they use enters the Candidate list by enquiring on the impacted actors and their strategies.
Source: [ 9 ]
Authorisation applications are made for one or several specific uses. Article 3 of REACH thus defines a “use” as: “ any processing, formulation, consumption, storage, keeping, treatment, filling into containers, transfer from one container to another, mixing, production of an article or any other use ”.
In the framework of an authorisation dossier, the description of the use applied for has to specify the market, the supply chain, processes or the type of articles concerned. The use applied for has to be consistent enough to cover the Exposure Scenario but also the Analysis of Alternatives. The Use applied for should not be mistaken with the identified use which corresponds to the REACH registration process. An identified use focuses on the process and does not consider performances or markets questions.
A few exceptions exist, for which the application for authorisation is not required:
If the production of an article may require an authorisation at some point, finished articles themselves do not require an authorisation to be put on the market, even though they still contain a substance subject to authorisation. Consequently, articles requiring the use of an Annex XIV substance can still be produced outside the EU and then imported. In that particular case, future restrictions procedure could however limit the placing on the market of such articles if a risk remains (art. 58.6 of REACH).
Source: [ 10 ]
The review period is the duration for which the EU Commission authorises the use of a substance after the Sunset date.
Following durations are considered for the review periods:
At the end of the review period, the application for authorisation is reassessed to evaluate the progress made in terms or research & development or substitution. Applications to extend the review period have to be made at the latest 18 months before the expiry date.
The European Commission may also reduce this duration if new circumstances appear, in terms of risks or impacts.
Only the Court of the European Union is qualified to rule on appeals for applications for authorisation. Member States are, in turn, responsible for controlling the decision's implementation.
The application for authorisation (AfA) is made up of three main parts: the Chemical Safety Report (CSR), the Analysis of Alternatives (AoA) and the Socio-Economic Analysis (SEA).
The goal of this dossier is to demonstrate that no alternative substance is immediately available, that risks are controlled and that the social and economic advantages of the use of the substance outweigh the risks to human health or the environment. The dossier usually takes 6 to 18 months of preparation and ECHA's guidelines [ 11 ] are available to assist with its drafting.
The application for authorisation should be filed before the Latest Application Date (LAD), set at 18 months before the sunset date. The LAD enables to benefit from a transitional period, pending the European Commission's decision.
An AfA can be made for one or several substances (in that case, grouping will need to be demonstrated on the basis of annex XI of REACH [ 12 ] [ 13 ] ), one or several uses applied for and by one or several companies. The latter case is called a joint application and it requires appointing a main applicant that will be the contact point for ECHA.
Two submission routes are planned by the REACh regulation:
For the adequate control route, the goal of the Chemical Safety Report is to prove that threshold values are respected; for the socio-economic route, the goal of the Chemical Safety Report is to demonstrate that risks are reduced to the minimum.
The Chemical Safety Report contains:
The AoA aims to demonstrate that no alternative is appropriate, i.e. technically and / or economically feasible, less risky and available.
The Analysis of Alternatives therefore presents all the substance's alternative solutions and contains:
The Socio-Economic Analysis is a compulsory document for the socio-economic route and can also complete an application justified by the adequate control route. It aims to demonstrate that the advantages of the use of the substance outweigh the risks to human health or the environment. For this purpose, applicants must compare two scenarios: the ‘use scenario’ (continued use of the substance) on the one hand and the ‘non-use scenario’ (cease of use of the substance) on the other hand to discuss their impacts.
It contains:
Dossiers should be submitted during submission windows in February, May, August and November. [ 14 ] ECHA strongly advise to follow these windows as plenary sessions of the two committees (RAC and SEAC) are organised in March, June, September and December of each year. Submitting before the plenary sessions, during the submission windows, therefore helps the efficient assessment of the application.
Applications are deemed received after business rules check is successfully passed and provided ECHA fees [ 15 ] are paid on time.
The examination of the dossier is carried out by the Risk Assessment Committee (RAC) and the Socio-Economic Analysis Committee (SEAC) and opens with a public consultation on alternatives. During 8 weeks, companies, NGOs or any other interested party have the possibility to comment on and possibly challenge the alternatives proposed by the applicant.
The consultation can be followed by additional discussions with the two Committees in order to clarify the application. This process is called Trialogue and stakeholders can be invited to participate. [ 16 ]
Duration of the examination varies according to the complexity and the clarity of the dossier. Committees however have the obligation to deliver their first opinion on the dossier 10 months after its submission at the latest. The dossier with the Committee's opinion is then sent to the Commission. The whole process can take up to 2 years.
As of May 4, 2015, [ 17 ] [ 18 ] 28 applications for authorisation had been filed for a total of 56 uses.
Each dossier requires implementing a specific strategy, being it to define the uses, the analysis of the industrial processes and associated risks, the alternatives, or the socio-economic impacts of the banning of the substance.
Committees expect each dossier to contain a precise description of the industrial process and the operational conditions that are representative of the dossier as well as the risk management measures implemented by the applicant [ 19 ]
The main issue in the application for authorisation process is the duration of the review period which will be granted. It is therefore critical to bring all the necessary precisions to the dossiers to justify the requested review period duration. A justification that is too weak or an argumentation that is too generic may induce the granting of a shorter-than-requested review period. [ 20 ]
Beyond the simple drafting of the application for authorisation dossier, the whole process implies both expertise [ 21 ] and deep analysis of a company's activity, on multiple aspects:
This analysis therefore requires an extensive collection of information and also, possibly, contacts with customers so as to strengthen the analysis of alternatives.
Public consultation is one of the core mechanisms of the authorisation process. Stakeholders’ (competing companies, universities, laboratories, NGOS, Member States, etc.) involvement in the consultation process has been growing over the last years (to reach up to 400 comments for a single dossier [ 17 ] ) and the influence of comments, in particular concerning alternatives, makes it a major step of the authorisation process. [ 22 ] In order to streamline this process, templates for comments and instructions are available on the ECHA website. [ 23 ]
Consulting costs of an application for authorisation have been estimated by ECHA and amounts, in average, to around 230,000 EUR for a single use. | https://en.wikipedia.org/wiki/REACH_authorisation_procedure |
rECOrd is a Local Biological Records Centre (LRC) serving Cheshire , Halton , Warrington and Wirral (including the vice-county 'pan-handle' boundary around Stockport ) - 'The Cheshire region'. It provides a local facility for the storage, validation and usage of Cheshire-based biological data under the National Biodiversity Network (NBN) project. It is one of a number of local Biological Records Centres across Britain which together aim to give complete geographic coverage of the UK.
The organisation is housed in Oakfield House at Chester Zoo . It provides support for biological recording and for biological recorders within the Cheshire region, allowing as wide access as is possible to both species and habitat records for the region commensurate with protecting those self-same species and habitats. This access aims to inform, educate and to provide real data upon which environmentalists, ecologists and planners, and other individuals and organisations can base decisions.
rECOrd deals with data for wildlife , biodiversity , nature , habitats , wildlife sites and geology , geomorphology and geodiversity .
rECOrd Online Data Input System (RODIS) is a facility for entering wildlife sighting information via the rECOrd website.
A mix of permanent staff, contractors and volunteers undertake data keying and verification duties, surveys and research historical data.
rECOrd is a non-profit making (not-for-profit) company, limited by guarantee (Company No.: 4046886), and is also a charity (Reg. No.: 1095859). David Bellamy is the organisation's patron, and Gordon McGregor Reid is its president.
The area covered is designated as 'the Cheshire region'.
rECOrd began its development in October 2000, managed by Steve J. McWilliam, and was fully launched on 12 July 2002 when it was formally opened by Sir Martin Doughty of English Nature. | https://en.wikipedia.org/wiki/RECOrd_(Local_Biological_Records_Centre) |
REFPROP is a software program for the prediction of thermophysical properties of fluids , developed by the National Institute of Standards and Technology (NIST). [ 1 ] [ 2 ] [ 3 ]
The primary component of REFPROP is an equation of state for each implemented fluid. For most pure fluids, the equation of state is obtained by fitting an expression for the Helmholtz free energy to experimental data. This formulation allows the computation of all equilibrium properties of the fluid, such as density, temperature, pressure, sound speed , heat capacity , second virial coefficients , vapor pressures , saturated liquid and vapor densities, enthalpy of vaporization , entropy , and the Joule-Thomson coefficient . [ 1 ]
REFPROP also predicts surface tension , viscosity , and thermal conductivity for many fluids, either using extended corresponding states formulations or fluid-specific equations fit directly to experimental data.
Various methods are used to compute the analogous properties of fluid mixtures.
The full list of fluids properties implemented in REFPROP v10.0 can be found in Table 2 of Huber, et al. (2022). [ 1 ]
REFPROP v10.0 implements equation of state models for 147 pure fluids, listed in Table 1. [ 1 ] Except for F 3 N , R-13, R-123, and R-152a, all of these are Helmholtz free energy formulations.
REFPROP v10.0 also predicts surface tension , viscosity , and thermal conductivity for most of the listed fluids. | https://en.wikipedia.org/wiki/REFPROP |
REFSMMAT is a term used by guidance, navigation, and control system flight controllers during the Apollo program , which carried over into the Space Shuttle program . [ 1 ] REFSMMAT stands for "Reference to Stable Member Matrix". [ 1 ] [ 2 ] : 387 It is a numerical definition of a fixed orientation in space and is usually (but not always) defined with respect to the stars. It was used by the Apollo Primary Guidance, Navigation and Control System (PGNCS) as a reference to which the gimbal-mounted platform at its core should be oriented. Every operation within the spacecraft that required knowledge of direction was carried out with respect to the orientation of the guidance platform, itself aligned according to a particular REFSMMAT.
During an Apollo flight, the REFSMMAT being used, and therefore the orientation of the guidance platform, would change as operational needs required it, but never during a guidance process—that is, one REFSMMAT might be in use from launch through Trans-Lunar Injection, another from TLI to Midpoint, but would not change during the middle of a burn or set of maneuvers. [ 2 ] : 150
One consideration in choosing each respective REFSMMAT was to avoid taking the spacecraft near the gimbal lock zone of its Inertial Measurement Unit during any expected spacecraft maneuvers, since the exact orientation of the "forbidden" range of spacecraft attitudes would depend on the current REFSMMAT. [ 2 ] : 178
Additionally, it was considered good practice to have the spacecraft displays show some meaningful attitude value that would be easy to monitor during an important engine burn. Flight controllers at mission control in Houston would calculate what attitude the spacecraft had to be at for that burn and would devise a REFSMMAT that matched it in some way. Then, when it came time for the burn, if the spacecraft was in its correct attitude, the crew would see their 8-ball display a simple attitude that would be easy to interpret, allowing errors to be easily tracked and corrected. [ 2 ] : 197
In the hallowed halls of mission control, Captain Refsmmat was a Kilroy -type character, conceived as a joke spoken to a 'Flight Dynamics Branch' rookie by Flight Controller RETRO John Llewellyn, and first drawn by flight controller FIDO Edward Louis Pavelka Jr. as the "ideal mission controller". 'Capt. Refsmmat' served during the Apollo and Skylab years as an aid to the esprit de corps within the mission control team. [ 2 ] : 146 [ 3 ]
This spacecraft or satellite related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/REFSMMAT |
RELIKT-1 from Russian : РЕЛИКТ-1 [ a ] (sometimes RELICT-1 ) was a Soviet cosmic microwave background anisotropy experiment launched on board the Prognoz 9 satellite on 1 July 1983. It operated until February 1984. It was the first CMB satellite (followed by the Cosmic Background Explorer in 1989) and measured the CMB dipole, the Galactic plane, and gave upper limits on the quadrupole moment .
A follow-up, RELIKT-2 , would have been launched around 1993, and a RELIKT-3 was proposed, but neither took place due to the dissolution of the Soviet Union .
RELIKT-1 was launched on board the Prognoz-9 satellite on 1 January 1983. The satellite was in a highly eccentric orbit, with perigee around 1,000 km and apogee around 750,000 km, and an orbital period of 26 days. [ 1 ]
RELIKT-1 observed at 37 GHz (8 mm), with a bandwidth of 0.4 GHz and an angular resolution of 5.8°. It used a superheterodyne, or Dicke-type modulation radiometer [ 2 ] with an automatic balancer for the two input levels with a 30-second time constant. The noise in 1 second was 31mK, [ 1 ] with a system temperature of 300K, and a receiver temperature of 110K. [ 3 ] The signal was sampled twice a second, and the noise was correlated between samples. [ 1 ]
The receiver used two corrugated horn antennas, one pointing parallel to the spacecraft spin axis, the other pointing at a parabolic antenna to point at 90° from the spin axis. The satellite rotated every 120 seconds. [ 1 ] The experiment weight 30 kilograms (66 lb), and consumed 50W of power. [ 3 ]
The radiometer was calibrated to 5% accuracy before launch, as was an internal noise source (which was used every four days during observations). [ 1 ] Additionally the moon was used as a calibrator, as it was observed twice a month, [ 3 ] and the in-flight system temperatures were measured to vary by 4% on a weekly basis. [ 1 ]
The satellite rotation axis was kept constant for a week, giving 5040 scans of a great circle, after which it was changed to a new axis. [ 1 ] The signal was recorded onto a tape recorder, and transmitted to Earth every four days. [ 4 ] It observed for 6 months, giving 31 different scans that covered the whole sky, all of which intersected at the ecliptic poles. The experiment ceased observations in February 1984, [ 1 ] after collecting 15 million measurements. [ 2 ]
It measured the CMB dipole, the Galactic plane, [ 2 ] and reported constraints on the quadrupole moment. [ 1 ]
The first dipole measurement was reported in 1984, while the telescope was still observing, at 2.1±0.5mK, and upper limits on the quadrupole of 0.2mK. [ 3 ] It also detected brighter-than-expected Galactic plane emission from compact HII regions. [ 5 ]
A reanalysis of the data by Strukov et al. in 1992 found a quadrupole ( Δ T / T ) q u a d {\displaystyle (\Delta T/T)_{quad}} between 6 × 10 − 6 {\displaystyle 6\times 10^{-6}} and 3.3 × 10 − 5 {\displaystyle 3.3\times 10^{-5}} at 90% confidence level, and also reported a negative anomaly at l=150°, b=-70° at a 99% confidence level, [ 6 ] [ 7 ] [ 8 ]
Another reanalysis of the data by Klypin, Stukov and Skulachev in 1992 found a dipole of 3.15±0.12mK, with a direction of 11h17m±10m and -7.5°±2.5°. It placed a limit on the CMB quadrupole of ( Δ T / T ) q u a d = 1.5 × 10 − 5 {\displaystyle (\Delta T/T)_{quad}=1.5\times 10^{-5}} with a 95% confidence level, assuming a Harrison-Zeldovich spectrum , or < 3.0 × 10 − 5 {\displaystyle <3.0\times 10^{-5}} without assuming a model. The results were close to those measured by the Cosmic Background Explorer [ 1 ] and the Tenerife Experiment . [ 5 ]
The second RELIKT satellite would have been launched in mid-1993. It would have had five channels to observe at 21.7 (13.8), 24.5 (8.7), 59.0 (5.1), 83.0 (3.6) and 193 GHz (1.6mm), [ 1 ] using degenerated paramps. [ 5 ] It would have had corrugated horns to give a resolution of 7°, and a more distant orbit to avoid contamination from the Moon and Sun, with a mission duration around 2 years, to give a better sensitivity than COBE. [ 1 ] It would have been cooled to 100K. It was constructed, and was undergoing tests in 1992. It would have been launched as the Libris satellite on a Molniya rocket. [ 4 ] The launch was put back to 1996, with expanded plans to observe with 1.5-3° resolution from two spacecraft in 1995, [ 1 ] but ultimately never took place because of the Soviet Union's break-up and lack of funding.
A RELIKT-3 was also planned, which would have observed at 34–90 GHz with a resolution around 1°. [ 1 ] | https://en.wikipedia.org/wiki/RELIKT-1 |
REPAIRtoire is a database of resources for systems biology of DNA damage and repair . [ 1 ]
This Biological database -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/REPAIRtoire |
A radio-frequency quadrupole ( RFQ ) beam cooler is a device for particle beam cooling , especially suited for ion beams . It lowers the temperature of a particle beam by reducing its energy dispersion and emittance , effectively increasing its brightness ( brilliance ). The prevalent mechanism for cooling in this case is buffer-gas cooling, whereby the beam loses energy from collisions with a light, neutral and inert gas (typically helium ). The cooling must take place within a confining field in order to counteract the thermal diffusion that results from the ion-atom collisions. [ citation needed ]
The quadrupole mass analyzer (a radio frequency quadrupole used as a mass filter) was invented by Wolfgang Paul in the late 1950s to early 60s at the University of Bonn , Germany. Paul shared the 1989 Nobel Prize in Physics for his work. Samples for mass analysis are ionized, for example by laser ( matrix-assisted laser desorption/ionization ) or discharge ( electrospray or inductively coupled plasma ) and the resulting beam is sent through the RFQ and "filtered" by scanning the operating parameters (chiefly the RF amplitude). This gives a mass spectrum, or fingerprint, of the sample. Residual gas analyzers use this principle as well.
Despite its long history, high-sensitivity high-accuracy mass measurements of atomic nuclei continue to be very important areas of research for many branches of physics . Not only do these measurements provide a better understanding of nuclear structures and nuclear forces but they also offer insight into how matter behaves in some of nature's harshest environments. At facilities such as ISOLDE at CERN and TRIUMF in Vancouver, for instance, measurement techniques are now being extended to short-lived radionuclei that only occur naturally in the interior of exploding stars. Their short half-lives and very low production rates at even the most powerful facilities require the very highest in sensitivity of such measurements.
Penning traps , the central element in modern high-accuracy high-sensitivity mass measurement installations, enable measurements of accuracies approaching 1 part in 10 11 on single ions. However, to achieve this Penning traps must have the ion to be measured delivered to it very precisely and with certainty that it is indeed the desired ion. This imposes severe requirements on the apparatus that must take the atomic nucleus out of the target in which it has been created, sort it from the myriad of other ions that are emitted from the target and then direct it so that it can be captured in the measurement trap.
Cooling these ion beams, particularly radioactive ion beams, has been shown to drastically improve the accuracy and sensitivity of mass measurements by reducing the phase space of the ion collections in question. Using a light neutral background gas, typically helium, charged particles originating from on-line mass separators undergo a number of soft collisions with the background gas molecules resulting in fractional losses of the ions' kinetic energy and a reduction of the ion ensemble's overall energy. In order for this to be effective, however, the ions need to be contained using transverse radiofrequency quadrupole (RFQ) electric fields during the collisional cooling process (also known as buffer gas cooling). These RFQ coolers operate on the same principles as quadrupole ion traps and have been shown to be particularly well suited for buffer gas cooling given their capacity for total confinement of ions having a large dispersion of velocities, corresponding to kinetic energies up to tens of electron volts. A number of the RFQ coolers have already been installed at research facilities around the world and a list of their characteristics can be found below.
COLETTE2
LPC2
SHIPTRAP2
JYFL2
JYFL3
ORNL2
ORNL3
LEBIT2
LEBIT3
ISCOOL2
ISCOOL3
ISCOOL4
ISOLTRAP2
TITAN2
TITAN3
TRIMP2
TRIMP3
SPIG2
SPIG3
CPT Cooler2 | https://en.wikipedia.org/wiki/RFQ_beam_cooler |
An RF antenna ion source (or radio frequency antenna ion source) is an internal multi- cusp design that can produce a particle beam of about ~30 to 40 mA current. It is used in high energy particle physics and in accelerator laboratories.
Previous RF antennas would penetrate the porcelain enamel coating on the antenna section at high RF power. This problem has been corrected in the development stage with a ten layer coating of titanium dioxide , with approximately 1 mm thick coating.
With the development of the RF antenna ion source, or "non- thermionic ion source," the ion source has an advantage over conventional cold cathodes and hot filament ion sources. The filament continuously burns out over time with a shorter lifespan, requiring venting of the ion source to atmosphere and rebuilding of the ion source.
This accelerator physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RF_antenna_ion_source |
An RF chain is a cascade of electronic components and sub-units which may include amplifiers , filters , mixers , attenuators and detectors . [ 1 ] It can take many forms, for example, as a wide-band receiver-detector for electronic warfare (EW) applications, as a tunable narrow-band receiver for communications purposes, as a repeater in signal distribution systems, or as an amplifier and up-converters for a transmitter-driver. In this article, the term RF (radio frequency) covers the frequency range "medium Frequencies" up to "microwave Frequencies", i.e. from 100 kHz to 20 GHz. [ 2 ] : 15
The key electrical parameters for an RF chain are system gain, noise figure (or noise factor ) and overload level. [ 3 ] : 2 Other important parameters, related to these properties, are sensitivity (the minimum signal level which can be resolved at the output of the chain); dynamic range (the total range of signals that the chain can handle from a maximum level down to smallest level that can be reliably processed) and spurious signal levels (unwanted signals produced by devices such as mixers and non-linear amplifiers). In addition, there may be concerns regarding the immunity to incoming interference or, conversely, the amount of undesirable radiation emanating from the chain. The tolerance of a system to mechanical vibration may be important too. Furthermore, the physical properties of the chain, such as size, weight and power consumption may also be important considerations.
An addition to considering the performance of the RF chain, the signal and signal-to-noise requirements of the various signal processing components, which may follow it, are discussed because they often determine the target figures for a chain.
Each two-port network in an RF chain can be described by a parameter set, which relates the voltages and currents appearing at the terminals of that network. [ 4 ] : 29 Examples are: impedance parameters , i.e. z-parameters ; admittance parameters , i.e. y-parameters or, for high frequency situations, scattering parameters , i.e. S-parameters. [ 5 ] [ 6 ] : 663 Scattering parameters avoid the need for ports to be open or short-circuited, which are difficult requirements to achieve at microwave frequencies.
In theory, if the parameter set is known for each of the components in an RF chain, then the response of the chain can be calculated precisely, whatever the configuration. Unfortunately, acquiring the detailed information required to carry out this procedure is usually an onerous task, especially when more than two or three components are in cascade. A simpler approach is to assume the chain is a cascade of impedance matched components and then, subsequently, to apply a tolerance spread for mismatch effects (see later).
A system spreadsheet has been a popular way of displaying the important parameters of a chain, in a stage-by-stage manner, for the frequency range of interest. [ 3 ] It has the advantage of highlighting key performance figures and also pin-pointing where possible problem areas may occur within the chain, which are not always apparent from a consideration of overall results. Such a chart can be compiled manually [ 3 ] : 139 or, more conveniently, by means of a computer program. [ 7 ] [ 8 ] [ 9 ] [ 10 ]
In addition, 'tookits' are available which provide aids to the system designer. [ 11 ] [ 12 ] [ 13 ]
Some routines, useful for spreadsheet development, are given next.
For the parameters considered below, the chain is assumed to contain a cascade of devices, which are (nominally) impedance matched. The procedures given here allow all calculations to be displayed in the spreadsheet in sequence and no macros are used. Although this makes for a longer spreadsheet, no calculations are hidden from the user.
For convenience, the spread sheet columns, show the frequency in sub-bands, with bandwidths sufficiently narrow to ensure that any gain ripple is sufficiently characterized.
Consider the n th stage in a chain of RF devices. The cumulative gain , noise figure , 1 dB compression point [ 14 ] [ 3 ] : 119 and output thermal noise power for the preceding n − 1 devices are given by Gcum n −1 , Fcum n −1 , Pcum n −1 and Ncum n −1 , respectively. We wish to determine the new cumulative figures, when the n th stage is included, i.e. the values of Gcum n , Fcum n , Pcum n and Ncum n , given that the n th stage has values of G n , F n , P1 n for its gain, noise figure and 1 dB compression point, respectively.
The cumulative gain, Gcum n after n stages, is given by
and Gcum n (dB) is given by
where Gcum n −1 [dB] is the total gain of the first n − 1 stages and G n [dB] is the gain of the n th stage.
Conversion equations between logarithmic and linear terms are:
and
The cumulative noise factor , after n stages of the overall cascade, Fcum n is given by
where Fcum n −1 is the noise factor of the first n − 1 stages, F n is the noise factor of the n th stage, and Gcum n is the overall gain of n stages.
The cumulative noise figure is then
For spreadsheet purposes, it is convenient to refer the 1 dB compression point [ 14 ] [ 17 ] to the input of the RF chain, i.e. P1cum n (input),
where P1cum n-1 is the 1 dB compression point at the input of the first n − 1 stages, P1 n is the 1 dB compression point for the n th stage, referred to its input and Gcum n is the overall gain including the n th stage. The unit is [mW] or [W].
Related parameters, such as IP3 or IM3 are helpful fictive numbers used to evaluate the system. The device would burn, applying IP3 input level. Accuracy of the measurement with spectrum analyzer is (HP/Agilent specs: ±1.0 dB, and ±0.5 dB custom device). In linear systems, this all results in AGC.
The thermal noise power present at the input of an RF chain, [ 18 ] : 44 [ 19 ] : 435 [ 20 ] : 229 is a maximum in a resistively matched system, and is equal to kTB , where k is the Boltzmann constant (= 1.380 649 × 10 −23 J⋅K −1 [ 21 ] ), T is the absolute temperature, and B is the bandwidth in Hz.
At a temperature of 17 °C (≡ 290 K), kTB = 4.003 × 10 −15 W/MHz ≡ −114 dBm for 1 MHz bandwidth.
The thermal noise after n stages of an RF chain, with total gain G T and noise figure F T is given by
where k = the Boltzmann constant, T is the temperature in kelvins and B is the bandwidth in hertz, or
where Ncum n (dBm) is the total noise power in dBm per 1 MHz of bandwidth,
In receivers, the cumulative gain is set to ensure that the output noise power of the chain at an appropriate level for the signal processing stages that follow. For example, the noise level at the input to an analog-to-digital converter (ADC) must not be at too low a level, otherwise the noise (and any signals within it) is not properly characterized (see the section on ADCs, later). On the other hand, too high a level results in the loss of dynamic range.
With the basic parameters of the chain determined, other related properties can be derived.
Sometimes performance at high signal levels is defined by means of the " second-order intercept point (I2)" and the " third-order intercept point (I3)", rather than by the 1 dB compression point. [ 14 ] These are notional signal levels which occur in two-signal testing and correspond to the theoretical points where second and third order inter-modulation products achieve the same power level as the output signal. [ 1 ] : 685 [ 3 ] : 91 The figure illustrates the situation.
In practice, the intercept levels are never achieved because an amplifier has gone into limiting before they are reached, but they are useful theoretical points from which to predict intercept levels at lower input powers. In dB terms, they decrease at twice the rate (IP2) and three times the rate (IP3) of the fundamental signals.
When products, stage to stage, add incoherently, the cumulative results for these products are derived by similar equations to that for the 1 dB compression point.
where I2cum n −1 is the second order intercept point at the input of the first n − 1 stages, I2 n is the third order intercept point for the n th stage, referred to its input and Gcum n is the overall gain including the nth stage.
Similarly,
where I3cum n-1 is the third order intercept point at the input of the first n − 1 stages, I3 n is the third order intercept point for the n th stage, referred to its input.
The cumulative intercept points are useful when determining the "spurious free dynamic range" [ 16 ] : 519 of a system.
There is an approximate relationship between the third order intercept level and the 1 dB compression level which is [ 22 ] : 59 [ 20 ] : 35
Although only an approximation, the relationship is found to apply to a large number of amplifiers. [ 17 ]
In the spread sheet, the total frequency band of interest B (Hz) is divided into M sub-bands (spreadsheet columns) of B / M (Hz) each, and for each sub-band ( m = 1 to M ) the thermal noise power is derived, as described above. In practice, these results will differ slightly, from column to column, if the system has gain ripple.
The signal-to-noise ratio (S:N) is the peak signal power of the pulse ( P sig ) divided by the total noise power ( P noise ) from the M frequency bins, i.e.
This is the S:N ratio at RF frequencies. It can be related to the video S:N ratio as shown next.
For spreadsheet purposes it can useful to find the RF signal to noise ratio which corresponds to a desired video signal to noise figure after demodulation or detection. As an RF chain usually has sufficient gain for any noise contribution from the detector diode to be ignored, the video S:N can be shown to be [ 22 ] : 115
where
[If there is significant gain variation across the band, then it can be divided into M sub-bands and results summed for these sub-bands, as described earlier.]
From the above equation, as the noise power in the RF band is P N = kTB R F ′, a relationship between RF and video S:N ratios can be found.
(This result can be found elsewhere [ 23 ] : 188 ).
Inverting the relationship gives the RF signal-to-noise ratio required to achieve a given video S:N ratio:
Signal sensitivity is important for receiving systems and refers to the minimum signal level at the input that is necessary to give a signal that can be resolved reliably by the detection process at the end of the RF chain. This parameter is less important in the case of repeaters and transmitter drivers where signal levels tend to be higher and other concerns such as stage overload and spurious signal generation tend to be more relevant.
Determining a value for system sensitivity can be difficult and depends on many things, including the method of detection, the signal coding method, the bandwidth of the RF channel, and whether or not digital processing is involved. Two important parameters used in assessing sensitivity performance of a system are [ 24 ] : 2.16 [ 15 ] : 204 the "probability of detection" and the "false alarm rate".
Statistical methods are often used in the decision process (see Tsui [ 25 ] : 20 and Skolnik [ 26 ] : 16 ).
Tangential sensitivity, (TSS), defines that input power which results in a video signal to noise ratio of approximately 8 dB from the detector. [ 25 ] : 16 The thumbnail shows an example of a typical detected pulse at the TSS limit, with the pulse + noise sitting at a level just clear of the noise floor. The TSS level is too low a value for reliable pulse detection in a practical scenario, but it can be determined with sufficient accuracy in bench tests on a receiver to give a quick guide figure for system performance.
In a wideband receiver, with a square-law detector, the TSS value at the chain input terminals is given by [ 25 ] : 18
From this, the S:N of the RF signal, at the input to the detector can be obtained when the video output is at TSS.
This equation shows that the S:N at RF is typically less than unity, in wideband systems, when the video output is at TSS. For example, if B R / B V = 500 then the equation gives (S:N) R = 0.17 (≈ −7.7 dB). (Note: a similar result is obtained by using the equation relating RF and video S:N ratios, given in the previous section [ 23 ] : 190 ).
The thumbnail shows the simulated video output (at TSS) corresponding to an RF pulse in wideband noise with S:N = 0.17 and a bandwidth ratio of 500.
The sensitivity of a system may be taken as the "minimum detectable signal". This is that level of signal that exceeds a threshold value by a suitable margin (If the level is set too low, noise spikes will exceed it too frequently and if the signal+noise does not exceed it by a sufficient margin then it may fall below the threshold giving pulse termination prematurely. So, in determining the minimum detectable signal, it is necessary to choose the "false alarm rate" and "probability of detection" values appropriate to the system requirement. To aid the designer, graphs are available, to help determine the necessary S:N ratio at the detector. [ 25 ] : 30 [ 26 ] : 28 [ 27 ] : 2.19 [ 28 ] : 21 [ 15 ] : 357
In the case of pulse detection of a signal in noise, following the detector in a wideband receiver, where the RF bandwidth greatly exceeds the video bandwidth, a guideline figure for reliable performance a S:N (at video) is 16 to 18 dB. [ 22 ] : 87 This is a useful figure for use in spreadsheets, and it corresponds to a probability of detection of over 99% for a Swerling 1 target [ 29 ] [ 30 ]
(Although lower values of S:N can give acceptable "probability of detection" and "false alarm rate" figures, the measurement of pulse lengths become less reliable because noise spikes on pulses may extend below the chosen threshold level).
As examples, thumbnails show simulated examples of a detected pulse, in noise, where S:N = 18 dB and 15 dB. As can be seen, if the S:N falls to 15 dB or lower, it becomes difficult to set a threshold level for pulse detection, that is clear of the noise floor, and yet does not result in early termination.
The video S:N ratio can be related to the RF S:N ratio, as shown earlier.
In scenarios, such as radar pulse detection, integration over several pulses may occur and a lower value of S:N then becomes acceptable. [ 26 ] : 30 In general, system sensitivity and pulse detection theory are specialized topics [ 20 ] : 12 and often involve statistical procedures not easily adapted for spreadsheets.
In the past, devices in an RF chain have often been inter-connected by short transmission lines , such as coaxial cable , [ 1 ] : 165 [ 31 ] [ 32 ] : 13–3 [ 4 ] : 165 (0.414" and 0.085"semi-rigid cables are popular [ 33 ] [ 2 ] : 481 ), by stripline [ 34 ] [ 4 ] : 168 [ 32 ] : 13–4 or by microstrip . [ 32 ] : 13–6 [ 34 ] Almost invariably, mismatches occur at the various interfaces.
Standard equations for a transmission line, terminated in a mismatch, are [ 35 ] [ 20 ]
If a transmission line is mismatched at both ends, multiple-reflected signals can be present on the line, resulting in ripple on the frequency response, as seen at the load.
Where only first time round echoes are considered (i.e. multiple reflections are ignored), the output response is given by
where
A typical plot is shown in the thumbnail.
This response has a ripple component with a peak-to-peak value Δ A , given by
The frequency difference from peak-to-peak (or trough-to-trough) of the ripple is given by ΔΩ where
An RF chain may contain many inter-stage links of various lengths. The overall result is obtained using
This can give an overall response which is far from flat. As an example, a random collection of 25 cascaded (but separated) links give the result shown. Here, a random selection of path delays are assumed, with α taken as unity and ρ 1 and ρ 2 taking the typical value 0.15 (a return loss ≈ 16 dB), for the frequency range 10 to 20 GHz
For this example, calibration at 50 MHz intervals would be advisable, in order to characterize this response.
The ripple amplitude would be reduced if the mismatches ρ 1 and ρ 2 were improved but, especially if the lengths of the interconnecting links were made shorter. An RF chain, made up of surface mounted components, interconnected by stripline, [ 4 ] : 168 which can be made physically small, may achieve less than 0.5 dB ripple. The use of integrated circuits would give lower ripple still (see, for example Monolithic microwave integrated circuit ).
The presence of a mixer in an RF chain complicates the spreadsheet because the frequency range at the output differs from that at the input. In addition, because mixers are non-linear devices, they introduce many inter-modulation products, which are undesirable, especially in wide-band systems.
For an input signal at frequency F sig and a local oscillator frequency F lo , the output frequencies of a mixer are given by
where m and n are integers.
Usually, for a mixer, the desired output is the frequency with n = m = 1. The other outputs are often referred to as "spurs" and are usually unwanted. Frequency plans are often drawn up, often as a separate spreadsheet, to minimize the consequences of these unwanted signals [ 36 ] [ 3 ] : 168 [ 37 ] [ 38 ]
Some general points regarding mixer performance are:
In a typical mixer, the 1 dB compression point is between 5 and 10 dB below the local oscillator power. [ 39 ]
Note that the approximate relationship between IP3 and P1 differs from that for amplifiers. For mixers, a very approximate expression is: [ 20 ] : 35
As this is very approximate, it is advisable to refer to the specification of the mixer in question, for clarification.
Dynamic Range ( D R ) is that range of input powers from that of a just detectable signal up to a level at which the chain overloads. [ 39 ]
D R is given by
where P max is the maximum signal power, discussed earlier, and P sens is the smallest input power for signal detection (see Sensitivity, discussed earlier).
(Several assumptions are made for the equations that follow. Firstly, if the incoming signal is polarized, then the antenna is rotated to match that polarization, secondly, it is assumed that the antenna output impedance is matched to that of the chain input port and, thirdly, when gain is quoted, this is the maximum gain of the antenna (sometimes referred to as the boresight gain))
When the power density of an incoming signal is P inc then the power at the antenna terminals is P R is given by
Where A eff is the effective area of the antenna (or the Antenna aperture ).
Power density, which is in watts per metre squared, can be related to electric field strength E R , given in volts per metre, by
The gain of the antenna is related to the effective aperture by [ 40 ] : 90 [ 6 ] : 746
In practice, the effective aperture of the antenna is smaller than the actual physical area. For a dish, the effective area is about 0.5 to 0.6 times the actual area, and for a rectangular horn antenna it is about 0.7 to 0.8 times the actual area. [ 6 ] : 747 For a dipole there is no actual physical area, but as a half-wave dipole has a power gain [ 40 ] : 35 of 1.62 and the effective area can be inferred from that.
Front end losses are those losses which occur prior to the first active device of a receiver chain. They often arise because of the operational requirements of a particular system, but should be minimized, where possible, to ensure the best possible system sensitivity. These losses add to the effective noise figure of the first amplifier stage, dB for dB. [ 20 ] : 15
Some losses are a consequence of the system construction, such as antenna to receiver feeder loss and, may include waveguide-to-coax. transition loss. Other losses arise from the necessity to include devices to protect the chain from high incident powers. For example, a radar system requires a transmit–receive (TR) cell [ 41 ] [ 42 ] [ 43 ] to protect the chain from the high-power signals of the radar's transmitter. Similarly, a front end limiter [ 44 ] is needed, on a ship, to protect the chain from the emissions of high-power transmitters located close by.
In addition, the system may include a band-pass filter at its input, to protect it from out-of-band signals, and this device will have some pass-band loss.
Detector diodes for RF and Microwaves may be point contact diodes, Schottky diodes , Gallium Arsenide or p-n junction devices. [ 45 ] Of these, Schottky diodes and junction diodes require biassing for best results. Also, silicon junction diodes perform less well at high frequencies.
A typical detector diode has a TSS of −45 to −50 dBm [ 25 ] : 136 [ 46 ] [ 47 ] and peak pulse powers of 20 dBm, although better figures are possible [ 48 ] ).
At low powers, diodes have a square-law characteristic, i.e. the output voltage is proportional to the input power, but at higher powers (above about −15 dBm) the device becomes linear, with the output voltage proportional to the input voltage.
Square law detectors can give detectable signals at video, in wideband systems, even when the RF S:N is less than unity. For example, using the RF-to-Video relationships given earlier, for a system which has a bandwidth of 6 GHz, and an RF S:N value of 0.185 (−7 dB), the video S:N (i.e. TSS) will be 6.31 (8 dB). (Tsui's equations give an RF S:N value of 0.171 for this example).
DLVAs [ 49 ] [ 22 ] : 72 have been commonly found in direction finding systems, using multiple channels, squinted antennas and amplitude comparison methods. [ 22 ] : 155 [ 50 ] They are also useful for compressing the dynamic range of incoming signals of receivers, prior to digitising. They cover frequency ranges such as 2–6 GHz and 6–18 GHz. There are also wideband devices available which cover the range 2–18 GHz.
A simple DLVA contains a broadband diode detector followed by an amplifier with a logarithmic characteristic and has an input power range of, typically, −45 dBm to 0 dBm, [ 51 ] [ 52 ] [ 53 ] which may be increased to −45 to +15 dBm in an extended-range DLVA. Two devices, together with an amplifier, can be combined to give an effective range of −65 dBm to +15 dBm.
In a successive-detection DLVA, which includes a low noise amplifier, the power range may to be, typically −65 dBm to +10 dBm [ 54 ] [ 52 ]
IFMs can provide a frequency measurement of a single pulse. [ 22 ] : 126 : 140 They incorporate a set of delay-line frequency discriminators, with delay lengths increasing in a binary or other sequence. [ 55 ] [ 56 ] They usually incorporate some gain of their own. The discriminator with the longest delay line establishes the frequency measurement accuracy and resolution, the shortest delay line correlator defines the unambiguous bandwidth of the DFD and the remaining correlators serve to resolve ambiguities. [ 57 ] Usually, there is an input, limiting amplifier present in the IFM. This boosts the received signal to a constant level for processing by the correlators, making the frequency-data-decoding task of the frequency processor easier, and to emphasise the "capture effect" when simultaneous signals are present. Normally the RF amplifier will produce a minimum of 10 dB limiting at the lowest specified signal input level. If the RF S:N ratio is too low, the output of the longest delay line correlator (which sets the frequency resolution of the IFM) will become degraded and noisy. At high S:N ratios (+10 dBm), the measured frequency accuracy approaches the correlator-limited rms error, but at approximately −3 dBm SNR, ambiguity errors appear, causing large measurement inaccuracies. [ 58 ]
The lowest input power level of a typical DDU is about −75 dBm, [ 58 ] and with a receiver noise figure of 10 dB, it gives a frequency accuracy of approximately 1 MHz [ 56 ] They have dynamic ranges of 65 to 75 dB and cover frequency bands such as 2–6 GHz, 6–18 GHz and some wideband devices cover 2–18 GHz. [ 59 ] [ 60 ] [ 56 ]
With the advent of digital techniques, analogous processes to those of an analog system have been realized. [ 61 ] [ 62 ]
An Analog-to-digital converter , [ 63 ] [ 64 ] located at the end of the RF chain, provides digital signals for further signal processing. As the ADC operates with sampled signals, it is necessary for the Nyquist–Shannon sampling theorem to be satisfied, if data is not to be lost. As shown earlier, a low-amplitude RF pulse immersed in wideband noise, can be detected by a square-law diode detector. Similarly spread spectrum signals can be recovered from below the noise floor by compression. Consequently, to ensure no loss of data, the chain gain should be high enough to ensure that thermal noise will activate the ADC adequately, so that any signals present within the noise, can be recovered correctly by the detection or compression process. Typically, the rms noise voltage present the input to the ADC should be one or two bits of the ADC range, but no lower. On the other hand, having excessive chain gain so that the noise floor is unnecessarily high, will result in the loss of dynamic range.
Consider, as an example, a chirp signal with time-bandwidth product of 200 and of amplitude of 1 / 2 LSB which is embedded in noise with an rms voltage of 1 LSB, present at the input to an ADC. he digitized, quantised output, relative to the mean value, is similar to the example in the left-hand figure below. After compression in the signal processor, a high amplitude pulse, whose magnitude is well above the noise is obtained, as shown in the right-hand figure.
This example happens to show, unintentionally, the benefits of dither [ 65 ] [ 66 ] [ 67 ] which is used to improve the linearity and dynamic range of an ADC. In the case of the signal considered here, if there was no noise present, but just the signal alone, its amplitude would be insufficient to operate the ADC. | https://en.wikipedia.org/wiki/RF_chain |
In a radio receiver circuit, the RF front end , short for radio frequency front end , is a generic term for all the circuitry between a receiver's antenna input up to and including the mixer stage. [ 1 ] It consists of all the components in the receiver that process the signal at the original incoming radio frequency (RF), before it is converted to a lower intermediate frequency (IF). In microwave and satellite receivers it is often called the low-noise block downconverter (LNB) and is often located at the antenna, so that the signal from the antenna can be transferred to the rest of the receiver at the more easily handled intermediate frequency.
For most superheterodyne architectures, the RF front end consists of: [ 2 ]
In digital receivers, particularly those in wireless devices such as cell phones and Wifi receivers, the intermediate frequency is digitized; sampled and converted to a binary digital form, and the rest of the processing – IF filtering and demodulation – is done by digital filters ( digital signal processing , DSP), as these are smaller, use less power and can have more selectivity. [ 3 ] In this type of receiver the RF front end is defined as everything from the antenna to the analog-to-digital converter (ADC) which digitizes the signal. [ 3 ] The general trend is to do as much of the signal processing in digital form as possible, and some receivers digitize the RF signal directly, without down-conversion to an IF, so here the front end is merely an RF filter in the simple receiver path/chain. | https://en.wikipedia.org/wiki/RF_front_end |
In the context of mobile radio communication systems, RF planning is the process of assigning frequencies , transmitter locations and parameters to a wireless communications system to evaluate coverage and capacity. Coverage is the distance at which the RF signal has sufficient strength to sustain a call/data session. Capacity relates to the system data rate.
The RF Planning process consists of four major stages.
A statistical propagation model (e.g. Hata, COST-231 Hata or Erceg-Greenstein) is used to approximate the coverage area of the planned sites and to eventually determine how many sites are required. The statistical propagation of the model does not include terrain effects and has a model for each type of environment (rural, urban, suburban, etc.). Two essential inputs at this level are simple radio transceiver characteristics and 'flat' map of the area. This fairly simplistic approach allows for a quick analysis of the number of sites that may be required to cover a certain area.
The second level of the RF Planning process relies on a more detailed propagation model. Automatic planning tools are often employed in this phase to perform detailed predictions. The propagation model takes into account the characteristics of the selected antenna, the terrain, and the land use and land clutter surrounding each site. This requires precise and accurate characterization of every transceiver and detailed, three-dimensional model of the terrain. Since these factors are considered, this propagation model provides a better estimate of the coverage of the sites than the initial statistical propagation model. Thus, its use, in conjunction with the RF link budget, produces a more accurate determination of the number of sites required. Following is a typical list of outputs produced at this stage:
The third phase of the RF planning process incorporates further detail into the RF plan. This stage includes items such as collecting drive data to be used to tune or calibrate the propagation prediction model, predicting the available data throughout each site, fine-tuning of parameter settings (e.g. antenna orientation, downtilting, frequency plan).
The final phase of the RF planning process involves continuous optimisation of the RF plan to accommodate for changes in the environment or additional service requirements (e.g. additional coverage or capacity). This phase starts from initial network deployment and involves collecting measurement data on a regular basis which could be via drive testing or centralised collection. The data is then used to plan new sites or to optimize the parameter settings (e.g. antenna orientation, downtilting, frequency plan) of existing sites. | https://en.wikipedia.org/wiki/RF_planning |
A radio-frequency power amplifier ( RF power amplifier ) is a type of electronic amplifier that converts a low-power radio-frequency (RF) signal into a higher-power signal. [ 1 ] Typically, RF power amplifiers are used in the final stage of a radio transmitter , their output driving the antenna . Design goals often include gain , power output, bandwidth, power efficiency, linearity (low signal compression at rated output), input and output impedance matching, and heat dissipation.
The operation of RF amplifier circuits is classified based on the proportion of the cycle of the sinusoidal radio signal the amplifier (transistor or vacuum tube) where current is conducting. Class-A , class-AB and class-B are considered the linear amplifier classes in which the active device is used as a controlled current source, while class-C is a nonlinear class in which the active device is used as a switch. The bias at the input of the active device determines the class of the amplifier.
A common trade-off in power amplifier design is the trade-off between efficiency and linearity. The previously named classes become more efficient, but less linear, in the order they are listed. Operating the active device as a switch results in higher efficiency, theoretically up to 100%, but lower linearity. [ 2 ] Among the switch-mode classes are class-D , class-E and class-F . [ 3 ] The class-D amplifier is not often used in RF applications because the finite switching speed of the active devices and possible charge storage in saturation could lead to a large I-V product, [ 2 ] which deteriorates efficiency.
Modern RF power amplifiers use solid-state devices , predominantly MOSFETs (metal–oxide–semiconductor field-effect transistors). [ 4 ] [ 5 ] [ 6 ] The earliest MOSFET-based RF amplifiers date back to the mid-1960s. [ 7 ] Bipolar junction transistors were also commonly used in the past, up until they were replaced by power MOSFETs , particularly LDMOS transistors, as the standard technology for RF power amplifiers by the 1990s, [ 4 ] [ 6 ] due to the superior RF performance of LDMOS transistors. [ 6 ] Generally speaking, solid-state power amplifiers contain four main components: input, output, amplification stage and power supply. [ 8 ]
MOSFET transistors and other modern solid-state devices have replaced vacuum tubes in most electronic devices, but tubes are still used in some high-power transmitters (see Valve RF amplifier ). Although mechanically robust, transistors are electrically fragile – they are easily damaged by excess voltage or current. Tubes are mechanically fragile but electrically robust – they can handle remarkably high electrical overloads without appreciable damage.
The basic applications of the RF power amplifier include driving to another high-power source, driving a transmitting antenna and exciting microwave cavity resonators. Among these applications, driving transmitter antennas is most well known. The transmitter–receivers are used not only for voice and data communication but also for weather sensing (in the form of a radar ). [ 9 ]
RF power amplifiers using LDMOS (laterally diffused MOSFET ) are the most widely used power semiconductor devices in wireless telecommunication networks, particularly mobile networks . [ 4 ] [ 10 ] [ 6 ] LDMOS-based RF power amplifiers are widely used in digital mobile networks such as 2G , 3G , [ 4 ] [ 6 ] and 4G [ 10 ] and the good cost/performance ratio make them the preferred option for amateur radio . [ 11 ]
Impedance transformations over large bandwidth are difficult to realize, so conventionally, most wideband amplifiers are designed to feed a 50 Ω output load. Transistor output power is then limited to
where
The external load is, by convention, Z L = 50 Ω . {\displaystyle Z_{\text{L}}=50~\Omega .} Therefore, there must be some sort of impedance matching that transforms from Z o {\displaystyle Z_{\text{o}}} to Z L = 50 Ω . {\displaystyle Z_{\text{L}}=50~\Omega .}
The loadline method is often used in RF power amplifier design. [ 12 ] | https://en.wikipedia.org/wiki/RF_power_amplifier |
An RF probe is a device which allows electronic test equipment to measure radio frequency (RF) signal in an electronic circuit .
In 1980 Reed Gleason and Eric Strid invented the first high frequency wafer probe while working at Tektronix. They later went on to found Cascade Microtech in 1983. [ 1 ]
RF energy may be challenging to measure for one or more reasons, depending on the nature of the circuit to be measured and the measuring equipment at hand.
The first kind of difficulty arises when the RF energy to be measured is at a frequency too high for available test equipment, such as a low-bandwidth oscilloscope , to process directly. In that case, the RF has to be converted to a DC or near-DC signal.
In this situation, a simple probe type sometimes called an RF detector can be used to convert the RF signal to DC. Such device will work as a RF rectifier and give a pulsed DC voltage . [ 2 ]
The second kind of difficulty arises when RF energy has to be measured in a circuit which is sensitive to small changes in its electrical environment. For example, with some oscillator circuits, the presence of an ordinary wire within a few centimeters of the active components may change the amplitude or frequency of oscillations, or even prevent the circuit from oscillating at all. In that case, the signal has to be acquired by a measurement probe which extracts very little energy from the circuit. This can be achieved by employing very thin conductors, or tiny coils kept at some minimum separation from the active elements of the circuit.
In a situation, where circuit loading rather than high frequency is the real problem, a variety of small-geometry, high impedance probes can be used, sometimes including an amplifier to boost the tiny amount of energy extracted from the circuit to a level that allows it to be measured by available high-frequency test equipment.
Coaxial structures with spring-loaded inner and outer conductors can serve as an RF probe for modern communication electronics. Such probes are for instance being used in mass-production, in-line testing of communication electronics such as mobile phone industry. [ 3 ] RF probes are especially relevant for switches and RF traces in printed circuit boards as well as terminations of RF components. In such systems, like many other RF circuits, there is a higher requirement of matching probe impedance with that of the DUT. Efficient matching avoids reflection which in turn leads to efficient power transfer. The second challenge to keep the power transfer efficient, is to keep the insertion loss as low as possible. Optimizing these parameters generally gets more challenging as the frequency increases. | https://en.wikipedia.org/wiki/RF_probe |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.