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In quantum mechanics , and especially quantum information theory, the purity of a normalized quantum state is a scalar defined as γ ≡ tr ( ρ 2 ) {\displaystyle \gamma \,\equiv \,\operatorname {tr} (\rho ^{2})} where ρ {\displaystyle \rho \,} is the density matrix of the state and tr {\displaystyle \operatorname {tr} } is the trace operation . The purity defines a measure on quantum states, giving information on how much a state is mixed .
The purity of a normalized quantum state satisfies 1 d ≤ γ ≤ 1 {\displaystyle {\frac {1}{d}}\leq \gamma \leq 1\,} , [ 1 ] where d {\displaystyle d} is the dimension of the Hilbert space upon which the state is defined. The upper bound is obtained by tr ( ρ ) = 1 {\displaystyle \operatorname {tr} (\rho )=1\,} and tr ( ρ 2 ) ≤ tr ( ρ ) {\displaystyle \operatorname {tr} (\rho ^{2})\leq \operatorname {tr} (\rho )\,} (see trace ).
If ρ {\displaystyle \rho \,} is a projection, which defines a pure state, then the upper bound is saturated: tr ( ρ 2 ) = tr ( ρ ) = 1 {\displaystyle \operatorname {tr} (\rho ^{2})=\operatorname {tr} (\rho )=1\,} (see Projections ). The lower bound is obtained by the completely mixed state, represented by the matrix 1 d I d {\displaystyle {\frac {1}{d}}I_{d}\,} .
The purity of a quantum state is conserved under unitary transformations acting on the density matrix in the form ρ ↦ U ρ U † {\displaystyle \rho \mapsto U\rho U^{\dagger }\,} , where U is a unitary matrix. Specifically, it is conserved under the time evolution operator U ( t , t 0 ) = e − i ℏ H ( t − t 0 ) {\displaystyle U(t,t_{0})=e^{{\frac {-i}{\hbar }}H(t-t_{0})}\,} , where H is the Hamiltonian operator. [ 1 ] [ 2 ]
A pure quantum state can be represented as a single vector | ψ ⟩ {\displaystyle |\psi \rangle } in the Hilbert space. In the density matrix formulation, a pure state is represented by the matrix ρ pure = | ψ ⟩ ⟨ ψ | . {\displaystyle \rho _{\text{pure}}=|\psi \rangle \langle \psi |.} However, a mixed state cannot be represented this way, and instead is represented by a convex combination of pure states ρ mixed = ∑ i p i | ψ i ⟩ ⟨ ψ i | , {\displaystyle \rho _{\text{mixed}}=\sum _{i}p_{i}|\psi _{i}\rangle \langle \psi _{i}|,} while ∑ i p i = 1 {\textstyle \sum _{i}p_{i}=1} for normalization. The purity parameter is related to the coefficients: If only one coefficient is equal to 1, the state is pure. Indeed, the purity is 1/ d when the state is completely mixed, i.e. ρ completely mixed = 1 d ∑ i = 1 d | ψ i ⟩ ⟨ ψ i | = 1 d I d , {\displaystyle \rho _{\text{completely mixed}}={\frac {1}{d}}\sum _{i=1}^{d}|\psi _{i}\rangle \langle \psi _{i}|={\frac {1}{d}}I_{d},} where | ψ i ⟩ {\displaystyle |\psi _{i}\rangle } are d orthonormal vectors that constitute a basis of the Hilbert space. [ 3 ]
On the Bloch sphere , pure states are represented by a point on the surface of the sphere, whereas mixed states are represented by an interior point. Thus, the purity of a state can be visualized as the degree to which the point is close to the surface of the sphere.
For example, the completely mixed state of a single qubit 1 2 I 2 {\textstyle {\frac {1}{2}}I_{2}\,} is represented by the center of the sphere, by symmetry.
A graphical intuition of purity may be gained by looking at the relation between the density matrix and the Bloch sphere, ρ = 1 2 ( I + a ⋅ σ ) , {\displaystyle \rho ={\tfrac {1}{2}}\left(I+\mathbf {a} \cdot {\boldsymbol {\sigma }}\right),} where a {\displaystyle \mathbf {a} } is the vector representing the quantum state (on or inside the sphere), and σ = ( σ x , σ y , σ z ) {\displaystyle {\boldsymbol {\sigma }}=(\sigma _{x},\sigma _{y},\sigma _{z})} is the vector of the Pauli matrices .
Since Pauli matrices are traceless, it still holds that tr( ρ ) = 1 . However, by virtue of ( a ⋅ σ ) ( b ⋅ σ ) = ( a ⋅ b ) I + i ( a × b ) ⋅ σ , {\displaystyle \left(\mathbf {a} \cdot {\boldsymbol {\sigma }}\right)\left(\mathbf {b} \cdot {\boldsymbol {\sigma }}\right)=\left(\mathbf {a} \cdot \mathbf {b} \right)\,I+i\left(\mathbf {a} \times \mathbf {b} \right)\cdot {\boldsymbol {\sigma }},} ρ 2 = 1 2 [ 1 2 ( 1 + | a | 2 ) I + a ⋅ σ ] , {\displaystyle \rho ^{2}={\tfrac {1}{2}}\left[{\tfrac {1}{2}}\left(1+|a|^{2}\right)I+\mathbf {a} \cdot {\boldsymbol {\sigma }}\right],} hence tr ( ρ 2 ) = 1 2 ( 1 + | a | 2 ) , {\textstyle \operatorname {tr} (\rho ^{2})={\frac {1}{2}}(1+|a|^{2}),} which agrees with the fact that only states on the surface of the sphere itself are pure (i.e. | a | = 1 {\displaystyle |a|=1} ).
Purity is trivially related to the linear entropy S L {\displaystyle S_{L}\,} of a state by
γ = 1 − S L . {\displaystyle \gamma =1-S_{L}\,.}
The linear entropy is a lower approximation to the von Neumann entropy S , which is defined as
S = ˙ − tr ( ρ ln ρ ) = − ⟨ ln ρ ⟩ . {\displaystyle S\,{\dot {=}}\,-\operatorname {tr} (\rho \ln \rho )=-\langle \ln \rho \rangle \,.}
The linear entropy then is obtained by expanding ln ρ = ln (1−(1− ρ )) , around a pure state, ρ 2 = ρ ; that is, expanding in terms of the non-negative matrix 1− ρ in the formal Mercator series for the logarithm, − ⟨ ln ρ ⟩ = ⟨ 1 − ρ ⟩ + 1 2 ⟨ ( 1 − ρ ) 2 ⟩ + 1 3 ⟨ ( 1 − ρ ) 3 ⟩ + ⋯ , {\displaystyle -\langle \ln \rho \rangle =\langle 1-\rho \rangle +{\frac {1}{2}}\langle (1-\rho )^{2}\rangle +{\frac {1}{3}}\langle (1-\rho )^{3}\rangle +\cdots ,} and retaining just the leading term. Both the linear and the von Neumann entropy measure the degree of mixing of a state, although the linear entropy is easier to calculate, as it does not require diagonalization of the density matrix. Some authors [ 4 ] define linear entropy with a different normalization S L = ˙ d d − 1 ( 1 − tr ( ρ 2 ) ) , {\displaystyle S_{L}\,{\dot {=}}\,{\tfrac {d}{d-1}}(1-\operatorname {tr} (\rho ^{2}))\,,} which ensures that the quantity ranges from zero to unity.
A 2- qubits pure state | ψ ⟩ A B ∈ H A ⊗ H B {\displaystyle |\psi \rangle _{AB}\in H_{A}\otimes H_{B}} can be written (using Schmidt decomposition ) as | ψ ⟩ A B = ∑ j λ j | j ⟩ A | j ⟩ B {\textstyle |\psi \rangle _{AB}=\sum _{j}\lambda _{j}|j\rangle _{A}|j\rangle _{B}} , where { | j ⟩ A } , { | j ⟩ B } {\displaystyle \{|j\rangle _{A}\},\{|j\rangle _{B}\}} are the bases of H A , H B {\displaystyle H_{A},H_{B}} respectively, and ∑ j λ j 2 = 1 , λ j ≥ 0 {\textstyle \sum _{j}\lambda _{j}^{2}=1,\lambda _{j}\geq 0} . Its density matrix is ρ A B = ∑ i , j λ i λ j | i ⟩ A ⟨ j | A ⊗ | i ⟩ B ⟨ j | B {\textstyle \rho ^{AB}=\sum _{i,j}\lambda _{i}\lambda _{j}|i\rangle _{A}\langle j|_{A}\otimes |i\rangle _{B}\langle j|_{B}} . The degree in which it is entangled is related to the purity of the states of its subsystems, ρ A = tr B ( ρ A B ) = ∑ j λ j 2 | j ⟩ A ⟨ j | A {\textstyle \rho ^{A}=\operatorname {tr} _{B}(\rho _{AB})=\sum _{j}\lambda _{j}^{2}|j\rangle _{A}\langle j|_{A}} , and similarly for ρ B {\displaystyle \rho ^{B}} (see partial trace ). If this initial state is separable (i.e. there's only a single λ j ≠ 0 {\displaystyle \lambda _{j}\neq 0} ), then ρ A , ρ B {\displaystyle \rho ^{A},\rho ^{B}} are both pure. Otherwise, this state is entangled and ρ A , ρ B {\displaystyle \rho ^{A},\rho ^{B}} are both mixed. For example, if | ψ ⟩ A B = | Φ + ⟩ = 1 2 ( | 0 ⟩ A ⊗ | 0 ⟩ B + | 1 ⟩ A ⊗ | 1 ⟩ B ) {\textstyle |\psi \rangle _{AB}=|\Phi ^{+}\rangle ={\frac {1}{\sqrt {2}}}(|0\rangle _{A}\otimes |0\rangle _{B}+|1\rangle _{A}\otimes |1\rangle _{B})} which is a maximally entangled state, then ρ A , ρ B {\displaystyle \rho ^{A},\rho ^{B}} are both completely mixed.
For 2-qubits (pure or mixed) states, the Schmidt number (number of Schmidt coefficients) is at most 2. Using this and Peres–Horodecki criterion (for 2-qubits), a state is entangled if its partial transpose has at least one negative eigenvalue. Using the Schmidt coefficients from above, the negative eigenvalue is − λ 0 λ 1 {\displaystyle -\lambda _{0}\lambda _{1}} . [ 5 ] The negativity N = − λ 0 λ 1 {\displaystyle {\mathcal {N}}=-\lambda _{0}\lambda _{1}} of this eigenvalue is also used as a measure of entanglement – the state is more entangled as this eigenvalue is more negative (up to − 1 2 {\textstyle -{\frac {1}{2}}} for Bell states ). For the state of subsystem A {\displaystyle A} (similarly for B {\displaystyle B} ), it holds that: ρ A = tr B ( | ψ ⟩ A B ⟨ ψ | A B ) = λ 0 2 | 0 ⟩ A ⟨ 0 | A + λ 1 2 | 1 ⟩ A ⟨ 1 | A {\displaystyle \rho ^{A}=\operatorname {tr} _{B}(|\psi \rangle _{AB}\langle \psi |_{AB})=\lambda _{0}^{2}|0\rangle _{A}\langle 0|_{A}+\lambda _{1}^{2}|1\rangle _{A}\langle 1|_{A}}
And the purity is γ = λ 0 4 + λ 1 4 = ( λ 0 2 + λ 1 2 ) 2 − 2 ( λ 0 λ 1 ) 2 = 1 − 2 N 2 {\displaystyle \gamma =\lambda _{0}^{4}+\lambda _{1}^{4}=(\lambda _{0}^{2}+\lambda _{1}^{2})^{2}-2(\lambda _{0}\lambda _{1})^{2}=1-2{\mathcal {N}}^{2}} .
One can see that the more entangled the composite state is (i.e. more negative), the less pure the subsystem state.
In the context of localization, a quantity closely related to the purity, the so-called inverse participation ratio (IPR) turns out to be useful. It is defined as the integral (or sum for finite system size) over the square of the density in some space, e.g., real space, momentum space , or even phase space, where the densities would be the square of the real space wave function | ψ ( x ) | 2 {\displaystyle |\psi (x)|^{2}} , the square of the momentum space wave function | ψ ~ ( k ) | 2 {\displaystyle |{\tilde {\psi }}(k)|^{2}} , or some phase space density like the Husimi distribution , respectively. [ 6 ]
The smallest value of the IPR corresponds to a fully delocalized state, ψ ( x ) = 1 / N {\displaystyle \psi (x)=1/{\sqrt {N}}} for a system of size N {\displaystyle N} , where the IPR yields ∑ x | ψ ( x ) | 4 = N / ( N 1 / 2 ) 4 = 1 / N {\textstyle \sum _{x}|\psi (x)|^{4}=N/(N^{1/2})^{4}=1/N} . Values of the IPR close to 1 correspond to localized states (pure states in the analogy), as can be seen with the perfectly localized state ψ ( x ) = δ x , x 0 {\displaystyle \psi (x)=\delta _{x,x_{0}}} , where the IPR yields ∑ x | ψ ( x ) | 4 = 1 {\textstyle \sum _{x}|\psi (x)|^{4}=1} . In one dimension IPR is directly proportional to the inverse of the localization length, i.e., the size of the region over which a state is localized. Localized and delocalized (extended) states in the framework of condensed matter physics then correspond to insulating and metallic states, respectively, if one imagines an electron on a lattice not being able to move in the crystal (localized wave function, IPR is close to one) or being able to move (extended state, IPR is close to zero).
In the context of localization, it is often not necessary to know the wave function itself; it often suffices to know the localization properties. This is why the IPR is useful in this context. The IPR basically takes the full information about a quantum system (the wave function; for a N {\displaystyle N} -dimensional Hilbert space one would have to store N {\displaystyle N} values, the components of the wave function) and compresses it into one single number that then only contains some information about the localization properties of the state. Even though these two examples of a perfectly localized and a perfectly delocalized state were only shown for the real space wave function and correspondingly for the real space IPR, one could obviously extend the idea to momentum space and even phase space; the IPR then gives some information about the localization in the space at consideration, e.g. a plane wave would be strongly delocalized in real space, but its Fourier transform then is strongly localized, so here the real space IPR would be close to zero and the momentum space IPR would be close to one. | https://en.wikipedia.org/wiki/Purity_(quantum_mechanics) |
A purlin (or historically purline , purloyne , purling , perling ) is a longitudinal, horizontal, structural member in a roof . In traditional timber framing there are three basic types of purlin: purlin plate, principal purlin, and common purlin.
Purlins also appear in steel frame construction. Steel purlins may be painted or greased for protection from the environment.
Information on the origin of the term "purlin" is scant. The Oxford Dictionary suggests a French origin, with the earliest quote using a variation of purlin in 1447, though the accuracy of this claim has been disputed.
A purlin plate in wood construction is also called an "arcade plate" in European English, [ 1 ] "under purlin", and "principal purlin". The term plate means a major, horizontal, supporting timber. Purlin plates are beams which support the mid-span of rafters and are supported by posts. By supporting the rafters they allow longer spans than the rafters alone could span, thus allowing a wider building. Purlin plates are very commonly found in large old barns in North America. A crown plate has similarities to a purlin plate but supports collar beams in the middle of a timber-framed building.
Principal purlins in wood construction, also called "major purlins" and "side purlins," are supported by principal rafters and support common rafters in what is known as a "double roof" (a roof framed with a layer of principal rafters and a layer of common rafters). Principal purlins are further classified by how they connect to the principal rafters: "through purlins" pass over the top; "butt purlins" tenon into the sides of the principal rafters; and "clasped purlins," of which only one historic U.S. example is known, [ citation needed ] ) are captured by a collar beam. Through purlins are further categorized as "trenched," "back," or "clasped;" butt purlins are classified as "threaded," "tenoned," and/or [ clarification needed ] "staggered." [ 2 ]
Common purlins in wood construction, also called a "major-rafter minor-purlin system". [ 3 ] Common purlins are typically "trenched through" the top sides (backs) of principal rafters and carry vertical roof sheathing (the key to identifying this type of roof system). Common purlin roofs in North America are found in areas settled by the English and may have been a new invention in the Massachusetts Bay Colony. No examples of framed buildings with common purlin roofs have been reported in England, however some stone barns in England have vertically boarded, common purlin roofs. Historically, these roofs are found in New England, the highest concentration in Maine, and isolated parts of New York and along the St. Lawrence River in Canada. One of the oldest surviving examples is in the Coffin House in Newbury, Massachusetts, from 1678. The purpose of a common purlin roof may be they allow a board roof , that is a roof of nothing but vertically laid boards with seams covered with battens or another layer of boards. [ 4 ]
In steel construction, the term purlin typically refers to roof framing members that span parallel to the building eave, [ 5 ] and support the roof decking or sheeting . The purlins are in turn supported by rafters or walls. Purlins are most commonly used in Steel Framed Building Systems, where Z-shapes are utilized in a manner that allows flexural continuity between spans.
Steel industry practice assigns structural shapes representative designations for convenient shorthand description on drawings and documentation: Channel sections, with or without flange stiffeners, are usually referenced as C shapes; Channel sections without flange stiffeners are also referenced as U shapes; Point symmetric sections that are shaped similar to the letter Z are referenced as Z shapes. Section designations can be regional and even specific to a manufacturer. In steel building construction , secondary members such as purlins (roof) and girts (wall) are frequently cold-formed steel C, Z or U sections, (or mill rolled) C sections.
Cold formed members can be efficient on a weight basis relative to mill rolled sections for secondary member applications. Additionally, Z sections can be nested for transportation bundling and, on the building, lapped at the supports to develop a structurally efficient continuous beam across multiple supports.
Note: The sketches in this section reference terminology commonly used in the UK and Australia. [ 6 ]
This article incorporates text from a publication now in the public domain : Chisholm, Hugh , ed. (1911). " Purlin ". Encyclopædia Britannica . Vol. 22 (11th ed.). Cambridge University Press. p. 665. | https://en.wikipedia.org/wiki/Purlin |
The Purnell equation is an equation used in analytical chemistry to calculate the resolution R s between two peaks in a chromatogram . [ 1 ] [ 2 ]
where
The higher the resolution, the better the separation.
This article about analytical chemistry is a stub . You can help Wikipedia by expanding it .
This article related to chromatography is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Purnell_equation |
The Purple Earth Hypothesis (PEH) is an astrobiological hypothesis , first proposed by molecular biologist Shiladitya DasSarma in 2007, [ 1 ] that the earliest photosynthetic life forms of Early Earth were based on the simpler molecule retinal rather than the more complex porphyrin -based chlorophyll , making the surface biosphere appear purplish rather than its current greenish color. [ 2 ] [ 3 ] It is estimated to have occurred between 3.5 and 2.4 billion years ago during the Archean eon , prior to the Great Oxygenation Event and Huronian glaciation . [ 4 ]
Retinal-containing cell membranes exhibit a single light absorption peak centered in the energy-rich green-yellow region of the visible spectrum , but transmit and reflect red and blue light, resulting in a magenta color. [ 5 ] Chlorophyll pigments, in contrast, absorb red and blue light, but little or no green light, which results in the characteristic green reflection of plants , green algae , cyanobacteria and other organisms with chlorophyllic organelles . The simplicity of retinal pigments in comparison to the more complex chlorophyll, their association with isoprenoid lipids in the cell membrane, as well as the discovery of archaeal membrane components in ancient sediments on the Early Earth are consistent with an early appearance of life forms with purple membranes prior to the turquoise of the Canfield ocean and later green photosynthetic organisms. [ citation needed ]
The discovery of archaeal membrane components in ancient sediments on the Early Earth support the PEH. [ citation needed ]
An example of retinal-based organisms that exist today are photosynthetic microbes collectively called Haloarchaea . [ 1 ] Many Haloarchaea contain the retinal derivative protein bacteriorhodopsin in their cell membrane , which carries out photon -driven proton pumping , generating a proton -motive gradient across the membrane and driving ATP synthesis . The process is a form of anoxygenic photosynthesis that does not involve carbon fixation , and the haloarchaeal membrane proton pump constitutes one of the simplest known bioenergetic systems for harvesting light energy .
Microorganisms with purple and green photopigments frequently co-exist in stratified colonies known as microbial mats , where they may utilize complementary regions of the solar spectrum. Co-existence of purple and green pigment-containing microorganisms in many environments suggests their co-evolution.
It is possible that the Early Earth's biosphere was initially dominated by retinal-powered archaeal colonies that absorbed all the green light, leaving the eubacteria that "lived in their shadows" to evolve utilizing the residual red and blue light spectrum . However, when porphyrin-based photoautotrophs evolved and started to photosynthesize, which included both the primitive purple bacteria using bacteriochlorophyll and cyanobacteria using chlorophyll, highly reactive dioxygen was released as a byproduct of water splitting and started to accumulate, first in the ocean and then in the atmosphere . Over the course of a billion years, large enough quantities of oxygen had been produced, the reducing capabilities of chemical compounds on the Earth's surface were depleted, and the once- reducing atmosphere eventually became a permanently oxidizing one with abundant free oxygen molecules — an event known as Great Oxygenation Event . This coincided with a 300 million year-long global ice age at beginning of the Proterozoic known as the Huronian glaciation (which might also have been partly caused by the oxidative depletion of the atmospheric methane — a powerful greenhouse gas — due to the Great Oxygenation) and devastated the anaerobic biota, leaving the niches open for eubacteria that evolved antioxident capabilities (both the aerobic proteobacteria and the photosynthetic cyanobacteria) to exploit and prosper. This also forced the surviving anaerobes to either live only in anoxic waters and deep sea oxygen minimum zones , or adapt a symbiotic life among aerobes (whose colonies would sometimes consume enough free oxygen to create pockets of hypoxia where anaerobes can thrive), which might have paved way for the long-term endosymbiosis between anaerobic archaea and aerobic eubacteria (which evolved into mitochondria ) that enabled eukaryotes to evolve.
However, the porphyrin-based nature of chlorophyll had created an evolutionary trap [ citation needed ] , dictating that chlorophyllic organisms cannot re-adapt to absorb the energy-rich and now-available green light, and therefore ended up reflecting and presenting a greenish color. The subsequent success of more advanced chlorophyllic organisms (particularly green algae and early plants ) in terrestrial colonization created an overall green biosphere all over Earth.
Astrobiologists have suggested that retinal pigments may serve as remote biosignatures in exoplanet research. [ 6 ] The Purple Earth hypothesis has great implications for the search for extraterrestrial life . Historically, scientists sought out planets reflecting light in the green-yellow range as possible hosts to photosynthetic organisms, due to the implied presence of chlorophyll. The hypothesis suggests that search methods should be expanded to planets reflecting blue and red light, since evolution of retinal-based photosynthesis is also probable, or possibly even more likely than the evolution of chlorophyllic systems. | https://en.wikipedia.org/wiki/Purple_Earth_hypothesis |
Purple Ocean was a bulletin board system (BBS) founded in June 1984 by system operator (SysOp) Dustin Malcom in Plano, Texas . These early BBS systems were typically run by individual users or small groups and were often hosted on personal computers in users’ homes or garages. They provided a space for users to share information and connect with others who shared their interests.
The Purple Ocean BBS was best known for its numerous gaming features including numerous different versions and scenarios of Trade Wars 1000, 2000, and 2002. At its peak, over 100 different Trade Wars universes were operated simultaneously with thousands of players logging on each day. The Purple Ocean BBS was also the first BBS in Texas to offer 38.4 kbit/s transfer rates for every node.
In the broader context of BBS history, Purple Ocean stood out as one of the largest North American gaming BBSs during the mid-1980s.
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Purple_Ocean |
VMware ESXi (formerly ESX ) is an enterprise-class , type-1 hypervisor developed by VMware , a subsidiary of Broadcom , for deploying and serving virtual computers . As a type-1 hypervisor, ESXi is not a software application that is installed on an operating system (OS); instead, it includes and integrates vital OS components, such as a kernel . [ 5 ]
After version 4.1 (released in 2010), VMware renamed ESX to ESXi . ESXi replaces Service Console (a rudimentary operating system) with a more closely integrated OS. ESX/ESXi is the primary component in the VMware Infrastructure software suite . [ 6 ]
The name ESX originated as an abbreviation of Elastic Sky X . [ 7 ] [ 8 ] In September 2004, the replacement for ESX was internally called VMvisor , but later changed to ESXi (as the "i" in ESXi stood for "integrated"). [ 9 ] [ 10 ]
ESX runs on bare metal (without running an operating system) [ 11 ] unlike other VMware products. [ 12 ] It includes its own kernel. In the historic VMware ESX, a Linux kernel was started first [ 13 ] and then used to load a variety of specialized virtualization components, including ESX, which is otherwise known as the vmkernel component. [ 14 ] The Linux kernel was the primary virtual machine; it was invoked by the service console. At normal run-time, the vmkernel was running on the bare computer, and the Linux-based service console ran as the first virtual machine. VMware dropped development of ESX at version 4.1, and now uses ESXi, which does not include a Linux kernel at all. [ 15 ]
The vmkernel is a microkernel [ 16 ] with three interfaces: hardware, guest systems, and the service console (Console OS).
The vmkernel handles CPU and memory directly, using scan-before-execution (SBE) to handle special or privileged CPU instructions [ 17 ] [ 18 ] and the SRAT (system resource allocation table) to track allocated memory. [ 19 ]
Access to other hardware (such as network or storage devices) takes place using modules. At least some of the modules derive from modules used in the Linux kernel . To access these modules, an additional module called vmklinux implements the Linux module interface. According to the README file, "This module contains the Linux emulation layer used by the vmkernel." [ 20 ]
The vmkernel uses the device drivers: [ 20 ]
These drivers mostly equate to those described in VMware's hardware compatibility list . [ 21 ] All these modules fall under the GPL . Programmers have adapted them to run with the vmkernel: VMware Inc. has changed the module-loading and some other minor things. [ 20 ]
In ESX (and not ESXi), the Service Console is a vestigial general purpose operating system most significantly used as bootstrap for the VMware kernel, vmkernel, and secondarily used as a management interface. Both of these Console Operating System functions are being deprecated from version 5.0, as VMware migrates exclusively to the ESXi model. [ 22 ] The Service Console, for all intents and purposes, is the operating system used to interact with VMware ESX and the virtual machines that run on the server.
In the event of a hardware error, the vmkernel can catch a Machine Check Exception. [ 23 ] This results in an error message displayed on a purple diagnostic screen. This is colloquially known as a purple diagnostic screen, or purple screen of death (PSoD, cf. blue screen of death (BSoD)).
Upon displaying a purple diagnostic screen, the vmkernel writes debug information to the core dump partition. This information, together with the error codes displayed on the purple diagnostic screen can be used by VMware support to determine the cause of the problem.
VMware ESX used to be available in two main types: ESX and ESXi, but as of version 5, the original ESX has been discontinued in favor of ESXi.
ESX and ESXi before version 5.0 do not support Windows 8/Windows 2012. These Microsoft operating systems can only run on ESXi 5.x or later. [ 24 ]
VMware ESXi, a smaller-footprint version of ESX, does not include the ESX Service Console. Before Broadcom acquired VMware, it was available - without the need to purchase a vCenter license - as a free download from VMware, with some features disabled. [ 25 ] [ 26 ] [ 27 ]
ESXi stands for "ESX integrated". [ 28 ]
VMware ESXi originated as a compact version of VMware ESX that allowed for a smaller 32 MB disk footprint on the host. With a simple configuration console for mostly network configuration and remote based VMware Infrastructure Client Interface, this allows for more resources to be dedicated to the guest environments.
Two variations of ESXi exist:
The same media can be used to install either of these variations depending on the size of the target media. [ 29 ] One can upgrade ESXi to VMware Infrastructure 3 [ 30 ] or to VMware vSphere 4.0 ESXi.
Originally named VMware ESX Server ESXi edition, through several revisions the ESXi product finally became VMware ESXi 3. New editions then followed: ESXi 3.5, ESXi 4, ESXi 5 and (as of 2024 [update] ) ESXi 8.
VMware has been sued by Christoph Hellwig, a Linux kernel developer. The lawsuit began on March 5, 2015. It was alleged that VMware had misappropriated portions of the Linux kernel, [ 31 ] [ 32 ] and, following a dismissal by the court in 2016, Hellwig announced he would file an appeal. [ 33 ]
The appeal was decided February 2019 and again dismissed by the German court, on the basis of not meeting "procedural requirements for the burden of proof of the plaintiff". [ 34 ]
In the last stage of the lawsuit in March 2019, the Hamburg Higher Regional Court also rejected the claim on procedural grounds. Following this, VMware officially announced that they would remove the code in question. [ 35 ] This followed with Hellwig withdrawing his case, and withholding further legal action. [ 36 ]
The following products operate in conjunction with ESX:
Network-connectivity between ESX hosts and the VMs running on it relies on virtual NICs (inside the VM) and virtual switches. The latter exists in two versions: the 'standard' vSwitch allowing several VMs on a single ESX host to share a physical NIC and the 'distributed vSwitch' where the vSwitches on different ESX hosts together form one logical switch. Cisco offers in their Cisco Nexus product-line the Nexus 1000v , an advanced version of the standard distributed vSwitch. A Nexus 1000v consists of two parts: a supervisor module (VSM) and on each ESX host a virtual Ethernet module (VEM). The VSM runs as a virtual appliance within the ESX cluster or on dedicated hardware (Nexus 1010 series) and the VEM runs as a module on each host and replaces a standard dvS (distributed virtual switch) from VMware.
Configuration of the switch is done on the VSM using the standard NX-OS CLI . It offers capabilities to create standard port-profiles which can then be assigned to virtual machines using vCenter.
There are several differences between the standard dvS and the N1000v; one is that the Cisco switch generally has full support for network technologies such as LACP link aggregation or that the VMware switch supports new features such as routing based on physical NIC load. However, the main difference lies in the architecture: Nexus 1000v is working in the same way as a physical Ethernet switch does while dvS is relying on information from ESX. This has consequences for example in scalability where the Kappa limit for a N1000v is 2048 virtual ports against 60000 for a dvS.
The Nexus1000v is developed in co-operation between Cisco and VMware and uses the API of the dvS. [ 41 ]
Because VMware ESX is a leader in the server-virtualization market, [ 42 ] software and hardware vendors offer a range of tools to integrate their products or services with ESX. Examples are the products from Veeam Software with backup and management applications [ 43 ] and a plugin to monitor and manage ESX using HP OpenView , [ 44 ] Quest Software with a range of management and backup-applications and most major backup-solution providers have plugins or modules for ESX. Using Microsoft Operations Manager (SCOM) 2007/2012 with a Bridgeways ESX management pack gives the user a realtime ESX datacenter health view.
Hardware vendors such as Hewlett Packard Enterprise and Dell include tools to support the use of ESX(i) on their hardware platforms. An example is the ESX module for Dell's OpenManage management platform. [ 45 ]
VMware has added a Web Client [ 46 ] since v5 but it will work on vCenter only and does not contain all features. [ 47 ]
As of September 2020, these are the known limitations of VMware ESXi 7.0 U1.
Some maximums in ESXi Server 7.0 may influence the design of data centers: [ 48 ] [ 49 ]
In terms of performance, virtualization imposes a cost in the additional work the CPU has to perform to virtualize the underlying hardware. Instructions that perform this extra work, and other activities that require virtualization, tend to lie in operating system calls. In an unmodified operating system, OS calls introduce the greatest portion of virtualization "overhead". [ citation needed ]
Paravirtualization or other virtualization techniques may help with these issues. VMware developed the Virtual Machine Interface for this purpose, and selected operating systems currently [update] support this. A comparison between full virtualization and paravirtualization for the ESX Server [ 50 ] shows that in some cases paravirtualization is much faster.
When using the advanced and extended network capabilities by using the Cisco Nexus 1000v distributed virtual switch the following network-related limitations apply: [ 41 ]
Regardless of the type of virtual SCSI adapter used, there are these limitations: [ 51 ] | https://en.wikipedia.org/wiki/Purple_Screen_of_Death |
Purple of Cassius is a purple pigment formed by the reaction of gold salts with tin(II) chloride . It has been used to impart glass with a red coloration (see cranberry glass ), as well as to determine the presence of gold as a chemical test .
Generally, the preparation of this material involves gold being dissolved in aqua regia , then reacted with a solution of tin(II) chloride. The tin(II) chloride reduces the chloroauric acid from the dissolution of gold in aqua regia to a colloid of elemental gold supported on tin dioxide to give a purple precipitate or coloration.
When used as a test, the intensity of the color correlates with the concentration of gold present. This test was first observed and refined by a German physician and alchemist, Andreas Cassius (1600–1676) of Hamburg , in 1665. Berzelius later made a detailed study of the purple of Cassius. The colour also attracted attention from Michael Faraday . [ 1 ]
Richard Adolf Zsigmondy , who earned the 1926 Nobel Prize for chemistry , says that "Several of the red gold divisions prepared with formaldehyde as well as those reduced with phosphorus appeared perfectly clear in ordinary daylight (like good red wine ). They did not settle out their gold, and I was therefore able to call them rightly chemical solutions . In Thomas Graham ’s dialysis , however, they behaved like colloidal suspensions : the gold particles did not pass through the parchment membrane . This showed my gold divisions their proper place, namely, that they belonged to the colloidal suspensions." [ 1 ]
Partially translated from the German Wikipedia article, Goldpurpur . | https://en.wikipedia.org/wiki/Purple_of_Cassius |
Paecillium Luangsa-ard, Hywel-Jones & Samson nom. prov. (2007) [ 1 ] Penicillium lilacinum Thom (1910) Penicillium amethystinum Wehmer (1923) Spicaria rubidopurpurea Aoki (1941) Paecilomyces lilacinus ( Thom ) Samson (1974)
Purpureocillium lilacinum is a species of filamentous fungus in the family Ophiocordycipitaceae . [ 3 ] It has been isolated from a wide range of habitats, including cultivated and uncultivated soils , forests , grassland , deserts , estuarine sediments and sewage sludge, and insects. It has also been found in nematode eggs, and occasionally from females of root-knot and cyst nematodes. In addition, it has frequently been detected in the rhizosphere of many crops. The species can grow at a wide range of temperatures – from 8 to 38 °C (46 to 100 °F) for a few isolates, with optimal growth in the range 26 to 30 °C (79 to 86 °F). It also has a wide pH tolerance and can grow on a variety of substrates. [ 4 ] [ 5 ] P. lilacinum has shown promising results for use as a biocontrol agent to control the growth of destructive root-knot nematodes .
The species was originally described by American mycologist Charles Thom in 1910, under than name Penicillium lilacinum . [ 6 ] Taxonomic synonyms include Penicillium amethystinum Wehmer and Spicaria rubidopurpurea Aoki. [ 2 ] In 1974, Robert A. Samson transferred the species to Paecilomyces . [ 4 ] Publications in the 2000s (decade) indicated that the genus Paecilomyces was not monophyletic , [ 7 ] and that close relatives were Paecilomyces nostocoides , Isaria takamizusanensis and Nomuraea atypicola . [ 8 ] The new genus Purpureocillium was created to hold the taxon. The generic name refers to the purple conidia produced by the fungus. [ 9 ]
Purpureocillium lilacinum forms a dense mycelium which gives rise to conidiophores . These bear phialides from the ends of which spores are formed in long chains. Spores germinate when suitable moisture and nutrients are available. Colonies on malt agar grow rather fast, attaining a diameter of 5–7 cm within 14 days at 25 °C (77 °F), consisting of a basal felt with a floccose overgrowth of aerial mycelium ; at first white, but when sporulating changing to various shades of vinaceous . The reverse side is sometimes uncolored but usually in vinaceous shades. The vegetative hyphae are smooth-walled, hyaline , and 2.5–4.0 μm wide. Conidiophores arising from submerged hyphae, 400–600 μm in length, or arising from aerial hyphae and half as long. Phialides consisting of a swollen basal part, tapering into a thin distinct neck. Conidia are in divergent chains, ellipsoid to fusiform in shape, and smooth walled to slightly roughened. Chlamydospores are absent. [ 4 ]
Purpureocillium lilacinum is highly adaptable in its life strategy: depending on the availability of nutrients in the surrounding microenvironments it may be entomopathogenic , [ 10 ] [ 11 ] [ 12 ] mycoparasitic , [ 13 ] saprophytic , [ 14 ] as well as nematophagous .
Purpureocillium lilacinum is an infrequent cause of human disease. [ 15 ] [ 16 ] Most reported cases involve patients with compromised immune systems , indwelling foreign devices, or intraocular lens implants. [ 17 ] [ 18 ] Research of the last decade suggests it may be an emerging pathogen of both immunocompromised [ 19 ] as well as immunocompetent adults. [ 20 ] It is one of the most common species causing hyalohyphomycosis along with Paecilomyces variotii . [ 9 ]
Plant-parasitic nematodes cause significant economic losses to a wide variety of crops. Chemical control is a widely used option for plant-parasitic nematode management. However, chemical nematicides are now being reappraised in respect of environmental hazard , high costs, limited availability in many developing countries or their diminished effectiveness following repeated applications.
Purpureocillium lilacinum was first observed in association with nematode eggs in 1966 [ 21 ] and the fungus was subsequently found parasitising the eggs of Meloidogyne incognita in Peru . [ 22 ] It has now been isolated from many cyst and root-knot nematodes and from soil in many locations. [ 23 ] [ 24 ] Several successful field trials using P. lilacinum against pest nematodes were conducted in Peru. [ 22 ] The Peruvian isolate was then sent to nematologists in 46 countries for testing, as part of the International Meloidogyne project, resulting in many more field trials on a range of crops in many soil types and climates. [ 25 ] Field trials, glasshouse trials and in vitro testing of P. lilacinum continues and more isolates have been collected from soil, nematodes and occasionally from insects. Isolates vary in their pathogenicity to plant-parasitic nematodes. Some isolates are aggressive parasites while others, though morphologically indistinguishable, are less or non-pathogenic. Sometimes isolates that looked promising in vitro or in glasshouse trials have failed to provide control in the field. [ 26 ]
Many enzymes produced by P. lilacinum have been studied. A basic serine protease with biological activity against Meloidogyne hapla eggs has been identified. [ 27 ] One strain of P. lilacinum has been shown to produce proteases and a chitinase , enzymes that could weaken a nematode egg shell so as to enable a narrow infection peg to push through. [ 28 ]
Before infecting a nematode egg, P. lilacinum flattens against the egg surface and becomes closely appressed to it. P. lilacinum produces simple appressoria anywhere on the nematode egg shell either after a few hyphae grow along the egg surface, or after a network of hyphae form on the egg. The presence of appressoria appears to indicate that the egg is, or is about to be, infected. In either case, the appressorium appears the same, as a simple swelling at the end of a hypha , closely appressed to the eggshell. Adhesion between the appressorium and nematode egg surface must be strong enough to withstand the opposing force produced by the extending tip of a penetration hypha. [ 29 ] When the hypha has penetrated the egg, it rapidly destroys the juvenile within, before growing out of the now empty egg shell to produce conidiophores and to grow towards adjacent eggs.
Paecilotoxin is a mycotoxin isolated from the fungus. [ 30 ] Its significance is unknown. Khan et al. (2003) tested one strain of P. lilacinum for the production of paecilotoxin and were unable to show toxin production in that strain, suggesting that toxin synthesis may vary among isolates. [ 31 ] [ 32 ] | https://en.wikipedia.org/wiki/Purpureocillium_lilacinum |
Pursuit predation is a form of predation in which predators actively give chase to their prey , either solitarily or as a group . It is an alternate predation strategy to ambush predation — pursuit predators rely on superior speed , endurance and/or teamwork to seize the prey, while ambush predators use concealment , luring , exploiting of surroundings and the element of surprise to capture the prey. While the two patterns of predation are not mutually exclusive , morphological differences in an organism's body plan can create an evolutionary bias favoring either type of predation.
Pursuit predation is typically observed in carnivorous species within the kingdom Animalia , such as cheetahs , lions , wolves and early Homo species. The chase can be initiated either by the predator, or by the prey if it is alerted to a predator's presence and attempt to flee before the predator gets close. The chase ends either when the predator successfully catches up and tackles the prey, or when the predator abandons the attempt after the prey outruns it and escapes.
One particular form of pursuit predation is persistence hunting , where the predator stalks the prey slowly but persistently to wear it down physically with fatigue or overheating ; some animals are examples of both types of pursuit.
There is still uncertainty as to whether predators behave with a general tactic or strategy while preying. [ 1 ] However, among pursuit predators there are several common behaviors. Often, predators will scout potential prey, assessing prey quantity and density prior to engaging in a pursuit. Certain predators choose to pursue prey primarily in a group of conspecifics; these animals are known as pack hunters or group pursuers. Other species choose to hunt alone. These two behaviors are typically due to differences in hunting success, where some groups are very successful in groups and others are more successful alone. Pursuit predators may also choose to either exhaust their metabolic resources rapidly [ 2 ] or pace themselves during a chase. [ 3 ] This choice can be influenced by prey species, seasonal settings, or temporal settings. Predators that rapidly exhaust their metabolic resources during a chase tend to first stalk their prey, slowly approaching their prey to decrease chase distance and time. When the predator is at a closer distance (one that would lead to easier prey capture), it finally gives chase. [ 4 ] Pacing pursuit is more commonly seen in group pursuit, as individual animals do not need to exert as much energy to capture prey. However, this type of pursuit requires group coordination, which may have varying degrees of success. Since groups can engage in longer chases, they often focus on separating a weaker or slower prey item during pursuit. [ 5 ] Morphologically speaking, while ambush predation requires stealth, [ 6 ] pursuit predation requires speed; pursuit predators are proportionally long-limbed and equipped with cursorial adaptations. [ 7 ] Current theories suggest that this proportionally long-limbed approach to body plan was an evolutionary countermeasure to prey adaptation. [ 7 ]
Group pursuers hunt with a collection of conspecifics. Group pursuit is usually seen in species of relatively high sociality ; in vertebrates, individuals often seem to have defined roles in pursuit.
African wild dog ( Lycaon pictus ) packs have been known to split into several smaller groups while in pursuit; one group initiates the chase, while the other travels ahead of the prey's escape path. The group of chase initiators coordinate their chase to lead the prey towards the location of the second group, where the prey's escape path will be effectively cut off. [ 8 ]
Bottlenose dolphins ( Tursiops ) have been shown exhibiting similar behaviors of pursuit role specialization. One group within the dolphin pod, known as the drivers, give chase to the fish - forcing the fish into a tight circle formation, while the other group of the pod, the barriers, approach the fish from the opposite direction. This two-pronged attack leaves the fish with only the option of jumping out of the water to escape the dolphins. However, the fish are completely vulnerable in the air; it is at this point when the dolphins leap out and catch the fish. [ 9 ]
In lion ( Panthera leo ) pack hunting, each member of the hunting group is assigned a position, from left wing to right wing, in order to better obtain prey. [ 10 ] Such specializations in roles within the group are thought to increase sophistication in technique; lion wing members are faster, and will drive prey toward the center where the larger, stronger, killing members of the pride will take down the prey. Many observations of group pursuers note an optimal hunting size in which certain currencies (mass of prey killed or number of prey killed) are maximized with respect to costs (kilometers covered or injuries sustained). [ 11 ] [ 12 ] Groups size is often dependent on aspects of the environment: number of prey, prey density, number of competitors, seasonal changes, etc. [ 13 ]
While birds are generally believed to be individual hunters, there are a few examples of birds that cooperate during pursuits. Harris's hawks ( Parabuteo unicinctus ) have two cooperative strategies for hunting: Surrounding and cover penetration, and long chase relay attack.
The first strategy involves a group of hawks surrounding prey hidden under some form of cover, while another hawk attempts to penetrate the prey's cover. The penetration attempt flushes the prey out from its cover where it is swiftly killed by one of the surrounding hawks. [ 14 ]
The second strategy is less commonly used: It involves a "relay attack" in which a group of hawks, led by a "lead" hawk, engage in a long chase for prey. The "lead" hawk will dive in order to kill the prey. If the dive is unsuccessful, the role of the "lead" shifts to another hawk who will then dive in another attempt to kill the prey. During one observed relay attack, 20 dives and hence 20 lead switches were exhibited. [ 14 ]
As in vertebrates, there are many species of invertebrates which actively pursue prey in groups and exhibit task specialization, but while the vertebrates change their behavior based on their role in hunting, invertebrate task delegation is usually based on actual morphological differences. The vast majority of eusocial insects have castes within a population which tend to differ in size and have specialized structures for different tasks. [ 15 ] This differentiation is taken to the extreme in the groups isoptera and hymenoptera , or termites and ants , bees , and wasps respectively.
Termite -hunting ants of the genus Pachycondyla , also known as Matabele ants, form raiding parties consisting of ants of different castes, such as soldier ants and worker ants. [ 16 ] Soldier ants are much larger than worker ants, with more powerful mandibles and more robust exoskeletons , and so they make up the front lines of raiding parties and are responsible for killing prey. Workers usually butcher and carry off the killed prey, while supporting the soldiers. The raiding parties are highly mobile and move aggressively into the colonies of termites, often breaking through their outer defenses and entering their mounds. The ants do not completely empty the mound of termites, instead they only take a few, allowing the termites to recover their numbers so that the ants have a steady stream of prey. [ 16 ]
Asian giant hornets , Vespa mandarinia , form similar raiding parties to hunt their prey, which usually consists of honeybees. [ 17 ] The giant hornets group together and as a team can decimate an entire honeybee colony, especially those of non-native European honeybees. Alone, the hornets are subject to attack by the smaller bees, who swarm the hornet and vibrate their abdomens to generate heat, collectively cooking the hornet until it dies. [ 17 ] By hunting in groups, the hornets avoid this problem.
While most big cat species are either solitary ambush predators or pack hunters , cheetahs ( Acinonyx jubatus ) are primarily solitary pursuit predators. Widely known as the fastest terrestrial animal with running speeds reaching 61–64 miles per hour (98–103 km/h; 27–29 m/s), cheetahs take advantage of their speed during chases. [ 18 ] [ 19 ] However, their speed and acceleration also have disadvantages, as both rely on anaerobic metabolism and can only be sustained for short periods of time. Studies show that cheetahs can maintain maximum speed for up to a distance of approximately 500 yards (460 m), [ 20 ] which is only about 20 seconds of sprinting, before fatigue and overheating set in. Due to these limitations, cheetahs are often observed quietly walking towards the prey to shorten the distance before running at moderate speeds during chases.
There are claims that the key to cheetahs' pursuit being successful may not be just burst of sheer speed. Cheetahs are extremely agile , able to change directions in very short amounts of time while running at very high speeds. This maneuverability can make up for unsustainable high-speed pursuits, as it allows a cheetah to quickly close the distance without having to decelerate when the prey suddenly changes direction. [ 21 ] Due to being lightly built, cheetahs will try to foot sweep and unbalance the prey, instead of grasping and tackling. Only after the prey has fallen over and thus momentarily stopped running, the cheetah will pounce and try to subdue it with a throat bite .
The Painted redstart ( Myioborus pictus ) is one of the most well documented flush pursuers. When flies, prey for redstarts, are alerted of the presence of predators, they respond by fleeing. Redstarts take advantage of this anti-predator response by spreading and orienting their easily noticeable wings and tails, alerting the flies, but only when they are in a position where the flies' escape path intersects with the redstart's central field of vision. When prey's path are in this field of vision, the redstart's prey capture rate is at its maximum. Once the flies begin to flee, the redstart begins to chase. It has been proposed that redstarts exploit two aspects of the visual sensitivity of their prey: sensitivity to the location of the stimulus in the prey's visual field and sensitivity to the direction of stimulus environment. [ 22 ] The effectiveness of this pursuit can also be explained by "rare enemy effect", an evolutionary consequence of multi-species predator-prey interactions. [ 22 ]
Dragonflies are skilled aerial pursuers; they have a 97% success rate for prey capture. [ 23 ] This success rate is a consequence of the "decision" on which prey to pursue, based on initial conditions. Observations of several species of perching dragonflies show more pursuit initiations at larger starting distances for larger size prey species than for much smaller prey. Further evidence points to a potential bias towards larger prey, due to more substantial metabolic rewards. This bias is in spite of the fact that larger prey are typically faster and choosing them results in less successful pursuits. Dragonflies high success rate for prey capture may also be due to their interception foraging method. [ 1 ] Unlike classical pursuit , in which the predator aims for the current position of their prey, dragonflies predict the prey's direction of motion, [ 24 ] as in parallel navigation . Perching dragonflies ( Libellulidae family), have been observed "staking out" high density prey spots prior to pursuit. [ 1 ] There are no noticeable distinctions in prey capture efficiency between males and females. Further, percher dragonflies are bound by their visual range. They are more likely to engage in pursuit when prey come within a subtended angle of around 1-2 degrees. Angles greater than this are outside of a dragonflies visual range. [ 1 ]
Current theory on the evolution of pursuit predation suggests that the behavior is an evolutionary countermeasure to prey adaptation. Prey animals vary in their likelihood to avoid predation, and it is predation failure that drives evolution of both prey and predator. [ 25 ] Predation failure rates vary wildly across the animal kingdom; raptorial birds can fail anywhere from 20% to 80% of the time in predation, while predatory mammals usually fail more than half the time. [ 25 ] Prey adaptation drives these low rates in three phases: the detection phase, the pursuit phase, and the resistance phase. [ 26 ] The pursuit phase drove the evolution of distinct behaviors for pursuit predation.
As selective pressure on prey is higher than on predators [ 25 ] adaptation usually occurs in prey long before the reciprocal adaptations in predators. Evidence in the fossil record supports this, with no evidence of modern pursuit predators until the late Tertiary period. [ 7 ] Certain adaptations, like long limbs in ungulates, that were thought to be adaptive for speed against predatory behavior have been found to predate predatory animals by over 20 million years. Because of this, modern pursuit predation is an adaptation that may have evolved separately and much later as a need for more energy in colder and more arid climates. [ 7 ] Longer limbs in predators, the key morphological adaptation required for lengthy pursuit of prey, is tied in the fossil record to the late Tertiary. It is now believed that modern pursuit predators like the wolf and lion evolved this behavior around this time period as a response to ungulates increasing feeding range. [ 7 ] As ungulate prey moved into a wider feeding range to discover food in response to changing climate, predators evolved the longer limbs and behavior necessary to pursue prey across larger ranges. In this respect, pursuit predation is not co-evolutionary with prey adaptation, but a direct response to prey. Prey's adaptation to climate is the key formative reason for evolving the behavior and morphological necessities of pursuit predation.
In addition to serving as a countermeasure to prey adaptation, pursuit predation has evolved in some species as an alternative, facultative mechanism for foraging. For example, polar bears typically act as specialized predators of seal pups and operate in a manner closely predicted by the optimal foraging theory . However, they have been seen to occasionally employ more energy-inefficient pursuit predation tactics on flightless geese. This alternative predatory strategy may serve as a back-up resource when optimal foraging is circumstantially impossible, or may even be a function of filling dietary needs. [ 27 ]
Pursuit predation revolves around a distinct movement interaction between predator and prey; as prey move to find new foraging areas, predators should move with them. Predators congregate in areas of high prey density, [ 28 ] and prey should therefore avoid these areas. [ 29 ] However, dilution factor may be a reason to stay in areas of high density due to a decreased risk of predation. Given the movements of predators over ranges in pursuit predation, though, dilution factor seems a less important cause for predation avoidance. Because of these interactions, spatial patterns of predators and prey are important in preserving population size. Attempts by prey to avoid predation and find food are coupled with predator attempts to hunt and compete with other predators. These interactions act to preserve populations. [ 30 ] Models of spatial patterns and synchrony of predator-prey relationships can be used as support for the evolution of pursuit predation as one mechanism to preserve these population mechanics. By pursuing prey over long distances, predators actually improve longterm survival of both their own population and prey population through population synchrony. Pursuit predation acts to even out population fluctuations by moving predatory animals from areas of high predator density to low predator density, and low prey density to high prey density. This keeps migratory populations in synchrony, which increases metapopulation persistence. [ 30 ] Pursuit predation's effect on population persistence is more marked over larger travel ranges. Predator and prey levels are usually more synchronous in predation over larger ranges, as population densities have more ability to even out. [ 31 ] Pursuit predation can then be supported as an adaptive mechanism for not just individual feeding success but also metapopulation persistence.
Just as the evolutionary arms race has led to the development of pursuit behavior of predators, so too has it led to the anti-predator adaptations of prey. Alarm displays such as eastern swamphen's tail flicking, white-tailed deer's tail flagging, and Thomson's gazelles' stotting have been observed deterring pursuit. [ 32 ] These tactic are believed to signal that a predator's presence is known and, therefore, pursuit will be much more difficult. These displays are more frequent when predators are at an intermediate distance away. Alarm displays are used more often when prey believe predators are more prone to change their decision to pursue. For instance, cheetahs, common predators of Thomson's gazelles, are less likely to change their choice to pursue. As such, gazelles stott less when cheetahs are present than when other predators are present. [ 32 ] In addition to behavioral adaptations, there are also morphological anti-predator adaptations to pursuit predators. For example, many birds have evolved rump feathers that fall off with much less force than the feathers of their other body parts. This allows for easier escape from predator birds, as avian predators often approach prey from their rump. [ 33 ]
In many species that fall prey to pursuit predation, gregariousness on a massive scale has evolved as a protective behavior. Such herds can be conspecific (all individuals are of one species) or heterospecific. This is primarily due to the confusion effect , which states that if prey animals congregate in large groups, predators will have more difficulty identifying and tracking specific individuals. [ 34 ] This effect has greater influence when individuals are visually similar and less distinguishable. In groups where individuals are visually similar, there is a negative correlation between group size and predator success rates. This may mean that the overall number of attacks decreases with larger group size or that the number of attacks per kill increases with larger group size. [ 35 ] This is especially true in open habitats, such as grasslands or open ocean ecosystems, where view of the prey group is unobstructed, in contrast to a forest or reef . Prey species in these open environments tend to be especially gregarious, with notable examples being starlings and sardines . When individuals of the herd are visually dissimilar, however, the success rate of predators increases dramatically. [ 35 ] In one study, wildebeest on the African Savannah were selected at random and had their horns painted white. This introduced a distinction, or oddity, into the population; researchers found that the wildebeest with white horns were preyed upon at substantially higher rates. [ 36 ] By standing out, individuals are not as easily lost in the crowd, and so predators are able to track and pursue them with higher fidelity. This has been proposed as the reason why many schooling fish show little to no sexual dimorphism , and why many species in heterospecific schools bear a close resemblance to other species in their school. [ 34 ] | https://en.wikipedia.org/wiki/Pursuit_predation |
A push-button (also spelled pushbutton ) or simply button is a simple switch mechanism to control some aspect of a machine or a process . Buttons are typically made out of hard material, usually plastic or metal . [ 1 ] The surface is usually flat or shaped to accommodate the human finger or hand, so as to be easily depressed or pushed. Buttons are most often biased switches , although many un-biased buttons (due to their physical nature) still require a spring to return to their un-pushed state.
Terms for the "pushing" of a button include pressing , depressing , mashing , slapping , hitting , and punching .
The "push-button" has been utilized in calculators , push-button telephones , kitchen appliances , and various other mechanical and electronic devices, home and commercial.
In industrial and commercial applications, push buttons can be connected together by a mechanical linkage so that the act of pushing one button causes the other button to be released. In this way, a stop button can "force" a start button to be released. This method of linkage is used in simple manual operations in which the machine or process has no electrical circuits for control.
Red pushbuttons can also have large heads (called mushroom heads) for easy operation and to facilitate the stopping of a machine. These pushbuttons are called emergency stop buttons and for increased safety are mandated by the electrical code in many jurisdictions. This large mushroom shape can also be found in buttons for use with operators who need to wear gloves for their work and could not actuate a regular flush-mounted push button.
As an aid for operators and users in industrial or commercial applications, a pilot light is commonly added to draw the attention of the user and to provide feedback if the button is pushed. Typically this light is included into the center of the pushbutton and a lens replaces the pushbutton hard center disk. The source of the energy to illuminate the light is not directly tied to the contacts on the back of the pushbutton but to the action the pushbutton controls. In this way a start button when pushed will cause the process or machine operation to be started and a secondary contact designed into the operation or process will close to turn on the pilot light and signify the action of pushing the button caused the resultant process or action to start.
To avoid an operator from pushing the wrong button in error , pushbuttons are often color-coded to associate them with their function. Commonly used colors are red for stopping the machine or process and green for starting the machine or process.
In popular culture , the phrase "the button" (sometimes capitalized) refers to a (usually fictional) button that a military or government leader could press to launch nuclear weapons .
Akin to fire alarm switches, some big red buttons, when deployed with suitable visual and audible warnings such as flashing lights and sirens for extreme exigent emergencies, are known as "scram switches" (from the slang term scram , "get out of here"). Generally, such buttons are connected to large scale functions, beyond a regular fire alarm, such as automated shutdown procedures, complete facility power cut, fire suppression like halon release, etc.
A variant of this is the scramble switch which triggers an alarm to activate emergent personnel to proactively attend to and go to such disasters. An air raid siren at an air base initiates such action, where the fighter pilots are alerted and " scrambled " to their planes to defend the base.
Push buttons were invented sometime in the late 19th century, certainly no later than 1880. [ 2 ] The name came from the French word bouton (something that sticks out), rather than from the kind of buttons used on clothing. [ 2 ] The initial public reaction was curiosity mixed with fear, some of which was due to widespread fear of electricity, which was a relatively new technology at the time. [ 2 ] | https://en.wikipedia.org/wiki/Push-button |
A Push Proxy Gateway is a component of WAP Gateways that pushes URL notifications to mobile handsets. Notifications typically include MMS , email, IM, ringtone downloads, and new device firmware notifications. Most notifications will have an audible alert to the user of the device. The notification will typically be a text string with a URL link. Note that only a notification is pushed to the device; the device must do something with the notification in order to download or view the content associated with it.
A push message is sent as an HTTP POST to the Push Proxy Gateway. The POST will be a multipart XML document, with the first part being the PAP (Push Access Protocol) Section and the second part being either a Service Indication or a Service Loading .
The POST contains at a minimum the URL being posted to (this is not standard across different PPG vendors), and the content type.
An example of a PPG POST:
The PAP XML contains at the minimum, a <pap> element, a <push-message> element, and an <address> element.
An example of a PAP XML:
--someboundarymesg
Content-Type: application/xml
The important parts of this PAP message are the address value and type. The value is typically a MSISDN and type indicates whether to send to an MSISDN (typical case) or to an IP Address. The TYPE is almost always MSISDN as the Push Initiator (PI) will not typically have the Mobile Station's IP address - which is generally dynamic. In the case of IP Address:
TYPE=USER@a.b.c.d
Additional capability of PAP can be found in the PAP article.
A PUSH Service Indication (SI) contains at a minimum an <si> element and an <indication> element.
An example of a Service Indication:
Once a push message is received from the Push Initiator, the PPG has two avenues for delivery. If the IP address of the Mobile Station is known to the PPG, the PPG can deliver directly to the mobile station over an IP bearer. This is known as "Connection Oriented Push". If the IP address of the mobile station is not known to the PPG, the PPG will deliver over an SMS bearer. Delivery over an SMS bearer is known as "Connectionless Push".
In Connectionless Push, an SMSC BIND is required for the PPG to deliver its push message to the mobile station. Typically, a PPG will have a local SMS queuing mechanism running locally that it BINDs to, and which in turn BINDs to the carrier's SMSC. This mechanism should allow for queuing in the event of an SMS infrastructure outage, and also provide for message throttling.
Since a WAP Push message can be larger than a single SMS message can contain, the push message may be broken up into multiple SMS messages, as a multipart SMS.
In Connection Oriented pushes (where the device supports it), an SMSC BIND is not required if the gateway is aware of the handsets IP Address. If the gateway is unable to determine the IP Address of the handset, or is unable to connect to the device, the push notification will be encoded and sent as an SMS .
Connection Oriented Push is used less frequently than Connectionless Push for several reasons including:
Many other attributes exist and are detailed in the specifications at the Open Mobile Alliance and other sites.
PPG vendors include Nokia Siemens Networks , Ericsson , Gemini Mobile Technologies , Openwave , Acision , Huawei , Azetti , Alcatel, WIT Software , ZTE, and open source Kannel . | https://en.wikipedia.org/wiki/Push_Proxy_Gateway |
The push of the past [ 1 ] [ 2 ] is a type of survivorship bias associated with evolutionary diversification when extinction is possible. Groups that survive a long time are likely to have “got off to a flying start”, [ 1 ] and this statistical bias creates an illusion of a true slow-down of diversification rate through time.
The evolutionary processes of speciation and extinction can be modelled with a stochastic “ birth–death model ” (BDM), which is an important component in the study of macroevolution . A BDM assigns each species a certain probability of splitting ( λ {\displaystyle \lambda } ) or going extinct ( μ {\displaystyle \mu } ) per interval of time. [ 3 ] This gives rise to an exponential distribution, with the number of species in a particular clade N at any time t given by
N ( t ) = N ( t 0 ) e ( λ − μ ) ( t − t 0 ) {\displaystyle N_{(t)}=N_{(t0)}e^{(\lambda -\mu )(t-t0)}} ,
although this expression only gives the expected value when N {\displaystyle N} and t {\displaystyle t} are large (see below).
In the special case of there being no extinction, this simplifies to the so-called " Yule process ".
A different type of plot of diversity through time, called a “lineage through time” (LTT) plot, retrospectively reconstructs the number of lineages that led to the living species of a group. This is equivalent to constructing a dated phylogeny and then counting how many branches are present at each time interval. As we know retrospectively that all such lineages survived until the present, it follows that no extinction is possible along them. It can be shown that the rate of production of new lineages through time is given by λ − μ {\displaystyle \lambda -\mu } . [ 2 ]
Rather than considering the distribution of all possible stochastic outcomes for given values of t , λ {\displaystyle t,\lambda } and μ {\displaystyle \mu } it is also possible to consider what happens when certain conditions of survivorship are imposed on the possible outcomes.
If a BDM is forward-modelled, i.e. if the fate of an original single species is modelled through time, then a wide range of possible outcomes can occur, as the process is stochastic. With significant extinction rates, any particular clade is likely to be short-lived. However, we know that relatively long-lived clades such as the plants or animals by definition did not go extinct. As a result, their patterns of diversification will be a sub-set of all the possible outcomes for diversifications with their particular values of λ {\displaystyle \lambda } and μ {\displaystyle \mu } - all patterns with early extinction will be excluded. Imposing the condition of survival on a clade implies that rates of early diversification will be higher than expected. It can be shown that for a long-lived clade, the expected initial short-term rate of diversification is approximately 2 λ {\displaystyle 2\lambda } , [ 2 ] [ 4 ] as opposed to the long-term rate of λ − μ {\displaystyle \lambda -\mu } . However, the wide confidence intervals on this value mean that values of initial diversification of up to 3 λ {\displaystyle 3\lambda } fall within the 95% range. Long-lived clades should thus show a characteristic early burst of diversification that quickly declines to the long-term rate, an effect called the "push of the past".
For a normal-sized clade, the push of the past is only observed in the raw count of species through time (e.g. that reconstructed from the fossil record), but the rate of lineage increase is affected as the present is approached. This is because recently created sub-clades within a particular group have an expected lifetime, and as the present is approached, these sub-clades will not have had time to go extinct. Thus, the rate of creation of reconstructed lineages should increase in the near past from λ − μ {\displaystyle \lambda -\mu } to λ {\displaystyle \lambda } in the present - living species by definition have an observed zero extinction rate. This theoretical apparent increase in the rate of lineage production has been termed the "pull of the present".
In reality, the “pull of the present” has proven difficult to demonstrate: rates of lineage production in reconstructed phylogenies often show a slow-down or even decrease as the present is approached. This conundrum has been much discussed, and two major solutions have been proposed: first, that diversification is diversity dependent, [ 5 ] so that as the carrying capacity of the environment is reached the rate of lineage production slows; secondly, that our modern species concept does not properly capture the “lineages” of BDM, and that speciation as we recognize it is only the end point of a drawn-out process of splitting of subpopulations through time, each of which could be considered to be a lineage in itself. [ 6 ]
For a given diversification rate of λ − μ {\displaystyle \lambda -\mu } , it is possible to consider high turnover (λ and μ high) and low turnover (λ and μ low) scenarios. [ 2 ] As the push of the past and pull of the present depend on the stochastic absence of extinction, it follows that both these effects are greatest when m is high, i.e. in high turnover situations. For example, if λ is 0.6 and μ 0.55 (both measured in rates per species per million years), the initial rate of species production would be 1.2 (2λ); but if they were 0.15 and 0.1 respectively, the initial rate would only be 0.3, even though the overall diversification rate ( λ − μ {\displaystyle \lambda -\mu } ) is the same in both cases, 0.05. it can be seen that the initial rate of diversification in the push of the past can be much greater than the background rate; in the first case here, 24 times higher. Such high rates have often been observed at the origin of major groups such as the animals and angiosperms. It is possible that such striking diversifications are thus simply an effect of survivorship bias, and that if overall rates could be measured at their time of origin (including those of groups that quickly went extinct) no unusual rates would be observed. Consideration of the null hypothesis of survivorship bias is thus important when assigning causes to apparent cases of early rapid diversification,
The effect of the push of the past appears to be the reason that crown groups tend to emerge early within the history of a group as a whole: groups that diversify readily tend to create early new lineages.
The push of the past is an expected effect whenever a small group is diversifying and its future survival is known to have occurred. It should thus also be seen in groups that were heavily affected by mass extinctions and went on to rediversify. [ 2 ] | https://en.wikipedia.org/wiki/Push_of_the_past |
pushd and popd are shell commands that together allow the user to revert to a previous working directory via the command line. They use a stack data structure for directory paths. pushd pushes the working directory path onto the stack and changes to the specified directory, and popd pops the most recent item from the stack and changes directory to the popped value. [ 1 ] [ 2 ] [ 3 ] [ 4 ]
Behavior varies if no argument is passed to pushd . On Unix, the command swaps the top two directories on the stack, which toggles between them. On Windows, the command lists the paths in the stack except for the current one.
The commands are widely available as builtin commands in many shells, such as Bash , [ 5 ] Command Prompt , PowerShell , C shell , tcsh , 4DOS , Hamilton C shell , KornShell , and FreeCOM . [ 6 ]
The stack of directory paths can be displayed via the dirs Unix command or Get-Location -stack PowerShell command. The working directory is at the top of the stack.
The first Unix shell to provide a directory stack was Bill Joy's C shell . [ citation needed ] The syntax for pushing and popping directories is essentially the same as that used now. [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/Pushd_and_popd |
A pusher centrifuge is a type of filtration device that offers continuous operation to de-water and wash materials such as relatively incompressible feed solids, free-draining crystalline materials, polymers and fibrous substances. It consists of a constant speed rotor and is fixed to one of several baskets. This assembly is applied with centrifugal force that is generated mechanically for smaller units and hydraulically for larger units to enable separation.
Pusher centrifuges can be used for a variety of applications. They were typically used in inorganic industries and later, extensively in chemical industries such as organic intermediates, plastics, food processing and rocket fuels .
A suspension feed enters the process to undergo pre-acceleration and distribution. The subsequent processes involve main filtration and intermediate de-watering, after which the main filtrate is collected. Wash liquid enters the washing step and final de-watering follows. Wash filtrate is extracted from these two stages. The final step involves discharge of solids which are then collected as the finished product. These process steps take place simultaneously in different parts of the centrifuge .
It is widely accepted due to its ease of modification, such as gas-tight and explosion protection configurations.
Pusher centrifuges are mainly used in chemical, pharmaceutical, food (mainly to produce sodium chloride as common salt ) and mineral industries. During the twentieth century, the pusher centrifuge was used for desiccation of comparatively large crystals and solids. [ 1 ]
Although pushers are typically used for inorganic products, they appear in chemical industries such as organic intermediates, plastics, food processing and rocket fuels. Organic intermediates include paraxylene , adipic acid , oxalic acid caprolactam, nitrocellulose , carboxymethylcellulose, etc.
In food processing, pusher centrifugation is used to produce monosodium glutamate, salt, lysine and saccharin. [ 2 ]
Pusher centrifugation is also used in the plastic industry, contributing to products such as PVC , polyethylene and polypropylene , and a number of other resins .
Individual products
The designs for pusher centrifuge are as follows:
Pushers come with eithermechanical and/or hydraulic drive units. Speed can vary.
Single-stage units can be cylindrical or cylindrical/conical with a single long basket and screen
Multistage (two-, three-, or four- stage designs): cylindrical and cylindrical/conical
Feed distributor design: conical/cylindrical or plate
The important parameters are screen area, acceleration level in the final drainage zone and cake thickness. Cake filtration affects residence time and volumetric throughput. Residence on the screen is controlled by the screen's length and diameter, cake thickness and the frequency and stroke length of the cake. [ 3 ]
Pushers utilise the cake layer to act as a filter, hence the feed normally contains high solid concentration containing fast draining, crystalline, granular or fibrous solids. The solid concentration ranges from 25-65 wt%. [ 2 ] The mean particle size suitable for pushers must be at least 150 μm. The capacity depends on the basket diameter and ranges from 1 ton/h to 120tons/h. [ 4 ]
The cake is under centrifugal force. It becomes drier as it progresses in the basket and is discharged from the pusher basket into the solid discharge housing (pusher centrifuge operation). The stroke length ranges from 30 to 80 mm and the stroke frequency is between 45 and 90strokes/min. [ 4 ]
The push efficiency is defined as the distance of the forward movement of the cake ring divided by the stroke length. The push efficiency is a function of the solid volumetric loading, which results in self-compensating control of varying rates. Up to 90% push efficiency is achievable depending on the cake properties. [ 4 ] dQ3ET42T
The equation for the filtration rate, Q: [ 4 ]
Where μ {\displaystyle \mu } and ρ {\displaystyle \rho } are viscosity and liquid density, respectively. Ω {\displaystyle \Omega } is the angular speed, K {\displaystyle K} is the average cake permeability, which is related to equation (2), r p , r c {\displaystyle r_{p},r_{c}} , and r b {\displaystyle r_{b}} are the radius of the liquid surface, cake surface and filter medium adjacent to the perforated bowl respectively, R m {\displaystyle R_{m}} is the combined resistance, α {\displaystyle \alpha } is the specific resistance and ρ s {\displaystyle \rho s} is the solid density.
The numerator describes the pusher's driving force, which is due to the hydrostatic pressure difference across the wall and the liquid surface. The denominator describes the resistance due to the cake layer and the filter medium.
Performance is a function of many parameters, including particle size, viscosity, solid concentration and cake quality. [ 2 ]
To create the cake layer, the particle size has to be as large as practically possible. Larger particle size increases the porosity of the cake layer and allows feed liquid to pass through. Particle shape is equally important, because it determines the surface area per unit mass. As it decreases, less surface area is available to bind moisture, providing a drier cake. [ 2 ]
Filtration rate is a function of the viscosity of the feed fluid. From equation (1), the relationship of the filtration rate is inversely proportional to the viscosity. Increasing viscosity means adding resistance to the fluid flow, which complicates separation of the fluids from the slurry. Consequently, the throughput of the pusher is de-rated. [ 2 ] [ 4 ]
In most cases the solids discharge capacity/hydraulic capacity is not the limiting factor. The usual limitation is the filtration rate. Therefore, more solids can be processed by increasing the feed slurry concentration.
The cake quality is determined by the purity and the amount of volatile matter.
Wash liquid is introduced on the cake in order to displace the mother liquor along with the impurities. [ 2 ] The cake wash ratio is normally between 0.1 and 0.3 kg wash/kg solids, which displace at least 95% of the feed fluid and impurities within the wash zone's normal residence time. [ 4 ]
The amount of volatile matter present in the discharge is a function of the centrifugal force (G) and the residence time at that force. Separation increases with G and hence favours the filtration rate as illustrated in equation (3). [ 4 ]
where G {\displaystyle G} is the centrifugal force, Ω {\displaystyle \Omega } is the angular speed, r {\displaystyle r} is the radius of the basket, and g {\displaystyle g} is the gravitational force.
By relating equation 3 to equation 1, the relationship of the centrifugal force is shown to be proportional to the filtration rate. As pushers often deal with fragile crystals, the movement of the pusher plate and acceleration in the feed funnel matter, because they can break some of the particles. [ 4 ] In addition to the movement plate, G can cause breakage and compaction, and volatile matter in the cake increases. The gentle movement of cake in low G, single stage, long basket designs results in low particle attrition. As more solids pass through, residence time decreases, which increases volatile matter in the discharge cake. [ 2 ]
The heuristics of pusher centrifuge design consider equipment size, operation sequence and recycle structure.
Overall approach: [ 4 ]
Variables considered in sizing equipment:
Equipment selection is based upon test results, references from similar processes and experience and considered in terms of:
For conical and cylindrical designs and assembly, the cone slant angle should not exceed sliding friction cake angle. Otherwise it would result in high vibration and poor performance. [ 4 ]
In order to optimise capacity and performance, it is desirable to pre-concentrate the feed slurry as much as possible. Some designs have a short conical section at the feed end for thickening within the unit, but generally it is preferable to thicken before entering the centrifuge with gravity settlers, hydrocyclones or inclined screens, producing a higher concentration of solids.
The volumetric throughput for multistage designs can be increased by increasing the forced cake height while still retaining acceptable push efficiency.
Selection of designs is usually done by scale-up from lab tests. Test data analysis should be rationalised in preparation for equipment scale-up. Computer-aided design software can assist in design and scale-up. Pilot-testing and rollout then follows. [ 5 ]
The majority of liquid contained within the mixture is drawn out at an early stage, in the feed zone of the slot screen. It is discharged into the filtrate housing. After formation of solid cakes, the main by-product produced is water, which may be used in all sorts of industrial usage. Filtration cakes are washed using nozzles or waste baskets.
Post-treatment processes are a function of the specifics of the waste stream and are diverse. [ 6 ]
Design advances have enhanced performance and broaden the application range. These include additional stages, push hesitation, horizontal split process housing, integrated hydraulics, seals, pre-drained funnels and an integrated thickening function.
B&P Process Equipment and Systems (B&P) makes the largest single-stage pusher centrifuge, which they claimed to be superior to multistage designs. [ 7 ] They claimed that additional impurities enter the liquid housing due to additional particles tumbling in each stage. The problem can be overcome by using a shorter inner basket with smaller diameter between the pusher plates and the basket and enabling pusher movement to take place between the pusher plate and the basket as well as between the inner basket and the outer basket. Compared to single-stage pushers that have pusher movement only between pusher plate and basket, multistage centrifuges have the advantages that the cake height is reduced, filtration resistance is lower and lesser force is required.
Push hesitation holds the pusher plate in the back stroke, allowing the cake to build on itself. The cake acts as the filtering media that can even capture finer solids. This reduces the loss of solids passing through the wedge slots. Although this modification reduces capacity, it has helped improved the solid capture efficiency and make pusher centrifuges applicable to smaller particles. [ 2 ]
This allows the removal of the rotating assembly without disassembling the basket and pusher centrifuge from the shafting assembly.
An automated mechanism allows the system to operate independently.
Shaft seals eliminate the possibility of cross-contamination between the hydraulic and process ends. Options include a centrifugal liquid ring seal and a non-contacting inert gas purged labyrinth seal that eliminates leakage.
The pre-drained funnel removes a portion of the feed fluid through a puncture surface. This feature helps to concentrate the feed, which is especially important for drainage-limited applications. However the funnel cannot be back-washed therefore this feature is only available for crystals that tend not to back-crystallise.
Integrating the thickening function enables the pusher to be loaded with mixture with as little as 30-35% wt of solid. It also reduces process costs of solid-liquid separation by as much as 20%. [ 8 ] | https://en.wikipedia.org/wiki/Pusher_centrifuge |
In algebraic topology , the pushforward of a continuous function f {\displaystyle f} : X → Y {\displaystyle X\rightarrow Y} between two topological spaces is a homomorphism f ∗ : H n ( X ) → H n ( Y ) {\displaystyle f_{*}:H_{n}\left(X\right)\rightarrow H_{n}\left(Y\right)} between the homology groups for n ≥ 0 {\displaystyle n\geq 0} .
Homology is a functor which converts a topological space X {\displaystyle X} into a sequence of homology groups H n ( X ) {\displaystyle H_{n}\left(X\right)} . (Often, the collection of all such groups is referred to using the notation H ∗ ( X ) {\displaystyle H_{*}\left(X\right)} ; this collection has the structure of a graded ring .) In any category , a functor must induce a corresponding morphism . The pushforward is the morphism corresponding to the homology functor.
We build the pushforward homomorphism as follows (for singular or simplicial homology ):
First, the map f : X → Y {\displaystyle f\colon X\to Y} induces a homomorphism between the singular or simplicial chain complex C n ( X ) {\displaystyle C_{n}\left(X\right)} and C n ( Y ) {\displaystyle C_{n}\left(Y\right)} defined by composing each singular n- simplex σ X : Δ n → X {\displaystyle \sigma _{X}\colon \Delta ^{n}\rightarrow X} with f {\displaystyle f} to obtain a singular n-simplex of Y {\displaystyle Y} , f # ( σ X ) = f σ X : Δ n → Y {\displaystyle f_{\#}\left(\sigma _{X}\right)=f\sigma _{X}\colon \Delta ^{n}\rightarrow Y} , and extending this linearly via f # ( ∑ t n t σ t ) = ∑ t n t f # ( σ t ) {\displaystyle f_{\#}\left(\sum _{t}n_{t}\sigma _{t}\right)=\sum _{t}n_{t}f_{\#}\left(\sigma _{t}\right)} .
The maps f # : C n ( X ) → C n ( Y ) {\displaystyle f_{\#}\colon C_{n}\left(X\right)\rightarrow C_{n}\left(Y\right)} satisfy f # ∂ = ∂ f # {\displaystyle f_{\#}\partial =\partial f_{\#}} where ∂ {\displaystyle \partial } is the boundary operator between chain groups, so ∂ f # {\displaystyle \partial f_{\#}} defines a chain map .
Therefore, f # {\displaystyle f_{\#}} takes cycles to cycles, since ∂ α = 0 {\displaystyle \partial \alpha =0} implies ∂ f # ( α ) = f # ( ∂ α ) = 0 {\displaystyle \partial f_{\#}\left(\alpha \right)=f_{\#}\left(\partial \alpha \right)=0} . Also f # {\displaystyle f_{\#}} takes boundaries to boundaries since f # ( ∂ β ) = ∂ f # ( β ) {\displaystyle f_{\#}\left(\partial \beta \right)=\partial f_{\#}\left(\beta \right)} .
Hence f # {\displaystyle f_{\#}} induces a homomorphism between the homology groups f ∗ : H n ( X ) → H n ( Y ) {\displaystyle f_{*}:H_{n}\left(X\right)\rightarrow H_{n}\left(Y\right)} for n ≥ 0 {\displaystyle n\geq 0} .
Two basic properties of the push-forward are:
(This shows the functoriality of the pushforward.)
A main result about the push-forward is the homotopy invariance : if two maps f , g : X → Y {\displaystyle f,g\colon X\rightarrow Y} are homotopic , then they induce the same homomorphism f ∗ = g ∗ : H n ( X ) → H n ( Y ) {\displaystyle f_{*}=g_{*}\colon H_{n}\left(X\right)\rightarrow H_{n}\left(Y\right)} .
This immediately implies (by the above properties) that the homology groups of homotopy equivalent spaces are isomorphic: The maps f ∗ : H n ( X ) → H n ( Y ) {\displaystyle f_{*}\colon H_{n}\left(X\right)\rightarrow H_{n}\left(Y\right)} induced by a homotopy equivalence f : X → Y {\displaystyle f\colon X\rightarrow Y} are isomorphisms for all n {\displaystyle n} . | https://en.wikipedia.org/wiki/Pushforward_(homology) |
Push–pull technology is an intercropping strategy for controlling agricultural pests by using repellent "push" plants and trap "pull" plants . [ 1 ] For example, cereal crops like maize or sorghum are often infested by stem borers . Grasses planted around the perimeter of the crop attract and trap the pests, whereas other plants, like Desmodium , planted between the rows of maize, repel the pests and control the parasitic plant Striga . Push–pull technology was developed at the International Centre of Insect Physiology and Ecology (ICIPE) in Kenya in collaboration with Rothamsted Research , UK. [ 2 ] and national partners. This technology has been taught to smallholder farmers through collaborations with universities, NGOs and national research organizations. [ 3 ]
Push–pull technology involves use of behaviour-modifying stimuli to manipulate the distribution and abundance of stemborers and beneficial insects for management of stemborer pests. It is based on in-depth understanding of chemical ecology , agrobiodiversity , plant-plant and insect-plant interactions , and involves intercropping a cereal crop with a repellent intercrop such as Desmodium uncinatum (silverleaf) [ 4 ] (push), with an attractive trap plant such as Napier grass (pull) planted as a border crop around this intercrop. Gravid stemborer females are repelled from the main crop and are simultaneously attracted to the trap crop.
The "push" in the intercropping scheme is provided by the plants that emit volatile chemicals ( kairomones ) which repel stemborer moths and drive them away from the main crop (maize or sorghum). The most commonly used species of push plants are legumes of the genus Desmodium (e.g. silverleaf Desmodium, D. uncinatum , and greenleaf Desmodium, D. intortum ). The Desmodium is planted in between the rows of maize or sorghum, where they emit volatile chemicals (such as (E)-β- ocimene and (E)-4,8-dimethyl-1,3,7-nonatriene) that repel the stemborer moths. These semiochemicals are also produced in grasses such as maize when they are damaged by insect herbivores, which may explain why they are repellent to stemborers. [ 1 ] [ 5 ] Being a low-growing plant, Desmodium does not interfere with the growth of crops, but can suppress weeds and help improve soil quality by increasing soil organic matter content, fixing nitrogen, and stabilizing soils from erosion. It also serves as a highly nutritious animal feed and effectively suppresses striga weeds through an allelopathic mechanism. Another plant showing good repellent properties is molasses grass ( Melinis minutiflora ), a nutritious animal feed with tick-repelling and stemborer larval parasitoid attractive properties. [ 5 ]
The approach relies on a combination of companion crops to be planted around and among maize or sorghum. Both domestic and wild grasses can help to protect the crops by attracting and trapping the stemborers . The grasses are planted in the border around the maize and sorghum fields where invading adult moths become attracted to chemicals emitted by the grasses themselves. Instead of landing on the maize or sorghum plants, the insects head for what appears to be a tastier meal. These grasses provide the "pull" in the "push–pull" strategy. They also serve as a haven for the borers' natural enemies. Good trap crops include well-known grasses such as Napier grass ( Pennisetum purpureum ), Signal grass ( Brachiaria brizantha ), and Sudan grass ( Sorghum vulgare sudanense ). Napier grass produces significantly higher levels of attractive volatile compounds ( green leaf volatiles ), cues used by gravid stemborer females to locate host plants, than maize or sorghum. There is also an increase of approximately 100-fold in the total amounts of these compounds produced in the first hour of nightfall by Napier grass (scotophase), the period at which stemborer moths seek host plants for laying eggs, causing the differential oviposition preference. [ 6 ] However, many of the stemborer larvae, about 80%, do not survive, as Napier grass tissues produce sticky sap in response to feeding by the larvae, which traps them, causing the death of about 80% of larvae. [ 3 ]
Recent large-scale field studies in East Africa show that maize grown in push–pull systems has higher levels of two benzoxazinoid glycosides, compounds known for their antiherbivore properties. These glycosides were present in greater abundance in maize leaves from push–pull fields compared to those from conventional fields. [ 7 ]
Desmodium also controls the parasitic weed, Striga , resulting in significant yield increases of about 2 tonnes/hectare (0.9 short tons per acre) per cropping season. [ citation needed ] In addition to benefits derived from increased nitrogen availability and competition for light, it was found that D. uncinatum strongly suppresses striga growth through allelopathy . [ 8 ] These effects are thought to be related to isoflavanones produced in Desmodium roots, which can either promote the germination of striga seeds or inhibit seedling growth, depending on their structure. Together, these effects result in the phenomenon known as "suicidal germination", thus reducing the striga seed bank in the soil. [ 3 ] Other Desmodium species have also been evaluated and have similar effects on stemborers and striga weed and are currently being used as intercrops in maize, sorghum and millets. [ 9 ]
Desmodium also enhances soil quality by increasing soil organic matter, nitrogen content, and soil biodiversity, as well as conserving moisture, moderating soil temperature and preventing erosion. [ 3 ] [ 10 ] [ 11 ] [ 12 ]
Push-pull agriculture leads to beneficial economic outcomes on the level of individual smallholder and subsistence farmers through larger income streams coming from the sale of surplus grain, desmodium seeds, fodder, and milk. [ 3 ] Economic study has calculated the return on investment of push-pull methods for farmers to be over 2.2 as compared to 1.8 for pesticide use, and .8 for monocrop. [ dubious – discuss ] [ 13 ] Although startup costs of push-pull technology are highly variable due to the requirements of labor to plant desmodium and Napier grass and purchase of these seeds, costs significantly decline in following growing years. [ 13 ] Push-pull technology has also been seen to help boost local economies. [ 3 ] Because these farmers have more income, they are able to spend money in their local economy which boosts the standards of living and prosperity of the community at large. [ 3 ]
The primary economic opponents to such methods are large multinational corporations such as Monsanto and others that produce seasonal inputs such as chemical pesticides, fertilizers and high-yield seeds that require such inputs. [ 3 ]
After controlling for extraneous maize yield determinants, it was found that there was a 61.9% maize yield increase with a 15.3% increase in the cost of maize production and a 38.6% increase in the average net income brought in from maize. [ 14 ]
In households where push-pull technology has been adopted in Kenya, increased economic earnings have been associated with more years of education, improved access to rural institutions, and attendance to a larger number of field days when compared with households that have not adopted the technology. [ 14 ] Additionally, if adoption of the technology continues at the current rate of 14.4%, a reduction of 75,077 people considered poor could be expected in a situation where the local economies remain closed, and 76,504 fewer people could be expected to be considered poor if the economies were open. [ 14 ]
Because push-pull technology was developed mainly outside of Sub-saharan Africa—where international agencies today aim to grow its impact the most—a lack of trust was initially faced. [ 15 ] This distrust was fueled by local suspicions that external agents had hidden self-interested agendas. [ 15 ] In relationships where resources to implement new technologies are also externally provided, farmers often feel that they must simply passively follow the instructions they are given; however, efforts have been made in Ethiopia to encourage farmer engagement with the development of push-pull technology and to thus make the process more collaborative and bridge this gap. [ 15 ] Additionally, as mentioned above, push-pull technology is very similar to traditional intercropping methods which has helped it gain community acceptance
Push-pull technology has also been more widely seen as culturally acceptable and congruent because of the way it provides traditional roles for men and women in the agriculture work. [ 15 ] Because push-pull technology can fit within existing family frameworks, the practice does not demand an overhaul of existing dynamics. [ 15 ] In order to further make the implementation of push-pull technology, farmers played a participatory and influential role in deciding how the technology would be carried out to best suit their needs and align with traditional practices. [ 15 ] For example, local farmers preferred to drill the lines in which seeds would be sown using an ox-drawn plough. [ 15 ] In general, by promoting the participatory leadership of local farmers, the prospects of sustainability of such projects are anticipated to be strengthened. [ 15 ]
Push–pull technology was developed at the International Centre of Insect Physiology and Ecology (ICIPE) in Kenya in collaboration with Rothamsted Research , UK. [ 2 ] and national partners in the 1990s. [ 16 ] Research and development for the push-pull strategy was funded by a number of partners including the Gatsby Charitable Foundation of the UK, the Rockefeller Foundation, the UK’s Department for International Development, and the Global Environment Facility of the UNEP, among others. [ 3 ]
This strategy is based around the use of locally available plants, not costly industrial inputs, thus making it both more economically feasible and more culturally appropriate as this method is in many ways similar to traditional African practices of intercropping. [ 3 ] For this reason, this method is anticipated to be a popular solution to food insecurity in Sub-Saharan Africa. While this strategy is less resource-intensive, it is more knowledge-intensive. [ 3 ] For this reason, mass media campaigns have been launched, public meetings held, printed materials disseminated, and farmer-to-farmer and farmer field school programs established in order to overcome knowledge barriers to the implementation of push-pull technology. [ 3 ] The most efficient, influential, and cost-effective methods of disseminating information and encouraging farmers to adopt push-pull methods have been identified to be field days (lead to approximately 26.8% increase in adoption), farmer field schools (22.2% chance of swaying farmers' decisions), and farmer teachers (18.1% chance of convincing farmers to adopt the technology). [ 13 ] Additionally, it has been found that over 80% of farmers who participate in field days adopt the technology on their land. [ 13 ]
Another measure that has been taken to boost adoption rates of push-pull technology is to distribute desmodium seeds and other inputs that are required to begin this practice. [ 13 ] Distribution of seeds and other required inputs has been made possible through partnerships with seed companies and local farmer groups. [ 13 ] In order to combat the former shortage and high cost of desmodium seeds that were limiting the spread of push-pull technology, intensive seed production initiatives have been launched and farmer groups have been encouraged to propagate the seeds themselves. [ 13 ] As a result of these measures, the market for desmodium seeds has been stimulated and the seeds have become more accessible to smallholder farmers looking to implement push-pull methods in their fields. [ 13 ]
In Kenya, Tanzania, and Uganda alone, push-pull technology has been adopted by 68,800 smallholder farmers; however, these numbers may be higher in reality because of gaps in reporting. [ 13 ] Because these areas in Sub-Saharan Africa often suffer from unreliable crop production as a result of stemborers and striga, soil infertility, and unsustainable supplies of fodder, the push-pull solution to these problems is expected to be adopted by more smallholder farmers in the future at an annual adoption rate of 30% and a potential annual adoption rate of 50% because of intensive education campaigns that have been launched. [ 13 ] | https://en.wikipedia.org/wiki/Push–pull_agricultural_pest_management |
A push-pull olefin is a type of olefin characterized by an electron-withdrawing substituent on one side of the double bond and an electron-donating substituent on the other side. This makes the pi bond very polarized . The rotational barrier for a push-pull olefin is lower than that of an ordinary olefin and this makes it an interesting candidate for a molecular switch , for instance azobenzenes . A push-pull configuration also helps to stabilize the double bond because the carbon-carbon bond has considerably less double bond character. For instance, cyclobutadiene is a very unstable molecule but with both olefinic bonds in push-pull configuration (two ester substituents and two tertiary amine substituents) the molecule is stable indeed. | https://en.wikipedia.org/wiki/Push–pull_olefin |
Push–pull perfusion is an in vivo sampling method most commonly used for measuring neurotransmitters in the brain. Developed by J.H. Gaddum in 1960, [ 1 ] this technique replaced the cortical cup technique for observing neurotransmitters.
In order to analyze concentrations of analytes such as neurotransmitters, a probe consisting of two concentric tubes is implanted in the region of interest. A pump then pushes a neutral fluid such as saline or Ringer's solution through one of the tubes, while another pump extracts the fluid through the other tube. While outside the tubes, the perfusion fluid picks up physiological substances such as neurotransmitters that are present in the area. The concentration of analytes of interest can then be measured in the expelled fluid, indicating in which concentration they are present at the site of interest at any given time. [ 2 ]
The advent of concentric microdialysis probes in the 1980s resulted in push-pull sampling falling out of favor, as such probes require less monitoring, and are less invasive than the higher flow rate push-pull probes (>10 microliter/min), which could result in lesions if flow is unbalanced. [ 3 ]
With the advent of microfluidics and miniaturized probes, low-flow push–pull sampling was developed in 2002. [ 4 ] By using flow rates of ~50 nL /min, this technique minimizes tissue damage while providing finer spatial resolution than microdialysis sampling. | https://en.wikipedia.org/wiki/Push–pull_perfusion |
A putative gene is an alignment segment of DNA that is believed to be a gene . Putative genes can share sequence similarities to already characterized genes and thus can be inferred to share a similar function, yet the exact function of putative genes remains unknown. [ 1 ] Newly identified sequences are considered putative gene candidates when homologs of those sequences are found to be associated with the phenotype of interest. [ 2 ]
Examples of studies involving putative genes include the discovery of 30 putative receptor genes found in rat vomeronasal organ (VNO) [ 3 ] and the identification of 79 putative TATA boxes found in many plant genomes. [ 4 ]
In order to define and characterize a biosynthetic gene cluster, all the putative genes within said cluster must first be identified and their functions must be characterized. This can be performed by complementation and knock out experiments. In the process of characterizing putative genes, the genome under study becomes increasingly well understood as more interactions can be identified. [ 5 ] Identification of putative genes is necessary to study genomic evolution, as significant proportion of genomes make up larger families of related genes. Genomic evolution occurs by processes such as duplication of individual genes, genome segments, or entire genomes. These processes can result in loss of function , altered function, or gain of function , and have drastic affects on the phenotype. [ 6 ] [ 7 ]
DNA mutations outside of a putative gene can act by positional effect, in which they alter the gene expression. These alterations leave the transcription unit and promoter of the gene intact, but may involve distal promoters, enhancer/silencer elements, or the local chromatin environment. These mutations can be associated with diseases or disorders associated with the gene.
Putative genes can be identified by clustering large groups of sequences by patterns and arranging by mutual similarity [ 8 ] or can be inferred by potential TATA boxes . [ 9 ]
Putative genes can also be identified by recognizing differences between well-known gene clusters and gene clusters with a unique profiling. [ 10 ]
Software tools have been developed in order to automatically identify putative genes. This is done by searching for gene families and testing the validity of uncharacterized genes by comparison to already identified genes. [ 11 ]
Protein products can be identified and used to characterize the putative gene that codes for it. [ 12 ]
This genetics article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Putative_gene |
Putrefaction is the fifth stage of death , following pallor mortis , livor mortis , algor mortis , and rigor mortis . This process references the breaking down of a body of an animal post-mortem . In broad terms, it can be viewed as the decomposition of proteins , and the eventual breakdown of the cohesiveness between tissues, and the liquefaction of most organs. This is caused by the decomposition of organic matter by bacterial or fungal digestion, which causes the release of gases that infiltrate the body's tissues, and leads to the deterioration of the tissues and organs.
The approximate time it takes putrefaction to occur is dependent on various factors. Internal factors that affect the rate of putrefaction include the age at which death has occurred, the overall structure and condition of the body, the cause of death, and external injuries arising before or after death. External factors include environmental temperature, moisture and air exposure, clothing, burial factors, and light exposure. Body farms are facilities that study the way various factors affect the putrefaction process.
The first signs of putrefaction are signified by a greenish discoloration on the outside of the skin, on the abdominal wall corresponding to where the large intestine begins, as well as under the surface of the liver.
Certain substances, such as carbolic acid , arsenic , strychnine , and zinc chloride , can be used to delay the process of putrefaction in various ways based on their chemical make up.
In thermodynamic terms, all organic tissues are composed of chemical energy, which, when not maintained by the constant biochemical maintenance of the living organism, begin to chemically break down due to the reaction with water into amino acids , known as hydrolysis . The breakdown of the proteins of a decomposing body is a spontaneous process . Protein hydrolysis is accelerated as the anaerobic bacteria of the digestive tract consume, digest, and excrete the cellular proteins of the body.
The bacterial digestion of the cellular proteins weakens the tissues of the body. As the proteins are continuously broken down to smaller components, the bacteria excrete gases and organic compounds , such as the functional-group amines putrescine (from ornithine ) and cadaverine (from lysine ), which carry the noxious odor of rotten flesh. Initially, the gases of putrefaction are constrained within the body cavities, but eventually diffuse through the adjacent tissues, and then into the circulatory system . Once in the blood vessels, the putrid gases infiltrate and diffuse to other parts of the body and the limbs.
The visual result of gaseous tissue-infiltration is notable bloating of the torso and limbs. The increased internal pressure of the continually rising volume of gas further stresses, weakens, and separates the tissues constraining the gas. In the course of putrefaction, the skin tissues of the body eventually rupture and release the bacterial gas. As the anaerobic bacteria continue consuming, digesting, and excreting the tissue proteins, the body's decomposition progresses to the stage of skeletonization . This continued consumption also results in the production of ethanol by the bacteria, which can make it difficult to determine the blood alcohol content (BAC) in autopsies, particularly in bodies recovered from water. [ 1 ]
Generally, the term decomposition encompasses the biochemical processes that occur from the physical death of the person (or animal) until the skeletonization of the body. Putrefaction is one of seven stages of decomposition ; as such, the term putrescible identifies all organic matter (animal and human) that is biochemically subject to putrefaction. In the matter of death by poisoning, the putrefaction of the body is chemically delayed by poisons such as antimony , arsenic , carbolic acid (phenol), nux vomica (plant), strychnine (pesticide), and zinc chloride .
The rough timeline of events during the putrefaction stage is as follows:
Order of organs' decomposition in the body: [ 2 ]
The rate of putrefaction is greatest in air, followed by water, soil, and earth. The exact rate of putrefaction is dependent upon many factors such as weather, exposure and location. Thus, refrigeration at a morgue or funeral home can retard the process, allowing for burial in three days or so following death without embalming . The rate increases dramatically in tropical climates. The first external sign of putrefaction in a body lying in air is usually a greenish discoloration of the skin over the region of the cecum , which appears in 12–24 hours. The first internal sign is usually a greenish discoloration on the undersurface of the liver.
Various factors affect the rate of putrefaction. [ 3 ] [ 4 ] [ 5 ]
Environmental temperature: Decomposition is accelerated by high atmospheric or environmental temperature, with putrefaction speed optimized between 21 °C (70 °F) and 38 °C (100 °F), further sped along by high levels of humidity. This optimal temperature assists in the chemical breakdown of the tissue and promotes microorganism growth. Decomposition nearly stops below 0 °C (32 °F) or above 48 °C (118 °F).
Moisture and air exposure: Putrefaction is ordinarily slowed by the body being submerged in water, due to diminished exposure to air. Air exposure and moisture can both contribute to the introduction and growth of microorganisms, speeding degradation. In a hot and dry environment, the body can undergo a process called mummification where the body is completely dehydrated and bacterial decay is inhibited.
Clothing: Loose-fitting clothing can speed up the rate of putrefaction, as it helps to retain body heat. Tight-fitting clothing can delay the process by cutting off blood supply to tissues and eliminating nutrients for bacteria to feed on.
Manner of burial: Speedy burial can slow putrefaction. Bodies within deep graves tend to decompose more slowly due to the diminished influences of changes in temperature. The composition of graves can also be a significant contributing factor, with dense, clay-like soil tending to speed putrefaction while dry and sandy soil slows it.
Light exposure: Light can also contribute indirectly, as flies and insects prefer to lay eggs in areas of the body not exposed to light, such as the crevices formed by the eyelids and nostrils. [ 3 ]
Age at time of death: Stillborn fetuses and infants putrefy slowly due to their sterility. Otherwise, however, younger people generally putrefy more quickly than older people. [ citation needed ]
Condition of the body: A body with a greater fat percentage and less lean body mass will have a faster rate of putrefaction, as fat retains more heat and it carries a larger amount of fluid in the tissues. [ 5 ]
Cause of death: The cause of death has a direct relationship to putrefaction speed, with bodies that died from acute violence or accident generally putrefying slower than those that died from infectious diseases. Certain poisons, such as potassium cyanide or strychnine , may also delay putrefaction, while chronic alcoholism and cocaine use will speed it. [ citation needed ]
External injuries: Antemortem or postmortem injuries can speed putrefaction as injured areas can be more susceptible to invasion by bacteria. [ citation needed ]
Certain poisonous substances to the body can delay the process of putrefaction. They include:
Embalming is the process of preserving human remains by delaying decomposition. This is acquired through the use of embalming fluid, which is a mixture of formaldehyde, methanol, and various other solvents. The most common reasons to preserve the body are for viewing purposes at a funeral, for above-ground interment or distant transportation of the deceased, and for medical or religious practices.
Body farms subject donated cadavers to various environmental conditions to study the process of human decomposition. [ 7 ] These include The University of Tennessee's Forensic Anthropologic Facility, Western Carolina Universities Osteology Research Station (FOREST), Texas State University's Forensic Anthropology Research Facility (FARF), Sam Houston State University's Southeast Texas Applied Forensic Science Facility (STAFS), Southern Illinois University's Complex for Forensic Anthropology Research, and Colorado Mesa University's Forensic Investigation Research Station. The Australian Facility for Taphonomic Experimental Research, near Sydney , is the first body farm located outside of the United States [ 8 ] In the United Kingdom there are several facilities which, instead of using human remains or cadavers, use dead pigs to study the decomposition process. Pigs are less likely to have infectious diseases than human cadavers, and are more readily available without any concern for ethical issues, but a human body farm is still highly sought after for further research. [ 9 ] Each body farm is unique in its environmental make-up, giving researchers a broader knowledge, and allowing research into how different environmental factors can affect the rate of decomposition significantly such as humidity, sun exposure, rain or snow, altitude level and more.
In alchemy , putrefaction is the same as fermentation , whereby a substance is allowed to rot or decompose undisturbed. In some cases, the commencement of the process is facilitated with a small sample of the desired material to act as a "seed", a technique akin to the use of a seed crystal in crystallization . [ citation needed ] | https://en.wikipedia.org/wiki/Putrefaction |
Putrefying/decay bacteria are bacteria involved in putrefaction of living matter. Along with other decomposers , they play a critical role in recycling nitrogen from dead organisms. [ 1 ] Putrefying bacteria also play a role in putrefaction and fermentation of proteins in the human gastrointestinal tract . [ 2 ]
Putrefying bacteria is a broad term used to define several species of bacteria involved in decomposition and fermentation. Putrefying bacteria play a key role in decomposing and fermenting substances within the body as well as the body itself after death. Putrefaction is defined as the final step of decomposition after death. [ 3 ] Because these bacteria play a role in decomposition after death, putrefying bacteria also play a key role in the nitrogen cycle. They deconstruct and convert substances from dead organisms so nitrifying bacteria can then convert these products into a usable form of nitrogen. [ 4 ]
The nitrogen cycle is a vital part of life, and is essential to carry out biosynthesis of nitrogen containing compounds. [ 5 ] Nitrogen is inaccessible to most organisms unless it is fixed, and this process can only be carried out by certain classes of prokaryotes. [ 4 ] Putrefying bacteria use amino acids or urea as an energy source to decompose dead organisms. In the process, they produce ammonium ions. Nitrifying bacteria then convert this ammonium into nitrate by oxidation, which can then be used by plants to create more proteins thus completing the nitrogen cycle. [ 6 ] This process is called nitrification. Energy from this oxidation reaction can also be used to synthesize organic compounds in a process called chemosynthesis . [ 7 ]
Putrefaction , i.e. fermentation of proteins, is considered the final step following death, and is carried out mainly by anaerobic organisms from the bowel. Putrefying bacteria produce a plethora of enzymes which aid in disintegration of the body. Because of the lack of immune function within the body, these bacteria spread through blood vessels and utilize the carbohydrates and proteins in the blood as an energy source. [ 3 ] The main bacterial species carrying out putrefaction is Cl. welchii . [ 8 ] This bacterium contributes to gas formation, breakdown of remaining blood clots, disintegration of tissue, and marked hemolysis.
This breakdown begins immediately after death, but is not noticeable to the naked eye until several hours after death. Within the following days, the body will begin to break down. The three characteristics of putrefaction are discoloration, disfiguration, and dissolution. There are many factors that could affect the rate of putrefaction in animals such as age, body composition, temperature, and if the body is located in a wet or dry area. [ 8 ] Temperature must be between 0 °C and 48 °C for putrefaction to occur. The established bacterial community also play a role in rate of putrefaction. Newborn children that have not been fed will decompose slower than a toddler's body because of the lack of an established gut microbiota. Older individuals tend to decompose slower than younger individuals. Individuals with inflammatory disease, eating disorders, sepsis, and other conditions that affect gut microbiota will all decompose at different rates.
The gut microbiome plays a huge role in human health, and having a healthy bacterial community is essential to living a healthy life—bacteria aid in digesting nutrients that a human's gastrointestinal tract cannot process independently. Putrefying bacteria in the gut play a key role in fermenting or decomposing proteins that are not broken down by the body. [ 2 ] The process of fermentation and putrefaction mainly occurs in the distal colon. [ 9 ] These bacteria contribute to the number of metabolites in the large intestine. The gut microbial community is extremely diverse, and putrefying bacteria include diverse bacterial species. [ 10 ] Some of these bacteria include Bacillus, Clostridium, Enterobacter, Escherichia, Fusobacterium, Salmonella , etc. [ 2 ] These bacterial communities are established by diet, and the microbial modes of transmission. Today's research has not yet fully explored the implications of putrefying bacteria in the human gut microbiome, however current data suggests these bacteria could be helpful or harmful to our systems depending on the circumstances. Some products of putrefying pathways, such as Indole , have been shown to help protect against intestinal worms. Some putrefying bacteria such as Fusobacteriota (formerly Fusobacteria ) contribute to harmful cancer and disease, such as colorectal carcinoma . [ 2 ] | https://en.wikipedia.org/wiki/Putrefying_bacteria |
Pwo polymerase is a thermostable DNA polymerase used for the polymerase chain reaction . The abbreviation stands for Pyrococcus woesei , a thermophilic archaeon, from which this polymerase was isolated. This polymerase breaks when reaching erroneous uracil in DNA from the chain extension and, through this readahead function, fewer defective DNA clones are synthesized. It is used much less than the usual Taq or Pfu polymerases. [ 1 ] This DNA polymerase, similar to other DNA polymerases from Archaebacteria is sensitive to Uracil residues in DNA and is strongly inhibited by dUTP or uracil residues in DNA. Other polymerases in this class are Pfu , Vent, Deep Vent and Pfx. [ 2 ] The inhibition of this class of thermostable DNA polymerases limit their use in some applications of PCR, i.e. use of dUTP for prevention of carryover contamination as well as application involving dU containing primers such as ligase free cloning methods or site directed mutagenesis using UNG. [ 3 ] | https://en.wikipedia.org/wiki/Pwo_DNA_polymerase |
PyAOP ( (7-Azabenzotriazol-1-yloxy)tripyrrolidinophosphonium hexafluorophosphate ) is a reagent used to prepare amides from carboxylic acids and amines in the context of peptide synthesis . [ 1 ] It can be prepared from 1-hydroxy-7-azabenzotriazole (HOAt) and a chlorophosphonium reagent under basic conditions. [ 2 ] It is a derivative of the HOAt family of amide bond forming reagents. It is preferred over HATU , because it does not engage in side reactions with the N-terminus of the peptide. [ 3 ] Compared to the HOBt -containing analog PyBOP , PyAOP is more reactive due to the additional nitrogen in the fused pyridine ring of the HOAt moiety. [ 4 ] Thermal hazard analysis by differential scanning calorimetry (DSC) shows PyAOP is potentially explosive. [ 5 ]
This article about an organic compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/PyAOP_reagent |
PyBOP (benzotriazol-1-yloxytripyrrolidinophosphonium hexafluorophosphate) is a reagent used to prepare amides from carboxylic acids and amines in the context of peptide synthesis . [ 3 ] It can be prepared from 1-hydroxybenzotriazole and a chlorophosphonium reagent under basic conditions. [ 4 ] It is a substitute for the BOP reagent that avoids the formation of the carcinogenic waste product HMPA . [ 5 ] Thermal hazard analysis by differential scanning calorimetry (DSC) shows PyBOP is potentially explosive. [ 6 ]
This article about an organic compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/PyBOP |
PyClone is a software that implements a Hierarchical Bayes statistical model to estimate cellular frequency patterns of mutations in a population of cancer cells using observed alternate allele frequencies , copy number , and loss of heterozygosity (LOH) information. PyClone outputs clusters of variants based on calculated cellular frequencies of mutations. [ 1 ]
According to the Clonal Evolution model proposed by Peter Nowell , a mutated cancer cell can accumulate more mutations as it progresses to create sub-clones. These cells divide and mutate further to give rise to other sub-populations. In compliance with the theory of natural selection, some mutations may be advantageous to the cancer cells and thus make the cell immune to previous treatment. Heterogeneity within a single cancer tumour can arise from single nucleotide polymorphism /variation (SNP/SNV) events, microsatellite shifts and instability , loss of heterozygosity (LOH), Copy number variation and karyotypic variations including chromosome structural aberrations and aneuploidy. Due to the current methods of molecular analysis where a mixed population of cancer cells are lysed and sequenced , heterogeneity within the tumour cell population is under-detected. This results in a lack of information on the clonal composition of cancer tumours and more knowledge in this area would aid in the decisions for therapies.
PyClone is a hierarchical Bayes statistical model that uses measurements of allele frequency and allele specific copy numbers to estimate the proportion of tumor cells harboring a mutation. By using deeply sequenced data to find putative clonal clusters, PyClone estimates the cellular prevalence, the portion of cancer cells harbouring a mutation, of the input sample. Progress has been made for measuring variant allele frequency with deep sequencing data but statistical approaches to cluster mutations into biologically relevant groups remain underdeveloped. The commonness of a mutation between cells is difficult to measure because the proportion of cells that harbour a mutation doesn't simply relate to allelic prevalence. This is due to allelic prevalence depending on multiple factors such as the proportion of 'contaminating' normal cells in the sample, the proportion of tumor cells harboring the mutation, the number of allelic copies of the mutation in each cell, and sources of technical noise. PyClone is among the first methods to incorporate variant allele frequencies (VAFs) with allele-specific copy numbers. [ 2 ] It also accounts for Allelic Imbalances, where alleles of a gene are expressed at different levels in a given cell, [ 3 ] which may occur in the cell due to Segmental CNVs and normal cell contamination.
PyClone requires 2 inputs:
For each mutation, the PyClone model divides the input sample into three sub-populations. The three sub-populations are the normal (non-malignant) population consisting of normal cells, the reference cancer population consisting of cancer cells wild type for the mutation, and the variant cancer cell population consisting of the cancer cells with at least one variant allele of the mutation.
PyClone implements four advances in its statistic model that were tested on simulated datasets :
Beta-binomial Emission Densities are used by PyClone and are more effective than binomial models used by previous tools. Beta-binomial emission densities more accurately model input datasets that have more variance in allelic prevalence measurements. Higher accuracy in modeling variance in allelic prevalence translates to a higher confidence in the clusterings outputted by PyClone.
PyClone acknowledges that some geometrical structures and properties, such as copy number , of the clonal population to be reconstructed is known. When not enough information is available or taken into account, the reconstruction is usually of low confidence and many solutions are possible. PyClone uses priors, flexible prior probability estimates, of possible mutational genotypes to link allelic prevalence measurements to zygosity and copy number variants and is one of the first methods to incorporate variant allele frequencies (VAFs) with allele-specific copy numbers. [ 5 ]
Instead of fixing the number of clusters prior to clustering, Bayesian nonparametric clustering is used to discover groupings of mutations and the number of groups simultaneously. This allows for cellular prevalence estimates to reflect uncertainty in this parameter.
Multiple samples from the same patient can be analyzed at the same time to leverage the scenario in which clonal populations are shared across samples. When multiple samples are sequenced, subclonal populations that are similar in allelic prevalence in some cells but not others can be differentiated from each other.
PyClone outputs posterior densities of cellular prevalences for the mutations in the sample and a matrix containing the probability any two mutations occur in the same cluster. Estimates of clonal populations from differing cellular prevalences of mutations are then generated from the posterior densities.
PyClone is used to analyze deeply sequenced (over 100× coverage) mutations to identify and quantify clonal populations in tumors. Some applications include:
Xenografting is used as a reasonable model to study human breast cancer but the consequences of engraftment and genomic propagation of xenografts have not been examined at a single-cell resolution. PyClone can be used to follow the clonal dynamics of initial grafts and serial propagation of primary and metastatic human breast cancers in immunodeficient mice. PyClone can predict how clonal dynamics differ after initial engraftment, over serial passage generations. [ 6 ]
Circulating tumour DNA (plasma DNA) Analysis can be used to track tumour burden and analyse cancer genomes non-invasively but the extent to which it represents metastatic heterogeneity is unknown. PyClone can be used to compare the clonal population structures present in the tumour and plasma samples from amplicon sequencing data. Stem and metastatic-clade mutation clusters can be inferred using PyClone and then compared to results from clonal ordering. [ 7 ]
Serial Time Point Sequencing: PyClone can be used to study the evolution of mutational clusters as cancer progresses. With samples taken from different time points, PyClone can identify the expansion and decline of initial clones and discover newly acquired subclones that arise during treatment. Understanding clonal dynamics improves understanding on how related cancers such as MDS , MPN and sAML compare in risk and give insight on the clinical significance of somatic mutations . [ 8 ]
Section sequencing : PyClone is most effective for section sequencing tumor DNA. Section sequencing is when samples are taken from different portions of a single tumour to infer clonal structure from differential cellular prevalence. An advantage of section sequencing is more statistical power and information on the spatial position and interactions of the clones, uncovering information on how tumors evolve in space.
A key assumption of the PyClone model is that all cells within a clonal population have the same genotype. This assumption is likely false since copy number alterations and loss of heterozygosity events are common in cancer cells. The amount of error introduced by this assumption depends on the variability of genotype of cells in the location of interest. For example, in solid tumors the cells of a sample are spatially close together resulting in a small error rate, but for liquid tumors the assumption may introduce more error as cancer cells are mobile.
Another assumption made is that the sample follows a perfect and persistent phylogeny. This means that no site mutates more than once in a clonal population and each site has at most one mutant genotype. Mutations that revert to normal genotype, deletions of segments of DNA harbouring mutations and recurrent mutations are not accounted for in PyClone as it would lead to unidentifiable explanations for some observed data.
In order to obtain input data for PyClone, cell lysis is a required step to prepare bulk sample sequencing. This results in the loss of information on the complete set of mutations defining a clonal population. PyClone can distinguish and identify the frequency of different clonal populations but can not identify exact mutations defining these populations.
Instead of clustering cells by mutational composition, PyClone clusters mutations that have similar cellular frequencies. In sub-clones that have similar cellular frequencies, PyClone will mistakenly cluster these subclones together. Chances of making this error decreases when using targeted deep sequencing with high coverage and joint analysis of multiple samples
A confounding factor of the PyClone model arises due to imprecise input information on the genotype of the sample and the depth of sequencing. Uncertainty arises in the posterior densities due to insufficient information on the genotype of mutations and depth of sequencing of the sample. This results in relying on the assumptions made by the PyClone model to interpret and cluster the sample.
SciClone [ 9 ] - SciClone is a Bayesian clustering method on single nucleotide variants (SNVs).
Clomial [ 10 ] - Clomial is a Bayesian clustering method with a decomposition process. Both Clomial and SciCloe limit the SNVs located in copy-number neutral region. The tumor is physically divided into subsections and deep sequenced to measure normal allele and variant allele. Their inference model uses Expectation-Maximization algorithm .
GLClone [ 11 ] – GLClone uses a hierarchical probabilistic model and Bayesian posteriors to calculate copy number alterations in sub-clones.
Cloe [ 12 ] - Cloe uses a phylogenetic latent feature model for analyzing sequencing data to distinguish the genotypes and the frequency of clones in a tumor.
PhyC [ 13 ] - PhyC uses an unsupervised learning approach to identify subgroups of patients through clustering the respective cancer evolutionary trees. They identified the patterns of different evolutionary modes in a simulation analysis, and also successfully detected the phenotype-related and cancer type-related subgroups to characterize tree structures within subgroups using actual datasets.
PhyloWGS [ 14 ] - PhyloWGS reconstructs tumor phylogenies and characterizes the subclonal populations present in a tumor sample using both SSMs and CNVs. | https://en.wikipedia.org/wiki/PyClone |
PyMOL is a source-available [ 2 ] molecular visualization system created by Warren Lyford DeLano . It was commercialized initially by DeLano Scientific LLC, which was a private software company dedicated to creating useful tools that become universally accessible to scientific and educational communities. It is currently commercialized by Schrödinger, Inc . As the original software license was a permissive licence , they were able to remove it; new versions are no longer released under the Python license , but under a custom license (granting broad use, redistribution, and modification rights, but assigning copyright to any version to Schrödinger, LLC.), [ 2 ] and some of the source code is no longer released. [ 3 ] PyMOL can produce high-quality 3D images of small molecules and biological macromolecules , such as proteins . PyMOL is widely used.
PyMOL is one of the few mostly open-source model visualization tools available for use in structural biology . The Py part of the software 's name refers to the program having been written in the programming language Python .
PyMOL uses OpenGL Extension Wrangler Library (GLEW) and FreeGLUT , and can solve Poisson–Boltzmann equations using the Adaptive Poisson Boltzmann Solver. [ 4 ] PyMOL used Tk for the GUI widgets and had native Aqua binaries for macOS through Schrödinger , which were replaced with a PyQt user interface on all platforms with the release of version 2.0. [ 5 ]
Early versions of PyMol were released under the Python License . On 1 August 2006, DeLano Scientific adopted a controlled-access download system for precompiled PyMOL builds (including betas) distributed by the company. Access to these executables is now limited to registered users who are paying customers; educational builds are available free to students and teachers. However, most of the current source code continues to be available for free, as are older precompiled builds. While the build systems for other platforms are open, the Windows API (WinAPI, Win32) build system is not, although unofficial Windows binaries are available online. [ 6 ] Anyone can either compile an executable from the Python-licensed source code or pay for a subscription to support services to obtain access to precompiled executables.
On 8 January 2010, Schrödinger, Inc. reached an agreement to acquire PyMOL. The firm assumed development, maintenance, support, and sales of PyMOL, including all then-valid subscriptions. They also continue to actively support the PyMOL open-source community. In 2017, Schrödinger revamped the distribution system to unify the user interface under Qt and the package management under Anaconda , and released it as PyMol v2. [ 5 ] This version restricts some new functionalities and adds a watermark to the visualization if used unlicensed beyond the 30-day trial period; the overall license policy is similar to the DeLano system. The source code remains mostly available, this time under a BSD-like license. [ 7 ] As with the previous distribution, unofficial Windows binaries in the wheel format are available, [ 6 ] and indeed Linux distributions continue to provide their own builds of the open-source code.
PyMOL applies ball-coloring by element. | https://en.wikipedia.org/wiki/PyMOL |
OpenMS is an open-source project for data analysis and processing in mass spectrometry and is released under the 3-clause BSD licence . It supports most common operating systems including Microsoft Windows , MacOS and Linux . [ 2 ] [ 3 ]
OpenMS has tools for analysis of proteomics data, providing algorithms for signal processing, feature finding (including de-isotoping), visualization in 1D (spectra or chromatogram level), 2D and 3D, map mapping and peptide identification. It supports label-free and isotopic-label based quantification (such as iTRAQ and TMT and SILAC ). OpenMS also supports metabolomics workflows and targeted analysis of DIA/SWATH data. [ 2 ] Furthermore, OpenMS provides tools for the analysis of cross linking data, including protein-protein, protein-RNA and protein-DNA cross linking. Lastly, OpenMS provides tools for analysis of RNA mass spectrometry data.
OpenMS was originally released in 2007 in version 1.0 and was described in two articles published in Bioinformatics in 2007 and 2008 and has since seen continuous releases. [ 4 ] [ 5 ] In 2009, the visualization tool TOPPView was published [ 6 ] and in 2012, the workflow manager and editor TOPPAS was described. [ 7 ] In 2013, a complete high-throughput label-free analysis pipeline using OpenMS 1.8 was described and compared with similar, proprietary software (such as MaxQuant and Progenesis QI ). The authors conclude that "[...] all three software solutions produce adequate and largely comparable quantification results; all have some weaknesses, and none can outperform the other two in every aspect that we examined. However, the performance of OpenMS is on par with that of its two tested competitors [...]". [ 8 ]
The OpenMS 1.10 release contained several new analysis tools, including OpenSWATH (a tool for targeted DIA data analysis ), a metabolomics feature finder and a TMT analysis tool. Furthermore, full support for TraML 1.0.0 and the search engine MyriMatch were added. [ 9 ] The OpenMS 1.11 release was the first release to contain fully integrated bindings to the Python programming language (termed pyOpenMS). [ 10 ] In addition, new tools were added to support QcML (for quality control) and for metabolomics accurate mass analysis. Multiple tools were significantly improved with regard to memory and CPU performance. [ 11 ]
With OpenMS 2.0, released in April 2015, the project provides a new version that has been completely cleared of GPL code and uses git (in combination with GitHub ) for its version control and ticketing system. Other changes include support for mzIdentML, mzQuantML and mzTab while improvements in the kernel allow for faster access to data stored in mzML and provide a novel API for accessing mass spectrometric data. [ 12 ] In 2016, the new features of OpenMS 2.0 were described in an article in Nature Methods . [ 2 ]
In 2024, OpenMS 3.0 [ 3 ] was released, providing support for a wide array of data analysis task in proteomics, metabolomics and MS-based transcriptomics.
OpenMS is currently developed with contributions from the group of Knut Reinert [ 13 ] at the Free University of Berlin , the group of Oliver Kohlbacher [ 14 ] at the University of Tübingen and the group of Hannes Roest [ 15 ] at University of Toronto .
OpenMS provides a set of over 100 different executable tools than can be chained together into pipelines for mass spectrometry data analysis (the TOPP Tools). It also provides visualization tools for spectra and chromatograms (1D), mass spectrometric heat maps (2D m/z vs RT ) as well as a three-dimensional visualization of a mass spectrometry experiment. Finally, OpenMS also provides a C++ library (with bindings to Python available since 1.11) for LC/MS data management and analyses accessible to developers to create new tools and implement their own algorithms using the OpenMS library. OpenMS is free software available under the 3-clause BSD licence (previously under the LGPL).
Among others, it provides algorithms for signal processing, feature finding (including de-isotoping), visualization, map mapping and peptide identification. It supports label-free and isotopic-label based quantification (such as iTRAQ and TMT and SILAC ).
The following graphical applications are part an OpenMS release: | https://en.wikipedia.org/wiki/PyOpenMS |
Python-based Simulations of Chemistry Framework ( PySCF ) is an ab initio computational chemistry program natively implemented in Python program language. [ 1 ] [ 2 ] The package aims to provide a simple, light-weight and efficient platform for quantum chemistry code developing and calculation. It provides various functions to do the Hartree–Fock , MP2 , density functional theory , MCSCF , coupled cluster theory at non-relativistic level and 4-component relativistic Hartree–Fock theory. [ 2 ] Although most functions are written in Python, the computation critical modules are intensively optimized in C. As a result, the package works as efficient as other C / Fortran -based quantum chemistry program. PySCF is developed by Qiming Sun. [ 2 ] PySCF2.0 is the latest version of the program. [ 3 ]
This article about chemistry software is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/PySCF |
A pycnidium (plural pycnidia ) is an asexual fruiting body produced by mitosporic fungi , for instance in the order Sphaeropsidales ( Deuteromycota , Coelomycetes ) or order Pleosporales ( Ascomycota , Dothideomycetes ). It is often spherical or inversely pearshaped ( obpyriform ) and its internal cavity is lined with conidiophores . When ripe, an opening generally appears at the top, through which the pycnidiospores escape. [ 1 ] [ 2 ] [ 3 ] | https://en.wikipedia.org/wiki/Pycnidium |
Pycniospores are a type of spore found in certain species of rust fungi . [ 1 ] [ 2 ] They are produced in special cup-like structures called pycnia or pynidia. Almost all fungi reproduce asexually with the production of spores. Spores may be colorless, green, yellow, orange, red, brown or black.
Sporangiospores (spore:spore, angion:sac) are spores formed inside the sporangium which is a spore sac.
Conidia (singular: conidium ) are spores produced at the tip of special branches called conidiophores.
Oidia (singular: oidium ). In several fungi, the hyphae is often divided into a large number of short pieces by transverse walls. Each piece is able to germinate into a new body. These pieces are called oidia (small egg ).
Chlamydospores (chlymus: mantle) are produced like oidia but differ from oidia in being thick walled. They are either terminal or intercalary.
This mycology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pycniospore |
Pycnonuclear fusion (from Ancient Greek πυκνός (pyknós) ' dense, compact, thick ' ) is a type of nuclear fusion reaction which occurs due to zero-point oscillations of nuclei around their equilibrium point bound in their crystal lattice . [ 1 ] [ 2 ] In quantum physics , the phenomenon can be interpreted as overlap of the wave functions of neighboring ions , and is proportional to the overlapping amplitude. [ 3 ] Under the conditions of above-threshold ionization , the reactions of neutronization and pycnonuclear fusion can lead to the creation of absolutely stable environments in superdense substances. [ 4 ]
The term " pycnonuclear " was coined by A.G.W. Cameron in 1959, but research showing the possibility of nuclear fusion in extremely dense and cold compositions was published by W. A. Wildhack in 1940. [ 5 ] [ 6 ]
Pycnonuclear reactions can occur anywhere and in any matter, but under standard conditions, the speed of the reaction is exceedingly low, and thus, have no significant role outside of extremely dense systems, neutron-rich and free electron-rich environments, such as the inner crust of a neutron star . [ 2 ] [ 7 ] A feature of pycnonuclear reactions is that the rate of the reaction is directly proportional to the density of the space that the reaction is occurring in, but is almost fully independent of the temperature of the environment. [ 3 ]
Pycnonuclear reactions are observed in neutron stars or white dwarfs , with evidence present of them occurring in lab-generated deuterium-tritium plasma. [ 3 ] [ 6 ] Some speculations also relate the fact that Jupiter emits more radiation than it receives from the Sun with pycnonuclear reactions or cold fusion . [ 3 ] [ 8 ]
In white dwarfs , the core of the star is cold, under which conditions, so, if treated classically, the nuclei that arrange themselves into a crystal lattice are in their ground state . The zero-point oscillations of nuclei in the crystal lattice with energy at the energy E 0 {\displaystyle E_{0}} at Gamow's peak equal to E 0 ∼ ℏ w {\displaystyle E_{0}\thicksim \hbar w} can overcome the Coulomb barrier , actuating pycnonuclear reactions. A semi-analytical model indicates that in white dwarfs, a thermonuclear runaway can occur at much earlier ages than that of the universe , as the pycnonuclear reactions in the cores of white dwarfs exceed the luminosity of the white dwarfs, allowing C-burning to occur, which catalyzes the formation of type Ia supernovas in accreting white dwarfs, whose mass is equal to the Chandrasekhar mass . [ 1 ] [ 9 ] [ 10 ] [ 11 ]
Some studies indicate that the contribution of pycnonuclear reactions towards instability of white dwarfs is only significant in carbon white dwarfs , while in oxygen white dwarfs, such instability is caused mostly due to electron capture . [ 12 ] Although other authors disagree that the pycnonuclear reactions can act as major long-term heating sources for massive (1.25 M ☉ ) white dwarfs, as their density would not suffice for a high rate of pycnonuclear reactions. [ 13 ]
While most studies indicate that at the end of their lifecycle, white dwarfs slowly decay into black dwarfs , where pycnonuclear reactions slowly turn their cores into Fe 56 {\displaystyle {\ce {^56Fe}}} , according to some versions, a collapse of black dwarfs is possible: M.E. Caplan (2020) theorizes that in the most massive black dwarfs (1.25 M ☉ ), due to their declining electron fraction resulting from Fe 56 {\displaystyle {\ce {^56Fe}}} production, they will exceed the Chandrasekhar limit in the very far future, speculating that their lifetime and delay time can stretch to up to 10 1100 years. [ 14 ]
As the neutron stars undergo accretion , the density in the crust increases, passing the electron capture threshold. As the electron capture threshold ( ρ = 1.455 ∗ 10 12 {\displaystyle \rho =1.455*10^{12}} g cm −3 ) is exceeded, it allows for the formation of light nuclei from the process of double electron capture ( Mg 40 + 2 e ⟶ Ne 34 + 6 n + {\displaystyle {\ce {^40Mg + 2e -> ^34Ne + 6n +}}} ν e ), forming the light neon nuclei and free neutrons , which further increases the density of the crust. As the density increases, the crystal lattices of neutron-rich nuclei are forced closer together due to gravitational collapse of accreting material , and at a point where the nuclei are pushed so close together that their zero-point oscillations allow them to break through the Coulomb barrier , fusion occurs. While the main site of pycnonuclear fusion within neutron stars is the inner crust , pycnonuclear reactions between light nuclei can occur even in the plasma ocean . [ 15 ] [ 16 ] Since the core of neutron stars was approximated to be 3 ∗ 10 14 {\displaystyle 3*10^{14}} g cm −3 , at such extreme densities, pycnonuclear reactions play a large role as demonstrated by Haensel & Zdunik, who showed that at densities of ρ = 10 12 − 10 13 {\displaystyle \rho =10^{12}-10^{13}} g cm −3 , they serve as a major heat source. [ 17 ] [ 18 ] [ 19 ] In the fusion processes of the inner crust, the burning of neutron-rich nuclei ( Ne 34 + Ne 34 ⟶ Ca 68 {\displaystyle {\ce {^{34}Ne + ^{34}Ne -> ^68Ca}}} ) [ 10 ] [ 15 ] releases a lot of heat, allowing pycnonuclear fusion to perform as a major energy source, possibly even acting as an energy basin for gamma-ray bursts . [ 1 ] [ 2 ]
Further studies have established that most magnetars are found at densities of ρ = 10 10 − 10 11 {\displaystyle \rho =10^{10}-10^{11}} g cm −3 , indicating that pycnonuclear reactions along with subsequent electron capture reactions could serve as major heat sources. [ 20 ]
In Wolf–Rayet stars , the triple-alpha reaction is accommodated by the low-energy of Be 8 {\displaystyle {\ce {^8Be}}} resonance . However, in neutron stars the temperature in the core is so low that the triple-alpha reactions can occur via the pycnonuclear pathway. [ 21 ]
As the density increases, the Gamow peak increases in height and shifts towards lower energy, while the potential barriers are depressed. If the potential barriers are depressed by the amount of E 0 {\displaystyle E_{0}} , the Gamow peak is shifted across the origin, making the reactions density-dependent, as the Gamow peak energy is much larger than the thermal energy. The material becomes a degenerate gas at such densities. Harrison proposed that models fully independent of temperature be called cryonuclear . [ 22 ]
Pycnonuclear reactions can proceed in two ways: direct ( Ne 34 + Ne 34 {\displaystyle {\ce {^{34}Ne + ^{34}Ne}}} or Mg 40 + Mg 40 {\displaystyle {\ce {^{40}Mg + ^{40}Mg}}} ) or through chain of electron capture reactions ( N 25 + Mg 40 {\displaystyle {\ce {^25N + ^40Mg}}} ). [ 23 ]
The current consensus on the rate of pycnonuclear reactions is not coherent. There are currently a lot of uncertainties to consider when modelling the rate of pycnonuclear reactions, especially in spaces with high numbers of free particles. The primary focus of current research is on the effects of crystal lattice deformation and the presence of free neutrons on the reaction rate. Every time fusion occurs, nuclei are removed from the crystal lattice - creating a defect. The difficulty of approximating this model lies within the fact that the further changes occurring to the lattice and the effect of various deformations on the rate are thus far unknown. Since neighbouring lattices can affect the rate of reaction too, negligence of such deformations could lead to major discrepancies. [ 10 ] [ 24 ] Another confounding variable would be the presence of free neutrons in the crusts of neutron stars . The presence of free neutrons could potentially affect the Coulomb barrier , making it either taller or thicker. A study published by D.G. Yakovlev in 2006 has shown that the rate calculation of the first pycnonuclear fusion of two Ne 34 {\displaystyle {\ce {^{34}Ne}}} nuclei in the crust of a neutron star can have an uncertainty magnitude of up to seven . In this study, Yakovlev also highlighted the uncertainty in the threshold of pycnonuclear fusion (e.g., at what density it starts), giving the approximate density required for the start of pycnonuclear fusion of ρ p y c ≈ 10 12 − 10 13 {\displaystyle \rho _{pyc}\thickapprox 10^{12}-10^{13}} g cm −3 , arriving at a similar conclusion as Haesnel and Zdunik. [ 10 ] [ 19 ] [ 25 ] According to Haesnel and Zdunik, additional uncertainty of rate calculations in neutron stars can also be due to uneven distribution of the crustal heating, which can impact the thermal states of neutron stars before and after accretion . [ 19 ]
In white dwarfs and neutron stars, the nuclear reaction rates can not only be affected by pycnonuclear reactions but also by the plasma screening of the Coulomb interaction. [ 2 ] [ 10 ] A Ukrainian Electrodynamic Research Laboratory "Proton-21", established that by forming a thin electron plasma layer on the surface of the target material, and, thus, forcing the self-compression of the target material at low temperatures, they could stimulate the process of pycnonuclear fusion. The startup of the process was due to the self-contracting plasma "scanning" the entire volume of the target material, screening the Coulomb field . [ 26 ]
Before delving into the mathematical model, it is important to understand that pycnonuclear fusion, in its essence, occurs due to two main events:
Both of these effects are heavily affected by screening. The term screening is generally used by nuclear physicists when referring to plasmas of particularly high density. In order for the pycnonuclear fusion to occur, the two particles must overcome the electrostatic repulsion between them - the energy required for this is called the Coulomb barrier. Due to the presence of other charged particles (mainly electrons) next to the reacting pair, they exert the effect of shielding - as the electrons create an electron cloud around the positively charged ions - effectively reducing the electrostatic repulsion between them, lowering the Coulomb barrier. This phenomenon of shielding is referred to as " screening ", and in cases where it is particularly strong, it is called " strong screening ". Consequently, in cases where the plasma has a strong screening effect, the rate of pycnonuclear fusion is substantially enhanced. [ 27 ]
Quantum tunnelling is the foundation of the quantum physical approach to pycnonuclear fusion. It is closely intertwined with the screening effect, as the transmission coefficient T {\displaystyle T} depends on the height of the potential barrier , the mass of the particles, and their relative velocity (since the total energy of the system depends on the kinetic energy). From this follows that the transmission coefficient is very sensitive to the effects of screening. Thus, the effect of screening not only contributes to the reduction of the potential barrier that allows for "classical" fusion to occur via the overlap of the wave functions of the zero-point oscillations of the particles, but also to the increase of the transmission coefficient, both of which increase the rate of pycnonuclear fusion. [ 11 ] [ 25 ]
On top of the other various jargon related to pycnonuclear fusion, the papers also introduce various regimes , that define the rate of pycnonuclear fusion. Specifically, they identify the zero-temperature , intermediate , and thermally-enhanced regimes as their main ones. [ 10 ]
The pioneers to the derivation of the rate of pycnonuclear fusion in one-component plasma (OCP) were Edwin Salpeter and David Van-Horn, with their article published in 1969. Their approach used a semiclassical method to solve the Schrödinger equation by using the Wentzel-Kramers-Brillouin (WKB) approximation, and Wigner-Seitz (WS) spheres. Their model is heavily simplified, and whilst it is primitive, is required to understand other approaches which largely extrapolated on the works of Salpeter & Van Horn. They employed the WS spheres to simplify the OCP into regions containing one ion each, with the ions situated on the vertices of a BCC crystal lattice. Then, using the WKB approximation, they resolved the effect of quantum tunnelling on the fusing nuclei. Extrapolating this to the entire lattice allowed them to arrive at their formula for the rate of pycnonuclear fusion: [ 10 ] P = 8 2 ρ μ A H ⟨ p ⟩ A v {\displaystyle P={8 \over 2}{\rho \over \mu _{A}H}\langle p\rangle _{A_{v}}} where ρ {\displaystyle \rho } is the density of the plasma, μ A {\displaystyle \mu _{A}} is the mean molecular weight per electron (atomic nucleus), H {\displaystyle H} is a constant equal to 1.66044 ∗ 10 − 24 {\displaystyle 1.66044*10^{-24}} and serves as a conversion factor from atomic mass units to grams, and ⟨ p ⟩ A v {\displaystyle \langle p\rangle _{A_{v}}} represents the thermal average of the pairwise reaction probability.
However, the big fault of the method proposed by Salpeter & Van-Horn is that they neglected the dynamic model of the lattice. This was improved upon by Schramm and Koonin in 1990. In their model, they found that the dynamic model cannot be neglected, but it is possible that the effects caused by the dynamicity can be cancelled out. [ 10 ] [ 21 ] | https://en.wikipedia.org/wiki/Pycnonuclear_fusion |
Pydlpoly is a molecular dynamics simulation package which is a modified version of DL-POLY with a Python language interface. Pydlpoly is written by Rochus Schmid in Ruhr University Bochum , Germany.
This article about molecular modelling software is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pydlpoly |
Pyknosis , or karyopyknosis , is the irreversible condensation of chromatin in the nucleus of a cell undergoing necrosis [ 1 ] or apoptosis . [ 2 ] It is followed by karyorrhexis , or fragmentation of the nucleus.
Pyknosis (from Ancient Greek πυκνός meaning "thick, closed or condensed") is also observed in the maturation of erythrocytes (a red blood cell) and the neutrophil (a type of white blood cell). The maturing metarubricyte (a stage in RBC maturation) will condense its nucleus before expelling it to become a reticulocyte . The maturing neutrophil will condense its nucleus into several connected lobes that stay in the cell until the end of its cell life.
Pyknotic nuclei are often found in the zona reticularis of the adrenal gland. They are also found in the keratinocytes of the outermost layer in parakeratinised epithelium.
Pyknosis, or the irreversible nuclear condensation (a nuclear morphology) in a cell (generally old vertebrate leukocyte cells) is the result of a cell undergoing either apoptosis or necrosis . [ 3 ] There are two types of pyknosis: nucleolytic pyknosis and anucleolytic pyknosis. Nucleolytic pyknosis occurs during apoptosis (a form of controlled/programmed cell death), while anucleolytic pyknosis occurs during necrosis. [ 4 ] Necrosis is a form of regulated cell death due to toxins, infections, and other acute stressors. [ 4 ] These stressors cause swelling/shape modification of cellular organelles leading to the eventual loss of stability and integrity of the cell membrane . [ 4 ]
In simpler terms, pyknosis is the process of nuclear shrinkage that may occur during both necrosis and apoptosis. Pyknosis is also characterized by eventual fragmentation ( karyorrhexis ) of the dense nuclear chromatin , resulting in dark, round, and dense nuclear fragments. [ 5 ] Karyorrhexis is the fragmentation of a pyknotic cell’s nucleus and the cleavage and condensing of chromatin. [ 5 ]
Apoptosis is characterized by nuclear condensation, shrinking of the cell, and blebbing of the nuclear and cell membrane, while necrosis is characterized by nuclear condensation, swelling of the cell, and breaks in the cell membrane. [ 6 ] Both necrosis and apoptosis are regulated by a few of the same proteins: caspase-activated DNase (CAD), endonuclease G and DNase I . Pyknosis occurs in both an apoptotic and a necrotic cell. Pyknosis in an apoptotic cell is identified by nuclear condensation, chromatin fragmentation, and the formation of a few large clumps which are enveloped by apoptotic extracellular vesicles , which are to be released when the cell dies. [ 6 ] Pyknosis in a necrotic cell is identified by nuclear condensation and fragmentation into small clumps that will be dissolved later in the process of the necrotic cell’s death. [ 6 ] Consequently, pyknosis can be distinguished into two types, nucleolytic pyknosis (apoptotic cells) and anucleolytic pyknosis (necrotic cells).
Nucleolytic pyknosis, which can also be referred to as apoptotic pyknosis, involves three main events. These are disrupting the nuclear membrane, the condensing of the chromatin, and lastly, nuclear cleavage/fragmentation. [ 4 ] Throughout these events the cell shrinks in size and the cell membrane undergoes blebbing, which is the forming of membrane bulges across the exterior-facing surface of the cell membrane. During the first event (the disruption of the nuclear membrane), several enzymes are used to cleave the proteins found in the nuclear membrane. These enzymes, caspase-3 and caspase-6 , both target and cleave nuclear membrane proteins, including NUP153 , LAP2, and B1 (proteins that are used for membrane structure and molecular transport). [ 4 ] This cleavage, in turn, results in a disruption of the interior of the membrane, which is an initiating factor for chromatin condensation (the second event of nucleolytic pyknosis). This is due to the fact that caspase-3 cleaves Acinus, which has DNA / RNA binding domains and ATPase activity to initiate the condensation of chromatin. [ 4 ]
Anucleolytic pyknosis, which can also be referred to as necrotic pyknosis, involves the swelling of the cell, followed by the separation of the nuclear membrane from chromatin, the eventual collapse of both the nuclear membrane and chromatin, and finally the cell membrane ruptures (the cell dies). [ 4 ] One protein that plays a significant role in necrotic pyknosis is the barrier-to-autointegration factor (BAF). The function of BAF is to facilitate the tethering of chromatin to the membrane of the nucleus, however in the case of necrosis, when BAF is phosphorylated , it will initiate the dissociation between the nuclear membrane and the condensed chromatin. [ 6 ] As a result, the nuclear membrane will collapse onto the condensed chromatin. Thus, the phosphorylation of BAF is a critical marker of necrotic pyknosis.
Pyknosis is a stage in the apoptotic or necrotic cell death pathways. It is an important stage that involves fragmentation and condensation of damaged DNA/chromatin. Without it, the apoptotic or necrotic cell death pathways would be interrupted. This disruption, in turn, may prompt the improper destruction or removal of a cell with damaged elements as well as other related issues. These issues include cell accumulation and uncontrolled cell growth, which results in the formation of cancerous and abnormal tissue masses known as tumors . Therefore, being able to observe or identify when a cell is pyknotic (which may indicate that the cell is undergoing apoptosis or necrosis) and if it then successfully undergoes apoptosis or necrosis, may be crucial in determining if the cell will undergo uncontrolled cell growth and contribute to the formation of a tumor.
Various techniques are used to detect/observe pyknosis. These techniques also help to differentiate between apoptotic or necrotic cells. The techniques are identified and described as follows:
When stains and dyes are applied to locate pyknotic cells in a tissue sample, the cell becomes easily identifiable. The stains/dyes target the nuclear and blebbed fragments of a pyknotic cell, making them dark (light contrast) and more readily seen when the sample is placed under a light microscope. Fluorescence microscopy and flow cytometry also use staining ( fluorescent stains ) to target the DNA/nuclear fragments of cells. The fluorescent staining creates a contrast between normal cell DNA and pyknotic cell DNA, because pyknotic cell nuclear material is condensed.
Gel electrophoresis is a standard technique that is frequently used to visualize DNA fragmentation (forming a ladder-like image on the gel), which is a characteristic of apoptosis and is associated with nuclear condensation (which characterizes pyknosis). Therefore, when referring to apoptosis, this technique is known as DNA laddering . Gel electrophoresis is also used to visualize the random DNA fragmentation of necrosis, which forms a smear on the gel.
Various assays of DNA fragmentation or condensation include the APO single-stranded DNA ( ssDNA ) assay which detects damaged DNA of cells undergoing apoptosis or necrosis, TUNEL assay which is used to locally find DNA strand breaks (DSBs), and ISEL. [ 8 ]
ISEL (in-situ labeling technique) is a labeling/tagging technique of apoptotic or necrotic cells. [ 8 ] ISEL specifically targets unfragmented DNA that has condensed into a nucleosome structure. [ 8 ]
The APO ssDNA assay detects apoptotic cells by using an antibody that specifically binds to the ssDNA, which is accumulated during apoptosis as a result of DNA fragmentation. [ 8 ] Therefore, the presence of ssDNA is an indicator of DNA damage in the apoptotic cell. For the assay process, cells are fixed (with e.g., formamide ), and these cells then undergo incubation (at a predetermined temperature), which subjects the DNA to thermal denaturation and exposes the ssDNA. [ 8 ] Next, the cells are incubated with an ssDNA-specific antibody along with a fluorescently labeled secondary antibody. [ 8 ] The fluorescence amounts as a measure of apoptosis which can then be quantified using flow cytometry.
The TUNEL assay, otherwise known as the terminal deoxynucleotidyl transferase dUTP nick-end labeling assay, is a technique that measures DNA damage and breakage during apoptosis. [ 8 ] During apoptosis, DNA fragmentation exposes numerous 3’OH ends, that are labeled with modified deoxy-uridine triphosphate (dUTP) by the TUNEL reaction. [ 8 ] Then, this modified dUTP can be identified with specific fluorescent antibodies which can identify modified nucleotides or by using tagged nucleotides themselves. [ 8 ] Flow cytometry can then be used to quantify fluorescence intensity, and thus provide a measure of apoptosis.
As mentioned above, caspase proteins, which are protease enzymes, promote DNA condensation and fragmentation via the caspase (or proteolytic) cascade. These caspase proteins include, for example, caspase 9 , caspase 6, caspase 7 , and caspase 3. The caspase cascade directly activates caspase-activated DNase (CAD) which initiates DNA fragmentation into smaller pieces resulting in chromatin condensation. The biochemical techniques used to detect caspase activity include ELISA and fluorometric and colorimetric assays. [ 8 ] | https://en.wikipedia.org/wiki/Pyknosis |
In mathematics, especially in topology , a pyknotic set is a sheaf of sets on the site of compact Hausdorff spaces (with some fixed Grothendieck universes ). The notion was introduced by Barwick and Haine to provide a convenient setting for homological algebra . [ 1 ] The term pyknotic comes from the Greek πυκνός, meaning dense, compact or thick. [ 2 ] The notion can be compared to other approaches of introducing generalized spaces for the purpose of homological algebra such as Clausen and Scholze‘s condensed sets or Johnstone‘s topological topos . [ 3 ]
Pyknotic sets form a coherent topos , while condensed sets do not. [ 4 ] Comparing pyknotic sets with his approach with Clausen, Scholze writes: [ 5 ]
In a recent preprint [BH19], Barwick and Haine set up closely related foundations, but using different set-theoretic conventions. In particular, they assume the existence of universes, fixing in particular a “tiny” and a “small” universe, and look at sheaves on tiny profinite sets with values in small sets; they term these pyknotic sets. In our language, placing ourselves in the small universe, this would be κ-condensed sets for the first strongly inaccessible cardinal κ they consider (the one giving rise to the tiny universe).
This topology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pyknotic_set |
Pyoluteorin is a natural antibiotic that is biosynthesized from a hybrid nonribosomal peptide synthetase (NRPS) and polyketide synthase (PKS) pathway. [ 1 ] Pyoluteorin was first isolated in the 1950s from Pseudomonas aeruginosa strains T359 and IFO 3455 [ 2 ] and was found to be toxic against oomycetes , bacteria , fungi , and against certain plants . [ 3 ] Pyoluteorin is most notable for its toxicity against the oomycete Pythium ultimum , [ 4 ] which is a plant pathogen that causes a global loss in agriculture. Currently, pyoluteorin derivatives are being studied as an Mcl-1 antagonist in order to target cancers that have elevated Mcl-1 levels. [ 5 ]
Pyoluteorin is synthesized from an NRPS/PKS hybrid pathway. The resorcinol ring is derived from a type I PKS [ 6 ] [ 7 ] while the dichloropyrrole [ clarification needed ] moiety is derived from a type II NRPS. [ 8 ] Pyoluteorin biosynthesis begins with the activation of L- proline to prolyl-AMP by the adenylation domain PltF. With prolyl-AMP still in the active site, the active form of the peptidyl carrier protein PltL binds to PltF. Then PltF catalyzes the aminoacylation of PltL by attaching L-proline to the thiol of the 4’phosphopantetheine arm of PltL. [ 9 ] Next, the dehydrogenase PltE desaturates the prolyl moiety on PltL to create pyrrolyl-PltL. The halogenation domain PltA then dichlorinates the pyrrole moiety first at position 5 and then at position 4 in a FADH2 dependent manner. [ 10 ] The dichloropyrroyl residue is then transferred to the type I PKS PltB and PltC, however, the mechanism of transfer is unknown. The addition of 3 malonyl-CoA monomers , cyclization , and release by the thioesterase PltG gives pyoluteorin. | https://en.wikipedia.org/wiki/Pyoluteorin |
Pyramidal alkenes are alkenes in which the two carbon atoms making up the double bond are not coplanar with their four substituents . This deformation results from geometric constraints. Pyramidal alkenes only are of interest because much can be learned from them about the nature of chemical bonding . [ 1 ]
Twisting to a 90° dihedral angle between two of the groups on the carbons requires less energy than the strength of a pi bond , and the bond still holds. The carbons of the double bond become pyramidal , which allows preserving some p orbital alignment—and hence pi bonding. The other two attached groups remain at a larger dihedral angle. This contradicts a common textbook assertion that the two carbons retain their planar nature when twisting, in which case the p orbitals would rotate enough away from each other to be unable to sustain a pi bond. In a 90°-twisted alkene, the p orbitals are only misaligned by 42° and the strain energy is only around 40 kcal/mol. In contrast, a fully broken pi bond has an energetic cost of around 65 kcal/mol. [ 2 ]
In cycloheptene ( 1.1 ) the cis isomer is an ordinary unstrained molecule, but the heptane ring is too small to accommodate a trans -configured alkene group resulting in strain and twisting of the double bond. The p-orbital misalignment is minimized by a degree of pyramidalization . In the related anti-Bredt molecules , it is not pyramidalization but twisting that dominates.
Pyramidalized cage alkenes also exist where symmetrical bending of the substituents predominates without p-orbital misalignment.
The pyramidalization angle φ ( b ) is defined as the angle between the plane defined by one of the doubly bonded carbons and its two substituents and the extension of the double bond and is calculated as:
the butterfly bending angle or folding angle ψ ( c ) is defined as the angle between two planes and can be obtained by averaging the two torsional angles R 1 C=CR 3 and R 2 C=CR 4 .
In alkenes 1.2 and 1.3 these angles are determined with X-ray crystallography as respectively 32.4°/22.7° and 27.3°/35.6°. Although stable, these alkenes are very reactive compared to ordinary alkenes. They are liable to dimerization creating cyclobutane rings, or react with oxygen to epoxides .
The compound tetradehydrodianthracene, also with a 35° pyramidalization angle, is synthesized in a photochemical cycloaddition of bromoanthracene followed by elimination of hydrogen bromide .
This compound is very reactive in Diels–Alder reactions due to through-space interactions between the two alkene groups. This enhanced reactivity enabled in turn the synthesis of the first-ever Möbius aromat .
In one study, [ 3 ] the strained alkene 4.4 was synthesized with the highest pyramidalizion angles yet, 33.5° and 34.3°. This compound is the double Diels–Alder adduct of the diiodo cyclophane 4.1 and anthracene 4.3 by reaction in presence of potassium tert-butoxide in refluxing dibutyl ether through a di aryne intermediate 4.2 . This is a stable compound but will slowly react with oxygen to an epoxide when left standing as a chloroform solution.
In one study, [ 4 ] isolation of a pyramidal alkene is not even possible by matrix isolation at extremely low temperatures unless stabilized by metal coordination :
A reaction of the di iodide 5.1 in Figure 5 with sodium amalgam in the presence of ethylenebis(triphenylphosphine)platinum(0) does not give the intermediate alkene 5.2 but the platinum stabilized 5.3 . The sigma bond in this compound is destroyed in reaction with ethanol . | https://en.wikipedia.org/wiki/Pyramidal_alkene |
In chemistry , pyramidal inversion (also umbrella inversion ) is a fluxional process in compounds with a pyramidal molecule, such as ammonia (NH 3 ) "turns inside out". [ 1 ] [ 2 ] It is a rapid oscillation of the atom and substituents, the molecule or ion passing through a planar transition state . [ 3 ] For a compound that would otherwise be chiral due to a stereocenter , pyramidal inversion allows its enantiomers to racemize . The general phenomenon of pyramidal inversion applies to many types of molecules, including carbanions , amines , phosphines , arsines , stibines , and sulfoxides . [ 4 ] [ 2 ]
The identity of the inverting atom has a dominating influence on the barrier. Inversion of ammonia is rapid at room temperature , inverting 30 billion times per second. Three factors contribute to the rapidity of the inversion: a low energy barrier (24.2 kJ/mol ; 5.8 kcal/mol), a narrow barrier width (distance between geometries), and the low mass of hydrogen atoms, which combine to give a further 80-fold rate enhancement due to quantum tunnelling . [ 5 ] In contrast, phosphine (PH 3 ) inverts very slowly at room temperature (energy barrier: 132 kJ/mol ). [ 6 ] Consequently, amines of the type RR′R"N usually are not optically stable (enantiomers racemize rapidly at room temperature), but P -chiral phosphines are. [ 7 ] Appropriately substituted sulfonium salts, sulfoxides , arsines , etc. are also optically stable near room temperature. Steric effects can also influence the barrier.
Pyramidal inversion in nitrogen and amines is known as nitrogen inversion . [ 8 ] It is a rapid oscillation of the nitrogen atom and substituents, the nitrogen "moving" through the plane formed by the substituents (although the substituents also move - in the other direction); [ 9 ] the molecule passing through a planar transition state . [ 10 ] For a compound that would otherwise be chiral due to a nitrogen stereocenter , nitrogen inversion provides a low energy pathway for racemization , usually making chiral resolution impossible. [ 11 ]
Ammonia exhibits a quantum tunnelling due to a narrow tunneling barrier, [ 12 ] and not due to thermal excitation. Superposition of two states leads to energy level splitting , which is used in ammonia masers .
The inversion of ammonia was first detected by microwave spectroscopy in 1934. [ 13 ]
In one study the inversion in an aziridine was slowed by a factor of 50 by placing the nitrogen atom in the vicinity of a phenolic alcohol group compared to the oxidized hydroquinone . [ 14 ]
The system interconverts by oxidation by oxygen and reduction by sodium dithionite .
Conformational strain and structural rigidity can effectively prevent the inversion of amine groups. Tröger's base analogs [ 15 ] (including the Hünlich's base [ 16 ] ) are examples of compounds whose nitrogen atoms are chirally stable stereocenters and therefore have significant optical activity . [ 17 ] | https://en.wikipedia.org/wiki/Pyramidal_inversion |
A pyranometer (from Greek πῦρ (pyr) ' fire ' and ἄνω (ano) ' above, sky ' ) is a type of actinometer used for measuring solar irradiance on a planar surface and it is designed to measure the solar radiation flux density (W/m 2 ) from the hemisphere above within a wavelength range 0.3 μm to 3 μm.
A typical pyranometer does not require any power to operate. However, recent technical development includes use of electronics in pyranometers, which do require (low) external power (see heat flux sensor ).
The solar radiation spectrum that reaches Earth's surface extends its wavelength approximately from 300 nm to 2800 nm.
Depending on the type of pyranometer used, irradiance measurements with different degrees of spectral sensitivity will be obtained.
To make a measurement of irradiance , it is required by definition that the response to "beam" radiation varies with the cosine of the angle of incidence. This ensures a full response when the solar radiation hits the sensor perpendicularly (normal to the surface, sun at zenith, 0° angle of incidence), zero response when the sun is at the horizon (90° angle of incidence, 90° zenith angle), and 0.5 at a 60° angle of incidence. It follows that a pyranometer should have a so-called "directional response" or "cosine response" that is as close as possible to the ideal cosine characteristic.
Following the definitions noted in the ISO 9060, [ 1 ] three types of pyranometer can be recognized and grouped in two different technologies: thermopile technology and silicon semiconductor technology.
The light sensitivity, known as ' spectral response' , depends on the type of pyranometer. The figure here above shows the spectral responses of the three types of pyranometer in relation to the solar radiation spectrum. The solar radiation spectrum represents the spectrum of sunlight that reaches the Earth's surface at sea level, at midday with A.M. ( air mass ) = 1.5. The latitude and altitude influence this spectrum. The spectrum is influenced also by aerosol and pollution.
A thermopile pyranometer (also called thermo-electric pyranometer) is a sensor based on thermopiles designed to measure the broad band of the solar radiation flux density from a 180° field of view angle. A thermopile pyranometer thus usually measures from 300 to 2800 nm with a largely flat spectral sensitivity (see the spectral response graph) The first generation of thermopile pyranometers had the active part of the sensor equally divided in black and white sectors. Irradiation was calculated from the differential measure between the temperature of the black sectors, exposed to the sun, and the temperature of the white sectors, sectors not exposed to the sun or better said in the shades.
In all thermopile technology, irradiation is proportional to the difference between the temperature of the sun exposed area and the temperature of the shadow area.
In order to attain the proper directional and spectral characteristics, a thermopile pyranometer is constructed with the following main components:
In the modern thermopile pyranometers the active (hot) junctions of the thermopile are located beneath the black coating surface and are heated by the radiation absorbed from the black coating. [ 2 ] The passive (cold) junctions of the thermopile are fully protected from solar radiation and in thermal contact with the pyranometer housing, which serves as a heat-sink. This prevents any alteration from yellowing or decay when measuring the temperature in the shade, thus impairing the measure of the solar irradiance.
The thermopile generates a small voltage in proportion to the temperature difference between the black coating surface and the instrument housing. This is of the order of 10 μV (microvolts) per W/m2, so on a sunny day the output will be around 10 mV (millivolts). Each pyranometer has a unique sensitivity, unless otherwise equipped with electronics for signal calibration .
Thermopile pyranometers are frequently used in meteorology , climatology , climate change research, building engineering physics , photovoltaic systems , and monitoring of photovoltaic power stations .
The solar energy industry, in a 2017 standard, IEC 61724-1:2017, [ 3 ] has defined the type and number of pyranometers that should be used depending on the size and category of solar power plant. That norm advises to install thermopile pyranometers horizontally (GHI, Global Horizontal Irradiation), and to install photovoltaic pyranometers in the plane of PV modules (POA, Plane Of Array) to enhance accuracy in Performance Ratio calculation.
To use the data measured by a pyranometer (horizontal or in-plane), quality assessment (QA) of the raw measured data is necessary. [ 4 ] This is because the pyranometer measurements typically suffer from environment-induced errors but also handling and neglect errors, such as:
Each of the above issues appears as a specific pattern in the measured time series. Thanks to this, the issues can be identified, the erroneous records flagged, and excluded from the dataset. The methods employed for data QA can be either manual, relying on an expert to identify the patterns, or automated, where an algorithm does the job. As many of the patterns are complex, not easily described, and require a particular context, manual QA is very common. A specialist software with suitable tools is required to perform the QA.
After the QA procedure, the remaining ‘clean’ dataset reflects the solar irradiance at the measurement site to within the uncertainty of measurement of the instrument. The ‘clean’ measured dataset can be optionally enhanced with data from a satellite-based solar irradiance model. This data is available globally for a much longer time period (typically decades into the past) than the data measured by the pyranometer. The satellite model data can be correlated (or site adapted) to the pyranometer-measured data to produce a dataset with a long time period of data accurate for the specific site, with a defined uncertainty. Such data can be used to perform bankable solar resource studies or produce Solar potential maps .
For monitoring of operational PV power plants, pyranometers play an essential role in verifying the solar irradiance available at any given time or over a certain time period. Due to weather variability, redundancy, and the spatial scale of contemporary solar plants (above 100MWp), multiple pyranometers are installed to provide accurate solar irradiation for each section of the PV power plant. IEC 61724-1:2017 [ 5 ] international standard for example calls for at least 4 Class A thermopile pyranometers to be installed at 100MWp PV power plant at all times.
Solar measurements that were QA’d could be used to derive Key Performance Indicators (KPI) such as Performance ratio* - metrics used in asset health monitoring or various contractual scenarios relating to energy produced (billing) or asset management (i.e. O&M). In these calculations, the measured sum of in-plane irradiation over a certain period is used as the determinant to which normalized produced PV electricity is compared to. Due to the difficulty of obtaining reliable in-plane measurements, especially in operational power plants, Energy Performance Index is increasingly being used instead of the older Performance ratio metric.
Also known as a photoelectric pyranometer in the ISO 9060, [ 6 ] a photodiode-based pyranometer can detect the portion of the solar spectrum between 400 nm and 1100 nm. The photodiode converts the aforementioned solar spectrum frequencies into current at high speed, thanks to the photoelectric effect . The conversion is influenced by the temperature with a raise in current produced by the raise in temperature (about 0,1% • °C)
A photodiode-based pyranometer is composed by a housing dome, a photodiode , and a diffuser or optical filters. The photodiode has a small surface area and acts as a sensor. The current generated by the photodiode is proportional to irradiance; an output circuit, such as a transimpedance amplifier , generates a voltage directly proportional to the photocurrent. The output is usually on the order of millivolts, the same order of magnitude as thermopile-type pyranometers.
Photodiode-based pyranometers are implemented where the quantity of irradiation of the visible solar spectrum, or of certain portions such as UV, IR or PAR ( photosynthetically active radiation ), needs to be calculated. This is done by using diodes with specific spectral responses.
Photodiode-based pyranometers are the core of luxmeters used in photography, cinema and lighting technique. Sometimes they are also installed close to modules of photovoltaic systems.
Built around the 2000s concurrently with the spread of photovoltaic systems, the photovoltaic pyranometer is an evolution of the photodiode pyranometer. It answered the need for a single reference photovoltaic cell when measuring the power of cell and photovoltaic modules. [ 7 ] Specifically, each cell and module is tested through flash tests by their respective manufacturers, and thermopile pyranometers do not possess the adequate speed of response nor the same spectral response of a cell. This would create obvious mismatch when measuring power, which would need to be quantified. [ 8 ] [ 9 ] In the technical documents, this pyranometer is also known as "reference cell".
The active part of the sensor is composed of a photovoltaic cell working in near short-circuit condition. As such, the generated current is directly proportionate to the solar radiation hitting the cell in a range between 350 nm and 1150 nm. When invested by a luminous radiation in the mentioned range, it produces current as a consequence of the photovoltaic effect . Its sensitivity is not flat, but it is same as that of Silicon photovoltaic cell. See the Spectral Response graph.
A photovoltaic pyranometer is essentially assembled with the following parts:
Silicon sensors such as the photodiode and the photovoltaic cell vary the output in function of temperature. In the more recent models, the electronics compensate the signal with the temperature, therefore removing the influence of temperature out of the values of solar irradiance. Inside several models, the case houses a board for the amplification and conditioning of the signal .
Photovoltaic pyranometers are used in solar simulators and alongside photovoltaic systems for the calculation of photovoltaic module effective power and system performance. Because the spectral response of a photovoltaic pyranometer is similar to that of a photovoltaic module, it may also be used for preliminary diagnosis of malfunction in photovoltaic systems.
Reference PV Cell or Solar Irradiance Sensor may have up to 5 inputs ensuring the connection of Module Temperature Sensor, Ambient Temperature Sensor, Wind speed sensor, Wind Direction Sensor, and Relative Humidity, with only one Modbus RTU output connected directly to the Datalogger. This combination is called “weather station” which is suitable for monitoring the Solar PV Plants. This feature is one of the main differences between the Thermopile Pyranometer and the Reference Cell Solar Irradiance Sensor .
Both thermopile-type and photovoltaic pyranometers are manufactured according to standards.
Thermopile pyranometers follow the ISO 9060 standard, which is also adopted by the World Meteorological Organization (WMO). This standard discriminates three classes.
The latest version of ISO 9060 , from 2018 uses the following classification: Class A for best performing, followed by Class B and Class C, while the older ISO 9060 standard from 1990 used ambiguous terms as "secondary standard", "first class" and "second class"., [ 10 ]
Differences in classes are due to a certain number of properties in the sensors: response time, thermal offsets, temperature dependence, directional error, non-stability, non-linearity, spectral selectivity and tilt response. These are all defined in ISO 9060. For a sensor to be classified in a certain category, it needs to fulfill all the minimum requirements for these properties.
‘Fast response’ and ‘spectrally flat’ are two sub-classifications, included in ISO 9060:2018. They help to further distinguish and categorise sensors. To gain the ‘fast response’ classification, the response time for 95% of readings must be less than 0.5 seconds; while ‘spectrally flat’ can apply to sensors with a spectral selectivity of less than 3% in the 0,35 to 1,5 μm spectral range. While most Class A pyranometers are ‘spectrally flat’, sensors in the ‘fast response’ sub-classification are much rarer. Most Class A pyranometers have a response time of 5 seconds or more.
The calibration is typically done having the World Radiometric Reference [ 11 ] (WRR) as an absolute reference. It is maintained by PMOD [ 12 ] in Davos , Switzerland . [ 13 ] In addition to the World Radiometric Reference, there are private laboratories such as ISO-Cal North America [ 14 ] who have acquired accreditation for these unique calibrations. For the Class A pyranometer, calibration is done following ASTM G167, [ 15 ] ISO 9847 [ 16 ] or ISO 9846. [ 17 ] [ 18 ] Class B and class C pyranometers are usually calibrated according to ASTM E824 [ 19 ] and ISO 9847. [ 20 ]
Photovoltaic pyranometers are standardized and calibrated under IEC 60904-4 for primary reference samples and under IEC 60904-2 for secondary reference samples and the instruments intended for sale.
In both standards, their respective traceability chain starts with the primary standard known as the group of cavity radiometer by the World Radiometric Reference (WRR). [ 21 ]
The natural output value of these pyranometers does not usually exceed tens of millivolt (mV). It is considered a "weak" signal, and as such, rather vulnerable to electromagnetic interferences , especially where the cable runs across decametrical distances or lies in photovoltaic systems. Thus, these sensors are frequently equipped with signal conditioning electronics, giving an output of 4-20 mA or 0-1 V.
Another solution implies greater immunities to noises, like Modbus over RS-485 , suitable for ambiances with electromagnetic interferences typical of medium-large scale photovoltaic power stations , or SDI-12 output, where sensors are part of a low power weather station. The equipped electronics often concur to easy integration in the system's SCADA .
Additional information can also be stored in the electronics of the sensor, like calibration history, serial number. | https://en.wikipedia.org/wiki/Pyranometer |
In organic chemistry , pyranose is a collective term for saccharides that have a chemical structure that includes a six-membered ring consisting of five carbon atoms and one oxygen atom (a heterocycle ). There may be other carbons external to the ring. The name derives from its similarity to the oxygen heterocycle pyran , but the pyranose ring does not have double bonds . A pyranose in which the anomeric −OH ( hydroxyl group ) at C(l) has been converted into an OR group is called a pyranoside .
The pyranose ring is formed by the reaction of the hydroxyl group on carbon 5 (C-5) of a sugar with the aldehyde at carbon 1. This forms an intramolecular hemiacetal . If reaction is between the C-4 hydroxyl and the aldehyde, a furanose is formed instead. [ 1 ] The pyranose form is thermodynamically more stable than the furanose form, which can be seen by the distribution of these two cyclic forms in solution. [ 2 ]
Hermann Emil Fischer won the Nobel Prize in Chemistry (1902) for his work in determining the structure of the D - aldohexoses . [ 1 ] However, the linear, free-aldehyde structures that Fischer proposed represent a very minor percentage of the forms that hexose sugars adopt in solution. It was Edmund Hirst and Clifford Purves, in the research group of Walter Haworth , who conclusively determined that the hexose sugars preferentially form a pyranose, or six-membered, ring. Haworth drew the ring as a flat hexagon with groups above and below the plane of the ring – the Haworth projection . [ 3 ]
A further refinement to the conformation of pyranose rings came when Sponsler and Dore (1926) realized that Sachse's mathematical treatment of six-membered rings could be applied to their X-ray structure of cellulose . [ 3 ] It was determined that the pyranose ring is puckered, to allow all of the carbon atoms of the ring to have close to the ideal tetrahedral geometry.
This puckering leads to a total of 38 distinct basic pyranose conformations : 2 chairs, 6 boats, 6 skew-boats, 12 half-chairs, and 12 envelopes. [ 4 ]
These conformers can interconvert with one another; however, each form may have very different relative energy, so a significant barrier to interconversion may be present. The energy of these conformations can be calculated from quantum mechanics ; an example of possible glucopyranose interconversions is given. [ 5 ]
The conformations of the pyranose ring are superficially similar to that of the cyclohexane ring. However, the specific nomenclature of pyranoses includes reference to the ring oxygen, and the presence of hydroxyls on the ring have distinct effects on its conformational preference. There are also conformational and stereochemical effects specific to the pyranose ring.
To name conformations of pyranose, first the conformer is determined. The common conformers are similar to those found in cyclohexane , and these form the basis of the name. Common conformations are chair (C), boat (B), skew (S), half-chair (H) or envelope (E). The ring atoms are then numbered; the anomeric , or hemiacetal, carbon is always 1. Oxygen atoms in the structure are, in general, referred to by the carbon atom they are attached to in the acyclic form, and designated O. Then:
As shown by the relative structure energies in the diagram above, the chair structures are the most stable carbohydrate form. This relatively defined and stable conformation means that the hydrogen atoms of the pyranose ring are held at relatively constant angles to one another. Carbohydrate NMR takes advantage of these dihedral angles to determine the configuration of each of the hydroxyl groups around the ring. | https://en.wikipedia.org/wiki/Pyranose |
Pyrenoids are sub-cellular phase-separated micro-compartments found in chloroplasts of many algae , [ 1 ] and in a single group of land plants, the hornworts . [ 2 ] [ 3 ] Pyrenoids are associated with the operation of a carbon-concentrating mechanism (CCM). Their main function is to act as centres of carbon dioxide (CO 2 ) fixation, by generating and maintaining a CO 2 -rich environment around the photosynthetic enzyme ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO). Pyrenoids therefore seem to have a role analogous to that of carboxysomes in cyanobacteria .
Algae are restricted to aqueous environments, even in aquatic habitats, and this has implications for their ability to access CO 2 for photosynthesis. CO 2 diffuses 10,000 times slower in water than in air, and is also slow to equilibrate. The result of this is that water, as a medium, is often easily depleted of CO 2 and is slow to gain CO 2 from the air. Finally, CO 2 equilibrates with bicarbonate ( HCO − 3 ) when dissolved in water, and does so on a pH -dependent basis. In sea water for example, the pH is such that dissolved inorganic carbon (DIC) is mainly found in the form of HCO − 3 . The net result of this is a low concentration of free CO 2 that is barely sufficient for an algal RuBisCO to run at a quarter of its maximum velocity , and thus, CO 2 availability may sometimes represent a major limitation of algal photosynthesis.
Pyrenoids were first described in 1803 by Vaucher [ 4 ] (cited in Brown et al. [ 5 ] ). The term was first coined by Schmitz [ 6 ] who also observed how algal chloroplasts formed de novo during cell division, leading Schimper to propose that chloroplasts were autonomous, and to surmise that all green plants had originated through the “unification of a colourless organism with one uniformly tinged with chlorophyll". [ 7 ] From these pioneering observations, Mereschkowski eventually proposed, in the early 20th century, the symbiogenetic theory and the genetic independence of chloroplasts.
In the following half-century, phycologists often used the pyrenoid as a taxonomic marker, but physiologists long failed to appreciate the importance of pyrenoids in aquatic photosynthesis. The classical paradigm, which prevailed until the early 1980s, was that the pyrenoid was the site of starch synthesis. [ 8 ] Microscopic observations were easily misleading as a starch sheath often encloses pyrenoids. The discovery of pyrenoid deficient mutants with normal starch grains in the green alga Chlamydomonas reinhardtii , [ 9 ] as well as starchless mutants with perfectly formed pyrenoids, [ 10 ] eventually discredited this hypothesis.
It was not before the early 1970s that the proteinaceous nature of the pyrenoid was elucidated, when pyrenoids were successfully isolated from a green alga, [ 11 ] and showed that up to 90% of it was composed of biochemically active RuBisCO. In the following decade, more and more evidence emerged that algae were capable of accumulating intracellular pools of DIC, and converting these to CO 2 , in concentrations far exceeding that of the surrounding medium. Badger and Price first suggested the function of the pyrenoid to be analogous to that of the carboxysome in cyanobacteria, in being associated with CCM activity. [ 12 ] CCM activity in algal and cyanobacterial photobionts of lichen associations was also identified using gas exchange and carbon isotope discrimination [ 13 ] and associated with the pyrenoid by Palmqvist [ 14 ] and Badger et al. [ 15 ] The Hornwort CCM was later characterized by Smith and Griffiths. [ 16 ]
From there on, the pyrenoid was studied in the wider context of carbon acquisition in algae, but has yet to be given a precise molecular definition.
There is substantial diversity in pyrenoid morphology and ultrastructure between algal species. The common feature of all pyrenoids is a spheroidal matrix, composed primarily of RuBisCO. [ 11 ] In most pyrenoid-containing organisms, the pyrenoid matrix is traversed by thylakoid membranes, which are in continuity with stromal thylakoids. In the unicellular red alga Porphyridium purpureum , individual thylakoid membranes appear to traverse the pyrenoid; [ 17 ] in the green alga Chlamydomonas reinhardtii , multiple thylakoids merge at the periphery of the pyrenoid to form larger tubules that traverse the matrix. [ 18 ] [ 19 ] Unlike carboxysomes, pyrenoids are not delineated by a protein shell (or membrane). A starch sheath is often formed or deposited at the periphery of pyrenoids, even when that starch is synthesised in the cytosol rather than in the chloroplast. [ 20 ]
When examined with transmission electron microscopy, the pyrenoid matrix appears as a roughly circular electron dense granular structure within the chloroplast. Early studies suggested that RuBisCO is arranged in crystalline arrays in the pyrenoids of the diatom Achnanthes brevipes [ 21 ] and the dinoflagellate Prorocentrum micans . [ 22 ] However, recent work has shown that RuBisCO in the pyrenoid matrix of the green alga Chlamydomonas is not in a crystalline lattice and instead the matrix behaves as a phase-separated, liquid-like organelle. [ 23 ]
In Porphyridium and in Chlamydomonas , there is a single highly conspicuous pyrenoid in a single chloroplast, visible using light microscopy. By contrast, in diatoms and dinoflagellates, there can be multiple pyrenoids. The Chlamydomonas pyrenoid has been observed to divide by fission during chloroplast division. [ 24 ] [ 23 ] In rare cases where fission did not occur, a pyrenoid appeared to form de novo. [ 23 ] Pyrenoids partially dissolved into the chloroplast stroma during every cell division, and this pool of dissolved components may condense into a new pyrenoid in cases where one is not inherited by fission.
In Chlamydomonas , specifically the model alga Chlamydomonas reinhardtii :
The proteome of the Chlamydomonas pyrenoid has been characterized, [ 30 ] and the localizations and protein-protein interactions of dozens of pyrenoid-associated proteins were systematically determined. [ 31 ] Proteins localized to the pyrenoid include RuBisCO activase, [ 32 ] nitrate reductase [ 33 ] and nitrite reductase. [ 34 ]
In Chlamydomonas , a high-molecular weight complex of two proteins (LCIB/LCIC) forms an additional concentric layer around the pyrenoid, outside the starch sheath, and this is currently hypothesised to act as a barrier to CO 2 -leakage or to recapture CO 2 that escapes from the pyrenoid. [ 35 ]
The confinement of the CO 2 -fixing enzyme into a subcellular micro-compartment, in association with a mechanism to deliver CO 2 to that site, is believed to enhance the efficacy of photosynthesis in an aqueous environment. Having a CCM favours carboxylation over wasteful oxygenation by RuBisCO. The molecular basis of the pyrenoid and the CCM have been characterised to some detail in the model green alga Chlamydomonas reinhardtii .
The current model of the biophysical CCM reliant upon a pyrenoid [ 36 ] [ 37 ] considers active transport of bicarbonate from the extracellular environment to the vicinity of RuBisCO, via transporters at the plasma membrane , the chloroplast membrane , and thylakoid membranes . Carbonic anhydrases in the periplasm and also in the cytoplasm and chloroplast stroma are thought to contribute to maintaining an intracellular pool of dissolved inorganic carbon, mainly in the form of bicarbonate. This bicarbonate is then thought to be pumped into the lumen of transpyrenoidal thylakoids, where a resident carbonic anhydrase is hypothesised to convert bicarbonate to CO 2 , and saturate RuBisCO with carboxylating substrate. It is likely that different algal groups evolved different types of CCMs, but it is generally taken that the algal CCM is articulated around a combination of carbonic anhydrases, inorganic carbon transporters, and some compartment to package RuBisCO.
Pyrenoids are highly plastic structures and the degree of RuBisCO packaging correlates with the state of induction of the CCM. In Chlamydomonas , when the CCM is repressed, for example when cells are maintained in a CO 2 -rich environment, the pyrenoid is small and the matrix is unstructured. [ 38 ] In the dinoflagellate Gonyaulax , the localisation of RuBisCO to the pyrenoid is under circadian control: when cells are photosynthetically active during the day, RuBisCO assembles into multiple chloroplasts at the centre of the cells; at night, these structures disappear. [ 39 ]
The algal CCM is inducible, and induction of the CCM is generally the result of low CO 2 conditions. Induction and regulation of the Chlamydomonas CCM was recently studied by transcriptomic analysis, revealing that one out of three genes are up- or down-regulated in response to changed levels of CO 2 in the environment. [ 40 ] Sensing of CO 2 in Chlamydomonas involves a “master switch”, which was co-discovered by two laboratories. [ 41 ] [ 42 ] This gene, Cia5/Ccm1, affects over 1,000 CO 2 -responsive genes [ 43 ] and also conditions the degree of packing of RuBisCO into the pyrenoid.
The CCM is only induced during periods of low CO 2 levels, and it was the existence of these trigger levels of CO 2 below which CCMs are induced that led researchers to speculate on the likely timing of origin of mechanisms like the pyrenoid.
There are several hypotheses as to the origin of pyrenoids. With the rise of large terrestrial based flora following the colonisation of land by ancestors of Charophyte algae , CO 2 levels dropped dramatically, with a concomitant increase in O 2 atmospheric concentration. It has been suggested that this sharp fall in CO 2 levels acted as an evolutionary driver of CCM development, and thus gave rise to pyrenoids [ 44 ] in doing so ensuring that rate of supply of CO 2 did not become a limiting factor for photosynthesis in the face of declining atmospheric CO 2 levels.
However, alternative hypotheses have been proposed. Predictions of past CO 2 levels suggest that they may have previously dropped as precipitously low as that seen during the expansion of land plants: approximately 300 MYA, during the Proterozoic Era . [ 45 ] This being the case, there might have been a similar evolutionary pressure that resulted in the development of the pyrenoid, though in this case, a pyrenoid or pyrenoid-like structure could have developed, and have been lost as CO 2 levels then rose, only to be gained or developed again during the period of land colonisation by plants. Evidence of multiple gains and losses of pyrenoids over relatively short geological time spans was found in hornworts. [ 2 ]
Pyrenoids are found in algal lineages, [ 1 ] irrespective of whether the chloroplast was inherited from a single endosymbiotic event (e.g. green and red algae , but not in glaucophytes ) or multiple endosymbiotic events ( diatoms , dinoflagellates , coccolithophores , cryptophytes , chlorarachniophytes , and euglenozoa ). Some algal groups, however, lack pyrenoids altogether: "higher" red algae and extremophile red algae , the green alga genera Chloromonas and Mougeotiopsis , [ 46 ] and " golden algae ". Pyrenoids are usually considered to be poor taxonomic markers and may have evolved independently many times. [ 47 ] | https://en.wikipedia.org/wiki/Pyrenoid |
Pyrethrin I is one of the two pyrethrins , natural organic compounds with potent insecticidal activity. It is an ester of (+)- trans - chrysanthemic acid with ( S )-( Z )- pyrethrolone .
The synthesis of pyrethrin I involves the esterification of (+)- trans -chrysanthemic acid with (S)-(Z)-pyrethrolone. One synthetic method for each of these is shown in the images below. Sobti and Dev of the Malti-Chem Research Centre in Nadesari, vadodara, India published this method for chrysanthemic acid in 1974. The starting material for the synthesis uses commercially available (+)-3α, 4α-epoxycarane ( 1 ). A lactone is eventually formed and the ring is opened by the use of a Grignard reagent to give (+)-trans-chrysanthemic acid. [ 1 ] The preparation of ( S )-pyrethrolone is essentially a 2 step synthesis. The starting material (S)-4-hydroxy-3-methyl-2-(2-propynyl)-2-cyclopenten-1-one ( 7 ) is also commercially available as the alcohol moiety of ETOC. Tetrakis(triphenylphosphine)palladium(0) , copper(I) iodide , triethylamine , and vinyl bromide are added to ( 7 ) to add two more carbons and form ( 8 ). The final step is the addition of an activated zinc compound to reduce the triple carbon bond to form the cis product, ( S )-pyrethrolone ( 9 ). [ 2 ] Although no journal articles specify the combining of the alcohol and acid moieties of pyrethrin I, they could be combined through an esterification process to form the wanted product. | https://en.wikipedia.org/wiki/Pyrethrin_I |
A pyrheliometer is an instrument that can measure direct beam solar irradiance . [ 1 ] Sunlight enters the instrument through a window and is directed onto a thermopile which converts heat to an electrical signal that can be recorded. The signal voltage is converted via a formula to measure watts per square metre.
Pyrheliometer measurement specifications are subject to International Organization for Standardization (ISO) and World Meteorological Organization (WMO) standards.
Comparisons between pyrheliometers for intercalibration are carried out regularly to measure the amount of solar energy received.
The aim of the International Pyrheliometer Comparisons, [ 2 ] which take place every 5 years at the World Radiation Centre [ 3 ] in Davos , is to ensure the world-wide transfer of the World Radiometric Reference.
During this event, all participants bring their instruments, solar-tracking and data acquisition systems to Davos to conduct simultaneous solar radiation measurements with the World Standard Group. [ 4 ]
Typical pyrheliometer measurement applications include scientific meteorological and climate observations, material testing research, and assessment of the efficiency of solar collectors and photovoltaic devices .
Pyrheliometers are typically mounted on a solar tracker . As the pyrheliometer only 'sees' the solar disk, it needs to be placed on a device that follows the path of the sun. | https://en.wikipedia.org/wiki/Pyrheliometer |
Pyric herbivory is the term for the interactions of fire with grazing on a grassland . [ 1 ] These interactions can promote biodiversity and function of grasslands. [ 1 ] Fire will increase the amount of grazing in a certain area, as grazing herbivores prefer the nutritious forage available in recently burned areas. [ 1 ] [ 2 ] Since herbivores do not prefer areas that have not been recently burned, fuel will accumulate in unburned areas. [ 2 ] This causes those areas to burn more easily in the future. [ 2 ] These interactions between fire and grazing across space and time are referred to as positive and negative feedbacks . [ 1 ] These interactions create heterogeneity across the landscape. [ 1 ] [ 2 ] [ 3 ] Pyric herbivory is important to ecosystems that have evolved with fire and grazing, such as grasslands. [ 4 ]
Pyric herbivory occurs because burning produces early successional plants that are more palatable and nutritious than late successional plants. [ 1 ] Because of this, herbivores prefer the forage that grows in recently burned areas. [ 1 ] Herbivores will graze more in the recently burned areas, causing leaf litter to build up in unburned areas. [ 1 ] This makes the unburned areas more prone to fire in the future. [ 1 ] Once fire occurs in a new area, herbivores will start grazing in that area. [ 1 ] [ 2 ] This creates shifting patterns of grazing and fire across the landscape. [ 2 ]
The shifting patterns of heterogeneity that are created by pyric herbivory changes the number and type of plant species present in the area. [ 2 ] This supports biodiversity of plants and wildlife in the area, restores and maintains ecosystem function, and aids in nutrient cycling . [ 1 ] [ 2 ] [ 3 ] It especially increases the availability of nitrogen and phosphorus by converting litter into ash. [ 3 ] A lack of disturbances such as fire and grazing can decrease biodiversity and soil function quality, as well as allow for woody encroachment . [ 3 ] [ 5 ]
There is a concern that agricultural livestock production will not be maintained when using conservation management strategies because of a need to lower stocking rates. [ 6 ] Pyric herbivory is a strategy that allows landowners to maintain stocking rates without losing livestock productivity and also improve the health of the grassland. [ 6 ]
There are social factors involved in whether a landowner chooses to implement pyric herbivory. [ 5 ] These factors include previous experience of the landowner, the landowner's perception of woody encroachment on the land, proximity to neighbors, and risk orientation. [ 5 ] Previous experience applying pyric herbivory will increase the landowner's likelihood to apply it as a management strategy. [ 5 ] | https://en.wikipedia.org/wiki/Pyric_herbivory |
Pyridine is a basic heterocyclic organic compound with the chemical formula C 5 H 5 N . It is structurally related to benzene , with one methine group (=CH−) replaced by a nitrogen atom (=N−) . It is a highly flammable, weakly alkaline , water-miscible liquid with a distinctive, unpleasant fish-like smell. Pyridine is colorless, but older or impure samples can appear yellow, due to the formation of extended, unsaturated polymeric chains, which show significant electrical conductivity . [ page needed ] [ 17 ] The pyridine ring occurs in many important compounds, including agrochemicals , pharmaceuticals , and vitamins . Historically, pyridine was produced from coal tar . As of 2016, it is synthesized on the scale of about 20,000 tons per year worldwide. [ 2 ]
Pyridine is diamagnetic . Its critical parameters are: pressure 5.63 MPa, temperature 619 K and volume 248 cm 3 /mol. [ 19 ] In the temperature range 340–426 °C its vapor pressure p can be described with the Antoine equation
where T is temperature, A = 4.16272, B = 1371.358 K and C = −58.496 K. [ 20 ]
Pyridine ring forms a C 5 N hexagon. Slight variations of the C−C and C−N distances as well as the bond angles are observed.
Pyridine crystallizes in an orthorhombic crystal system with space group Pna2 1 and lattice parameters a = 1752 pm , b = 897 pm, c = 1135 pm, and 16 formula units per unit cell (measured at 153 K). For comparison, crystalline benzene is also orthorhombic, with space group Pbca , a = 729.2 pm, b = 947.1 pm, c = 674.2 pm (at 78 K), but the number of molecules per cell is only 4. [ 18 ] This difference is partly related to the lower symmetry of the individual pyridine molecule (C 2v vs D 6h for benzene). A tri hydrate (pyridine·3H 2 O) is known; it also crystallizes in an orthorhombic system in the space group Pbca , lattice parameters a = 1244 pm, b = 1783 pm, c = 679 pm and eight formula units per unit cell (measured at 223 K). [ 21 ]
The optical absorption spectrum of pyridine in hexane consists of bands at the wavelengths of 195, 251, and 270 nm. With respective extinction coefficients ( ε ) of 7500, 2000, and 450 L·mol −1 ·cm −1 , these bands are assigned to π → π*, π → π*, and n → π* transitions. The compound displays very low fluorescence . [ 22 ]
The 1 H nuclear magnetic resonance (NMR) spectrum shows signals for α-( δ 8.5), γ-(δ7.5) and β-protons (δ7). By contrast, the proton signal for benzene is found at δ7.27. The larger chemical shifts of the α- and γ-protons in comparison to benzene result from the lower electron density in the α- and γ-positions, which can be derived from the resonance structures. The situation is rather similar for the 13 C NMR spectra of pyridine and benzene: pyridine shows a triplet at δ (α-C) = 150 ppm, δ(β-C) = 124 ppm and δ(γ-C) = 136 ppm, whereas benzene has a single line at 129 ppm. All shifts are quoted for the solvent-free substances. [ 23 ] Pyridine is conventionally detected by the gas chromatography and mass spectrometry methods. [ 24 ]
Pyridine has a conjugated system of six π electrons that are delocalized over the ring. The molecule is planar and, thus, follows the Hückel criteria for aromatic systems. In contrast to benzene, the electron density is not evenly distributed over the ring, reflecting the negative inductive effect of the nitrogen atom. For this reason, pyridine has a dipole moment and a weaker resonant stabilization than benzene ( resonance energy 117 kJ/mol in pyridine vs. 150 kJ/mol in benzene). [ 25 ]
The ring atoms in the pyridine molecule are sp 2 -hybridized . The nitrogen is involved in the π-bonding aromatic system using its unhybridized p orbital. The lone pair is in an sp 2 orbital, projecting outward from the ring in the same plane as the σ bonds . As a result, the lone pair does not contribute to the aromatic system but importantly influences the chemical properties of pyridine, as it easily supports bond formation via an electrophilic attack. [ 26 ] However, because of the separation of the lone pair from the aromatic ring system, the nitrogen atom cannot exhibit a positive mesomeric effect .
Many analogues of pyridine are known where N is replaced by other heteroatoms from the same column of the Periodic Table of Elements (see figure below). Substitution of one C–H in pyridine with a second N gives rise to the diazine heterocycles (C 4 H 4 N 2 ), with the names pyridazine , pyrimidine , and pyrazine .
Impure pyridine was undoubtedly prepared by early alchemists by heating animal bones and other organic matter, [ 27 ] but the earliest documented reference is attributed to the Scottish scientist Thomas Anderson . [ 28 ] [ 29 ] In 1849, Anderson examined the contents of the oil obtained through high-temperature heating of animal bones . [ 29 ] Among other substances, he separated from the oil a colorless liquid with unpleasant odor, from which he isolated pure pyridine two years later. He described it as highly soluble in water, readily soluble in concentrated acids and salts upon heating, and only slightly soluble in oils.
Owing to its flammability, Anderson named the new substance pyridine , after Greek : πῦρ (pyr) meaning fire . The suffix idine was added in compliance with the chemical nomenclature, as in toluidine , to indicate a cyclic compound containing a nitrogen atom. [ 30 ] [ 31 ]
The chemical structure of pyridine was determined decades after its discovery. Wilhelm Körner (1869) [ 32 ] and James Dewar (1871) [ 33 ] [ 34 ] suggested that, in analogy between quinoline and naphthalene , the structure of pyridine is derived from benzene by substituting one C–H unit with a nitrogen atom. [ 35 ] [ 36 ] The suggestion by Körner and Dewar was later confirmed in an experiment where pyridine was reduced to piperidine with sodium in ethanol . [ 37 ] [ 38 ] In 1876, William Ramsay combined acetylene and hydrogen cyanide into pyridine in a red-hot iron-tube furnace. [ 39 ] This was the first synthesis of a heteroaromatic compound. [ 24 ] [ 40 ]
The first major synthesis of pyridine derivatives was described in 1881 by Arthur Rudolf Hantzsch . [ 41 ] The Hantzsch pyridine synthesis typically uses a 2:1:1 mixture of a β- keto acid (often acetoacetate ), an aldehyde (often formaldehyde ), and ammonia or its salt as the nitrogen donor. First, a double hydrogenated pyridine is obtained, which is then oxidized to the corresponding pyridine derivative. Emil Knoevenagel showed that asymmetrically substituted pyridine derivatives can be produced with this process. [ 42 ]
The contemporary methods of pyridine production had a low yield, and the increasing demand for the new compound urged to search for more efficient routes. A breakthrough came in 1924 when the Russian chemist Aleksei Chichibabin invented a pyridine synthesis reaction , which was based on inexpensive reagents. [ 43 ] This method is still used for the industrial production of pyridine. [ 2 ]
Pyridine is not abundant in nature, except for the leaves and roots of belladonna ( Atropa belladonna ) [ 44 ] and in marshmallow ( Althaea officinalis ). [ 45 ] Pyridine derivatives, however, are often part of biomolecules such as alkaloids .
In daily life, trace amounts of pyridine are components of the volatile organic compounds that are produced in roasting and canning processes, e.g. in fried chicken, [ 46 ] sukiyaki , [ 47 ] roasted coffee, [ 48 ] potato chips, [ 49 ] and fried bacon . [ 50 ] Traces of pyridine can be found in Beaufort cheese , [ 51 ] vaginal secretions , [ 52 ] black tea , [ 53 ] saliva of those suffering from gingivitis , [ 54 ] and sunflower honey . [ 55 ]
Trace amounts of up to 16 μg/m 3 have been detected in tobacco smoke. [ 24 ] Minor amounts of pyridine are released into environment from some industrial processes such as steel manufacture, [ 56 ] processing of oil shale , coal gasification , coking plants and incinerators . [ 24 ] The atmosphere at oil shale processing plants can contain pyridine concentrations of up to 13 μg/m 3 , [ 57 ] and 53 μg/m 3 levels were measured in the groundwater in the vicinity of a coal gasification plant. [ 58 ] According to a study by the US National Institute for Occupational Safety and Health , about 43,000 Americans work in contact with pyridine. [ 59 ]
Pyridine has historically been added to foods to give them a bitter flavour, although this practise is now banned in the U.S. [ 60 ] [ 61 ] It may still be added to ethanol to make it unsuitable for drinking. [ 62 ]
Historically, pyridine was extracted from coal tar or obtained as a byproduct of coal gasification . The process is labor-consuming and inefficient: coal tar contains only about 0.1% pyridine, [ 63 ] and therefore a multi-stage purification was required, which further reduced the output. Nowadays, most pyridines are synthesized from ammonia, aldehydes, and nitriles, a few combinations of which are suited for pyridine itself. Various name reactions are also known, but they are not practiced on scale. [ 2 ]
In 1989, 26,000 tonnes of pyridine was produced worldwide. Other major derivatives are 2- , 3- , 4-methylpyridines and 5-ethyl-2-methylpyridine . The combined scale of these alkylpyridines matches that of pyridine itself. [ 2 ] Among the largest 25 production sites for pyridine, eleven are located in Europe (as of 1999). [ 24 ] The major producers of pyridine include Evonik Industries , Rütgers Chemicals, Jubilant Life Sciences , Imperial Chemical Industries , and Koei Chemical. [ 2 ] Pyridine production significantly increased in the early 2000s, with an annual production capacity of 30,000 tonnes in mainland China alone. [ 64 ] The US–Chinese joint venture Vertellus is currently the world leader in pyridine production. [ 65 ]
The Chichibabin pyridine synthesis was reported in 1924 and the basic approach underpins several industrial routes. [ 43 ] In its general form, the reaction involves the condensation reaction of aldehydes , ketones , α,β-unsaturated carbonyl compounds , or any combination of the above, in ammonia or ammonia derivatives . Application of the Chichibabin pyridine synthesis suffer from low yields, often about 30%, [ 66 ] however the precursors are inexpensive. In particular, unsubstituted pyridine is produced from formaldehyde and acetaldehyde . First, acrolein is formed in a Knoevenagel condensation from the acetaldehyde and formaldehyde. The acrolein then condenses with acetaldehyde and ammonia to give dihydropyridine , which is oxidized to pyridine. This process is carried out in a gas phase at 400–450 °C. Typical catalysts are modified forms of alumina and silica . The reaction has been tailored to produce various methylpyridines . [ 2 ]
Pyridine can be prepared by dealkylation of alkylated pyridines, which are obtained as byproducts in the syntheses of other pyridines. The oxidative dealkylation is carried out either using air over vanadium(V) oxide catalyst, [ 67 ] by vapor-dealkylation on nickel -based catalyst, [ 68 ] [ 69 ] or hydrodealkylation with a silver - or platinum -based catalyst. [ 70 ] Yields of pyridine up to be 93% can be achieved with the nickel-based catalyst. [ 2 ] Pyridine can also be produced by the decarboxylation of nicotinic acid with copper chromite . [ 71 ]
The trimerization of a part of a nitrile molecule and two parts of acetylene into pyridine is called Bönnemann cyclization . This modification of the Reppe synthesis can be activated either by heat or by light . While the thermal activation requires high pressures and temperatures, the photoinduced cycloaddition proceeds at ambient conditions with CoCp 2 (cod) (Cp = cyclopentadienyl, cod = 1,5-cyclooctadiene ) as a catalyst, and can be performed even in water. [ 72 ] A series of pyridine derivatives can be produced in this way. When using acetonitrile as the nitrile, 2-methylpyridine is obtained, which can be dealkylated to pyridine.
The Kröhnke pyridine synthesis provides a fairly general method for generating substituted pyridines using pyridine itself as a reagent which does not become incorporated into the final product. The reaction of pyridine with bromomethyl ketones gives the related pyridinium salt, wherein the methylene group is highly acidic. This species undergoes a Michael-like addition to α,β-unsaturated carbonyls in the presence of ammonium acetate to undergo ring closure and formation of the targeted substituted pyridine as well as pyridinium bromide. [ 73 ]
The Ciamician–Dennstedt rearrangement [ 74 ] entails the ring-expansion of pyrrole with dichlorocarbene to 3-chloropyridine . [ 75 ] [ 76 ] [ 77 ]
In the Gattermann–Skita synthesis, [ 78 ] a malonate ester salt reacts with dichloro methylamine . [ 79 ]
Other methods include the Boger pyridine synthesis and Diels–Alder reaction of an alkene and an oxazole . [ 80 ]
Several pyridine derivatives play important roles in biological systems. While its biosynthesis is not fully understood, nicotinic acid (vitamin B 3 ) occurs in some bacteria , fungi , and mammals . Mammals synthesize nicotinic acid through oxidation of the amino acid tryptophan , where an intermediate product, the aniline derivative kynurenine , creates a pyridine derivative, quinolinate and then nicotinic acid. On the contrary, the bacteria Mycobacterium tuberculosis and Escherichia coli produce nicotinic acid by condensation of glyceraldehyde 3-phosphate and aspartic acid . [ 81 ]
Because of the electronegative nitrogen in the pyridine ring, pyridine enters less readily into electrophilic aromatic substitution reactions than benzene derivatives. [ 82 ] Instead, in terms of its reactivity, pyridine resembles nitrobenzene . [ 83 ]
Correspondingly pyridine is more prone to nucleophilic substitution , as evidenced by the ease of metalation by strong organometallic bases. [ 84 ] [ 85 ] The reactivity of pyridine can be distinguished for three chemical groups. With electrophiles , electrophilic substitution takes place where pyridine expresses aromatic properties. With nucleophiles , pyridine reacts at positions 2 and 4 and thus behaves similar to imines and carbonyls . The reaction with many Lewis acids results in the addition to the nitrogen atom of pyridine, which is similar to the reactivity of tertiary amines. The ability of pyridine and its derivatives to oxidize, forming amine oxides ( N -oxides), is also a feature of tertiary amines. [ 86 ]
The nitrogen center of pyridine features a basic lone pair of electrons . This lone pair does not overlap with the aromatic π-system ring, consequently pyridine is basic , having chemical properties similar to those of tertiary amines . Protonation gives pyridinium , C 5 H 5 NH + .The p K a of the conjugate acid (the pyridinium cation) is 5.25. The structures of pyridine and pyridinium are almost identical. [ 87 ] The pyridinium cation is isoelectronic with benzene. Pyridinium p - toluenesulfonate (PPTS) is an illustrative pyridinium salt; it is produced by treating pyridine with p -toluenesulfonic acid . In addition to protonation , pyridine undergoes N-centred alkylation , acylation , and N -oxidation . Pyridine and poly(4-vinyl) pyridine have been shown to form conducting molecular wires with remarkable polyenimine structure on UV irradiation , a process which accounts for at least some of the visible light absorption by aged pyridine samples. These wires have been theoretically predicted to be both highly efficient electron donors and acceptors, and yet are resistant to air oxidation. [ 88 ]
Owing to the decreased electron density in the aromatic system, electrophilic substitutions are suppressed in pyridine and its derivatives. Friedel–Crafts alkylation or acylation , usually fail for pyridine because they lead only to the addition at the nitrogen atom. Substitutions usually occur at the 3-position, which is the most electron-rich carbon atom in the ring and is, therefore, more susceptible to an electrophilic addition.
Direct nitration of pyridine is sluggish. [ 89 ] [ 90 ] Pyridine derivatives wherein the nitrogen atom is screened sterically and/or electronically can be obtained by nitration with nitronium tetrafluoroborate (NO 2 BF 4 ). In this way, 3-nitropyridine can be obtained via the synthesis of 2,6-dibromopyridine followed by nitration and debromination. [ 91 ] [ 92 ]
Sulfonation of pyridine is even more difficult than nitration. However, pyridine-3-sulfonic acid can be obtained. Reaction with the SO 3 group also facilitates addition of sulfur to the nitrogen atom, especially in the presence of a mercury(II) sulfate catalyst. [ 84 ] [ 93 ]
In contrast to the sluggish nitrations and sulfonations, the bromination and chlorination of pyridine proceed well. [ 2 ]
Oxidation of pyridine occurs at nitrogen to give pyridine N -oxide . The oxidation can be achieved with peracids : [ 94 ]
Some electrophilic substitutions on the pyridine are usefully effected using pyridine N -oxide followed by deoxygenation. Addition of oxygen suppresses further reactions at nitrogen atom and promotes substitution at the 2- and 4-carbons. The oxygen atom can then be removed, e.g., using zinc dust. [ 95 ]
In contrast to benzene ring, pyridine efficiently supports several nucleophilic substitutions. The reason for this is relatively lower electron density of the carbon atoms of the ring. These reactions include substitutions with elimination of a hydride ion and elimination-additions with formation of an intermediate aryne configuration, and usually proceed at the 2- or 4-position. [ 84 ] [ 85 ]
Many nucleophilic substitutions occur more easily not with bare pyridine but with pyridine modified with bromine, chlorine, fluorine, or sulfonic acid fragments that then become a leaving group. So fluorine is the best leaving group for the substitution with organolithium compounds . The nucleophilic attack compounds may be alkoxides , thiolates, amines , and ammonia (at elevated pressures). [ 96 ]
In general, the hydride ion is a poor leaving group and occurs only in a few heterocyclic reactions. They include the Chichibabin reaction , which yields pyridine derivatives aminated at the 2-position. Here, sodium amide is used as the nucleophile yielding 2-aminopyridine. The hydride ion released in this reaction combines with a proton of an available amino group, forming a hydrogen molecule. [ 85 ] [ 97 ]
Analogous to benzene, nucleophilic substitutions to pyridine can result in the formation of pyridyne intermediates as hetero aryne . For this purpose, pyridine derivatives can be eliminated with good leaving groups using strong bases such as sodium and potassium tert-butoxide . The subsequent addition of a nucleophile to the triple bond has low selectivity, and the result is a mixture of the two possible adducts. [ 84 ]
Pyridine supports a series of radical reactions, which is used in its dimerization to bipyridines. Radical dimerization of pyridine with elemental sodium or Raney nickel selectively yields 4,4'-bipyridine , [ 98 ] or 2,2'-bipyridine , [ 99 ] which are important precursor reagents in the chemical industry. One of the name reactions involving free radicals is the Minisci reaction . It can produce 2- tert -butylpyridine upon reacting pyridine with pivalic acid , silver nitrate and ammonium in sulfuric acid with a yield of 97%. [ 84 ]
Lewis acids easily add to the nitrogen atom of pyridine, forming pyridinium salts. The reaction with alkyl halides leads to alkylation of the nitrogen atom. This creates a positive charge in the ring that increases the reactivity of pyridine to both oxidation and reduction. The Zincke reaction is used for the selective introduction of radicals in pyridinium compounds (it has no relation to the chemical element zinc ).
Piperidine is produced by hydrogenation of pyridine with a nickel -, cobalt -, or ruthenium -based catalyst at elevated temperatures. [ 100 ] The hydrogenation of pyridine to piperidine releases 193.8 kJ/mol, [ 101 ] which is slightly less than the energy of the hydrogenation of benzene (205.3 kJ/mol). [ 101 ]
Partially hydrogenated derivatives are obtained under milder conditions. For example, reduction with lithium aluminium hydride yields a mixture of 1,4-dihydropyridine, 1,2-dihydropyridine, and 2,5-dihydropyridine. [ 102 ] Selective synthesis of 1,4-dihydropyridine is achieved in the presence of organometallic complexes of magnesium and zinc , [ 103 ] and (Δ3,4)-tetrahydropyridine is obtained by electrochemical reduction of pyridine. [ 104 ] Birch reduction converts pyridine to dihydropyridines. [ 105 ]
Pyridine is a Lewis base , donating its pair of electrons to a Lewis acid. Its Lewis base properties are discussed in the ECW model . Its relative donor strength toward a series of acids, versus other Lewis bases, can be illustrated by C-B plots . [ 106 ] [ 107 ] One example is the sulfur trioxide pyridine complex (melting point 175 °C), which is a sulfation agent used to convert alcohols to sulfate esters . Pyridine- borane ( C 5 H 5 NBH 3 , melting point 10–11 °C) is a mild reducing agent.
Transition metal pyridine complexes are numerous. [ 108 ] [ 109 ] Typical octahedral complexes have the stoichiometry MCl 2 (py) 4 and MCl 3 (py) 3 . Octahedral homoleptic complexes of the type M(py) + 6 are rare or tend to dissociate pyridine. Numerous square planar complexes are known, such as Crabtree's catalyst . [ 110 ] The pyridine ligand replaced during the reaction is restored after its completion.
The η 6 coordination mode, as occurs in η 6 benzene complexes, is observed only in sterically encumbered derivatives that block the nitrogen center. [ 111 ]
The main use of pyridine is as a precursor to the herbicides paraquat and diquat . [ 2 ] The first synthesis step of insecticide chlorpyrifos consists of the chlorination of pyridine. Pyridine is also the starting compound for the preparation of pyrithione -based fungicides . [ 24 ] Cetylpyridinium and laurylpyridinium, which can be produced from pyridine with a Zincke reaction , are used as antiseptic in oral and dental care products. [ 62 ] Pyridine is easily attacked by alkylating agents to give N -alkylpyridinium salts. One example is cetylpyridinium chloride .
It is also used in the textile industry to improve network capacity of cotton. [ 62 ]
Pyridine is used as a polar, basic, low-reactive solvent, for example in Knoevenagel condensations . [ 24 ] [ 113 ] It is especially suitable for the dehalogenation, where it acts as the base for the elimination reaction . In esterifications and acylations, pyridine activates the carboxylic acid chlorides and anhydrides. Even more active in these reactions are the derivatives 4-dimethylaminopyridine (DMAP) and 4-(1-pyrrolidinyl) pyridine. Pyridine is also used as a base in some condensation reactions . [ 114 ]
As a base, pyridine can be used as the Karl Fischer reagent , but it is usually replaced by alternatives with a more pleasant odor, such as imidazole . [ 115 ]
Pyridinium chlorochromate , pyridinium dichromate , and the Collins reagent (the complex of chromium(VI) oxide ) are used for the oxidation of alcohols. [ 116 ]
Pyridine is a toxic, flammable liquid with a strong and unpleasant fishy odour. Its odour threshold of 0.04 to 20 ppm is close to its threshold limit of 5 ppm for adverse effects, [ 117 ] thus most (but not all) adults will be able to tell when it is present at harmful levels. Pyridine easily dissolves in water and harms both animals and plants in aquatic systems. [ 118 ]
Pyridine has a flash point of 20 °C and is therefore highly flammable. Combustion produces toxic fumes which can include bipyridines , nitrogen oxides , and carbon monoxide . [ 12 ]
Pyridine can cause chemical burns on contact with the skin and its fumes may be irritating to the eyes or upon inhalation. [ 119 ] Pyridine depresses the nervous system giving symptoms similar to intoxication with vapor concentrations of above 3600 ppm posing a greater health risk. [ 2 ] The effects may have a delayed onset of several hours and include dizziness, headache, lack of coordination , nausea, salivation , and loss of appetite. They may progress into abdominal pain, pulmonary congestion and unconsciousness. [ 120 ] The lowest known lethal dose (LD Lo ) for the ingestion of pyridine in humans is 500 mg/kg.
Prolonged exposure to pyridine may result in liver, heart and kidney damage. [ 12 ] [ 24 ] [ 121 ] Evaluations as a possible carcinogenic agent showed that there is inadequate evidence in humans for the carcinogenicity of pyridine, although there is sufficient evidence in experimental animals. Therefore, IARC considers pyridine as possibly carcinogenic to humans (Group 2B). [ 122 ]
Exposure to pyridine would normally lead to its inhalation and absorption in the lungs and gastrointestinal tract, where it either remains unchanged or is metabolized . The major products of pyridine metabolism are N -methylpyridiniumhydroxide, which are formed by N -methyltransferases (e.g., pyridine N -methyltransferase ), as well as pyridine N -oxide, and 2-, 3-, and 4-hydroxypyridine, which are generated by the action of monooxygenase . In humans, pyridine is metabolized only into N -methylpyridiniumhydroxide. [ 12 ] [ 121 ]
Pyridine is readily degraded by bacteria to ammonia and carbon dioxide. [ 123 ] The unsubstituted pyridine ring degrades more rapidly than picoline , lutidine , chloropyridine , or aminopyridines , [ 124 ] and a number of pyridine degraders have been shown to overproduce riboflavin in the presence of pyridine. [ 125 ] Ionizable N -heterocyclic compounds, including pyridine, interact with environmental surfaces (such as soils and sediments) via multiple pH-dependent mechanisms, including partitioning to soil organic matter , cation exchange , and surface complexation. [ 126 ] Such adsorption to surfaces reduces bioavailability of pyridines for microbial degraders and other organisms, thus slowing degradation rates and reducing ecotoxicity . [ 127 ]
The systematic name of pyridine, within the Hantzsch–Widman nomenclature recommended by the IUPAC , is azinine . However, systematic names for simple compounds are used very rarely; instead, heterocyclic nomenclature follows historically established common names. IUPAC discourages the use of azinine / azine in favor of pyridine . [ 128 ] The numbering of the ring atoms in pyridine starts at the nitrogen (see infobox). An allocation of positions by letter of the Greek alphabet (α-γ) and the substitution pattern nomenclature common for homoaromatic systems ( ortho , meta , para ) are used sometimes. Here α ( ortho ), β ( meta ), and γ ( para ) refer to the 2, 3, and 4 position, respectively. The systematic name for the pyridine derivatives is pyridinyl , wherein the position of the substituted atom is preceded by a number. However, the historical name pyridyl is encouraged by the IUPAC and used instead of the systematic name. [ 129 ] The cationic derivative formed by the addition of an electrophile to the nitrogen atom is called pyridinium . | https://en.wikipedia.org/wiki/Pyridine |
Pyridine- N -oxide is the heterocyclic compound with the formula C 5 H 5 NO. This colourless, hygroscopic solid is the product of the oxidation of pyridine . Its synthesis was first reported by Jakob Meisenheimer , who used peroxybenzoic acid as the oxidant. [ 1 ] The compound is used infrequently as an oxidizing reagent in organic synthesis . [ 2 ]
The structure of pyridine- N -oxide is very similar to that of pyridine with respect to the parameters for the ring. The molecule is planar. The N–O distance is 1.34 Å. The C–N–C angle is 124°, 7° wider than in pyridine. [ 3 ]
The oxidation of pyridine can be achieved with a number of peroxy acids, including peracetic acid and peroxybenzoic acid. [ 4 ] Oxidation can also be effected by a modified Dakin reaction using a urea–hydrogen peroxide complex, [ 5 ] and sodium perborate [ 6 ] or, using methylrhenium trioxide ( CH 3 ReO 3 ) as catalyst, with sodium percarbonate . [ 7 ]
Pyridine N -oxide is five orders of magnitude less basic than pyridine: the p K a of protonated pyridine- N -oxide is 0.8. [ 8 ] Protonated derivatives are isolable, e.g., [C 5 H 5 NOH]Cl. [ 4 ] Further demonstrating its (feeble) basicity, pyridine- N -oxide also serves as a ligand in coordination chemistry . A host of transition metal complexes of pyridine- N -oxides are known.
Treatment of the pyridine- N -oxide with phosphorus oxychloride gives 4- and 2-chloropyridines . [ 9 ]
Pyridine-N-oxides are uncommon in nature. 2-(Methyldithio)pyridine-N-oxide and related compounds have been isolated from species of Allium . [ 10 ]
The N -oxides of various pyridines are precursors to useful drugs: [ 11 ]
The compound is a skin irritant. [ 2 ] | https://en.wikipedia.org/wiki/Pyridine-N-oxide |
This page provides supplementary chemical data on pyridine .
The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet ( MSDS ) for this chemical from a reliable source such as eChemPortal , and follow its directions. MSDS is available from Sigma - Aldrich .
Table data obtained from CRC Handbook of Chemistry and Physics 44th ed. | https://en.wikipedia.org/wiki/Pyridine_(data_page) |
Pyridinium chlorochromate ( PCC ) is a yellow-orange salt with the formula [C 5 H 5 NH] + [CrO 3 Cl] − . It is a reagent in organic synthesis used primarily for oxidation of alcohols to form carbonyls . A variety of related compounds are known with similar reactivity. PCC offers the advantage of the selective oxidation of alcohols to aldehydes or ketones, whereas many other reagents are less selective. [ 1 ]
PCC consists of a pyridinium cation, [C 5 H 5 NH] + , and a tetrahedral chlorochromate anion, [CrO 3 Cl] − . Related salts are also known, such as 1-butylpyridinium chlorochromate, [C 5 H 5 N(C 4 H 9 )][CrO 3 Cl] and potassium chlorochromate .
PCC is commercially available. Discovered by accident , [ 3 ] the reagent was originally prepared via addition of pyridine into a cold solution of chromium trioxide in concentrated hydrochloric acid : [ 4 ]
In one alternative method, formation of toxic chromyl chloride (CrO 2 Cl 2 ) fumes during the making of the aforementioned solution were minimized by simply changing the order of addition: a cold solution of pyridine in concentrated hydrochloric acid was added to solid chromium trioxide under stirring. [ 5 ]
PCC is used as an oxidant . In particular, it has proven to be highly effective in oxidizing primary and secondary alcohols to aldehydes and ketones , respectively. The reagent is more selective than the related Jones' Reagent , so there is little chance of over-oxidation to form carboxylic acids if acidified potassium permanganate is used as long as water is not present in the reaction mixture. A typical PCC oxidation involves addition of an alcohol to a suspension of PCC in dichloromethane . [ 6 ] [ 7 ] [ 8 ] The general reaction is:
For example, the triterpene lupeol was oxidized to lupenone : [ 9 ]
With tertiary alcohols, the chromate ester formed from PCC can isomerize via a [3,3]-sigmatropic reaction and following oxidation yield an enone, in a reaction known as the Babler oxidation:
This type of oxidative transposition reaction has been synthetically utilized, e.g. for the synthesis of morphine . [ 10 ]
Using other common oxidants in the place of PCC usually leads to dehydration, because such alcohols cannot be oxidized directly.
PCC also converts suitable unsaturated alcohols and aldehydes to cyclohexenones . This pathway, an oxidative cationic cyclization, is illustrated by the conversion of (−)- citronellol to (−)- pulegone .
PCC also effects allylic oxidations , for example, in conversion of dihydrofurans to furanones . [ 1 ]
Other more convenient or less toxic reagents for oxidizing alcohols include dimethyl sulfoxide , which is used in Swern and Pfitzner–Moffatt oxidations, and hypervalent iodine compounds , such as the Dess–Martin periodinane .
One disadvantage to the use of PCC is its toxicity, which it shares with other hexavalent chromium compounds. | https://en.wikipedia.org/wiki/Pyridinium_chlorochromate |
Pyridinium p -toluenesulfonate ( PPTS ) is a colourless solid salt of pyridine and p -toluenesulfonic acid .
In organic synthesis , PPTS is used as a weakly acidic catalyst , providing an organic soluble source of pyridinium (C 5 H 5 NH + ) ions. For example, PPTS is used to deprotect silyl ethers or tetrahydropyranyl ethers when a substrate is unstable to stronger acid catalysts. It is also a commonly used catalyst for the preparation of acetals and ketals from aldehydes and ketones. | https://en.wikipedia.org/wiki/Pyridinium_p-toluenesulfonate |
Pyridinium perbromide (also called pyridinium bromide perbromide , pyridine hydrobromide perbromide , or pyridinium tribromide ) is an organic chemical composed of a pyridinium cation and a tribromide anion. It can also be considered as a complex containing pyridinium bromide—the salt of pyridine and hydrogen bromide —with an added bromine (Br 2 ). The chemical is a solid whose reactivity is similar to that of bromine. It is thus a strong oxidizing agent used as a source of electrophilic bromine in halogenation reactions. [ 1 ] The analogous quinoline compound behaves similarly. [ 2 ]
Pyridinium tribromide can be obtained by reacting pyridinium bromide with bromine or thionyl bromide . [ 3 ]
Pyridinium tribromide is a red crystalline solid [ 1 ] which is virtually insoluble in water. [ 4 ]
Pyridinium tribromide is used as a brominating agent of ketones , phenols , and ethers . [ 4 ] As a stable solid, it can be more easily handled and weighed precisely, especially important properties for use in small scale reactions. One example from the original publications on this chemical is the bromination of the 3-ketosteroid 1 to 2,4-dibromocholestanone ( 2 ): [ 1 ] | https://en.wikipedia.org/wiki/Pyridinium_perbromide |
Pyrimidine ( C 4 H 4 N 2 ; / p ɪ ˈ r ɪ . m ɪ ˌ d iː n , p aɪ ˈ r ɪ . m ɪ ˌ d iː n / ) is an aromatic , heterocyclic , organic compound similar to pyridine ( C 5 H 5 N ). [ 3 ] One of the three diazines (six-membered heterocyclics with two nitrogen atoms in the ring), it has nitrogen atoms at positions 1 and 3 in the ring. [ 4 ] : 250 The other diazines are pyrazine (nitrogen atoms at the 1 and 4 positions) and pyridazine (nitrogen atoms at the 1 and 2 positions).
In nucleic acids , three types of nucleobases are pyrimidine derivatives : cytosine (C), thymine (T), and uracil (U).
The pyrimidine ring system has wide occurrence in nature [ 5 ] as substituted and ring fused compounds and derivatives, including the nucleotides cytosine , thymine and uracil , thiamine (vitamin B1) and alloxan . It is also found in many synthetic compounds such as barbiturates and the HIV drug zidovudine . Although pyrimidine derivatives such as alloxan were known in the early 19th century, a laboratory synthesis of a pyrimidine was not carried out until 1879, [ 5 ] when Grimaux reported the preparation of barbituric acid from urea and malonic acid in the presence of phosphorus oxychloride . [ 6 ] The systematic study of pyrimidines began [ 7 ] in 1884 with Pinner , [ 8 ] who synthesized derivatives by condensing ethyl acetoacetate with amidines . Pinner first proposed the name “pyrimidin” in 1885. [ 9 ] The parent compound was first prepared by Gabriel and Colman in 1900, [ 10 ] [ 11 ] by conversion of barbituric acid to 2,4,6-trichloropyrimidine followed by reduction using zinc dust in hot water.
The nomenclature of pyrimidines is straightforward. However, like other heterocyclics, tautomeric hydroxyl groups yield complications since they exist primarily in the cyclic amide form. For example, 2-hydroxypyrimidine is more properly named 2-pyrimidone. A partial list of trivial names of various pyrimidines exists. [ 12 ] : 5–6
Physical properties are shown in the data box. A more extensive discussion, including spectra, can be found in Brown et al. [ 12 ] : 242–244
Per the classification by Albert , [ 13 ] : 56–62 six-membered heterocycles can be described as π-deficient. Substitution by electronegative groups or additional nitrogen atoms in the ring significantly increase the π-deficiency. These effects also decrease the basicity. [ 13 ] : 437–439
Like pyridines, in pyrimidines the π-electron density is decreased to an even greater extent. Therefore, electrophilic aromatic substitution is more difficult while nucleophilic aromatic substitution is facilitated. An example of the last reaction type is the displacement of the amino group in 2-aminopyrimidine by chlorine [ 14 ] and its reverse. [ 15 ]
Electron lone pair availability ( basicity ) is decreased compared to pyridine. Compared to pyridine, N -alkylation and N -oxidation are more difficult. The p K a value for protonated pyrimidine is 1.23 compared to 5.30 for pyridine. Protonation and other electrophilic additions will occur at only one nitrogen due to further deactivation by the second nitrogen. [ 4 ] : 250 The 2-, 4-, and 6- positions on the pyrimidine ring are electron deficient analogous to those in pyridine and nitro- and dinitrobenzene. The 5-position is less electron deficient and substituents there are quite stable. However, electrophilic substitution is relatively facile at the 5-position, including nitration and halogenation. [ 12 ] : 4–8
Reduction in resonance stabilization of pyrimidines may lead to addition and ring cleavage reactions rather than substitutions. One such manifestation is observed in the Dimroth rearrangement .
Pyrimidine is also found in meteorites , but scientists still do not know its origin. Pyrimidine also photolytically decomposes into uracil under ultraviolet light. [ 16 ]
Pyrimidine biosynthesis creates derivatives —like orotate, thymine, cytosine, and uracil— de novo from carbamoyl phosphate and aspartate.
As is often the case with parent heterocyclic ring systems, the synthesis of pyrimidine is not that common and is usually performed by removing functional groups from derivatives. Primary syntheses in quantity involving formamide have been reported. [ 12 ] : 241–242
As a class, pyrimidines are typically synthesized by the principal synthesis involving cyclization of β-di carbonyl compounds with N–C–N compounds. Reaction of the former with amidines to give 2-substituted pyrimidines, with urea to give 2- pyrimidinones , and guanidines to give 2- aminopyrimidines are typical. [ 12 ] : 149–239
Pyrimidines can be prepared via the Biginelli reaction and other multicomponent reactions . [ 17 ] Many other methods rely on condensation of carbonyls with diamines for instance the synthesis of 2-thio-6-methyluracil from thiourea and ethyl acetoacetate [ 18 ] or the synthesis of 4-methylpyrimidine with 4,4-dimethoxy-2-butanone and formamide . [ 19 ]
A novel method is by reaction of N -vinyl and N -aryl amides with carbonitriles under electrophilic activation of the amide with 2-chloro-pyridine and trifluoromethanesulfonic anhydride : [ 20 ]
Because of the decreased basicity compared to pyridine, electrophilic substitution of pyrimidine is less facile. Protonation or alkylation typically takes place at only one of the ring nitrogen atoms. Mono- N -oxidation occurs by reaction with peracids. [ 4 ] : 253–254
Electrophilic C -substitution of pyrimidine occurs at the 5-position, the least electron-deficient. Nitration , nitrosation , azo coupling , halogenation , sulfonation , formylation , hydroxymethylation, and aminomethylation have been observed with substituted pyrimidines. [ 12 ] : 9–13
Nucleophilic C -substitution should be facilitated at the 2-, 4-, and 6-positions but there are only a few examples. Amination and hydroxylation have been observed for substituted pyrimidines. Reactions with Grignard or alkyllithium reagents yield 4-alkyl- or 4-aryl pyrimidine after aromatization. [ 12 ] : 14–15
Free radical attack has been observed for pyrimidine and photochemical reactions have been observed for substituted pyrimidines. [ 12 ] : 15–16 Pyrimidine can be hydrogenated to give tetrahydropyrimidine. [ 12 ] : 17
Three nucleobases found in nucleic acids , cytosine (C), thymine (T), and uracil (U), are pyrimidine derivatives:
In DNA and RNA , these bases form hydrogen bonds with their complementary purines . Thus, in DNA, the purines adenine (A) and guanine (G) pair up with the pyrimidines thymine (T) and cytosine (C), respectively.
In RNA , the complement of adenine (A) is uracil (U) instead of thymine (T), so the pairs that form are adenine : uracil and guanine : cytosine .
Very rarely, thymine can appear in RNA, or uracil in DNA, but when the other three major pyrimidine bases are represented, some minor pyrimidine bases can also occur in nucleic acids . These minor pyrimidines are usually methylated versions of major ones and are postulated to have regulatory functions. [ 21 ]
These hydrogen bonding modes are for classical Watson–Crick base pairing . Other hydrogen bonding modes ("wobble pairings") are available in both DNA and RNA, although the additional 2′-hydroxyl group of RNA expands the configurations, through which RNA can form hydrogen bonds. [ 22 ]
In March 2015, NASA Ames scientists reported that, for the first time, complex DNA and RNA organic compounds of life , including uracil , cytosine and thymine , have been formed in the laboratory under outer space conditions, using starting chemicals, such as pyrimidine, found in meteorites . Pyrimidine, like polycyclic aromatic hydrocarbons (PAHs), the most carbon-rich chemical found in the universe , may have been formed in red giants or in interstellar dust and gas clouds. [ 23 ] [ 24 ] [ 25 ]
In order to understand how life arose, knowledge is required of the chemical pathways that permit formation of the key building blocks of life under plausible prebiotic conditions . The RNA world hypothesis holds that in the primordial soup there existed free-floating ribonucleotides , the fundamental molecules that combine in series to form RNA . Complex molecules such as RNA must have emerged from relatively small molecules whose reactivity was governed by physico-chemical processes. RNA is composed of pyrimidine and purine nucleotides, both of which are necessary for reliable information transfer, and thus natural selection and Darwinian evolution . Becker et al. showed how pyrimidine nucleosides can be synthesized from small molecules and ribose , driven solely by wet-dry cycles. [ 26 ] Purine nucleosides can be synthesized by a similar pathway. 5’-mono-and diphosphates also form selectively from phosphate-containing minerals, allowing concurrent formation of polyribonucleotides with both the pyrimidine and purine bases. Thus a reaction network towards the pyrimidine and purine RNA building blocks can be established starting from simple atmospheric or volcanic molecules. | https://en.wikipedia.org/wiki/Pyrimidine |
Pyrimidine analogues are antimetabolites which mimic the structure of metabolic pyrimidines .
Pyrimidine antimetabolites are commonly used to treat cancer by interfering with DNA replication. [ 1 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pyrimidine_analogue |
Pyrimidine biosynthesis occurs both in the body and through organic synthesis. [ 1 ]
De Novo biosynthesis of a pyrimidine is catalyzed by three gene products CAD, DHODH and UMPS. The first three enzymes of the process are all coded by the same gene in CAD which consists of carbamoyl phosphate synthetase II , aspartate carbamoyltransferase and dihydroorotase . Dihydroorotate dehydrogenase (DHODH) unlike CAD and UMPS is a mono-functional enzyme and is localized in the mitochondria. UMPS is a bifunctional enzyme consisting of orotate phosphoribosyltransferase (OPRT) and orotidine monophosphate decarboxylase (OMPDC) . Both, CAD and UMPS are localized around the mitochondria, in the cytosol. [ 6 ] In Fungi , a similar protein exists but lacks the dihydroorotase function: another protein catalyzes the second step.
In other organisms ( Bacteria , Archaea and the other Eukaryota ), the first three steps are done by three different enzymes. [ 7 ]
Pyrimidines are ultimately catabolized (degraded) to CO 2 , H 2 O , and urea . Cytosine can be broken down to uracil , which can be further broken down to N-carbamoyl-β-alanine , and then to beta-alanine , CO 2 , and ammonia by beta-ureidopropionase . Thymine is broken down into β-aminoisobutyrate which can be further broken down into intermediates eventually leading into the citric acid cycle .
β-aminoisobutyrate acts as a rough indicator for rate of DNA turnover. [ 8 ]
Through negative feedback inhibition, the end-products UTP and UDP prevent the enzyme CAD from catalyzing the reaction in animals. Conversely, PRPP and ATP act as positive effectors that enhance the enzyme's activity. [ 9 ]
Modulating the pyrimidine metabolism pharmacologically has therapeutical uses, and could implement in cancer treatment. [ 10 ]
Pyrimidine synthesis inhibitors are used in active moderate to severe rheumatoid arthritis and psoriatic arthritis , as well as in multiple sclerosis . Examples include Leflunomide and Teriflunomide (the active metabolite of leflunomide).
In order to understand how life arose, knowledge is required of the chemical pathways that permit formation of the key building blocks of life under plausible prebiotic conditions . The RNA world hypothesis holds that in the primordial soup there existed free-floating pyrimidine and purine ribonucleotides , the fundamental molecules that combine in series to form RNA . Complex molecules such as RNA must have emerged from relatively small molecules whose reactivity was governed by physico-chemical processes. RNA is composed of pyrimidine and purine nucleotides, both of which are necessary for reliable information transfer, and thus natural selection and Darwinian evolution . Becker et al. showed how pyrimidine nucleosides can be synthesized from small molecules and ribose , driven solely by wet-dry cycles. [ 11 ] | https://en.wikipedia.org/wiki/Pyrimidine_biosynthesis |
Pyrimidine dimers represent molecular lesions originating from thymine or cytosine bases within DNA , resulting from photochemical reactions . [ 1 ] [ 2 ] These lesions, commonly linked to direct DNA damage , [ 3 ] are induced by ultraviolet light (UV), particularly UVC , result in the formation of covalent bonds between adjacent nitrogenous bases along the nucleotide chain near their carbon–carbon double bonds, [ 4 ] the photo-coupled dimers are fluorescent . [ 5 ] Such dimerization , which can also occur in double-stranded RNA (dsRNA) involving uracil or cytosine , leads to the creation of cyclobutane pyrimidine dimers (CPDs) and 6–4 photoproducts . These pre- mutagenic lesions modify the DNA helix structure, resulting in abnormal non-canonical base pairing and, consequently, adjacent thymines or cytosines in DNA will form a cyclobutane ring when joined together and cause a distortion in the DNA. This distortion prevents DNA replication and transcription mechanisms beyond the dimerization site. [ 6 ]
While up to 100 such reactions per second may transpire in a skin cell exposed to sunlight resulting in DNA damage , they are typically rectified promptly through DNA repair , such as through photolyase reactivation or nucleotide excision repair , with the latter being prevalent in humans. Conversely, certain bacteria utilize photolyase, powered by sunlight, to repair pyrimidine dimer-induced DNA damage. Unrepaired lesions may lead to erroneous nucleotide incorporation by polymerase machinery. Overwhelming DNA damage can precipitate mutations within an organism's genome , potentially culminating in cancer cell formation. [ 7 ] Unrectified lesions may also interfere with polymerase function, induce transcription or replication errors , or halt replication. Notably, pyrimidine dimers contribute to sunburn and melanin production, and are a primary factor in melanoma development in humans.
Pyrimidine dimers encompass several types, each with distinct structures and implications for DNA integrity. [ citation needed ]
Cyclobutane pyrimidine dimer (CPD) is a dimer which features a four-membered ring formed by the fusion of two double-bonded carbons from adjacent pyrimidines. CPDs disrupt the formation of the base pair during DNA replication , potentially leading to mutations . [ 8 ] [ 9 ] [ 10 ]
The 6–4 photoproduct (6–4 pyrimidine– pyrimidone , or 6–4 pyrimidine–pyrimidinone) is an alternate dimer configuration consisting of a single covalent bond linking the carbon at the 6 (C6) position of one pyrimidine ring and carbon at the 4 (C4) position of the adjoining base's ring. [ 11 ] This type of conversion occurs at one third the frequency of CPDs and has a higher mutagenic risk. [ 12 ]
A third type of molecular lesion is a Dewar pyrimidinone, resulting from the reversible isomerization of a 6–4 photoproduct under further light exposure. [ 13 ]
Mutagenesis, the process of mutation formation, is significantly influenced by translesion polymerases which often introduce mutations at sites of pyrimidine dimers. This occurrence is noted both in prokaryotes , through the SOS response to mutagenesis, and in eukaryotes . Despite thymine-thymine CPDs being the most common lesions induced by UV, translesion polymerases show a tendency to incorporate adenines , resulting in the accurate replication of thymine dimers more often than not. Conversely, cytosines that are part of CPDs are susceptible to deamination , leading to a cytosine to thymine transition, thereby contributing to the mutation process. [ 14 ]
Pyrimidine dimers introduce local conformational changes in the DNA structure , which allow recognition of the lesion by repair enzymes. [ 15 ] In most organisms (excluding placental mammals such as humans) they can be repaired by photoreactivation. [ 16 ] Photoreactivation is a repair process in which photolyase enzymes reverse CPDs using photochemical reactions. In addition, some photolyases can also repair 6-4 photoproducts of UV induced DNA damage. Photolyase enzymes utilize flavin adenine dinucleotide (FAD) as a cofactor in the repair process. [ 17 ]
The UV dose that reduces a population of wild-type yeast cells to 37% survival is equivalent (assuming a Poisson distribution of hits) to the UV dose that causes an average of one lethal hit to each of the cells of the population. [ 18 ] The number of pyrimidine dimers induced per haploid genome at this dose was measured as 27,000. [ 18 ] A mutant yeast strain defective in the three pathways by which pyrimidine dimers were known to be repaired in yeast was also tested for UV sensitivity. It was found in this case that only one or, at most, two unrepaired pyrimidine dimers per haploid genome are lethal to the cell. [ 18 ] These findings thus indicate that the repair of thymine dimers in wild-type yeast is highly efficient. [ citation needed ]
Nucleotide excision repair , sometimes termed "dark reactivation", is a more general mechanism for repair of lesions and is the most common form of DNA repair for pyrimidine dimers in humans. This process works by using cellular machinery to locate the dimerized nucleotides and excise the lesion. Once the CPD is removed, there is a gap in the DNA strand that must be filled. DNA machinery uses the undamaged complementary strand to synthesize nucleotides off of and consequently fill in the gap on the previously damaged strand. [ 6 ]
Xeroderma pigmentosum (XP) is a rare genetic disease in humans in which genes that encode for NER proteins are mutated and result in decreased ability to combat pyrimidine dimers that form as a result of UV damage. Individuals with XP are also at a much higher risk of cancer than others, with a greater than 5,000 fold increased risk of developing skin cancers. [ 7 ] Some common features and symptoms of XP include skin discoloration, and the formation of multiple tumors proceeding UV exposure. [ citation needed ]
A few organisms have other ways to perform repairs:
Another type of repair mechanism that is conserved in humans and other non-mammals is translesion synthesis. Typically, the lesion associated with the pyrimidine dimer blocks cellular machinery from synthesizing past the damaged site. However, in translesion synthesis, the CPD is bypassed by translesion polymerases, and replication and or transcription machinery can continue past the lesion. One specific translesion DNA polymerase, DNA polymerase η, is deficient in individuals with XPD. [ 20 ]
Direct DNA damage is reduced by sunscreen, which also reduces the risk of developing a sunburn. When the sunscreen is at the surface of the skin, it filters the UV rays, which attenuates the intensity. Even when the sunscreen molecules have penetrated into the skin, they protect against direct DNA damage, because the UV light is absorbed by the sunscreen and not by the DNA. [ 21 ] Sunscreen primarily works by absorbing the UV light from the sun through the use of organic compounds, such as oxybenzone or avobenzone. These compounds are able to absorb UV energy from the sun and transition into higher-energy states. Eventually, these molecules return to lower energy states, and in doing so, the initial energy from the UV light can be transformed into heat. This process of absorption works to reduce the risk of DNA damage and the formation of pyrimidine dimers. UVA light makes up 95% of the UV light that reaches earth, whereas UVB light makes up only about 5%. UVB light is the form of UV light that is responsible for tanning and burning. Sunscreens work to protect from both UVA and UVB rays. Overall, sunburns exemplify DNA damage caused by UV rays, and this damage can come in the form of free radical species, as well as dimerization of adjacent nucleotides. [ 22 ] | https://en.wikipedia.org/wiki/Pyrimidine_dimer |
Pyrimidine biosynthesis occurs both in the body and through organic synthesis. [ 1 ]
De Novo biosynthesis of a pyrimidine is catalyzed by three gene products CAD, DHODH and UMPS. The first three enzymes of the process are all coded by the same gene in CAD which consists of carbamoyl phosphate synthetase II , aspartate carbamoyltransferase and dihydroorotase . Dihydroorotate dehydrogenase (DHODH) unlike CAD and UMPS is a mono-functional enzyme and is localized in the mitochondria. UMPS is a bifunctional enzyme consisting of orotate phosphoribosyltransferase (OPRT) and orotidine monophosphate decarboxylase (OMPDC) . Both, CAD and UMPS are localized around the mitochondria, in the cytosol. [ 6 ] In Fungi , a similar protein exists but lacks the dihydroorotase function: another protein catalyzes the second step.
In other organisms ( Bacteria , Archaea and the other Eukaryota ), the first three steps are done by three different enzymes. [ 7 ]
Pyrimidines are ultimately catabolized (degraded) to CO 2 , H 2 O , and urea . Cytosine can be broken down to uracil , which can be further broken down to N-carbamoyl-β-alanine , and then to beta-alanine , CO 2 , and ammonia by beta-ureidopropionase . Thymine is broken down into β-aminoisobutyrate which can be further broken down into intermediates eventually leading into the citric acid cycle .
β-aminoisobutyrate acts as a rough indicator for rate of DNA turnover. [ 8 ]
Through negative feedback inhibition, the end-products UTP and UDP prevent the enzyme CAD from catalyzing the reaction in animals. Conversely, PRPP and ATP act as positive effectors that enhance the enzyme's activity. [ 9 ]
Modulating the pyrimidine metabolism pharmacologically has therapeutical uses, and could implement in cancer treatment. [ 10 ]
Pyrimidine synthesis inhibitors are used in active moderate to severe rheumatoid arthritis and psoriatic arthritis , as well as in multiple sclerosis . Examples include Leflunomide and Teriflunomide (the active metabolite of leflunomide).
In order to understand how life arose, knowledge is required of the chemical pathways that permit formation of the key building blocks of life under plausible prebiotic conditions . The RNA world hypothesis holds that in the primordial soup there existed free-floating pyrimidine and purine ribonucleotides , the fundamental molecules that combine in series to form RNA . Complex molecules such as RNA must have emerged from relatively small molecules whose reactivity was governed by physico-chemical processes. RNA is composed of pyrimidine and purine nucleotides, both of which are necessary for reliable information transfer, and thus natural selection and Darwinian evolution . Becker et al. showed how pyrimidine nucleosides can be synthesized from small molecules and ribose , driven solely by wet-dry cycles. [ 11 ] | https://en.wikipedia.org/wiki/Pyrimidine_metabolism |
The mineral pyrite ( / ˈ p aɪ r aɪ t / PY -ryte ), [ 6 ] or iron pyrite , also known as fool's gold , is an iron sulfide with the chemical formula Fe S 2 (iron (II) disulfide). Pyrite is the most abundant sulfide mineral . [ 7 ]
Pyrite's metallic luster and pale brass-yellow hue give it a superficial resemblance to gold , hence the well-known nickname of fool's gold . The color has also led to the nicknames brass , brazzle , and brazil , primarily used to refer to pyrite found in coal . [ 8 ] [ 9 ]
The name pyrite is derived from the Greek πυρίτης λίθος ( pyritēs lithos ), 'stone or mineral which strikes fire', [ 10 ] in turn from πῦρ ( pŷr ), 'fire'. [ 11 ] In ancient Roman times, this name was applied to several types of stone that would create sparks when struck against steel ; Pliny the Elder described one of them as being brassy, almost certainly a reference to what is now called pyrite. [ 12 ]
By Georgius Agricola 's time, c. 1550 , the term had become a generic term for all of the sulfide minerals . [ 13 ]
Pyrite is usually found associated with other sulfides or oxides in quartz veins , sedimentary rock , and metamorphic rock , as well as in coal beds and as a replacement mineral in fossils , but has also been identified in the sclerites of scaly-foot gastropods . [ 14 ] Despite being nicknamed "fool's gold", pyrite is sometimes found in association with small quantities of gold. A substantial proportion of the gold is " invisible gold " incorporated into the pyrite. It has been suggested that the presence of both gold and arsenic is a case of coupled substitution but as of 1997 the chemical state of the gold remained controversial. [ 15 ]
Pyrite gained a brief popularity in the 16th and 17th centuries as a source of ignition in early firearms , most notably the wheellock , where a sample of pyrite was placed against a circular file to strike the sparks needed to fire the gun. [ 16 ]
Pyrite is used with flintstone and a form of tinder made of stringybark by the Kaurna people of South Australia , as a traditional method of starting fires. [ 17 ]
Pyrite has been used since classical times to manufacture copperas ( ferrous sulfate ). Iron pyrite was heaped up and allowed to weather (an example of an early form of heap leaching ). The acidic runoff from the heap was then boiled with iron to produce iron sulfate. In the 15th century, new methods of such leaching began to replace the burning of sulfur as a source of sulfuric acid . By the 19th century, it had become the dominant method. [ 18 ]
Pyrite remains in commercial use for the production of sulfur dioxide , for use in such applications as the paper industry , and in the manufacture of sulfuric acid. Thermal decomposition of pyrite into FeS ( iron(II) sulfide ) and elemental sulfur starts at 540 °C (1,004 °F); at around 700 °C (1,292 °F), p S 2 is about 1 atm . [ 19 ]
A newer commercial use for pyrite is as the cathode material in Energizer brand non-rechargeable lithium metal batteries . [ 20 ]
Pyrite is a semiconductor material with a band gap of 0.95 eV . [ 21 ] Pure pyrite is naturally n-type, in both crystal and thin-film forms, potentially due to sulfur vacancies in the pyrite crystal structure acting as n-dopants. [ 22 ]
During the early years of the 20th century, pyrite was used as a mineral detector in radio receivers, and is still used by crystal radio hobbyists. Until the vacuum tube matured, the crystal detector was the most sensitive and dependable detector available—with considerable variation between mineral types and even individual samples within a particular type of mineral. Pyrite detectors occupied a midway point between galena detectors and the more mechanically complicated perikon mineral pairs. Pyrite detectors can be as sensitive as a modern 1N34A germanium diode detector. [ 23 ] [ 24 ]
Pyrite has been proposed as an abundant, non-toxic, inexpensive material in low-cost photovoltaic solar panels. [ 25 ] Synthetic iron sulfide was used with copper sulfide to create the photovoltaic material. [ 26 ] More recent efforts are working toward thin-film solar cells made entirely of pyrite. [ 22 ]
Pyrite is used to make marcasite jewelry . Marcasite jewelry, using small faceted pieces of pyrite, often set in silver , has been made since ancient times and was popular in the Victorian era . [ 27 ] At the time when the term became common in jewelry making, "marcasite" referred to all iron sulfides including pyrite, and not to the orthorhombic FeS 2 mineral marcasite which is lighter in color, brittle and chemically unstable, and thus not suitable for jewelry making. Marcasite jewelry does not actually contain the mineral marcasite. The specimens of pyrite, when it appears as good quality crystals, are used in decoration. They are also very popular in mineral collecting. Among the sites that provide the best specimens are Soria and La Rioja provinces (Spain). [ 28 ]
In value terms, China ($47 million) constitutes the largest market for imported unroasted iron pyrites worldwide, making up 65% of global imports. China is also the fastest growing in terms of the unroasted iron pyrites imports, with a CAGR of +27.8% from 2007 to 2016. [ 29 ]
In July 2020 scientists reported that they have observed a voltage-induced transformation of normally diamagnetic pyrite into a ferromagnetic material, which may lead to applications in devices such as solar cells or magnetic data storage. [ 30 ] [ 31 ]
Researchers at Trinity College Dublin , Ireland have demonstrated that FeS 2 can be exfoliated into few-layers just like other two-dimensional layered materials such as graphene by a simple liquid-phase exfoliation route. This is the first study to demonstrate the production of non-layered 2D-platelets from 3D bulk FeS 2 . Furthermore, they have used these 2D-platelets with 20% single walled carbon-nanotube as an anode material in lithium-ion batteries, reaching a capacity of 1000 mAh/g close to the theoretical capacity of FeS 2 . [ 32 ]
In 2021, a natural pyrite stone has been crushed and pre-treated followed by liquid-phase exfoliation into two-dimensional nanosheets, which has shown capacities of 1200 mAh/g as an anode in lithium-ion batteries. [ 33 ]
From the perspective of classical inorganic chemistry , which assigns formal oxidation states to each atom, pyrite and marcasite are probably best described as Fe 2+ [S 2 ] 2− . This formalism recognizes that the sulfur atoms in pyrite occur in pairs with clear S–S bonds. These persulfide [ − S–S − ] units can be viewed as derived from hydrogen disulfide , H 2 S 2 . Thus pyrite would be more descriptively called iron persulfide, not iron disulfide. In contrast, molybdenite , Mo S 2 , features isolated sulfide S 2− centers and the oxidation state of molybdenum is Mo 4+ . The mineral arsenopyrite has the formula Fe As S. Whereas pyrite has [S 2 ] 2− units, arsenopyrite has [AsS] 3− units, formally derived from deprotonation of arsenothiol (H 2 AsSH). Analysis of classical oxidation states would recommend the description of arsenopyrite as Fe 3+ [AsS] 3− . [ 34 ]
Iron-pyrite FeS 2 represents the prototype compound of the crystallographic pyrite structure. The structure is cubic and was among the first crystal structures solved by X-ray diffraction . [ 35 ] It belongs to the crystallographic space group Pa 3 and is denoted by the Strukturbericht notation C2. Under thermodynamic standard conditions the lattice constant a {\displaystyle a} of stoichiometric iron pyrite FeS 2 amounts to 541.87 pm . [ 36 ] The unit cell is composed of a Fe face-centered cubic sublattice into which the S 2 ions are embedded. (Note though that the iron atoms in the faces are not equivalent by translation alone to the iron atoms at the corners.) The pyrite structure is also seen in other MX 2 compounds of transition metals M and chalcogens X = O , S , Se and Te . Certain dipnictides with X standing for P , As and Sb etc. are also known to adopt the pyrite structure. [ 37 ]
The Fe atoms are bonded to six S atoms, giving a distorted octahedron. The material is a semiconductor . The Fe ions are usually considered to be low spin divalent state (as shown by Mössbauer spectroscopy as well as XPS). The material as a whole behaves as a Van Vleck paramagnet , despite its low-spin divalency. [ 38 ]
The sulfur centers occur in pairs, described as S 2 2− . [ 39 ] Reduction of pyrite with potassium gives potassium dithioferrate , KFeS 2 . This material features ferric ions and isolated sulfide (S 2− ) centers.
The S atoms are tetrahedral, being bonded to three Fe centers and one other S atom. The site symmetry at Fe and S positions is accounted for by point symmetry groups C 3 i and C 3 , respectively. The missing center of inversion at S lattice sites has important consequences for the crystallographic and physical properties of iron pyrite. These consequences derive from the crystal electric field active at the sulfur lattice site, which causes a polarization of S ions in the pyrite lattice. [ 40 ] The polarisation can be calculated on the basis of higher-order Madelung constants and has to be included in the calculation of the lattice energy by using a generalised Born–Haber cycle . This reflects the fact that the covalent bond in the sulfur pair is inadequately accounted for by a strictly ionic treatment. [ 41 ]
Arsenopyrite has a related structure with heteroatomic As–S pairs rather than S-S pairs. Marcasite also possesses homoatomic anion pairs, but the arrangement of the metal and diatomic anions differs from that of pyrite. Despite its name, chalcopyrite ( CuFeS 2 ) does not contain dianion pairs, but single S 2− sulfide anions.
Pyrite usually forms cuboid crystals, sometimes forming in close association to form raspberry-shaped masses called framboids . However, under certain circumstances, it can form anastomosing filaments or T-shaped crystals. [ 42 ] Pyrite can also form shapes almost the same as a regular dodecahedron , known as pyritohedra, and this suggests an explanation for the artificial geometrical models found in Europe as early as the 5th century BC. [ 43 ] [ clarification needed ]
Cattierite ( Co S 2 ), vaesite ( Ni S 2 ) and hauerite ( Mn S 2 ), as well as sperrylite ( Pt As 2 ) are similar in their structure and belong also to the pyrite group.
Bravoite is a nickel-cobalt bearing variety of pyrite, with > 50% substitution of Ni 2+ for Fe 2+ within pyrite. Bravoite is not a formally recognised mineral, and is named after the Peruvian scientist Jose J. Bravo (1874–1928). [ 44 ]
Pyrite is distinguishable from native gold by its hardness, brittleness and crystal form. Pyrite fractures are very uneven , sometimes conchoidal because it does not cleave along a preferential plane. Native gold nuggets , or glitters, do not break but deform in a ductile way. Pyrite is brittle, gold is malleable.
Natural gold tends to be anhedral (irregularly shaped without well defined faces), whereas pyrite comes as either cubes or multifaceted crystals with well developed and sharp faces easy to recognise. Well crystallised pyrite crystals are euhedral ( i.e. , with nice faces). Pyrite can often be distinguished by the striations which, in many cases, can be seen on its surface. Chalcopyrite ( CuFeS 2 ) is brighter yellow with a greenish hue when wet and is softer (3.5–4 on Mohs' scale). [ 45 ] Arsenopyrite (FeAsS) is silver white and does not become more yellow when wet.
Iron pyrite is unstable when exposed to the oxidizing conditions prevailing at the Earth's surface: iron pyrite in contact with atmospheric oxygen and water, or damp, ultimately decomposes into iron oxyhydroxides ( ferrihydrite , FeO(OH)) and sulfuric acid ( H 2 SO 4 ). This process is accelerated by the action of Acidithiobacillus bacteria which oxidize pyrite to first produce ferrous ions ( Fe 2+ ), sulfate ions ( SO 2− 4 ), and release protons ( H + , or H 3 O + ). In a second step, the ferrous ions ( Fe 2+ ) are oxidized by O 2 into ferric ions ( Fe 3+ ) which hydrolyze also releasing H + ions and producing FeO(OH). These oxidation reactions occur more rapidly when pyrite is finely dispersed (framboidal crystals initially formed by sulfate reducing bacteria (SRB) in argillaceous sediments or dust from mining operations).
Pyrite oxidation by atmospheric O 2 in the presence of moisture ( H 2 O ) initially produces ferrous ions ( Fe 2+ ) and sulfuric acid which dissociates into sulfate ions and protons , leading to acid mine drainage (AMD). An example of acid rock drainage caused by pyrite is the 2015 Gold King Mine waste water spill . [ 46 ]
Pyrite oxidation is sufficiently exothermic that underground coal mines in high-sulfur coal seams have occasionally had serious problems with spontaneous combustion . [ 47 ] The solution is the use of buffer blasting and the use of various sealing or cladding agents to hermetically seal the mined-out areas to exclude oxygen. [ 48 ]
In modern coal mines, limestone dust is sprayed onto the exposed coal surfaces to reduce the hazard of dust explosions . This has the secondary benefit of neutralizing the acid released by pyrite oxidation and therefore slowing the oxidation cycle described above, thus reducing the likelihood of spontaneous combustion. In the long term, however, oxidation continues, and the hydrated sulfates formed may exert crystallization pressure that can expand cracks in the rock and lead eventually to roof fall . [ 49 ]
Building stone containing pyrite tends to stain brown as pyrite oxidizes. This problem appears to be significantly worse if any marcasite is present. [ 50 ] The presence of pyrite in the aggregate used to make concrete can lead to severe deterioration as pyrite oxidizes. [ 51 ] In early 2009, problems with Chinese drywall imported into the United States after Hurricane Katrina were attributed to pyrite oxidation, followed by microbial sulfate reduction which released hydrogen sulfide gas ( H 2 S ). These problems included a foul odor and corrosion of copper wiring. [ 52 ] In the United States, in Canada, [ 53 ] and more recently in Ireland, [ 54 ] [ 55 ] [ 56 ] where it was used as underfloor infill, pyrite contamination has caused major structural damage. Concrete exposed to sulfate ions, or sulfuric acid, degrades by sulfate attack : the formation of expansive mineral phases, such as ettringite (small needle crystals exerting a huge crystallization pressure inside the concrete pores) and gypsum creates inner tensile forces in the concrete matrix which destroy the hardened cement paste, form cracks and fissures in concrete, and can lead to the ultimate ruin of the structure. Normalized tests for construction aggregate [ 57 ] certify such materials as free of pyrite or marcasite.
Pyrite is the most common of sulfide minerals and is widespread in igneous, metamorphic, and sedimentary rocks. It is a common accessory mineral in igneous rocks, where it also occasionally occurs as larger masses arising from an immiscible sulfide phase in the original magma. It is found in metamorphic rocks as a product of contact metamorphism . It also forms as a high-temperature hydrothermal mineral , though it occasionally forms at lower temperatures. [ 2 ]
Pyrite occurs both as a primary mineral, present in the original sediments, and as a secondary mineral, deposited during diagenesis . [ 2 ] Pyrite and marcasite commonly occur as replacement pseudomorphs after fossils in black shale and other sedimentary rocks formed under reducing environmental conditions. [ 58 ] Pyrite is common as an accessory mineral in shale, where it is formed by precipitation from anoxic seawater, and coal beds often contain significant pyrite. [ 59 ]
Notable deposits are found as lenticular masses in Virginia, U.S., and in smaller quantities in many other locations. Large deposits are mined at Rio Tinto in Spain and elsewhere in the Iberian Peninsula. [ 60 ]
In the beliefs of the Thai people (especially those in the south), pyrite is known as Khao tok Phra Ruang , Khao khon bat Phra Ruang (ข้าวตอกพระร่วง, ข้าวก้นบาตรพระร่วง) or Phet na tang , Hin na tang (เพชรหน้าทั่ง, หินหน้าทั่ง). It is believed to be a sacred item that has the power to prevent evil, black magic or demons. [ 61 ] [ 62 ] | https://en.wikipedia.org/wiki/Pyrite |
Pyrococcus yayanosii is a strictly anaerobic , hyperthermophilic archaeon , first identified through samples from the Mid-Atlantic Ridge . [ 1 ] Isolated from a deep-sea hydrothermal vent , it is characterized as a motile Gram-negative marine bacteria that is roughly cocci shaped and 1-1.5 μm in diameter, with lophotrichous flagellation. [ 1 ] As the current most thermophilic species within the order of Thermococcales , P. yayanosii exhibit various selective conditions for growth, including high pressures and temperatures, with an average doubling time of 50 minutes. [ 1 ] Genome analysis reveal a 49 percent guanine - cytosine DNA content with Pyrococcus furiosus being its closest species relative. [ 1 ]
Pyrococcus yayanosii are unicellular organisms that are salt-dependent, residing in environments that exhibit moderate concentrations of NaCl. [ 1 ] Through utilizing an anaerobic growth method, P. yayanosii is capable of using various simple and complex substrates for fermentation. [ 1 ] While this pathway results in slower growth rates compared to aerobic metabolism, elemental sulfur has been found to promote growth for this species. [ 2 ] Similar to some hydrothermal vent microbes, P. yayanosii employs sulfur assimilation in facilitating biological processes, thereby producing byproducts such as 3'-Phosphoadenosine 5'-monophosphate (pAp). [ 3 ]
Pyrococcus yayanosii was originally isolated by Birrien et al. (2011) on the Serpentine cruise of March 2007 in the Central Equatorial Atlantic. The research team collected black smoker samples at a depth of 4100m on the Mid-Atlantic Ridge , specifically at the Ashadze site, an active hydrothermal vent field. [ 1 ]
Due to the strict conditions of P. yayanosii for growth, special care was taken to incubate the samples anaerobically at an optimal pressure of 52 MPa and temperature of 98 °C. [ 1 ] Growth of an isolated colony designated as strain CH1 T was observed after two days under these conditions. The cloning and sequencing of the 16S rRNA gene , as well as microscopic observation, verified the purity of the CH1 T isolate. [ 1 ]
After purity confirmation, a light microscope was used to observe the isolated strain CH1 T . [ 1 ] Certain traits were being screened for, as Pyrococcus species are known for their characteristic spherical (cocci) shape as well as their flagellar motility. [ 4 ] [ 5 ] The cells of CH1 T appeared to resemble irregular cocci shapes and were observed frequently as single cells or in pairs, or infrequently in a line formation. [ 1 ] The researchers also noticed that individual cells were especially motile. This finding prompted the use of a Spot Test Flagella kit, which confirmed the presence of a polar spot of flagella . Other tests performed included the Gram stain , varied substrate utilization assays, and direct cell counting . These tests characterized Pyrococccus yayanosii as a gram-negative bacterium with the ability to metabolize proteinaceous substrates and carbohydrates for energy and release hydrogen sulfide . [ 1 ]
Cells of strain CH1 T were harvested in their peak growth phase, followed by DNA being isolated by chemical extraction. [ 1 ] Through amplification , sequencing and analysis of the 16S rRNA gene, strain CH1 T was classified to belong within the genus Pyrococcus , sharing a gene sequence most similar to Pyrococcus furiosus . [ 1 ]
Birrien et al. (2011) compared the DNA sequences of three Pyrococcus reference species ( P. furiosus , P. abyssi , P. horikoshii ) to the DNA isolated from strain CH1T and found that the DNA similarity values between them were significantly lower than the similarity values between the two distinct species P. abyssi and P. horikoshii . This provided evidence that strain CH1 T itself was a distinct species, and thus was named Pyrococcus yayanosii , in honour of a pioneer in microbiological research, Aristides Yayanos, who specialized in the study of piezophilic bacteria. [ 1 ]
The discovery of P. yayanosii opened many doors for broader future research. As P. yayanosii is both an obligate piezophile and hyperthermophile, [ 2 ] the organism is an attractive model for studying early life evolution and the biochemical strategies underlying piezophilic adaptation. In 2014, Li et al. generated a derivative strain, P. yayanosii A1, which is facultatively (originally obligately) piezophilic. This strain can grow under both atmospheric pressure and high-pressure conditions while maintaining similar physiology (optimal temperature, pH, and salt concentration) to wild type P. yayanosii. [ 6 ] The ability to cultivate A1 under normal atmospheric conditions simplifies genetic manipulations. The researchers subsequently constructed several plasmids that were able to genetically manipulate the A1 strain. The transformation efficiency reached significant levels, indicating an effective system for gene disruption. [ 6 ] This system can be applied in future studies on the functional genomics of P. yayanosii. Consequently, it would further allow researchers to investigate the molecular mechanisms that underpin piezophilic and hyperthermophilic adaptation, potentially providing insights into early life evolution and the adaptation of microorganisms to extreme environments.
Isolated from the deepest hydrothermal vent field explored to date, P. yayanosii is a strictly anaerobic organism adapted to a deep ocean, seawater environment lacking oxygen. [ 1 ] It is considered an extremophile as it grows under high temperatures and high pressures.
Incubation experiments of P. yayanosii allowed identification of its optimal conditions. The specific strain CH1 T was found to have an optimal temperature of 98 °C despite being capable of growing at temperatures between 80 and 108 °C. [ 1 ] Similarly, while this strain exhibits optimal growth at a pH of around 7.5 to 8, it is capable of growth when exposed to a pH range between 6.0 and 9.5. [ 1 ] It has a salinity optimum nearing 3.5% in weight by volume, with a range where growth is possible from 2.5 to 5.5%. [ 1 ] An optimal pressure of 52 MPa was identified for P. yayanosii . [ 7 ] While some studies identified stressful pressures at 20 and 80 MPa, with growth rates half as great as the rate at the optimum, others observed no growth was observed for the strain CH1 T below 20 MPa and above 120 MPa. [ 1 ] [ 7 ]
Other substrates were also tested as potential carbon and energy sources; P. yayanosii was able to use casein , cellobiose , sucrose , glucose , starch , chitin , pyruvate , glycerol , and acetate for fermentation . The addition of elemental sulfur also promoted its growth. [ 1 ]
Multiple mechanisms are thought allow P. yayanosii to adapt to changes in hydrostatic pressures .
First, a gene expression analysis revealed an overrepresentation of genes involved in energy production and conversion, with genes coding for ATP - and ADP-synthase , as well as hydrogenases and ferredoxin oxidoreductases . [ 7 ] More specifically, transcriptome and proteome analyses showed that while the genes associated with hydrogenases are downregulated under stressful conditions, the proteins associated with these energy pathways are upregulated. [ 7 ]
The hydrogenase energy pathway involves the production of protons , and it has been hypothesized that other upregulated genes associated with ATPase could contribute to maintaining pH homeostasis . [ 7 ]
Several CRISPR-cas clusters, which are usually associated with immunity and pathogen resistance, are also regulated (either upregulated or downregulated) under stressuful pressures. [ 7 ]
Additionally, chemotaxis genes upregulated at stressful pressure could increase the motility of the organism, which in turn is thought to help the organism seek nutrients. [ 7 ]
Similarly, proteins associated with ribosome recycling and subunits synthesis are upregulated in stressfully high and low pressures, enhancing the synthesis and activity of proteins. [ 7 ]
Evolutionarily, Genomic Islands (GIs) contribute to gene modification and plasticity and thereby promote the genetic diversity and adaptation of species to their environment. [ 8 ] In P. yayanosii , 15 GIs were identified from DNA fragments. [ 8 ] The transcription levels of the largest of these GIs, PYG1, revealed variations in gene expression under different temperature and pressure conditions. It was found to be generally nonessential but to facilitate adaptation in stressful conditions. [ 8 ] Experiments involving removing PYG1 also highlighted a tradeoff in the adaptation to high pressure versus high temperature. [ 8 ] This GI bears a resemblance to GIs and similar structures in other extremophilic archea such as Thermococcus barophilus and Pyrococcus abyssi . [ 8 ]
In this GI, a potential toxin-antitoxin system was identified, with toxin gene pygT and antitoxin gene pygA. [ 9 ] Experiments conducted using mutant strains and different pressure conditions suggested that this system might play a role in both plasmid stability and adaptation to high hydrostatic pressure. [ 9 ]
The genome of P. yayanosii CH1 T was completey sequenced , and analyses found a proteome of 1,926 proteins, 21% of which are still only hypothetical . [ 10 ] [ 11 ]
PYCH_01220 is one of the hypothetical proteins with a crystal structure composed of two domains. [ 11 ] Previous research found similarity between this protein and Escherichia coli ' s ribonuclease colicin D, suggesting that its potential function could be to bind the nucleic acids of DNA. [ 11 ]
A complete genome mapping of P. Yayanosii led to the discovery of a gene hypothesized to produce an amylopullulanase, referred henceforth as Pul PY. [ 12 ] Pullulanase is responsible for debranching α-1, 6 glycosidic linkages in oligosaccharides . Subsequent NCBI Protein Blast analysis allowed researchers to deduce active site structure and homology testing showed substantial similarities to other Pyrococcus and Thermococcus species. [ 12 ] Tests reveals that Pul PY has optimal temperature of 95 °C and is able to maintain a minimum 80% functionality around 100 °C. [ 12 ] Pul PY functions optimally at pH 6.6 and showed significant functionality within a pH range of 5.8-8.0. [ 12 ] Additional comparative testing for thermal stability against other thermostable enzymes found similarity with Pyrococcus woesei , proving significant thermostability. [ 12 ]
Due to its ability to survive in extreme conditions over a long period of time, Pul PY is ideal for use in starch liquefaction. [ 12 ] When used in conjunction with amylase , it can improve the efficiency of hydrolysis. [ 12 ]
pApase is a type of enzyme responsible for breaking down 3 ′ -phosphoadenosine 5 ′ -monophosphate (pAp) into AMP and phosphate. Prior to testing P. yayanosii pApase, not much was known about the archaeal methods of pAp turnover. [ 3 ] Inspection of the gene cluster involved in assimilatory sulfate reduction yielded PYCH_17540, which codes for pApase. [ 3 ] Homologic testing shows that this pApase is derived from a common ancestor with NmA nucleases , which are bacterial in nature. [ 3 ]
Testing shows that pApase functions optimally at pH 6.5, while maintaining significant performance within a pH range of 5.5-8.0. [ 3 ] pApase shows positive linear correlation between temperature and performance within 25-90 °C, showing approximately 4 times more turnover at 90 °C compared to 25 °C. [ 3 ] Additionally, pApase requires co-factors for optimal functionality. Cobalt is the best cofactor, being closely followed by Nickel and Manganese . [ 3 ]
Archael pApase also has a high specificity for substrates. [ 3 ] It is only capable of attaching to and hydrolysing cyclic nucelotides, nanoRNAs and small ssDNA. [ 3 ]
The structure of pApase includes a DHH domain attached to a DHHA1 domain via a long α-helix , where the cleft between its domains is the active site . [ 3 ] In comparison to bacterial pApase, the α-helix is much longer, which makes the active site smaller and thus, more substrate specific. [ 3 ]
Pyrococcus yayanosii naturally possess a thermostable ferritin, PcFn, capable of withstanding high temperature exposures up to 110 °C. [ 13 ] Understanding this protein can provide future directions clinically in developing drugs with well-maintained efficiency despite storage under higher temperatures. The synthesis of PcFn into thermostable magnetoferritins (M-PcFn) by monodispered iron oxide nanoparticles form crystalline core structures with negligible change in hydrodynamic diameters. [ 13 ] This finding in regards to resistance to change reinforce that PcFn plays a critical role in thermostability, thereby influencing the overall properties observed in P. yayanosii . These noticeable characteristics found in M-PcFn, such as PcFn5000, offer insight on approaches that can increase thermostability of molecules and substances. [ 13 ]
In addition to the species' resistance to molecular changes in structure, the 51st and 298th residues found in L- asparaginase II of P. yayanosii interplay in thermostability. [ 14 ] These residues allow for molecular maintenance and increased thermostability through supporting a tightly bound C terminal, reducing surface charges at reaction regions, and retaining loop rigidity. [ 14 ] Recognition on the influence of amino acids on heat tolerance introduce alternative perspectives into industrial applications and new findings.
While only the cold shock-inducible and sugar-inducible promoters were previously identified within the order Thermococcales, a recent study found a high hydrostatic pressure (HHP) inducible promoter in P. yayanosii . [ 15 ] Given promoters are known to be regions where gene transcription occurs, identification of the HHP promoter can provide biological knowledge on the interactive dynamics between the components that allow for transcription . Hence, the proteins produced as a product of translation can introduce analysis into mechanisms that allow for tolerance to high pressure, thereby providing insight useful to improve industrial equipment.
Pyrococcus yayanosii was found to exhibit low variability with respect to the core lipids , which are essential components that determine bacterial structure and function. [ 16 ] Given that lipids are abundant in various systems, such as biologically within cells and chemically within organic compounds , and are key determinants to heat adaptability, knowledge may be borrowed from this organism in constructing pharmaceutical products that incorporate heat resistance properties. Therefore, this finding offers new avenues of exploration that may be key to industrial development. | https://en.wikipedia.org/wiki/Pyrococcus_yayanosii |
Pyroelectric fusion refers to the technique of using pyroelectric crystals to generate high strength electrostatic fields to accelerate deuterium ions ( tritium might also be used someday) into a metal hydride target also containing deuterium (or tritium) with sufficient kinetic energy to cause these ions to undergo nuclear fusion . It was reported in April 2005 by a team at UCLA . The scientists used a pyroelectric crystal heated from −34 to 7 °C (−29 to 45 °F), combined with a tungsten needle to produce an electric field of about 25 gigavolts per meter to ionize and accelerate deuterium nuclei into an erbium deuteride target. Though the energy of the deuterium ions generated by the crystal has not been directly measured, the authors used 100 keV (a temperature of about 10 9 K ) as an estimate in their modeling. [ 1 ] At these energy levels, two deuterium nuclei can fuse to produce a helium-3 nucleus, a 2.45 MeV neutron and bremsstrahlung . Although it makes a useful neutron generator, the apparatus is not intended for power generation since it requires far more energy than it produces. [ 2 ] [ 3 ] [ 4 ] [ 5 ]
The process of light ion acceleration using electrostatic fields and deuterium ions to produce fusion in solid deuterated targets was first demonstrated by Cockcroft and Walton in 1932 (see Cockcroft–Walton generator ). That process is used in miniaturized versions of their original accelerator, in the form of small sealed tube neutron generators , for petroleum exploration .
The process of pyroelectricity has been known from ancient times. [ 6 ] The first use of a pyroelectric field to accelerate deuterons was in a 1997 experiment conducted by Drs. V.D. Dougar Jabon, G.V. Fedorovich, and N.V. Samsonenko. [ 7 ] This group was the first to utilize a lithium tantalate ( LiTaO 3 ) pyroelectric crystal in fusion experiments.
The novel idea with the pyroelectric approach to fusion is in its application of the pyroelectric effect to generate accelerating electric fields. This is done by heating the crystal from −34 °C to +7 °C over a period of a few minutes.
Nuclear D-D fusion driven by pyroelectric crystals was proposed by Naranjo and Putterman in 2002. [ 8 ] It was also discussed by Brownridge and Shafroth in 2004. [ 9 ] The possibility of using pyroelectric crystals in a neutron production device (by D-D fusion) was proposed in a conference paper by Geuther and Danon in 2004 [ 10 ] and later in a publication discussing electron and ion acceleration by pyroelectric crystals. [ 11 ] None of these later authors had prior knowledge of the earlier 1997 experimental work conducted by Dougar Jabon, Fedorovich, and Samsonenko which mistakenly believed that fusion occurred within the crystals. [ 7 ] The key ingredient of using a tungsten needle to produce sufficient ion beam current for use with a pyroelectric crystal power supply was first demonstrated in the 2005 Nature paper, although in a broader context tungsten emitter tips have been used as ion sources in other applications for many years. In 2010, it was found that tungsten emitter tips are not necessary to increase the acceleration potential of pyroelectric crystals; the acceleration potential can allow positive ions to reach kinetic energies between 300 and 310 keV. [ 12 ]
In April 2005, a UCLA team headed by chemistry professor James K. Gimzewski [ 13 ] and physics professor Seth Putterman utilized a tungsten probe attached to a pyroelectric crystal to increase the electric field strength. [ 14 ] Brian Naranjo, a graduate student working under Putterman, conducted the experiment demonstrating the use of a pyroelectric power source for producing fusion on a laboratory bench top device. [ 15 ] The device used a lithium tantalate ( LiTaO 3 ) pyroelectric crystal to ionize deuterium atoms and to accelerate the deuterons towards a stationary erbium dideuteride ( Er D 2 ) target. Around 1000 fusion reactions per second took place, each resulting in the production of an 820 keV helium-3 nucleus and a 2.45 MeV neutron. The team anticipates applications of the device as a neutron generator or possibly in microthrusters for space propulsion .
A team at Rensselaer Polytechnic Institute , led by Yaron Danon and his graduate student Jeffrey Geuther, improved upon the UCLA experiments using a device with two pyroelectric crystals and capable of operating at non-cryogenic temperatures. [ 16 ] [ 17 ]
Pyroelectric fusion has been hyped in the news media, [ 18 ] which overlooked the work of Dougar Jabon, Fedorovich and Samsonenko. [ 7 ] Pyroelectric fusion is not related to the earlier claims of fusion reactions, having been observed during sonoluminescence ( bubble fusion ) experiments conducted under the direction of Rusi Taleyarkhan of Purdue University . [ 19 ] Naranjo of the UCLA team was one of the main critics of these earlier prospective fusion claims from Taleyarkhan. [ 20 ]
The first successful results with pyroelectric fusion using a tritiated target was reported in 2010. [ 21 ] Putterman and Naranjo worked with T. Venhaus of Los Alamos National Laboratory to measure a 14.1 MeV neutron signal far above background. | https://en.wikipedia.org/wiki/Pyroelectric_fusion |
Pyroelectricity (from Greek: pyr (πυρ), "fire" and electricity ) is a property of certain crystals which are naturally electrically polarized and as a result contain large electric fields. [ 1 ] Pyroelectricity can be described as the ability of certain materials to generate a temporary voltage when they are heated or cooled. [ 2 ] [ 3 ] The change in temperature modifies the positions of the atoms slightly within the crystal structure , so that the polarization of the material changes. This polarization change gives rise to a voltage across the crystal. If the temperature stays constant at its new value, the pyroelectric voltage gradually disappears due to leakage current . The leakage can be due to electrons moving through the crystal, ions moving through the air, or current leaking through a voltmeter attached across the crystal. [ 3 ] [ 4 ]
Pyroelectric charge in minerals develops on the opposite faces of asymmetric crystals. The direction in which the propagation of the charge tends is usually constant throughout a pyroelectric material, but, in some materials, this direction can be changed by a nearby electric field. These materials are said to exhibit ferroelectricity .
All known pyroelectric materials are also piezoelectric . Despite being pyroelectric, novel materials such as boron aluminum nitride (BAlN) and boron gallium nitride (BGaN) have zero piezoelectric response for strain along the c-axis at certain compositions, [ 5 ] the two properties being closely related. However, note that some piezoelectric materials have a crystal symmetry that does not allow pyroelectricity.
Pyroelectric materials are mostly hard and crystals; however, soft pyroelectricity can be achieved by using electrets . [ 6 ]
Pyroelectricity is measured as the change in net polarization (a vector) proportional to a change in temperature. The total pyroelectric coefficient measured at constant stress is the sum of the pyroelectric coefficients at constant strain (primary pyroelectric effect) and the piezoelectric contribution from thermal expansion (secondary pyroelectric effect). Under normal circumstances, even polar materials do not display a net dipole moment . As a consequence, there are no electric dipole equivalents of bar magnets because the intrinsic dipole moment is neutralized by "free" electric charge that builds up on the surface by internal conduction or from the ambient atmosphere. Polar crystals only reveal their nature when perturbed in some fashion that momentarily upsets the balance with the compensating surface charge.
Spontaneous polarization is temperature dependent, so a good perturbation probe is a change in temperature which induces a flow of charge to and from the surfaces. This is the pyroelectric effect. All polar crystals are pyroelectric, so the 10 polar crystal classes are sometimes referred to as the pyroelectric classes. Pyroelectric materials can be used as infrared and millimeter wavelength radiation detectors.
An electret is the electrical equivalent of a permanent magnet.
The pyroelectric coefficient may be described as the change in the spontaneous polarization vector with temperature: [ 7 ] p i = ∂ P S , i ∂ T {\displaystyle p_{i}={\frac {\partial P_{S,i}}{\partial T}}} where p i (Cm −2 K −1 ) is the vector for the pyroelectric coefficient.
The first record of the pyroelectric effect was made in 1707 by Johann Georg Schmidt , who noted that the "[hot] tourmaline could attract the ashes from the warm or burning coals, as the magnet does iron, but also repelling them again [after the contact]". [ 8 ] In 1717 Louis Lemery noticed, as Schmidt had, that small scraps of non-conducting material were first attracted to tourmaline, but then repelled by it once they contacted the stone. [ 9 ] In 1747 Linnaeus first related the phenomenon to electricity (he called tourmaline Lapidem Electricum , "the electric stone"), [ 10 ] although this was not proven until 1756 by Franz Ulrich Theodor Aepinus . [ 11 ]
Research into pyroelectricity became more sophisticated in the 19th century. In 1824 Sir David Brewster gave the effect the name it has today. [ 12 ] Both William Thomson in 1878 [ 13 ] and Woldemar Voigt in 1897 [ 14 ] helped develop a theory for the processes behind pyroelectricity. Pierre Curie and his brother, Jacques Curie , studied pyroelectricity in the 1880s, leading to their discovery of some of the mechanisms behind piezoelectricity. [ 15 ]
It is mistakenly attributed to Theophrastus (c. 314 BC) the first record of pyroelectricity. The misconception arose soon after the discovery of the pyroelectric properties of tourmaline , which made mineralogists of the time associate the legendary stone Lyngurium with it. [ 16 ] Lyngurium is described in the work of Theophrastus as being similar to amber , without specifying any pyroelectric properties. [ 17 ]
All crystal structures belong to one of thirty-two crystal classes based on the number of rotational axes and reflection planes they possess that leave the crystal structure unchanged ( point groups ). Of the thirty-two crystal classes, twenty-one are non-centrosymmetric (not having a centre of symmetry ). Of these twenty-one, twenty exhibit direct piezoelectricity , the remaining one being the cubic class 432. Ten of these twenty piezoelectric classes are polar, i.e., they possess a spontaneous polarization, having a dipole in their unit cell, and exhibit pyroelectricity. If this dipole can be reversed by the application of an electric field, the material is said to be ferroelectric . Any dielectric material develops a dielectric polarization (electrostatics) when an electric field is applied, but a substance which has such a natural charge separation even in the absence of a field is called a polar material. Whether or not a material is polar is determined solely by its crystal structure. Only 10 of the 32 point groups are polar. All polar crystals are pyroelectric, so the ten polar crystal classes are sometimes referred to as the pyroelectric classes.
Piezoelectric crystal classes: 1, 2, m, 222, mm2, 4, -4, 422, 4mm, -42m, 3, 32, 3m, 6, -6, 622, 6mm, -62m, 23, -43m
Pyroelectric: 1, 2, m, mm2, 3, 3m, 4, 4mm, 6, 6mm
Two effects which are closely related to pyroelectricity are ferroelectricity and piezoelectricity . Normally materials are very nearly electrically neutral on the macroscopic level. However, the positive and negative charges which make up the material are not necessarily distributed in a symmetric manner. If the sum of charge times distance for all elements of the basic cell does not equal zero the cell will have an electric dipole moment (a vector quantity). The dipole moment per unit volume is defined as the dielectric polarization. If this dipole moment changes with the effect of applied temperature changes, applied electric field, or applied pressure, the material is pyroelectric, ferroelectric, or piezoelectric, respectively.
The ferroelectric effect is exhibited by materials which possess an electric polarization in the absence of an externally applied electric field such that the polarization can be reversed if the electric field is reversed. Since all ferroelectric materials exhibit a spontaneous polarization, all ferroelectric materials are also pyroelectric (but not all pyroelectric materials are ferroelectric).
The piezoelectric effect is exhibited by crystals (such as quartz or ceramic) for which an electric voltage across the material appears when pressure is applied. Similar to pyroelectric effect, the phenomenon is due to the asymmetric structure of the crystals that allows ions to move more easily along one axis than the others. As pressure is applied, each side of the crystal takes on an opposite charge, resulting in a voltage drop across the crystal.
Pyroelectricity should not be confused with thermoelectricity : In a typical demonstration of pyroelectricity, the whole crystal is changed from one temperature to another, and the result is a temporary voltage across the crystal. In a typical demonstration of thermoelectricity, one part of the device is kept at one temperature and the other part at a different temperature, and the result is a permanent voltage across the device as long as there is a temperature difference. Both effects convert temperature change to electrical potential, but the pyroelectric effect converts temperature change over time into electrical potential, while the thermoelectric effect converts temperature change with position into electrical potential.
Although artificial pyroelectric materials have been engineered, the effect was first discovered in minerals such as tourmaline . The pyroelectric effect is also present in bone and tendon . [ 18 ]
The most important example is gallium nitride , a semiconductor. [ 19 ] The large electric fields in this material are detrimental in light emitting diodes (LEDs), but useful for the production of power transistors. [ citation needed ]
Progress has been made in creating artificial pyroelectric materials, usually in the form of a thin film, using gallium nitride ( Ga N ), caesium nitrate ( Cs N O 3 ), polyvinyl fluorides , derivatives of phenylpyridine , and cobalt phthalocyanine . Lithium tantalate ( Li Ta O 3 ) is a crystal exhibiting both piezoelectric and pyroelectric properties, which has been used to create small-scale nuclear fusion (" pyroelectric fusion "). [ 20 ] Recently, pyroelectric and piezoelectric properties have been discovered in doped hafnium oxide ( Hf O 2 ), which is a standard material in CMOS manufacturing. [ 21 ]
Pyroelectric materials, which generate electrical charges in response to temperature fluctuations, have diverse applications due to their ability to convert thermal energy into electricity or detect thermal changes. Key applications include:
Very small changes in temperature can produce a pyroelectric potential. Passive infrared sensors are often designed around pyroelectric materials, as the heat of a human or animal from several feet away is enough to generate a voltage. [ 22 ]
A pyroelectric can be repeatedly heated and cooled (analogously to a heat engine ) to generate usable electrical power. An example of a heat engine is the movement of the pistons in an internal combustion engine like that found in a gasoline powered automobile. [ 25 ] [ 24 ]
One group calculated that a pyroelectric in an Ericsson cycle could reach 50% of Carnot efficiency , [ 26 ] [ 27 ] while a different study found a material that could, in theory, reach 84-92% of Carnot efficiency [ 28 ] (these efficiency values are for the pyroelectric itself, ignoring losses from heating and cooling the substrate , other heat-transfer losses, and all other losses elsewhere in the system)
Possible advantages of pyroelectric generators for generating electricity (as compared to the conventional heat engine plus electrical generator ) include:
Although a few patents have been filed for such a device, [ 32 ] such generators do not appear to be anywhere close to commercialization.
Pyroelectric materials have been used to generate large electric fields necessary to steer deuterium ions in a nuclear fusion process. This is known as pyroelectric fusion .
Despite their promising applications, pyroelectric materials face several challenges that must be addressed for broader adoption. One key limitation is the trade-off between pyroelectric coefficients, dielectric properties, and thermal stability, which affects overall performance and efficiency. Additionally, the efficiency of pyroelectric energy harvesting is highly dependent on rapid temperature fluctuations, making it challenging to achieve consistent power output in practical applications. Integration into flexible and biocompatible designs for wearable and miniaturized devices also remains a significant hurdle. Ongoing research aims to enhance figures of merit (FoMs), optimize phase transitions near morphotropic boundaries, and develop hybrid systems that combine pyroelectricity with other energy-harvesting mechanisms for multifunctional applications. Despite these challenges, the versatility of pyroelectric materials positions them as critical components for sustainable energy solutions and next-generation sensor technologies. [ 30 ] [ 24 ] | https://en.wikipedia.org/wiki/Pyroelectricity |
Pyrogallol is an organic compound with the formula C 6 H 3 (OH) 3 . It is a water-soluble, white solid although samples are typically brownish because of its sensitivity toward oxygen. [ 3 ] It is one of three isomers of benzenetriols .
It is produced in the manner first reported by Scheele in 1786: heating gallic acid to induce decarboxylation. [ 3 ]
Gallic acid is also obtained from tannin . Many alternative routes have been devised. One preparation involves treating para -chlorophenoldisulfonic acid with potassium hydroxide , [ 4 ] a variant on the time-honored route to phenols from sulfonic acids . [ 5 ]
Polyhydroxybenzenes are relatively electron-rich. One manifestation is the easy C-acetylation of pyrogallol. [ 6 ]
It was once used in hair dyeing , dyeing of suturing materials. It also has antiseptic properties.
In alkaline solution, pyrogallol undergoes deprotonation. Such solutions absorb oxygen from the air, turning brown. This conversion can be used to determine the amount of oxygen in a gas sample, notably by the use of the Orsat apparatus . Alkaline solutions of pyrogallol have been used for oxygen absorption in gas analysis.
Pyrogallol was also used as a developing agent in the 19th and early 20th centuries in black-and-white developers. Hydroquinone is more commonly used today. Its use is largely historical except for special purpose applications. It was still used by a few notable photographers including Edward Weston . In those days it had a reputation for erratic and unreliable behavior, due possibly to its propensity for oxidation. It experienced a revival starting in the 1980s due largely to the efforts of experimenters Gordon Hutchings and John Wimberley . Hutchings spent over a decade working on pyrogallol formulas, eventually producing one he named PMK for its main ingredients: pyrogallol, Metol , and Kodalk (the trade name of Kodak for sodium metaborate). This formulation resolved the consistency issues, and Hutchings found that an interaction between the greenish stain given to film by pyro developers and the color sensitivity of modern variable-contrast photographic papers gave the effect of an extreme compensating developer . From 1969 to 1977, Wimberley experimented with the Pyrogallol developing agent. He published his formula for WD2D in 1977 in Petersen's Photographic. PMK and other modern pyro formulations are now used by many black-and-white photographers. The Film Developing Cookbook has examples. [ 7 ]
Another developer mainly based on pyrogallol was formulated by Jay DeFehr . The 510-pyro, [ 8 ] is a concentrate that uses triethanolamine as alkali , and pyrogallol, ascorbic acid , and phenidone as combined developers in a single concentrated stock solution with long shelf life. This developer has both staining and tanning properties and negatives developed with it are immune to the callier effect . It can be used for small and large negative formats.
The Darkroom Cookbook (Alternative Process Photography) has examples. [ 9 ]
Pyrogallol use, e.g. in hair dye formulations, is declining because of concerns about its toxicity. [ 10 ] Its LD 50 (oral, rat) is 300 mg/kg. [ 3 ]
Pure pyrogallol was found to be extremely genotoxic when inserted into cultured cells , but α amylase proteins protect against its toxicity during everyday exposure. [ 11 ] [ 12 ] | https://en.wikipedia.org/wiki/Pyrogallol |
A pyrogallolarene (also calix[4]pyrogallolarene ) is a macrocycle , or a cyclic oligomer , based on the condensation of pyrogallol (1,2,3-trihydroxybenzene) and an aldehyde . Pyrogallolarenes are a type of calixarene , and a subset of resorcinarenes that are substituted with a hydroxyl at the 2-position.
Pyrogallolarenes, like all resorcinarenes, form inclusion complexes with other molecules forming a host–guest complex . Pyrogallolarenes (like resorcinarenes) self-assemble into larger supramolecular structures forming a hydrogen-bonded hexamer. The pyrogallolarene hexamer is unique from those formed from resorcinarene, in that it does not incorporate solvent molecules into the structure. [ 1 ] [ 2 ] Both in the crystalline state and in organic solvents , six molecules will form an assembly with an internal volume of around one cubic nanometer (nanocapsules) and shapes similar to the Archimedean solids . A number of solvent or other molecules may reside in the capsule interior. The pyrogallolarene hexamer is generally more stable than the resorcinarene hexamer, even in polar solvents. [ 3 ]
The pyrogallolarene macrocycle is typically prepared by condensation of pyrogallol and an aldehyde in concentrated acid solution in the presence of an alcohol solvent, usually methanol or ethanol . The reaction conditions can usually be carefully adjusted to precipitate the pure product or the product may be purified by recrystallization.
Pyrogallol[4]arene is simply made by mixing a solvent-free dispersion of isovaleraldehyde with pyrogallol, and a catalytic amount of p -toluenesulfonic acid , in a mortar and pestle . [ 4 ] | https://en.wikipedia.org/wiki/Pyrogallolarenes |
Pyroglutamyl-histidyl-glycine ( pEHG ) is an endogenous tripeptide that acts as a tissue-specific antimitotic and selectively inhibits the proliferation of colon epithelial cells. [ 1 ] Early research indicated that pEHG had anorectic effects in mice and was possibly involved in the pathophysiology of anorexia nervosa . [ 2 ] However, subsequent studies have found that pEHG lacks anorectic effects and does not alter food intake in mice. [ 3 ] [ 4 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pyroglutamyl-histidyl-glycine |
A pyrolant (from Greek pyr , fire) is an energetic material that generates hot flames upon combustion . Pyrolants are metal-based pyrotechnic compositions containing virtually any oxidizer.
The term was originally coined by Kuwahara in 1992, [ 1 ] in a paper on magnesium/Teflon/Viton , to distinguish between compositions that serve as propellants and those yielding hot flames which are not necessarily suitable for propellant purposes.
Thermites constitute a subdivision of pyrolants referring to mixtures containing a narrow range of oxygen-based oxidizers only, [ 2 ] [ 3 ] Hence the term thermite cannot be used interchangeably with "pyrolant".
A similar common term is propellant , which describes either a homogeneous or composite material that generates thrust upon combustion, but which may contain fuels instead of or in addition to the metals contained in thermites .
Pyrolants are generally characterized by high combustion temperatures (> 2000 K) and high amounts of condensed reaction products at equilibrium conditions such as metal oxides , fluorides and soot .
Typical pyrolants find use as pyrotechnic initiators ( Zr / BaCrO 4 [ 4 ] or Zr/ KClO 4 ), illuminating flare ( Mg / NaNO 3 ) [ 5 ] and decoy flare compositions (Mg/ (C 2 F 4 ) n ) [ 6 ] | https://en.wikipedia.org/wiki/Pyrolant |
Pyrolysis is a process involving the separation of covalent bonds in organic matter by thermal decomposition within an inert environment without oxygen. [ 1 ] [ 2 ] [ 3 ]
The word pyrolysis is coined from the Greek -derived elements pyro- (from Ancient Greek πῦρ : pûr - "fire, heat, fever") and lysis ( λύσις : lúsis - "separation, loosening").
Pyrolysis is most commonly used in the treatment of organic materials. It is one of the processes involved in the charring of wood [ 4 ] or pyrolysis of biomass. In general, pyrolysis of organic substances produces volatile products and leaves char , a carbon-rich solid residue. Extreme pyrolysis, which leaves mostly carbon as the residue, is called carbonization . Pyrolysis is considered one of the steps in the processes of gasification or combustion. [ 5 ] [ 6 ] Laypeople often confuse pyrolysis gas with syngas . [ why? ] Pyrolysis gas has a high percentage of heavy tar fractions, which condense at relatively high temperatures, preventing its direct use in gas burners and internal combustion engines, unlike syngas.
The process is used heavily in the chemical industry , for example, to produce ethylene , many forms of carbon , and other chemicals from petroleum, coal, and even wood, or to produce coke from coal . It is used also in the conversion of natural gas (primarily methane ) into hydrogen gas and solid carbon char, recently introduced on an industrial scale. [ 7 ] Aspirational applications of pyrolysis would convert biomass into syngas and biochar , waste plastics back into usable oil, or waste into safely disposable substances.
Pyrolysis is one of the various types of chemical degradation processes that occur at higher temperatures (above the boiling point of water or other solvents). It differs from other processes like combustion and hydrolysis in that it usually does not involve the addition of other reagents such as oxygen ( O 2 , in combustion) or water (in hydrolysis). [ 8 ] Pyrolysis produces solids ( char ), condensable liquids, (light and heavy oils and tar ), and non-condensable gasses. [ 9 ] [ 10 ] [ 11 ] [ 12 ]
Pyrolysis is different from gasification . In the chemical process industry, pyrolysis refers to a partial thermal degradation of carbonaceous materials that takes place in an inert (oxygen free) atmosphere and produces both gases, liquids and solids. The pyrolysis can be extended to full gasification that produces mainly gaseous output, [ 13 ] often with the addition of e.g. water steam to gasify residual carbonic solids, see Steam reforming .
Specific types of pyrolysis include:
Other pyrolysis types come from a different classification that focuses on the pyrolysis operating conditions and heating system used, which have an impact on the yield of the pyrolysis products.
Vapor residence time: 10-100 min
Heating rate: 0.1-1 °C/s
Feedstock size: 5-50 mm
Biochar~35
Gases~35
Vapor residence time: 0.5-20 s
Heating rate: 1.0-10 °C/s
Feedstock size: 1-5 mm
Biochar~25
Gases~35
Vapor residence time: 0.5-5 s
Heating rate: 10-200 °C/s
Feedstock size: <3 mm
Biochar~20
Gases~30
Vapor residence time: <5 s
Heating rate: >1000 °C/s
Feedstock size: <0.2 mm
Biochar~12
Gases~13
Vapor residence time: >15 s
Heating rate: 10-300 °C/s
Vapor residence time: 10-100 min
Heating rate: 0.1-1 °C/s
Biochar~22
Gases~45
Pyrolysis has been used for turning wood into charcoal since ancient times. The ancient Egyptians used the liquid fraction obtained from the pyrolysis of cedar wood, in their embalming process. [ 17 ]
The dry distillation of wood remained the major source of methanol into the early 20th century. [ 18 ] Pyrolysis was instrumental in the discovery of many chemical substances, such as phosphorus from ammonium sodium hydrogen phosphate NH 4 NaHPO 4 in concentrated urine , oxygen from mercuric oxide , and various nitrates . [ citation needed ]
Pyrolysis generally consists in heating the material above its decomposition temperature , breaking chemical bonds in its molecules. The fragments usually become smaller molecules, but may combine to produce residues with larger molecular mass, even amorphous covalent solids . [ citation needed ]
In many settings, some amounts of oxygen, water, or other substances may be present, so that combustion, hydrolysis, or other chemical processes may occur besides pyrolysis proper. Sometimes those chemicals are added intentionally, as in the burning of firewood , in the traditional manufacture of charcoal , and in the steam cracking of crude oil. [ citation needed ]
Conversely, the starting material may be heated in a vacuum or in an inert atmosphere to avoid chemical side reactions (such as combustion or hydrolysis). Pyrolysis in a vacuum also lowers the boiling point of the byproducts, improving their recovery.
When organic matter is heated at increasing temperatures in open containers, the following processes generally occur, in successive or overlapping stages: [ citation needed ]
Because pyrolysis takes place at high temperatures which exceed the autoignition temperature of the produced gases, an explosion risk exists if oxygen is present. To control the temperature of pyrolysis systems careful temperature control is needed and can be accomplished with an open source pyrolysis controller. [ 20 ] Pyrolysis also produces various toxic gases, mainly carbon monoxide . The greatest risk of fire, explosion and release of toxic gases comes when the system is starting up and shutting down, operating intermittently, or during operational upsets. [ 21 ]
Inert gas purging is essential to manage inherent explosion risks. The procedure is not trivial and failure to keep oxygen out has led to accidents. [ 22 ]
Conversion of CBD to THC can be brought about by pyrolysis. [ 23 ] [ 24 ]
Pyrolysis has many applications in food preparation. [ 25 ] Caramelization is the pyrolysis of sugars in food (often after the sugars have been produced by the breakdown of polysaccharides ). The food goes brown and changes flavor. The distinctive flavors are used in many dishes; for instance, caramelized onion is used in French onion soup . [ 26 ] [ 27 ] The temperatures needed for caramelization lie above the boiling point of water. [ 26 ] Frying oil can easily rise above the boiling point. Putting a lid on the frying pan keeps the water in, and some of it re-condenses, keeping the temperature too cool to brown for longer time.
Pyrolysis of food can also be undesirable, as in the charring of burnt food (at temperatures too low for the oxidative combustion of carbon to produce flames and burn the food to ash ).
Carbon and carbon-rich materials have desirable properties but are nonvolatile, even at high temperatures. Consequently, pyrolysis is used to produce many kinds of carbon; these can be used for fuel, as reagents in steelmaking (coke), and as structural materials.
Charcoal is a less smoky fuel than pyrolyzed wood. [ 28 ] Some cities ban, or used to ban, wood fires; when residents only use charcoal (and similarly treated rock coal, called coke ) air pollution is significantly reduced. In cities where people do not generally cook or heat with fires, this is not needed. In the mid-20th century, "smokeless" legislation in Europe required cleaner-burning techniques, such as coke fuel [ 29 ] and smoke-burning incinerators [ 30 ] as an effective measure to reduce air pollution [ 29 ]
The coke-making or "coking" process consists of heating the material in "coking ovens" to very high temperatures (up to 900 °C or 1,700 °F) so that the molecules are broken down into lighter volatile substances, which leave the vessel, and a porous but hard residue that is mostly carbon and inorganic ash. The amount of volatiles varies with the source material, but is typically 25–30% of it by weight. High temperature pyrolysis is used on an industrial scale to convert coal into coke . This is useful in metallurgy , where the higher temperatures are necessary for many processes, such as steelmaking . Volatile by-products of this process are also often useful, including benzene and pyridine . [ 31 ] Coke can also be produced from the solid residue left from petroleum refining.
The original vascular structure of the wood and the pores created by escaping gases combine to produce a light and porous material. By starting with a dense wood-like material, such as nutshells or peach stones , one obtains a form of charcoal with particularly fine pores (and hence a much larger pore surface area), called activated carbon , which is used as an adsorbent for a wide range of chemical substances.
Biochar is the residue of incomplete organic pyrolysis, e.g., from cooking fires. It is a key component of the terra preta soils associated with ancient indigenous communities of the Amazon basin . [ 32 ] Terra preta is much sought by local farmers for its superior fertility and capacity to promote and retain an enhanced suite of beneficial microbiota, compared to the typical red soil of the region. Efforts are underway to recreate these soils through biochar , the solid residue of pyrolysis of various materials, mostly organic waste.
Carbon fibers are filaments of carbon that can be used to make very strong yarns and textiles. Carbon fiber items are often produced by spinning and weaving the desired item from fibers of a suitable polymer , and then pyrolyzing the material at a high temperature (from 1,500–3,000 °C or 2,730–5,430 °F). The first carbon fibers were made from rayon , but polyacrylonitrile has become the most common starting material. For their first workable electric lamps , Joseph Wilson Swan and Thomas Edison used carbon filaments made by pyrolysis of cotton yarns and bamboo splinters, respectively.
Pyrolysis is the reaction used to coat a preformed substrate with a layer of pyrolytic carbon . This is typically done in a fluidized bed reactor heated to 1,000–2,000 °C or 1,830–3,630 °F. Pyrolytic carbon coatings are used in many applications, including artificial heart valves . [ 33 ]
Pyrolysis is the basis of several methods for producing fuel from biomass , i.e. lignocellulosic biomass . [ 34 ] Crops studied as biomass feedstock for pyrolysis include native North American prairie grasses such as switchgrass and bred versions of other grasses such as Miscantheus giganteus . Other sources of organic matter as feedstock for pyrolysis include greenwaste, sawdust, waste wood, leaves, vegetables, nut shells, straw, cotton trash, rice hulls, and orange peels. [ 5 ] Animal waste including poultry litter, dairy manure, and potentially other manures are also under evaluation. Some industrial byproducts are also suitable feedstock including paper sludge, distillers grain, [ 35 ] and sewage sludge. [ 36 ]
In the biomass components, the pyrolysis of hemicellulose happens between 210 and 310 °C. [ 5 ] The pyrolysis of cellulose starts from 300 to 315 °C and ends at 360–380 °C, with a peak at 342–354 °C. [ 5 ] Lignin starts to decompose at about 200 °C and continues until 1000 °C. [ 37 ]
Synthetic diesel fuel by pyrolysis of organic materials is not yet economically competitive. [ 38 ] Higher efficiency is sometimes achieved by flash pyrolysis , in which finely divided feedstock is quickly heated to between 350 and 500 °C (660 and 930 °F) for less than two seconds.
Syngas is usually produced by pyrolysis. [ 25 ]
The low quality of oils produced through pyrolysis can be improved by physical and chemical processes, [ 39 ] which might drive up production costs, but may make sense economically as circumstances change.
There is also the possibility of integrating with other processes such as mechanical biological treatment and anaerobic digestion . [ 40 ] Fast pyrolysis is also investigated for biomass conversion. [ 41 ] Fuel bio-oil can also be produced by hydrous pyrolysis .
Methane pyrolysis [ 42 ] is an industrial process for "turquoise" hydrogen production from methane by removing solid carbon from natural gas . [ 43 ] This one-step process produces hydrogen in high volume at low cost (less than steam reforming with carbon sequestration ). [ 44 ] No greenhouse gas is released. No deep well injection of carbon dioxide is needed. Only water is released when hydrogen is used as the fuel for fuel-cell electric heavy truck transportation, [ 45 ] [ 46 ] [ 47 ] [ 48 ] [ 49 ] gas turbine electric power generation, [ 50 ] [ 51 ] and hydrogen for industrial processes including producing ammonia fertilizer and cement. [ 52 ] [ 53 ] Methane pyrolysis is the process operating around 1065 °C for producing hydrogen from natural gas that allows removal of carbon easily (solid carbon is a byproduct of the process). [ 54 ] [ 55 ] The industrial quality solid carbon can then be sold or landfilled and is not released into the atmosphere, avoiding emission of greenhouse gas (GHG) or ground water pollution from a landfill.
In 2015, a company called Monolith Materials built a pilot plant in Redwood City, CA to study scaling Methane Pyrolysis using renewable power in the process. [ 56 ] A successful pilot project then led to a larger commercial-scale demonstration plant in Hallam, Nebraska in 2016. [ 57 ] As of 2020, this plant is operational and can produce around 14 metric tons of hydrogen per day. In 2021, the US Department of Energy backed Monolith Materials' plans for major expansion with a $1B loan guarantee. [ 58 ] The funding will help produce a plant capable of generating 164 metric tons of hydrogen per day by 2024. Pilots with gas utilities and biogas plants are underway with companies like Modern Hydrogen. [ 59 ] [ 60 ] Volume production is also being evaluated in the BASF "methane pyrolysis at scale" pilot plant, [ 7 ] the chemical engineering team at University of California - Santa Barbara [ 61 ] and in such research laboratories as Karlsruhe Liquid-metal Laboratory (KALLA). [ 62 ] Power for process heat consumed is only one-seventh of the power consumed in the water electrolysis method for producing hydrogen. [ 63 ]
The Australian company Hazer Group was founded in 2010 to commercialise technology originally developed at the University of Western Australia. The company was listed on the ASX in December 2015. It is completing a commercial demonstration project to produce renewable hydrogen and graphite from wastewater and iron ore as a process catalyst use technology created by the University of Western Australia (UWA). The Commercial Demonstration Plant project is an Australian first, and expected to produce around 100 tonnes of fuel-grade hydrogen and 380 tonnes of graphite each year starting in 2023. [ citation needed ] It was scheduled to commence in 2022. "10 December 2021: Hazer Group (ASX: HZR) regret to advise that there has been a delay to the completion of the fabrication of the reactor for the Hazer Commercial Demonstration Project (CDP). This is expected to delay the planned commissioning of the Hazer CDP, with commissioning now expected to occur after our current target date of 1Q 2022." [ 64 ] The Hazer Group has collaboration agreements with Engie for a facility in France in May 2023, [ 65 ] A Memorandum of Understanding with Chubu Electric & Chiyoda in Japan April 2023 [ 66 ] and an agreement with Suncor Energy and FortisBC to develop 2,500 tonnes per Annum Burrard-Hazer Hydrogen Production Plant in Canada April 2022 [ 67 ] [ 68 ]
The American company C-Zero's technology converts natural gas into hydrogen and solid carbon. The hydrogen provides clean, low-cost energy on demand, while the carbon can be permanently sequestered. [ 69 ] C-Zero announced in June 2022 that it closed a $34 million financing round led by SK Gas, a subsidiary of South Korea's second-largest conglomerate, the SK Group. SK Gas was joined by two other new investors, Engie New Ventures and Trafigura, one of the world's largest physical commodities trading companies, in addition to participation from existing investors including Breakthrough Energy Ventures, Eni Next, Mitsubishi Heavy Industries, and AP Ventures. Funding was for C-Zero's first pilot plant, which was expected to be online in Q1 2023. The plant may be capable of producing up to 400 kg of hydrogen per day from natural gas with no CO2 emissions. [ 70 ]
One of the world's largest chemical companies, BASF , has been researching hydrogen pyrolysis for more than 10 years. [ 71 ]
Pyrolysis is used to produce ethylene , the chemical compound produced on the largest scale industrially (>110 million tons/year in 2005). In this process, hydrocarbons from petroleum are heated to around 600 °C (1,112 °F) in the presence of steam; this is called steam cracking . The resulting ethylene is used to make antifreeze ( ethylene glycol ), PVC (via vinyl chloride ), and many other polymers, such as polyethylene and polystyrene. [ 72 ]
The process of metalorganic vapour-phase epitaxy (MOCVD) entails pyrolysis of volatile organometallic compounds to give semiconductors, hard coatings, and other applicable materials. The reactions entail thermal degradation of precursors, with deposition of the inorganic component and release of the hydrocarbons as gaseous waste. Since it is an atom-by-atom deposition, these atoms organize themselves into crystals to form the bulk semiconductor. Raw polycrystalline silicon is produced by the chemical vapor deposition of silane gases:
Gallium arsenide , another semiconductor, forms upon co-pyrolysis of trimethylgallium and arsine .
Pyrolysis can also be used to treat municipal solid waste and plastic waste . [ 6 ] [ 19 ] [ 73 ] The main advantage is the reduction in volume of the waste. In principle, pyrolysis will regenerate the monomers (precursors) to the polymers that are treated, but in practice the process is neither a clean nor an economically competitive source of monomers. [ 74 ] [ 75 ] [ 76 ]
In tire waste management, tire pyrolysis is a well-developed technology. [ 77 ] Other products from car tire pyrolysis include steel wires, carbon black and bitumen. [ 78 ] The area faces legislative, economic, and marketing obstacles. [ 79 ] Oil derived from tire rubber pyrolysis has a high sulfur content, which gives it high potential as a pollutant; consequently it should be desulfurized. [ 80 ] [ 81 ]
Alkaline pyrolysis of sewage sludge at low temperature of 500 °C can enhance H 2 production with in-situ carbon capture. The use of NaOH (sodium hydroxide) has the potential to produce H 2 -rich gas that can be used for fuels cells directly. [ 36 ] [ 82 ]
In early November 2021, the U.S. State of Georgia announced a joint effort with Igneo Technologies to build an $85 million large electronics recycling plant in the Port of Savannah . The project will focus on lower-value, plastics-heavy devices in the waste stream using multiple shredders and furnaces using pyrolysis technology. [ 83 ]
Waste from pyrolysis itself can also be used for useful products. For example, contaminant-rich retentate from liquid-fed pyrolysis of postconsumer multilayer packaging waste can be used as novel building composite materials, which have higher compression strengths (10-12 MPa) than construction bricks and brickworks (7 MPa), as well as 57% lower density, 0.77 g/cm 3 . [ 84 ]
Pyrolysis has also been used for trying to mitigate tobacco waste. One method was done where tobacco waste was separated into two categories TLW (Tobacco Leaf Waste) and TSW (Tobacco Stick Waste). TLW was determined to be any waste from cigarettes and TSW was determined to be any waste from electronic cigarettes. Both TLW and TSW were dried at 80 °C for 24 hours and stored in a desiccator. [ 85 ] Samples were grounded so that the contents were uniform. Tobacco Waste (TW) also contains inorganic (metal) contents, which was determined using an inductively coupled plasma-optical spectrometer. [ 85 ] Thermo-gravimetric analysis was used to thermally degrade four samples (TLW, TSW, glycerol , and guar gum ) and monitored under specific dynamic temperature conditions. [ 85 ] About one gram of both TLW and TSW were used in the pyrolysis tests. During these analysis tests, CO 2 and N 2 were used as atmospheres inside of a tubular reactor that was built using quartz tubing. For both CO 2 and N 2 atmospheres the flow rate was 100 mL min −1 . [ 85 ] External heating was created via a tubular furnace. The pyrogenic products were classified into three phases. The first phase was biochar , a solid residue produced by the reactor at 650 °C. The second phase liquid hydrocarbons were collected by a cold solvent trap and sorted by using chromatography. The third and final phase was analyzed using an online micro GC unit and those pyrolysates were gases.
Two different types of experiments were conducted: one-stepwise pyrolysis and two-stepwise pyrolysis. One-stepwise pyrolysis consisted of a constant heating rate (10 °C min −1 ) from 30 to 720 °C. [ 85 ] In the second step of the two-stepwise pyrolysis test the pyrolysates from the one-stepwise pyrolysis were pyrolyzed in the second heating zone which was controlled isothermally at 650 °C. [ 85 ] The two-stepwise pyrolysis was used to focus primarily on how well CO 2 affects carbon redistribution when adding heat through the second heating zone. [ 85 ]
First noted was the thermolytic behaviors of TLW and TSW in both the CO 2 and N 2 environments. For both TLW and TSW the thermolytic behaviors were identical at less than or equal to 660 °C in the CO 2 and N 2 environments. The differences between the environments start to occur when temperatures increase above 660 °C and the residual mass percentages significantly decrease in the CO 2 environment compared to that in the N 2 environment. [ 85 ] This observation is likely due to the Boudouard reaction, where we see spontaneous gasification happening when temperatures exceed 710 °C. [ 86 ] [ 87 ] Although these observations were seen at temperatures lower than 710 °C it is most likely due to the catalytic capabilities of inorganics in TLW. [ 85 ] It was further investigated by doing ICP-OES measurements and found that a fifth of the residual mass percentage was Ca species. CaCO 3 is used in cigarette papers and filter material, leading to the explanation that degradation of CaCO 3 causes pure CO 2 reacting with CaO in a dynamic equilibrium state. [ 85 ] This being the reason for seeing mass decay between 660 °C and 710 °C. Differences in differential thermogram (DTG) peaks for TLW were compared to TSW. TLW had four distinctive peaks at 87, 195, 265, and 306 °C whereas TSW had two major drop offs at 200 and 306 °C with one spike in between. [ 85 ] The four peaks indicated that TLW contains more diverse types of additives than TSW. [ 85 ] The residual mass percentage between TLW and TSW was further compared, where the residual mass in TSW was less than that of TLW for both CO 2 and N 2 environments concluding that TSW has higher quantities of additives than TLW.
The one-stepwise pyrolysis experiment showed different results for the CO 2 and N 2 environments. During this process the evolution of 5 different notable gases were observed. Hydrogen, Methane, Ethane, Carbon Dioxide, and Ethylene all are produced when the thermolytic rate of TLW began to be retarded at greater than or equal to 500 °C. Thermolytic rate begins at the same temperatures for both the CO 2 and N 2 environment but there is higher concentration of the production of Hydrogen, Ethane, Ethylene, and Methane in the N 2 environment than that in the CO 2 environment. The concentration of CO in the CO 2 environment is significantly greater as temperatures increase past 600 °C and this is due to CO 2 being liberated from CaCO 3 in TLW. [ 85 ] This significant increase in CO concentration is why there is lower concentrations of other gases produced in the CO 2 environment due to a dilution effect. [ 85 ] Since pyrolysis is the re-distribution of carbons in carbon substrates into three pyrogenic products. [ 85 ] The CO 2 environment is going to be more effective because the CO 2 reduction into CO allows for the oxidation of pyrolysates to form CO. In conclusion the CO 2 environment allows a higher yield of gases than oil and biochar. When the same process is done for TSW the trends are almost identical therefore the same explanations can be applied to the pyrolysis of TSW. [ 85 ]
Harmful chemicals were reduced in the CO 2 environment due to CO formation causing tar to be reduced. One-stepwise pyrolysis was not that effective on activating CO 2 on carbon rearrangement due to the high quantities of liquid pyrolysates (tar). Two-stepwise pyrolysis for the CO 2 environment allowed for greater concentrations of gases due to the second heating zone. The second heating zone was at a consistent temperature of 650 °C isothermally. [ 85 ] More reactions between CO 2 and gaseous pyrolysates with longer residence time meant that CO 2 could further convert pyrolysates into CO. [ 85 ] The results showed that the two-stepwise pyrolysis was an effective way to decrease tar content and increase gas concentration by about 10 wt.% for both TLW (64.20 wt.%) and TSW (73.71%). [ 85 ]
Pyrolysis is also used for thermal cleaning , an industrial application to remove organic substances such as polymers , plastics and coatings from parts, products or production components like extruder screws , spinnerets [ 88 ] and static mixers . During the thermal cleaning process, at temperatures from 310 to 540 °C (600 to 1,000 °F), [ 89 ] organic material is converted by pyrolysis and oxidation into volatile organic compounds , hydrocarbons and carbonized gas. [ 90 ] Inorganic elements remain. [ 91 ]
Several types of thermal cleaning systems use pyrolysis:
Pyrolysis is used in the production of chemical compounds, mainly, but not only, in the research laboratory.
The area of boron-hydride clusters started with the study of the pyrolysis of diborane ( B 2 H 6 ) at ca. 200 °C. Products include the clusters pentaborane and decaborane . These pyrolyses involve not only cracking (to give H 2 ), but also re condensation . [ 97 ]
The synthesis of nanoparticles , [ 98 ] zirconia [ 99 ] and oxides [ 100 ] utilizing an ultrasonic nozzle in a process called ultrasonic spray pyrolysis (USP).
Polycyclic aromatic hydrocarbons (PAHs) can be generated from the pyrolysis of different solid waste fractions, [ 12 ] such as hemicellulose , cellulose , lignin , pectin , starch , polyethylene (PE), polystyrene (PS), polyvinyl chloride (PVC), and polyethylene terephthalate (PET). PS, PVC, and lignin generate significant amount of PAHs. Naphthalene is the most abundant PAH among all the polycyclic aromatic hydrocarbons. [ 103 ]
When the temperature is increased from 500 to 900 °C, most PAHs increase. With increasing temperature, the percentage of light PAHs decreases and the percentage of heavy PAHs increases. [ 104 ] [ 105 ]
Thermogravimetric analysis (TGA) is one of the most common techniques to investigate pyrolysis with no limitations of heat and mass transfer. The results can be used to determine mass loss kinetics. [ 5 ] [ 19 ] [ 6 ] [ 37 ] [ 73 ] Activation energies can be calculated using the Kissinger method or peak analysis-least square method (PA-LSM). [ 6 ] [ 37 ]
TGA can couple with Fourier-transform infrared spectroscopy (FTIR) and mass spectrometry . As the temperature increases, the volatiles generated from pyrolysis can be measured. [ 106 ] [ 82 ]
In TGA, the sample is loaded first before the increase of temperature, and the heating rate is low (less than 100 °C min −1 ). Macro-TGA can use gram-scale samples to investigate the effects of pyrolysis with mass and heat transfer. [ 6 ] [ 107 ]
Pyrolysis mass spectrometry (Py-GC-MS) is an important laboratory procedure to determine the structure of compounds. [ 108 ] [ 109 ]
In recent years, machine learning has attracted significant research interest in predicting yields, optimizing parameters, and monitoring pyrolytic processes. [ 110 ] [ 111 ] | https://en.wikipedia.org/wiki/Pyrolysis |
Pyrolysis gasoline or pygas is a naphtha -range product with high aromatics content. [ 1 ] It is a by-product of high temperature naphtha cracking during ethylene and propylene production, a high octane number mixture that contains aromatics from the aromatization reactions, olefins , and paraffins ranging from C5s to C12s. The mixture has its own CAS Number: 68477-58-7.
Pygas has high potential for use as a gasoline blending mixture and/or as a source of aromatics. Currently, pygas is generally used as a gasoline blending mixture due to its high octane number. [ 2 ] Depending on the feedstock used to produce the olefins , steam cracking can produce a benzene-rich liquid by-product called pyrolysis gasoline . Pyrolysis gasoline can be blended with other hydrocarbons as a gasoline additive, or distilled (in BTX process) to separate it into its components, including benzene .
Raw pyrolysis gasoline (RPG, raw pygas) is rich in benzene and is usually subjected to hydrogenation . Hydrogenated pyrolysis gasoline (HPG, hydrogenated pygas) is a common feedstock of BTX plants for benzene and toluene extraction. [ 3 ] | https://en.wikipedia.org/wiki/Pyrolysis_gasoline |
Pyrolysis oil , sometimes also known as biocrude or bio-oil , is a synthetic fuel with few industrial applications and under investigation as substitute for petroleum . It is obtained by heating dried biomass without oxygen in a reactor at a temperature of about 500 °C (900 °F) with subsequent cooling, separation from the aqueous phase and other processes. Pyrolysis oil is a kind of tar and normally contains levels of oxygen too high to be considered a pure hydrocarbon . This high oxygen content results in non-volatility, corrosiveness, partial miscibility with fossil fuels , thermal instability, and a tendency to polymerize when exposed to air. [ 1 ] As such, it is distinctly different from petroleum products. Removing oxygen from bio-oil or nitrogen from algal bio-oil is known as upgrading. [ 2 ]
There are few standards for pyrolysis oil because of few efforts to produce it. One is from ASTM . [ 3 ]
Pyrolysis is a well established technique for decomposition of organic material at elevated temperatures in the absence of oxygen into oil and other constituents. In second-generation biofuel applications—forest and agricultural residues, waste wood, yard waste, and energy crops can be used as feedstock. [ citation needed ]
When wood is heated above 270 °C (518 °F) it begins a process of decomposition called carbonization . In the absence of oxygen, the final product is charcoal . If sufficient oxygen is present, the wood will burn when it reaches a temperature of about 400–500 °C (752–932 °F) leaving wood ash behind. If wood is heated away from air, the moisture is first driven off and until this is complete, the wood temperature remains at about 100–110 °C (212–230 °F). When the wood is dry its temperature rises, and at about 270 °C (518 °F) it begins to spontaneously decompose and generate heat. This is the well known exothermic reaction which takes place in the burning of charcoal. At this stage evolution of carbonization by-products starts. These substances are given off gradually as the temperature rises and at about 450 °C (842 °F) the evolution is complete.
The solid residue, charcoal, is mainly carbon (about 70%), with the remainder being tar-like substances which can be driven off or decomposed completely only by raising the temperature to above about 600 °C to produce Biochar , a high-carbon, fine-grained residue that today is produced through modern pyrolysis processes, which is the direct thermal decomposition of biomass in the absence of oxygen, which prevents combustion , to obtain an array of solid (biochar), liquid—Pyrolysis oil (bio-oil/pyrolysis-oil), and gas ( syngas ) products. The specific yield from the pyrolysis is dependent on process conditions. such as temperature, and can be optimized to produce either energy or biochar. [ 4 ] Temperatures of 400–500 °C (752–932 °F) produce more char , while temperatures above 700 °C (1,292 °F) favor the yield of liquid and gaseous fuel components. [ 5 ] Pyrolysis occurs more quickly at higher temperatures, typically requiring seconds instead of hours. High temperature pyrolysis is also known as gasification , and produces primarily syngas. [ 5 ] Typical yields are 60% bio-oil, 20% biochar, and 20% syngas. By comparison, slow pyrolysis can produce substantially more char (~50%). For typical inputs, the energy required to run a “fast” pyrolyzer is approximately 15% of the energy that it outputs. [ 6 ] Modern pyrolysis plants can use the syngas created by the pyrolysis process and output 3–9 times the amount of energy required to run. [ citation needed ]
Algae may be subjected to high temperatures (~500 °C) and normal atmospheric pressures. The resultant products include oil and nutrients such as nitrogen, phosphorus, and potassium. [ 7 ]
There are numerous papers on the pyrolysis of lignocellulosic biomass. However, very few reports are available for algal bio-oil production via pyrolysis. Miao et al. (2004b) performed fast pyrolysis of Chllorella protothecoides and Microcystis areuginosa at 500 °C, and bio-oil yields of 18% and 24% were obtained, respectively. The bio-oil exhibited a higher carbon and nitrogen content, lower oxygen content than wood bio-oil. When Chlorella protothecoides was cultivated heterotrophically, bio-oil yield increased to 57.9% with a heating value of 41 MJ/kg (Miao et al., 2004a). Recently when microalgae become a hot research topic as the third generation of biofuel, pyrolysis has drawn more attention as a potential conversion method for algal biofuel production. Pan et al. (2010) investigated slow pyrolysis of Nannochloropsis sp. residue with and without the presence of HZSM-5 catalyst and obtained bio-oil rich in aromatic hydrocarbons from catalytic pyrolysis. Algal pyrolytic liquids separate into two phases with the top phase called bio-oil (Campanella et al., 2012; Jena et al., 2011a). The higher heating values (HHV) of algal bio-oil are in the range of 31−36 MJ/kg, generally higher than those of lignocellulosic feedstocks. Pyrolytic bio-oil consists of compounds with lower mean molecular weights and contains more low boiling compounds than bio-oil produced by hydrothermal liquefaction. These properties are similar to those of Illinois shale oil (Jena et al., 2011a; Vardon et al., 2012), which may indicate that pyrolytic bio-oil is suited for replacing petroleum. In addition, the high protein content in microalgae led to a high N content in the bio-oil, resulting in undesirable NOx emissions during combustion and deactivation of acidic catalysts when co-processed in existing 10 crude oil refineries. Algal bio-oil had better qualities in many aspects than those produced from lignocellulosic biomass. For example, algal bio-oil has a higher heating value, a lower oxygen content and a greater than 7 pH value. However, upgrading towards the removal of nitrogen and oxygen in the bio-oil is still necessary before it can be used as drop-in fuels. [ 8 ]
Hydrothermal liquefaction (HTL) is a thermal depolymerization process used to convert wet biomass into an oil [ 9 ] —sometimes referred to as bio-oil or biocrude—under a moderate temperature and high pressure [ 10 ] of 350 °C (662 °F) and 3,000 pounds per square inch (21,000 kPa). The crude-like oil (or bio-oil) has high energy density with a lower heating value of 33.8-36.9 MJ/kg and 5-20 wt% oxygen and renewable chemicals. [ 11 ] [ 12 ]
The HTL process differs from pyrolysis as it can process wet biomass and produce a bio-oil that contains approximately twice the energy density of pyrolysis oil. Pyrolysis is a related process to HTL, but biomass must be processed and dried in order to increase the yield. [ 13 ] The presence of water in pyrolysis drastically increases the heat of vaporization of the organic material, increasing the energy required to decompose the biomass. Typical pyrolysis processes require a water content of less than 40% to suitably convert the biomass to bio-oil. This requires considerable pretreatment of wet biomass such as tropical grasses, which contain a water content as high as 80-85%, and even further treatment for aquatic species, which can contain higher than 90% water content. The properties of the resulting bio-oil are affected by temperature, reaction time, algae species, algae concentration, reaction atmosphere, and catalysts, in subcritical water reaction conditions. [ citation needed ]
Bio-oil typically requires significant additional treatment to render it suitable as a refinery feedstock to replace crude oil derived from petroleum , coal-oil , or coal-tar .
Tar is a black mixture of hydrocarbons and free carbon obtained from a wide variety of organic materials through destructive distillation . [ 14 ] [ 15 ] [ 16 ] Tar can be produced from coal , wood , petroleum , or peat . [ 16 ]
Wood-tar creosote is a colourless to yellowish greasy liquid with a smoky odor, produces a sooty flame when burned, and has a burned taste. It is non-buoyant in water, with a specific gravity of 1.037 to 1.087, retains fluidity at a very low temperature, and boils at 205–225 °C . When transparent, it is in its purest form. Dissolution in water requires up to 200 times the amount of water as the base creosote. The creosote is a combination of natural phenols: primarily guaiacol and creosol (4-methylguaiacol), which will typically constitute 50% of the oil; second in prevalence, cresol and xylenol ; the rest being a combination of monophenols and polyphenols .
Pitch is a name for any of a number of viscoelastic polymers . Pitch can be natural or manufactured, derived from petroleum, coal tar [ 17 ] or plants.
Black liquor and Tall oil is a viscous liquid by-product of wood pulp manufacturing.
Rubber oil is the product of the pyrolysis method for recycling used tires.
Biofuels are synthesized from intermediary products such as syngas using methods that are identical in processes involving conventional feedstocks, first generation and second generation biofuels. The distinguishing feature is the technology involved in producing the intermediary product, rather than the ultimate off-take.
A Biorefinery is a facility that integrates biomass conversion processes and equipment to produce fuels, power, heat, and value-added chemicals from biomass . The biorefinery concept is analogous to today's petroleum refinery , which produce multiple fuels and products from petroleum. [ 18 ]
Bio-oil is a recent contender technique for carbon sequestration. Corn stalks are converted by pyrolysis into bio-oil, which is then pumped underground. [ 24 ]
Currently, bio-oil has few industrial uses. A reported application is in the production of zinc oxide as thermal source. [ 25 ] In this use, the fuel has substituted heavy fuel oils as a biogenic source of heat. [ 26 ] The bio-oil is used in the kiln burners as a direct substitute with little to no change in the operational results. The fuel has higher water and oxygen content which makes a higher volumetric flow for the same heat capacity. | https://en.wikipedia.org/wiki/Pyrolysis_oil |
Pyrolytic chromium carbide coating ( PCC ) is a technology for protection and reworking of rapidly wearing parts of manufacturing equipment working in extreme environmental conditions, using vacuum deposition technology. Coating mechanical parts can help with problems of corrosion , adhering, high-temperature and mechanical wear thus reducing unplanned repairs and loss of production.
The features of PCC coatings are:
Protection of instruments and machinery parts surface exposed to simultaneous impact of corrosion, erosion, sealing, pickup, high temperature, abrasive and mechanical wear. | https://en.wikipedia.org/wiki/Pyrolytic_chromium_carbide_coating |
Pyrometallurgy is a branch of extractive metallurgy . It consists of the thermal treatment of minerals and metallurgical ores and concentrates to bring about physical and chemical transformations in the materials to enable recovery of valuable metals. [ 1 ] Pyrometallurgical treatment may produce products able to be sold such as pure metals, or intermediate compounds or alloys , suitable as feed for further processing. Examples of elements extracted by pyrometallurgical processes include the oxides of less reactive elements like iron , copper , zinc , chromium , tin , and manganese . [ 2 ]
Pyrometallurgical processes are generally grouped into one or more of the following categories: [ 3 ]
Most pyrometallurgical processes require energy input to sustain the temperature at which the process takes place. The energy is usually provided in the form of combustion or from electrical heat. When sufficient material is present in the feed to sustain the process temperature solely by exothermic reaction (i.e. without the addition of fuel or electrical heat), the process is said to be "autogenous". Processing of some sulfide ores exploit the exothermicity of their combustion.
Calcination is thermal decomposition of a material. Examples include decomposition of hydrates such as ferric hydroxide to ferric oxide and water vapor, the decomposition of calcium carbonate to calcium oxide and carbon dioxide as well as iron carbonate to iron oxide:
Calcination processes are carried out in a variety of furnaces, including shaft furnaces , rotary kilns , and fluidized bed reactors .
Roasting consists of thermal gas–solid reactions, which can include oxidation, reduction, chlorination, sulfation, and pyrohydrolysis.
The most common example of roasting is the oxidation of metal sulfide ores. The metal sulfide is heated in the presence of air to a temperature that allows the oxygen in the air to react with the sulfide to form sulfur dioxide gas and solid metal oxide. The solid product from roasting is often called " calcine ". In oxidizing roasting, if the temperature and gas conditions are such that the sulfide feed is completely oxidized, the process is known as " dead roasting ". Sometimes, as in the case of pre-treating reverberatory or electric smelting furnace feed, the roasting process is performed with less than the required amount of oxygen to fully oxidize the feed. In this case, the process is called " partial roasting " because the sulfur is only partially removed. Finally, if the temperature and gas conditions are controlled such that the sulfides in the feed react to form metal sulfates instead of metal oxides, the process is known as " sulfation roasting ". Sometimes, temperature and gas conditions can be maintained such that a mixed sulfide feed (for instance a feed containing both copper sulfide and iron sulfide) reacts such that one metal forms a sulfate and the other forms an oxide, the process is known as " selective roasting " or " selective sulfation ".
Smelting involves thermal reactions in which at least one product is a molten phase.
Metal oxides can then be smelted by heating with coke or charcoal (forms of carbon ), a reducing agent that liberates the oxygen as carbon dioxide leaving a refined mineral. Concern about the production of carbon dioxide is only a recent worry, following the identification of the enhanced greenhouse effect .
Carbonate ores are also smelted with charcoal, but sometimes need to be calcined first. [ citation needed ]
Other materials may need to be added as flux , aiding the melting of the oxide ores and assisting in the formation of a slag , as the flux reacts with impurities, such as silicon compounds. [ citation needed ]
Smelting usually takes place at a temperature above the melting point of the metal, but processes vary considerably according to the ore involved and other matters. [ citation needed ]
Refining is the removal of impurities from materials by a thermal process. This covers a wide range of processes, involving different kinds of furnace or other plant.
The term " refining " can also refer to certain electrolytic processes. Accordingly, some kinds of pyrometallurgical refining are referred to as " fire refining ". | https://en.wikipedia.org/wiki/Pyrometallurgy |
A pyrometer , or radiation thermometer , is a type of remote sensing thermometer used to measure the temperature of distant objects. Various forms of pyrometers have historically existed. In the modern usage, it is a device that from a distance determines the temperature of a surface from the amount of the thermal radiation it emits, a process known as pyrometry , a type of radiometry .
The word pyrometer comes from the Greek word for fire, "πῦρ" ( pyr ), and meter , meaning to measure. The word pyrometer was originally coined to denote a device capable of measuring the temperature of an object by its incandescence , visible light emitted by a body which is at least red-hot. [ 1 ] Infrared thermometers , can also measure the temperature of cooler objects, down to room temperature, by detecting their infrared radiation flux. Modern pyrometers are available for a wide range of wavelengths and are generally called radiation thermometers . [ 2 ]
It is based on the principle that the intensity of light received by the observer depends upon the distance of the observer from the source and the temperature of the distant source. A modern pyrometer has an optical system and a detector. The optical system focuses the thermal radiation onto the detector. The output signal of the detector (temperature T ) is related to the thermal radiation or irradiance j ⋆ {\displaystyle j^{\star }} of the target object through the Stefan–Boltzmann law , the constant of proportionality σ, called the Stefan–Boltzmann constant and the emissivity ε of the object:
This output is used to infer the object's temperature from a distance, with no need for the pyrometer to be in thermal contact with the object; most other thermometers (e.g. thermocouples and resistance temperature detectors (RTDs)) are placed in thermal contact with the object and allowed to reach thermal equilibrium .
Pyrometry of gases presents difficulties. These are most commonly overcome by using thin-filament pyrometry or soot pyrometry. Both techniques involve small solids in contact with hot gases. [ citation needed ]
The term "pyrometer" was coined in the 1730s by Pieter van Musschenbroek , better known as the inventor of the Leyden jar . His device, of which no surviving specimens are known, may be now called a dilatometer because it measured the dilation of a metal rod. [ 3 ]
The earliest example of a pyrometer thought to be in existence is the Hindley Pyrometer held by the London Science Museum , dating from 1752, produced for the Royal collection. The pyrometer was a well known enough instrument that it was described in some detail by the mathematician Euler in 1760. [ 4 ]
Around 1782 potter Josiah Wedgwood invented a different type of pyrometer (or rather a pyrometric device ) to measure the temperature in his kilns, [ 5 ] which first compared the color of clay fired at known temperatures, but was eventually upgraded to measuring the shrinkage of pieces of clay, which depended on kiln temperature (see Wedgwood scale for details). [ 6 ] Later examples used the expansion of a metal bar. [ 7 ]
In the 1860s–1870s brothers William and Werner Siemens developed a platinum resistance thermometer , initially to measure temperature in undersea cables, but then adapted for measuring temperatures in metallurgy up to 1000 °C, hence deserving a name of a pyrometer.
Around 1890 Henry Louis Le Chatelier developed the thermoelectric pyrometer. [ 8 ]
The first disappearing-filament pyrometer was built by L. Holborn and F. Kurlbaum in 1901. [ 9 ] This device had a thin electrical filament between an observer's eye and an incandescent object. The current through the filament was adjusted until it was of the same colour (and hence temperature) as the object, and no longer visible; it was calibrated to allow temperature to be inferred from the current. [ 10 ]
The temperature returned by the vanishing-filament pyrometer and others of its kind, called brightness pyrometers, is dependent on the emissivity of the object. With greater use of brightness pyrometers, it became obvious that problems existed with relying on knowledge of the value of emissivity. Emissivity was found to change, often drastically, with surface roughness, bulk and surface composition, and even the temperature itself. [ 11 ]
To get around these difficulties, the ratio or two-color pyrometer was developed. They rely on the fact that Planck's law , which relates temperature to the intensity of radiation emitted at individual wavelengths, can be solved for temperature if Planck's statement of the intensities at two different wavelengths is divided. This solution assumes that the emissivity is the same at both wavelengths [ 10 ] and cancels out in the division. This is known as the gray-body assumption . Ratio pyrometers are essentially two brightness pyrometers in a single instrument. The operational principles of the ratio pyrometers were developed in the 1920s and 1930s, and they were commercially available in 1939. [ 9 ]
As the ratio pyrometer came into popular use, it was determined that many materials, of which metals are an example, do not have the same emissivity at two wavelengths. [ 12 ] For these materials, the emissivity does not cancel out, and the temperature measurement is in error. The amount of error depends on the emissivities and the wavelengths where the measurements are taken. [ 10 ] Two-color ratio pyrometers cannot measure whether a material's emissivity is wavelength-dependent.
To more accurately measure the temperature of real objects with unknown or changing emissivities, multiwavelength pyrometers were envisioned at the US National Institute of Standards and Technology and described in 1992. [ 9 ] Multiwavelength pyrometers use three or more wavelengths and mathematical manipulation of the results to attempt to achieve accurate temperature measurement even when the emissivity is unknown, changing or differs according to wavelength of measurement. [ 10 ] [ 11 ] [ 12 ]
Pyrometers are suited especially to the measurement of moving objects or any surfaces that cannot be reached or cannot be touched. Contemporary multispectral pyrometers are suitable for measuring high temperatures inside combustion chambers of gas turbine engines with high accuracy. [ 13 ]
Temperature is a fundamental parameter in metallurgical furnace operations. Reliable and continuous measurement of the metal temperature is essential for effective control of the operation. Smelting rates can be maximized, slag can be produced at the optimal temperature, fuel consumption is minimized and refractory life may also be lengthened. Thermocouples were the traditional devices used for this purpose, but they are unsuitable for continuous measurement because they melt and degrade.
Salt bath furnaces operate at temperatures up to 1300 °C and are used for heat treatment . At very high working temperatures with intense heat transfer between the molten salt and the steel being treated, precision is maintained by measuring the temperature of the molten salt. Most errors are caused by slag on the surface, which is cooler than the salt bath. [ 14 ]
The tuyère pyrometer is an optical instrument for temperature measurement through the tuyeres , which are normally used for feeding air or reactants into the bath of the furnace.
A steam boiler may be fitted with a pyrometer to measure the steam temperature in the superheater .
A hot air balloon is equipped with a pyrometer for measuring the temperature at the top of the envelope in order to prevent overheating of the fabric.
Pyrometers may be fitted to experimental gas turbine engines to measure the surface temperature of turbine blades. Such pyrometers can be paired with a tachometer to tie the pyrometer output with the position of an individual turbine blade . Timing combined with a radial position encoder allows engineers to determine the temperature at exact points on blades moving past the probe. | https://en.wikipedia.org/wiki/Pyrometer |
A substance is pyrophoric (from Ancient Greek : πυροφόρος , pyrophoros , 'fire-bearing') if it ignites spontaneously in air at or below 54 °C (129 °F) (for gases) or within 5 minutes after coming into contact with air (for liquids and solids). [ 1 ] Examples are organolithium compounds and triethylborane . Pyrophoric materials are often water-reactive as well and will ignite when they contact water or humid air. They can be handled safely in atmospheres of argon or (with a few exceptions) nitrogen . Class D fire extinguishers are designated for use in fires involving metals but not pyrophoric materials in general. A related concept is hypergolicity , in which two compounds spontaneously ignite when mixed.
The creation of sparks from metals is based on the pyrophoricity of small metal particles, and pyrophoric alloys are made for this purpose. [ 2 ] Practical applications include the sparking mechanisms in lighters and various toys, using ferrocerium ; starting fires without matches, using a firesteel ; the flintlock mechanism in firearms; and spark testing ferrous metals.
Small amounts of pyrophoric liquids are often supplied in a glass bottle with a polytetrafluoroethylene -lined septum . Larger amounts are supplied in metal tanks similar to gas cylinders, designed so a needle can fit through the valve opening. A syringe, carefully dried and flushed of air with an inert gas , is used to extract the liquid from its container.
When working with pyrophoric solids, researchers often employ a sealed glove box flushed with inert gas. Since these specialized glove boxes are expensive and require specialized and frequent maintenance, many pyrophoric solids are sold as solutions, or dispersions in mineral oil or lighter hydrocarbon solvents, so they can be handled in the atmosphere of the laboratory, while still maintaining an oxygen- and moisture-free environment. Mildly pyrophoric solids such as lithium aluminium hydride and sodium hydride can be handled in the air for brief periods of time, but the containers must be flushed with inert gas before the material is returned to the container for storage. | https://en.wikipedia.org/wiki/Pyrophoricity |
Pyrophosphatases , also known as diphosphatases , are acid anhydride hydrolases that act upon diphosphate bonds. [ 1 ]
Examples include:
This EC 3.6 enzyme -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pyrophosphatase |
In chemistry , pyrophosphates are phosphorus oxyanions that contain two phosphorus atoms in a P−O−P linkage. A number of pyrophosphate salts exist, such as disodium pyrophosphate ( Na 2 H 2 P 2 O 7 ) and tetrasodium pyrophosphate ( Na 4 P 2 O 7 ), among others. Often pyrophosphates are called diphosphates . The parent pyrophosphates are derived from partial or complete neutralization of pyrophosphoric acid . The pyrophosphate bond is also sometimes referred to as a phosphoanhydride bond, a naming convention which emphasizes the loss of water that occurs when two phosphates form a new P−O−P bond, and which mirrors the nomenclature for anhydrides of carboxylic acids . Pyrophosphates are found in ATP and other nucleotide triphosphates, which are important in biochemistry. The term pyrophosphate is also the name of esters formed by the condensation of a phosphorylated biological compound with inorganic phosphate , as for dimethylallyl pyrophosphate . This bond is also referred to as a high-energy phosphate bond.
Pyrophosphoric acid is a tetraprotic acid, with four distinct p K a 's: [ 1 ]
The pKa's occur in two distinct ranges because deprotonations occur on separate phosphate groups. For comparison with the p K a s for phosphoric acid are 2.14, 7.20, and 12.37.
At physiological pHs , pyrophosphate exists as a mixture of doubly and singly protonated forms.
Disodium pyrophosphate is prepared by thermal condensation of sodium dihydrogen phosphate or by partial deprotonation of pyrophosphoric acid. [ 2 ]
Pyrophosphates are generally white or colorless. The alkali metal salts are water-soluble. [ 3 ] They are good complexing agents for metal ions (such as calcium and many transition metals) and have many uses in industrial chemistry. Pyrophosphate is the first member of an entire series of polyphosphates . [ 4 ]
The anion P 2 O 4− 7 is abbreviated PP i , standing for i norganic p yro p hosphate . It is formed by the hydrolysis of ATP into AMP in cells .
For example, when a nucleotide is incorporated into a growing DNA or RNA strand by a polymerase , pyrophosphate (PP i ) is released. Pyrophosphorolysis is the reverse of the polymerization reaction in which pyrophosphate reacts with the 3′-nucleosidemonophosphate ( NMP or dNMP), which is removed from the oligonucleotide to release the corresponding triphosphate ( dNTP from DNA, or NTP from RNA).
The pyrophosphate anion has the structure P 2 O 4− 7 , and is an acid anhydride of phosphate . It is unstable in aqueous solution and hydrolyzes into inorganic phosphate:
or in biologists' shorthand notation:
In the absence of enzymic catalysis, hydrolysis reactions of simple polyphosphates such as pyrophosphate, linear triphosphate, ADP , and ATP normally proceed extremely slowly in all but highly acidic media. [ 5 ]
(The reverse of this reaction is a method of preparing pyrophosphates by heating phosphates.)
This hydrolysis to inorganic phosphate effectively renders the cleavage of ATP to AMP and PP i irreversible , and biochemical reactions coupled to this hydrolysis are irreversible as well.
PP i occurs in synovial fluid , blood plasma , and urine at levels sufficient to block calcification and may be a natural inhibitor of hydroxyapatite formation in extracellular fluid (ECF). [ 6 ] Cells may channel intracellular PP i into ECF. [ 7 ] ANK is a nonenzymatic plasma-membrane PP i channel that supports extracellular PP i levels. [ 7 ] Defective function of the membrane PP i channel ANK is associated with low extracellular PP i and elevated intracellular PP i . [ 6 ] Ectonucleotide pyrophosphatase/phosphodiesterase (ENPP) may function to raise extracellular PP i . [ 7 ]
From the standpoint of high energy phosphate accounting, the hydrolysis of ATP to AMP and PP i requires two high-energy phosphates, as to reconstitute AMP into ATP requires two phosphorylation reactions.
The plasma concentration of inorganic pyrophosphate has a reference range of 0.58–3.78 μM (95% prediction interval). [ 8 ]
Isopentenyl pyrophosphate converts to geranyl pyrophosphate , the precursor to tens of thousands of terpeness and terpenoids . [ 9 ] [ 10 ]
Various diphosphates are used as emulsifiers , stabilisers , acidity regulators , raising agents , sequestrants , and water retention agents in food processing. [ 11 ] They are classified in the E number scheme under E450: [ 12 ]
In particular, various formulations of diphosphates are used to stabilize whipped cream . [ 13 ] | https://en.wikipedia.org/wiki/Pyrophosphate |
Pyroprocessing (from Greek Πυρος = fire ) is a process in which materials are subjected to high temperatures (typically over 800 °C) in order to bring about a chemical or physical change. Pyroprocessing includes such terms as ore-roasting , calcination and sintering . Equipment for pyroprocessing includes kilns , electric arc furnaces and reverberatory furnaces .
Cement manufacturing is a very common example of pyroprocessing. The raw material mix ( raw meal ) is fed to a kiln where pyroprocessing takes place. As with most industries, pyroprocessing is the most energy-intensive part of the industrial process.
Argonne National Laboratory pioneered the development of pyrochemical processing, or pyroprocessing, a high-temperature method of recycling reactor waste into fuel, demonstrating it paired with the EBR-II and then proposed commercializing it in the Integral Fast Reactor . The latter was cancelled by the Clinton Administration in 1994. [ 1 ] In 2016, Argonne National Laboratory researchers are developing and refining several pyroprocessing technologies for both light water and fast reactors, with most based on electrorefining rather than conventional wet-chemical/ PUREX , to improve the technologies’ commercial viability by increasing their process efficiency and scalability. [ 2 ]
Animations of the processing technology are also available. [ 3 ] [ 4 ]
Pyroprocessing of nuclear fuel rods, as an alternative to nuclear reprocessing, only attempts to combine separated plutonium with other, such as neptunium, americium, or curium. Theoretically, you could still reuse mixed, pyroprocessed plutonium to generate nuclear power, but it wouldn’t be pure enough for other uses. [ 5 ]
In South Korea due to the historical Section 123 Agreement between ROK and the U.S, [ 6 ] neither enrichment nor PUREX related reprocessing were permitted, with researchers therefore increasingly viewing the "proliferation resistant" pyroprocessing cycle, as the solution for the nation's growing spent fuel inventory, in 2017 forming a collaboration with the U.S and Japan to advance the economics of the process. [ 7 ] [ 8 ] In 2019, proponents of molten salt reactor (MSR) fuel cycles, frequently argue pairing the uncommercialized MSR with the pyroprocessing fuel cycle, as the MSR fuel is already in molten salt form, eliminating two process conversion steps, that of to-and-from metallic fuel, that both the commercially proposed IFR would have required and its antecedent physically demonstrated, when pyroprocessing was fielded in the EBR-II . [ 9 ] | https://en.wikipedia.org/wiki/Pyroprocessing |
Pyrosequencing is a method of DNA sequencing (determining the order of nucleotides in DNA) based on the "sequencing by synthesis" principle, in which the sequencing is performed by detecting the nucleotide incorporated by a DNA polymerase . Pyrosequencing relies on light detection based on a chain reaction when pyrophosphate is released. Hence, the name pyrosequencing.
The principle of pyrosequencing was first described in 1993 [ 1 ] by, Bertil Pettersson, Mathias Uhlen and Pål Nyren by combining the solid phase sequencing method [ 2 ] using streptavidin coated magnetic beads with recombinant DNA polymerase lacking 3´to 5´exonuclease activity (proof-reading) and luminescence detection using the firefly luciferase enzyme. [ 3 ] A mixture of three enzymes ( DNA polymerase , ATP sulfurylase and firefly luciferase ) and a nucleotide ( dNTP ) are added to single stranded DNA to be sequenced and the incorporation of nucleotide is followed by measuring the light emitted. The intensity of the light determines if 0, 1 or more nucleotides have been incorporated, thus showing how many complementary nucleotides are present on the template strand. The nucleotide mixture is removed before the next nucleotide mixture is added. This process is repeated with each of the four nucleotides until the DNA sequence of the single stranded template is determined.
A second solution-based method for pyrosequencing was described in 1998 [ 4 ] by Mostafa Ronaghi , Mathias Uhlen and Pål Nyren . In this alternative method, an additional enzyme apyrase is introduced to remove nucleotides that are not incorporated by the DNA polymerase. This enabled the enzyme mixture including the DNA polymerase , the luciferase and the apyrase to be added at the start and kept throughout the procedure, thus providing a simple set-up suitable for automation. An automated instrument based on this principle was introduced to the market the following year by the company Pyrosequencing.
A third microfluidic variant of the pyrosequencing method was described in 2005 [ 5 ] by Jonathan Rothberg and co-workers at the company 454 Life Sciences . This alternative approach for pyrosequencing was based on the original principle of attaching the DNA to be sequenced to a solid support and they showed that sequencing could be performed in a highly parallel manner using a microfabricated microarray . This allowed for high-throughput DNA sequencing and an automated instrument was introduced to the market. This became the first next generation sequencing instrument starting a new era in genomics research, with rapidly falling prices for DNA sequencing allowing whole genome sequencing at affordable prices.
"Sequencing by synthesis" involves taking a single strand of the DNA to be sequenced and then synthesizing its complementary strand enzymatically. The pyrosequencing method is based on detecting the activity of DNA polymerase (a DNA synthesizing enzyme) with another chemoluminescent enzyme . Essentially, the method allows sequencing a single strand of DNA by synthesizing the complementary strand along it, one base pair at a time, and detecting which base was actually added at each step. The template DNA is immobile, and solutions of A, C, G, and T nucleotides are sequentially added and removed from the reaction. Light is produced only when the nucleotide solution complements the first unpaired base of the template. The sequence of solutions which produce chemiluminescent signals allows the determination of the sequence of the template. [ 6 ]
For the solution-based version of pyrosequencing, the single-strand DNA ( ssDNA ) template is hybridized to a sequencing primer and incubated with the enzymes DNA polymerase , ATP sulfurylase , luciferase and apyrase , and with the substrates adenosine 5´ phosphosulfate (APS) and luciferin .
The process can be represented by the following equations:
where:
Currently, a limitation of the method is that the lengths of individual reads of DNA sequence are in the neighborhood of 300-500 nucleotides, shorter than the 800-1000 obtainable with chain termination methods (e.g. Sanger sequencing). This can make the process of genome assembly more difficult, particularly for sequences containing a large amount of repetitive DNA . Lack of proof-reading activity limits accuracy of this method.
The company Pyrosequencing AB in Uppsala, Sweden was founded with venture capital provided by HealthCap in order to commercialize machinery and reagents for sequencing short stretches of DNA using the pyrosequencing technique. Pyrosequencing AB was listed on the Stockholm Stock Exchange in 1999. It was renamed to Biotage in 2003. [ 7 ] The pyrosequencing business line was acquired by Qiagen in 2008. Pyrosequencing technology was further licensed to 454 Life Sciences . 454 developed an array-based pyrosequencing technology which emerged as a platform for large-scale DNA sequencing , including genome sequencing and metagenomics .
Roche announced the discontinuation of the 454 sequencing platform in 2013. [ 8 ] | https://en.wikipedia.org/wiki/Pyrosequencing |
Pyroshock , also known as pyrotechnic shock , is the dynamic structural shock that occurs when an explosion or impact occurs on a structure. Davie and Bateman describe it as: "Pyroshock is the response of a structure to high frequency (thousands of hertz), high-magnitude stress waves that propagate throughout the structure as a result of an explosive event such as an explosive charge to separate two stages of a multistage rocket." [ 1 ] It is of particular relevance to the defense and aerospace industries in that they utilize many vehicles and/or components that use explosive devices to accomplish mission tasks. Examples include rocket stage separation, missile payload deployment, pilot ejection , automobile airbag inflators, etc. Of significance is the survival and integrity of the equipment after the explosive device has activated so that the vehicle can accomplish its task. There are examples of flight vehicles Boeing-The Aerospace Corp which have crashed after a routine explosive device deployment, the cause of the crash being determined as be a result of a computer failure due to the explosive device. The resultant energies are often high g -force and high frequency which can cause problems for electronic components which have small items with resonant frequencies near those induced by the pyroshock.
The structural environment is very high magnitude for a relatively short duration and presents many difficulties to capture faithfully. From full scale, high fidelity pre-runs using actual flight hardware, to actual in-flight data, to simulating the event in the test laboratory, there are many possible pitfalls: instrumentation, signal conditioning, amplification, filtration, data acquisition, data sampling, and analysis. In order to verify defense and aerospace vehicle integrity, pyroshock testing is performed in a controlled laboratory environment.
Pyroshock testing can be performed using explosive charges or by high energy short duration mechanical impacts. The acceleration time history of a pyroshock approximates decaying sinusoids. Shock response spectrum (SRS) analysis is used to measure the acceleration as a function of frequency and the total energy of the applied shock pulse. The SRS is a curve that represents the response of many damped single degree-of-freedom oscillators to a shock pulse. The damped oscillators are tuned to specific octave or frequency bands.
"Pyroshock testing techniques first evolved in support of the aerospace community." [ 2 ] There are two options for measuring pyroshock. Extreme high frequencies found in pyroshock typically excite the resonant frequency of the accelerometer. As a result, the accelerometer can easily be over ranged or driven nonlinear due to this resonance excitation. In some situations, the frequency environments associated with severe mechanical shock may be so expansive, the acceleration levels so high, or the other directional inputs so severe that successful measurements simply cannot be obtained. There is no single accelerometer design that is optimum for every measurement challenge. A brief summary of each technology is shown below:
PyroShock | https://en.wikipedia.org/wiki/Pyroshock |
A pyrotechnic composition is a substance or mixture of substances designed to produce an effect by heat, light, sound, gas/smoke or a combination of these, as a result of non-detonative self-sustaining exothermic chemical reactions. Pyrotechnic substances do not rely on oxygen from external sources to sustain the reaction.
Basic types of pyrotechnic compositions are:
Some pyrotechnic compositions are used in industry and aerospace for generation of large volumes of gas in gas generators (e.g. in airbags ), in pyrotechnic fasteners , and in other similar applications. They are also used in military pyrotechnics, when production of large amount of noise, light, or infrared radiation is required; e.g. missile decoy flares , flash powders , and stun grenades . A new class of reactive material compositions is now under investigation by military.
Many pyrotechnic compositions – especially involving aluminium and perchlorates – are often highly sensitive to friction, impact, and static electricity . Even as little as 0.1–10 millijoules spark can set off certain mixtures.
Pyrotechnic compositions are usually homogenized mixtures of small particles of fuels and oxidizers. The particles can be grains or flakes. Generally, the higher the surface area of the particles, the higher the reaction rate and burning speed. For some purposes, binders are used to turn the powder into a solid material.
Typical fuels are based on metal or metalloid powders. A flash powder composition may specify multiple different fuels. Some fuels can also serve as binders. Common fuels include:
When metallic fuels are used, the metal particle size is important. A larger surface area to volume ratio leads to a faster reaction; this means that smaller particle sizes produce a faster-burning composition. The shape also matters. Spherical particles, like those produced by atomizing molten metal, are undesirable. Thin and flat particles, like those produced by milling metal foil, have higher reaction surface and therefore are ideal when faster reaction is desired. Using nanoparticles can drastically affect the reaction rates; metastable intermolecular composites exploit this.
A suitable metal fuel may be dangerous on its own, even before it is mixed with an oxidizer. Careful handling is required to avoid the production of pyrophoric metal powders.
Perchlorates , chlorates and nitrates are the most commonly used oxidizers for flash powders. Other possibilities include permanganates , chromates , and some oxides . Generally, the less the oxidizer, the slower the burning and the more light produced. For use at very high temperatures, sulfates can be used as oxidizers in combination with very strongly reducing fuels.
Oxidizers in use include:
Corresponding sodium salts can be substituted for potassium ones. | https://en.wikipedia.org/wiki/Pyrotechnic_composition |
A pyrotechnic heat source , also called heat pellet , is a pyrotechnic device based on a pyrotechnic composition with a suitable igniter . Its role is to produce controlled amount of heat. Pyrotechnic heat sources are usually based on thermite -like (or sometimes delay composition -like) fuel- oxidizer compositions with slow burn rate, high production of heat at desired temperature, and low to zero production of gases.
Pyrotechnic heat sources can be activated by multiple means. Electric match and percussion cap are the most common ones.
Pyrotechnic heat sources are often used for activation of thermal batteries , where they serve to melt the electrolyte. There are two main types of design. One uses a fuze strip (containing barium chromate and powdered zirconium metal in a ceramic paper) along the edge of the heat pellets to initiate burning. The fuze strip is typically fired by an electrical igniter or squib by application of electric current. The second design uses a center hole in the battery stack into which the high-energy electrical igniter fires a mixture of hot gases and incandescent particles. The center-hole design allows much faster activation times (tens of milliseconds) vs. hundreds of milliseconds for the edge-strip design. Battery activation can also be accomplished by a percussion primer , similar to a shotgun shell . It is desired that the pyrotechnic source be gasless. The standard heat source typically consist of mixtures of iron powder and potassium perchlorate in weight ratios of typically 88/12, 86/14, and 84/16. The higher the potassium perchlorate level, the higher the heat output (nominally 200, 259, and 297 calories/gram, respectively). The size and thickness of the iron-perchlorate pellets has little influence on their burn rate, however the effect of density, composition, and particle size have significant effect on the burn rate and can be used for its adjusting for desired heat output profile. [ 1 ] Another composition in use is zirconium with barium chromate . [ 2 ] Another mixture is 46.67 wt.% of titanium , 23.33% of amorphous boron , and about 30% barium chromate . Yet another one is 45 wt.% tungsten , 40.5% barium chromate , 14.5% potassium perchlorate , and 1% vinyl alcohol acetate resin binder. [ 3 ]
Reactions producing intermetallic components, e.g. zirconium with boron , can be used when entirely gasless operation, non- hygroscopic behavior, and independence on environmental pressure are desired. [ 4 ]
Heat paper can be prepared by impregnating paper or a fiberglass tape with a slurry of the mixture of fuel and oxidizer. [ 4 ]
A pyrotechnic heat source can be a direct part of a pyrotechnic composition e.g. in chemical oxygen generators a heat source composition with large surplus of oxidizer is used; the heat produced by burning the composition is used for thermal decomposition of the oxidizer. Relatively cold-burning compositions are used for production of colored smoke or for dispersion of aerosol of e.g. pesticides or CS gas , providing the heat of sublimation of the desired compound.
A phase moderating component of the composition, which forms together with the combustion products a mixture with at least one distinct temperature of phase transition , may be used for stabilizing the burning temperature as a form of phase-change material . [ 5 ] | https://en.wikipedia.org/wiki/Pyrotechnic_heat_source |
In pyrotechnics , a pyrotechnic initiator (also initiator or igniter ) is a device containing a pyrotechnic composition used primarily to ignite other, more difficult-to-ignite materials, such as thermites , gas generators , and solid-fuel rockets . The name is often used also for the compositions themselves.
Pyrotechnic initiators are often controlled electrically (called electro-pyrotechnic initiators ), e.g. using a heated bridgewire or a bridge resistor . They are somewhat similar to blasting caps or other detonators , but they differ in that there is no intention to produce a shock wave . An example of such pyrotechnic initiator is an electric match .
The energetic material used, often called pyrogen , is usually a pyrotechnic composition made of a fuel and oxidizer, where the fuel produces a significant amount of hot particles that cause/promote the ignition of the desired material.
Initiator compositions are similar to flash powders , but they differ in burning speed, as explosion is not intended, and have intentionally high production of hot particles. They also tend to be easier to ignite than thermites , with which they also share similarities.
Common oxidizers used are potassium perchlorate and potassium nitrate . Common fuels used are titanium , titanium(II) hydride , zirconium , zirconium hydride , and boron . The size of the fuel particles is determined to produce hot particles with the required burning time.
More exotic materials can be used, e.g. carboranes . [ 1 ]
For special applications, pyrophoric igniters can be used which burst into flame in contact with air. Triethylborane /TEA-TEB was used as an igniter for the Lockheed SR-71 jet engines, the Rocketdyne F-1 engine on the first stage of the Saturn V, NPO Energomash's RD-180 engine used on the first stage of the Atlas V, and SpaceX's Merlin engine used on the first stage of the Falcon 9.
One of the most common initiators is ZPP , or zirconium – potassium perchlorate – a mixture of metallic zirconium and potassium perchlorate. This mixture is used in the NASA Standard Initiator , [ 2 ] which is used to ignite various pyrotechnic systems, including the NASA standard detonator . [ 3 ] It yields rapid pressure rise, generates little gas, emits hot particles when ignited, is thermally stable, has long shelf life, and is stable under vacuum. It is sensitive to static electricity .
Another common igniter formula is BPN , BKNO3 , or boron – potassium nitrate , a mixture of 25% boron and 75% potassium nitrate by weight. It is used e.g. by NASA . It is thermally stable, stable in vacuum, and its burn rate is independent of pressure.
In comparison with black powder, BPN burns significantly hotter and leaves more of solid residues, therefore black powder is favored for multiple-use systems.
BPN's high temperature makes it suitable for uses where rapid and reproducible initiation is critical, e.g. for airbags , rocket engines, and decoy flares . It is however relatively expensive.
BPN can be also used as an ingredient of solid rocket propellants .
BPN can be ignited by a laser. [ 4 ] A semiconductor laser of at least 0.4 watts output can be used for ignition in vacuum. [ 5 ]
Other mixtures encountered are aluminium - potassium perchlorate and titanium -aluminium-potassium perchlorate. [ 6 ]
Metal hydride -oxidizer mixtures replace the metal with its corresponding hydride . They are generally safer to handle than the corresponding metal-oxidizer compositions. During burning they also release hydrogen , which can act as a secondary fuel. Zirconium hydride, titanium hydride, and boron hydride are commonly used.
ZHPP ( zirconium hydride – potassium perchlorate ) is a variant of ZPP that uses zirconium hydride instead of pure zirconium. It is significantly safer to handle than ZPP. [ 7 ]
THPP (titanium hydride potassium perchlorate) is a mixture of titanium(II) hydride and potassium perchlorate. It is similar to ZHPP. Like ZHPP, it is safer to handle than titanium-potassium perchlorate. [ 7 ]
Formation of an intermetallic compound can be a strongly exothermic reaction, usable as an initiator.
Titanium - boron composition is one of the hottest pyrotechnic reactions in common usage. It is solid-state, gasless. It can be used as a pyrotechnic initiator or for heating confined gas to perform mechanical work. [ 8 ]
Nickel - aluminium laminates can be used as electrically initiated pyrotechnic initiators. NanoFoil is such material, commercially available.
Palladium -clad aluminium wires can be used as a fuse wire, known as Pyrofuze . [ 9 ] The reaction is initiated by heat, typically supplied by electric current pulse. The reaction begins at 600 °C, the melting point of aluminium, and proceeds violently to temperature of 2200–2800 °C. The reaction does not need presence of oxygen, and the wire is consumed. [ 10 ]
Pyrofuze comes as a solid wire of different diameters (from 0.002" to 0.02"), braided wire, ribbon, foil, and granules. Palladium, platinum , or palladium alloyed with 5% ruthenium can be used together with aluminium. [ 11 ] [ 12 ] Pyrofuze bridgewires can be used in squibs and electric matches . Pyrofuze foils can be used for e.g. sealing of various dispensers or fire extinguishing systems. [ 13 ] Palladium-magnesium composition can also be used, but is not commercially available or not at least as common. [ 14 ]
BNCP , ( cis -bis-(5-nitrotetrazolato)tetraminecobalt(III) perchlorate ) is another common initiator material. It is relatively insensitive. It undergoes deflagration to detonation transition in a relatively short distance, allowing its use in detonators . Its burning byproducts are of relatively little harm to environment. [ 15 ] It can be ignited by a laser diode .
Lead azide (Pb(N 3 ) 2 , or PbN 6 ) is occasionally used in pyrotechnic initiators.
Other materials sensitive to heat can be used as well, e.g. HMTD , [ 16 ] tetrazene explosive , lead mononitro-resorcinates, lead dinitro-resorcinates, and lead trinitro-resorcinates. [ 17 ] | https://en.wikipedia.org/wiki/Pyrotechnic_initiator |
Pyrotechnic stars are pellets of pyrotechnic composition which may contain metal powders, salts or other compounds that, when ignited, burn a certain color or make a certain spark effect. They are a part of all projectile -type fireworks . The most common is the aerial shell . When watching this firework, it will launch into the sky, burning a lifting charge . Once the shell has attained proper altitude, due to other mechanisms within the firework, it will ignite the stars.
Stars are either rolled, pumped or cut.
Stars are allowed to dry for several days before being placed into fireworks.
Priming the stars is often necessary because they may be hard to ignite. Priming consists of coating the surface of the star with a more easily ignited substance, such as black powder.
Stars can be used in aerial shells, Roman candles , star mines , and certain bottle rockets . When used in aerial shells, the stars may sometimes be required to be "primed" with an ignition coating, consisting of a pyrotechnic mixture with an ignition temperature lower than that of the star. This is usually done if the star composition does not ignite easily.
This pyrotechnics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pyrotechnic_star |
Pyrotol is a catalyst used in the industrial production of benzene through a process known as pyrolysis . It is a proprietary chromium - alumina catalyst manufactured by Clariant International (formerly known as Sud-Chemie) and licensed exclusively to CB&I Lummus Technology, Inc. It is completely unrelated to the explosive pyrotol .
This catalysis article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pyrotol_catalyst |
In statistics, Pyrrho's lemma is the result that if one adds just one extra variable as a regressor from a suitable set to a linear regression model, one can get any desired outcome in terms of the coefficients (signs and sizes), as well as predictions, the R-squared, the t-statistics, prediction- and confidence-intervals. The argument for the coefficients was advanced by Herman Wold and Lars Juréen [ 1 ] but named, extended to include the other statistics and explained more fully by Theo Dijkstra. [ 2 ] Dijkstra named it after the sceptic philosopher Pyrrho and concludes his article by noting that this lemma provides "some ground for a wide-spread scepticism concerning products of extensive datamining". One can only prove that a model 'works' by testing it on data different from the data that gave it birth. [ 3 ]
The result has been discussed in the context of econometrics . [ 4 ] | https://en.wikipedia.org/wiki/Pyrrho's_lemma |
Pyrrole–imidazole polyamides (PIPs) are a class of polyamides have the ability to bind to minor grooves found in the DNA helix. [ 1 ] [ 2 ] Scientists are experimenting with it as a drug-delivery mode that can switch genes on and off, as well as epigenetic modification in gene therapy . [ 3 ]
This biotechnology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pyrrole–imidazole_polyamides |
Pyrrolizidine alkaloid sequestration by insects is a strategy to facilitate defense and mating. Various species of insects have been known to use molecular compounds from plants for their own defense and even as their pheromones or precursors to their pheromones. A few Lepidoptera have been found to sequester chemicals from plants which they retain throughout their life and some members of Erebidae are examples of this phenomenon. [ 1 ] Starting in the mid-twentieth century researchers investigated various members of Arctiidae, and how these insects sequester pyrrolizidine alkaloids (PAs) during their life stages, and use these chemicals as adults for pheromones or pheromone precursors. PAs are also used by members of the Arctiidae for defense against predators throughout the life of the insect. [ 2 ]
Pyrrolizidine alkaloids are a group of chemicals produced by plants as secondary metabolites , all of which contain a pyrrolizidine nucleus. This nucleus is made up of two pyrrole rings bonded by one carbon and one nitrogen. There are two forms in which PAs can exist and will readily interchange between: a pro-toxic free base form, also called a tertiary amine , or in a non-toxic form of N-oxide . [ 3 ]
Researchers have collected data that strongly suggests that PAs can be registered by taste receptors of predators , acting as a deterrent from being ingested. [ 4 ] Taste receptors are also used by the various moth species that sequester PAs, which often stimulates them to feed. [ 5 ] As of 2005, all of the PA sequestering insects that have been studied have all evolved a system to keep concentrations of the PA pro-toxic form low within the insect's tissues. [ 5 ]
Researchers have found a number of Arctiidae that use PAs for protection and for male pheromones or precursors of the male pheromones, and some studies have found evidence suggesting PAs have behavioral and developmental effects. Estigmene acrea , [ 6 ] Cosmosoma myrodora , [ 7 ] Utetheisa ornatrix , [ 8 ] [ 9 ] Creatonotos gangis and Creatonotos transiens [ 10 ] are all members of the family Arctiidae and found to use PAs for their defense and/or male pheromones. Parsimony suggests that the sequestering of PAs in the larval stage evolved in the subfamily Arctiinae common ancestor. The loss of ability to sequester and use PAs has occurred in a number of species, along with the switch from larval uptake to adult uptake of PAs occurring multiple times within the Arctiinae taxon. [ 5 ]
Members of Arctiidae typically sequester PAs from their diets, but sometimes must specifically ingest fluids excreted by plants that are not a part of their diets. [ 2 ] Sequestered PAs are kept in various tissues and varying concentration which is dependent upon the species. [ 5 ] PAs are found in the cuticle of all studied Arctiidae mentioned here, but some also package these chemicals into their spermatophores as seen in Creatonotos gangis and Creatonotos transiens . [ 10 ] The display of PAs on the exoskeleton is believed to cue predators to the unpalatability of the prey .
Eisner and Eisner looked at the palatability of PA positive and negative U. ornatrix to wolf spiders , Lycosa ceratiola , in both the larval form and adult form. [ 8 ] They found that the pyrrolizidine-positive organisms were typically released unharmed by spiders except in two field circumstances where the larvae were probably envenomated prior to the spider's release and died two days after the attack. All of the PA-negative organisms were eaten by spiders. These findings were in line with prior studies done by Eisner and Meinwald which looked at orb weavers and U. ornatrix , along with spiders being fed beetle larva covered in PAs, which they rejected. [ 4 ] All of these findings support PAs being used for defense against predation.
Studies have further elucidated the defenses and uses of PAs in Arctiidae. One study researched C. myrodora and how PAs protect this species from spider predation among other things. [ 7 ] It found that PAs ingested from fluids excreted by plants aided in defense from predation. All organisms permitted access to PA-containing diets that were fed to spiders were cut loose from the webs. Females that had PA-deprived diets, but were allowed to mate with PA-positive males, were also released from the spider's webs. Further observations showed that male C. myrodora have a pair of pouches where they produce PA-laden filaments, which are typically released over the female prior to copulation as a nuptial gift . Experiments show that the filaments give the females more PAs, explaining why spiders released mated PA-negative females from their webs. Most of the PAs from the males were subsequently transferred to the eggs when deposited. Three clusters of eggs that were laid after copulation with a PA-positive male all tested positive for alkaloids and the one cluster that resulted from a PA-negative male copulation tested negative. By the eggs getting a dose of PAs, the authors suggest that the eggs are being protected from predators such as Coccinellidae beetles. [ 7 ]
Jordan and others’ study found a very interesting effect of the larval ingestion of PAs. Male Estigmene acrea moths that consumed PAs in their diet as larvae produced hydroxydanaidal , a volatile PA compound, and displayed their coremata : a bifid, inflatable male-specific organ, used in dispersing pheromones in the adult stage. Larvae that were fed diets without PAs rarely displayed their coremata and did not produce hydroxydanaidal. E. acrea have been observed in the wild displaying their coremata, an activity which attracts both males and females and is known as lekking . Lekking was described by Willis and Birch in 1982, but larvae raised in the laboratory prior to this study rarely engaged in lekking or corematal displays. Scientists were unsure of why this phenomenon didn't occur in the lab, but laboratory raised larvae were usually reared on commercially available food which lacks PAs. The authors suggest that the PAs are used by the males to attract other moths by releasing the volatile PA hydroxydanaidal into the air. It is suggested in this study that this strategy of mate attraction came about by tapping into the PA affinity already programmed into the moths for feeding, which is further supported by the observation that E. acrea females release their pheromones a little bit later in the evening than the males. [ 6 ]
Similar uses of coremata to attract other moths have been observed in C. gangis and C. transiens along with altered development of coremata when larvae are reared without PAs. [ 10 ] Boppre and Schneider observed adult males of these two species that were not permitted to eat PAs. Their coremata only developed into two, stalk-like projections with very few hairs arising from these stalks. Males that were given plants that produced PAs to feed upon, developed long coremata with four tubes, each longer than the males body, and each tube was highly pubescent. The authors suggest from this observation that there is a basic corematal phenotype, the two stalked coremata, and that PAs are required to form full coremata which is much larger and more elaborate than the basic corematal expression. These observations were further investigated by feeding larvae different amounts of PAs which had a direct correlation to the development of the coremata, which reached a maximum plateau around 2 mg of PAs ingested while in larval form. Similar to Jordan and others’ findings, the males raised on a diet devoid of PAs did not produce hydroxydanaidal. [ 10 ] | https://en.wikipedia.org/wiki/Pyrrolizidine_alkaloid_sequestration |
Pyruvate cycling commonly refers to an intracellular loop of spatial movements and chemical transformations involving pyruvate . Spatial movements occur between mitochondria and cytosol and chemical transformations create various Krebs cycle intermediates. In all variants, pyruvate is imported into the mitochondrion for processing through part of the Krebs cycle. In addition to pyruvate, alpha-ketoglutarate may also be imported. At various points, the intermediate product is exported to the cytosol for additional transformations and then re-imported. Three specific pyruvate cycles are generally considered, [ 1 ] each named for the principal molecule exported from the mitochondrion: malate, citrate, and isocitrate. Other variants may exist, such as dissipative or "futile" pyruvate cycles. [ 2 ] [ 3 ]
This cycle is usually studied in relation to Glucose Stimulated Insulin Secretion ( or GSIS ) and there is thought to be a relationship between the insulin response and NADPH produced from this cycle [ 4 ] [ 5 ] but the specifics are not clear and particular confusion exists about the role of malic enzymes. [ 6 ] [ 7 ] It has been observed in various cell types including islet cells.
The pyruvate-malate cycle was described in liver and kidney preparations as early as 1971. [ 8 ] | https://en.wikipedia.org/wiki/Pyruvate_cycling |
Pyruvate decarboxylation or pyruvate oxidation , also known as the link reaction (or oxidative decarboxylation of pyruvate [ 1 ] ), is the conversion of pyruvate into acetyl-CoA by the enzyme complex pyruvate dehydrogenase complex . [ 2 ] [ 3 ]
The reaction may be simplified as:
Pyruvate oxidation is the step that connects glycolysis and the Krebs cycle . [ 4 ] In glycolysis, a single glucose molecule (6 carbons) is split into 2 pyruvates (3 carbons each). Because of this, the link reaction occurs twice for each glucose molecule to produce a total of 2 acetyl-CoA molecules, which can then enter the Krebs cycle.
Energy-generating ions and molecules , such as amino acids and carbohydrates , enter the Krebs cycle as acetyl coenzyme A and oxidize in the cycle. [ 5 ] The pyruvate dehydrogenase complex (PDC) catalyzes the decarboxylation of pyruvate, resulting in the synthesis of acetyl-CoA, CO 2 , and NADH . In eukaryotes , this enzyme complex regulates pyruvate metabolism , and ensures homeostasis of glucose during absorptive and post-absorptive state metabolism. [ 6 ] As the Krebs cycle occurs in the mitochondrial matrix , the pyruvate generated during glycolysis in the cytosol is transported across the inner mitochondrial membrane by a pyruvate carrier under aerobic conditions. [ citation needed ] | https://en.wikipedia.org/wiki/Pyruvate_decarboxylation |
Pyruvate dehydrogenase complex ( PDC ) is a complex of three enzymes that converts pyruvate into acetyl-CoA by a process called pyruvate decarboxylation . [ 1 ] Acetyl-CoA may then be used in the citric acid cycle to carry out cellular respiration , and this complex links the glycolysis metabolic pathway to the citric acid cycle . Pyruvate decarboxylation is also known as the "pyruvate dehydrogenase reaction" because it also involves the oxidation of pyruvate. [ 2 ] The levels of pyruvate dehydrogenase enzymes play a major role in regulating the rate of carbohydrate metabolism and are strongly stimulated by the evolutionarily ancient hormone insulin . The PDC is opposed by the activity of pyruvate dehydrogenase kinase , and this mechanism plays a pivotal role in regulating rates of carbohydrate and lipid metabolism in many physiological states across taxa, including feeding, starvation, diabetes mellitus , hyperthyroidism , and hibernation .
The multi-enzyme complex is related structurally and functionally to the oxoglutarate dehydrogenase and branched-chain oxo-acid dehydrogenase multi-enzyme complexes. A role for insulin in the regulation of glucose homeostasis, pyruvate dehydrogenase levels, and the generation of AMP-activated protein kinase (AMPK) in the electron transport chain has been evolutionarily conserved across species. A shift in substrate utilization can be induced by conditions such as eating or fasting, and the oxidation of either glucose or fatty acids tends to suppress the use of the other substrate (a phenomenon known as the Randle cycle ). The intake of macronutrients stimulates the secretion and release of insulin and other chemical messengers such as glucagon-like peptide 1 (GLP-1), which act to regulate glucose levels, insulin sensitivity , satiety, and fat balance in the body. In the postprandial period, insulin is produced by the pancreas and serves to activate carbohydrate metabolism and stimulate glucose disposal in order to meet metabolic demands and prevent glucotoxicity . When insulin is unable to efficiently stimulate glucose utilization, the body's tissues become resistant to its hypoglycemic effects, promoting the development of a state of insulin resistance over time. This can happen because of chronic exposure to hyperinsulinemia due to poor diet, sedentary lifestyle, obesity, and other potentially modifiable risk factors . The phenomenon is similar to leptin resistance and can potentially lead to many deleterious health effects stemming from chronically elevated insulin levels, such as excessive fat storage and de novo synthesis , hepatic and peripheral insulin resistance, nonalcoholic fatty liver disease ] (NAFLD), hypertension and dyslipidemia , and decreased resting energy expenditure (REE) caused by impaired diet-induced thermogenesis .
The reaction catalysed by Pyruvate dehydrogenase complex is:
The E1 subunit, called the pyruvate dehydrogenase subunit, is either a homodimer (comprising two “α” chains, e.g. in Escherichia coli ) or a heterotetramer of two different chains (two “α” and two “β” chains). A magnesium ion forms a 4-coordinate complex with three, polar amino acid residues (Asp, Asn, and Tyr) located on the alpha chain, and the thiamine diphosphate (TPP) cofactor directly involved in decarboxylation of the pyruvate . [ 3 ] [ 4 ]
The E2 subunit, or dihydrolipoyl acetyltransferase, for both prokaryotes and eukaryotes, is generally composed of three domains. The N-terminal domain (the lipoyl domain), consists of 1–3 lipoyl groups of approximately 80 amino acids each. The peripheral subunit binding domain (PSBD), serves as a selective binding site for other domains of the E1 and E3 subunits. Finally, the C-terminal (catalytic) domain catalyzes the transfer of acetyl groups and acetyl-CoA synthesis. [ 5 ] In Gammaproteobacteria, 24 copies of E2 form the cubic core of the pyruvate dehydrogenase complex, in which 8 E2 homotrimers are located at the vertices of the cubic core particle.
The E3 subunit, called the Dihydrolipoyl dehydrogenase enzyme, is characterized as a homodimer protein wherein two cysteine residues, engaged in disulfide bonding , and the FAD cofactor in the active site facilitate its main purpose as an oxidizing catalyst. One example of E3 structure, found in Pseudomonas putida , is formed such that each individual homodimer subunit contains two binding domains responsible for FAD binding and NAD binding, as well as a central domain and an interface domain. [ 6 ] [ 7 ]
An auxiliary protein unique to most eukaryotes is the E3 binding protein (E3BP), which serves to bind the E3 subunit to the PDC complex. In the case of human E3BP, hydrophobic proline and leucine residues in the BP interact with the surface recognition site formed by the binding of two identical E3 monomers. [ 8 ]
Initially, pyruvate and thiamine pyrophosphate (TPP or vitamin B 1 ) are bound by pyruvate dehydrogenase subunits. [ 1 ] The thiazolium ring of TPP is in a zwitterionic form, and the anionic C2 carbon performs a nucleophilic attack on the C2 (ketone) carbonyl of pyruvate. The resulting intermediate undergoes decarboxylation to produce an acyl anion equivalent (see cyanohydrin or aldehyde-dithiane umpolung chemistry, as well as benzoin condensation ). This anion attacks S1 of an oxidized lipoate species that is attached to a lysine residue. In a ring-opening S N 2-like mechanism, S2 is displaced as a sulfide or sulfhydryl moiety. Subsequent collapse of the tetrahedral intermediate ejects thiazole, releasing the TPP cofactor and generating a thioacetate on S1 of lipoate. The E1-catalyzed process is the rate-limiting step of the whole pyruvate dehydrogenase complex.
At this point, the lipoate-thioester functionality is translocated into the Dihydrolipoyl transacetylase (E2) active site, [ 1 ] where a transacylation reaction transfers the acetyl from the "swinging arm" of lipoyl to the thiol of coenzyme A . This produces acetyl-CoA , which is released from the enzyme complex and subsequently enters the citric acid cycle . E2 can also be known as lipoamide reductase-transacetylase.
The dihydrolipoate , covalently bound to a lysine residue of the complex, is then transferred to the Dihydrolipoyl dehydrogenase (E3) active site, [ 1 ] where it undergoes a flavin -mediated oxidation, similar in chemistry to e.g. thioredoxin reductase. First, FAD oxidizes dihydrolipoate back to its lipoate (disulfide) resting state, producing FADH 2 . Then, the substrate NAD + oxidizes FADH 2 back to its FAD resting state, producing NADH and H + .
In all organisms, PDC is a large complex composed of multiple copies of the three catalytic subunits E1, E2 and E3. Another common feature of all PDCs is the fact that the subunit E2 forms the core of the complex to which the peripheral subunits E1 and E3 bind. Eukaryotic PDCs contain an additional, non-catalytic subunit in the core termed E3 binding protein (E3BP) (sometimes also "protein X"). In PDCs with a hetero-oligomeric core with multiple copies of E2 and E3BP, E1 exclusively associates with E2, and E3 only binds to E3BP. In contrast, E1 and E3 compete for binding to E2 in bacterial PDCs with a homo-oligomeric E2 core. While the peripheral enzyme E3 is a homodimer in all organisms, the peripheral enzyme E1 is an alpha 2 beta 2 heterotetramerin eukaryotes.
In Gram-negative bacteria, e.g. Escherichia coli , PDC consists of a central cubic core made up from 24 molecules of dihydrolipoyl transacetylase (E2).
Up to 16 homodimers of pyruvate dehydrogenase (E1) and 8 homodimers of dihydrolipoyl dehydrogenase (E3) bind to the 24 peripheral subunit binding domains (PSBDs) of the E2 24-mer.
In Gammaproteobacteria , the specificity of PSBD for binding either E1 or E3 is determined by the oligomeric state of PSBD. In each E2 homotrimer, two of the three PSBDs dimerize. While two E1 homodimers cooperatively bind dimeric PSBD, the remaining, unpaired PSBD specifically interacts with one E3 homodimer. PSBD dimerization thus determines the subunit composition of the pyruvate dehydrogenase complex when fully saturated with the peripheral subunits E1 and E3, which has a stoichiometry of E1:E2:E3 (monomers) = 32:24:16 [ 9 ]
In contrast, in Gram-positive bacteria (e.g. Bacillus stearothermophilus ) and eukaryotes the central PDC core contains 60 E2 molecules arranged into an icosahedron. This E2 subunit “core” coordinates to 30 subunits of E1 and 12 copies of E3.
Eukaryotes also contain 12 copies of an additional core protein, E3 binding protein (E3BP) which bind the E3 subunits to the E2 core. [ 10 ] The exact location of E3BP is not completely clear. Cryo-electron microscopy has established that E3BP binds to each of the icosahedral faces in yeast. [ 11 ] However, it has been suggested that it replaces an equivalent number of E2 molecules in the bovine PDC core.
Up to 60 E1 or E3 molecules can associate with the E2 core from Gram-positive bacteria - binding is mutually exclusive. In eukaryotes E1 is specifically bound by E2, while E3 associates with E3BP. It is thought that up to 30 E1 and 6 E3 enzymes are present, although the exact number of molecules can vary in vivo and often reflects the metabolic requirements of the tissue in question.
Pyruvate dehydrogenase is inhibited when one or more of the three following ratios are increased: ATP / ADP , NADH /NAD + and acetyl-CoA / CoA . [ citation needed ]
In eukaryotes PDC is tightly regulated by its own specific Pyruvate dehydrogenase kinase (PDK) and Pyruvate dehydrogenase phosphatase (PDP), deactivating and activating it respectively. [ 12 ]
Products of the reaction act as allosteric inhibitors of the PDC, because they activate PDK. Substrates in turn inhibit PDK, reactivating PDC.
During starvation , PDK increases in amount in most tissues, including skeletal muscle , via increased gene transcription . Under the same conditions, the amount of PDP decreases. The resulting inhibition of PDC prevents muscle and other tissues from catabolizing glucose and gluconeogenesis precursors. Metabolism shifts toward fat utilization , while muscle protein breakdown to supply gluconeogenesis precursors is minimized, and available glucose is spared for use by the brain . [ citation needed ]
Calcium ions have a role in regulation of PDC in muscle tissue, because it activates PDP, stimulating glycolysis on its release into the cytosol - during muscle contraction . Some products of these transcriptions release H2 into the muscles. This can cause calcium ions to decay over time. [ citation needed ]
In eukaryotic cells the pyruvate decarboxylation occurs inside the mitochondrial matrix, after transport of the substrate, pyruvate, from the cytosol . The transport of pyruvate into the mitochondria is via the transport protein pyruvate translocase. Pyruvate translocase transports pyruvate in a symport fashion with a proton (across the inner mitochondrial membrane), which may be considered to be a form of secondary active transport, but further confirmation/support may be needed for the usage of "secondary active transport" desciptor here (Note: the pyruvate transportation method via the pyruvate translocase appears to be coupled to a proton gradient according to S. Papa et al., 1971, seemingly matching secondary active transport in definition). [ 13 ]
Alternative sources say "transport of pyruvate across the outer mitochondrial membrane appears to be easily accomplished via large non-selective channels such as voltage-dependent anion channels , which enable passive diffusion" and transport across inner mitochondrial membrane is mediated by mitochondrial pyruvate carrier 1 (MPC1) and mitochondrial pyruvate carrier 2 (MPC2). [ 14 ]
Upon entry into the mitochondrial matrix, the pyruvate is decarboxylated, producing acetyl-CoA (and carbon dioxide and NADH). This irreversible reaction traps the acetyl-CoA within the mitochondria (the acetyl-CoA can only be transported out of the mitochondrial matrix under conditions of high oxaloacetate via the citrate shuttle, a TCA intermediate that is normally sparse). The carbon dioxide produced by this reaction is nonpolar and small, and can diffuse out of the mitochondria and out of the cell. [ citation needed ]
In prokaryotes , which have no mitochondria, this reaction is either carried out in the cytosol, or not at all. [ citation needed ]
It was found that pyruvate dehydrogenase enzyme found in the mitochondria of eukaryotic cells closely resembles an enzyme from Geobacillus stearothermophilus , which is a species of gram-positive bacteria . Despite similarities of the pyruvate dehydrogenase complex with gram-positive bacteria, there is little resemblance with those of gram-negative bacteria . Similarities of the quaternary structures between pyruvate dehydrogenase and enzymes in gram-positive bacteria point to a shared evolutionary history which is distinctive from the evolutionary history of corresponding enzymes found in gram-negative bacteria. Through an endosymbiotic event, pyruvate dehydrogenase found in the eukaryotic mitochondria points to ancestral linkages dating back to gram-positive bacteria. [ 15 ]
Pyruvate dehydrogenase complexes share many similarities with branched chain 2-oxoacid dehydrogenase (BCOADH), particularly in their substrate specificity for alpha-keto acids. Specifically, BCOADH catalyzes the degradation of amino acids and these enzymes would have been prevalent during the periods on prehistoric Earth dominated by rich amino acid environments. The E2 subunit from pyruvate dehydrogenase evolved from the E2 gene found in BCOADH while both enzymes contain identical E3 subunits due to the presence of only one E3 gene. Since the E1 subunits have a distinctive specificity for particular substrates, the E1 subunits of pyruvate dehydrogenase and BCOADH vary but share genetic similarities. The gram-positive bacteria and cyanobacteria that would later give rise to mitochondria and chloroplast found in eukaryotic cells retained the E1 subunits that are genetically related to those found in the BCOADH enzymes. [ 16 ] [ 17 ]
Pyruvate dehydrogenase deficiency (PDCD) can result from mutations in any of the enzymes or cofactors used to build the complex. Its primary clinical finding is lactic acidosis . [ 18 ] Such PDCD mutations, leading to subsequent deficiencies in NAD and FAD production, hinder oxidative phosphorylation processes that are key in aerobic respiration. Thus, acetyl-CoA is instead reduced via anaerobic mechanisms into other molecules like lactate, leading to an excess of bodily lactate and associated neurological pathologies. [ 19 ]
While pyruvate dehydrogenase deficiency is rare, there are a variety of different genes when mutated or nonfunctional that can induce this deficiency. First, the E1 subunit of pyruvate dehydrogenase contains four different subunits: two alpha subunits designated as E1-alpha and two beta subunits designated as E1-beta. The PDHA1 gene found in the E1-alpha subunits, when mutated, causes 80% of the cases of pyruvate dehydrogenase deficiency because this mutation abridges the E1-alpha protein. Decreased functional E1 alpha prevents pyruvate dehydrogenase from sufficiently binding to pyruvate, thus reducing the activity of the overall complex. [ 20 ] When the PDHB gene found in the E1 beta subunit of the complex is mutated, this also leads to pyruvate dehydrogenase deficiency. [ 21 ] Likewise, mutations found on other subunits of the complex, like the DLAT gene found on the E2 subunit, the PDHX gene found on the E3 subunit, as well as a mutation on a pyruvate dehydrogenase phosphatase gene, known as PDP1, have all been traced back to pyruvate dehydrogenase deficiency, while their specific contribution to the disease state is unknown. [ 22 ] [ 23 ] [ 24 ]
Glucose
Hexokinase
Glucose 6-phosphate
Glucose-6-phosphate isomerase
Fructose 6-phosphate
Phosphofructokinase-1
Fructose 1,6-bisphosphate
Fructose-bisphosphate aldolase
Dihydroxyacetone phosphate
+
Glyceraldehyde 3-phosphate
Triosephosphate isomerase
2 × Glyceraldehyde 3-phosphate
Glyceraldehyde-3-phosphate dehydrogenase
2 × 1,3-Bisphosphoglycerate
Phosphoglycerate kinase
2 × 3-Phosphoglycerate
Phosphoglycerate mutase
2 × 2-Phosphoglycerate
Phosphopyruvate hydratase ( enolase )
2 × Phosphoenolpyruvate
Pyruvate kinase
2 × Pyruvate | https://en.wikipedia.org/wiki/Pyruvate_dehydrogenase_complex |
Pyruvic acid (CH 3 COCOOH) is the simplest of the alpha-keto acids , with a carboxylic acid and a ketone functional group. Pyruvate , the conjugate base , CH 3 COCOO − , is an intermediate in several metabolic pathways throughout the cell.
Pyruvic acid can be made from glucose through glycolysis , converted back to carbohydrates (such as glucose) via gluconeogenesis , or converted to fatty acids through a reaction with acetyl-CoA . [ 3 ] It can also be used to construct the amino acid alanine and can be converted into ethanol or lactic acid via fermentation .
Pyruvic acid supplies energy to cells through the citric acid cycle (also known as the Krebs cycle) when oxygen is present ( aerobic respiration ), and alternatively ferments to produce lactate when oxygen is lacking. [ 4 ]
In 1834, Théophile-Jules Pelouze distilled tartaric acid and isolated glutaric acid and another unknown organic acid. Jöns Jacob Berzelius characterized this other acid the following year and named pyruvic acid because it was distilled using heat. [ 5 ] [ 6 ] The correct molecular structure was deduced by the 1870s. [ 7 ]
Pyruvic acid is a colorless liquid with a smell similar to that of acetic acid and is miscible with water. [ 8 ] In the laboratory, pyruvic acid may be prepared by heating a mixture of tartaric acid and potassium hydrogen sulfate , [ 9 ] by the oxidation of propylene glycol by a strong oxidizer (e.g., potassium permanganate or bleach ), or by the hydrolysis of acetyl cyanide , formed by reaction of acetyl chloride with potassium cyanide : [ citation needed ]
Pyruvate is an important chemical compound in biochemistry . It is the output of the metabolism of glucose known as glycolysis . [ 10 ] One molecule of glucose breaks down into two molecules of pyruvate, [ 10 ] which are then used to provide further energy, in one of two ways. Pyruvate is converted into acetyl-coenzyme A , which is the main input for a series of reactions known as the Krebs cycle (also known as the citric acid cycle or tricarboxylic acid cycle). Pyruvate is also converted to oxaloacetate by an anaplerotic reaction , which replenishes Krebs cycle intermediates; also, the oxaloacetate is used for gluconeogenesis . [ citation needed ]
These reactions are named after Hans Adolf Krebs , the biochemist awarded the 1953 Nobel Prize for physiology, jointly with Fritz Lipmann , for research into metabolic processes. The cycle is also known as the citric acid cycle or tricarboxylic acid cycle, because citric acid is one of the intermediate compounds formed during the reactions. [ citation needed ]
If insufficient oxygen is available, the acid is broken down anaerobically , creating lactate in animals and ethanol in plants and microorganisms (and in carp [ 11 ] ). Pyruvate from glycolysis is converted by fermentation to lactate using the enzyme lactate dehydrogenase and the coenzyme NADH in lactate fermentation , or to acetaldehyde (with the enzyme pyruvate decarboxylase ) and then to ethanol in alcoholic fermentation . [ citation needed ]
Pyruvate is a key intersection in the network of metabolic pathways . Pyruvate can be converted into carbohydrates via gluconeogenesis , to fatty acids or energy through acetyl-CoA , to the amino acid alanine , and to ethanol . Therefore, it unites several key metabolic processes. [ citation needed ]
In the last step of glycolysis , phosphoenolpyruvate (PEP) is converted to pyruvate by pyruvate kinase . This reaction is strongly exergonic and irreversible; in gluconeogenesis , it takes two enzymes, pyruvate carboxylase and PEP carboxykinase , to catalyze the reverse transformation of pyruvate to PEP. [ citation needed ]
Compound C00074 at KEGG Pathway Database. Enzyme 2.7.1.40 at KEGG Pathway Database. Compound C00022 at KEGG Pathway Database.
Click on genes, proteins and metabolites below to link to respective articles. [ § 1 ]
Pyruvate decarboxylation by the pyruvate dehydrogenase complex produces acetyl-CoA .
Carboxylation by pyruvate carboxylase produces oxaloacetate .
Transamination by alanine transaminase produces alanine .
Reduction by lactate dehydrogenase produces lactate .
Pyruvic acid is an abundant carboxylic acid in secondary organic aerosols . [ 12 ]
Pyruvate is sold as a weight-loss supplement , though credible science has yet to back this claim. A systematic review of six trials found a statistically significant difference in body weight with pyruvate compared to placebo . However, all of the trials had methodological weaknesses and the magnitude of the effect was small. The review also identified adverse events associated with pyruvate such as diarrhea, bloating, gas, and increase in low-density lipoprotein (LDL) cholesterol. The authors concluded that there was insufficient evidence to support the use of pyruvate for weight loss. [ 13 ]
There is also in vitro as well as in vivo evidence in hearts that pyruvate improves metabolism by NADH production stimulation and increases cardiac function. [ 14 ] [ 15 ]
Glucose
Hexokinase
Glucose 6-phosphate
Glucose-6-phosphate isomerase
Fructose 6-phosphate
Phosphofructokinase-1
Fructose 1,6-bisphosphate
Fructose-bisphosphate aldolase
Dihydroxyacetone phosphate
+
Glyceraldehyde 3-phosphate
Triosephosphate isomerase
2 × Glyceraldehyde 3-phosphate
Glyceraldehyde-3-phosphate dehydrogenase
2 × 1,3-Bisphosphoglycerate
Phosphoglycerate kinase
2 × 3-Phosphoglycerate
Phosphoglycerate mutase
2 × 2-Phosphoglycerate
Phosphopyruvate hydratase ( enolase )
2 × Phosphoenolpyruvate
Pyruvate kinase
2 × Pyruvate | https://en.wikipedia.org/wiki/Pyruvic_acid |
The Pyréolophore [ a ] ( French: [piʁeɔlɔfɔʁ] ) was an early internal combustion engine and the first made to power a boat. It was invented in the early 19th century in Chalon-sur-Saône , France, by the Niépce brothers: Nicéphore (who went on to invent photography ) and Claude . In 1807 the brothers ran a prototype internal combustion engine, and on 20 July 1807 a patent was granted by Napoleon Bonaparte after it had successfully powered a boat upstream on the river Saône .
The Pyréolophore ran on what were believed to be "controlled dust explosions " of various experimental fuels. The fuels included mixtures of Lycopodium powder (the spores of Lycopodium, or clubmoss ), finely crushed coal dust, and resin.
Operating independently, in 1807 the Swiss engineer François Isaac de Rivaz built the de Rivaz engine , a hydrogen-powered internal combustion engine. These practical engineering projects may have followed the 1680 theoretical design of an internal combustion engine by the Dutch scientist Christiaan Huygens . The separate, virtually contemporaneous implementations of this design in different modes of transport means that the de Rivaz engine may be correctly described as the first use of an internal combustion engine in an automobile (1808), whilst the Pyréolophore was the first use of an internal combustion engine in a boat (1807).
The Niépce brothers were living in Nice when they conceived of a project to create an engine based on the newly defined principle of hot air expanding during an explosion; their challenge was to find a way to harness the energy released in a series of explosions. [ 1 ]
In 1806 the Niépce brothers had presented a paper on their research to the French National Commission of the Academy of Science ( French : Institute National de Science ). The Commission's verdict was:
The fuel ordinarily used by MM. Niépce is made of lycopodium spores, the combustion of which is the most intense and the easiest; however this material being costly, they replaced it with pulverized coal and mixed it if necessary with a small portion of resin, which works very well, as was proved by many experiments. In Mm. Niépces' machine no portion of heat is dispersed in advance; the moving force is an instantaneous result, and all the fuel effect is used to produce the dilatation that causes the moving force.
In 1807 the brothers constructed and ran a prototype internal combustion engine, and received a patent for ten years from the Bureau of Arts and Trades ( French : Bureau des Arts et Métiers ) in Paris. [ 3 ] The patent was signed by Emperor Napoleon Bonaparte and dated 20 July 1807, [ 1 ] the same year that Swiss engineer François Isaac de Rivaz constructed and ran a hydrogen-powered internal combustion engine. It is not clear how much these practical engineering projects owe to the theoretical designs of 1680 by the Dutch scientist Christiaan Huygens . [ 1 ] [ 3 ]
The Pyréolophore ran on controlled dust explosions of various experimental fuels, including various mixtures of finely crushed coal dust, Lycopodium powder, and resin. De Rivaz, meanwhile, was using a mixture of hydrogen and oxygen. [ 4 ]
To prove the utility of the Pyréolophore to the patent commission, the brothers installed it on a boat, which it powered upstream on the river Saône . The total weight was 9 quintals , about 900 kg (2,000 lb), [ 5 ] fuel consumption was reported as "one hundred and twenty-five grains per minute" (about 125 grains or 8 grams per minute), and the performance was 12–13 explosions per minute. The boat was propelled forward as the Pyréolophore sucked in the river water at the front and then pumped it out toward the rear. [ 1 ] Thus, the Commissioners concluded that "the machine proposed under the name Pyreolophore by Mm. Niépce is ingenious, that it may become very interesting by its physical and economical results, and deserves the approbation of the Commission." [ 1 ]
The operation of the Pyréolophore was first described in a meeting at the Academy of Sciences on 15 December 1806. Lazare Carnot noted that "there was a bright flash of the 'spores of lycopodium' inside their sealed copper machine... The Niépce brothers, by their own device and without using water, have managed to create a commotion (explosion) in a confined space which is so strong that the effects appear to be comparable to a steam engine or fire pump". [ 1 ]
The Pyréolophore operated as a series of discrete burns at a frequency of about 12 per minute to power a boat. Power was delivered in pulses, each pulse forcing water from the engine's tail pipe set under the boat and pointing toward its stern. The boat was pushed forward at each pulse by the reactive force of the ejected mass of water. [ 6 ]
A Pyréolophore engine consists of two principal interconnected chambers: a firelighting chamber and a combustion chamber. There is also a bellows for injecting air, a fuel dispenser, an ignition device, and a submerged exhaust pipe. There is a means of storing energy at each explosion in order to work the mechanism as it prepares itself for the next cycle. [ 6 ]
A mechanically operated bellows injects a jet of air into the first chamber where ignition will take place. Mechanical timing lets fall a measured amount of powder fuel into the jet so that it is blown along and mixed with it. Under the control of the mechanical timing mechanism a smoldering fuse is introduced to this fuel air jet at the precise moment it passes the fuse location. The fuse then withdraws behind a metal plate. The now burning ball of powder and air travels through a wide nozzle into the main combustion chamber where a fast, almost explosive, burn takes place. The whole system now being almost airtight, a build-up of pressure follows. The pressure acts against the column of water in the exhaust pipe and expels it from the system. As the flow of exhaust gas moves into the tail pipe, it moves a loose piston in the combustion chamber which extracts and stores sufficient power to work the machine's timing mechanisms. Energy from this piston is stored by lifting weights attached to a balance wheel. The return of this wheel to its lower position under the pull of the weights governs the timing for the next cycle by operating the bellows, fuel dispenser, the fuse and valves at the correct points in the cycle. The tail pipe, being under the boat, fills with water ready for the next discharge. The fall of the timing piston also expels the exhaust gases via a pipe above the ignition chamber, which is closed off by a valve during the burn part of the cycle. [ 6 ]
On 24 December 1807, the brothers reported to Lazare Carnot that they had developed a new, highly flammable fuel (powder) by mixing one part resin with nine parts of crushed coal dust. [ 1 ] [ 7 ]
In 1817 the brothers achieved another first by using a rudimentary fuel injection system. [ 8 ]
By 1817 there was insufficient progress to attract subsidy and investment, so the ten-year patent expired. Worried about losing control of the engine, Claude traveled first to Paris and then to England in an attempt to further the project. He received the patent consent of King George III on 23 December 1817. [ 9 ] This was not the key to success. Over the next ten years, Claude remained in London, settled in Kew and descended into delirium , whereby he squandered much of the family fortune chasing inappropriate business opportunities for the Pyréolophore. [ 10 ] [ 11 ] Nicéphore, meanwhile, was also occupied with the task of inventing photography . [ 12 ]
In 1824, after the brothers' project had lost momentum, the French physicist Nicolas Léonard Sadi Carnot scientifically established the thermodynamic theory of idealized heat engines. This highlighted the flaw in the design of the Pyréolophore, whereby it needed a compression mechanism to increase the difference between the upper and lower working temperatures and potentially unlock sufficient power and efficiency. [ citation needed ]
To celebrate the bicentenary, the Paris Photographic Institute (Spéos) and the Niépce House Museum produced a 3D animation of the working machine in 2010. Manuel Bonnet and Jean-Louis Bruley of the Maison Nicéphore Nièpce and Hadrien Duhamel of the École Nationale Supérieure d'Arts et Métiers (ENSAM) created the video. [ 6 ] | https://en.wikipedia.org/wiki/Pyréolophore |
The Pythagoras Award , or The Pythagoras Prize , or The Pitagor Prize (named after Pythagoras - a Greek philosopher, mathematician and scientist, Bulgarian : Награда Питагор), established in 2008, is an award given annually to Bulgarian nationals by the Ministry of Science and Education of Bulgaria in recognition for outstanding scientific achievements. [ 1 ]
The Pythagoras Prizes are the most prestigious Scientific awards in Bulgaria, frequently referred as the Bulgarian Nobel Prizes . There are several categories each with its own award. [ 2 ] The Pythagoras statuettes symbolize The Third Eye which provides perception beyond ordinary sight. The statuettes are designed by the famous Bulgarian sculptor Georgi Chapkanov .
1. Pythagoras Grand Prize for Seminal Contribution to Advancement of Science
2. Pythagoras Grand Prize for Principal Investigator of International Synergy Project
3. Pythagoras Grand Prize for Young Scientist
4. Pythagoras Prize for Distinguished Scientist in Natural Science and Engineering
5. Pythagoras Prize for Distinguished Scientist in Physiology and Medicine
6. Pythagoras Prize for Distinguished Scientist in Humanities and Social Science
7. Pythagoras Prize for Bulgarian Scientist abroad for Seminal Contribution to Science
8. Pythagoras Prize for Scientific Team with Successful Commercialization of Scientific Results
9. Pythagoras Prize for Scientific Book
10. Pythagoras Prize for Company with the Largest Endowment to Science
Year 2016 [ 3 ] [ 4 ]
Prof. Elka Bakalova
Prof. Peter Kralchevski
Dr. Antonia Toncheva
Prof. Vladimir Bozhinov
Prof. Irini Doichinova
Prof. Ivaylo Turnev
Prof. Veselin Petrov
Dr. Aleksander Kumurdzhiev
Prof. Nikolay Nihrizov
Dr. Milen Vrabevski
Prof. Tenio Popmintchev
Year 2014
Prof. Plamen Ch. Ivanov
This science awards article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pythagoras_Award |
Pythagorean Triangles is a book on right triangles , the Pythagorean theorem , and Pythagorean triples . It was originally written in the Polish language by Wacław Sierpiński (titled Trójkąty pitagorejskie ), and published in Warsaw in 1954. [ 1 ] [ 2 ] Indian mathematician Ambikeshwar Sharma translated it into English, with some added material from Sierpiński, and published it in the Scripta Mathematica Studies series of Yeshiva University (volume 9 of the series) in 1962. [ 3 ] Dover Books republished the translation in a paperback edition in 2003. [ 4 ] [ 5 ] There is also a Russian translation of the 1954 edition. [ 4 ]
As a brief summary of the book's contents, reviewer Brian Hopkins quotes The Pirates of Penzance : "With many cheerful facts about the square of the hypotenuse." [ 4 ]
The book is divided into 15 chapters (or 16, if one counts the added material as a separate chapter). [ 4 ] [ 6 ] The first three of these define the primitive Pythagorean triples (the ones in which the two sides and hypotenuse have no common factor), derive the standard formula for generating all primitive Pythagorean triples, compute the inradius of Pythagorean triangles, and construct all triangles with sides of length at most 100. [ 6 ]
Chapter 4 considers special classes of Pythagorean triangles, including those with sides in arithmetic progression, nearly-isosceles triangles, and the relation between nearly-isosceles triangles and square triangular numbers . The next two chapters characterize the numbers that can appear in Pythagorean triples, and chapters 7–9 find sets of many Pythagorean triangles with the same side, the same hypotenuse, the same perimeter, the same area, or the same inradius. [ 6 ]
Chapter 10 describes Pythagorean triangles with a side or area that is a square or cube, connecting this problem to Fermat's Last Theorem . After a chapter on Heronian triangles , Chapter 12 returns to this theme, discussing triangles whose hypotenuse and sum of sides are squares. Chapter 13 relates Pythagorean triangles to rational points on a unit circle , Chapter 14 discusses right triangles whose sides are unit fractions rather than integers, and Chapter 15 is about the Euler brick problem, a three-dimensional generalization of Pythagorean triangles, and related problems on integer-sided tetrahedra . [ 4 ] [ 6 ] Sadly, in giving an example of a Heronian tetrahedron found by E. P. Starke, the book repeats a mistake of Starke in calculating its volume. [ 7 ]
The book is aimed at mathematics teachers, in order to inspire their interest in this subject, [ 1 ] but (despite complaining that some of its proofs are overly complicated) reviewer Donald Vestal also suggests this as a "fun book for a mostly general audience". [ 6 ]
Reviewer Brian Hopkins suggests that some of the book's material could be simplified using modular notation and linear algebra, and that the book could benefit by updating it to include a bibliography, index, more than its one illustration, and pointers to recent research in this area such as the Boolean Pythagorean triples problem . Nevertheless, he highly recommends it to mathematics teachers and readers interested in "thorough and elegant proofs". [ 4 ] Reviewer Eric Stephen Barnes rates Sharma's translation as "very readable". [ 3 ] The editors of zbMATH write of the Dover edition that "It is a pleasure to have this classic text available again". [ 5 ] | https://en.wikipedia.org/wiki/Pythagorean_Triangles |
A Pythagorean cup (also known as a Pythagoras cup , greedy cup , cup of justice , anti greedy goblet or Tantalus cup [ citation needed ] ) is a practical joke device in a form of a drinking cup , credited to Pythagoras of Samos . When it is filled beyond a certain point, a siphoning effect causes the cup to drain its entire contents through the base. The cup has been used to make statements about greed .
Pythagorean siphons were originally introduced by Pythagoras in 6th century B.C. [ citation needed ]
A Pythagorean cup looks like a normal drinking cup, except that the bowl has a central column in it, giving it a shape like a bundt pan . The central column of the bowl is positioned directly over the stem of the cup and over a hole at the bottom of the stem. A small open pipe runs from this hole almost to the top of the central column, where there is an open chamber. The chamber is connected by a second pipe to the bottom of the central column, where a hole in the column exposes the pipe to (the contents of) the bowl of the cup. [ 1 ]
When the cup is filled, liquid rises through the second pipe up to the chamber at the top of the central column, following Pascal's principle of communicating vessels . As long as the level of the liquid does not rise beyond the level of the chamber, the cup functions as normal. If the level rises further, however, the liquid spills through the chamber into the first pipe and out of the bottom. Gravity then creates a siphon through the central column, causing the entire content of the cup to be emptied through the hole at the bottom of the stem. [ 2 ]
A Pythagorean siphon is composed of four chambers with one chamber in the center that liquids can escape through. As liquid fills up the four chambers, the pressure acting on the liquids remains constant and so the level of liquid in each chamber remains the same. Once the liquid reaches the top of the Pythagorean siphon it begins to escape through the central chamber as the effects of gravity take hold.
As this process happens, the liquid from both two chambers next to each side of the central chamber forms a seal above the central chamber due to the surface tension of the liquids. Due to this seal, air can then not escape through the central chamber, so the weight of the water in the central chamber forces all the remaining liquid in every chamber to pour out of the Pythagorean siphon.
Most modern American flush toilets operate on the same principle: when the water level in the bowl rises high enough, a siphon is created, emptying the bowl. [ 3 ]
The fabric softener tray in a top-load washing machine operates by utilizing a Pythagorean siphon to distribute fabric softener diluted with water across the clothing in the washing machine. Before starting the washing machine, the user pours fabric softener below the maximum fabric softener line in the loading tray. This line designates the point where if the softener were to be poured above it, then all the fabric softener would resultingly escape the device due to the mechanics of the Pythagorean siphon. As one pours the fabric softener under the line, it does not escape anywhere because it has not begun to escape through the center chamber.
Once the washing machine works to distribute the fabric softener into the tub of the machine, it pours water above the fabric softener loading tray so that the liquid goes over the maximum fill line. This starts the Pythagorean siphon process, as the mixture begins to pour through the central chamber, thus causing a seal from the surface tension of the liquids across all the chambers. The weight of the fabric softener diluted with water has no access to the outside air because of the seal which then causes all the mixture to be poured directly into the washing machine. [ 4 ] [ 5 ] [ 6 ] | https://en.wikipedia.org/wiki/Pythagorean_cup |
A Pythagorean quadruple is a tuple of integers a , b , c , and d , such that a 2 + b 2 + c 2 = d 2 . They are solutions of a Diophantine equation and often only positive integer values are considered. [ 1 ] However, to provide a more complete geometric interpretation, the integer values can be allowed to be negative and zero (thus allowing Pythagorean triples to be included) with the only condition being that d > 0 . In this setting, a Pythagorean quadruple ( a , b , c , d ) defines a cuboid with integer side lengths | a | , | b | , and | c | , whose space diagonal has integer length d ; with this interpretation, Pythagorean quadruples are thus also called Pythagorean boxes . [ 2 ] In this article we will assume, unless otherwise stated, that the values of a Pythagorean quadruple are all positive integers.
A Pythagorean quadruple is called primitive if the greatest common divisor of its entries is 1. Every Pythagorean quadruple is an integer multiple of a primitive quadruple. The set of primitive Pythagorean quadruples for which a is odd can be generated by the formulas a = m 2 + n 2 − p 2 − q 2 , b = 2 ( m q + n p ) , c = 2 ( n q − m p ) , d = m 2 + n 2 + p 2 + q 2 , {\displaystyle {\begin{aligned}a&=m^{2}+n^{2}-p^{2}-q^{2},\\b&=2(mq+np),\\c&=2(nq-mp),\\d&=m^{2}+n^{2}+p^{2}+q^{2},\end{aligned}}} where m , n , p , q are non-negative integers with greatest common divisor 1 such that m + n + p + q is odd. [ 3 ] [ 4 ] [ 1 ] Thus, all primitive Pythagorean quadruples are characterized by the identity ( m 2 + n 2 + p 2 + q 2 ) 2 = ( 2 m q + 2 n p ) 2 + ( 2 n q − 2 m p ) 2 + ( m 2 + n 2 − p 2 − q 2 ) 2 . {\displaystyle (m^{2}+n^{2}+p^{2}+q^{2})^{2}=(2mq+2np)^{2}+(2nq-2mp)^{2}+(m^{2}+n^{2}-p^{2}-q^{2})^{2}.}
All Pythagorean quadruples (including non-primitives, and with repetition, though a , b , and c do not appear in all possible orders) can be generated from two positive integers a and b as follows:
If a and b have different parity , let p be any factor of a 2 + b 2 such that p 2 < a 2 + b 2 . Then c = a 2 + b 2 − p 2 / 2 p and d = a 2 + b 2 + p 2 / 2 p . Note that p = d − c .
A similar method exists [ 5 ] for generating all Pythagorean quadruples for which a and b are both even. Let l = a / 2 and m = b / 2 and let n be a factor of l 2 + m 2 such that n 2 < l 2 + m 2 . Then c = l 2 + m 2 − n 2 / n and d = l 2 + m 2 + n 2 / n . This method generates all Pythagorean quadruples exactly once each when l and m run through all pairs of natural numbers and n runs through all permissible values for each pair.
No such method exists if both a and b are odd, in which case no solutions exist as can be seen by the parametrization in the previous section.
The largest number that always divides the product abcd is 12. [ 6 ] The quadruple with the minimal product is (1, 2, 2, 3).
Given a Pythagorean quadruple ( a , b , c , d ) {\displaystyle (a,b,c,d)} where d 2 = a 2 + b 2 + c 2 {\displaystyle d^{2}=a^{2}+b^{2}+c^{2}} then d {\displaystyle d} can be defined as the norm of the quadruple in that d = a 2 + b 2 + c 2 {\displaystyle d={\sqrt {a^{2}+b^{2}+c^{2}}}} and is analogous to the hypotenuse of a Pythagorean triple.
Every odd positive number other than 1 and 5 can be the norm of a primitive Pythagorean quadruple d 2 = a 2 + b 2 + c 2 {\displaystyle d^{2}=a^{2}+b^{2}+c^{2}} such that a , b , c {\displaystyle a,b,c} are greater than zero and are coprime. [ 7 ] All primitive Pythagorean quadruples with the odd numbers as norms up to 29 except 1 and 5 are given in the table below.
Similar to a Pythagorean triple which generates a distinct right triangle, a Pythagorean quadruple will generate a distinct Heronian triangle . [ 8 ] If a , b , c , d is a Pythagorean quadruple with a 2 + b 2 + c 2 = d 2 {\textstyle a^{2}+b^{2}+c^{2}=d^{2}} it will generate a Heronian triangle with sides x , y , z as follows: x = d 2 − a 2 y = d 2 − b 2 z = d 2 − c 2 {\displaystyle {\begin{aligned}x&=d^{2}-a^{2}\\y&=d^{2}-b^{2}\\z&=d^{2}-c^{2}\end{aligned}}} It will have a semiperimeter s = d 2 {\textstyle s=d^{2}} , an area A = a b c d {\textstyle A=abcd} and an inradius r = a b c / d {\textstyle r=abc/d} .
The exradii will be: r x = b c d / a , r y = a c d / b , r z = a b d / c . {\displaystyle {\begin{aligned}r_{x}&=bcd/a,\\r_{y}&=acd/b,\\r_{z}&=abd/c.\end{aligned}}} The circumradius will be: R = ( d 2 − a 2 ) ( d 2 − b 2 ) ( d 2 − c 2 ) 4 a b c d = a b c d ( 1 / a 2 + 1 / b 2 + 1 / c 2 − 1 / d 2 ) 4 {\displaystyle R={\frac {(d^{2}-a^{2})(d^{2}-b^{2})(d^{2}-c^{2})}{4abcd}}={\frac {abcd(1/a^{2}+1/b^{2}+1/c^{2}-1/d^{2})}{4}}}
The ordered sequence of areas of this class of Heronian triangles can be found at (sequence A367737 in the OEIS ).
A primitive Pythagorean quadruple ( a , b , c , d ) parametrized by ( m , n , p , q ) corresponds to the first column of the matrix representation E ( α ) of conjugation α (⋅) α by the Hurwitz quaternion α = m + ni + pj + qk restricted to the subspace of quaternions spanned by i , j , k , which is given by E ( α ) = ( m 2 + n 2 − p 2 − q 2 2 n p − 2 m q 2 m p + 2 n q 2 m q + 2 n p m 2 − n 2 + p 2 − q 2 2 p q − 2 m n 2 n q − 2 m p 2 m n + 2 p q m 2 − n 2 − p 2 + q 2 ) , {\displaystyle E(\alpha )={\begin{pmatrix}m^{2}+n^{2}-p^{2}-q^{2}&2np-2mq&2mp+2nq\\2mq+2np&m^{2}-n^{2}+p^{2}-q^{2}&2pq-2mn\\2nq-2mp&2mn+2pq&m^{2}-n^{2}-p^{2}+q^{2}\\\end{pmatrix}},} where the columns are pairwise orthogonal and each has norm d . Furthermore, we have that 1 / d E ( α ) belongs to the orthogonal group S O ( 3 , Q ) {\displaystyle SO(3,\mathbb {Q} )} , and, in fact, all 3 × 3 orthogonal matrices with rational coefficients arise in this manner. [ 9 ]
There are 31 primitive Pythagorean quadruples in which all entries are less than 30. | https://en.wikipedia.org/wiki/Pythagorean_quadruple |
The Pythagorean trigonometric identity , also called simply the Pythagorean identity , is an identity expressing the Pythagorean theorem in terms of trigonometric functions . Along with the sum-of-angles formulae , it is one of the basic relations between the sine and cosine functions.
The identity is
As usual, sin 2 θ {\displaystyle \sin ^{2}\theta } means ( sin θ ) 2 {\textstyle (\sin \theta )^{2}} .
Any similar triangles have the property that if we select the same angle in all of them, the ratio of the two sides defining the angle is the same regardless of which similar triangle is selected, regardless of its actual size: the ratios depend upon the three angles, not the lengths of the sides. Thus for either of the similar right triangles in the figure, the ratio of its horizontal side to its hypotenuse is the same, namely cos θ .
The elementary definitions of the sine and cosine functions in terms of the sides of a right triangle are:
sin θ = o p p o s i t e h y p o t e n u s e = b c cos θ = a d j a c e n t h y p o t e n u s e = a c {\displaystyle {\begin{alignedat}{3}\sin \theta &={\frac {\mathrm {opposite} }{\mathrm {hypotenuse} }}={\frac {b}{c}}\\\cos \theta &={\frac {\mathrm {adjacent} }{\mathrm {hypotenuse} }}={\frac {a}{c}}\end{alignedat}}}
The Pythagorean identity follows by squaring both definitions above, and adding; the left-hand side of the identity then becomes
o p p o s i t e 2 + a d j a c e n t 2 h y p o t e n u s e 2 {\displaystyle {\frac {\mathrm {opposite} ^{2}+\mathrm {adjacent} ^{2}}{\mathrm {hypotenuse} ^{2}}}}
which by the Pythagorean theorem is equal to 1. This definition is valid for all angles, due to the definition of defining x = cos θ and y sin θ for the unit circle and thus x = c cos θ and y = c sin θ for a circle of radius c and reflecting our triangle in the y -axis and setting a = x and b = y .
Alternatively, the identities found at Trigonometric symmetry, shifts, and periodicity may be employed. By the periodicity identities we can say if the formula is true for −π < θ ≤ π then it is true for all real θ . Next we prove the identity in the range π / 2 < θ ≤ π . To do this we let t = θ − π / 2 , t will now be in the range 0 < t ≤ π/2 . We can then make use of squared versions of some basic shift identities (squaring conveniently removes the minus signs):
sin 2 θ + cos 2 θ = sin 2 ( t + 1 2 π ) + cos 2 ( t + 1 2 π ) = cos 2 t + sin 2 t = 1. {\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =\sin ^{2}\left(t+{\tfrac {1}{2}}\pi \right)+\cos ^{2}\left(t+{\tfrac {1}{2}}\pi \right)=\cos ^{2}t+\sin ^{2}t=1.}
Finally, it remains is to prove the formula for −π < θ < 0 ; this can be done by squaring the symmetry identities to get
sin 2 θ = sin 2 ( − θ ) and cos 2 θ = cos 2 ( − θ ) . {\displaystyle \sin ^{2}\theta =\sin ^{2}(-\theta ){\text{ and }}\cos ^{2}\theta =\cos ^{2}(-\theta ).}
The two identities 1 + tan 2 θ = sec 2 θ 1 + cot 2 θ = csc 2 θ {\displaystyle {\begin{aligned}1+\tan ^{2}\theta &=\sec ^{2}\theta \\1+\cot ^{2}\theta &=\csc ^{2}\theta \end{aligned}}} are also called Pythagorean trigonometric identities. [ 1 ] If one leg of a right triangle has length 1, then the tangent of the angle adjacent to that leg is the length of the other leg, and the secant of the angle is the length of the hypotenuse.
tan θ = b a , sec θ = c a . {\displaystyle {\begin{aligned}\tan \theta &={\frac {b}{a}}\,,\\\sec \theta &={\frac {c}{a}}\,.\end{aligned}}}
In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity involving the cotangent and the cosecant also follows from the Pythagorean theorem.
The following table gives the identities with the factor or divisor that relates them to the main identity.
The unit circle centered at the origin in the Euclidean plane is defined by the equation: [ 2 ]
Given an angle θ , there is a unique point P on the unit circle at an anticlockwise angle of θ from the x -axis, and the x - and y -coordinates of P are: [ 3 ]
x = cos θ and y = sin θ . {\displaystyle x=\cos \theta \ {\text{ and }}\ y=\sin \theta .}
Consequently, from the equation for the unit circle, cos 2 θ + sin 2 θ = 1 , {\displaystyle \cos ^{2}\theta +\sin ^{2}\theta =1,} the Pythagorean identity.
In the figure, the point P has a negative x -coordinate, and is appropriately given by x = cos θ , which is a negative number: cos θ = −cos(π − θ ) . Point P has a positive y -coordinate, and sin θ = sin(π − θ ) > 0 . As θ increases from zero to the full circle θ = 2π , the sine and cosine change signs in the various quadrants to keep x and y with the correct signs. The figure shows how the sign of the sine function varies as the angle changes quadrant.
Because the x - and y -axes are perpendicular, this Pythagorean identity is equivalent to the Pythagorean theorem for triangles with hypotenuse of length 1 (which is in turn equivalent to the full Pythagorean theorem by applying a similar-triangles argument). See Unit circle for a short explanation.
The trigonometric functions may also be defined using power series , namely for x (an angle measured in radians ): [ 4 ] [ 5 ]
sin x = ∑ n = 0 ∞ ( − 1 ) n ( 2 n + 1 ) ! x 2 n + 1 , cos x = ∑ n = 0 ∞ ( − 1 ) n ( 2 n ) ! x 2 n . {\displaystyle {\begin{aligned}\sin x&=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1},\\\cos x&=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n)!}}x^{2n}.\end{aligned}}}
Using the multiplication formula for power series at Multiplication and division of power series (suitably modified to account for the form of the series here) we obtain
sin 2 x = ∑ i = 0 ∞ ∑ j = 0 ∞ ( − 1 ) i ( 2 i + 1 ) ! ( − 1 ) j ( 2 j + 1 ) ! x ( 2 i + 1 ) + ( 2 j + 1 ) = ∑ n = 1 ∞ ( ∑ i = 0 n − 1 ( − 1 ) n − 1 ( 2 i + 1 ) ! ( 2 ( n − i − 1 ) + 1 ) ! ) x 2 n = ∑ n = 1 ∞ ( ∑ i = 0 n − 1 ( 2 n 2 i + 1 ) ) ( − 1 ) n − 1 ( 2 n ) ! x 2 n , cos 2 x = ∑ i = 0 ∞ ∑ j = 0 ∞ ( − 1 ) i ( 2 i ) ! ( − 1 ) j ( 2 j ) ! x ( 2 i ) + ( 2 j ) = ∑ n = 0 ∞ ( ∑ i = 0 n ( − 1 ) n ( 2 i ) ! ( 2 ( n − i ) ) ! ) x 2 n = ∑ n = 0 ∞ ( ∑ i = 0 n ( 2 n 2 i ) ) ( − 1 ) n ( 2 n ) ! x 2 n . {\displaystyle {\begin{aligned}\sin ^{2}x&=\sum _{i=0}^{\infty }\sum _{j=0}^{\infty }{\frac {(-1)^{i}}{(2i+1)!}}{\frac {(-1)^{j}}{(2j+1)!}}x^{(2i+1)+(2j+1)}\\&=\sum _{n=1}^{\infty }\left(\sum _{i=0}^{n-1}{\frac {(-1)^{n-1}}{(2i+1)!(2(n-i-1)+1)!}}\right)x^{2n}\\&=\sum _{n=1}^{\infty }\left(\sum _{i=0}^{n-1}{2n \choose 2i+1}\right){\frac {(-1)^{n-1}}{(2n)!}}x^{2n},\\\cos ^{2}x&=\sum _{i=0}^{\infty }\sum _{j=0}^{\infty }{\frac {(-1)^{i}}{(2i)!}}{\frac {(-1)^{j}}{(2j)!}}x^{(2i)+(2j)}\\&=\sum _{n=0}^{\infty }\left(\sum _{i=0}^{n}{\frac {(-1)^{n}}{(2i)!(2(n-i))!}}\right)x^{2n}\\&=\sum _{n=0}^{\infty }\left(\sum _{i=0}^{n}{2n \choose 2i}\right){\frac {(-1)^{n}}{(2n)!}}x^{2n}.\end{aligned}}}
In the expression for sin 2 , n must be at least 1, while in the expression for cos 2 , the constant term is equal to 1. The remaining terms of their sum are (with common factors removed)
∑ i = 0 n ( 2 n 2 i ) − ∑ i = 0 n − 1 ( 2 n 2 i + 1 ) = ∑ j = 0 2 n ( − 1 ) j ( 2 n j ) = ( 1 − 1 ) 2 n = 0 {\displaystyle \sum _{i=0}^{n}{2n \choose 2i}-\sum _{i=0}^{n-1}{2n \choose 2i+1}=\sum _{j=0}^{2n}(-1)^{j}{2n \choose j}=(1-1)^{2n}=0}
by the binomial theorem . Consequently, sin 2 x + cos 2 x = 1 , {\displaystyle \sin ^{2}x+\cos ^{2}x=1,} which is the Pythagorean trigonometric identity.
When the trigonometric functions are defined in this way, the identity in combination with the Pythagorean theorem shows that these power series parameterize the unit circle, which we used in the previous section. This definition constructs the sine and cosine functions in a rigorous fashion and proves that they are differentiable , so that in fact it subsumes the previous two.
Sine and cosine can be defined as the two solutions to the differential equation : [ 6 ]
y ″ + y = 0 {\displaystyle y''+y=0}
satisfying respectively y (0) = 0 , y ′ (0) = 1 and y (0) = 1 , y ′ (0) = 0 . It follows from the theory of ordinary differential equations that the first solution, sine, has the second, cosine, as its derivative , and it follows from this that the derivative of cosine is the negative of the sine. The identity is equivalent to the assertion that the function
z = sin 2 x + cos 2 x {\displaystyle z=\sin ^{2}x+\cos ^{2}x}
is constant and equal to 1. Differentiating using the chain rule gives:
d d x z = 2 sin x cos x + 2 cos x ( − sin x ) = 0 , {\displaystyle {\frac {d}{dx}}z=2\sin x\cos x+2\cos x(-\sin x)=0,} so z is constant. A calculation confirms that z (0) = 1 , and z is a constant so z = 1 for all x , so the Pythagorean identity is established.
A similar proof can be completed using power series as above to establish that the sine has as its derivative the cosine, and the cosine has as its derivative the negative sine. In fact, the definitions by ordinary differential equation and by power series lead to similar derivations of most identities.
This proof of the identity has no direct connection with Euclid 's demonstration of the Pythagorean theorem.
Using Euler's formula e i θ = cos θ + i sin θ {\displaystyle e^{i\theta }=\cos \theta +i\sin \theta } and factoring cos 2 θ + sin 2 θ {\displaystyle \cos ^{2}\theta +\sin ^{2}\theta } as the complex difference of two squares ,
1 = e i θ e − i θ = ( cos θ + i sin θ ) ( cos θ − i sin θ ) = cos 2 θ + sin 2 θ . {\displaystyle {\begin{aligned}1&=e^{i\theta }e^{-i\theta }\\[3mu]&=(\cos \theta +i\sin \theta )(\cos \theta -i\sin \theta )\\[3mu]&=\cos ^{2}\theta +\sin ^{2}\theta .\end{aligned}}} | https://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity |
A Pythagorean triple consists of three positive integers a , b , and c , such that a 2 + b 2 = c 2 . Such a triple is commonly written ( a , b , c ) , a well-known example is (3, 4, 5) . If ( a , b , c ) is a Pythagorean triple, then so is ( ka , kb , kc ) for any positive integer k . A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle .
A primitive Pythagorean triple is one in which a , b and c are coprime (that is, they have no common divisor larger than 1). [ 1 ] For example, (3, 4, 5) is a primitive Pythagorean triple whereas (6, 8, 10) is not. Every Pythagorean triple can be scaled to a unique primitive Pythagorean triple by dividing ( a , b , c ) by their greatest common divisor . Conversely, every Pythagorean triple can be obtained by multiplying the elements of a primitive Pythagorean triple by a positive integer (the same for the three elements).
The name is derived from the Pythagorean theorem , stating that every right triangle has side lengths satisfying the formula a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} ; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples. For instance, the triangle with sides a = b = 1 {\displaystyle a=b=1} and c = 2 {\displaystyle c={\sqrt {2}}} is a right triangle, but ( 1 , 1 , 2 ) {\displaystyle (1,1,{\sqrt {2}})} is not a Pythagorean triple because the square root of 2 is not an integer. Moreover, 1 {\displaystyle 1} and 2 {\displaystyle {\sqrt {2}}} do not have an integer common multiple because 2 {\displaystyle {\sqrt {2}}} is irrational .
Pythagorean triples have been known since ancient times. The oldest known record comes from Plimpton 322 , a Babylonian clay tablet from about 1800 BC, written in a sexagesimal number system. [ 2 ]
When searching for integer solutions, the equation a 2 + b 2 = c 2 is a Diophantine equation . Thus Pythagorean triples are among the oldest known solutions of a nonlinear Diophantine equation.
There are 16 primitive Pythagorean triples of numbers up to 100:
Other small Pythagorean triples such as (6, 8, 10) are not listed because they are not primitive; for instance (6, 8, 10) is a multiple of (3, 4, 5).
Each of these points (with their multiples) forms a radiating line in the scatter plot to the right.
Additionally, these are the remaining primitive Pythagorean triples of numbers up to 300:
Euclid's formula [ 3 ] is a fundamental formula for generating Pythagorean triples given an arbitrary pair of integers m and n with m > n > 0 . The formula states that the integers
form a Pythagorean triple. For example, given
generate the primitive triple (3,4,5):
The triple generated by Euclid 's formula is primitive if and only if m and n are coprime and exactly one of them is even. When both m and n are odd, then a , b , and c will be even, and the triple will not be primitive; however, dividing a , b , and c by 2 will yield a primitive triple when m and n are coprime. [ 4 ]
Every primitive triple arises (after the exchange of a and b , if a is even) from a unique pair of coprime numbers m , n , one of which is even. It follows that there are infinitely many primitive Pythagorean triples. This relationship of a , b and c to m and n from Euclid's formula is referenced throughout the rest of this article.
Despite generating all primitive triples, Euclid's formula does not produce all triples—for example, (9, 12, 15) cannot be generated using integer m and n . This can be remedied by inserting an additional parameter k to the formula. The following will generate all Pythagorean triples uniquely:
where m , n , and k are positive integers with m > n , and with m and n coprime and not both odd.
That these formulas generate Pythagorean triples can be verified by expanding a 2 + b 2 using elementary algebra and verifying that the result equals c 2 . Since every Pythagorean triple can be divided through by some integer k to obtain a primitive triple, every triple can be generated uniquely by using the formula with m and n to generate its primitive counterpart and then multiplying through by k as in the last equation.
Choosing m and n from certain integer sequences gives interesting results. For example, if m and n are consecutive Pell numbers , a and b will differ by 1. [ 5 ]
Many formulas for generating triples with particular properties have been developed since the time of Euclid.
That satisfaction of Euclid's formula by a, b, c is sufficient for the triangle to be Pythagorean is apparent from the fact that for positive integers m and n , m > n , the a , b , and c given by the formula are all positive integers, and from the fact that
A proof of the necessity that a, b, c be expressed by Euclid's formula for any primitive Pythagorean triple is as follows. [ 6 ] All such primitive triples can be written as ( a , b , c ) where a 2 + b 2 = c 2 and a , b , c are coprime . Thus a , b , c are pairwise coprime (if a prime number divided two of them, it would be forced also to divide the third one). As a and b are coprime, at least one of them is odd. If we suppose that a is odd, then b is even and c is odd (if both a and b were odd, c would be even, and c 2 would be a multiple of 4, while a 2 + b 2 would be congruent to 2 modulo 4 , as an odd square is congruent to 1 modulo 4).
From a 2 + b 2 = c 2 , {\displaystyle a^{2}+b^{2}=c^{2},} assume a is odd. We obtain c 2 − a 2 = b 2 {\displaystyle c^{2}-a^{2}=b^{2}} and hence ( c − a ) ( c + a ) = b 2 . {\displaystyle (c-a)(c+a)=b^{2}.} Then ( c + a ) b = b ( c − a ) . {\displaystyle {\tfrac {(c+a)}{b}}={\tfrac {b}{(c-a)}}.} Since ( c + a ) b {\displaystyle {\tfrac {(c+a)}{b}}} is rational, we set it equal to m n {\displaystyle {\tfrac {m}{n}}} in lowest terms. Thus ( c − a ) b = n m , {\displaystyle {\tfrac {(c-a)}{b}}={\tfrac {n}{m}},} being the reciprocal of ( c + a ) b . {\displaystyle {\tfrac {(c+a)}{b}}.} Then solving
for c b {\displaystyle {\tfrac {c}{b}}} and a b {\displaystyle {\tfrac {a}{b}}} gives
As m n {\displaystyle {\tfrac {m}{n}}} is fully reduced, m and n are coprime, and they cannot both be even. If they were both odd, the numerator of m 2 − n 2 2 m n {\displaystyle {\tfrac {m^{2}-n^{2}}{2mn}}} would be a multiple of 4 (because an odd square is congruent to 1 modulo 4), and the denominator 2 mn would not be a multiple of 4. Since 4 would be the minimum possible even factor in the numerator and 2 would be the maximum possible even factor in the denominator, this would imply a to be even despite defining it as odd. Thus one of m and n is odd and the other is even, and the numerators of the two fractions with denominator 2 mn are odd. Thus these fractions are fully reduced (an odd prime dividing this denominator divides one of m and n but not the other; thus it does not divide m 2 ± n 2 ). One may thus equate numerators with numerators and denominators with denominators, giving Euclid's formula
A longer but more commonplace proof is given in Maor (2007) [ 7 ] and Sierpiński (2003). [ 8 ] Another proof is given in Diophantine equation § Example of Pythagorean triples , as an instance of a general method that applies to every homogeneous Diophantine equation of degree two.
Suppose the sides of a Pythagorean triangle have lengths m 2 − n 2 , 2 mn , and m 2 + n 2 , and suppose the angle between the leg of length m 2 − n 2 and the hypotenuse of length m 2 + n 2 is denoted as β . Then tan β 2 = n m {\displaystyle \tan {\tfrac {\beta }{2}}={\tfrac {n}{m}}} and the full-angle trigonometric values are sin β = 2 m n m 2 + n 2 {\displaystyle \sin {\beta }={\tfrac {2mn}{m^{2}+n^{2}}}} , cos β = m 2 − n 2 m 2 + n 2 {\displaystyle \cos {\beta }={\tfrac {m^{2}-n^{2}}{m^{2}+n^{2}}}} , and tan β = 2 m n m 2 − n 2 {\displaystyle \tan {\beta }={\tfrac {2mn}{m^{2}-n^{2}}}} . [ 9 ]
The following variant of Euclid's formula is sometimes more convenient, as being more symmetric in m and n (same parity condition on m and n ).
If m and n are two odd integers such that m > n , then
are three integers that form a Pythagorean triple, which is primitive if and only if m and n are coprime. Conversely, every primitive Pythagorean triple arises (after the exchange of a and b , if a is even) from a unique pair m > n > 0 of coprime odd integers.
In the presentation above, it is said that all Pythagorean triples are uniquely obtained from Euclid's formula "after the exchange of a and b , if a is even". Euclid's formula and the variant above can be merged as follows to avoid this exchange, leading to the following result.
Every primitive Pythagorean triple can be uniquely written
where m and n are positive coprime integers, and ε = 1 2 {\displaystyle \varepsilon ={\frac {1}{2}}} if m and n are both odd, and ε = 1 {\displaystyle \varepsilon =1} otherwise. Equivalently, ε = 1 2 {\displaystyle \varepsilon ={\frac {1}{2}}} if a is odd, and ε = 1 {\displaystyle \varepsilon =1} if a is even.
The properties of a primitive Pythagorean triple ( a , b , c ) with a < b < c (without specifying which of a or b is even and which is odd) include:
In addition, special Pythagorean triples with certain additional properties can be guaranteed to exist:
Euclid's formula for a Pythagorean triple
can be understood in terms of the geometry of rational points on the unit circle ( Trautman 1998 ).
In fact, a point in the Cartesian plane with coordinates ( x , y ) belongs to the unit circle if x 2 + y 2 = 1 . The point is rational if x and y are rational numbers , that is, if there are coprime integers a , b , c such that
By multiplying both members by c 2 , one can see that the rational points on the circle are in one-to-one correspondence with the primitive Pythagorean triples.
The unit circle may also be defined by a parametric equation
Euclid's formula for Pythagorean triples and the inverse relationship t = y / ( x + 1) mean that, except for (−1, 0) , a point ( x , y ) on the circle is rational if and only if the corresponding value of t is a rational number. Note that t = y / ( x + 1) = b / ( a + c ) = n / m is also the tangent of half of the angle that is opposite the triangle side of length b .
There is a correspondence between points on the unit circle with rational coordinates and primitive Pythagorean triples. At this point, Euclid's formulae can be derived either by methods of trigonometry or equivalently by using the stereographic projection .
For the stereographic approach, suppose that P ′ is a point on the x -axis with rational coordinates
Then, it can be shown by basic algebra that the point P has coordinates
This establishes that each rational point of the x -axis goes over to a rational point of the unit circle. The converse, that every rational point of the unit circle comes from such a point of the x -axis, follows by applying the inverse stereographic projection. Suppose that P ( x , y ) is a point of the unit circle with x and y rational numbers. Then the point P ′ obtained by stereographic projection onto the x -axis has coordinates
which is rational.
In terms of algebraic geometry , the algebraic variety of rational points on the unit circle is birational to the affine line over the rational numbers. The unit circle is thus called a rational curve , and it is this fact which enables an explicit parameterization of the (rational number) points on it by means of rational functions.
A 2D lattice is a regular array of isolated points where if any one point is chosen as the Cartesian origin (0, 0), then all the other points are at ( x , y ) where x and y range over all positive and negative integers. Any Pythagorean triangle with triple ( a , b , c ) can be drawn within a 2D lattice with vertices at coordinates (0, 0) , ( a , 0) and (0, b ) . The count of lattice points lying strictly within the bounds of the triangle is given by ( a − 1 ) ( b − 1 ) − gcd ( a , b ) + 1 2 ; {\displaystyle {\tfrac {(a-1)(b-1)-\gcd {(a,b)}+1}{2}};} [ 29 ] for primitive Pythagorean triples this interior lattice count is ( a − 1 ) ( b − 1 ) 2 . {\displaystyle {\tfrac {(a-1)(b-1)}{2}}.} The area (by Pick's theorem equal to one less than the interior lattice count plus half the boundary lattice count) equals a b 2 {\displaystyle {\tfrac {ab}{2}}} .
The first occurrence of two primitive Pythagorean triples sharing the same area occurs with triangles with sides (20, 21, 29), (12, 35, 37) and common area 210 (sequence A093536 in the OEIS ). The first occurrence of two primitive Pythagorean triples sharing the same interior lattice count occurs with (18108, 252685, 253333), (28077, 162964, 165365) and interior lattice count 2287674594 (sequence A225760 in the OEIS ). Three primitive Pythagorean triples have been found sharing the same area: (4485, 5852, 7373) , (3059, 8580, 9109) , (1380, 19019, 19069) with area 13123110. As yet, no set of three primitive Pythagorean triples have been found sharing the same interior lattice count.
By Euclid's formula all primitive Pythagorean triples can be generated from integers m {\displaystyle m} and n {\displaystyle n} with m > n > 0 {\displaystyle m>n>0} , m + n {\displaystyle m+n} odd and gcd ( m , n ) = 1. {\displaystyle \gcd(m,n)=1.} Hence there is a 1 to 1 mapping of rationals (in lowest terms) to primitive Pythagorean triples where n m {\displaystyle {\tfrac {n}{m}}} is in the interval ( 0 , 1 ) {\displaystyle (0,1)} and m + n {\displaystyle m+n} odd.
The reverse mapping from a primitive triple ( a , b , c ) {\displaystyle (a,b,c)} where c > b > a > 0 {\displaystyle c>b>a>0} to a rational n m {\displaystyle {\tfrac {n}{m}}} is achieved by studying the two sums a + c {\displaystyle a+c} and b + c . {\displaystyle b+c.} One of these sums will be a square that can be equated to ( m + n ) 2 {\displaystyle (m+n)^{2}} and the other will be twice a square that can be equated to 2 m 2 . {\displaystyle 2m^{2}.} It is then possible to determine the rational n m . {\displaystyle {\tfrac {n}{m}}.}
In order to enumerate primitive Pythagorean triples the rational can be expressed as an ordered pair ( n , m ) {\displaystyle (n,m)} and mapped to an integer using a pairing function such as Cantor's pairing function . An example can be seen at (sequence A277557 in the OEIS ). It begins
Pythagorean triples can likewise be encoded into a square matrix of the form
A matrix of this form is symmetric . Furthermore, the determinant of X is
which is zero precisely when ( a , b , c ) is a Pythagorean triple. If X corresponds to a Pythagorean triple, then as a matrix it must have rank 1.
Since X is symmetric, it follows from a result in linear algebra that there is a column vector ξ = [ m n ] T such that the outer product
holds, where the T denotes the matrix transpose . Since ξ and -ξ produce the same Pythagorean triple, the vector ξ can be considered a spinor (for the Lorentz group SO(1, 2)). In abstract terms, the Euclid formula means that each primitive Pythagorean triple can be written as the outer product with itself of a spinor with integer entries, as in ( 1 ).
The modular group Γ is the set of 2×2 matrices with integer entries
with determinant equal to one: αδ − βγ = 1 . This set forms a group , since the inverse of a matrix in Γ is again in Γ, as is the product of two matrices in Γ. The modular group acts on the collection of all integer spinors. Furthermore, the group is transitive on the collection of integer spinors with relatively prime entries. For if [ m n ] T has relatively prime entries, then
where u and v are selected (by the Euclidean algorithm ) so that mu + nv = 1 .
By acting on the spinor ξ in ( 1 ), the action of Γ goes over to an action on Pythagorean triples, provided one allows for triples with possibly negative components. Thus if A is a matrix in Γ , then
gives rise to an action on the matrix X in ( 1 ). This does not give a well-defined action on primitive triples, since it may take a primitive triple to an imprimitive one. It is convenient at this point (per Trautman 1998 ) to call a triple ( a , b , c ) standard if c > 0 and either ( a , b , c ) are relatively prime or ( a /2, b /2, c /2) are relatively prime with a /2 odd. If the spinor [ m n ] T has relatively prime entries, then the associated triple ( a , b , c ) determined by ( 1 ) is a standard triple. It follows that the action of the modular group is transitive on the set of standard triples.
Alternatively, restrict attention to those values of m and n for which m is odd and n is even. Let the subgroup Γ(2) of Γ be the kernel of the group homomorphism
where SL(2, Z 2 ) is the special linear group over the finite field Z 2 of integers modulo 2 . Then Γ(2) is the group of unimodular transformations which preserve the parity of each entry. Thus if the first entry of ξ is odd and the second entry is even, then the same is true of A ξ for all A ∈ Γ(2) . In fact, under the action ( 2 ), the group Γ(2) acts transitively on the collection of primitive Pythagorean triples ( Alperin 2005 ).
The group Γ(2) is the free group whose generators are the matrices
Consequently, every primitive Pythagorean triple can be obtained in a unique way as a product of copies of the matrices U and L .
By a result of Berggren (1934) , all primitive Pythagorean triples can be generated from the (3, 4, 5) triangle by using the three linear transformations T 1 , T 2 , T 3 below, where a , b , c are sides of a triple:
In other words, every primitive triple will be a "parent" to three additional primitive triples.
Starting from the initial node with a = 3 , b = 4 , and c = 5 , the operation T 1 produces the new triple
and similarly T 2 and T 3 produce the triples (21, 20, 29) and (15, 8, 17).
The linear transformations T 1 , T 2 , and T 3 have a geometric interpretation in the language of quadratic forms . They are closely related to (but are not equal to) reflections generating the orthogonal group of x 2 + y 2 − z 2 over the integers. [ 30 ]
Alternatively, Euclid's formulae can be analyzed and proved using the Gaussian integers . [ 31 ] Gaussian integers are complex numbers of the form α = u + vi , where u and v are ordinary integers and i is the square root of negative one . The units of Gaussian integers are ±1 and ±i. The ordinary integers are called the rational integers and denoted as ' Z '. The Gaussian integers are denoted as Z [ i ] . The right-hand side of the Pythagorean theorem may be factored in Gaussian integers:
A primitive Pythagorean triple is one in which a and b are coprime , i.e., they share no prime factors in the integers. For such a triple, either a or b is even, and the other is odd; from this, it follows that c is also odd.
The two factors z := a + bi and z* := a − bi of a primitive Pythagorean triple each equal the square of a Gaussian integer. This can be proved using the property that every Gaussian integer can be factored uniquely into Gaussian primes up to units . [ 32 ] (This unique factorization follows from the fact that, roughly speaking, a version of the Euclidean algorithm can be defined on them.) The proof has three steps. First, if a and b share no prime factors in the integers, then they also share no prime factors in the Gaussian integers. (Assume a = gu and b = gv with Gaussian integers g , u and v and g not a unit. Then u and v lie on the same line through the origin. All Gaussian integers on such a line are integer multiples of some Gaussian integer h . But then the integer gh ≠ ±1 divides both a and b .) Second, it follows that z and z* likewise share no prime factors in the Gaussian integers. For if they did, then their common divisor δ would also divide z + z* = 2 a and z − z* = 2 ib . Since a and b are coprime, that implies that δ divides 2 = (1 + i)(1 − i) = i(1 − i) 2 . From the formula c 2 = zz* , that in turn would imply that c is even, contrary to the hypothesis of a primitive Pythagorean triple. Third, since c 2 is a square, every Gaussian prime in its factorization is doubled, i.e., appears an even number of times. Since z and z* share no prime factors, this doubling is also true for them. Hence, z and z* are squares.
Thus, the first factor can be written
The real and imaginary parts of this equation give the two formulas:
For any primitive Pythagorean triple, there must be integers m and n such that these two equations are satisfied. Hence, every Pythagorean triple can be generated from some choice of these integers.
If we consider the square of a Gaussian integer we get the following direct interpretation of Euclid's formula as representing the perfect square of a Gaussian integer.
Using the facts that the Gaussian integers are a Euclidean domain and that for a Gaussian integer p | p | 2 {\displaystyle |p|^{2}} is always a square it is possible to show that a Pythagorean triple corresponds to the square of a prime Gaussian integer if the hypotenuse is prime.
If the Gaussian integer is not prime then it is the product of two Gaussian integers p and q with | p | 2 {\displaystyle |p|^{2}} and | q | 2 {\displaystyle |q|^{2}} integers. Since magnitudes multiply in the Gaussian integers, the product must be | p | | q | {\displaystyle |p||q|} , which when squared to find a Pythagorean triple must be composite. The contrapositive completes the proof.
There are a number of results on the distribution of Pythagorean triples. In the scatter plot, a number of obvious patterns are already apparent. Whenever the legs ( a , b ) of a primitive triple appear in the plot, all integer multiples of ( a , b ) must also appear in the plot, and this property produces the appearance of lines radiating from the origin in the diagram.
Within the scatter, there are sets of parabolic patterns with a high density of points and all their foci at the origin, opening up in all four directions. Different parabolas intersect at the axes and appear to reflect off the axis with an incidence angle of 45 degrees, with a third parabola entering in a perpendicular fashion. Within this quadrant, each arc centered on the origin shows that section of the parabola that lies between its tip and its intersection with its semi-latus rectum .
These patterns can be explained as follows. If a 2 / 4 n {\displaystyle a^{2}/4n} is an integer, then ( a , | n − a 2 / 4 n | {\displaystyle |n-a^{2}/4n|} , n + a 2 / 4 n {\displaystyle n+a^{2}/4n} ) is a Pythagorean triple. (In fact every Pythagorean triple ( a , b , c ) can be written in this way with integer n , possibly after exchanging a and b , since n = ( b + c ) / 2 {\displaystyle n=(b+c)/2} and a and b cannot both be odd.) The Pythagorean triples thus lie on curves given by b = | n − a 2 / 4 n | {\displaystyle b=|n-a^{2}/4n|} , that is, parabolas reflected at the a -axis, and the corresponding curves with a and b interchanged. If a is varied for a given n (i.e. on a given parabola), integer values of b occur relatively frequently if n is a square or a small multiple of a square. If several such values happen to lie close together, the corresponding parabolas approximately coincide, and the triples cluster in a narrow parabolic strip. For instance, 38 2 = 1444 , 2 × 27 2 = 1458 , 3 × 22 2 = 1452 , 5 × 17 2 = 1445 and 10 × 12 2 = 1440 ; the corresponding parabolic strip around n ≈ 1450 is clearly visible in the scatter plot.
The angular properties described above follow immediately from the functional form of the parabolas. The parabolas are reflected at the a -axis at a = 2 n , and the derivative of b with respect to a at this point is –1; hence the incidence angle is 45°. Since the clusters, like all triples, are repeated at integer multiples, the value 2 n also corresponds to a cluster. The corresponding parabola intersects the b -axis at right angles at b = 2 n , and hence its reflection upon interchange of a and b intersects the a -axis at right angles at a = 2 n , precisely where the parabola for n is reflected at the a -axis. (The same is of course true for a and b interchanged.)
Albert Fässler and others provide insights into the significance of these parabolas in the context of conformal mappings. [ 33 ] [ 34 ]
The case n = 1 of the more general construction of Pythagorean triples has been known for a long time. Proclus , in his commentary to the 47th Proposition of the first book of Euclid's Elements , describes it as follows:
Certain methods for the discovery of triangles of this kind are handed down, one which they refer to Plato, and another to Pythagoras . (The latter) starts from odd numbers. For it makes the odd number the smaller of the sides about the right angle; then it takes the square of it, subtracts unity and makes half the difference the greater of the sides about the right angle; lastly it adds unity to this and so forms the remaining side, the hypotenuse. ...For the method of Plato argues from even numbers. It takes the given even number and makes it one of the sides about the right angle; then, bisecting this number and squaring the half, it adds unity to the square to form the hypotenuse, and subtracts unity from the square to form the other side about the right angle. ... Thus it has formed the same triangle that which was obtained by the other method.
In equation form, this becomes:
a is odd (Pythagoras, c. 540 BC):
a is even (Plato, c. 380 BC):
It can be shown that all Pythagorean triples can be obtained, with appropriate rescaling, from the basic Platonic sequence ( a , ( a 2 − 1)/2 and ( a 2 + 1)/2 ) by allowing a to take non-integer rational values. If a is replaced with the fraction m / n in the sequence, the result is equal to the 'standard' triple generator (2 mn , m 2 − n 2 , m 2 + n 2 ) after rescaling. It follows that every triple has a corresponding rational a value which can be used to generate a similar triangle (one with the same three angles and with sides in the same proportions as the original). For example, the Platonic equivalent of (56, 33, 65) is generated by a = m / n = 7/4 as ( a , ( a 2 –1)/2, ( a 2 +1)/2) = (56/32, 33/32, 65/32) . The Platonic sequence itself can be derived [ clarification needed ] by following the steps for 'splitting the square' described in Diophantus II.VIII .
The equation,
is equivalent to the special Pythagorean triple,
There is an infinite number of solutions to this equation as solving for the variables involves an elliptic curve . Small ones are,
One way to generate solutions to a 2 + b 2 = c 2 + d 2 {\displaystyle a^{2}+b^{2}=c^{2}+d^{2}} is to parametrize a, b, c, d in terms of integers m, n, p, q as follows: [ 35 ]
Given two sets of Pythagorean triples,
the problem of finding equal products of a non-hypotenuse side and the hypotenuse,
is easily seen to be equivalent to the equation,
and was first solved by Euler as a , b , c , d = 133 , 59 , 158 , 134. {\displaystyle a,b,c,d=133,59,158,134.} Since he showed this is a rational point in an elliptic curve , then there is an infinite number of solutions. In fact, he also found a 7th degree polynomial parameterization.
For the case of Descartes' circle theorem where all variables are squares,
Euler showed this is equivalent to three simultaneous Pythagorean triples,
There is also an infinite number of solutions, and for the special case when a + b = c {\displaystyle a+b=c} , then the equation simplifies to,
with small solutions as a , b , c , d = 3 , 5 , 8 , 14 {\displaystyle a,b,c,d=3,5,8,14} and can be solved as binary quadratic forms .
No Pythagorean triples are isosceles , because the ratio of the hypotenuse to either other side is √ 2 , but √ 2 cannot be expressed as the ratio of 2 integers .
There are, however, right-angled triangles with integral sides for which the lengths of the non-hypotenuse sides differ by one, such as,
and an infinite number of others. They can be completely parameterized as,
where { x, y } are the solutions to the Pell equation x 2 − 2 y 2 = − 1. {\displaystyle x^{2}-2y^{2}=-1.}
If a , b , c are the sides of this type of primitive Pythagorean triple then the solution to the Pell equation is given by the recursive formula
This sequence of primitive Pythagorean triples forms the central stem (trunk) of the rooted ternary tree of primitive Pythagorean triples.
When it is the longer non-hypotenuse side and hypotenuse that differ by one, such as in
then the complete solution for the primitive Pythagorean triple a , b , c is
and
where integer m > 0 {\displaystyle m>0} is the generating parameter.
It shows that all odd numbers (greater than 1) appear in this type of almost-isosceles primitive Pythagorean triple. This sequence of primitive Pythagorean triples forms the right hand side outer stem of the rooted ternary tree of primitive Pythagorean triples.
Another property of this type of almost-isosceles primitive Pythagorean triple is that the sides are related such that
for some integer K {\displaystyle K} . Or in other words a b + b a {\displaystyle a^{b}+b^{a}} is divisible by c {\displaystyle c} such as in
Starting with 5, every second Fibonacci number is the length of the hypotenuse of a right triangle with integer sides, or in other words, the largest number in a Pythagorean triple, obtained from the formula ( F n F n + 3 ) 2 + ( 2 F n + 1 F n + 2 ) 2 = F 2 n + 3 2 . {\displaystyle (F_{n}F_{n+3})^{2}+(2F_{n+1}F_{n+2})^{2}=F_{2n+3}^{2}.} The sequence of Pythagorean triangles obtained from this formula has sides of lengths
The middle side of each of these triangles is the sum of the three sides of the preceding triangle. [ 38 ]
There are several ways to generalize the concept of Pythagorean triples.
The expression
is a Pythagorean n -tuple for any tuple of positive integers ( m 1 , ..., m n ) with m 2 1 > m 2 2 + ... + m 2 n . The Pythagorean n -tuple can be made primitive by dividing out by the largest common divisor of its values.
Furthermore, any primitive Pythagorean n -tuple a 2 1 + ... + a 2 n = c 2 can be found by this approach. Use ( m 1 , ..., m n ) = ( c + a 1 , a 2 , ..., a n ) to get a Pythagorean n -tuple by the above formula and divide out by the largest common integer divisor, which is 2 m 1 = 2( c + a 1 ) . Dividing out by the largest common divisor of these ( m 1 , ..., m n ) values gives the same primitive Pythagorean n -tuple; and there is a one-to-one correspondence between tuples of setwise coprime positive integers ( m 1 , ..., m n ) satisfying m 2 1 > m 2 2 + ... + m 2 n and primitive Pythagorean n -tuples.
Examples of the relationship between setwise coprime values m → {\displaystyle {\vec {m}}} and primitive Pythagorean n -tuples include: [ 39 ]
Since the sum F ( k , m ) of k consecutive squares beginning with m 2 is given by the formula, [ 40 ]
one may find values ( k , m ) so that F ( k , m ) is a square, such as one by Hirschhorn where the number of terms is itself a square, [ 41 ]
and v ≥ 5 is any integer not divisible by 2 or 3. For the smallest case v = 5 , hence k = 25 , this yields the well-known cannonball-stacking problem of Lucas ,
a fact which is connected to the Leech lattice .
In addition, if in a Pythagorean n -tuple ( n ≥ 4 ) all addends are consecutive except one, one can use the equation, [ 42 ]
Since the second power of p cancels out, this is only linear and easily solved for as p = F ( k , m ) − 1 2 {\displaystyle p={\tfrac {F(k,m)-1}{2}}} though k , m should be chosen so that p is an integer, with a small example being k = 5 , m = 1 yielding,
Thus, one way of generating Pythagorean n -tuples is by using, for various x , [ 43 ]
where q = n –2 and where
A generalization of the concept of Pythagorean triples is the search for triples of positive integers a , b , and c , such that a n + b n = c n , for some n strictly greater than 2. Pierre de Fermat in 1637 claimed that no such triple exists, a claim that came to be known as Fermat's Last Theorem because it took longer than any other conjecture by Fermat to be proved or disproved. The first proof was given by Andrew Wiles in 1994.
Another generalization is searching for sequences of n + 1 positive integers for which the n th power of the last is the sum of the n th powers of the previous terms. The smallest sequences for known values of n are:
For the n = 3 case, in which x 3 + y 3 + z 3 = w 3 , {\displaystyle x^{3}+y^{3}+z^{3}=w^{3},} called the Fermat cubic , a general formula exists giving all solutions.
A slightly different generalization allows the sum of ( k + 1) n th powers to equal the sum of ( n − k ) n th powers. For example:
There can also exist n − 1 positive integers whose n th powers sum to an n th power (though, by Fermat's Last Theorem , not for n = 3) ; these are counterexamples to Euler's sum of powers conjecture . The smallest known counterexamples are [ 44 ] [ 45 ] [ 15 ]
A Heronian triangle is commonly defined as one with integer sides whose area is also an integer. The lengths of the sides of such a triangle form a Heronian triple ( a, b, c ) for a ≤ b ≤ c .
Every Pythagorean triple is a Heronian triple, because at least one of the legs a , b must be even in a Pythagorean triple, so the area ab /2 is an integer. Not every Heronian triple is a Pythagorean triple, however, as the example (4, 13, 15) with area 24 shows.
If ( a , b , c ) is a Heronian triple, so is ( ka , kb , kc ) where k is any positive integer; its area will be the integer that is k 2 times the integer area of the ( a , b , c ) triangle.
The Heronian triple ( a , b , c ) is primitive provided a , b , c are setwise coprime . (With primitive Pythagorean triples the stronger statement that they are pairwise coprime also applies, but with primitive Heronian triangles the stronger statement does not always hold true, such as with (7, 15, 20) .) Here are a few of the simplest primitive Heronian triples that are not Pythagorean triples:
By Heron's formula , the extra condition for a triple of positive integers ( a , b , c ) with a < b < c to be Heronian is that
or equivalently
be a nonzero perfect square divisible by 16.
Primitive Pythagorean triples have been used in cryptography as random sequences and for the generation of keys. [ 46 ] | https://en.wikipedia.org/wiki/Pythagorean_triple |
In mathematics, and especially topology , a Pytkeev space is a topological space that satisfies qualities more subtle than a convergence of a sequence . They are named after E. G. Pytkeev, who proved in 1983 that sequential spaces have this property. [ 1 ]
Let X be a topological space. For a subset S of X let S denote the closure of S . Then a point x is called a Pytkeev point if for every set A with x ∈ A \ { x } , there is a countable π {\displaystyle \pi } -net of infinite subsets of A . A Pytkeev space is a space in which every point is a Pytkeev point. [ 2 ]
This topology-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pytkeev_space |
In continuum mechanics , the Péclet number ( Pe , after Jean Claude Eugène Péclet ) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is defined to be the ratio of the rate of advection of a physical quantity by the flow to the rate of diffusion of the same quantity driven by an appropriate gradient . In the context of species or mass transfer , the Péclet number is the product of the Reynolds number and the Schmidt number ( Re × Sc ). In the context of the thermal fluids , the thermal Péclet number is equivalent to the product of the Reynolds number and the Prandtl number ( Re × Pr ).
The Péclet number is defined as
For mass transfer, it is defined as
where L is the characteristic length , u the local flow velocity , D the mass diffusion coefficient , Re the Reynolds number, Sc the Schmidt number.
Such ratio can also be re-written in terms of times, as a ratio between the characteristic temporal intervals of the system:
For P e L ≫ 1 {\displaystyle \mathrm {Pe_{L}} \gg 1} the diffusion happens in a much longer time compared to the advection, and therefore the latter of the two phenomena predominates in the mass transport.
For heat transfer , the Péclet number is defined as
where Pr the Prandtl number, and α the thermal diffusivity ,
where k is the thermal conductivity , ρ the density , and c p the specific heat capacity .
In engineering applications the Péclet number is often very large. In such situations, the dependency of the flow upon downstream locations is diminished, and variables in the flow tend to become "one-way" properties. Thus, when modelling certain situations with high Péclet numbers, simpler computational models can be adopted. [ 1 ]
A flow will often have different Péclet numbers for heat and mass. This can lead to the phenomenon of double diffusive convection .
In the context of particulate motion the Péclet number has also been called Brenner number , with symbol Br , in honour of Howard Brenner . [ 2 ]
The Péclet number also finds applications beyond transport phenomena, as a general measure for the relative importance of the random fluctuations and of the systematic average behavior in mesoscopic systems. [ 3 ] | https://en.wikipedia.org/wiki/Péclet_number |
Péter R. Surján (born August 30, 1955 [ 1 ] ) is a Hungarian theoretical chemist who is known for his research on application of the theory of second quantization in quantum chemistry .
In 2016 a festschrift from Theoretical Chemistry Accounts journal was published in his name [ 2 ] which is also published as a book in Highlights in Theoretical Chemistry series by the Springer Nature . [ 3 ] He is currently a professor and a former dean of the Faculty of Science of the Eötvös Loránd University . [ 4 ]
Surján received his Master's degree in physics in 1978 and his PhD in quantum chemistry in 1981, both from ( Eötvös Loránd University . [ citation needed ] In 1986, he was a Candidate of Science . [ 5 ] From there, he worked at the Technical University of Budapest as a senior researcher in physics from 1990 to 1995 before moving to Eötvös Loránd University, where he has been since. He has taught in the Department of Theoretical Chemistry since 1991, becoming a full professor in 1998, and has been the Director of the Bolyai College (2007-2012) and the Institute of Chemistry (2008-2012). [ citation needed ] He was also the dean of the Faculty of Science. [ 4 ]
Surján is a member of the Hungarian Academy of Sciences (1998) [ 5 ] and has been on the editorial boards of the Journal of Mathematical Chemistry [ 6 ] and Interdisciplinary Sciences: Computational Life Sciences . [ 7 ] He has also been a guest editor for the International Journal of Quantum Chemistry . [ 8 ] Surján has published more than 190 papers in his scientific career. His first paper was published in 1980.
This biographical article about a scientist is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Péter_Surján |
In mathematics , a character sum is a sum ∑ χ ( n ) {\textstyle \sum \chi (n)} of values of a Dirichlet character χ modulo N , taken over a given range of values of n . Such sums are basic in a number of questions, for example in the distribution of quadratic residues , and in particular in the classical question of finding an upper bound for the least quadratic non-residue modulo N . Character sums are often closely linked to exponential sums by the Gauss sums (this is like a finite Mellin transform ).
Assume χ is a non-principal Dirichlet character to the modulus N .
The sum taken over all residue classes mod N is then zero. This means that the cases of interest will be sums Σ {\displaystyle \Sigma } over relatively short ranges, of length R < N say,
A fundamental improvement on the trivial estimate Σ = O ( N ) {\displaystyle \Sigma =O(N)} is the Pólya–Vinogradov inequality , established independently by George Pólya and I. M. Vinogradov in 1918, [ 1 ] [ 2 ] stating in big O notation that
Assuming the generalized Riemann hypothesis , Hugh Montgomery and R. C. Vaughan have shown [ 3 ] that there is the further improvement
Another significant type of character sum is that formed by
for some function F , generally a polynomial . A classical result is the case of a quadratic, for example,
and χ a Legendre symbol . Here the sum can be evaluated (as −1), a result that is connected to the local zeta-function of a conic section .
More generally, such sums for the Jacobi symbol relate to local zeta-functions of elliptic curves and hyperelliptic curves ; this means that by means of André Weil 's results, for N = p a prime number , there are non-trivial bounds
The constant implicit in the notation is linear in the genus of the curve in question, and so (Legendre symbol or hyperelliptic case) can be taken as the degree of F . (More general results, for other values of N , can be obtained starting from there.)
Weil's results also led to the Burgess bound , [ 4 ] applying to give non-trivial results beyond Pólya–Vinogradov, for R a power of N greater than 1/4.
Assume the modulus N is a prime.
for any integer r ≥ 3. [ 5 ] | https://en.wikipedia.org/wiki/Pólya-Vinogradov_inequality |
The Pólya enumeration theorem , also known as the Redfield–Pólya theorem and Pólya counting , is a theorem in combinatorics that both follows from and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set . The theorem was first published by J. Howard Redfield in 1927. In 1937 it was independently rediscovered by George Pólya , who then greatly popularized the result by applying it to many counting problems, in particular to the enumeration of chemical compounds .
The Pólya enumeration theorem has been incorporated into symbolic combinatorics and the theory of combinatorial species .
Let X be a finite set and let G be a group of permutations of X (or a finite symmetry group that acts on X ). The set X may represent a finite set of beads, and G may be a chosen group of permutations of the beads. For example, if X is a necklace of n beads in a circle, then rotational symmetry is relevant so G is the cyclic group C n , while if X is a bracelet of n beads in a circle, rotations and reflections are relevant so G is the dihedral group D n of order 2 n . Suppose further that Y is a finite set of colors — the colors of the beads — so that Y X is the set of colored arrangements of beads (more formally: Y X is the set of functions X → Y {\displaystyle X\to Y} .) Then the group G acts on Y X . The Pólya enumeration theorem counts the number of orbits under G of colored arrangements of beads by the following formula:
where m = | Y | {\displaystyle m=|Y|} is the number of colors and c ( g ) is the number of cycles of the group element g when considered as a permutation of X .
In the more general and more important version of the theorem, the colors are also weighted in one or more ways, and there could be an infinite number of colors provided that the set of colors has a generating function with finite coefficients. In the univariate case, suppose that
is the generating function of the set of colors, so that there are f w colors of weight w for each integer w ≥ 0. In the multivariate case, the weight of each color is a vector of integers and there is a generating function f ( t 1 , t 2 , ...) that tabulates the number of colors with each given vector of weights.
The enumeration theorem employs another multivariate generating function called the cycle index :
where n is the number of elements of X and c k ( g ) is the number of k -cycles of the group element g as a permutation of X .
A colored arrangement is an orbit of the action of G on the set Y X (where Y is the set of colors and Y X denotes the set of all functions φ: X → Y ). The weight of such an arrangement is defined as the sum of the weights of φ( x ) over all x in X . The theorem states that the generating function F of the number of colored arrangements by weight is given by:
or in the multivariate case:
To reduce to the simplified version given earlier, if there are m colors and all have weight 0, then f ( t ) = m and
In the celebrated application of counting trees (see below) and acyclic molecules, an arrangement of "colored beads" is actually an arrangement of arrangements, such as branches of a rooted tree. Thus the generating function f for the colors is derived from the generating function F for arrangements, and the Pólya enumeration theorem becomes a recursive formula.
How many ways are there to color the sides of a three-dimensional cube with m colors, up to rotation of the cube? The rotation group C of the cube acts on the six sides of the cube, which are equivalent to beads. Its cycle index is
which is obtained by analyzing the action of each of the 24 elements of C on the 6 sides of the cube, see here for the details.
We take all colors to have weight 0 and find that there are
different colorings.
A graph on m vertices can be interpreted as an arrangement of colored beads. The set X of "beads" is the set of ( m 2 ) {\displaystyle {\binom {m}{2}}} possible edges, while the set of colors Y = {black, white} corresponds to edges that are present (black) or absent (white). The Pólya enumeration theorem can be used to calculate the number of graphs up to isomorphism with a fixed number of vertices, or the generating function of these graphs according to the number of edges they have. For the latter purpose, we can say that a black or present edge has weight 1, while an absent or white edge has weight 0. Thus f ( t ) = 1 + t {\displaystyle f(t)=1+t} is the generating function for the set of colors. The relevant symmetry group is G = S m , {\displaystyle G=S_{m},} the symmetric group on m letters. This group acts on the set X of possible edges: a permutation φ turns the edge {a, b} into the edge {φ(a), φ(b)}. With these definitions, an isomorphism class of graphs with m vertices is the same as an orbit of the action of G on the set Y X of colored arrangements; the number of edges of the graph equals the weight of the arrangement.
The eight graphs on three vertices (before identifying isomorphic graphs) are shown at the right. There are four isomorphism classes of graphs, also shown at the right.
The cycle index of the group S 3 acting on the set of three edges is
(obtained by inspecting the cycle structure of the action of the group elements; see here ). Thus, according to the enumeration theorem, the generating function of graphs on 3 vertices up to isomorphism is
which simplifies to
Thus there is one graph each with 0 to 3 edges.
The cycle index of the group S 4 acting on the set of 6 edges is
(see here .) Hence
which simplifies to
These graphs are shown at the right.
The set T 3 of rooted ternary trees consists of rooted trees where every node (or non-leaf vertex) has exactly three children (leaves or subtrees). Small ternary trees are shown at right. Note that rooted ternary trees with n nodes are equivalent to rooted trees with n vertices of degree at most 3 (by ignoring the leaves). In general, two rooted trees are isomorphic when one can be obtained from the other by permuting the children of its nodes. In other words, the group that acts on the children of a node is the symmetric group S 3 . We define the weight of such a ternary tree to be the number of nodes (or non-leaf vertices).
One can view a rooted, ternary tree as a recursive object which is either a leaf or a node with three children which are themselves rooted ternary trees. These children are equivalent to beads; the cycle index of the symmetric group S 3 that acts on them is
The Polya enumeration theorem translates the recursive structure of rooted ternary trees into a functional equation for the generating function F(t) of rooted ternary trees by number of nodes. This is achieved by "coloring" the three children with rooted ternary trees, weighted by node number, so that the color generating function is given by f ( t ) = F ( t ) {\displaystyle f(t)=F(t)} which by the enumeration theorem gives
as the generating function for rooted ternary trees, weighted by one less than the node number (since the sum of the children weights does not take the root into account), so that
This is equivalent to the following recurrence formula for the number t n of rooted ternary trees with n nodes:
where a , b and c are nonnegative integers.
The first few values of t n {\displaystyle t_{n}} are
The simplified form of the Pólya enumeration theorem follows from Burnside's lemma , which says that the number of orbits of colorings is the average of the number of elements of Y X {\displaystyle Y^{X}} fixed by the permutation g of G over all permutations g . The weighted version of the theorem has essentially the same proof, but with a refined form of Burnside's lemma for weighted enumeration. It is equivalent to apply Burnside's lemma separately to orbits of different weight.
For clearer notation, let x 1 , x 2 , … {\displaystyle x_{1},x_{2},\ldots } be the variables of the generating function f of Y {\displaystyle Y} . Given a vector of weights ω {\displaystyle \omega } , let x ω {\displaystyle x^{\omega }} denote the corresponding monomial term of f . Applying Burnside's lemma to orbits of weight ω {\displaystyle \omega } , the number of orbits of this weight is
where ( Y X ) ω , g {\displaystyle (Y^{X})_{\omega ,g}} is the set of colorings of weight ω {\displaystyle \omega } that are also fixed by g . If we then sum over all possible weights, we obtain
Meanwhile a group element g with cycle structure j 1 ( g ) , j 2 ( g ) , … , j n ( g ) {\displaystyle j_{1}(g),j_{2}(g),\ldots ,j_{n}(g)} will contribute the term
to the cycle index of G . The element g fixes an element ϕ ∈ Y X {\displaystyle \phi \in Y^{X}} if and only if the function φ is constant on every cycle q of g . For every such cycle q, the generating function by weight of | q | identical colors from the set enumerated by f is
It follows that the generating function by weight of the points fixed by g is the product of the above term over all cycles of g , i.e.
Substituting this in the sum over all g yields the substituted cycle index as claimed. | https://en.wikipedia.org/wiki/Pólya_enumeration_theorem |
The Pörner Group is an Austrian technology orientated, engineering and contracting company working on projects for the process industry . The headquarters are situated in Vienna , Austria. The group of companies specialises in various engineering industries such as oil refineries, chemical plants, petrochemical plants, gas plants, power generation, industrial production and the pharmaceutical industry. The organization is made up of a network of several medium-sized companies in these industries.
The Pörner Group offers technologies to the world market and supplies complete process plants for: bitumen (Biturox), solvent deasphalting (SDA Plus), dewaxing and deoiling (Dewaxing / Deoiling), spray micronization (Micronization) as well as BTX aromatics extraction (Aromex) and formaldehyde and derivates. Climate-friendly technologies are also provided, such as: Bio-Silicates from rice hulls (Pörner Bio-Silicates), Pörner Bitumen Packing System and Power-to-X (PtX) and Fisch-Tropsch processes for PtX.
The Pörner Group was founded by Kurt Thomas Pörner, Who began the Pörner Technical Bureau in 1972. The company grew from there, opening its first subsidiary in Linz in 1975. In the 1970s Pörner Ingenieurgesellschaft mbH, situated in Vienna , Austria , acquired the rights to license the Biturox® process for upgrading bitumen by means of selective air oxidation developed by the Austrian oil company OMV . Pörner licensed its first Biturox® plant to NIOC Isfahan in Iran. [ 1 ]
In parallel with the rapid growth of the industry in Europe and worldwide, in the 1980s the Pörner Group expanded and realized several larger projects for refineries as well as for environmental facilities.
In 1992 the Pörner Group opened its first foreign subsidiary in Grimma, Germany which specialises in process plants for the chemical industry. Shortly thereafter another Austrian subsidiary in Kundl, Tyrol was founded to supply the pharmaceutical industry, energy supply and industrial building services in the area.
In 2003 the Pörner group acquired 100% shares in EDL Anlagenbau Gesellschaft, a Leipzig , Germany based company. EDL specializes in refinery, chemical, petrochemical and gas sector clients. [ 2 ] In 2019, EDL Anlagenbau Gesellschaft also signed a cooperation agreement for a study. This study, done in cooperation with the Rotterdam The Hague Innovation Airport aims to develop a demonstration plant that produces renewable jet fuel from air. It will use Climeworks ’ direct air capture technology. [ 3 ] [ 4 ]
In 2005 the Pörner Bitumen Packing System was launched and earned the Pörner Group the Austrian State Prize for Consulting . [ 5 ] The system allows bitumen to be packed and transported by alternative means, namely in cold state, rather than the traditional way of long distance bulk transportation [ 6 ] (see Asphalt ). [ 6 ] [ 7 ]
Gazintek was the next acquisition for the Pörner Group, with the company buying 70% of the shares in 2005 and the remainder in 2007. The company, rebranded to Pörner Kyiv in 2021, is mainly focused on providing detailed engineering services for the gas industry. Gazintek does business with European and Russian companies who have worldwide interests including Africa and Asia.
The Pörner group also has a subsidiary in Romania , focusing on engineering of process plants to service the refineries in the area.
In 2015 Pörner Ingenieurgesellschaft received the nomination of the State Award "Engineering Consulting 2015" for the project "Clean Air for Siberia: Planning a desulfurization plant for Norilsk Nickel". [ 8 ] In the same year Pörner developed its own modern concept "Anlagenbau 4.0" for the best possible project realisation. [ 9 ]
In 2016 Pörner granted its 50th Biturox® license worldwide. The bitumen oxidation technology Biturox® was licensed to HPCL-Mittal Energy Limited (HMEL) in India. [ 10 ] In March 2016, OOO "Pörner Group Russia” has officially become an independent subsidiary of the Pörner Group in Moscow. [ 11 ]
In 2018 Pörner opened a representative office in Burghausen , Germany. [ 12 ]
On March 1, 2020, a new competence center ‘Pörner Water′ was created in the Vienna head office. [ 13 ]
TAF Thermische Apparate Freiberg GmbH has been a member of the Pörner Group since 2011 and has been operating as a subsidiary of Pörner Ingenieurgesellschaft mbH since April 2022. The company specialises in gasification technologies and is a developer and supplier of special solutions in mechanical and plant engineering, especially for higher process temperatures and/or under higher process pressures.
In 2022 Pörner celebrated its 50th anniversary and their subsidiary, EDL celebrated its 30th anniversary in 2021. | https://en.wikipedia.org/wiki/Pörner_Group |
Pātīgaṇita is the term used in pre-modern Indian mathematical literature to denote the area of mathematics dealing with arithmetic and mensuration. [ 1 ] The term is a compound word formed by combining the words pātī and gaṇita . The former is a non-Sanskrit word meaning a "board" and the latter is a Sanskrit word meaning "science of calculation". Thus the term pātīgaṇita literally means the science of calculations which requires a board (on which dust or sand is spread out) for performing the calculations, or "board-computation" in short. The usage of the term became popular among authors of Indian mathematical works about the beginning of the seventh century CE. [ 2 ] [ 3 ] It may be noted that Brahmagupta (c. 598 – c. 668 CE) has not used this term. Instead, he uses the term dhūlīkarma ( dhūlī is the Sanskrit term for dust). The terminology pātīgaṇita may be contrasted with "bījagaṇita" which denotes the area of mathematics referred to as algebra.
The term Pātīgaṇita is also the title of a work composed by Sridhara , an Indian mathematician who flourished during the 8th-9th century CE. [ 1 ]
According to Brahmagupta there are 20 operations ( parikarma -s) and 8 determinations (also called logistics) ( vyavahāra -s) that come under pātīgaṇita . He has stated as such in his Brahma-sphuṭa-siddhānta without specifying what these are. The commentators of Brahmasphuṭa-siddhānta have listed the following as the 20 operations and the 8 determinations. [ 3 ]
The earliest work dealing with the topics that come under pāṭīgaṇita that has survived to the present day is the Bakhshali manuscript some portions of which has been carbon dated as 224–383 CE. The following are the currently available texts which deal arithmetic and mensuration. They may contain more material than the 20 operations and the eight determinations that are listed as the topics that come under pāṭīgaṇita .
In these works one can see references to several older works, but none of them have survived to the present day. The lost works include Pātīgaṇita of Lalla (8th century CE) and Govindakṛti of Govindasvāmi (9th century CE).
The following astronomical treatises deal with arithmetic and mensuration in one of the chapters:
In Indian mathematical literature, Śrīdhara is the only author who has composed a work titled Pāṭīgaṇita . He has composed another work titled Pāṭīgaṇita-sāra which is a short summary of his Pāṭīgaṇita . [ 4 ] At the very beginning of the work, the author has listed the operations and the determinations that he is going to discuss in the work. According to Śrīdhara, there are 29 operations and nine determinations whereas Brahmagupta talks about only 20 operations and eight determinations. The operations specified in Śrīdhara's Pāṭīgaṇita are the following: [ 1 ]
The nine determinations specified by Śrīdhara are the eight determinations specified by Brahmagupta and śūnya-tatva (mathematics of zero).
Only one manuscript of Pāṭīgaṇita is currently available and it is incomplete. Discussions on some of the 29 operations and some of the nine determinations are missing from the extant manuscript. | https://en.wikipedia.org/wiki/Pātīgaṇita |
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