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Scotlandite is a sulfite mineral first discovered in a mine at Leadhills in South Lanarkshire , Scotland , an area known to mineralogists and geologists for its wide range of different mineral species found in the veins that lie deep in the mine shafts. This specific mineral is found in the Susanna vein of Leadhills , where the crystals are formed as chisel-shaped or bladed. [ 4 ] Scotlandite was actually the first naturally occurring sulfite , which has the ideal chemical formula of Pb S O 3 . The mineral has been approved by the Commission on New Minerals and Mineral Names, IMA, to be named scotlandite for Scotland. [ 2 ]
Scotlandite is found in association with pyromorphite , anglesite , lanarkite , leadhillite , susannite , and barite . It occurs in cavities in massive barite and anglesite , and is closely associated with lanarkite and susannite . Scotlandite represents the latest phase in the crystallization sequence of the associated lead secondary minerals. It can often be found in the vuggy anglesite as yellowish single crystals up to 1 millimeter in length that sometimes arrange in a fan-shaped aggregates. Anglesite can usually be recognized in a very thin coating on scotlandite which is used to protect the sulfite from further oxidation. A second variety of scotlandite can also occur in discontinuously distributed cavities between the anglesite mass containing the first variety and the barite matrix. This variety is characterized by tiny, whitish to water-clear crystals, and crystal clusters less than one millimeter in size, which encrust large portions of the interior of the cavities. Scotlandite is a uniquely rare mineral, as it occurs in small amounts in few locations around the world. [ 2 ]
Scotlandite is a pale yellow, greyish-white, colorless, transparent mineral with an adamantine or pearly luster. It exhibits a hardness of 2 on the Mohs hardness scale . [ 3 ] Scotlandite occurs as chisel-shaped or bladed crystals elongated along the c-axis, with a tendency to form radiating clusters. Its crystals are characterized by the {100}, {010}, {011}, {021}, {031}, and {032}. faces . Scotlandite shows perfect cleavage along the {100} plane and a less good one along the {010} plane. The measured density is 6.37 g/cm 3 . [ 2 ]
Scotlandite is biaxial positive , which means it will refract light along two axes. The mineral is optically biaxial positive , 2V meas. 35° 24'(Na). The refractive indices are: α ~ 2.035, β ~ 2.040, and γ ~ 2.085 (Na). Dispersion is strong, v >> r. The extinction is β//b, and α [001] = 20° (γ [100] = 4° in the obtuse angle β. H(Mohs) < 2. D = 6.37 and calculated D x = 6.40 g cm −3 . [ 2 ] The infrared spectrum of scotlandite shows conclusively that it is an anhydrous sulfite , with no OH groups or other polyatomic anions being present. It is also proven by electron microprobe analysis and infrared spectroscopy that scotlandite must be a polymorph of lead sulfite. [ 2 ]
Scotlandite is a sulfite compared with chemically related compounds, it is very close to the value of anglesite (6.38 g cm −3 ), but distinctly different from that of lanarkite (6.92 g cm −3 ). Orthorhombic lead sulfite is of higher density (D meas = 6.54, calculated D x = 6.56 g cm −3 ), and has the same chemical properties as well. [ 2 ] The empirical chemical formula for scotlandite calculated on the basis of Pb+S = 2, is Pb l.06 S 0.94 O 2.94 or more ideally PbSO 3 . [ 3 ]
[ 3 ] [ 2 ]
A small crystal of scotlandite, showing some cleavage faces, was examined using Weissenberg and precession techniques. Scotlandite is in the monoclinic crystal system. The only systematic extinctions observed from the single crystal patterns were 0k0 where k was odd. Thus the possible space group is either P2 or P2/m. The unit cell parameters obtained from the single crystal study were used to index the X-ray powder pattern and were then refined with the indexed powder data. [ 2 ] A subsequent study determined the space group is P2 1 /m (no. 11) with unit cell dimensions: a = 4.505 Å , b = 5.333 Å, c = 6.405 Å; β= 106.24°; Z = 2. If the present a and c axes are interchanged, the unit cell of scotlandite is very similar, isotypic, to that of molybdomenite , PbSeO 3 . Lead is coordinated to nine oxygen atoms with Pb-O av =2.75 Å, and possibly further to one sulfur atom with Pb−S=3.46 Å. The average S−O distance in the pyramidal SO 3 group is 1.52 Å. [ 5 ]
List of Minerals | https://en.wikipedia.org/wiki/PbSO3 |
soluble in ammonium acetate (≥ 6 mol/L)
soluble in ammonium tartrate in presence of ammonium chloride and ammonia
Lead(II) sulfate (PbSO 4 ) is a white solid, which appears white in microcrystalline form. It is also known as fast white , milk white , sulfuric acid lead salt or anglesite .
It is often seen in the plates/electrodes of car batteries , as it is formed when the battery is discharged (when the battery is recharged, then the lead sulfate is transformed back to metallic lead and sulfuric acid on the negative terminal or lead dioxide and sulfuric acid on the positive terminal). Lead sulfate is poorly soluble in water.
Anglesite (lead(II) sulfate, PbSO 4 ) adopts the same orthorhombic crystal structure as celestite ( strontium sulfate , SrSO 4 ) and barite ( barium sulfate , BaSO 4 ). All three minerals' structures are in the space group Pbnm (number 62) . [ 6 ] Each lead(II) ion is surrounded by 12 oxygen atoms from 7 sulfate ions, forming a PbO 12 polyhedron. [ 7 ] The lead–oxygen distances range from 2.612 Å to 3.267 Å and the average distance is 2.865 Å. [ 6 ]
Lead(II) sulfate is prepared by treating lead oxide, hydroxide or carbonate with warm sulfuric acid or by treating a soluble lead salt with sulfuric acid.
Alternatively, it can be made by the interaction of solutions of lead nitrate and sodium sulfate.
Lead sulfate is toxic by inhalation, ingestion and skin contact. It is a cumulative poison , and repeated exposure may lead to anemia, kidney damage, eyesight damage or damage to the central nervous system (especially in children). It is also corrosive - contact with the eyes can lead to severe irritation or burns. Typical threshold limit value is 0.15 mg/m 3 .
The naturally occurring mineral anglesite , PbSO 4 , occurs as an oxidation product of primary lead sulfide ore,
A number of lead basic sulfates are known: PbSO 4 ·PbO; PbSO 4 ·2PbO; PbSO 4 ·3PbO; PbSO 4 ·4PbO. They are used in manufacturing of active paste for lead–acid batteries. A related mineral is leadhillite , 2PbCO 3 ·PbSO 4 ·Pb(OH) 2 .
At high concentration of sulfuric acid (>80%), lead hydrogensulfate, Pb(HSO 4 ) 2 , forms. [ 8 ]
Lead(II) sulfate can be dissolved in concentrated HNO 3 , HCl, H 2 SO 4 producing acidic salts or complex compounds, and in concentrated alkali giving soluble tetrahydroxidoplumbate(II) [Pb(OH) 4 ] 2− complexes.
Lead(II) sulfate decomposes when heated above 1000 °C: | https://en.wikipedia.org/wiki/PbSO4 |
Lead telluride is a compound of lead and tellurium (PbTe). It crystallizes in the NaCl crystal structure with Pb atoms occupying the cation and Te forming the anionic lattice. It is a narrow gap semiconductor with a band gap of 0.32 eV. [ 4 ] It occurs naturally as the mineral altaite .
PbTe has proven to be a very important intermediate thermoelectric material . The performance of thermoelectric materials can be evaluated by the figure of merit, Z T = S 2 σ T / κ {\displaystyle ZT=S^{2}\sigma T/\kappa } , in which S {\displaystyle S} is the Seebeck coefficient , σ {\displaystyle \sigma } is the electrical conductivity and κ {\displaystyle \kappa } is the thermal conductivity . In order to improve the thermoelectric performance of materials, the power factor ( S 2 σ {\displaystyle S^{2}\sigma } ) needs to be maximized and the thermal conductivity needs to be minimized. [ 6 ]
The PbTe system can be optimized for power generation applications by improving the power factor via band engineering. It can be doped either n-type or p-type with appropriate dopants. Halogens are often used as n-type doping agents. PbCl 2 , PbBr 2 and PbI 2 are commonly used to produce donor centers. Other n-type doping agents such as Bi 2 Te 3 , TaTe 2 , MnTe 2 , will substitute for Pb and create uncharged vacant Pb-sites. These vacant sites are subsequently filled by atoms from the lead excess and the valence electrons of these vacant atoms will diffuse through crystal. Common p-type doping agents are Na 2 Te, K 2 Te and Ag 2 Te. They substitute for Te and create vacant uncharged Te sites. These sites are filled by Te atoms which are ionized to create additional positive holes. [ 7 ] With band gap engineering, the maximum zT of PbTe has been reported to be 0.8 - 1.0 at ~650K.
Collaborations at Northwestern University boosted the zT of PbTe by significantly reducing its thermal conductivity using ‘all-scale hierarchical architecturing'. [ 8 ] With this approach, point defects, nanoscale precipitates and mesoscale grain boundaries are introduced as effective scattering centers for phonons with different mean free paths, without affecting charge carrier transport. By applying this method, the record value for zT of PbTe that has been achieved in Na doped PbTe-SrTe system is approximately 2.2. [ 9 ]
In addition, PbTe is also often alloyed with tin to make lead tin telluride , which is used as an infrared detector material. | https://en.wikipedia.org/wiki/PbTe |
Stolzite is a mineral , a lead tungstate ; with the formula Pb W O 4 . It is similar to, and often associated with, wulfenite which is the same chemical formula except that the tungsten is replaced by molybdenum . Stolzite crystallizes in the tetragonal crystal system and is dimorphous with the monoclinic form raspite . [ 4 ]
Lead tungstate crystals have the optical transparency of glass combined with much higher density (8.28 g/cm 3 vs ~2.2 g/cm 3 for fused silica ). They are used as scintillators in particle physics because of their short radiation length (0.89 cm), low Molière radius (2.2 cm), quick scintillation response, and radiation hardness. [ 6 ] Lead tungstate crystals are used in the Compact Muon Solenoid's electromagnetic calorimeter. [ 6 ]
It was first described in 1820 by August Breithaupt , who called it Scheelbleispath and then by François Sulpice Beudant in 1832, who called it scheelitine. In 1845, Wilhelm Karl Ritter von Haidinger coined the name stolzite for an occurrence in the Ore Mountains , Bohemia (today the Czech Republic ), naming it after Joseph Alexi Stolz of Teplice in Bohemia. [ 4 ] [ 5 ] It occurs in oxidized hydrothermal tungsten-lead ore deposits typically in association with raspite , cerussite , anglesite , pyromorphite and mimetite . [ 3 ]
This article about a specific mineral or mineraloid is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/PbWO4 |
Palladium(II) nitrate is the inorganic compound with the formula Pd(NO 3 ) 2 .(H 2 O) x where x = 0 or 2. The anhydrous and dihydrate are deliquescent solids. According to X-ray crystallography , both compounds feature square planar Pd(II) with unidentate nitrate ligands. The anhydrous compound, which is a coordination polymer , is yellow. [ 1 ] [ 2 ]
As a solution in nitric acid, Pd(NO 3 ) 2 catalyzes the conversion of alkenes to dinitrate esters. Its pyrolysis affords palladium oxide . [ 3 ]
Hydrated palladium nitrate may be prepared by dissolving palladium oxide hydrate in dilute nitric acid followed by crystallization. The nitrate crystallizes as yellow-brown deliquescent prisms. The anhydrous material is obtained by treating palladium metal with fuming nitric acid . [ 1 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pd(NO3)2 |
Palladium(II,IV) fluoride , also known as palladium trifluoride , is a chemical compound of palladium and fluorine . It has the empirical formula PdF 3 , but is better described as the mixed-valence compound palladium(II) hexafluoropalladate(IV), Pd II [Pd IV F 6 ], and is often written as Pd[PdF 6 ] or Pd 2 F 6 . [ 1 ] [ 2 ]
Pd[PdF 6 ] is the most stable product of the reaction of fluorine and metallic palladium. [ 1 ]
Pd[PdF 6 ] is paramagnetic , and both Pd(II) and Pd(IV) occupy octahedral sites in the crystal structure . [ 2 ] [ 3 ] The Pd II -F distance is 2.17 Å, whereas the Pd IV -F distance is 1.90 Å. [ 4 ] | https://en.wikipedia.org/wiki/Pd2F6 |
Palladium(II) chloride , also known as palladium dichloride and palladous chloride , are the chemical compounds with the formula PdCl 2 . PdCl 2 is a common starting material in palladium chemistry – palladium-based catalysts are of particular value in organic synthesis . It is prepared by the reaction of chlorine with palladium metal at high temperatures.
Two forms of PdCl 2 are known, denoted α and β. In both forms, the palladium centres adopt a square-planar coordination geometry that is characteristic of Pd(II). Furthermore, in both forms, the Pd(II) centers are linked by μ 2 -chloride bridges . The α-form of PdCl 2 is a polymer , consisting of "infinite" slabs or chains. The β-form of PdCl 2 is molecular , consisting of an octahedral cluster of six Pd atoms. Each of the twelve edges of this octahedron is spanned by Cl − . PtCl 2 adopts similar structures, whereas NiCl 2 adopts the CdCl 2 motif, featuring hexacoordinated Ni(II). [ 1 ]
Two further polymorphs , γ-PdCl 2 and δ-PdCl 2 , have been reported and show negative thermal expansion . The high-temperature δ form contains planar ribbons of edge-connected PdCl 4 squares, like α-PdCl 2 . The low-temperature γ form has corrugated layers of corner-connected PdCl 4 squares. [ 2 ]
Palladium(II) chloride is prepared by dissolving palladium metal in aqua regia or hydrochloric acid in the presence of chlorine . Alternatively, it may be prepared by heating palladium sponge metal with chlorine gas at 500 °C. [ 3 ] [ 4 ] [ 5 ] [ 6 ]
Palladium(II) chloride is a common starting point in the synthesis of other palladium compounds. It is not particularly soluble in water or non-coordinating solvents, so the first step in its utilization is often the preparation of labile but soluble Lewis base adducts , such as bis(benzonitrile)palladium dichloride and bis(acetonitrile)palladium dichloride . [ 7 ] These complexes are prepared by treating PdCl 2 with hot solutions of the nitriles:
Although occasionally recommended, inert-gas techniques are not necessary if the complex is to be used in situ . As an example, bis(triphenylphosphine)palladium(II) dichloride may be prepared from palladium(II) chloride by reacting it with triphenylphosphine in benzonitrile: [ 8 ]
Further reduction in the presence of more triphenylphosphine gives tetrakis(triphenylphosphine)palladium(0) ; the second reaction may be carried out without purifying the intermediate dichloride: [ 9 ]
Alternatively, palladium(II) chloride may be solubilized in the form of the tetrachloropalladate(II) anion, such as in sodium tetrachloropalladate , by reacting with the appropriate alkali metal chloride in water: [ 10 ] Palladium(II) chloride is insoluble in water, whereas the product dissolves:
This compound may also further react with phosphines to give phosphine complexes of palladium. [ 10 ]
Palladium chloride may also be used to give heterogeneous palladium catalysts: palladium on barium sulfate , palladium on carbon , and palladium chloride on carbon. [ 11 ]
Even when dry, palladium(II) chloride is able to rapidly stain stainless steel . Thus, palladium(II) chloride solutions are sometimes used to test for the corrosion -resistance of stainless steel. [ 12 ]
Palladium(II) chloride is sometimes used in carbon monoxide detectors. Carbon monoxide reduces palladium(II) chloride to palladium:
Residual PdCl 2 is converted to red PdI 2 , the concentration of which may be determined colorimetrically: [ 13 ]
Palladium(II) chloride is used in the Wacker process for production of aldehydes and ketones from alkenes .
Palladium(II) chloride can also be used for the cosmetic tattooing of leukomas in the cornea . | https://en.wikipedia.org/wiki/PdCl2 |
Bis(acetonitrile)palladium dichloride is the coordination complex with the formula PdCl 2 (NCCH 3 ) 2 . It is the adduct of two acetonitrile ligands with palladium(II) chloride . It is a yellow-brown solid that is soluble in organic solvents. The compound is a reagent and a catalyst for reactions that require soluble Pd(II). [ 1 ] The compound is similar to bis(benzonitrile)palladium dichloride . It reacts with 1,5-cyclooctadiene to give dichloro(1,5-cyclooctadiene)palladium .
This catalysis article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/PdCl2(MeCN)2 |
Bis(benzonitrile)palladium dichloride is the coordination complex with the formula PdCl 2 (NCC 6 H 5 ) 2 . It is the adduct of two benzonitrile (PhCN) ligands with palladium(II) chloride . It is a yellow-brown solid that is soluble in organic solvents. The compound is a reagent and a precatalyst for reactions that require soluble Pd(II). [ 1 ] A closely related compound is bis(acetonitrile)palladium dichloride .
The complex is prepared by dissolving PdCl 2 in warm benzonitrile . [ 2 ] The PhCN ligands are labile, and the complex reverts to PdCl 2 in noncoordinating solvents. According to X-ray crystallography , the two PhCN ligands are mutually trans. [ 3 ] | https://en.wikipedia.org/wiki/PdCl2(PhCN)2 |
Bis(triphenylphosphine)palladium chloride is a coordination compound of palladium containing two triphenylphosphine and two chloride ligands. It is a yellow solid that is soluble in some organic solvents. It is used for palladium-catalyzed coupling reactions , e.g. the Sonogashira–Hagihara reaction . The complex is square planar . Many analogous complexes are known with different phosphine ligands.
This compound may be prepared by treating palladium(II) chloride with triphenylphosphine : [ 2 ] [ 3 ]
Upon reduction with hydrazine in the presence of excess triphenylphosphine, the complex is a precursor to tetrakis(triphenylphosphine)palladium , Pd(PPh 3 ) 4 : [ 4 ]
Several crystal structures containing PdCl 2 (PPh 3 ) 2 have been reported. In all of the structures, PdCl 2 (PPh 3 ) 2 adopts a square planar coordination geometry and the trans isomeric form . [ 5 ] [ 6 ] [ 7 ] [ 8 ]
The complex is used as a pre-catalyst for a variety of coupling reactions. [ 9 ]
The Suzuki reaction was once limited by high levels of catalyst and the limited availability of boronic acids. Replacements for halides were also found, increasing the number of coupling partners for the halide or pseudohalide as well. Using bis(triphenylphosphine)palladium chloride as the catalyst, triflates and boronic acids have been coupled on an 80 kilogram scale in good yield. [ 10 ] The same catalyst is effective for the Sonogashira coupling . [ 11 ] | https://en.wikipedia.org/wiki/PdCl2P2 |
Palladium(II) fluoride , also known as palladium difluoride , is the chemical compound of palladium and fluorine with the formula PdF 2 .
PdF 2 is prepared by refluxing palladium(II,IV) fluoride , Pd II [Pd IV F 6 ], with selenium tetrafluoride , SeF 4 .
Like its lighter congener nickel(II) fluoride , PdF 2 adopts a rutile -type crystal structure , [ 2 ] [ 3 ] containing octahedrally coordinated palladium, which has the electronic configuration t 6 2g e 2 g . This configuration causes PdF 2 to be paramagnetic [ 4 ] due to two unpaired electrons, one in each e g -symmetry orbital of palladium.
Palladium fluoride is an insoluble powder used in infrared optical sensors , [ 5 ] and in situations where reactivity to oxygen makes palladium oxide unsuitable. | https://en.wikipedia.org/wiki/PdF2 |
Palladium(II,IV) fluoride , also known as palladium trifluoride , is a chemical compound of palladium and fluorine . It has the empirical formula PdF 3 , but is better described as the mixed-valence compound palladium(II) hexafluoropalladate(IV), Pd II [Pd IV F 6 ], and is often written as Pd[PdF 6 ] or Pd 2 F 6 . [ 1 ] [ 2 ]
Pd[PdF 6 ] is the most stable product of the reaction of fluorine and metallic palladium. [ 1 ]
Pd[PdF 6 ] is paramagnetic , and both Pd(II) and Pd(IV) occupy octahedral sites in the crystal structure . [ 2 ] [ 3 ] The Pd II -F distance is 2.17 Å, whereas the Pd IV -F distance is 1.90 Å. [ 4 ] | https://en.wikipedia.org/wiki/PdF3 |
Palladium (IV) fluoride , also known as palladium tetrafluoride , is the chemical compound of palladium and fluorine with the chemical formula PdF 4 . The palladium atoms in PdF 4 are in the +4 oxidation state . [ 2 ] [ 3 ]
Palladium tetrafluoride has been prepared by reacting palladium(II,IV) fluoride with fluorine gas at pressures around 7 atm and at 300 °C for several days. [ 1 ]
Crystals are composed of octahedral PdF6 units, with four fluorides from each octahedron shared (bridging between octahedra). [ 4 ]
PdF 4 is a strong oxidising agent and undergoes rapid hydrolysis in moist air. [ 1 ] | https://en.wikipedia.org/wiki/PdF4 |
Palladium hexafluoride is an inorganic chemical compound of palladium metal and fluorine with the chemical formula PdF 6 . [ 1 ] It is reported to be a still hypothetical compound . [ 2 ] This is one of many palladium fluorides .
Fluorination of palladium powder with atomic fluoride at 900–1700 Pa. [ 3 ]
Palladium hexafluoride is predicted to be stable. [ 4 ] The compound is reported to form dark red solid that decomposes to PdF 4 . Palladium hexafluoride is a very powerful oxidizing agent . [ 3 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/PdF6 |
Bis(triphenylphosphine)palladium chloride is a coordination compound of palladium containing two triphenylphosphine and two chloride ligands. It is a yellow solid that is soluble in some organic solvents. It is used for palladium-catalyzed coupling reactions , e.g. the Sonogashira–Hagihara reaction . The complex is square planar . Many analogous complexes are known with different phosphine ligands.
This compound may be prepared by treating palladium(II) chloride with triphenylphosphine : [ 2 ] [ 3 ]
Upon reduction with hydrazine in the presence of excess triphenylphosphine, the complex is a precursor to tetrakis(triphenylphosphine)palladium , Pd(PPh 3 ) 4 : [ 4 ]
Several crystal structures containing PdCl 2 (PPh 3 ) 2 have been reported. In all of the structures, PdCl 2 (PPh 3 ) 2 adopts a square planar coordination geometry and the trans isomeric form . [ 5 ] [ 6 ] [ 7 ] [ 8 ]
The complex is used as a pre-catalyst for a variety of coupling reactions. [ 9 ]
The Suzuki reaction was once limited by high levels of catalyst and the limited availability of boronic acids. Replacements for halides were also found, increasing the number of coupling partners for the halide or pseudohalide as well. Using bis(triphenylphosphine)palladium chloride as the catalyst, triflates and boronic acids have been coupled on an 80 kilogram scale in good yield. [ 10 ] The same catalyst is effective for the Sonogashira coupling . [ 11 ] | https://en.wikipedia.org/wiki/PdP2Cl2 |
Pdr1p (Pleiotropic Drug Resistance 1p) is a transcription factor found in yeast and is a key regulator of genes involved in general drug response. It induces the expression of ATP-binding cassette transporter , which can export toxic substances out of the cell, allowing cells to survive under general toxic chemicals. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] It binds to DNA sequences that contain certain motifs called pleiotropic drug response element (PDRE). [ 1 ] Pdr1p is encoded by a gene called PDR1 (also known as YGL013C) on chromosome VII. [ 2 ] [ 6 ]
Pdr1p is a main regulator of PDR genes and is known to target about 50 genes. [ 1 ] [ 7 ] Pdr1p binds to sequence 5'-TCCGYGGR-3' of PDRE, which is located within the promoter sequences of its target genes. [ 8 ] [ 9 ] 218 genes are reported to possess PDRE. [ 10 ] Pdr1p is observed to bind PDRE sites on DNA at basal level and also after simulation with toxins. This shows that Pdr1p-DNA interaction isn't dependent on toxic stimulation. This also suggests an involvement of activator(s) or co-activator(s) that induce PDR genes along with Pdr1p. [ 1 ] Pdr1p has a functional homolog called Pdr3p encoded by gene called PDR3 . Pdr3p is known to be regulated by Pdr3p and Pdr1p. [ 11 ] Pdr1p can form a homodimer with itself or heterodimer with Pdr3p. [ 12 ] [ 5 ]
Loss of function studies of both PDR1 and PDR3 revealed that Pdr1p mutant shows lower tolerance (grows less in culture) against organic toxins such as cycloheximide and oligomycin . This confirms the functions of Prf1p that confer stronger drug response phenotype than Pdr3p. However, Pdr3p is crucial for PDR responses since cells containing loss of function mutation in both PDR1 and PDR3 genes weren't able to grow at all in the presence of those two toxins. [ 9 ]
Both Pdr1p and Pdr3p regulate Pdr5p, which is an ATP-binding cassette transporter . [ 9 ] A single amino acid substitution mutation, which is a gain of function mutation of Pdr1p denoted as pdr1-3 (F815S, substitution mutation of Phenylalanine at 815th of the polypeptide by Serine ) leads to an over-expression of mRNA of PDR5 , which codes for Pdr5p. [ 13 ] For cells treated with fluphenazine , Pdr1p was the only transcription factor necessary for PDR response genes induction. But at basal level, Pdr1p can be partially compensated by Pdr3p, a functional homolog of Pdr1p. [ 1 ]
Pdr1p and Pdr3p is a part of Gal4 transcription factor family due to their zinc-finger DNA binding motif, which is located in N-terminus end of Pdr1p. Pdr1p also contains a long internal region of many inhibitory domains and possess a C-terminal transcription activation domain (amino acids 879–1036). The transcriptional activation domain is rich in glutamine and asparagine , which is theorized to facilitate in protein-protein interaction via hydrogen bonding . [ 11 ] [ 10 ] A study found that DNA-binding domain of Pdr1p was sufficient for recognizing its endogenous target genes. [ 14 ] Strong drug resistance phenotype of yeasts with pdr1-3 is speculated due to its inability to bind to ligands that otherwise cause conformational change to inhibit the transcriptional activity of Pdr1p. [ 10 ]
Pdr1p and Pdr3p also interact with other transcription factors and their associated networks such as Yap1p, which controls oxidative stress response, and Rpn4p, which regulates proteasome activities, depending on the kinds of toxins cells face. [ 8 ] It is known that Pdr1p induces the expression of Rpn4p. [ 10 ]
Drugs or toxic chemicals are useful in killing pathogenic bacteria or tumor cells, and studying how they mechanistically develop tolerance to a wide range of drugs can improve anti-bacterial and cancer therapeutics. [ 12 ] Pdr5p has a similar mechanism of actions and functions to human multidrug resistance protein , whose overexpression is shown to provide chemical tolerance to cancer cells. Studying Pdr5p and how it is regulated by Pdr1p in yeast can give insights into how multi drug resistance occurs in mammals. [ 15 ]
By using pdr1-3 and fusing the promoter of Pdr5p to genes that code for membrane proteins of interests, yeast membrane proteins such as Pdr5p, Yor1, and Drs2 can be expressed highly so that they can be efficiently cloned and purified for further studies. [ 16 ] | https://en.wikipedia.org/wiki/Pdr1p |
The term peace ecology has been used by Christos Kyrou of American University to describe a proposed theoretical framework that is intended to provide " a better understanding, of the inherent capacities of the environment to inform and sustain peace. " [ 1 ]
Peace ecology was introduced by Professor Christos Kyrou, of American University first in an article at the annual meeting of the International Studies Association , in San Diego , California , Mar 22, 2006. [ 1 ] It was later published in its completed form in an article with the title Peace Ecology: An Emerging Paradigm In Peace Studies in The International Journal of Peace Studies, Volume 12 #1, 2007. [ 2 ]
With a follow-up article submitted for the Conference on Cutting Edge Theories and Recent Developments in Conflict Resolution, September 27 and 28, 2007, at Syracuse, NY, Dr. Kyrou examined various methodological perspectives from Peace Ecology. [ 3 ]
Dr. Kyrou, together with his graduate and undergraduate students at the International Peace & Conflict Resolution Division of the School of International Service at The American University in Washington DC continue their effort to expand the practical and theoretical potential of Peace Ecology. [ 4 ] | https://en.wikipedia.org/wiki/Peace_ecology |
The peace lines or peace walls are a series of separation barriers in Northern Ireland that separate predominantly Irish republican or nationalist Catholic neighbourhoods from predominantly British loyalist or unionist Protestant neighbourhoods. They have been built at urban interface areas in Belfast and elsewhere.
The majority of peace walls are located in Belfast, but they also exist in other regions of Northern Ireland with more than 32 kilometres (20 miles) in total. [ 1 ]
Although temporary peace walls were built in Belfast in the 1920s (in Ballymacarett) and 1930s (in Sailortown), the first peace lines of " the Troubles " era were built in 1969, following the outbreak of civil unrest and the 1969 Northern Ireland riots . They were initially built as temporary structures, but due to their effectiveness they have become wider, longer, more numerous and more permanent. Originally few in number, they have multiplied over the years, from 18 in the early 1990s to at least 59 as of late 2017; [ 2 ] in total they stretch over 34 kilometres (21 miles), with most located in Belfast. They have been increased in both height and number since the Good Friday Agreement of 1998 . [ 3 ] Three-quarters of Belfast's estimated 97 peace lines and related structures (such as gates and closed roads) are in the north and west of the city. [ 4 ] These are also the poorer and more disadvantaged areas of Belfast. 67% of deaths during the sectarian violence occurred within 500 metres (550 yd) of one of these "interface structures". [ 5 ]
The stated purpose of the peace lines is to minimize inter-communal violence between Catholics (most of whom are nationalists who self-identify as Irish [ 6 ] ) and Protestants (most of whom are unionists who self-identify as British [ 6 ] ).
The peace lines range in length from a few hundred meters (yards) to over 5 kilometres (3 mi). They may be made of iron, brick, steel or a combination of the three and are up to 8 metres (25 feet) high. [ 7 ] [ 8 ] Some have gates in them (sometimes staffed by police ) that allow passage during daylight but are closed at night.
In recent years, they have become locations for tourism. Black taxis now take groups of tourists around Belfast's peace lines, trouble spots and famous murals .
The most prominent peace lines in the past few years separate the nationalist Falls Road and unionist Shankill Road areas of West Belfast; the nationalist Short Strand from the unionist Cluan Place areas of East Belfast, the unionist Corcrain Road and the nationalist Obins Drive in Portadown and the unionist Fountain Estate and nationalist Bishop Street area of Derry .
In 2008, a public discussion began about how and when the peace lines could be removed. [ 9 ] Belfast City Council agreed to develop a strategy regarding the removal of peace walls on 1 September 2011. [ 10 ] [ 11 ] At the end of 2011, several local community initiatives resulted in the opening of a number of interface structures for a trial period. [ 12 ] A study was released in 2012 indicating that 69% of residents believe that the peace walls are still necessary because of potential violence. [ 13 ]
In January 2012, the International Fund for Ireland launched a Peace Walls funding programme to support local communities who want to work towards beginning to remove the peace walls. [ 14 ] In May 2013, the Northern Ireland Executive committed to the removal of all peace lines by mutual consent by 2023. [ 15 ]
In 2017, the Belfast Interface Project published a study entitled "Interface Barriers, Peacelines & Defensive Architecture" that identified 97 separate walls, barriers and interfaces in Belfast. [ 16 ] A history of the development of these structures can be found at the Peacewall Archive. [ 17 ]
In September 2017, the Northern Ireland Department of Justice published its Interface Programme, established to deliver the commitment made by the Northern Ireland Executive to remove all Interface structures by 2023 under the Together: Building a United Community Strategy. [ 18 ] [ 19 ]
In September 2019, a series of events were held in Belfast to mark the anniversary of 50 years of peace lines in the city. This included an international conference alongside other events to discuss the past and possible future of the peace lines. [ 20 ]
Category | https://en.wikipedia.org/wiki/Peace_lines |
A browser speed test is a computer benchmark that scores the performance of a web browser , by measuring the browser's efficiency in completing a predefined list of tasks. In general the testing software is available online, located on a website, where different algorithms are loaded and performed in the browser client. Typical test tasks are rendering and animation, DOM transformations, string operations, mathematical calculations, sorting algorithms , graphic performance tests and memory instructions.
Browser speed tests have been used during browser wars to prove superiority of specific web browsers. The popular Acid3 test is no particular speed test but checks browser conformity to web standards (though it checks whether a general performance goal is met).
Speedometer was originally developed by the WebKit team at Apple and released in 2014 and was updated in 2018. [ 1 ] Speedometer 2.0 tests a browser's Web app responsiveness by timing simulated user interactions.
This benchmark simulates user actions for adding, completing, and removing to-do items using multiple examples in TodoMVC. Each example in TodoMVC implements the same todo application using DOM APIs in different ways. Some call DOM APIs directly from ECMAScript 5 (ES5), ECMASCript 2015 (ES6), ES6 transpiled to ES5, and Elm transpiled to ES5. Others use one of eleven popular JavaScript frameworks: React, React with Redux, Ember.js, Backbone.js, AngularJS, (new) Angular, Vue.js, jQuery, Preact, Inferno, and Flight. Many of these frameworks are used on the most popular websites in the world, such as Facebook and Twitter. The performance of these types of operations depends on the speed of the DOM APIs, the JavaScript engine, CSS style resolution, layout, and other technologies.
Peacekeeper is a platform-independent benchmark by Futuremark that tests rendering, mathematical and memory operations. It takes approx. 5 minutes for execution and tells the results of other browsers with different CPUs. Futuremark stopped maintaining Peacekeeper in July 2015. [ 2 ] The test was taken offline in March 2018 and is no longer available.
Microsoft maintains a suite of performance-oriented tests, often designed to test and stress JavaScript and rendering performance. These tests are typically designed to highlight IE 's performance [ citation needed ] , but are compatible with other major browsers.
WebXPRT is a cross-platform browser benchmark that runs HTML5- and JavaScript-based workloads. [ 3 ] The benchmark provides scores for six individual workloads, as well as an overall score. [ 4 ] WebXPRT is published by the BenchmarkXPRT Development Community, which is administered by Principled Technologies, and is one of the BenchmarkXPRT benchmarks. WebXPRT 4 is the most current version of WebXPRT. [ 5 ]
Performance test for HTML5 3D applications. It tests performance in both Canvas3D and WebGL .
A Mozilla test suite based on SunSpider tests. It takes several minutes for execution and displays very detailed information about every single test task.
Another JavaScript test suite from Mozilla, released September 14, 2010. [ 6 ]
A JavaScript test suite developed by Apple. [ 7 ]
SunSpider is a benchmark created by the webkit team that aims to measure JavaScript performance on tasks relevant to the current and near future use of JavaScript in the real world, such as encryption and text manipulation. [ 8 ] The suite further attempts to be balanced and statistically sound. [ 9 ]
Version 0.9 was released by the WebKit team in December 2007. [ 10 ] It was well-received, [ 11 ] and other browser developers also use it to compare the JavaScript performance of different browsers. [ 12 ]
Version 0.9.1 was released in April 2010. [ 13 ]
Version 1.0 was released in April 2013. [ 14 ]
A JavaScript test suite by Google , used to optimize the Google Chrome web browser. It does not test rendering performance. It was superseded by Google's Octane benchmark.
Google's JavaScript test suite which replaces the V8 benchmark. According to Google, "Octane v.1 consists of 13 tests, 5 new ones and 8 from the original V8 Benchmark Suite." [ 15 ] Octane v.2 supplanted v.1, consisting of "17 tests, four more than Octane v1." [ 16 ]
As of April 12 2017, Google no longer maintains Octane. [ 17 ]
This tests vector, bitmap, and text rendering for both Adobe Flash and HTML5. | https://en.wikipedia.org/wiki/Peacekeeper_(benchmark) |
Peak is an artificial intelligence company headquartered in Manchester , UK . [ 1 ] It was founded in 2015 [ 2 ] and has additional offices in Jaipur , India , and New York City , United States. It is known for its artificial intelligence platform, a SaaS platform that allows data scientists to build AI workflows, invoke them on ingested data and expose the results via APIs and/or built-in web applications, as well as abstracting the underlying cloud infrastructure . [ 3 ]
The company was founded by CEO Richard Potter, David Leitch and Atul Sharma. [ 4 ] In 2015, Peak was one of the winners of the Tech North Northern Stars competition. [ 5 ] In 2017, it secured £2.5 million in Series A capital funding from MMC Ventures [ 6 ] for investment in machine learning and artificial intelligence technologies [ 7 ] and was named as one of the top five startups in Manchester by Wired magazine . [ 8 ] In 2018, it was chosen to work as part of Arsenal F.C. 's Innovation Lab [ 9 ] and it was one of the 37 fastest growing technology companies in the UK selected to join the Tech City UK Upscale programme. [ 10 ]
In April 2020, the company raised $12 million in extended series A funding, which is required to sustain its growth, commercial expansion, and R&D efforts. [ 11 ]
In February 2021, Peak announced a $21 million Series B funding round – led by investors Oxx, Praetura Ventures, MMC Ventures and Arete – to further make AI accessible to non-tech companies. [ 12 ] In August 2021, Peak announced a $75 million Series C funding round, led by SoftBank Vision Fund 2 . [ 13 ]
In March 2025, Peak was acquired by leading global software company, UiPath . [ 14 ] | https://en.wikipedia.org/wiki/Peak_(company) |
Peak bone mass is the maximum amount of bone a person has during their life. [ 1 ] It typically occurs in the early 20s in females and late 20s in males. [ 2 ] Peak bone mass is typically lower in females than males, and is also lower in White people and Asians compared to black populations. [ 1 ] A way to determine bone mass is to look at the size and density of the mineralized tissue in the periosteal envelope and using the bone mineral density (BMD) of a person can help determine the strength of that bone. [ 3 ] Research has shown that puberty affects bone size much more because during this time males typically undergo a longer bone maturation period than women which is why women are more prone to osteoporosis than men. [ 3 ] | https://en.wikipedia.org/wiki/Peak_bone_mass |
Peak calling is a computational method used to identify areas in a genome that have been enriched with aligned reads as a consequence of performing a ChIP-sequencing or MeDIP-seq experiment. These areas are those where a protein interacts with DNA . [ 1 ] When the protein is a transcription factor , the enriched area is its transcription factor binding site (TFBS). Popular software programs include MACS. [ 2 ] Wilbanks and colleagues [ 3 ] is a survey of the ChIP-seq peak callers, and Bailey et al. [ 4 ] is a description of practical guidelines for peak calling in ChIP-seq data.
Peak calling may be conducted on transcriptome/exome as well to RNA epigenome sequencing data from MeRIPseq [ 5 ] or m6Aseq [ 6 ] for detection of post-transcriptional RNA modification sites with software programs, such as exomePeak. [ 7 ] Many of the peak calling tools are optimized for only some kind of assays such as only for transcription-factor ChIP-seq or only for DNase-Seq . [ 8 ] However new generation of peak callers such as DFilter [ 9 ] are based on generalized optimal theory of detection and has been shown to work for nearly all kinds for tag profile signals from next-gen sequencing data. It is also possible to do more complex analysis using such tools like combining multiple ChIP-seq signal to detect regulatory sites. [ 10 ] In the context of ChIP-exo, this process is known as 'peak-pair calling'. [ 11 ]
Differential peak calling is about identifying significant differences in two ChIP-seq signals. One can distinguish between one-stage and two-stage differential peak callers. One stage differential peak callers work in two phases: first, call peaks on individual ChIP-seq signals and second, combine individual signals and apply statistical tests to estimate differential peaks. DBChIP, [ 12 ] MACS2 , and MAnorm [ 13 ] are examples for one stage differential peak callers.
Two stage differential peak callers segment two ChIP-seq signals and identify differential peaks in one step. They take advantage of signal segmentation approaches such as Hidden Markov Models . Examples for two-stage differential peak callers are ChIPDiff, [ 14 ] ODIN. [ 15 ] and THOR. Differential peak calling can also be applied in the context of analyzing RNA-binding protein binding sites. [ 16 ]
This molecular or cell biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peak_calling |
Peak information rate ( PIR ) is a burstable rate set on routers and/or switches that allows throughput overhead. Related to committed information rate (CIR) which is a committed rate speed guaranteed/capped. For example, a CIR of 10 Mbit/s PIR of 12 Mbit/s allows you access to 10 Mbit/s minimum speed with burst/spike control that allows a throttle of an additional 2 Mbit/s; this allows for data transmission to "settle" into a flow. [ 1 ] [ 2 ] PIR is defined in MEF Standard 10.4 Subscriber Ethernet Service Attributes [ 3 ]
Excess information rate ( EIR ) is the magnitude of the burst above the CIR (PIR = EIR + CIR). [ citation needed ]
Maximum information rate ( MIR ) in reference to broadband wireless refers to maximum bandwidth the subscriber unit will be delivered from the wireless access point in kbit/s. [ 4 ]
This computer networking article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peak_information_rate |
A peak programme meter ( PPM ) is an instrument used in professional audio that indicates the level of an audio signal .
Different kinds of PPM fall into broad categories:
In professional use, which requires consistent level measurements across an industry, audio level meters often comply with a formal standard. This ensures that all compliant meters indicate the same level for a given audio signal. The principal standard for PPMs is IEC 60268-10. It describes two different quasi-PPM designs that have roots in meters originally developed in the 1930s for the AM radio broadcasting networks of Germany (Type I) and the United Kingdom (Type II). The term Peak Programme Meter usually refers to these IEC-specified types and similar designs. Though originally designed for monitoring analogue audio signals, these PPMs are now also used with digital audio.
PPMs do not provide effective loudness monitoring . Newer types of meter do, and there is now a push within the broadcasting industry to move away from the traditional level meters in this article to two new types: loudness meters based on EBU Tech. 3341 and oversampling true PPMs. The former would be used to standardise broadcast loudness to −23 LUFS and the latter to prevent digital clipping . [ 2 ]
In common with many other types of audio level meter, PPMs originally used electro-mechanical displays. These took the form of moving-coil panel meters or mirror galvanometers with demanding 'ballistics': the key requirement being that the indicated level should rise as quickly as possible with negligible overshoot . These displays require active driver electronics.
Nowadays PPMs are often implemented as 'bargraph' incremental displays using solid-state illuminated segments in a vertical or horizontal array. For these, IEC 60268-10 requires a minimum of 100 segments and a resolution better than 0.5 dB at the higher levels.
Many operators prefer the moving-coil meter type of display, in which a needle moves in an arc, because they feel the angular movement is easier for the human eye to monitor than the linear movement of a bar graph. [ 3 ]
PPMs can also be implemented in software—in a general-purpose computer or by a dedicated device that inserts a PPM image into a picture signal for display on a picture monitor.
A variety of terms such as 'line-up level' and 'operating level' exist, and their meaning may vary from place to place. In an attempt bring clarity to level definitions in the context of programme transmission from one country to another, where different technical practices may apply, ITU-R Rec. BS.645 defined three reference levels: Measurement Level (ML), Alignment Level (AL) and Permitted Maximum Level (PML). This document shows the reading corresponding to these levels for several types of meter. [ 4 ] Alignment Level is the level of a steady sine-wave alignment tone. Permitted Maximum Level refers to the permitted maximum meter indication that operators should aim for on speech, music etc., not tone.
PPMs often use white-on-black displays, to minimise eyestrain especially with extended periods of use.
PPMs are usually calibrated in one of these ways:
Whichever scheme is used, usually there is a scale mark corresponding to Alignment Level.
Most PPMs have an approximately logarithmic scale, i.e., roughly linear in decibels, to provide useful indications over a wide dynamic range .
Quasi-PPMs use a short integration time so they can register peaks longer than a few milliseconds in duration. In the original context of AM radio broadcasting in the 1930s, overloads due to shorter peaks were considered unimportant on the grounds that the human ear could not detect distortion due to momentary clipping. Ignoring momentary clipping made it possible to increase average modulation levels. In modern digital audio practice, where quality standards are hopefully much higher than AM radio in the 1930s, clipping of even short peaks is usually regarded as something to avoid.
On typical, real-world audio signals, a quasi-PPM under-reads the true peak by 6 to 8 dB. [ 5 ] Nevertheless, quasi-PPMs are still widely used in the digital age because of their usefulness in achieving programme balance. Overloads are avoided by allowing, typically, 9 dB of headroom when controlling digital levels with a quasi-PPM.
The extent to which quasi-PPMs show less than the true amplitude of momentary peaks is determined by the 'integration time'. This is defined by IEC 60268-10 as, "...the duration of a burst of sinusoidal voltage of 5000 Hz at reference level that results in an indication 2 dB below reference indication." [ 6 ] [ 7 ] This standard also contains tables showing the difference between indicated and true peaks for tone bursts of other durations. The longer the integration time, the greater the difference between the true and indicated peaks.
In earlier standards, different methods of measurement and criteria were used, such as 0.2 Neper or 80% voltage instead of 2 dB, but the practical difference between them was small. [ 8 ]
A Type I PPM has an integration time of 5 milliseconds and a Type II PPM has an integration time of 10 milliseconds.
All PPMs have a return time much longer than the integration time, to give the operator more time to see the peaks and reduce eye strain. Type I PPMs fall back 20 dB in 1.7 seconds. Type II PPMs fall back 24 dB in 2.8 seconds.
The PPM was originally developed, independently in both Germany and the United Kingdom, for use in AM radio broadcasting networks in the 1930s. These were quasi-peak meters with some features in common but otherwise substantially different. They are superior to earlier types of meter that were not good for monitoring peak audio levels.
In about 1936 and 1937, German broadcasters developed a peak programme meter with a mirror galvanometer known as a "Lichtzeigerinstrument" (light pointer) for the display. The system consisted of a drive amplifier (e.g., ARD types U21 and U71) and a separate display unit (e.g., ARD types J47 and J48). [ 9 ] A stereo version, known as a "Doppel-Lichtzeigerinstrument" contained two mirror galvanometer displays in a single housing. Such displays were still used until the 1970s, when solid-state bargraph displays became the norm.
The design became standardised as DIN 45406. It evolved into the Type I meter in IEC 60268-10 and it is still known colloquially as a DIN PPM. Compared to the Type II designs it has faster integration and return times, a much wider dynamic range and a semi-logarithmic scale, and is calibrated in dB relative to Permitted Maximum Level. It remains in use in much of northern Europe. [ 10 ]
In German broadcasting, the nominal analogue signal corresponding to Permitted Maximum Level was standardised by ARD at 1.55 volts (+6 dBu), and this is the usual sensitivity of a DIN-type PPM for an indication of 0 dB. Alignment Level (−3 dBu) is shown on the meter by a scale mark at −9.
In Scandinavia a variant of the DIN PPM known as 'Nordic' is used. It has the same integration and return times but a different scale, with 'TEST' corresponding to Alignment Level (0 dBu) and +9 corresponding to Permitted Maximum Level (+9 dBu). [ 3 ] [ 10 ] [ 11 ] Compared to the DIN scale, the Nordic scale is more logarithmic and covers a somewhat smaller dynamic range.
The BBC used a number of methods of measuring programme volume in its early years, including the 'volume indicator' and 'slide-back voltmeter'.
By 1932, when the BBC moved to purpose-built facilities in Broadcasting House , the first audio meter called a 'programme meter' was introduced. It was developed by Charles Holt-Smith of the Research Department and became known as the 'Smith meter'. This was the first meter with white markings on a black background. It was driven by a circuit that gave a roughly logarithmic transfer characteristic, so it could be calibrated in decibels . The overall characteristics were the product of the driver circuit and the movement's ballistics.
The first of the PPMs was designed by C. G. Mayo, also of the BBC's Research Department. It came into service in 1938. It kept the Smith meter's logarithmic, white-on-black display, and included all the key design features that are still used to this day with only slight modification: full-wave rectification , fast integration and slow return times, and a simple scale calibrated from 1 to 7.
Mayo and others determined the integration and return times by a series of experiments. At first, they intended to create a true peak meter to prevent transmitters from exceeding 100% modulation. They created a prototype meter with an integration time of about 1 ms. They found that the ear tolerates distortion of only a few ms, and that a 'registration time' of 4 ms is sufficient. They made the return time a compromise between a rapid return, which was tiring to the eye—and a slow return, which made control difficult. Engineers decided that the meter should take between 2s and 3s to drop back 26 dB. [ 12 ] [ 13 ]
The BBC PPM became the subject of several formal standards: BS 4297:1968 (superseded); BS5428:Part 9:1981 (superseded) and then BS 6840-10:1991. The text of the latter is identical to the Type IIa PPM in IEC 60268-10:1991. [ 10 ]
Alignment level (0 dBu) and Permitted Maximum Level (+8 dBu) correspond to scale marks '4' and '6' respectively.
The BBC PPM was adopted by commercial broadcasters in the UK. Other organisations around the world, including the EBU , CBC and ABC used the same dynamics but with slightly different scales. [ 10 ]
Modern British PPMs have a 4 dB spacing between the scale marks. Older designs had a 6 dB spacing between '1' and '2'. This discrepancy can sometimes also be found at the equivalent position on the derived CBC and ABC scales.
From its inception in 1939 until 2009, the PPM display was available in the form of an electro-mechanical, moving-coil meter movement with a demanding ballistic specification. For many years these were manufactured by Ernest Turner and Company, [ 12 ] and in later years by Sifam, based in Torquay. In 2009, Sifam announced it was ending production of the Type 74 dual-needle meter movement. In 2010, Sifam ended all PPM meter movement manufacturing. Three major users—Bryant Unlimited, Canford Audio, and TSL—placed final orders with Sifam for large stocks of the meters to supply manufacturing and maintenance activities for several years. [ 14 ]
In the UK, twin-needle PPMs are sometimes used for stereo. Red and green needles are used for left and right. White and yellow needles are used for sum and difference (M and S). A more recent variation is to use a black needle with a dayglo orange tip for S instead of yellow.
The sensitivity of the S indication can be increased on some meter installations by 20 dB; this is to aid line-up procedures, e.g., of stereo mic pairs, or the azimuth of analogue tape machine heads, which rely on cancellation of the S signal.
M and S meters are normally aligned to the 'M6' standard in which M = (L + R) − 6 dB and S = (L − R) − 6 dB. In other words, the sum and difference signals are each attenuated by 6 dB before being displayed on the meter. As a result, signals of identical amplitude and phase in the left and right channels make the M meter show exactly the same deflection as for the individual L and R meters. This is because summing two identical signals produces a result 6 dB louder than either source, but the M and S meters show summed signals attenuated by 6 dB to compensate. The M6 standard means that dual mono sources (e.g. a presenter panned to the centre of a stereo sound stage) can be peaked to 6 in both channels, with the M meter also showing 6.
The M6 format has largely replaced the earlier 'M3' standard in which the sum and difference attenuation is only 3 dB. This M3 format is designed to give a more accurate indication of the level of the summed mono signal when working with conventional stereo material. The premise is that in summing two signals of similar level but carrying non-phase-coherent sounds (i.e. typical stereo material), the result averages 3 dB more than either source channel (rather than 6 dB more). The M3 standard means that true stereo material can be peaked to 6 in both channels, with the M meter also showing 6. However, dual-mono sources can only be peaked to 5.25 in each channel to keep the M meter at 6.
Note: the chosen M6/M3 metering standard does not affect the relative audible balance of sounds panned to one side versus the centre – that is determined solely by the panning law of the mixing console's pan-pot.
The M6 standard is deemed a simpler form of metering for untrained broadcasters to use as it keeps the M meter at '4' for Alignment Level and '6' for peaks, without the operator having to remember to subtract 3 dB.
Commercial broadcasting in the UK initially used M3 [ 16 ] but had switched to M6 by 1980. This was mandated by the IBA 's Engineering Code of Practice. [ 17 ] BBC installations used M3 until 1999. The BBC now uses M6 in both radio and TV, although much legacy equipment is still configured for the 'traditional' M3 standard.
The EBU PPM is a variant of the British PPM designed for the control of programme levels in international programme exchange. It is formalised as the Type IIb PPM in IEC 60268-10. It is identical to the British PPM except for the scale plate, which is calibrated in dB relative to Alignment Level, which is marked 'TEST'. There are also ticks at 2 dB intervals and at +9 dB, corresponding to Permitted Maximum Level.
In the late 1930s PPMs were considered for use in the US, but rejected in favour of a 'Standard Volume Indicator' ( VU meter ) on grounds of cost. Joint research by CBS , NBC and Bell Labs found that using an experimental design of PPM (with a relatively long integration time of 25 ms) in the control of programme levels gave only a 1 dB advantage over the VU meter, in terms of average output level for a given amount of distortion. It was felt that this was too small to justify the much greater expense. It was also found that VU meters gave more consistent readings than PPMs when comparing programme levels at the sending and receiving end of long lines subject to group delay , which altered the waveform. [ 18 ] This finding has been disputed by others. [ 19 ]
A widely believed myth is that the PPM was developed as a superior alternative to the VU meter. In fact, the PPM came first, and if anything the VU meter was developed as an economical alternative to the PPM. [ 18 ]
By 1980, ABC had about 100 PPMs in use in control rooms in New York and its Washington News Bureau, and was ordering new consoles with PPMs fitted. These were Type II PPMs with the seven marks labelled −22, −16, −12, −8, −4, 0 and +4. ABC found that a modified version of the EBU meter based on the VU-meter 'A scale' was best, since it let operators use their usual jargon such as 'zero level' etc. [ 19 ] The appearance is similar to an EBU scale except that the numbers are 8 dB lower.
To aid alignment on both VU meters and PPMS, ABC in New York used a special test signal known as ATS. A 440 Hz tone alternated between steady tone at +8 dBu (indicated at 0 VU and −8 PPM) and tone bursts at +16 dBu (indicated at 0 VU and 0 PPM). [ 19 ]
By 1978 PPMs were in use at the Canadian Broadcasting Corporation's Vancouver plant. Some 30 or 40 PPMs were in use, with just one or two VU meters retained for settling telco disputes. These are Type II PPMs with the seven marks labelled −6, 0, +4, +8, +12, +16 and +20: this scaling shows absolute levels in dBu (or dBm into 600 Ω). The appearance is similar to the ABC PPM except that all the numbers are 16 dB higher. [ 19 ]
The South African Broadcasting Corporation (SABC) uses a Type II PPM modified with a black-on-white scale plate calibrated in percentage and dB relative to Permitted Maximum Level, which is +6 dBu. Alignment Level is 0 dBu or 50%.
IEC 60268-18 is a partial standard for a PPM designed for use with digital audio in both professional and consumer use, using "incremental dot or bar type displays or numerical displays". Such a display shows level relative to 0 dBFS. The integration time can have any value less than 5 ms − thus both true-peak and quasi-peak meters can comply, and different meters may indicate very different levels despite compliance with the standard. The return time has the same value as a Type I meter: 1.7±0.3 seconds for a 20 dB fall. [ 20 ]
IEC 60268-10 specifies three variants: Types I, IIa and IIb, known colloquially as the DIN, British and EBU types respectively. Types IIa and IIb differ only in the scale marks. [ 6 ]
The Nordic, ABC, CBC and SABC variants are not specified in IEC 60268-10. The Nordic PPM uses Type I ballistics with a different scale. The ABC, CBC and SABC variants use Type II ballistics with different scales.
Parameters for the VU meter and Nagra modulometer are included in the table below for comparison. Some information has been obtained from ITU-T Rec. J.15. [ 8 ]
The 'modulometer' is a proprietary type of quasi-PPM found on Nagra products. It has an integration time (−2 dB) of 7.5 ms, [ 21 ] and a semi-logarithmic scale with an appearance between that of a VU meter and a DIN-type PPM. A stereo version ("double modulometer") uses a meter movement with two coaxial needles.
In typical practice for Nagra analogue tape recorders, Alignment Level is regarded as −8 and maximum level 0. Thus sound recordists using location mixers would typically send a tone at 0 VU or PPM 4 (British) and adjust the Nagra recorder's gain to read −8 on the modulometer.
Some newer digital recorders, e.g., the Nagra VI, have modulometers displayed as bargraphs calibrated in dBFS. [ 22 ] For these, Alignment Level is as for any other digital PPM, i.e., −18 dBFS (EBU) or −20 dBFS (SMPTE).
To use PPMs effectively to control sound levels it is necessary to understand design rationale and limitations.
Many engineers prefer the PPM to the much slower VU meter used in the US—but it does require some interpretation in use. Though it gives a useful overload warning, it does not represent either true peak level or subjective loudness. The BBC have tables showing recommended settings for different types of programme, such as speech, classical music etc., which attempt to take account of the latter.
Regardless of the kind of programme, there is usually a nominal Permitted Maximum Level, as indicated on a PPM. Operators are expected to keep levels below it, within reason. Practices vary between countries and organisations. In the UK, the Permitted Maximum Level is 8 dB above Alignment Level, corresponding to '6' on the British PPM scale. ITU-T standards for international sound programme circuits specify a Permitted Maximum Level of 9 dB above Alignment Level. Accordingly, +9 dB is represented by a mark on the EBU PPM scale.
Because quasi-peak PPMs indicate neither loudness nor true peaks but something between the two, it is important to allow sufficient headroom when using them in the control of digital audio levels. The EBU convention (R68) provides for this by defining Alignment Level as −18 dBFS. [ 23 ] Thus a peak to the Permitted Maximum Level as indicated on a quasi-PPM corresponds to −9 or −10 dBFS. This 9-10 dB margin allows for operator error, the true peak typically being several dB higher than the PPM indication, and that subsequent signal processing (e.g., sample rate conversion) may increase the amplitude.
SMPTE RP 0155 recommends a different alignment level, corresponding to 0 VU, of −20 dBFS. [ 24 ] The two conventions result in line-up tone levels that differ by 2 dB, but in practice the level of programme modulation tends to be similar.
The SMPTE and the EBU agree that regardless of whether −18 or −20 dBFS is used as the Alignment Level, that level should be declared and that in both cases programme should peak to a Permitted Maximum Level of −9 dBFS when measured on an IEC 60268-10 quasi-PPM with an integration time of 10 milliseconds. [ 25 ]
IEC 60268-10 is concerned mainly with the highly specified Type I and Type II PPMs used in broadcasting. It does however also contain a brief section on PPMs for 'secondary and consumer' applications. The requirements include a minimum of a 12-segment bargraph type display covering a range of −42 dB to +6 dB relative to nominal maximum level, and the same integration and return times as a Type I PPM. [ 6 ] | https://en.wikipedia.org/wiki/Peak_programme_meter |
The peak–end rule is a psychological heuristic in which people judge an experience largely based on how they felt at its peak (i.e., its most intense point) and at its end, rather than based on the total sum or average of every moment of the experience. The effect occurs regardless of whether the experience is pleasant or unpleasant. To the heuristic, other information aside from that of the peak and end of the experience is not lost, but it is not used. This includes net pleasantness or unpleasantness and how long the experience lasted. The peak–end rule is thereby a specific form of the more general extension neglect and duration neglect .
The peak–end rule is an elaboration on the snapshot model of remembered utility proposed by Barbara Fredrickson and Daniel Kahneman . This model dictates that an event is not judged by the entirety of an experience, but by prototypical moments (or snapshots ) as a result of the representativeness heuristic . [ 1 ] The remembered value of snapshots dominates the actual value of an experience. Fredrickson and Kahneman theorized that these snapshots are actually the average of the most affectively intense moment of an experience and the feeling experienced at the end. [ 2 ] The effects of the duration of an experience upon retrospective evaluation are extremely slight. Fredrickson and Kahneman labeled this phenomenon duration neglect . [ 1 ] The peak–end rule is applicable only when an experience has definite beginning and end periods.
A 1993 study titled "When More Pain Is Preferred to Less: Adding a Better End" by Kahneman, Fredrickson, Charles Schreiber, and Donald Redelmeier provided groundbreaking evidence for the peak–end rule. Participants were subjected to two different versions of a single unpleasant experience. The first trial had subjects submerge a hand in 14 °C water for 60 seconds. The second trial had subjects submerge the other hand in 14 °C water for 60 seconds, but then keep their hand submerged for an additional 30 seconds, during which the temperature was raised to 15 °C. Subjects were then offered the option of which trial to repeat. Against the law of temporal monotonicity , subjects were more willing to repeat the second trial, despite a prolonged exposure to uncomfortable temperatures. Kahneman et al. concluded that "subjects chose the long trial simply because they liked the memory of it better than the alternative (or disliked it less)." [ 3 ]
Similarly, a 1996 study by Kahneman and Redelmeier assessed patients' appraisals of uncomfortable colonoscopy or lithotripsy procedures and correlated the remembered experience with real-time findings. They found that patients consistently evaluated the discomfort of the experience based on the intensity of pain at the worst (peak) and final (end) moments. This occurred regardless of length or variation in intensity of pain within the procedure. [ 4 ]
Another study by Kahneman and Ziv Carmon identified a boundary condition for the peak–end rule. Participants interacted with a computer program that had them wait to be served, while assessing their satisfaction as they were waiting. Kahneman and Carmon found that how participants felt at the final moment of the experience was a good predictor of their responses when they were asked to retrospectively evaluate their experiences. For example, participants who felt very dissatisfied during much of the experience but were satisfied in the final few seconds (because the waiting line moved faster than expected toward the end) summarized the experience as satisfying. Kahneman and Carmon concluded that real time experiences that are based on expectations are discounted after the fact if those expectations are unfulfilled. [ 5 ]
A third study by Kahneman, Redelmeier, and Joel Katz corroborated and expanded upon the discoveries made in the 1996 study. Colonoscopy patients were randomly divided into two groups. One underwent a colonoscopy procedure wherein the scope was left in for three extra minutes, but not moved, creating a sensation that was uncomfortable, but not painful. The other group underwent a typical colonoscopy procedure. Kahneman et al. found that, when asked to retrospectively evaluate their experiences, patients who underwent the longer procedure rated their experience as less unpleasant than patients who underwent the typical procedure. Moreover, the patients in the prolonged discomfort group were far more likely to return for subsequent procedures because a less painful end led them to evaluate the procedure more positively than those who faced a shorter procedure. [ 6 ]
People exhibit better memory for more intensely emotional events than less intensely emotional events. The precise cause of this is unclear, but it has been demonstrated, for decades, across a wide variety of surveys and experiments. [ 7 ] [ 8 ] [ 9 ] In addition, people do not always recognize that the events that they remember are more emotionally intense than the "average" event of its kind. This failure to correct for the atypicality of extreme memories can lead people to believe those extreme moments are representative of the "set" being judged. Boston Red Sox fans asked to recall any one game they saw when the Red Sox won, for example, tended to recall the best game they could remember. They only realized this game was unrepresentative of past winning games by the Red Sox if they were explicitly asked to recall the best game they could remember, as evidenced by their subsequent affective forecasts . [ 9 ] This bias for more intense emotional experiences is evident in nostalgic preferences . People asked to recall a television show or movie from the past tend to recall the most enjoyable show or movie that they can remember, and use this extreme example to rate all shows from its era unless they are also able to spontaneously recall shows or movies that are worse than the first show or movie they remember. [ 10 ]
People exhibit serial position effects such that they have better memory for both the beginning and end of sequences, phenomena known as primacy bias and recency bias , respectively. A paper by Garbinsky, Morewedge, and Shiv (2014) found evidence that for extended hedonic experiences, better memory for the end of the experience than the beginning (recency > primacy) can be attributed to memory interference effects . [ 11 ] As a person eats potato chips, for example, the formation of a new memory of the most recently eaten chip makes it harder for them to recall how the previously eaten chips tasted. Garbinsky and colleagues found that (1) recency effects better predicted recalled enjoyment of a small meal (e.g., eating 5 or 15 chips) than did primacy effects, (2) that people had a worse memory for the first bite of the meal than the last bite of the meal, but (3) providing people with their ratings of the first bite lead them to use their enjoyment of that first bite as much as their enjoyment of the last bite when rating their overall enjoyment of the meal.
Since most consumer interactions have set beginnings and ends, they fit the peak–end model. As a consequence, negative occurrences in any consumer interaction can be counteracted by establishing a firmly positive peak and end. This can be accomplished through playing music customers enjoy, giving out free samples, or paying a clerk to hold the door for patrons as they leave. As Scott Stratten has suggested, "A really great salesperson who helps with an exchange can erase negative experiences along the way. The long wait in line and the bad music in the changing room are forgotten". [ 12 ] However, as research by Talya Miron-Shatz suggests, retrospective evaluations of day-long experiences do not appear to follow the peak–end rule, which brings into question the applicability of this rule to approximately day-length consumer–business interactions, such as hotel stays. [ 13 ]
Another business application is the price setting strategy in marketing practice. The peak-end rule suggests that reference price , an internal price benchmark, is formed as a weighted average of the highest observed price and the most recent price. Among all four reference price models (the peak-end model, extrapolative expectations model, adaptive expectations model , and rational expectations model ), the peak-end model is the most plausible representation of consumer's cognitive processes at an individual level. [ 14 ]
De Maeyer and Estelami suggest that occasionally raising the price of the brand above the desirable level may restore the reference price for the brand. However, due to its inherent risks, this tactic may only be effective under certain circumstances. First, the tactic should be used only sparingly and for a short period. If the brand adjusts its price level too often, it could confuse customers and may be regarded as “unreliable”. A long period of exceptionally high price may distort consumers’ price perceptions on the brand and result in a loss of consumers. Second, the tactic is best suited to frequently purchased products (e.g., food, music, fragrance) where the frequency of sales minimizes the impact of the lost sale during the peak-price period. [ 14 ]
Another study by Nasiry and Popescu examines the effect of low peak price and its interaction with loss aversion in optimal pricing strategies. They discovered that steep discounts could permanently erode demand in the future, as lowest prices remain salient in the memory anchoring process. Thus, companies should avoid deep discounts to maintain their brand price perception. They also pointed out the limitation of temporary price-raising strategy as being short-lived because these high prices affect only the reference price in the next period. [ 15 ]
A study by Kang, Daniels, and Schweitzer [ 16 ] proposed a "streak-end rule" which extends the peak-end rule to sequences of binary events. They argued that, for sequences of binary events (such as workers being repeatedly assigned to do tasks that are either hard or easy ), streaks are the psychological analogue of peaks. They found that volunteer workers' turnover decisions were disproportionately influenced by "streaks" (i.e., when a worker experienced many hard tasks in a row) and "ends" (i.e., when a worker's most recent task was a hard task).
In 2006, a study was carried out at the University of Canterbury in Christchurch, New Zealand, analyzing the implications of the peak–end rule on the perceived happiness experienced on vacations. The study found that participants' remembered overall happiness was approximately predicted by the peak–end rule, although it was actually better predicted by their happiness during the "most memorable or most unusual 24-h period". [ 17 ] Still, the duration of a vacation appeared to have negligible effects on remembered happiness. [ 17 ] The results of the study could be applied to choosing more economical durations for vacations.
The peak–end rule is particularly salient in regard to medical procedures, since it suggests that it is preferable to have longer procedures that include a period of decreased discomfort than to have shorter procedures. [ 13 ] In particular, the rule "suggests that the memory of a painful medical treatment is likely to be less aversive if relief from the pain is gradual than if relief is abrupt". [ 3 ] Furthermore, the quality of a remembered procedure can drastically influence medical futures. If people recall necessary but onerous procedures more positively, then they are more likely to return for repeat procedures later in life.
However, factoring the effect of the peak–end rule upon evaluations of medical procedures is problematic, since adding a period of decreasing pain to a procedure is still added pain. Even though this certainly yields a better memory of the process, the patient still endures more pain than is strictly necessary. [ 6 ] Doctors and patients are forced to confront the choice between objectively less painful forms of treatment and forms of treatment that will be remembered more favorably. Kahneman claims that "it is safe to assume that few patients will agree to expose themselves to pain for the sole purpose of improving a future memory". [ 3 ]
The peak-end rule also applies to educational practice, especially to peer assessment. A study by Hoogerheide and his team analyzes the effects of the peak-end rule in children's experience of receiving peer assessments. The result shows that the peak-end rule likely influences children's perception and memory of the assessment as well as their learning outcomes and motivation. [ 18 ]
The study contains two experiments with different overall tones, one positive and one negative. In each experiment, students received two versions of assessments with different lengths. In the overall negative assessment, the extended version comprises an extra moderately negative rating at the end. Similarly, the extended positive assessment ends with an additional moderately positive rating. In both experiments, the students reported that the extended assessment was remembered as more pleasant and less difficult to deal with. Based on the result, Hoogerheide advises that teachers should structure the feedback by ending with the best part of the assessment. When the assessment is overall negative, it is better to end with the most pleasant or most easily acceptable part of the negative feedbacks. Similarly, the positive assessment should end on a high note rather than the most unpleasant part. [ 18 ]
While the peak-end rule in human eating behavior may not be as general as in other contexts, studies have discovered some contextual factors that are influenced by the rule. For example, the peak-end rule works for the evaluation of food when the price is low. Conversely, for expensive food, people tend to rely on their initial experience rather than the peak or end experience. A potential reason is that high-price payers form a higher expectation on the service than low-price payers do. If their high expectation initially deviates from the actual experience, the valuation on the overall service could be driven primarily by the beginning experience. [ 19 ] Those paying low price may not have much expectation and therefore consider the peak to be much higher than high-price payers do. Thus, they are more likely to be influenced by the peak-end rule when evaluating the overall experience.
The theory is formed in a pizza study [ 19 ] where people chose to pay $4 or $8 for their pizza buffet. For those paid $4, both the tastes of the last and the peak slices significantly predict the general evaluation for overall food taste. In contrast, for those paid $8, the first slice is more important in predicting the overall enjoyment. Therefore, in order to maximize customer satisfaction, higher-priced restaurants should put their best food in front of the consumer first. In a buffet setting, they could provide some signage to make more popular items salient or place the most popular foods first in the line. In lower-priced restaurants, serving tasty desserts at the end may increase customer's overall satisfaction.
The effect of the peak-end rule in eating behavior also depends on personal factors such as self-restraint level on food choice. Robinson et al. discovered that for unrestrained eaters key moments in eating experiences have a disproportionately large influence on remembered enjoyment of eating. However, restrained eaters’ judgements on food are not influenced by the peak or end of the recent eating experience but by other cognitive factors such as semantic knowledge and beliefs about food that are already formed. [ 20 ]
Critiques of the peak–end rule typically derive from its conflation of a complex mental evaluation into a simplistic framework. A 2008 study found some support for the peak–end rule, but also found that it was "not an outstandingly good predictor" of remembered experiential value, and that the happiness of the most memorable part of an experience predicted remembered happiness better than did the happiness of the peak or of the end. [ 17 ] Additionally, the extreme effect of peaks fades more rapidly over time, causing peaks to be recalled less positively and troughs recalled less negatively over time. Episodic memory endures for only a few weeks; at some point, mental accounting shifts over to semantic memory , leading to potential over-valuation of the "end" and diminished weighting of the peak. [ citation needed ] Additionally, memories that are available for evaluation may change due to the fading affect associated with memory or differing goals in recall. [ 17 ] Goal orientation or initial expectations can also affect the weighting of a peak or an end, causing an end to be over-weighted as the culmination of a goal. [ 2 ] Finally, Ariely and Carmon have theorized that evaluations of past events are affected by feelings at the time of evaluation. [ 21 ] | https://en.wikipedia.org/wiki/Peak–end_rule |
In mathematics , specifically in the study of ordinary differential equations , the Peano existence theorem , Peano theorem or Cauchy–Peano theorem , named after Giuseppe Peano and Augustin-Louis Cauchy , is a fundamental theorem which guarantees the existence of solutions to certain initial value problems .
Peano first published the theorem in 1886 with an incorrect proof. [ 1 ] In 1890 he published a new correct proof using successive approximations. [ 2 ]
Let D {\displaystyle D} be an open subset of R × R {\displaystyle \mathbb {R} \times \mathbb {R} } with f : D → R {\displaystyle f\colon D\to \mathbb {R} } a continuous function and y ′ ( t ) = f ( t , y ( t ) ) {\displaystyle y'(t)=f\left(t,y(t)\right)} a continuous , explicit first-order differential equation defined on D , then every initial value problem y ( t 0 ) = y 0 {\displaystyle y\left(t_{0}\right)=y_{0}} for f with ( t 0 , y 0 ) ∈ D {\displaystyle (t_{0},y_{0})\in D} has a local solution z : I → R {\displaystyle z\colon I\to \mathbb {R} } where I {\displaystyle I} is a neighbourhood of t 0 {\displaystyle t_{0}} in R {\displaystyle \mathbb {R} } ,
such that z ′ ( t ) = f ( t , z ( t ) ) {\displaystyle z'(t)=f\left(t,z(t)\right)} for all t ∈ I {\displaystyle t\in I} . [ 3 ]
The solution need not be unique: one and the same initial value ( t 0 , y 0 ) {\displaystyle (t_{0},y_{0})} may give rise to many different solutions z {\displaystyle z} .
By replacing y {\displaystyle y} with y − y 0 {\displaystyle y-y_{0}} , t {\displaystyle t} with t − t 0 {\displaystyle t-t_{0}} , we may assume t 0 = y 0 = 0 {\displaystyle t_{0}=y_{0}=0} . As D {\displaystyle D} is open there is a rectangle R = [ − t 1 , t 1 ] × [ − y 1 , y 1 ] ⊂ D {\displaystyle R=[-t_{1},t_{1}]\times [-y_{1},y_{1}]\subset D} .
Because R {\displaystyle R} is compact and f {\displaystyle f} is continuous, we have sup R | f | ≤ C < ∞ {\displaystyle \textstyle \sup _{R}|f|\leq C<\infty } and by the Stone–Weierstrass theorem there exists a sequence of Lipschitz functions f k : R → R {\displaystyle f_{k}:R\to \mathbb {R} } converging uniformly to f {\displaystyle f} in R {\displaystyle R} . Without loss of generality, we assume sup R | f k | ≤ 2 C {\displaystyle \textstyle \sup _{R}|f_{k}|\leq 2C} for all k {\displaystyle k} .
We define Picard iterations y k , n : I = [ − t 2 , t 2 ] → R {\displaystyle y_{k,n}:I=[-t_{2},t_{2}]\to \mathbb {R} } as follows, where t 2 = min { t 1 , y 1 / ( 2 C ) } {\displaystyle t_{2}=\min\{t_{1},y_{1}/(2C)\}} . y k , 0 ( t ) ≡ 0 {\displaystyle y_{k,0}(t)\equiv 0} , and y k , n + 1 ( t ) = ∫ 0 t f k ( t ′ , y k , n ( t ′ ) ) d t ′ {\displaystyle \textstyle y_{k,n+1}(t)=\int _{0}^{t}f_{k}(t',y_{k,n}(t'))\,\mathrm {d} t'} . They are well-defined by induction: as
( t ′ , y k , n + 1 ( t ′ ) ) {\displaystyle (t',y_{k,n+1}(t'))} is within the domain of f k {\displaystyle f_{k}} .
We have
where L k {\displaystyle L_{k}} is the Lipschitz constant of f k {\displaystyle f_{k}} . Thus for maximal difference M k , n ( t ) = sup t ′ ∈ [ 0 , t ] | y k , n + 1 ( t ′ ) − y k , n ( t ′ ) | {\displaystyle \textstyle M_{k,n}(t)=\sup _{t'\in [0,t]}|y_{k,n+1}(t')-y_{k,n}(t')|} , we have a bound M k , n ( t ) ≤ L k | ∫ 0 t M k , n − 1 ( t ′ ) d t ′ | {\displaystyle \textstyle M_{k,n}(t)\leq L_{k}\left|\int _{0}^{t}M_{k,n-1}(t')\,\mathrm {d} t'\right|} , and
By induction, this implies the bound M k , n ( t ) ≤ 2 C L k n | t | n + 1 / ( n + 1 ) ! {\displaystyle M_{k,n}(t)\leq 2CL_{k}^{n}|t|^{n+1}/(n+1)!} which tends to zero as n → ∞ {\displaystyle n\to \infty } for all t ∈ I {\displaystyle t\in I} .
The functions y k , n {\displaystyle y_{k,n}} are equicontinuous as for − t 2 ≤ t < t ′ ≤ t 2 {\displaystyle -t_{2}\leq t<t'\leq t_{2}} we have
so by the Arzelà–Ascoli theorem they are relatively compact . In particular, for each k {\displaystyle k} there is a subsequence ( y k , φ k ( n ) ) n ∈ N {\displaystyle (y_{k,\varphi _{k}(n)})_{n\in \mathbb {N} }} converging uniformly to a continuous function y k : I → R {\displaystyle y_{k}:I\to \mathbb {R} } . Taking limit n → ∞ {\displaystyle n\to \infty } in
we conclude that y k ( t ) = ∫ 0 t f k ( t ′ , y k ( t ′ ) ) d t ′ {\displaystyle \textstyle y_{k}(t)=\int _{0}^{t}f_{k}(t',y_{k}(t'))\,\mathrm {d} t'} . The functions y k {\displaystyle y_{k}} are in the closure of a relatively compact set, so they are themselves relatively compact. Thus there is a subsequence y ψ ( k ) {\displaystyle y_{\psi (k)}} converging uniformly to a continuous function z : I → R {\displaystyle z:I\to \mathbb {R} } . Taking limit k → ∞ {\displaystyle k\to \infty } in y ψ ( k ) ( t ) = ∫ 0 t f ψ ( k ) ( t ′ , y ψ ( k ) ( t ′ ) ) d t ′ {\displaystyle \textstyle y_{\psi (k)}(t)=\int _{0}^{t}f_{\psi (k)}(t',y_{\psi (k)}(t'))\,\mathrm {d} t'} we conclude that z ( t ) = ∫ 0 t f ( t ′ , z ( t ′ ) ) d t ′ {\displaystyle \textstyle z(t)=\int _{0}^{t}f(t',z(t'))\,\mathrm {d} t'} , using the fact that f ψ ( k ) {\displaystyle f_{\psi (k)}} are equicontinuous by the Arzelà–Ascoli theorem. By the fundamental theorem of calculus , z ′ ( t ) = f ( t , z ( t ) ) {\displaystyle z'(t)=f(t,z(t))} in I {\displaystyle I} .
The Peano theorem can be compared with another existence result in the same context, the Picard–Lindelöf theorem . The Picard–Lindelöf theorem both assumes more and concludes more. It requires Lipschitz continuity , while the Peano theorem requires only continuity; but it proves both existence and uniqueness where the Peano theorem proves only the existence of solutions. To illustrate, consider the ordinary differential equation
According to the Peano theorem, this equation has solutions, but the Picard–Lindelöf theorem does not apply since the right hand side is not Lipschitz continuous in any neighbourhood containing 0. Thus we can conclude existence but not uniqueness. It turns out that this ordinary differential equation has two kinds of solutions when starting at y ( 0 ) = 0 {\displaystyle y(0)=0} , either y ( t ) = 0 {\displaystyle y(t)=0} or y ( t ) = t 2 / 4 {\displaystyle y(t)=t^{2}/4} . The transition between y = 0 {\displaystyle y=0} and y = ( t − C ) 2 / 4 {\displaystyle y=(t-C)^{2}/4} can happen at any C {\displaystyle C} .
The Carathéodory existence theorem is a generalization of the Peano existence theorem with weaker conditions than continuity.
The Peano existence theorem cannot be straightforwardly extended to a general Hilbert space H {\displaystyle {\mathcal {H}}} : for an open subset D {\displaystyle D} of R × H {\displaystyle \mathbb {R} \times {\mathcal {H}}} , the continuity of f : D → R {\displaystyle f\colon D\to \mathbb {R} } alone is insufficient for guaranteeing the existence of solutions for the associated initial value problem. [ 4 ] | https://en.wikipedia.org/wiki/Peano_existence_theorem |
In numerical analysis , the Peano kernel theorem is a general result on error bounds for a wide class of numerical approximations (such as numerical quadratures ), defined in terms of linear functionals . It is attributed to Giuseppe Peano . [ 1 ]
Let V [ a , b ] {\displaystyle {\mathcal {V}}[a,b]} be the space of all functions f {\displaystyle f} that are differentiable on ( a , b ) {\displaystyle (a,b)} that are of bounded variation on [ a , b ] {\displaystyle [a,b]} , and let L {\displaystyle L} be a linear functional on V [ a , b ] {\displaystyle {\mathcal {V}}[a,b]} . Assume that that L {\displaystyle L} annihilates all polynomials of degree ≤ ν {\displaystyle \leq \nu } , i.e. L p = 0 , ∀ p ∈ P ν [ x ] . {\displaystyle Lp=0,\qquad \forall p\in \mathbb {P} _{\nu }[x].} Suppose further that for any bivariate function g ( x , θ ) {\displaystyle g(x,\theta )} with g ( x , ⋅ ) , g ( ⋅ , θ ) ∈ C ν + 1 [ a , b ] {\displaystyle g(x,\cdot ),\,g(\cdot ,\theta )\in C^{\nu +1}[a,b]} , the following is valid: L ∫ a b g ( x , θ ) d θ = ∫ a b L g ( x , θ ) d θ , {\displaystyle L\int _{a}^{b}g(x,\theta )\,d\theta =\int _{a}^{b}Lg(x,\theta )\,d\theta ,} and define the Peano kernel of L {\displaystyle L} as k ( θ ) = L [ ( x − θ ) + ν ] , θ ∈ [ a , b ] , {\displaystyle k(\theta )=L[(x-\theta )_{+}^{\nu }],\qquad \theta \in [a,b],} using the notation ( x − θ ) + ν = { ( x − θ ) ν , x ≥ θ , 0 , x ≤ θ . {\displaystyle (x-\theta )_{+}^{\nu }={\begin{cases}(x-\theta )^{\nu },&x\geq \theta ,\\0,&x\leq \theta .\end{cases}}} The Peano kernel theorem [ 1 ] [ 2 ] states that, if k ∈ V [ a , b ] {\displaystyle k\in {\mathcal {V}}[a,b]} , then for every function f {\displaystyle f} that is ν + 1 {\textstyle \nu +1} times continuously differentiable , we have L f = 1 ν ! ∫ a b k ( θ ) f ( ν + 1 ) ( θ ) d θ . {\displaystyle Lf={\frac {1}{\nu !}}\int _{a}^{b}k(\theta )f^{(\nu +1)}(\theta )\,d\theta .}
Several bounds on the value of L f {\displaystyle Lf} follow from this result: | L f | ≤ 1 ν ! ‖ k ‖ 1 ‖ f ( ν + 1 ) ‖ ∞ | L f | ≤ 1 ν ! ‖ k ‖ ∞ ‖ f ( ν + 1 ) ‖ 1 | L f | ≤ 1 ν ! ‖ k ‖ 2 ‖ f ( ν + 1 ) ‖ 2 {\displaystyle {\begin{aligned}|Lf|&\leq {\frac {1}{\nu !}}\|k\|_{1}\|f^{(\nu +1)}\|_{\infty }\\[5pt]|Lf|&\leq {\frac {1}{\nu !}}\|k\|_{\infty }\|f^{(\nu +1)}\|_{1}\\[5pt]|Lf|&\leq {\frac {1}{\nu !}}\|k\|_{2}\|f^{(\nu +1)}\|_{2}\end{aligned}}}
where ‖ ⋅ ‖ 1 {\displaystyle \|\cdot \|_{1}} , ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} and ‖ ⋅ ‖ ∞ {\displaystyle \|\cdot \|_{\infty }} are the taxicab , Euclidean and maximum norms respectively. [ 2 ]
In practice, the main application of the Peano kernel theorem is to bound the error of an approximation that is exact for all f ∈ P ν {\displaystyle f\in \mathbb {P} _{\nu }} . The theorem above follows from the Taylor polynomial for f {\displaystyle f} with integral remainder:
defining L ( f ) {\displaystyle L(f)} as the error of the approximation, using the linearity of L {\displaystyle L} together with exactness for f ∈ P ν {\displaystyle f\in \mathbb {P} _{\nu }} to annihilate all but the final term on the right-hand side, and using the ( ⋅ ) + {\displaystyle (\cdot )_{+}} notation to remove the x {\displaystyle x} -dependence from the integral limits. [ 3 ] | https://en.wikipedia.org/wiki/Peano_kernel_theorem |
In mathematical logic , Peano–Russell notation was Bertrand Russell 's application of Giuseppe Peano 's logical notation to the logical notions of Frege and was used in the writing of Principia Mathematica in collaboration with Alfred North Whitehead : [ 1 ]
"The notation adopted in the present work is based upon that of Peano, and the following explanations are to some extent modelled on those which he prefixes to his Formulario Mathematico ." (Chapter I: Preliminary Explanations of Ideas and Notations, page 4)
In the notation, variables are ambiguous in denotation, preserve a recognizable identity appearing in various places in logical statements within a given context, and have a range of possible determination between any two variables which is the same or different. When the possible determination is the same for both variables, then one implies the other; otherwise, the possible determination of one given to the other produces a meaningless phrase. The alphabetic symbol set for variables includes the lower and upper case Roman letters as well as many from the Greek alphabet.
The four fundamental functions are the contradictory function , the logical sum , the logical product , and the implicative function . [ 2 ]
The contradictory function applied to a proposition returns its negation.
The logical sum applied to two propositions returns their disjunction.
The logical product applied to two propositions returns the truth-value of both propositions being simultaneously true.
The implicative function applied to two ordered propositions returns the truth value of the first implying the second proposition.
Equivalence is written as p ≡ q {\displaystyle p\equiv q} , standing for p ⊃ q ⋅ q ⊃ p {\displaystyle p\supset q\cdot q\supset p} . [ 3 ]
Assertion is same as the making of a statement between two full stops.
An asserted proposition is either true or an error on the part of the writer. [ 4 ]
Inference is equivalent to the rule modus ponens , where p ⋅ p ⊃ q . ⊃ q {\displaystyle p\cdot p\supset q.\supset q} [ 5 ]
In addition to the logical product, dots are also used to show groupings of functions of propositions. In the above example, the dot before the final implication function symbol groups all of the previous functions on that line together as the antecedent to the final consequent.
The notation includes definitions as complex functions of propositions, using the equals sign "=" to separate the defined term from its symbolic definition, ending with the letters "Df". [ 6 ] | https://en.wikipedia.org/wiki/Peano–Russell_notation |
Peanut agglutinin ( PNA ) is plant lectin protein derived from the fruits of Arachis hypogaea . Peanut agglutinin may also be referred to as Arachis hypogaea lectin . Lectins recognise and bind particular sugar sequences in carbohydrates; peanut agglutinin binds the carbohydrate sequence Gal -β(1-3)- GalNAc . The name "peanut agglutinin" originates from its ability to stick together ( agglutinate ) cells, such as neuraminidase -treated erythrocytes , [ 1 ] which have glycoproteins or glycolipids on their surface which include the Gal-β(1-3)-GalNAc carbohydrate sequence.
The protein is 273 amino acids in length with the first 23 residues acting as a signal peptide which is subsequently cleaved. It has a Uniprot accession of P02872 . There are over 20 structures of this protein in the PDB which reveal and all beta-sheet protein with a tetrameric quaternary structure. It is a member of the Lectin_legB PFAM family.
Available Structures of peanut agglutinin
Because peanut agglutinin specifically binds a particular carbohydrate sequence it finds use in a range of methods for cell biology and biochemistry . For example in PNA- affinity chromatography the binding specificity of peanut agglutinin is used to isolate glycosylated molecules which have the sugar sequence Gal-β(1-3)-GalNAc. Peanut agglutinin activity is inhibited by lactose and galactose which compete for the binding site.
Other uses include:
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peanut_agglutinin |
A pear switch is a particular type of electrical switch that usually has the appearance of a small pear. Its operation is very simple, with a button that, depending on the type, is pressed to activate or deactivate a circuit or is simply pressed like a pushbutton , for example in photographic enlarger switches. [ 1 ] [ 2 ]
It is characterized by its form and function. Unlike conventional switches that are fixed to the wall, the pear switch is suspended from the cable. By pressing the pear, the electrical contacts close the circuit. Its most common use is for hanging lamps, bed headboards, bedside tables, or generally in situations where you do not want to mount the switch on the wall. [ citation needed ]
It is pear-shaped, oval or spherical, made of wood or plastic, which is connected to a mechanism that has a spring with an electrical contact. It is an automatic mechanism with a spring, similar to a push button but taking into account that there is a model that is bistable and returns the switch to its default position after pressing twice, changing the initial condition of the electrical circuit or restaurant, connecting or blocking the circulation of current in said electrical circuit. [ 1 ]
There are two kinds: | https://en.wikipedia.org/wiki/Pear_switch |
Pearl.com [ 1 ] [ 2 ] is an "online paid question-and-answer service" based in San Francisco . [ 3 ] [ 4 ] [ 5 ] "People aren't always willing to wait" [ 6 ] in "legal, medical and other advice" [ 5 ] led to "a growing number of those help-seekers are getting their guidance online."
Pearl.com began in 2003 as JustAnswer . Founder Andy Kurtzig had previously begun (and subsequently sold) a software company automating newspaper classifieds called Anser , a pun on his mother 's ASK Group 's name. [ 3 ] The time period from attempting to obtaining funding until attaining significant revenue was described as "unusually long:" nine years. [ 3 ] Once up and running, their offerings included traditionally high-priced fields such as law and medicine, but also "assistance from computer technicians and relationship counselors." [ 5 ] By 2014, based on "the regulatory landscape involved" Pearl undertook to "overhaul" their expert teams. [ 7 ]
Regarding providing legal advice for "$30 to $40" and glossing over "details that could more easily emerge face to face" founder Andy Kurtzig conceded that an in-person followup may be needed. He said to The Wall Street Journal his service enables "to get key insights that will cut your appointment time from three hours to less than an hour.” [ 5 ]
This Web - software -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pearl.com |
In superconductivity , a Pearl vortex is a vortex of supercurrent in a thin film of type-II superconductor , first described in 1964 by Judea Pearl . [ 1 ] A Pearl vortex is similar to Abrikosov vortex except for its magnetic field profile which, due to the dominant air-metal interface, diverges sharply as 1/ r {\displaystyle r} at short distances from the center, and decays slowly, like 1/ r 2 {\displaystyle r^{2}} at long distances. Abrikosov's vortices, in comparison, have very short range interaction and diverge as log ( 1 / r ) {\displaystyle \log(1/r)} near the center.
In Pearl's thesis, [ 2 ] he uses the London equations to derive the magnetic response of a thin superconducting film in the Meissner state . For a film where the thickness is on the order of the superconducting coherence length or smaller, the ability to screen magnetic field is geometrically suppressed. Whereas in a bulk superconductor the characteristic length scale over which magnetic field can penetrate is the London penetration depth λ {\displaystyle \lambda } , in a thin film this is increased to the Pearl length Λ P = 2 λ 2 / d {\displaystyle \Lambda _{P}=2\lambda ^{2}/d} . This occurs because in a thin film, inductive coupling through free space plays a stronger role in magnetic field penetration.
This suppressed screening plays a role in film dynamics far beyond vortex dynamics. In most models, including Ginzburg-Landau theory , this can be accounted for by substituting Λ P {\displaystyle \Lambda _{P}} instead of λ {\displaystyle \lambda } Because the London equations assume a film in the Meissner state, Ginzburg-Landau theory is a more natural choice for studying vortex dynamics. Studying vortices in Ginzburg-Landau theory with a magnetic penetration depth of λ {\displaystyle \lambda } yields Abrikosov vortices, while using a magnetic penetration depth of Λ P {\displaystyle \Lambda _{P}} gives the dynamics of Pearl vortices.
Because the magnetic penetration depth of Pearl vortices is a function of both geometry and material properties, their existence implies that in sufficiently thin films the modified Ginzburg-Landau parameter κ = Λ P / ξ {\displaystyle \kappa =\Lambda _{P}/\xi } may become greater than 1 / 2 {\displaystyle 1/{\sqrt {2}}} even in films with Type-I superconductor behavior in the bulk. In other words, type-I superconducting thin films can host Pearl vortices, when normally in the bulk they transition directly from the Meissner state to the normal state with applied magnetic field. [ 3 ]
Additionally, the long interaction length of Pearl vortices enable the Berezinskii-Kosterlitz-Thouless transition (BKT) to occur in superconducting thin films. The short interaction length of Abrikosov vortices was identified as insufficient to support a BKT transition. However, Beasley, Mooij, and Orlando [ 4 ] showed that Pearl vortices could theoretically enable a BKT transition in thin film superconductors.
A transport current flowing through a superconducting film may cause these vortices to move with a constant velocity v {\displaystyle v} proportional to, and perpendicular to the transport current. [ 5 ] Because of their proximity to the surface, and their sharp field divergence at their centers, Pearl's vortices
can actually be seen by a scanning SQUID microscope . [ 6 ] [ 7 ] [ 8 ] The characteristic length governing the distribution of the magnetic field around the vortex center is given by the ratio Λ = 2 λ 2 {\displaystyle \Lambda =2\lambda ^{2}} / d {\displaystyle d} , also known as "Pearl length," where d {\displaystyle d} is the film thickness and λ {\displaystyle \lambda } is London penetration depth . [ 9 ] Because this ratio can reach macroscopic dimensions (~1 mm) by making the film sufficiently thin, it can
be measured relatively easy and used to estimate the density of superconducting electrons. [ 8 ]
At distances shorter than the Pearl's length, vortices behave like a Coulomb gas (1/ r {\displaystyle r} repulsive force). | https://en.wikipedia.org/wiki/Pearl_vortex |
Pearlite is a two-phased , lamellar (or layered) structure composed of alternating layers of ferrite (87.5 wt%) and cementite (12.5 wt%) that occurs in some steels and cast irons . During slow cooling of an iron-carbon alloy, pearlite forms by a eutectoid reaction as austenite cools below 723 °C (1,333 °F) (the eutectoid temperature). Pearlite is a microstructure occurring in many common grades of steels.
The eutectoid composition of austenite is approximately 0.8% carbon ; steel with less carbon content ( hypoeutectoid steel ) will contain a corresponding proportion of relatively pure ferrite crystallites that do not participate in the eutectoid reaction and cannot transform into pearlite. Likewise steels with higher carbon content ( hypereutectoid steels ) will form cementite before reaching the eutectoid point. The proportion of ferrite and cementite forming above the eutectoid point can be calculated from the iron/iron—carbide equilibrium phase diagram using the lever rule .
Steels with pearlitic (eutectoid composition) or near-pearlitic microstructure (near-eutectoid composition) can be drawn into thin wires. Such wires, often bundled into ropes, are commercially used as piano wires, ropes for suspension bridges, and as steel cord for tire reinforcement. High degrees of wire drawing (logarithmic strain above 3) leads to pearlitic wires with yield strengths of several gigapascals. It makes pearlite one of the strongest structural bulk materials on earth. [ 1 ] Some hypereutectoid pearlitic steel wires, when cold wire drawn to true (logarithmic) strains above 5, can even show a maximal tensile strength above 6 GPa (870 ksi). [ 2 ] Although pearlite is used in many engineering applications, the origin of its extreme strength is not well understood. It has been recently shown that cold wire drawing not only strengthens pearlite by refining the lamellae structure, but also simultaneously causes partial chemical decomposition of cementite, associated with an increased carbon content of the ferrite phase, deformation induced lattice defects in ferrite lamellae, [ 3 ] and even a structural transition from crystalline to amorphous cementite. The deformation-induced decomposition and microstructural change of cementite is closely related to several other phenomena such as a strong redistribution of carbon and other alloy elements like silicon and manganese in both the cementite and the ferrite phase; a variation of the deformation accommodation at the phase interfaces due to a change in the carbon concentration gradient at the interfaces; and mechanical alloying. [ 4 ]
Pearlite was first identified by Henry Clifton Sorby and initially named sorbite, however the similarity of microstructure to nacre and especially the optical effect caused by the scale of the structure made the alternative name more popular.
Pearlite forms as a result of the cooperative growth of ferrite and cementite during the decomposition of austenite. The morphology of pearlite is significantly affected by the cooling rate and coiling temperature. At lower coiling temperatures, pearlite forms with finer lamellar spacing, resulting in enhanced mechanical properties due to the finer distribution of ferrite and cementite layers. Conversely, at higher coiling temperatures, pearlite forms with coarser lamellae, and a smaller amount of pearlite is observed as coarse cementite particles tend to dominate the structure. The carbon diffusion during the formation of pearlite, just ahead of the growth front, is critical in determining the thickness of the lamellae and, consequently, the strength of the steel. [ 5 ]
Bainite is a similar structure with lamellae much smaller than the wavelength of visible light and thus lacks this pearlescent appearance. It is prepared by more rapid cooling. Unlike pearlite, whose formation involves the diffusion of all atoms, bainite grows by a displacive transformation mechanism.
The transformation of pearlite to austenite takes place at lower critical temperature of 723 °C (1,333 °F). At this temperature pearlite changes to austenite because of nucleation process.
Eutectoid steel can in principle be transformed completely into pearlite; hypoeutectoid steels can also be completely pearlitic if transformed at a temperature below the normal eutectoid. [ 6 ] [ 7 ] Pearlite can be hard and strong but is not particularly tough . It can be wear-resistant because of a strong lamellar network of ferrite and cementite. Examples of applications include cutting tools , high strength wires , knives , chisels , and nails . | https://en.wikipedia.org/wiki/Pearlite |
Pearls in Graph Theory: A Comprehensive Introduction is an undergraduate-level textbook on graph theory by Nora Hartsfield and Gerhard Ringel . It was published in 1990 by Academic Press [ 1 ] [ 2 ] [ 3 ] with a revised edition in 1994 [ 4 ] and a paperback reprint of the revised edition by Dover Books in 2003. [ 5 ] The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. [ 5 ]
The "pearls" of the title include theorems , proofs , problems, and examples in graph theory . The book has ten chapters; after an introductory chapter on basic definitions, the remaining chapters material on graph coloring ; Hamiltonian cycles and Euler tours ; extremal graph theory ; subgraph counting problems including connections to permutations , derangements , and Cayley's formula ; graph labelings ; planar graphs , the four color theorem , and the circle packing theorem ; near-planar graphs; and graph embedding on topological surfaces. [ 4 ] [ 5 ]
The book also includes several unsolved problems such as the Oberwolfach problem on covering complete graphs by cycles , the characterization of magic graphs , and Ringel's Earth–Moon problem on coloring biplanar graphs . [ 3 ]
Despite its subtitle "A comprehensive introduction", the book is short and its selection of topics reflects author Ringel's personal interests. [ 1 ] [ 5 ] Important topics in graph theory that are not covered [ 1 ] [ 4 ] include symmetries of graphs , cliques , connections between graphs and linear algebra including adjacency matrices , algebraic graph theory and spectral graph theory , connectivity of a graph (or even biconnected components ), Hall's marriage theorem , line graphs , interval graphs , and the theory of tournaments . There is also only one chapter of coverage on algorithms and real-world applications of graph theory. [ 1 ] [ 4 ] [ 5 ] Also, the book omits "difficult or long proofs". [ 2 ] [ 5 ]
The book is written as a lower-level undergraduate textbook and recommends that students using it have previously taken a course in discrete mathematics . Nevertheless, it can be read and understood by students with only a high school background in mathematics. Reviewer L. W. Beineke writes that the variety of levels of the exercises is one of the strengths of the book, [ 4 ] and reviewer John S. Maybee writes that they are "extensive" and provide interesting connections to additional topics; [ 1 ] however, reviewer J. Sedláček criticizes them as "routine". [ 2 ]
Although several reviewers complained about the book's spotty or missing coverage of important topics, [ 1 ] [ 4 ] [ 5 ] reviewer Joan Hutchinson praised its choice of topics as "refreshingly different" and noted that, among many previous texts on graph theory, none had as much depth of coverage of topological graph theory . [ 3 ] Other reviewer complaints include a misattributed example, [ 2 ] a bad definition of the components of a graph that failed to apply to graphs with one component, [ 5 ] and a proof of the five-color theorem that only applies to special planar maps instead of all planar graphs. [ 3 ]
Despite these complaints, Beineke writes that, as an undergraduate text, "this book has much to offer". [ 4 ] Maybee writes that the book was "a joy to read", provided better depth of coverage on some topics than previous graph theory texts, and would be helpful reading for "many graph theorists". [ 1 ] Hutchinson praises it as providing "a splendid, enticingly elementary yet comprehensive introduction to topological graph theory". [ 3 ] | https://en.wikipedia.org/wiki/Pearls_in_Graph_Theory |
The Pearson symbol , or Pearson notation , is used in crystallography as a means of describing a crystal structure . [ 1 ] It was originated by William Burton Pearson and is used extensively in Pearson's handbook of crystallographic data for intermetallic phases. [ 2 ] The symbol is made up of two letters followed by a number. For example:
The two letters in the Pearson symbol specify the Bravais lattice , and more specifically, the lower-case letter specifies the crystal family , while the upper-case letter the lattice type . [ 3 ] The number at the end of the Pearson symbol gives the number of the atoms in the conventional unit cell (atoms which satisfy 1 > x , y , z ≥ 0 {\displaystyle 1>x,y,z\geq 0} for the atom's position ( x , y , z ) {\displaystyle (x,y,z)} in the unit cell). [ 4 ] The following two tables give the six letters possible for the crystal family and the five letters posible for the lattice type:
The letters A, B and C were formerly used instead of S. When the centred face cuts the X axis, the Bravais lattice is called A-centred. In analogy, when the centred face cuts the Y or Z axis, we have B- or C-centring respectively. [ 5 ]
The fourteen possible Bravais lattices are identified by the first two letters:
The Pearson symbol does not uniquely identify the space group of a crystal structure. For example, both the NaCl structure (space group Fm 3 m) and diamond (space group Fd 3 m) have the same Pearson symbol cF8. Due to this constraint, the Pearson symbol should only be used to designate simple structures (elements, some binary compound) where the number of atoms per unit cell equals, ideally, the number of translationally equivalent points.
Confusion also arises in the rhombohedral lattice, which is alternatively described in a centred hexagonal ( a = b, c, α = β = 90°, γ = 120° ) or primitive rhombohedral ( a = b = c, α = β = γ ) setting. The more commonly used hexagonal setting has 3 translationally equivalent points per unit cell. The Pearson symbol refers to the hexagonal setting in its letter code (hR), but the following figure gives the number of translationally equivalent points in the primitive rhombohedral setting. Examples: hR1 and hR2 are used to designate the Hg and Bi structures respectively.
Because there are many possible structures that can correspond to one Pearson symbol, a prototypical compound may be useful to specify. [ 4 ] Examples of how to write this would be hP12-MgZn 2 {\displaystyle _{2}} or cF8-C. Prototypical compounds for particular structures can be found on the Inorganic Crystal Structure Database (ICSD) or on the AFLOW Library of Crystallographic Prototypes. [ 6 ] [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/Pearson_symbol |
The Peaucellier–Lipkin linkage (or Peaucellier–Lipkin cell , or Peaucellier–Lipkin inversor ), invented in 1864, was the first true planar straight line mechanism – the first planar linkage capable of transforming rotary motion into perfect straight-line motion , and vice versa. It is named after Charles-Nicolas Peaucellier (1832–1913), a French army officer, and Yom Tov Lipman Lipkin (1846–1876), a Lithuanian Jew and son of the famed Rabbi Israel Salanter . [ 1 ] [ 2 ]
Until this invention, no planar method existed of converting exact straight-line motion to circular motion, without reference guideways. In 1864, all power came from steam engines , which had a piston moving in a straight-line up and down a cylinder. This piston needed to keep a good seal with the cylinder in order to retain the driving medium, and not lose energy efficiency due to leaks. The piston does this by remaining perpendicular to the axis of the cylinder, retaining its straight-line motion. Converting the straight-line motion of the piston into circular motion was of critical importance. Most, if not all, applications of these steam engines, were rotary.
The mathematics of the Peaucellier–Lipkin linkage is directly related to the inversion of a circle.
There is an earlier straight-line mechanism, whose history is not well known, called the Sarrus linkage . This linkage predates the Peaucellier–Lipkin linkage by 11 years and consists of a series of hinged rectangular plates, two of which remain parallel but can be moved normally to each other. Sarrus' linkage is of a three-dimensional class sometimes known as a space crank , unlike the Peaucellier–Lipkin linkage which is a planar mechanism.
In the geometric diagram of the apparatus, six bars of fixed length can be seen: OA , OC , AB , BC , CD , DA . The length of OA is equal to the length of OC , and the lengths of AB , BC , CD , and DA are all equal forming a rhombus . Also, point O is fixed. Then, if point B is constrained to move along a circle (for example, by attaching it to a bar with a length halfway between O and B ; path shown in red) which passes through O , then point D will necessarily have to move along a straight line (shown in blue). In contrast, if point B were constrained to move along a line (not passing through O ), then point D would necessarily have to move along a circle (passing through O ).
Many different over-all proportions of this linkage are possible. Since points O , B , D must be collinear at all points in the linkage's motion, and countless arm length combinations are viable, then mirror symmetry across OBD isn't necessary. With OBD staying collinear, the only requirement to achieve the intended straight-line motion of D are that AB = AD , that BC = DC , and for B to be constrained to a circular path which crosses O . Otherwise, there is no fixed relationship between the lengths of the sides of the ABCD figure, the radius of the constraining circular path of B , and the lengths of OA or OC .
First, it must be proven that points O , B , D are collinear . This may be easily seen by observing that the linkage is mirror-symmetric about line OD , so point B must fall on that line.
More formally, triangles △ BAD and △ BCD are congruent because side BD is congruent to itself, side BA is congruent to side BC , and side AD is congruent to side CD . Therefore, angles ∠ ABD and ∠ CBD are equal.
Next, triangles △ OBA and △ OBC are congruent, since sides OA and OC are congruent, side OB is congruent to itself, and sides BA and BC are congruent. Therefore, angles ∠ OBA and ∠ OBC are equal.
Finally, because they form a complete circle, we have
but, due to the congruences, ∠ OBA = ∠ OBC and ∠ DBA = ∠ DBC , thus
therefore points O , B , and D are collinear.
Let point P be the intersection of lines AC and BD . Then, since ABCD is a rhombus , P is the midpoint of both line segments BD and AC . Therefore, length BP = length PD .
Triangle △ BPA is congruent to triangle △ DPA , because side BP is congruent to side DP , side AP is congruent to itself, and side AB is congruent to side AD . Therefore, angle ∠ BPA = angle ∠ DPA . But since ∠ BPA + ∠ DPA = 180° , then 2 × ∠ BPA = 180° , ∠ BPA = 90° , and ∠ DPA = 90° .
Let:
Then:
Since OA and AD are both fixed lengths, then the product of OB and OD is a constant:
and since points O , B , D are collinear, then D is the inverse of B with respect to the circle (O, k ) with center O and radius k .
Thus, by the properties of inversive geometry , since the figure traced by point D is the inverse of the figure traced by point B , if B traces a circle passing through the center of inversion O , then D is constrained to trace a straight line. But if B traces a straight line not passing through O , then D must trace an arc of a circle passing through O . Q.E.D.
Peaucellier–Lipkin linkages (PLLs) may have several inversions. A typical example is shown in the opposite figure, in which a rocker-slider four-bar serves as the input driver. To be precise, the slider acts as the input, which in turn drives the right grounded link of the PLL, thus driving the entire PLL.
Sylvester ( Collected Works , Vol. 3, Paper 2) writes that when he showed a model to Kelvin , he “nursed it as if it had been his own child, and when a motion was made to relieve him of it, replied ‘No! I have not had nearly enough of it—it is the most beautiful thing I have ever seen in my life.’”
A monumental-scale sculpture implementing the linkage in illuminated struts is on permanent exhibition in Eindhoven, Netherlands . The artwork measures 22 by 15 by 16 metres (72 ft × 49 ft × 52 ft), weighs 6,600 kilograms (14,600 lb), and can be operated from a control panel accessible to the general public. [ 3 ] | https://en.wikipedia.org/wiki/Peaucellier–Lipkin_linkage |
Pebble is a discontinued smartwatch developed by Pebble Technology Corporation based in Palo Alto, California that shipped from 2013 to 2016. A brainchild of Eric Migicovsky , funding was conducted through a Kickstarter campaign in 2012. It was the most funded project in Kickstarter history at the time, raising $10.3 million. [ 17 ] Pebble watches can be connected to Android and iOS devices to show notifications and messages. An online app store distributed Pebble-compatible apps from many developers including ESPN , Uber , Runkeeper , and GoPro . Pebble has been succeeded by Core Devices, a company founded by Eric Migicovsky manufacturing new PebbleOS devices under the Core name.
A steel-bodied variant to the original Pebble, the Pebble Steel , was announced at CES 2014 and released in February 2014. It had a thinner body, tactile metal buttons, and a Corning Gorilla Glass screen. In 2015, Pebble launched its second generation of smartwatches: the Pebble Time and Time Steel. The devices were similarly funded through Kickstarter, raising $20.3 million from over 75,000 backers and again breaking records for the site.
In December 2016, Pebble officially announced that the company would be shut down, and would no longer manufacture or continue support for any devices, nor honor any existing warranties. The company was sold to Fitbit , and many members of the Pebble staff joined the company. [ 18 ] [ 4 ] Support for the Pebble app store, online forum, cloud development tool, voice recognition, and voice replies ceased in June 2018, [ 19 ] although support for some online services was restored by the unofficial "Rebble" community.
Google acquired Fitbit in 2021, which still owned the rights to Pebble's operating system, brand, and designs. In January 2025, Google announced that the source code that the operating system Pebble smartwatches use, PebbleOS , would be open-sourced with founder Eric Migicovsky also announcing future devices and creating the website RePebble to market and explain the devices. [ 20 ] [ 21 ] In March 2025, Migicovsky announced new devices would be produced using PebbleOS under the Core Devices brand name. [ 22 ]
The original Pebble Smartwatch was designed based on a concept by Eric Migicovsky describing a watch that could display messages from a smartphone and select Android devices. Migicovsky successfully took his idea through the Y Combinator business incubator program, and unusually for a startup company at Y Combinator, Migicovsky's business actually generated revenue during the program. [ 23 ] Migicovsky was able to raise US$375,000 from angel investors such as Tim Draper of Draper Fisher Jurvetson , but was unable to raise additional funds. [ 23 ] Discussing his inability to raise further funds, Migicovsky told the Los Angeles Times , "I wasn't extremely surprised... hardware is much harder to raise money for. We were hoping we could convince some people to our vision, but it didn't work out." [ 24 ]
After raising venture capital for the product under their former name, Allerta (which had already developed and sold the inPulse smartwatch for BlackBerry devices), the company failed to attract traditional investors under their new Pebble brand name, [ 23 ] so the company pursued crowd funding in April 2012.
Migicovsky's company, Pebble Technology, launched a Kickstarter campaign on April 11, 2012 , with an initial fundraising target of $100,000. Backers spending $115 would receive a Pebble when they became available ($99 for the first 200), [ 25 ] effectively pre-ordering the $150 Pebble at a discounted price. [ 24 ] Within two hours of going live, the project had met its $100,000 goal, and within six days, the project had become the most funded project in the history of Kickstarter to that point, raising over $4.7 million with 30 days left in the campaign. [ 24 ] [ 26 ]
On May 10, 2012 , Pebble Technology announced they were limiting the number of pre-orders. On May 18, 2012 , funding closed with $10,266,845 pledged by 68,929 people. [ 27 ] At the time, the product held the world record for the most money raised for a Kickstarter project. [ 28 ]
Pebble worked with consulting firm Dragon Innovation to identify suppliers and manufacturers. [ 2 ] After overcoming manufacturing difficulties with the prototype design, Pebble started mass production with Foxlink Group in January 2013, initially producing 15,000 watches per week. Shipping was originally expected to begin in September 2012, [ 29 ] but manufacturing difficulties were encountered. The first units began shipping on January 23, 2013 . [ 30 ]
Pebble shipped 300,000 units by December 2013 , [ 31 ] over 400,000 by March 2014 , [ 32 ] 450,000 as of July 2014 [update] , [ 33 ] 1 million by December 31, 2014 , [ 34 ] and 2 million by December 7, 2017. [ 4 ]
The watch featured a 32-millimetre (1.26 in) 144 × 168 pixel black and white memory LCD using an ultra low-power " transflective LCD " manufactured by Sharp ; it contained a backlight, vibration motor, magnetometer , ambient light sensors, and three-axis accelerometer . [ 9 ] [ 35 ] [ 36 ] [ 37 ] [ 38 ] It can communicate with an Android device using both Bluetooth 2.1 and Bluetooth 4.0 ( Bluetooth Low Energy ) through Stonestreet One's Bluetopia+MFi software stack. [ 39 ] Bluetooth 4.0 low energy (LE) was not initially supported, but was later added through a firmware update in November 2013. [ 40 ] The watch is charged through a modified USB -cable that attaches magnetically to the watch to maintain water resistance capability, [ 36 ] with a reported seven-day battery life. [ 41 ] Water-resistance was added during development based on feedback from Kickstarter backers. [ 42 ] The Pebble has a waterproof rating of 5 atm , which means it can be submerged down to 40 metres (130 ft), and was tested in both fresh and salt water, allowing the user to shower, dive or swim while wearing the watch. [ 43 ]
As of February 2014 [update] , the Pebble app store contained over 1,000 applications. [ 44 ] Applications included notification support for emails, calls, text messages and social media activity; stock prices; activity tracking (movement, sleep, estimates of calories burned); remote controls for smartphones, cameras and home appliances; turn-by-turn directions (using the GPS receiver in a smartphone or tablet); display of RSS or JSON feeds; and hundreds of custom watch faces.
The Pebble was announced to ship with several apps pre-installed, including a cycling app to measure speed, distance, and pace through GPS, and a golf rangefinder app supporting more than 25,000 courses. Not all announced apps were ready when the watch started shipping. CEO Eric Migicovsky announced on January 9, 2013, that updates for the watch's operating system would be released every 2–3 weeks until all features were added. [ 36 ]
The Pebble's apps used data received from a connected phone for distance, speed, and range information. More apps were downloadable via a mobile phone or tablet, and a software development kit (SDK) was freely available. [ 45 ]
Pebble integrates with Android and iOS phones through a companion app to send notifications to the watch. [ 46 ] Messaging and phone call apps were supported, in addition to most 3rd party applications. [ 47 ]
The watch's firmware operating system is based on the FreeRTOS kernel and uses Newlib , the STM32 Peripheral Library , the Ragel state machine compiler, and an unnamed UTF-8 Decoder. [ 48 ]
Gadgetbridge [ 49 ] is an alternative companion application for Android. It is open source, does not require account creation, and supports features such as notifications, music playback and watch application installation/removal.
Linux users can interface with the Pebble using libpebble. This enabled experimental services on several Linux distros including Maemo , the OS used on the Nokia N900 . There was also a commercial app called Rockwatch for MeeGo , the OS used by the Nokia N9 , that provided services including managing the Pebble's firmware and apps running on the watch. [ 50 ] [ 51 ] [ 52 ]
Pebble Technology announced that an open Pebble software development kit (SDK) would be released before shipment of the watches began. [ 53 ] A proof-of-concept watchface SDK and documentation were released on April 12, 2013. [ 54 ] [ 55 ] Eventually, Pebble SDK version 1.0 was released was limited to development for watch faces, simple applications, and games. SDK version 2.0 (later renamed PebbleKit) was released on May 17, 2013, and added support for two-way communication between Pebbles and smartphones running iOS or Android via the AppMessage framework. [ 56 ]
As of February 2015 [update] , the PebbleKit SDK included APIs to access bluetooth messaging, background workers, the accelerometer, the compass, and supported C and JavaScript (with some limitations) for developing apps. [ 57 ] Applications written using the second PebbleKit SDK were not backwards compatible with 1.x apps, and developers were required to port their apps to the second-gen firmware. [ 58 ]
The original Pebble Smartwatch was released to mixed reviews. The design was acclaimed for being innovative. [ 59 ] CNET praised the design, readability, and water-resistance of the Pebble Steel, but criticized the limit of eight user-installed apps and the lack of a heart-rate monitor. [ 60 ] Later watches in the Pebble series were described similarly: as simple and effective but lacking some features of competitors like the Apple Watch . [ 61 ] [ 62 ] Some concerns were also expressed by iFixit about build quality and reliability, while also commending the watch's repairability. [ 63 ]
On February 24, 2015, Pebble announced the Pebble Time , their second-generation Pebble smartwatch via its Kickstarter campaign.
The Pebble Time Steel is a stainless steel variant of the Pebble Time smartwatch, available in multiple finishes: silver, black or gold with either a leather or steel band. [ 64 ] Pebble claims it has a 10-day battery life.
The Pebble Time Round is also made of stainless steel and 2.5d Gorilla Glass with five finishes. Pebble claims it has a 2-day battery life, dramatically decreased because of the shape and size but still significantly longer-lasting than the Apple Watch 's 16-hour life.
Pebble's second generation comes with various improvements over its predecessors, such as a 64-colour e-paper display with Gorilla Glass [ 65 ] a thinner and more ergonomic chassis, plastic casing and a microphone. The Pebble Time retains the seven-day battery life and water resistance found on the previous two Pebble watches. It has a 150mAh battery.
Alongside the Pebble Time Steel, Pebble announced its open hardware platform called "Smartstraps". This lets developers develop new third-party straps that connects to a special port at the back of the watch and can add new features like GPS, heart rate monitors, extended battery life and other things to the watch. This new platform prevents smartwatch bloat and making the watch bulky like most of its competitors' smartwatches.
The Pebble Time also included a new interface designed around a timeline, [ 66 ] which is similar to what was found in Google Now on Android Wear . In December 2015, all remaining Pebbles got a firmware update, enabling support for the timeline and removing the maximum of 8 apps-restriction, letting additional apps load directly from the connected phone. It is backwards compatible with all previous apps and watch faces.
Third parties have created apps for Pebble Time, such as contactless payment (tap to pay). [ 67 ]
The Pebble Time retailed for $199. [ 68 ] The project reached its Kickstarter funding goal of $500,000 in 17 minutes. [ 69 ] The project took 49 minutes to reach $1 million, which is a Kickstarter record. [ 70 ] The project raised $10.3 million in 48 hours, another Kickstarter record. On March 3, 2015, Pebble Time became the most funded Kickstarter ever with nearly $14 million funded, while having 24 days left in its campaign. [ 71 ] At the end of the funding, March 27, 2015, Pebble Time received pledges of $20,338,986 from 78,471 backers. [ 72 ]
Pebble 2, the company's 3rd generation smartwatch, launched on Kickstarter on May 24, 2016, with an offer period of 36 days at discounted introductory pricing, and shipment of the new models anticipated in the October–November 2016 timeframe. [ 73 ] Among the new features was a heart rate monitor (On +HR models), microphone, and water resistance rated for 30 m (98 ft) depth, Which was 10m less than the original Pebble because of the Pebble 2's Microphone. Many new features were documented as part of the Kickstarter prospectus, while other technical specifications of the forthcoming products are not yet disclosed.
The Pebble 2 product line added a new device called the Pebble Core, "a tiny wearable computer with Android 5.0" featuring a 3G modem, GPS, and Spotify integration backed by an open development community. [ 74 ] Pebble 2 was officially released in September 2016 with a new design and functions at $129. [ 75 ] When Pebble sold parts of its company to Fitbit in late 2016, Gizmodo criticized the company for collecting $12.8 million in the product's Kickstarter and delaying shipments for half a year without being forthright with their supporters. Kickstarter backers who have not received the product were expected to receive refunds in 2017. [ 76 ]
On December 7, 2016, Pebble Technology filed for insolvency [ 77 ] with Fitbit acquiring much of the company's assets and some employees. The selling of Pebble brand to Fitbit was credited to Charles River Ventures who invested $15 million in the company in 2013. [ 78 ] The purchase excluded Pebble's hardware, as stated by Fitbit. The deal was focused on Pebble's software engineers and testers, and the acquisition of intellectual property such as the Pebble watch's operating system, watch apps, cloud services, and its patents. [ 79 ]
Further clarification on the transition timeline and efforts to render Pebble OS and its watchfaces/apps more self-sufficient was posted to the Pebble Dev Blog on December 14, 2016. [ 80 ]
Fitbit paid $23 million for Pebble's intellectual property, [ 81 ] despite Pebble's debt and other obligations exceeding that. [ 82 ] Fitbit did not take on Pebble's debt. The remainder of Pebble's assets, including product inventory and server equipment, was set to be sold off separately. Following the acquisition, Pebble's offices were closed and Fitbit held control over the use of the Pebble brand. The former Pebble engineers were relocated to Fitbit's offices in San Francisco. As a result, Pebble was forced to cancel shipments for its Pebble 2, Time 2, and Pebble Core smartwatches, refunding Kickstarter backers. [ 83 ] [ 84 ] [ 4 ]
An unofficial developer group called Rebble was created to extend support for the Pebble watches' online services that were discontinued on June 30, 2018. Pebble users and enthusiasts created the website in December 2016 following the announcement of Pebble's shutdown. [ 85 ] Users can switch their devices from the original Pebble web services to the Rebble Web Services to restore some of the lost features; some features, such as weather and dictation require a US$3 monthly subscription to cover the costs. [ 86 ] [ 87 ]
On January 27, 2025, Google announced that the PebbleOS codebase would be open-sourced. [ 20 ] Migicovsky announced that a new model was being developed, as of February 3, 2025. Two new watches running PebbleOS were announced on March 18, 2025 under the Core Devices name. The two revealed watches were the Core 2 Duo, a 1.2 inch black and white e-paper display smartwatch inspired by the Pebble 2, and the Core Time 2, a 1.5 inch color e-paper display smartwatch with a touch screen, metal body, and heart rate sensor. Both watches feature step tracking, IPX8 water resistance, and a 30 day battery life. [ 88 ] [ 89 ] | https://en.wikipedia.org/wiki/Pebble_(watch) |
Pebble Time is a discontinued smartwatch developed by Pebble Technology and assembled by Foxlink, released on 14 May 2015. This is the first Pebble to introduce a color e-paper display, as well as a microphone, a new charging cable and a new Pebble Time-optimized operating system . [ 5 ]
In early 2015, Pebble announced the product, as well as its fundraising on Kickstarter . The watch received $1M in 49 minutes, breaking a current record, and was the most funded Kickstarter campaign from March 2015 to March 2022, reaching $20.4M all the way to its deadline, from over 78,741 backers. [ 6 ] [ 7 ]
Pebble ceased operating in June 2018, with the technology sold to Fitbit . [ 8 ]
After releasing the Pebble smartwatch, Pebble CEO Eric Migicovsky announced the Pebble Time, the second generation smartwatch of Pebble.
The project was established on Kickstarter , a crowdsourcing website, and reached its goal ($500K) in 17 minutes, $1M in 49 minutes, $10.3M in 2 days, breaking another Kickstarter goal, and finally earning $20.4M by its deadline on 3 March 2015, making it the most funded Kickstarter project to date. [ 9 ] Until March 2022, the Pebble Time Smartwatch was officially the most successful campaign on Kickstarter, with almost 80,000 backers pledging $20 million. [ 7 ] [ 10 ]
Pebble's smartwatches connect to both Android and iOS phones, and using a Bluetooth connection, run native apps that control music on the connected smartphone, display calendars, show fitness/sleep data from Pebble Health, and allow users to set timers. [ 11 ] Pebble also has an app store where users can download apps from companies including RunKeeper , ESPN , Uber , Nest , TripAdvisor , Pandora Radio , and Yelp onto their watches. [ 12 ] Users can also respond to text messages with the Pebble's microphone, check the weather, create checklists, make voice notes, and view Google Maps directions. [ 13 ]
Pebble Time uses Pebble OS version 3.0. This OS is compatible with its color e-paper display. The OS features updated transitions between screens which "morph" into other features due to the constrained space of the watch's face. [ 14 ] The OS version is also backward compatible with other features in previous versions of Pebble OS. It works with apps, watchfaces, and settings tailored for Pebble OS v. 2 or lower, as well as its predecessors. Pebble Time still retains most of the features from the original Pebble smartwatch, such as Bluetooth connectivity, and is currently only compatible with the smartwatch itself.
Timeline is a new feature on Pebble OS 3, which currently is only compatible with Pebble Time. It enables the wearer to look at past and future notes, either reminders, alarms, app notifications, scores, weather reports or others. The completed or viewed notifications, ESPN scores, and calendar events are in the "past" section, which is highlighted yellow. The future calendar events, weather reports, or reminders are in the "future" section, which is highlighted blue. To access either, the wearer uses the buttons to look at desired information. [ 15 ]
The smartwatch comes with a Gorilla Glass 64-color e-paper always-on display developed by JDI with 144x168 resolution and has a pixel density of 182 ppi. This is the first Pebble smartwatch to have a color display, and still retains a LED backlight as well. The watch also has a vibrating motor for silent alarms, and smart notifications. The watch comes with a redesigned charging cable that, like its predecessor's cable, magnetically attaches itself to the watch in order to maintain its water resistance. Unlike its predecessor, the cable attaches to the back of the watch rather than the side, and has the potential to transfer data rather than just power. The band attaches with standard 22 mm pins. The watch is also equipped with an ambient light sensor and 6 axis accelerometer. [ 16 ]
Pebble Time, as a feature, has a small accessory port on the back of the watchface. Pebble Technology, Corp announced on its developer site that it is possible to create accessory ports on watchbands, otherwise known as "smartstraps". It enables the wearer to attach additional equipment to the watch, including sensors, batteries, and miscellaneous. As a hazard, the "smartstraps" will affect the watch's battery life. As of summer 2015, the "smartstrap" API is still in beta testing. [ 17 ] Two smartstraps were funded on Kickstarter so far: the Pagaré strap, which gives Apple Pay -like contactless payment features to the Pebble, and the Tylt Vü strap, which gives Qi capabilities to the Pebble, as well as heart rate measurement. [ 18 ]
The Pebble Time Steel is a variant of the Pebble Time, with a steel and leather style and 10-day battery life, while retaining full waterproofing and all of the Pebble Time's features. [ 19 ] It has a Marine Grade steel chassis encasing it, with bezel and a PVD matte polishing finish, a 2.5D color e-paper display, and depending on color finish, comes with either a 22 mm Italian leather band with stainless steel PVD-coated buckles and "Quick Release" pins, or a 22 mm stainless steel band with PVD coating and detailing sold separately.
The Pebble Time Round is a variant of the Pebble Time. It was available for pre-order on September 23, 2015. The watch includes a 2-day battery with 15 minutes of charging giving the watch one day of battery life. The watch has the same 64 color e-paper display as the other Pebble Times. It was available with two watch strap sizes: 14 mm and 20 mm with different color combinations for each size. The Pebble Time Round has all the same features as the Pebble Time, including the microphone for dictating text message replies, but featured a thinner, round style. [ 20 ]
The Pebble Time 2 was the planned second version of the Pebble Time. It was announced via Kickstarter on May 24, 2016. The Time 2 would have featured a larger 228x200 1.5 inch color display, an optical heart rate monitor and improvements to Pebble Health. The Time 2 would have included all the same features of previous Time models. [ 21 ]
The Pebble Time 2 was never publicly released due to the insolvency of Pebble . [ citation needed ]
Critics praised the battery life, Android support, and color screen, but derided its Apple support, its "retro-techie" design, and its overall quality.
The Verge gave the watch a 6.8 on its score, summing up by saying that while it is fun at some points, "the Pebble Time doesn't do enough to change that." [ 15 ] CNET also gave it 3.5 out of 5 stars for the editor's rating, and a 7.8 overall, saying that "[the] Pebble Time adds a few key improvements and a color screen..., but owners of previous Pebble[s] may not see a need to upgrade yet." [ 11 ] Digital Trends gave it 2.5 out of 5 stars, praising the battery life, screen, design, and water resistance, but derided its software support, design, settings, interface, and price, saying that "Pebble has been left behind." [ 22 ] Tom's Guide gave it 3.5 out of 5 stars, concluding that while it isn't the perfect smartwatch, "it's the most practical wrist companion for Android" [ 23 ] Wired gave it a 6/10, and summed up its use by saying that they want the idea, "[but not] the watch." [ 24 ] PC Magazine gave it a 4 out of 5, stating it "excellent" and as an "Editor's Choice", saying that "[it's a] solid choice for first-time smartwatch buyers."
CNET gave it 3.5 out 5 stars for the editor's rating, but a point higher compared to Pebble Time for its overall rating, stating that "[it's better] as a more budget-friendly watch." [ 25 ] Tom's Guide gave it 3.5 out of 5 stars, saying that it's "the company's most luxurious smartwatch to date, but it's a better choice for Android users." [ 26 ] | https://en.wikipedia.org/wiki/Pebble_Time |
A process related to the sol-gel route is the Pechini, or liquid mix, process (named after its American inventor, Maggio Pechini). An aqueous solution of suitable oxides or salts is mixed with an alpha hydroxycarboxylic acid such as citric acid. Chelation, or the formation of complex ring-shaped compounds around the metal cations, takes place in the solution. A polyhydroxy alcohol is then added, and the liquid is heated to 150–250 °C (300–480 °F) to allow the chelates to polymerize, or form large, cross-linked networks. As excess water is removed by heating, a solid polymeric resin results. [ 1 ] Eventually, at still higher temperatures of 500–900 °C (930–1,650 °F), the resin is decomposed or charred, and ultimately a mixed oxide is obtained. Particle size is extremely small, typically 20 to 50 nanometres (although there is agglomeration of these particles into larger clusters), with intimate mixing taking place on the atomic scale. [ 2 ]
The Pechini method was proposed in 1967 as a technique of depositing dielectric films of titanates and niobates of lead and alkaline-earth elements in the production of capacitors. Later, the process was customised for the in-lab synthesis of multicomponent finely dispersed oxide materials. [ 3 ] [ 4 ]
This method has been used for synthesizing over 100 mixed metal oxides including lanthanum manganite for solid oxide fuel cells and BaTiO3 (Lessing 1989). [ 5 ] Unlike the sol–gel process in which the metal alkoxide participates in the gel-forming reactions this process is based on a gelation reaction between the alcohol and acid used as solvents. A polymeric resin containing a good distribution of cations is obtained which yields the oxide upon calcination. The use of polyacrylic acid with higher functionality results in highly cross-linked resins containing a more uniform distribution of the reacting cations. The gel structures can be varied depending on the acid-to-alcohol ratio. A low organic content is preferred to decrease the calcination time and temperature in order to obtain fine-grained materials with low carbon contents. [ 6 ] [ 7 ] | https://en.wikipedia.org/wiki/Pechini_process |
The Pechmann condensation is a synthesis of coumarins , starting from a phenol and a carboxylic acid or ester containing a β- carbonyl group. [ 1 ] The condensation is performed under acidic conditions. The mechanism involves an esterification/transesterification followed by attack of the activated carbonyl ortho to the oxygen to generate the new ring. The final step is a dehydration, as seen following an aldol condensation . It was discovered by the German chemist Hans von Pechmann [ 2 ] .
To synthesize coumarin derivatives, β-ketoesters can be condensed with phenols under acidic conditions. [ 3 ] In this case, a transesterification reaction occurs first with the formation of the phenol ester. This is then followed by ring closure, similar to Friedel-Crafts alkylation .
With simple phenols, the conditions are harsh, although yields may still be good. [ 4 ]
With highly activated phenols such as resorcinol , the reaction can be performed under much milder conditions. This provides a useful route to umbelliferone derivatives:
For coumarins unsubstituted at the 4-position, the method requires the use of formylacetic acid or ester. These are unstable and not commercially available, but the acid may be produced in situ from malic acid and sulfuric acid above 100 °C. As soon as it forms, the formylacetic acid performs the Pechmann condensation. In the example shown, umbelliferone itself is produced, albeit in low yield:
The mechanism of the reaction has been studied in details with theoretical treatment. [ 5 ]
The study shown that reaction takes place on oxo-form, and not on enolic-form. Three different oxo-routes have been proposed.
In a variation the reaction of phenols and beta-ketoesters and phosphorus pentoxide yields a chromone . This reaction is called Simonis chromone cyclization . [ 6 ] [ 7 ] The ketone in the ketoester is activated by P 2 O 5 for reaction with the phenol hydroxyl group first, the ester group in it is then activated for electrophilic attack of the arene. | https://en.wikipedia.org/wiki/Pechmann_condensation |
G. W. Peck is a pseudonymous attribution used as the author or co-author of a number of published academic papers in mathematics . Peck is sometimes humorously identified with George Wilbur Peck , a former governor of the US state of Wisconsin . [ 1 ]
Peck first appeared as the official author of a 1979 paper entitled "Maximum antichains of rectangular arrays". [ 2 ] The name "G. W. Peck" is derived from the initials of the actual writers of this paper: Ronald Graham , Douglas West , George B. Purdy , Paul Erdős , Fan Chung , and Daniel Kleitman . The paper initially listed Peck's affiliation as Xanadu , but the editor of the journal objected, so Ron Graham gave him a job at Bell Labs . Since then, Peck's name has appeared on some sixteen publications, [ 3 ] primarily as a pseudonym of Daniel Kleitman. [ 1 ]
In reference to "G. W. Peck", Richard P. Stanley defined a Peck poset to be a graded partially ordered set that is rank symmetric , rank unimodal , and strongly Sperner . [ 4 ] The posets in the original paper by G. W. Peck are not quite Peck posets, as they lack the property of being rank symmetric. | https://en.wikipedia.org/wiki/Peck_poset |
In Euclidean geometry , for a plane curve C and a given fixed point O , the pedal equation of the curve is a relation between r and p where r is the distance from O to a point on C and p is the perpendicular distance from O to the tangent line to C at the point. The point O is called the pedal point and the values r and p are sometimes called the pedal coordinates of a point relative to the curve and the pedal point. It is also useful to measure the distance of O to the normal p c (the contrapedal coordinate ) even though it is not an independent quantity and it relates to ( r , p ) as p c := r 2 − p 2 . {\textstyle p_{c}:={\sqrt {r^{2}-p^{2}}}.}
Some curves have particularly simple pedal equations and knowing the pedal equation of a curve may simplify the calculation of certain of its properties such as curvature . These coordinates are also well suited for solving certain type of force problems in classical mechanics and celestial mechanics .
For C given in rectangular coordinates by f ( x , y ) = 0, and with O taken to be the origin, the pedal coordinates of the point ( x , y ) are given by: [ 1 ]
The pedal equation can be found by eliminating x and y from these equations and the equation of the curve.
The expression for p may be simplified if the equation of the curve is written in homogeneous coordinates by introducing a variable z , so that the equation of the curve is g ( x , y , z ) = 0. The value of p is then given by [ 2 ]
where the result is evaluated at z =1
For C given in polar coordinates by r = f (θ), then
where ϕ {\displaystyle \phi } is the polar tangential angle given by
The pedal equation can be found by eliminating θ from these equations. [ 3 ]
Alternatively, from the above we can find that
where p c := r 2 − p 2 {\displaystyle p_{c}:={\sqrt {r^{2}-p^{2}}}} is the "contrapedal" coordinate, i.e. distance to the normal. This implies that if a curve satisfies an autonomous differential equation in polar coordinates of the form:
its pedal equation becomes
As an example take the logarithmic spiral with the spiral angle α:
Differentiating with respect to θ {\displaystyle \theta } we obtain
hence
and thus in pedal coordinates we get
or using the fact that p c 2 = r 2 − p 2 {\displaystyle p_{c}^{2}=r^{2}-p^{2}} we obtain
This approach can be generalized to include autonomous differential equations of any order as follows: [ 4 ] A curve C which a solution of an n -th order autonomous differential equation ( n ≥ 1 {\displaystyle n\geq 1} ) in polar coordinates
is the pedal curve of a curve given in pedal coordinates by
where the differentiation is done with respect to p {\displaystyle p} .
Solutions to some force problems of classical mechanics can be surprisingly easily obtained in pedal coordinates.
Consider a dynamical system:
describing an evolution of a test particle (with position x {\displaystyle x} and velocity x ˙ {\displaystyle {\dot {x}}} ) in the plane in the presence of central F {\displaystyle F} and Lorentz like G {\displaystyle G} potential. The quantities:
are conserved in this system.
Then the curve traced by x {\displaystyle x} is given in pedal coordinates by
with the pedal point at the origin. This fact was discovered by P. Blaschke in 2017. [ 5 ]
As an example consider the so-called Kepler problem , i.e. central force problem, where the force varies inversely as a square of the distance:
we can arrive at the solution immediately in pedal coordinates
where L {\displaystyle L} corresponds to the particle's angular momentum and c {\displaystyle c} to its energy. Thus we have obtained the equation of a conic section in pedal coordinates.
Inversely, for a given curve C , we can easily deduce what forces do we have to impose on a test particle to move along it.
For a sinusoidal spiral written in the form
the polar tangential angle is
which produces the pedal equation
The pedal equation for a number of familiar curves can be obtained setting n to specific values: [ 6 ]
A spiral shaped curve of the form
satisfies the equation
and thus can be easily converted into pedal coordinates as
Special cases include:
For an epi- or hypocycloid given by parametric equations
the pedal equation with respect to the origin is [ 7 ]
or [ 8 ]
with
Special cases obtained by setting b = a ⁄ n for specific values of n include:
Other pedal equations are:, [ 9 ] | https://en.wikipedia.org/wiki/Pedal_equation |
A pedalboard (also called a pedal keyboard , pedal clavier , or, with electronic instruments, a bass pedalboard [ 1 ] ) is a keyboard played with the feet that is usually used to produce the low-pitched bass line of a piece of music. A pedalboard has long, narrow lever-style keys laid out in the same semitone scalar pattern as a manual keyboard , with longer keys for C, D, E, F, G, A, and B, and shorter, raised keys for C ♯ , D ♯ , F ♯ , G ♯ and A ♯ . Training in pedal technique is part of standard organ pedagogy in church music and art music.
Pedalboards are found at the base of the console of most pipe organs , pedal pianos , theatre organs , and electronic organs . Standalone pedalboards such as the 1970s-era Moog Taurus bass pedals are occasionally used in progressive rock and fusion music. In the 21st century, MIDI pedalboard controllers are used with synthesizers, electronic Hammond-style organs , and with digital pipe organs. Pedalboards are also used with pedal pianos and with some harpsichords , clavichords , and carillons (church bells).
The first use of pedals on a pipe organ grew out of the need to hold bass drone notes, to support the polyphonic musical styles that predominated in the Renaissance. Indeed, the term pedal point , which refers to a prolonged bass tone under changing upper harmonies, derives from the use of the organ pedalboard to hold sustained bass notes. [ 2 ] These earliest pedals were wooden stubs nicknamed mushrooms , [ 3 ] [ 4 ] which were placed at the height of the feet. These pedals, which used simple pull-downs connected directly to the manual keys, are found in organs dating to the 13th century. The pedals on French organs were composed of short stubs of wood projecting out of the floor, which were mounted in pedalboards that could be either flat or tilted. Organists were unable to play anything but simple bass lines or slow-moving plainsong melodies on these short stub-type pedals. Organist E. Power Biggs , in the liner notes for his album Organs of Spain noted that "One can learn to play them, but fluent pedal work is impossible".
There were two approaches used for the accidental notes (colloquially referred to as the "black" notes). The first approach can be seen in the 1361 Halberstadt organ, which uses shorter black keys placed above the white keys. Other organs positioned the black keys on the same level and depth as the white keys. The first pedal keyboards only had three or four notes. [ 3 ] Eventually, organ designers augmented this range by using eight notes, an approach now called a "short octave" keyboard, because it does not include accidental notes such as C ♯ , D ♯ , F ♯ , G ♯ , and A ♯ . [ 3 ] The 17th-century north German organ builder Arp Schnitger used an F ♯ and G ♯ in the lowest octave of the manuals and pedal keyboards, but not a C ♯ and D ♯ . From the 16th to 18th centuries, short octave keyboards were also used in the lowest octave of upper manual keyboards.
By the 14th century, organ designers were building separate windchests for the pedal division, to supply the pipes with the large amount of wind that bass notes need to speak. These windchests were often built into tall structures called "organ towers". Until the 15th century, most pedal keyboards only triggered the existing Hauptwerk pipes already used by the upper manual keyboards. Beginning in the 15th century, some organ designers began giving pedal keyboards their own set of pipes and stops. In the 15th and 16th centuries, the pedal division usually consisted of a few 8′ ranks and a single 16′ rank. By the early 17th century, pedal divisions became more complex, with a richer variety of pipes and tones. Nevertheless, the pedal division was usually inconsistent from one country to another.
By the beginning of the 17th century, organ designers began to give pedalboards on large organs a larger range, encompassing twenty-eight to thirty notes. As well, German organ designers began to use longer, narrower pedals, with a wider space between the pedals. By this point, most pedals were given a smoother lever-action by including a fulcrum at the back of each pedal. These design changes allowed performers to play more complex, fast-moving pedal lines. This gave rise to the dramatic pedal solos found in German organ works from composers from the North German organ school, such as Dieterich Buxtehude , Johann Adam Reincken and J.S. Bach . In Bach's organ music the cantus firmus melody, which is usually a hymn tune , is often performed in the pedal, using a reed stop to make it stand out.
Several sources, including an encyclopedia on the organ, claim that the pedalboard design improvements of the 17th century allowed the organist to actuate the pedals either with the toe of the foot or with the heel. [ 3 ] However, organist Ton Koopman argues that
"Bach's complete oeuvre [can be played] with the pedal technique of his time, in other words without the use of the heel." Koopman claims that in "Bach's day toe and heel pedalling was not yet known, as is evident from his organ works, in which all the pedal parts can be played with the toe." [ 5 ] What evolved as the "German" pedal technique in the late 18th and early 19th century promoted heel-and-toe pedaling, while the "French" style was predicated on the "toe only" pedal technique.
In the 17th and 18th centuries, pedalboards were rare in England. A critic for the New York Times in 1895 argued that this may explain why Handel's published organ works are generally lighter-sounding than those of J.S. Bach. [ 6 ] In the 17th and 18th centuries, the pedal part of organ music was rarely given its own staff. Instead, the organ part would be put into two staves, which were mostly used for the upper and lower manual parts. When the composer wanted a part played with the pedal keyboard, they marked Pedal , Ped. , or simply P . Often, composers omitted these signs, and player had to decide if the range of all the parts or the lowest part was appropriate for the pedal keyboard. [ 7 ] This lack of specification is in keeping with many other aspects of Baroque musical performance practice , such as the use of improvised chords by organists and harpsichord players in the figured bass tradition and the use of improvised ornaments by solo singers and instrumentalists.
In the late 1820s, the pedalboard was still fairly unfamiliar in the UK. In the organ at the Church of St James at Bermondsey in 1829, "a finger [manual] keyboard was added for those unable to play with their feet." If an organist was performing a piece with a pedal part, "an assistant was needed to play the bottom line of the finger keyboard, offset on the bass side of the console." [ 8 ] In 1855 in England, Henry Willis patented a concave design for the pedalboard that also radiated the ends keyboard outward and used longer keys, bringing the end keys closer to the performer. This design became common in the UK and in the US in the late 19th century, and by 1903, the American Guild of Organists (AGO) adopted it as their standard.
In the 19th century and early 20th century, the pedal division also underwent changes. The pedal divisions of the Baroque era often included a small number of higher-pitched stops, which allowed performers to perform higher melodies on the pedalboard. In the 19th century and early 20th century, organ designers omitted most of these higher-pitched stops, and used pedal divisions which were dominated by 8′ and 16′ stops. This design change, which coincided with the musical trend for music with a deep, rich bass part, meant that players used the pedalboard mainly for bass parts.
By the mid-19th century, the pedal part of organ music was increasingly given its own staff, which meant that composers and transcribers began writing organ music in three-stave systems (right hand, left hand, and pedal keyboard). [ 7 ] Whereas early organ composers left the way that pedal keyboard lines were played to the player's discretion, in the later 19th century, composers began to indicate specific foot actions.
In addition to telling the organist whether to use the left or right foot, symbols indicate whether they should use the toe or heel. A "^" symbol indicates the toe, and a "u" or "o" indicates the heel. Symbols below notes indicate the left foot, and above notes indicates the right foot.
Swedish organist L. Nilson published a method for the pedal keyboard, the English translation of which was titled A System of Technical Studies in Pedal Playing for the Organ (Schirmer, 1904). Nilson lamented that it "...is a melancholy fact that only very few eminent organists since Bach's time have made it their business to lift pedal-playing out of its primitive confusion..." (page 1 of Preface). He argued that the great organ pedagogues such as Kittel and Abbe Vogler did not make any efforts to improve the "...system of playing on the pedals". Nilson makes one exception from this critique: the organ method of J. Lemmens, who he praises as having reformed pedal playing by introducing "...sound principles of execution" (page 2 of Preface). Nilson's pedal method includes scale and arpeggio studies, polyphonic studies with both feet playing in contrary motion, studies written in parallel octaves, and studies written in thirds.
In the 1990s, standalone electronic MIDI controller pedalboards became widely available on the market. MIDI pedalboards do not produce any tones by themselves, and so they must be connected to a MIDI-compatible electronic keyboard or MIDI sound module and an amplified loudspeaker to produce musical tones. In the 1990s and 21st century, some churches [ which? ] began using electronic-trigger equipped pedalboards for the 16′ and 32′ stops. The MIDI information from the electronic pedalboard sensors triggers pipe organ sounds from digital sound modules (e.g., Wicks CM-100, Ahlborn Archive Modules, or Walker Technical sound generation), [ citation needed ] which are then amplified through loudspeakers.
These MIDI systems can be much less expensive than metal or wooden bass pipes, which are very costly to purchase and install, due to their heavy weight (up to one ton per pipe), large size, and need for large amounts of wind. Another rationale for using MIDI systems is that it may be easier to get a focused sound with a MIDI system, because all of the bass tone emanates from a single speaker or set of speakers. With traditional pipes, it can be difficult to give the pedal division a focused sound, because the large pipes tend to be spread out over the entire organ pipe chest.
This cost-saving measure has been the subject of controversy in the organ scene. Advocates of MIDI pedal divisions [ who? ] argue that a good quality MIDI system produces a better tone than an inexpensive set of bass pipes with money-saving "shortcuts" such as using stopped pipes and resultant tones to reduce the number of required pipes. However, critics [ who? ] dislike the way that the use of MIDI pedal divisions blends electronically amplified lower voices with the natural, wind-driven upper ranks. Willi Apel and Peter Williams argue that by definition, an organ must make its sound by air flowing through pipes. Some critics [ who? ] argue that the bass tone from a MIDI pedal division, which comes from an amplified 12-inch subwoofer , is not as "natural" and "open-sounding" as the vibrations from a massive, wind-driven 32-foot pipe.
Pedalboards range in size from 13 notes on small spinet organs designed for in-home use (an octave, conventionally C 2 –C 3 ) to 42 notes (three and a half octaves, G 1 –C 5 ) on church or concert organs. Modern pipe organs typically have 30- or 32-note pedalboards, while some electronic organs and many older pipe organs have 25-note pedalboards.
Besides the number of pedals, the two main identifying aspects of a pedalboard are:
Exact design specifications for pedalboards are published in Great Britain by the RCO , in the United States by the AGO (which requires a design similar to the RCO's), and in Germany by the BDO (which allows both 30- and 32-note pedalboards, of both concave/radiating and concave/parallel varieties).
In an organ with more than one keyboard, the stops and the ranks that the stops control are separated into different divisions, in which the ranks of pipes are grouped together so that they make a "focused" or coherent sound. The pedal division, which is played from the pedal keyboard, usually includes more stops of 16′ pitch. The sound of the pedal division is generally voiced so that the pedal division complements the sound of the great division. Common 16′ stops found in the pedal division include the 16′ Bourdon, the 16′ Principal, and the 16′ Trombone. Eight foot stops include the 8′ Open Diapason. Pedal divisions may also include higher-register stops, such as the 4′ Choral Bass or various mixtures. When pedal parts are performed, a 16′ stop is usually paired with an 8′ one to provide more definition. For pedal parts that need accentuation, such as the Cantus Firmus melody in a 17th-century organ piece, many organs have a nasal-sounding reed stop in the pedal division, or a 4′ Principal designated on the stop knob as "Choralbass".
A few pedalboards have a pedal divide system that lets the organist split the pedalboard at its midpoint. With this system, an organist can play a melody with the right foot and a bass part with the left. [ citation needed ] The divided pedal is a type of coupler. It allows the sounds played on the pedals to be split, so the lower octave (principally that of the left foot) plays stops from the pedal division while the upper half (played by the right foot), plays stops from one of the manual divisions. The choice of manual is at the discretion of the performer, as is the 'split point' of the system.
The system can be found on the organs of Gloucester Cathedral , having been added by Nicholson & Co (Worcester) Ltd / David Briggs and Truro Cathedral , having been added by Mander Organs / David Briggs , as well as on the new nave console of Ripon Cathedral .
In some organs, a wooden panel called a "kickboard" or "kneeboard" is installed above the pedalboard, between the pedals and the lowest manual keyboard. Expression pedals, coupler controls and toe studs (to activate stops or stop combinations) may be located on or set into the kickboard. Expression pedals are used to open and close shades or shutters that enclose the pipes of a given division. Combination pistons are used to make rapid stop changes from the console on organs with electric stop action. Toe studs are pistons that can be operated by the feet, which change either the pedal stops or the entire organ.
In some organs, a "pedalboard check" mechanism serves as a safety catch, to shut off the pedalboard keys. The mechanism prevents accidental foot contact with the pedalboard from sounding notes in a section written only for the upper manuals.
The works of Dutch composer , organist , and pedagogue Jan Pieterszoon Sweelinck (1562–1621) contain the earliest example of an independent part for the pedal, rather than a sustained bass drone. His work straddled the end of the Renaissance and beginning of the Baroque eras, and he helped establish the north German organ tradition .
Dieterich Buxtehude (1637–1707), who was the most renowned composer of his time, was famous for his "...virtuosity and innovation at the pedal board." The young Johann Sebastian Bach was influenced by Buxtehude, who used the pedal board "as a full-fledged keyboard and devot[ed] virtuoso passages to it." [ citation needed ] J.S. Bach used the pedal to perform the melody in works such as his setting of the Christmas hymn, In Dulci Jubilo , in which the main theme in the tenor voice is played in the pedal on a higher-pitched stop. Bach also wrote compositions that use the pedal for dramatic virtuoso displays of scales and figurated passage-work in preludes, toccatas, fantasias and fugues.
There are a small number of organ compositions that are written solely for the pedal keyboard. English organist and composer George Thalben-Ball (1896–1987) wrote a piece entitled “Variations on a Theme by Paganini” for pedal keyboard. Based on Paganini 's “ Caprice No. 24 ”, a virtuoso work for solo violin, it includes pedal glissandi , leaps from one end of the pedalboard to the other, and four-note chords. [ 9 ]
Firmin Swinnen (1885–1972) was a Belgian organist who became famous in the US in the 1920s for his theater organ improvisations during silent films . Swinnen wrote a pedal cadenza for an arrangement of Widor's Fifth Symphony . The cadenza was published separately by The American Organist . The publisher promoted the cadenza it as the "most daring, the most musical Pedal Cadenza obtainable"; this praise is corroborated by reviewers who were at the performance, who remarked at the complex footwork required by the work. [ citation needed ] The symphony was performed 29 times during the week of its premiere, to "...literally screaming audiences...who had never seen such a sight as an organist up on a lift [platform] in the spotlight playing with his feet alone". [ 10 ]
After injuring his left arm in 2008, the principal organist for the Tabernacle Choir at Temple Square ( Richard Elliott ) prepared an arrangement of “Go Tell It On the Mountain” which begins with an entire verse played solely on the pedalboard to accommodate his then-injured arm. As his arm healed he added additional verses with the most demanding notes played with his right hand. [ 11 ] The video of his unusual performance has garnered millions of views on YouTube.
Although the pedalboard is most frequently used for the bass part, composers from the 17th century to the present have often used it for higher parts as well. In his serene Le Banquet Céleste Olivier Messiaen places the tune, registered for 4′ flute (and higher mutation ranks), in the pedals.
From the early 20th century, composers have increasingly demanded an advanced pedal technique at the organ. Performers display their virtuosity in such works as Wilhelm Middelschulte 's Perpetuum mobile , Leo Sowerby 's Pageant (1931), and Jeanne Demessieux 's Six études , Op. 5 (1944), which recall the dramatic organ pedal solos of the Baroque era.
Pedal keyboards were developed for the clavichord and harpsichords during the Baroque era so that organists could practise the pedal parts of their organ repertoire when they had no-one available to work the bellows for a church organ or, in the wintertime, to avoid having to practice on a church organ in an unheated church . Johann Sebastian Bach owned a pedal harpsichord and his organ trio sonatas BWV 525–530, Passacaglia and Fugue in C minor BWV 582 , Toccata and Fugue in D minor BWV 565 , and other works sound well when played on the instrument.
The pedal piano (or pedalier piano) [ 12 ] is a kind of piano that includes a pedalboard [ 13 ]
There are two types of pedal piano:
Wolfgang Amadeus Mozart owned a fortepiano with independent pedals, built for him in 1785 . Robert Schumann had an upright pedal piano with 29 notes. In the 21st century, pedal pianos, the Doppio Borgato are made in the Borgato workshop in Italy . The bass pedalboard has 37 notes, A0 to A3 (rather than the standard 30 or 32 on an organ).
Some large carillon systems for playing church bells include a pedalboard for the lowest-pitched bells. Carillon pedal keys activate a pull-down coupler that visibly moves the keys of the manual clavier and heavy clappers for the largest bells. These keys resemble the "button keys" of early organs, and are played by the player's toes. Because this non-legato technique involves no sliding, shoes with leather soles are not required.
After jazz organist Jimmy Smith popularized the Hammond organ in jazz in the 1950s, many jazz pianists "... who thought that getting organ-ized would be a snap ..." realized that the Hammond "... B-3 required not only a strong left hand, but studied coordination on the pedals to create the strong and solid "jazz bass" feel." [ 14 ] Barbara Dennerlein combines advanced pedalboard techniques with agile playing on the manuals . Organists who play the bassline on the lower manual may do short taps on the bass pedals – often on the tonic of a tune's key and in the lowest register of the pedalboard – to simulate the low, resonant sound of a plucked upright bass string.
In popular music, pedaling style may be more varied and idiosyncratic, in part because jazz or pop organists may be self-taught. Also, pedaling styles may differ due to the design of electromechanical organs and spinet organs, many of which have shorter pedalboards designed to play primarily with the left foot, so that the right foot can control a volume (swell) pedal.
In the 1970s, some progressive rock groups such as Yes , Pink Floyd , Genesis , Atomic Rooster and Rush used standalone Moog Taurus bass pedalboard synths, which were nicknamed "bass pedals" (despite the fact that the Taurus could play in a wide range, from bass to treble range). The Taurus generated an analog synth bass tone for amplification by a bass amp . Other groups, such as Led Zeppelin and Van Der Graaf Generator used the bass pedals of the Hammond organ in place of a bass guitar for several of their recordings and for live performances.
Other users included metal and hard rock bands such as Yngwie Malmsteen , Styx , and Francis Buchholz of the Scorpions , and Justin Harris of Menomena . Ex-Genesis guitarist Steve Hackett had a set mounted waist high, which his brother, John Hackett , played with his hands for the intro of Clocks – The Angel Of Mons from the album Spectral Mornings . Adam Jones of Tool uses the Moog Taurus along with an Access Virus B synth to trigger live effects. The keyboardist for the rock group Emerson, Lake & Palmer took this idea to its logical conclusion by performing all of the first movement, and part of the second of The Three Fates on the organ of Royal Festival Hall in London .
As well, some pop groups (e.g., The Police , Muse , U2 ) and fusion bands have used bass pedalboards to produce sounds in the bass range. They are most commonly used by keyboard players as an adjunct to keyboards, but can be played in combination with other instruments (e.g., by the bass guitar or electric guitar player), or by themselves.
Standalone pedalboards usually have a 13-note range and short pedals, which limits the types of basslines to fairly simple passages. A group's bass guitarist or electric guitarist playing the pedalboard from a standing position can only use one foot at a time, which further limits what they can play. The BASYN analog bass synthesizer is a two- VCO analog synthesizer with a 13-note "button board"—with momentary push-button switches in place of pedals. Another variant used in rock bands is a bass pedalboard laid out as a tablature representation of part of the four strings of an electric bass guitar . [ citation needed ]
In the 1990s, standalone electronic MIDI controller pedalboards became widely available. Unlike the Moog Taurus pedalboards, MIDI pedalboards do not produce tones by themselves, but control a MIDI-compatible electronic keyboard or MIDI sequencer. In jazz organ trios , a keyboardist using this type of pedalboard usually connects it to a MIDI-compatible electronic Hammond organ-style keyboard . On modern electronic synthesizers such as the Yamaha Electone , the pedals are not limited to traditional bass notes but may instead produce many different sounds, including high-register tones. While MIDI pedalboards are typically used for musical sounds, since they use MIDI, technically the footpedals could be used to trigger lights or other electronic elements of a show.
MIDI pedalboards offer a range of features. Some MIDI pedalboards contain velocity-sensitive triggers, which produce MIDI velocity information for musical dynamics. MIDI pedalboards such as the 13-note Roland PK-5 include a row of MIDI toe switches above the pedal keyboard, so the performer can select preset tones or MIDI channels or change the octave. Larger 25-note Roland pedalboards also include an expression pedal for controlling the volume or other parameters.
In the 2000s, controller designer Keith McMillen developed a 13-note velocity-sensitive pedalboard, the 12 Step foot controller , a MIDI controller with a USB output that can be connected to a MIDI -equipped synthesizer or sound module . McMillen's pedalboard differs from other pedalboards in that it senses a variety of types of velocity and pressure, which the user can program to cause different effects on the synthesizer patch. McMillen's pedalboard can be programmed so that pressing an individual pedal triggers chords (up to five simultaneous notes), which a one person band could use to provide accompaniment for live shows. [ 15 ]
The Roland PK-9 and the Hammond XPK-200 are 20-note pedalboards that sound from low C to a high G. The Nord PedalKeys is a 27-note pedalboard, going from a low C to a high D. As compared with a 25-note pedalboard, the PedalKeys adds a high C# and a high D.
Some MIDI pedalboards are designed for the church pipe organ market, which means that they use AGO specifications such as a 32-note range. Most pipe organ-style MIDI pedalboards are too unwieldy for transportation, so they are typically installed under the upper manuals. However, a German company makes a MIDI pedalboard with a hinge in the middle and wheels on the underside for easy transport. Since AGO-specification MIDI pedalboards are often priced in between US$ 1000 and US$3000, some amateur home organists make DIY MIDI pedalboards by retrofitting an old pedalboard with MIDI. Due to the popularity of theater organs and Hammond organs during the 1950s and 1960s, many organ parts are on the market—including pedalboards (often with less than 32 notes, such as 20 or 25 notes) that cost under US$300. After the pedalboard is cleaned up and glass reed switches are repaired or replaced, the pedal contacts are soldered into a keyboard matrix circuit -equipped MIDI encoder, which then connects to any MIDI device to produce the sound of an organ or other instrument. [ 16 ] | https://en.wikipedia.org/wiki/Pedal_keyboard |
The Pederson process is a process of refining aluminum that first separates iron by reducing it to metal , and reacting alumina with lime to produce calcium aluminate, which is then leached with sodium hydroxide . [ 1 ] It is more environmentally friendly than the more well-known Bayer process . [ 2 ] This is because instead of producing alumina slag, also known as red mud , it produces pig iron as a byproduct . [ 3 ] Red mud is considered both an economic and environmental challenge in the aluminum industry because it is considered a waste, with little benefit. It destroys the environment with its high pH , and is costly to maintain , even when in a landfill . [ 4 ] Iron, however, is used in the manufacture of steel , and has structural uses in civil engineering and chemical uses as a catalyst . [ 5 ]
The Pedersen Process was invented by Harald Pedersen in the 1920s and used in Norway for over 40 years before shutting down due to the Pedersen Process being less economically competitive than the Bayer Process. [ 6 ] However, it is believed a modern Pedersen process could be economically viable with "low-quality" bauxite , as even though "low-quality" bauxite has less alumina in the form of trihydrate gibbsite, it has more iron oxide which would be converted to pig iron in the smelting process instead of red mud. [ 2 ]
In most of today's smelting , aluminum ore, also known as bauxite , is first smelted into alumina through the Bayer Process . This step could be replaced by the Pedersen process -- either result in alumina. Unlike the smelting processes of iron and coal into steel or copper and tin into bronze , which require thermal energy , alumina must be smelted with electrical energy . This is done through the Hall–Héroult process , producing 99.5–99.8% pure aluminum. [ 2 ] [ 7 ] | https://en.wikipedia.org/wiki/Pedersen_process |
Pediatric endocrinology ( British : Paediatric) is a medical subspecialty dealing with disorders of the endocrine glands , such as variations of physical growth and sexual development in childhood, diabetes and many more. [ citation needed ]
By age, pediatric endocrinologists, depending upon the age range of the patients they treat, care for patients from infancy to late adolescence and young adulthood. [ citation needed ]
The most common disease of the specialty is type 1 diabetes , which usually accounts for at least 50% of a typical clinical practice. The next most common problem is growth disorders, especially those amenable to growth hormone treatment . Pediatric endocrinologists are usually the primary physicians involved in the medical care of infants and children with intersex disorders. The specialty also deals with hypoglycemia and other forms of hyperglycemia in childhood, variations of puberty , as well other adrenal , thyroid , and pituitary problems. Many pediatric endocrinologists have interests and expertise in bone metabolism, lipid metabolism, adolescent gynecology, or inborn errors of metabolism . [ citation needed ]
Most pediatric endocrinologists in North America and many from around the world can trace their professional genealogy to Lawson Wilkins , who pioneered the specialty in the pediatrics department of Johns Hopkins School of Medicine and the Harriet Lane Home in Baltimore in between the late 1940s and the mid-1960s. [ citation needed ]
In the United States and Canada, pediatric endocrinology is a subspecialty of the American Board of Pediatrics or the American Osteopathic Board of Pediatrics , with board certification following fellowship training. It is a relatively small and primarily cognitive specialty, with few procedures and an emphasis on diagnostic evaluation. [ 1 ]
Training for pediatric endocrinology consists of a 3-year fellowship following completion of a 3-year pediatrics residency. The fellowship, and the specialty, are heavily research-oriented and academically based, although less exclusively now than in past decades.
The principal North American professional association was originally named the Lawson Wilkins Pediatric Endocrine Society, [ 2 ] now renamed the Pediatric Endocrine Society. Other longstanding pediatric endocrine associations include the European Society for Paediatric Endocrinology, the British Society for Paediatric Endocrinology, the Australasian Paediatric Endocrine Group and the Japanese Society for Pediatric Endocrinology. Professional associations of the specialty continue to proliferate.
In 2021, the Pediatric Endocrine Society offered updated recommendations for use of growth-promoting hormone therapy and related medications in children. The Guidelines for Growth Hormone and Insulin-Like Growth Factor-1 Treatment in Children and Adolescents were updated from 2003 and reflect the continuing controversy over how to diagnose, categorize and treat growth failure in children. [ 3 ] The guideline was developed following the GRADE approach (Grading of Recommendations, Assessment, Development, and Evaluation). [ 4 ]
In 2021, the Pediatric Endocrine Society released a position statement in support of Gender Affirming Care (GAC). In it the society states, "Puberty suppression and/or gender-affirming hormone therapy is recommended within this evidence-based approach on a case-by-case basis as medically necessary and is potentially lifesaving." [ 5 ] This position is at odds with the position of England's National Health Service ( NHS ) which maintains that evidence for puberty blockers and hormone treatment for gender transition wholly is inadequate, [ 6 ] and has decided to stop routine prescribing of puberty blockers. [ 7 ] | https://en.wikipedia.org/wiki/Pediatric_endocrinology |
Pedocal is a subdivision of the zonal soil order . It is a class of soil which forms in semiarid and arid regions. It is rich in calcium carbonate and has low soil organic matter . With only a thin A horizon ( topsoil ), and intermittent precipitation calcite , other soluble minerals ordinarily removed by water may build up in the B horizon ( subsoil ) forming a cemented layer known as caliche . It is not used in the current United States system of soil classification but the term commonly shows up in college geology texts.
Baldwin, M.; C.E. Kellogg; J. Thorp (1938). "Soil Classification". Soils and Men: Yearbook of Agriculture 1938 . U.S. Government Printing Office, Washington, D.C. pp. 979– 1001.
Brevik, Eric C. (November 2002). "Soil Classification in Geology Textbooks" (PDF) . Journal of Geoscience Education . 50 (5): 539– 543. doi : 10.5408/1089-9995-50.5.539 . S2CID 116487861 . Retrieved 2006-04-06 .
Marshak, Stephen (2004). Essentials of Geology ((First Edition) ed.). W. W. Norton & Company, Inc. ISBN 0-393-92411-4 .
This soil science –related article is a stub . You can help Wikipedia by expanding it .
This geochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pedocal |
A pedometer , or step-counter , is a device, usually portable and electronic or electromechanical , that counts each step a person takes by detecting the motion of the person's hands or hips . Because the distance of each person's step varies, an informal calibration , performed by the user, is required if presentation of the distance covered in a unit of length (such as in kilometers or miles) is desired, though there are now pedometers that use electronics and software to determine how a person's step varies automatically. Distance traveled (by walking or any other means) can be measured directly by a GPS receiver .
Used originally by sports and physical fitness enthusiasts, pedometers are now becoming popular as an everyday exercise counter and motivator. Often worn on the belt and kept on all day, it can record how many steps the wearer has walked that day, and thus the kilometers or miles (distance = number of steps × step length). Some pedometers will also erroneously record movements other than walking, such as bending to tie one's shoes, or road bumps incurred while riding a vehicle, though the most advanced devices record fewer of these 'false steps'. Step counters can give encouragement to compete with oneself in getting fit and losing weight.
A total of 10,000 steps per day, equivalent to 8 kilometres (5.0 mi), is recommended by some to be the benchmark for an active lifestyle, although this point is debated among experts, and the target originated in a marketing campaign by a manufacturer of pedometers. [ 1 ] Thirty minutes of moderate walking are equivalent to 3,000-4,000 steps as determined by a pedometer. [ 2 ] Step counters are being integrated into an increasing number of portable consumer electronic devices such as music players, smartphones, mobile phones and watches (called activity trackers )
Pedometers can be a motivation tool for people wanting to increase their physical activity. Various websites exist to allow people to track their progress; however, many will also find entering their daily step count and a heart-beat count onto a calendar to be motivational as well.
Clinical studies have shown Pedometers to increase physical activity and reduce blood pressure levels and Body Mass Index . A study published in the Journal of The American Medical Association Nov. 2007 [ 3 ] concluded, “The results suggest that the use of a pedometer is associated with significant increases in physical activity and significant decreases in body mass index and blood pressure.”
A daily target of 10,000 steps was first proposed. [ 4 ] The target has been recommended by the US Surgeon General and by the UK Department of Health . [ 5 ] [ 6 ] The main criticisms of setting a universal target are that it is not achievable for older persons with mobility problems or people with chronic diseases, but on the other hand, the target is probably too low for children. [ 5 ]
One criticism of the pedometer is that it does not record intensity, but this can be done by making step goals time limited (for example, 1000 steps in 10 minutes counts as moderate exercise). [ 7 ]
Leonardo da Vinci (1452–1519) envisioned a mechanical pedometer as a device with military applications. [ 8 ] [ 9 ] The Germanic National Museum in Nuremberg has a pedometer in its collection from around 1590 (see photo). In 1685 Gottfried Leibniz wrote of his time in France, "...several years ago [1672–1674] I saw for the first time an instrument which, when carried, automatically records the number of steps taken by a pedestrian." [ 10 ] In 1780 Abraham-Louis Perrelet of Switzerland created a pedometer, measuring the steps and distance while walking; it was based on a 1770 mechanism of his to power a self-winding watch. [ 11 ] A mechanical pedometer obtained from France was introduced in the US by Thomas Jefferson . [ 12 ] It is not known if he modified the design; although this pedometer is widely attributed to Jefferson, [ 13 ] [ 14 ] proof is difficult to obtain as he did not apply for patents on any of his inventions. [ 15 ]
In 1963, in the lead up to the 1964 Tokyo Olympics , Dr Iwao Ohya, head of one of Tokyo's biggest clinics, told Tokyo engineer Juri Kato of clockmaker Yamasa Tokei Keiki ( Tokei means clocks and Keiki meters) how concerned Ohya was at the low levels of physical activity in 1960s Japan ; the solution, said Ohya, was for everyone to walk 10,000 steps a day. [ 16 ] In 1965, after two years of tinkering, Juri Kato produced the Manpo-kei — the ten-thousand step-meter . [ 16 ] A pedometer called a manpo-kei (meaning "10,000 steps meter" Japanese : 万歩計 ) was marketed in 1965 by Y. Hatano, who claimed that 10,000 steps a day was ideal. [ 17 ] [ failed verification – see discussion ]
The effect in 1965 of the release by Yamasa of the Manpo-kei pedometer in Japan was significant. [ 16 ] [ 17 ] Soon after, the Japan 10,000-step Walking Association sprang up, which shortly had chapters in all 47 prefectures, organising regular walks that could be measured with the Yamasa device. [ 16 ]
On 26 February 1980, Juri Kato's son Yasuji Kato filed a pedometer patent with the USPTO , currently assigned to Yamasa Tokei Meter Co Ltd. [ 18 ]
In 2015, the Japanese Ministry of Health, Labour and Welfare also recommended 10,000 steps per day. [ 19 ] However, this recommendation is not based on solid evidence. [ 20 ]
The technology for a pedometer includes a mechanical sensor and software that counts steps. Early forms used a mechanical switch to detect steps together with a simple counter. If one shakes these devices, one hears a lead ball sliding back and forth, or a pendulum striking stops as it swings. Today advanced step counters rely on MEMS inertial sensors and sophisticated software to detect steps. These MEMS sensors have either 1-, 2- or 3-axis detection of acceleration. The use of MEMS inertial sensors permits more accurate detection of steps and fewer false positives. The software technology used to interpret the output of the inertial sensor and "make sense of accurate steps" varies widely. The problem is compounded by the fact that in modern day-to-day life, such step-counters are expected to count accurately on locations where users frequently carry their devices (attached to the belt, shirt/pants pocket, hand bag, backpack). In recent years more advanced approaches to measure steps have been made with the use of computer vision . [ 21 ]
The accuracy of step counters varies widely between devices. Typically, step counters are reasonably accurate at a walking pace on a flat surface if the device is placed in its optimal position (usually vertically on the belt clip).
Although traditional step counters are affected dramatically when placed at different angles and locations, recent advances have made them more robust to those non-ideal placements. Still, most step counters falsely count steps when a user is driving a car or makes other habitual motions that the device encounters throughout the day. This error accumulates for users with moderate commutes to work. [ 22 ] Accuracy of distance measurement also depends on the user entered step-length.
The best pedometers are accurate to within ± 5% error. [ 23 ] [ 24 ]
Apple and Nike, Inc. introduced the Nike+iPod Sport Kit , which uses a motion sensor that fits into a Nike shoe or in a pocket worn on the laces of other brands of shoes. The sensor communicates with an iPhone (3GS or higher), iPod touch (2nd generation or higher), iPod nano (4th generation or higher), or dedicated adapter to transmit workout information such as elapsed time, distance traveled, and calories burned.
The iPhone 5s was the first iPhone to contain an Apple Motion Coprocessor which was denoted the M7 chip paired with the first 64-bit ARM-based Apple processor, the Apple A7 SoC (System on a Chip). The addition of the separate always on coprocessor allows the main CPU to snooze while it tracks the motion of the phone, through the use of an inertial measurement unit (IMU) consisting of an accelerometer , MEMS gyroscope and digital compass . This means that it will know when you're jogging or when you're in the car, and can take that information and store it without needing to drain the battery by having the main CPU run. It can retrofit the data to apps that you download at a later date, meaning any M7-enabled app that uses the new CoreMotion API will be able to give you information on recent training.
The iPhone 6 and 6 Plus contains the next generation of the Apple Motion Coprocessors with the M8 motion coprocessor, this chip was paired with the vastly improved Apple A8 SoC processor and gained the added sensor input of a Bosch Sensortech Barometer allowing the M8 to sense changes in elevation by the change in barometric pressure .
The iPhone 6s and 6s Plus improved the Apple Motion Coprocessors by integrating it into the die of the new Apple A9 SoC processor. This saves space allowing for the reduction of the logic board size as well as reduced power usage within the phone. This chip is also at the heart of the first-generation iPhone SE . A variant of the Apple A9, the Apple A9X also incorporates the M9 processor on-die and drives the Apple iPad Pro .
The Apple Watch extended step-counting capability to Apple's first wearable device using the accelerometer and gyroscope integrated in the Apple S1 SIP ( System in package ). Apple Watch works in parallel with a connected iPhone to improve accuracy of the user's step count. [ 25 ]
The Fitbit is an always-on electronic pedometer, that in addition to counting steps also displays distance traveled, altitude climbed (via a number of flights of steps count), calories burned, current intensity, and time of day. Worn in an armband at night, it also purports to measure the length and quality of a user's sleep. Inbuilt is a daily target, of 10,000 steps and 10 flights of stairs. Connected by USB with a computer, the user's data is automatically uploaded and displayed via a web-based profile page, that keeps track of historical data, to which can be added food consumption data. Based on activity users are awarded badges for daily step and climbing targets, as well as 'lifetime' awards for same. In the US and UK users can also download an iOS or Android app for recording and display of data. [ citation needed ] Most Fitbit devices estimate distance traveled based on steps counted, the intensity of the steps and the user's profile data (specifically gender and height). Individuals can improve the accuracy of their stride length settings by measuring and calibrating their average stride length. [ citation needed ] Some higher-end Fitbit models include additional features such as heart rate monitoring and GPS tracking .
Since most smartphones, iPod Touches and some MP3 players are enhanced with an integrated accelerometer it is possible to introduce pedometer functionality to these devices. This option was successfully realized by a number of smartphone application developers, [ 26 ] [ 27 ] enabling any fitness-savvy smartphone owner to track the number of steps taken as well as distance travelled and calories used.
This is the first integrated phone with an always-on pedometer which counts steps like a traditional pedometer. The sensor is made by ADI. This handset was introduced in Japan in 2004 and has sold over 3 million units. [ 28 ]
The Nokia 5500 Sports Phone uses an embedded 3 axis MEMS inertial sensor to detect the steps a user takes. The pedometer application tracks steps taken, time elapsed and distance traveled. However the application cannot run continuously as it drains the phone's battery and is therefore of limited use.
Nokia Sports Tracker features pedometer for Nokia Symbian phones with an Accelerometer . Accelerometers are included in phones to save correct orientation on photos and to improve the GPS positioning feature.
Nokia Step Counter is a free application available at Nokia Beta Labs which works on a wide range of N-Series Nokia phones. The pedometer application tracks steps taken, time elapsed and distance traveled. This application can be left running all day as it is not a huge drain on the battery.
The Sony Ericsson W710 and W580 Walkman phones use embedded 2 axis MEMS inertial sensors to detect the steps a user takes. The W710 is a clamshell phone and displays the user's steps on the external display. The W710 must be closed in order for it to count steps. When the step counter is activated, it counts detected steps during the day, and at midnight it stores the counter in a day-by-day history and resets it to zero.
On November 1, 2008, Nintendo released the Nintendo DS title Personal Trainer: Walking ( Japanese : 歩いてわかる 生活リズム DS , Aruite Wakaru Seikatsu Rhythm DS ) , which includes two pedometers. They connect to the game card via infrared signals.
On September 12, 2009, Nintendo released Pokémon HeartGold and SoulSilver in Japan. Each game comes bundled with a device called a Pokéwalker , which functions as a pedometer and allows players to transfer one Pokémon from their game to the Pokéwalker via infrared signals. Unlike the Personal Trainer: Walking pedometers, the Pokéwalker features a small LCD screen and multiple buttons. Walking with the Pokéwalker earns experience points for the Pokémon . [ 29 ]
The Nintendo 3DS, released March 27, 2011, features an internal pedometer that counts and records daily step counts while in sleep mode. Every hundred steps earns a Play Coin, which can be spent on a variety of extras and bonuses. [ 30 ] This pedometer is easily fooled, however, and 'steps' can be created by simply lifting the device up and down in the hand with a motion similar to walking. [ 31 ] [ unreliable source? ]
On October 31, 2013, Nintendo released Wii Fit U , which was able to interface with the Fit Meter, which was a pedometer with similar hardware to the Pokéwalker, but instead themed around Wii Fit U and with the ability to store and display the user's Mii . It could be checked into the game via the infrared transceiver on top of the Wii U Gamepad , and could track the altitude of the player while walking.
Released May 2010, by Philips . This MP3 capable pedometer measures aerobic intensity and matches songs on the playlist to keep the user engaged and motivated. [ 32 ]
Tractivity is a group of health-related services that include a sensor that is worn on a shoe. The Tractivity sensor logs the distance a person walks or runs, the calories burned and the time the person was active, which they can then view on a private web page. Tractivity's online web application provides a graphical experience and motivational resource to encourage people to lead healthier lifestyles. Tractivity accounts for the variation in a walker's or runner's stride length that occurs as pace changes. The sensors wirelessly transfer activity data to a secure server for viewing on an individual's computer. [ 33 ]
Android integrates a step counter with version 4.4 (KitKat). [ 34 ]
A device already supporting this sensor is the Nexus 5 . Another smartphone is the Samsung Galaxy S5 , which features a built-in pedometer that uses the S Health (later renamed to Samsung Health) software to display daily step counts, as well as other fitness information. Most Samsung devices now include this software bundled as standard. | https://en.wikipedia.org/wiki/Pedometer |
The pedosphere (from Ancient Greek πέδον ( pédon ) ' ground, earth ' and σφαῖρα ( sphaîra ) ' sphere ' ) is the outermost layer of the Earth that is composed of soil and subject to soil formation processes. It exists at the interface of the lithosphere , atmosphere , hydrosphere and biosphere . [ 1 ] The pedosphere is the skin of the Earth and only develops when there is a dynamic interaction between the atmosphere (air in and above the soil), biosphere (living organisms), lithosphere (unconsolidated regolith and consolidated bedrock ) and the hydrosphere (water in, on and below the soil). The pedosphere is the foundation of terrestrial life on Earth.
The pedosphere acts as the mediator of chemical and biogeochemical flux into and out of these respective systems and is made up of gaseous, mineralic, fluid and biologic components. The pedosphere lies within the Critical Zone, a broader interface that includes vegetation, pedosphere, aquifer systems, regolith and finally ends at some depth in the bedrock where the biosphere and hydrosphere cease to make significant changes to the chemistry at depth. As part of the larger global system, any particular environment in which soil forms is influenced solely by its geographic position on the globe as climatic, geologic, biologic and anthropogenic changes occur with changes in longitude and latitude.
The pedosphere lies below the vegetative cover of the biosphere and above the hydrosphere and lithosphere. The soil forming process (pedogenesis) can begin without the aid of biology but is significantly quickened in the presence of biologic reactions, where it forms a soil carbon sponge . [ 2 ] Soil formation begins with the chemical and/or physical breakdown of minerals to form the initial material that overlies the bedrock substrate. Biology quickens this by secreting acidic compounds that help break rock apart. Particular biologic pioneers are lichen , mosses and seed bearing plants, [ 3 ] but many other inorganic reactions take place that diversify the chemical makeup of the early soil layer. Once weathering and decomposition products accumulate, a coherent soil body allows the migration of fluids both vertically and laterally through the soil profile , causing ion exchange between solid, fluid and gaseous phases. As time progresses, the bulk geochemistry of the soil layer will deviate away from the initial composition of the bedrock and will evolve to a chemistry that reflects the type of reactions that take place in the soil. [ 4 ]
The primary conditions for soil development are controlled by the chemical composition of the rock on which the soil will be. Rock types that form the base of the soil profile are often either sedimentary (carbonate or siliceous), igneous or metaigneous ( metamorphosed igneous rocks) or volcanic and metavolcanic rocks. The rock type and the processes that lead to its exposure at the surface are controlled by the regional geologic setting of the specific area under study, which revolve around the underlying theory of plate tectonics , subsequent deformation , uplift , subsidence and deposition .
Metaigneous and metavolcanic rocks form the largest component of cratons and are high in silica . Igneous and volcanic rocks are also high in silica, but with non-metamorphosed rock, weathering becomes faster and the mobilization of ions is more widespread. Rocks high in silica produce silicic acid as a weathering product. There are few rock types that lead to localized enrichment of some of the biologically limiting elements like phosphorus (P) and nitrogen (N). Phosphatic shale (< 15% P 2 O 5 ) and phosphorite (> 15% P 2 O 5 ) form in anoxic deep water basins that preserve organic material. [ 5 ] Greenstone (metabasalt), phyllite , and schist release up to 30–50% of the nitrogen pool. [ 6 ] Thick successions of carbonate rocks are often deposited on craton margins during sea level rise. The widespread dissolution of carbonate and evaporites leads to elevated levels of Mg 2+ , HCO − 3 , Sr 2+ , Na + , Cl − and SO 2− 4 ions in aqueous solution. [ 7 ]
The process of soil formation is dominated by chemical weathering of silicate minerals, aided by acidic products of pioneering plants and organisms as well as carbonic acid inputs from the atmosphere. Carbonic acid is produced in the atmosphere and soil layers through the carbonation reaction. [ 4 ]
This is the dominant form of chemical weathering and aides in the breakdown of carbonate minerals (such as calcite and dolomite ) and silicate minerals (such as feldspar ). The breakdown of the Na-feldspar, albite , by carbonic acid to form kaolinite clay is as follows: [ 4 ]
Evidence of this reaction in the field would be elevated levels of bicarbonate ( HCO − 3 ), sodium and silica ions in the water runoff.
The breakdown of carbonate minerals: [ 4 ] [ 7 ]
The further dissolution of carbonic acid (H 2 CO 3 ) and bicarbonate ( HCO − 3 ) produces CO 2 gas. Oxidization is also a major contributor to the breakdown of many silicate minerals and formation of secondary minerals ( diagenesis ) in the early soil profile. Oxidation of olivine (FeMgSiO 4 ) releases Fe, Mg and Si ions. [ 8 ] The Mg is soluble in water and is carried in the runoff , but the Fe often reacts with oxygen to precipitate Fe 2 O 3 ( hematite ), the oxidized state of iron oxide. Sulfur , a byproduct of decaying organic material, will also react with iron to form pyrite (FeS 2 ) in reducing environments. Pyrite dissolution leads to low pH levels due to elevated H + ions and further precipitation of Fe 2 O 3 [ 4 ] ultimately changing the redox conditions of the environment.
Inputs from the biosphere may begin with lichen and other microorganisms that secrete oxalic acid . These microorganisms, associated with the lichen community or independently inhabiting rocks, include blue-green algae , green algae , various fungi , and numerous bacteria. [ 9 ] Lichen has long been viewed as the pioneers of soil development as the following 1997 Isozaki statement suggests:
The initial conversion of rock into soil is carried on by the pioneer lichens and their successors, the mosses, in which the hair-like rhizoids assume the role of roots in breaking down the surface into fine dust. [ 10 ]
However, lichens are not necessarily the only pioneering organisms nor the earliest form of soil formation as it has been documented that seed-bearing plants may occupy an area and colonize quicker than lichen. Also, eolian sedimentation (wind generated) can produce high rates of sediment accumulation. Nonetheless, lichen can certainly withstand harsher conditions than most vascular plants, and although they have slower colonization rates, they do form the dominant group in alpine regions .
Organic acids released from plant roots include acetic acid and citric acid . During the decay of organic matter phenolic acids are released from plant matter and humic acid and fulvic acid are released by soil microbes. These organic acids speed up chemical weathering by combining with some of the weathering products in a process known as chelation . In the soil profile, these organic acids are often concentrated at the top of the profile, while carbonic acid plays a larger role towards the bottom of the profile or below in the aquifer. [ 4 ]
As the soil column develops further into thicker accumulations, larger animals come to inhabit the soil and continue to alter the chemical evolution of their respective niche . Earthworms aerate the soil and convert large amounts of organic matter into rich humus , improving soil fertility . Small burrowing mammals store food, grow young and may hibernate in the pedosphere altering the course of soil evolution. Large mammalian herbivores above ground transport nutrients in form of nitrogen-rich waste and phosphorus-rich antlers, while predators leave phosphorus-rich piles of bones on the soil surface, leading to localized enrichment of the soil.
Nutrient cycling in lakes and freshwater wetlands depends heavily on redox conditions. [ 4 ] Under a few millimeters of water, heterotrophic bacteria metabolize and consume oxygen. They therefore deplete the soil of oxygen and create the need for anaerobic respiration . Some anaerobic microbial processes include denitrification , sulfate reduction and methanogenesis and are responsible for the release of N 2 (nitrogen), H 2 S ( hydrogen sulfide ) and CH 4 ( methane ). Other anaerobic microbial processes are linked to changes in the oxidation state of iron and manganese. As a result of anaerobic decomposition, the soil stores large amounts of organic carbon because the soil carbon sponge stays intact. [ 4 ]
The reduction potential describes which way chemical reactions will proceed in oxygen deficient soils and controls the nutrient cycling in flooded systems. Reduction potential is used to express the likelihood of an environment to receive electrons [ 4 ] and therefore become reduced. For example, if a system already has plenty of electrons (anoxic, organic-rich shale ) it is reduced. In a system, it will likely donate electrons to a part that has a low concentration of electrons, or an oxidized environment, to equilibrate to the chemical gradient. An oxidized environment has high redox potential, whereas a reduced environment has a low redox potential.
The redox potential is controlled by the oxidation state of the chemical species, pH and the amount of O 2 there is in the system. The oxidizing environment accepts electrons because of the presence of O 2 , which acts as an electron acceptor: [ 4 ]
This equation will tend to move to the right in acidic conditions. Higher redox potentials are found at lower pH levels. Bacteria, heterotrophic organisms, consume oxygen while decomposing organic material. This depletes the soils of oxygen, thus decreasing the redox potential. At high redox potential, the oxidized form of iron, ferric iron (Fe 3+ ), will be deposited commonly as hematite . In low redox conditions, decomposition rates decrease and the deposition of ferrous iron (Fe 2+ ) increase.
By using analytical geochemical tools such as X-ray fluorescence or inductively coupled mass spectrometry the two forms of Fe (Fe 2+ and Fe 3+ ) can be measured in ancient rocks therefore determining the redox potential for ancient soils. Such a study was done on Permian through Triassic rocks (300–200 million years old) in Japan and British Columbia. The geologists found hematite throughout the early and middle Permian but began to find the reduced form of iron in pyrite within the ancient soils near the end of the Permian and into the Triassic. These results suggest that conditions became less oxygen rich, even anoxic, during the late Permian, which eventually led to the greatest extinction in Earth’s history, the P-T extinction . [ 11 ]
Decomposition in anoxic or reduced soils is also carried out by sulfur-reducing bacteria which, instead of O 2 use SO 2− 4 as an electron acceptor and produce hydrogen sulfide (H 2 S) and carbon dioxide in the process: [ 4 ]
The H 2 S gas percolates upwards and reacts with Fe 2+ and precipitates pyrite, acting as a trap for the toxic H 2 S gas. However, H 2 S is still a large fraction of emissions from wetland soils. [ 12 ] In most freshwater wetlands there is little sulfate ( SO 2− 4 ) so methanogenesis becomes the dominant form of decomposition by methanogenic bacteria only when sulfate is depleted. Acetate , a compound that is a byproduct of fermenting cellulose is split by methanogenic bacteria to produce methane (CH 4 ) and carbon dioxide (CO 2 ), which are released to the atmosphere. Methane is also released during the reduction of CO 2 by the same bacteria. [ 4 ]
In the pedosphere it is safe to assume that gases are in equilibrium with the atmosphere. [ 7 ] Because plant roots and soil microbes release CO 2 to the soil, the concentration of bicarbonate ( HCO − 3 ) in soil waters is much greater than that in equilibrium with the atmosphere, [ 13 ] the high concentration of CO 2 and the occurrence of metals in soil solutions results in lower pH levels in the soil. Gases that escape from the pedosphere to the atmosphere include the gaseous byproducts of carbonate dissolution, decomposition, redox reactions and microbial photosynthesis . The main inputs from the atmosphere are aeolian sedimentation, rainfall and gas diffusion. Eolian sedimentation includes anything that can be entrained by wind or that stays suspended in air and includes a wide variety of aerosol particles, biological particles like pollen, and dust particles. Nitrogen is the most abundant constituent in rain (after water), as water vapor utilizes aerosol particles to nucleate rain droplets. [ 4 ]
Soil is well developed in the forest as suggested by the thick humus layers, rich diversity of large trees and animals that live there. Forest soils can form a thick soil carbon sponge. In forests, precipitation exceeds evapotranspiration which results in an excess of water that percolates downward through the soil layers. Slow rates of decomposition leads to large amounts of fulvic acid , greatly enhancing chemical weathering. The downward percolation , in conjunction with chemical weathering leaches Mg, Fe, and aluminium (Al) from the soil and transports them downward, a process known as podzolization . This process leads to marked contrasts in the appearance and chemistry of the soil layers. [ 4 ]
Tropical forests receive more insolation and rainfall over longer growing seasons than any other environment on earth. With these elevated temperatures, insolation and rainfall, biomass is extremely productive leading to the production of as much as 800 grams of carbon per square meter per year (8 tons of C/hectare/year). [ 4 ] Higher temperatures and larger amounts of water contribute to higher rates of chemical weathering. Increased rates of decomposition cause smaller amounts of fulvic acid to percolate and leach metals from the zone of active weathering. Thus, in stark contrast to soil in temperate forests, tropical forests have little to no podzolization and therefore do not have marked visual and chemical contrasts with the soil layers. Instead, the mobile metals Mg, Fe and Al are precipitated as oxide minerals giving the soil a rusty red color. [ 4 ]
Precipitation in grasslands is equal to or less than evapotranspiration and causes soil development to operate in relative drought. [ 4 ] Leaching and migration of weathering products is therefore decreased. Large amounts of evaporation cause a buildup of calcium (Ca), and other large cations flocculate clay minerals and fulvic acids in the upper soil profile. Low amounts of precipitation and high levels of evapotranspiration limit the downward percolation of water and organic acids, reducing chemical weathering and soil development. The depth to the maximum concentration of clay increases in areas of increased precipitation and leaching. When leaching is decreased, the calcium precipitates as calcite (CaCO 3 ) in the lower soil levels, a layer known as caliche .
Deserts behave similarly to grasslands but operate in constant drought as precipitation is less than evapotranspiration. Chemical weathering proceeds more slowly than in grasslands and beneath the caliche layer may be a layer of gypsum and halite . [ 4 ] To study soils in deserts, pedologists have used the concept of chronosequences to relate the timing and development of the soil layers. It has been shown that phosphorus leaches very quickly from the system, and soil P-levels decrease with age. [ 14 ] Furthermore, carbon buildup in the soils is decreased due to slower decomposition rates. As a result, the rates of carbon circulation in the biogeochemical cycle is decreased. [ citation needed ] | https://en.wikipedia.org/wiki/Pedosphere |
Peek Inc. was a technology company founded in 2007. Headquartered in New York City from 2008 to 2012, the company offered a series of mobile handheld devices that provided access to email and various social networks.
Peek was founded in 2007 by three of the first four employees at Virgin Mobile USA : [ 1 ] Rob Gray, Virgin's first head of product marketing, CEO Dr. Amol Sarva , and John Tantum, Virgin's first employee and first President. [ 2 ] The company had offices in New York City, New Delhi, India, Nanjing , China, and staff in Arizona , California, and Toronto .
Peek's product is a family of applications for mobile devices that major device producers license and pre-install onto systems. These applications include push email, Instant Message and chat, social networking apps, synchronization and backup, and other mobile features. These apps are tailored to the lower-cost and simpler hardware that dominates the global phone market and rely on the Peek cloud architecture to offload computing and storage from the phone to the cloud.
In September 2008, the original Peek email device was launched in the United States and was sold at the price of USD$99.00. On September 12, 2008, Peek received its first review in a major outlet when David Pogue called it "sweet", "simple" and "elegant", and predicted that Peek's model would win "quiet, gradual popular acceptance by normal people". [ 3 ]
In April 2009, Peek launched their second device, the Peek Pronto, which supported Push email ('instant' delivery), Microsoft Exchange , increased support for email attachments (PDFs, DOC, and pictures), and unlimited texting support.
TwitterPeek is a mobile device that allows users to send and receive tweets using Twitter . It is the first Twitter-only mobile device. It went on sale on November 3, 2009. Its price was set at USD$100.00 and came with six months of service. The service costs USD$8.00 monthly, but users could also pay USD$200.00 upfront for lifetime service. [ 4 ]
In 2010, Peek refreshed its lineup with Peek 9, adding Facebook, Twitter, and other social and news features.
In 2011, the first 3rd party handsets were launched by fast-growing producers such as MicroMax in India. The Peek software brings smartphone features to these low-cost handhelds.
In 2012, Peek announced that it was going to end support for all Peek devices and instead shift its attention to the cloud. [ 5 ]
The 2008 Peek device was designed by Peek in partnership with IDEO and BYD, and its architecture is based on the Texas Instruments Locosto chipset with an ARM core. It uses a customized, lightweight operating system nicknamed "Peekux" which is based on Nucleus RTOS by Mentor Graphics . [ 6 ]
The Peek device's client firmware is C/C++ code written for the TI environment. Flavors of the Peek application for alternative operating environments from other RTOSes to BREW, to Windows, and to Android have all been spotted. [ 7 ]
The core of Peek's real time mobile messaging platform is a cloud application. The environment is a conventional web application LAMP stack and relies in part on Amazon Web Services. [ 8 ]
This cloud application has been deployed on many partner company devices since 2010. [ 9 ]
When Peek's first device launched, Time selected Peek as one of the 50 Best Inventions of the Year 2008. [ 10 ] It was voted on Time.com as the #1 entry in the Gadget of the Year review.
Elizabeth Woyke of Forbes wrote, "At a time when the economy is melting and one-time bankers are on the street, [Peek] is betting customers will embrace the no-fuss simplicity—not to mention the modest price—of the Peek." [ 11 ]
Tony Long, a journalist of Gadget Lab from Wired.com reviewed Peek as a device that "delivers peak email performance", and that using the device was "a breeze... even without operating instructions". He recommended the Peek device to those who would like access to their "e-mail from time to time, or if [they] believe that simplicity in all things is the key to life". [ 12 ]
Wired magazine's December 2008 issue named Peek their #1 Gadget in their "Gear of the Year" review: "Not every gadget needs a carnival of features. Take the Peek, which tackles just a single task: mobile email. No phone, no browser, no camera—and no apologies. It won't satisfy convergence-rabid smartphone fetishists, but for the rest of the world (i.e., the majority of it), this one-trick pony is a godsend. In terms of looks, its slim profile stands up to the big boys. But the real treat is the interface." [ 13 ]
After the Peek Pronto launch, International Design Magazine featured Peek Pronto on the cover of its 2009—and final—Annual Design Review. [ 14 ]
TwitterPeek, on the other hand, met broad skepticism in the press. [ 15 ] [ 16 ] [ 17 ] CNN.com 2009 Year in Review listed it as one of the top 10 biggest technology failures of 2009. [ 15 ] Gizmodo went as far as to name TwitterPeek as one of the "50 Worst Gadgets of the Decade." [ 17 ]
In 2010, Peek 9's enhanced features were met by Engadget's reviewers as "dancing with a full list of features" and "Peek 9 is nine times faster than Pronto, adds PeekMaps, weather, Twitter, and Facebook". [ 18 ] TechCrunch's gadget reviewers said Peek 9 "brings a whole new level of cool to the not-a-smartphone device. It seems nearly everything is updated from the mail service to the hardware. It’s a mighty big update for Peek, but somehow all this goodness rings up for less than the previous generation—even the service plan is cheaper now." [ 19 ]
On October 14, 2010, older Peek devices were disconnected from the network [ 20 ] and Peek offered all its users a free, new replacement Peek 9 device to continue their service.
In 2011, Peek expanded their push email technology globally and is now part of their "Genius Cloud" platform for low-cost feature phones.
On January 24, 2012, GSMA nominated Peek for the best cloud technology.
On January 30, 2012, Peek users reported their devices abruptly stopped working, despite having paid USD$200 for "lifelong service".
On February 1, 2012, Peek announced that it had terminated service for all its dedicated hardware in a move to cloud-only service. Peek's CEO, Amol Sarva stated that the abandoned products were "seriously old" and have reached their end of life, with only a "handful of users" left in the US. "Unfortunately, we cannot maintain the network forever for a few users, so that end time has come. The networks are changing standards, protocols etc., and the old units are now end-of-life. We have lots going with rapid adoption of our software by phone brands around the world, so Peek is flat out building for a number of platforms that our OEM customers are deploying like Android and Mediatek. We are not offering a Peek-made device to replace these old ones."
"Peek isn't in the hardware business anymore. Since last year, the company has been selling "the genius cloud", a series of services designed to make inexpensive feature phones smarter. Sarva notes that his product has just been nominated for the GSMA's Best Technology award which will be handed out at MWC later this month. He says that these services are the logical continuation of what Peek has been about since day one—"building smartphone features on ultra low-cost platforms"—and that they're making huge inroads with the countless Chinese manufacturers who sell unbranded phones in emerging markets, many of whom are "feeding off Nokia's carcass." [ 21 ] | https://en.wikipedia.org/wiki/Peek_(mobile_Internet_device) |
The peeler centrifuge is a device that performs by rotating filtration basket in an axis. A centrifuge follows on the principle of centrifugal force to separate solids from liquids by density difference. High rotation speed provides high centrifugal force that allows the suspended solid in feed to settle on the inner surface of basket. There are three kinds of centrifuge, horizontal , vertical peeler centrifuge and siphon peeler centrifuge . These classes of instrument apply to various areas such as fertilisers , pharmaceutical , plastics and food including artificial sweetener and modified starch .
[ 4 ] Centrifugal Acceleration
Solid body rotation
Fluid Viscosity and Inertia
Cake dryness
Total solid recovery
Critical Speed
Mitsubishi Peeler Centrifuge
[ 11 ] Over many advantages, the manual scrapping, dismantling of deposited solid bed is limitation of this process. | https://en.wikipedia.org/wiki/Peeler_centrifuge |
Peer-to-Patent Australia [ 1 ] was an initiative designed to improve the patent examination process and the quality of issued patents by connecting the review of pending patents to an open network of experts online.
Peer-to-Patent Australia is focused on helping patent offices perform high-quality examinations of pending patent applications by enlisting the public to help find and explain prior art . The objective of Peer-to-Patent Australia is to improve the patent examination process and the quality of issued patents by inviting members of the public to identify and nominate prior art relevant to the assessment of novelty and inventiveness of participating patent applications. [ citation needed ] This initiative allows the patent office to harness the expertise of qualified people within the community when assessing patent applications by inviting members of the public to identify and nominate prior art relevant to the assessment of novelty and inventiveness of participating patent applications. In doing so, it connects with the broader initiative to use Web 2.0 technologies to enhance and invigorate government administration through citizen engagement.
To justify the award of a patent in Australia, the invention claimed must be novel and involve an inventive step when compared with the prior art base. The prior art base is the state of the art, or the technology in existence, immediately before the priority date, which is usually the date that the patent application is filed. In other words, to justify the grant of a patent, an invention must not have been seen before and must be inventive in the eyes of someone skilled in the relevant art when compared with the existing technology.
Prior art can include earlier patents, academic papers, magazine articles, web pages, and even physical examples. Patent examiners compare a claimed invention with the prior art to determine if a given invention is both novel and not obvious to a person of ordinary skill and creativity of the invention.
Currently in Australia, patent examiners have the sole responsibility for searching for prior art. They have a time budget of a few hours. Peer-to-Patent attempts to improve the patent process by markedly expanding the prior art search. The reasoning behind the proposal is that if prior art exists for an invention, particularly non-patent prior art, someone in the world knows about it. This knowledgeable person may be competitors in the same field, students or professors, or owners of an earlier embodiment of the invention. Peer-to-Patent Australia encourages such people to submit examples of prior art and creates communities of people worldwide who are interested in discovering prior art.
Peer-to-Patent uses social software features to facilitate discussion amongst groups of volunteer experts. Users can upload prior art references, participate in discussion forums, rate other user submissions, add research references, invite others, and more. This helps the examiners focus their attention on the submission(s) of prior art that have the highest relevance to an application.
If successful, the project will promote the public interest by improving the quality of issued patents. The public only benefits when monopoly rights are granted for inventions that truly represent a novel and inventive advance over the existing state of the art. The benefit to innovators is that improving the quality of issued patents leads to clearer patent landscapes and reduces the uncertainty surrounding freedom to operate.
The benefit to participating applicants is that their applications will undergo a more rigorous examination against the strictures of novelty and inventiveness and are likely to be more robust as a consequence.
The more robust a patent, the more valuable it is and the less likely it is to be challenged, which is a benefit that represents significant cost savings over time to consumers, patent holders and the public at large. More robust patents are less likely to be litigated or disputed in licensing discussions. As a consequence, the marketplace for such inventions will be more efficient, with time and money not being wasted on ill-conceived litigation. In addition, the identification and elimination of weak claims early in the examination process ultimately saves the applicant money by avoiding the expensive process of pursuing or enforcing non-meritorious patent claims. Finally, it is anticipated that open peer review will encourage applicants to file better constructed and clearer applications and lower the incentive for those who might seek to file low quality applications.
The review process in no way abrogates the responsibility of the patent examiner to assess a patent application. Prior art submitted by Peer-to-Patent Australia is solely designed to assist a patent examiner. The patent examiner remains the arbiter of whether a patent is to be granted.
Peer-to-Patent has generated considerable support internationally. The recent pilot projects run in the United States had the backing of users of the patent system such as IBM, Microsoft, Hewlett-Packard, General Electric, Intel and Yahoo!, who all recognised potential of the project and put forward applications to be peer reviewed.
So far, Peer-to-Patent Australia has the backing of IBM, Hewlett-Packard, General Electric, Aristocrat Technologies Australia Pty Ltd and Residex Pty Ltd.
Peer-to-Patent Australia will initially run as a six-month pilot. The first pilot project is set to launch on 9 November 2009.
Up to 40 business method patent , computer software and related patent applications which are open for public inspection will each be posted on the Peer-to-Patent Australia website for a 90-day period. During that time, members of community will be invited to review those patent applications, submit prior art references and comment on the relevance of any prior art that has been put forward.
Each patent application included in the project will be open to peer review for a three-month period. During that time, members of the public can identify prior art references and comment on the relevance of any prior art that has been put forward. At the end of the review period, Peer-to-Patent Australia will forward the top 10 prior art submissions, as selected by the community of reviewers, to IP Australia for consideration in the examination process.
Only applications that have been laid open for public inspection and for which an examination request has been made by the applicant will be included in the pilot. All attempts will be made to include patent applications from a broad range of patent applicants. No more than 10 patent applications from a single patent applicant, inventor, assignee or their affiliates shall be selected for inclusion in the pilot.
The project uses a consent based model. Patent applicants will be asked to consent to having their applications included in the pilot. Patent applicants will be asked to consent to having their applications included in the pilot. A patent application will not be included in the pilot without the express written consent of the applicant or applicants.
The objective of the pilot is to test whether an open community of reviewers can effectively locate prior art that might not otherwise be located by patent examiners during a typical examination. This is an initiative that builds upon the growing trend to use modern Web 2.0 technology to enhance and invigorate government administration through citizen engagement.
After the pilot period has concluded, IP Australia and the Queensland University of Technology will evaluate the project’s success.
Peer-to-Patent Australia is a joint initiative of the Queensland University of Technology (QUT), IP Australia (which houses the Australian patent office). It is also the result of collaboration between of the Queensland University of Technology and New York Law School .
Peer-to-Patent Australia is based upon the successful Peer-to-Patent projects run by the New York Law School in collaboration with the United States Patent and Trademark Office (USPTO) and is part of a push to make Peer-to-Patent an international phenomenon.
Except where otherwise noted, content on the Peer-to-Patent Australia web site is available for noncommercial use through a Creative Commons license. | https://en.wikipedia.org/wiki/Peer-to-Patent_Australia |
Peer-to-peer video sharing is a basic service on top of the IP Multimedia Subsystem (IMS).
Early proprietary implementations might also run a simple SIP infrastructure, too.
The GSM Association calls it "Video Share". The peer-to-peer video sharing functionality is defined by the Phase 1 of the GSMA Video Share service.
For a more detailed description of the full GSMA Video Share service, please see the Wikipedia entry for Video Share .
The most basic form is typically connected to a classical circuit-switched (CS) telephone call.
While talking on the CS line the speaker can start in parallel a multimedia IMS session. The session is normally a video stream, with audio being optional (since there is an audio session already open on the CS domain). It is also possible to share photos or files.
Actually, P2P video sharing does not require a full IMS implementation. It could work with a pure IETF Session Initiation Protocol (SIP) infrastructure and simple HTTP Digest authentication.
However, mobile operators may want to use it without username/password provisioning and the related frauds problems. One possible solution is the Early IMS Authentication method.
In the future USIM/ISIM based authentication could be introduced, too.
So the IMS adds up extra security and management features that are normally required by a mobile operator by default.
The early Nokia implementation requires the manual setting of an attribute in the phone book. When the video session is triggered (by simply pulling down the back-side camera cover on a 6680), the video sharing client looks up the destination URI based on the MSISDN number of the B party of the current open CS voice call. The video sharing is possible only if this number has a valid entry in the phone book and a valid URI for the SIP call.
However, this method is not really scalable, since the user has to enter very complex strings into the phone book manually. Because this service does not involve any application server, it is difficult to make a good business model for it.
Usually, the first commercial services were based on the idea that video sharing will increase the length of the voice sessions, and the resulting increased revenue would be enough to cover the costs of the video sharing service.
The P2P video sharing was introduced in 2004 by Nokia. Two major operators started commercial implementations: "Turbo Call" [ 1 ] from Telecom Italia Mobile (TIM) in Italy and Telecomunicações Móveis Nacionais, SA (TMN) in Portugal.
The first handsets to support P2P video sharing were the Nokia 6630 and 6680. The 6680 is especially suited for turning on the video sharing by having a slider on top of the back-side camera.
Later the Nokia N70 was added to the commercially supported handsets.
TIM Italy reported about 10% penetration (based on the potentially available customers with appropriate handsets). | https://en.wikipedia.org/wiki/Peer-to-peer_video_sharing |
Peer Bork (born 4 May 1963 [ 1 ] ) is a German bioinformatician . [ 2 ] He is Interim Director General of the European Molecular Biology Laboratory (EMBL). [ 3 ] Prior to his appointment he served as director of the EMBL site in Heidelberg , in south-west Germany. [ 4 ]
Bork received his PhD in biochemistry in 1990 from the Leipzig University and his habilitation in theoretical biophysics in 1995 from the Humboldt University of Berlin . He was appointed a group leader at EMBL in 1995. [ 5 ] He has worked on the microbiomes of humans and other animals. [ 2 ]
He is on the board of editorial reviewers of Science , [ 6 ] and is a senior editor of the journal Molecular Systems Biology . [ 7 ]
In 2000, Bork was elected as a Member of the European Molecular Biology Organization , [ 8 ] and in 2008 he received the Nature "mid-career achievement" award for science mentoring in Germany. [ 9 ] He was appointed a member of the German National Academy of Sciences Leopoldina in 2014. [ 5 ] He received an honorary doctorate from the University of Würzburg [ 5 ] in 2014 and Utrecht University in 2017. [ 10 ]
In 2021, Bork was awarded the Novozymes Prize "for developing groundbreaking, publicly available and integrative bioinformatic tools" by the Novo Nordisk Foundation [ 11 ] . He was also awarded the 2021 International Society for Computational Biology 'Accomplishments by a Senior Scientist Award' for "tremendous contributions to bioinformatics on a plethora of fronts within the field". [ 12 ] | https://en.wikipedia.org/wiki/Peer_Bork |
In mathematics , Peetre's inequality, named after Jaak Peetre , says that for any real number t {\displaystyle t} and any vectors x {\displaystyle x} and y {\displaystyle y} in R n , {\displaystyle \mathbb {R} ^{n},} the following inequality holds: ( 1 + | x | 2 1 + | y | 2 ) t ≤ 2 | t | ( 1 + | x − y | 2 ) | t | . {\displaystyle \left({\frac {1+|x|^{2}}{1+|y|^{2}}}\right)^{t}~\leq ~2^{|t|}(1+|x-y|^{2})^{|t|}.}
The inequality was proved by J. Peetre in 1959 and has founds applications in functional analysis and Sobolev spaces .
This article incorporates material from Peetre's inequality on PlanetMath , which is licensed under the Creative Commons Attribution/Share-Alike License .
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peetre's_inequality |
In mathematics , the (linear) Peetre theorem, named after Jaak Peetre , is a result of functional analysis that gives a characterisation of differential operators in terms of their effect on generalized function spaces , and without mentioning differentiation in explicit terms. The Peetre theorem is an example of a finite order theorem in which a function or a functor , defined in a very general way, can in fact be shown to be a polynomial because of some extraneous condition or symmetry imposed upon it.
This article treats two forms of the Peetre theorem. The first is the original version which, although quite useful in its own right, is actually too general for most applications.
Let M be a smooth manifold and let E and F be two vector bundles on M . Let
be the spaces of smooth sections of E and F . An operator
is a morphism of sheaves which is linear on sections such that the support of D is non-increasing : supp Ds ⊆ supp s for every smooth section s of E . The original Peetre theorem asserts that, for every point p in M , there is a neighborhood U of p and an integer k (depending on U ) such that D is a differential operator of order k over U . This means that D factors through a linear mapping i D from the k - jet of sections of E into the space of smooth sections of F :
where
is the k -jet operator and
is a linear mapping of vector bundles.
The problem is invariant under local diffeomorphism, so it is sufficient to prove it when M is an open set in R n and E and F are trivial bundles. At this point, it relies primarily on two lemmas:
We begin with the proof of Lemma 1.
We now prove Lemma 2.
Let M be a compact smooth manifold (possibly with boundary ), and E and F be finite dimensional vector bundles on M . Let
is a smooth function (of Fréchet manifolds ) which is linear on the fibres and respects the base point on M :
The Peetre theorem asserts that for each operator D , there exists an integer k such that D is a differential operator of order k . Specifically, we can decompose
where i D {\displaystyle i_{D}} is a mapping from the jets of sections of E to the bundle F . See also intrinsic differential operators .
Consider the following operator:
where f ∈ C ∞ ( R d ) {\displaystyle f\in C^{\infty }(\mathbb {R} ^{d})} and S r {\displaystyle S_{r}} is the sphere centered at x 0 {\displaystyle x_{0}} with radius r {\displaystyle r} . This is in fact the Laplacian, as can be seen using Taylor's theorem. We show will show L {\displaystyle L} is a differential operator by Peetre's theorem. The main idea is that since L f ( x 0 ) {\displaystyle Lf(x_{0})} is defined only in terms of f {\displaystyle f} 's behavior near x 0 {\displaystyle x_{0}} , it is local in nature; in particular, if f {\displaystyle f} is locally zero, so is L f {\displaystyle Lf} , and hence the support cannot grow.
The technical proof goes as follows.
Let M = R d {\displaystyle M=\mathbb {R} ^{d}} and E {\displaystyle E} and F {\displaystyle F} be the rank 1 {\displaystyle 1} trivial bundles.
Then Γ ∞ ( E ) {\displaystyle \Gamma ^{\infty }(E)} and Γ ∞ ( F ) {\displaystyle \Gamma ^{\infty }(F)} are simply the space C ∞ ( R d ) {\displaystyle C^{\infty }(\mathbb {R} ^{d})} of smooth functions on R d {\displaystyle \mathbb {R} ^{d}} . As a sheaf, F ( U ) {\displaystyle {\mathcal {F}}(U)} is the set of smooth functions on the open set U {\displaystyle U} and restriction is function restriction.
To see L {\displaystyle L} is indeed a morphism, we need to check ( L u ) | V = L ( u | V ) {\displaystyle (Lu)|V=L(u|V)} for open sets U {\displaystyle U} and V {\displaystyle V} such that V ⊆ U {\displaystyle V\subseteq U} and u ∈ C ∞ ( U ) {\displaystyle u\in C^{\infty }(U)} . This is clear because for x ∈ V {\displaystyle x\in V} , both [ ( L u ) | V ] ( x ) {\displaystyle [(Lu)|V](x)} and [ L ( u | V ) ] ( x ) {\displaystyle [L(u|V)](x)} are simply lim r → 0 2 d r 2 1 | S r | ∫ S r ( u ( y ) − u ( x ) ) d y {\displaystyle \lim _{r\to 0}{\frac {2d}{r^{2}}}{\frac {1}{|S_{r}|}}\int _{S_{r}}(u(y)-u(x))dy} , as the S r {\displaystyle S_{r}} eventually sits inside both U {\displaystyle U} and V {\displaystyle V} anyway.
It is easy to check that L {\displaystyle L} is linear:
Finally, we check that L {\displaystyle L} is local in the sense that s u p p L f ⊆ s u p p f {\displaystyle suppLf\subseteq suppf} . If x 0 ∉ s u p p ( f ) {\displaystyle x_{0}\notin supp(f)} , then ∃ r > 0 {\displaystyle \exists r>0} such that f = 0 {\displaystyle f=0} in the ball of radius r {\displaystyle r} centered at x 0 {\displaystyle x_{0}} . Thus, for x ∈ B ( x 0 , r ) {\displaystyle x\in B(x_{0},r)} ,
for r ′ < r − | x − x 0 | {\displaystyle r'<r-|x-x_{0}|} , and hence ( L f ) ( x ) = 0 {\displaystyle (Lf)(x)=0} .
Therefore, x 0 ∉ s u p p L f {\displaystyle x_{0}\notin suppLf} .
So by Peetre's theorem, L {\displaystyle L} is a differential operator. | https://en.wikipedia.org/wiki/Peetre_theorem |
A peg loom is a simple weaving loom . Handheld weaving sticks use the same principle.
A peg loom is a board, usually wooden, with one or more rows of holes, and a set of wooden or nylon pegs which fit into these holes. Each peg is a dowel with a hole drilled along its diameter near one end. Handheld weaving sticks are similar to the pegs, but tapered at the hole end and pointed at the other end. [ 1 ] : 2–3 Plastic looms are also made for the educational market. [ 2 ]
Double-length warp threads are threaded through the hole in each peg or stick, and the loose ends knotted. The pegs are inserted into the loom, or the sticks are handheld, and the weft thread is woven around the pegs or sticks. As the work progresses, it is slid off the pegs or sticks onto the trailing warp threads. [ 1 ] : 6–26 Different yarns can be used to create patterns, [ 1 ] : 128–140 and when using sticks a curved piece of work can be created by weaving less often round certain sticks.
Looms are made in a range of sizes. As an example, one English company makes looms from 200–1,200 millimetres (8–47 in), with 9-63 holes. Most of their looms have three rows of holes, with 6mm pegs at spacings of 12.5mm and 9mm holes at spacings of 18.5 and 25.4mm. [ 3 ] A larger scale peg loom has been used to create sleeping mats for homeless people from recycled plastic carrier bags. [ 4 ]
It has been said that stick weaving was used by people of the Great Lakes region of North America in the 1500s when French trappers first encountered them, and that in the 18th century it was taught to children to develop their manual dexterity before they entered the weaving trade. [ 5 ]
This article about textiles is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peg_loom |
Peggoty Mutai is a Kenyan chemist.
Born in Kericho , her interests include medicinal chemistry, in particular working with the search for new treatments against parasitic worms . [ 1 ]
After studying at the University of Nairobi , Kenya, where she obtained her Bachelor of Science and her Master's degree in pharmacy and pharmaceutical analysis, she was accepted at McGill University in Canada to continue pursuing her doctorate, which she had started at the University of Cape Town , South Africa. [ 2 ] Mutai returned to the University of Cape town to finish her doctorate in 2014. Mutai was among the fifteen Fellows chosen by the L'Oréal-UNESCO Awards for Women in Science to receive an international scholarship to pursue their research projects in 2012. [ 3 ] She is currently a lecturer for the department of Pharmacology and Pharmacognosy at the University of Nairobi and the section head of Pharmacognosy.
She has stated that her love of science was stimulated by her love of nature and the serene natural environment she experienced in childhood. [ 4 ]
Mutai's doctoral research involved studying parasitic worms and neglected tropical diseases. [ 4 ] Her subsequent research interests have included treatments for neglected tropical diseases. [ 5 ] [ 6 ] | https://en.wikipedia.org/wiki/Peggoty_Mutai |
Pegol is a term used in generic names for pharmaceutical drugs to indicate the presence of a polyethylene glycol attachment ( pegylation ). The term is used for monoclonal antibodies and engineered proteins as well as for small molecules . The purpose of the pegylation is to extend the half-life of the drug. [ 1 ]
Examples include:
This pharmacology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pegol |
In theoretical physics , the Peierls bracket is an equivalent description [ clarification needed ] of the Poisson bracket . It can be defined directly from the action and does not require the canonical coordinates and their canonical momenta to be defined in advance. [ clarification needed ]
The bracket [ clarification needed ]
is defined as
as the difference between some kind of action of one quantity on the other, minus the flipped term.
In quantum mechanics , the Peierls bracket becomes a commutator i.e. a Lie bracket .
This article incorporates material from the Citizendium article " Peierls bracket ", which is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License but not under the GFDL .
Peierls, R. "The Commutation Laws of Relativistic Field Theory,"
Proc. R. Soc. Lond. August 21, 1952 214 1117 143-157.
This article about theoretical physics is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peierls_bracket |
Peierls stress (or Peierls-Nabarro stress, also known as the lattice friction stress [ 1 ] ) is the force (first described by Rudolf Peierls and modified by Frank Nabarro ) needed to move a dislocation within a plane of atoms in the unit cell . The magnitude varies periodically as the dislocation moves within the plane. Peierls stress depends on the size and width of a dislocation and the distance between planes. Because of this, Peierls stress decreases with increasing distance between atomic planes. Yet since the distance between planes increases with planar atomic density, slip of the dislocation is preferred on closely packed planes.
Where:
The Peierls stress also relates to the temperature sensitivity of the yield strength of material because it very much depends on both short-range atomic order and atomic bond strength. As temperature increases, the vibration of atoms increases, and thus both peierls stress and yield strength decrease as a result of weaker atomic bond strength at high temperatures.
This crystallography -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peierls_stress |
A Peierls transition or Peierls distortion is a distortion of the periodic lattice of a one-dimensional crystal. Atomic positions oscillate, so that the perfect order of the 1-D crystal is broken. [ 1 ] It is named after Rudolf Peierls .
Peierls' theorem [ 2 ] states that a one-dimensional equally spaced chain with one electron per ion is unstable .
This theorem was first espoused in the 1930s by Rudolf Peierls . It can be proven using a simple model of the potential for an electron in a 1-D crystal with lattice spacing a {\displaystyle a} . The periodicity of the crystal creates energy band gaps in the ϵ − k {\displaystyle \epsilon -k} diagram at the edge of the Brillouin zone k a = ± π {\displaystyle ka=\pm \pi } (similar to the result of the Kronig–Penney model , which helps to explain the origin of band gaps in semiconductors). If the ions each contribute one electron, then the band will be half-filled, up to values of k a = ± π / 2 {\displaystyle ka=\pm \pi /2} in the ground state.
Imagine a lattice distortion where every other ion moves closer to one neighbor and further away from the other, the unfavourable energy of the long bond between ions is outweighed by the energy gain of the short bond. The period has just doubled from a {\displaystyle a} to 2 a {\displaystyle 2a} . In essence, the proof relies on the fact that doubling the period would introduce new band gaps located at multiples of k a = ± π / 2 {\displaystyle ka=\pm \pi /2} ; see the figure in the right. This would cause small energy savings, based on the distortion of the bands in the vicinity of the new gaps. Approaching k a = ± π / 2 {\displaystyle ka=\pm \pi /2} , the distortion due to the introduction of the new band gap will cause the electrons to be at a lower energy than they would be in the perfect crystal. Therefore, this lattice distortion becomes energetically favorable when the energy savings due to the new band gaps outweighs the elastic energy cost of rearranging the ions. Of course, this effect will be noticeable only when the electrons are arranged close to their ground state – in other words, thermal excitation should be minimized. Therefore, the Peierls transition should be seen at low temperature. This is the basic argument for the occurrence of the Peierls transition, sometimes called dimerization.
The earliest written record of the Peierls transition was presented at the 1954 École de physique des Houches . These lecture notes (shown below) contain Rudolf Peierls' handwritten equations and figures, and can be viewed [ 3 ] in the library of the Institut Laue–Langevin , in Grenoble , France .
Peierls’ discovery gained experimental backing during the effort to find new superconducting materials. In 1964, Dr. William Little of the Stanford University Department of Physics theorized that a certain class of polymer chains may experience a high T c superconducting transition. [ 4 ] The basis for his assertion was that the lattice distortions that lead to pairing of electrons in the BCS theory of superconductivity could be replaced instead by rearranging the electron density in a series of side chains. This means that now electrons would be responsible for creating the Cooper pairs instead of ions. Because the transition temperature is inversely proportional to the square root of the mass of the charged particle responsible for the distortions, the T c should be improved by a corresponding factor:
The subscript i represents "ion", while e represents "electron". The predicted benefit in superconducting transition temperature was therefore a factor of about 300.
In the 1970s, various organic materials such as TTF-TCNQ were synthesized. [ 5 ] What was found is that these materials underwent an insulating transition rather than a superconducting one. Eventually it was realized that these were the first experimental observations of the Peierls transition. With the introduction of new band gaps after the lattice becomes distorted, electrons must overcome this new energy barrier in order to become free to conduct. The simple model of the Peierls distortion as a rearrangement of ions in a 1-D chain could describe why these materials became insulators rather than superconductors.
Peierls predicted that the rearrangement of the ion cores in a Peierls transition would produce periodic fluctuations in the electron density. These are commonly called charge density waves , and they are an example of collective charge transport. Several materials systems have verified the existence of these waves. Good candidates are weakly coupled molecular chains, where electrons can move freely along the direction of the chains, but motion is restricted perpendicular to the chains. NbSe 3 and K 0.3 MoO 3 are two examples in which charge density waves have been observed at relatively high temperatures of 145 K and 180 K respectively. [ 6 ]
Furthermore, the 1-D nature of the material causes a breakdown of the Fermi liquid theory for electron behavior. Therefore, a 1-D conductor should behave as a Luttinger liquid instead. A Luttinger liquid is a paramagnetic one-dimensional metal without Landau quasi-particle excitations.
1-D metals have been the subject of much research. Here are a few examples of both theoretical and experimental research efforts to illustrate the broad range of topics: | https://en.wikipedia.org/wiki/Peierls_transition |
In logic , Peirce's law is named after the philosopher and logician Charles Sanders Peirce . It was taken as an axiom in his first axiomatisation of propositional logic . It can be thought of as the law of excluded middle written in a form that involves only one sort of connective, namely implication.
In propositional calculus , Peirce's law says that (( P → Q )→ P )→ P . Written out, this means that P must be true if there is a proposition Q such that the truth of P follows from the truth of "if P then Q ".
Peirce's law does not hold in intuitionistic logic or intermediate logics and cannot be deduced from the deduction theorem alone.
Under the Curry–Howard isomorphism , Peirce's law is the type of continuation operators, e.g. call/cc in Scheme . [ 1 ]
Here is Peirce's own statement of the law:
Peirce goes on to point out an immediate application of the law:
Warning : As explained in the text, " a " here does not denote a propositional atom, but something like the quantified propositional formula ∀ p p {\displaystyle \forall p\,p} . The formula (( x → y ) → a ) → x would not be a tautology if a were interpreted as an atom.
In intuitionistic logic, if P {\displaystyle P} is proven or rejected, or if Q {\displaystyle Q} is proven valid, then Peirce's law for the two propositions holds. But the law's special case when Q {\displaystyle Q} is rejected, called consequentia mirabilis , is equivalent to excluded middle already over minimal logic . This also means that Piece's law entails classical logic over intuitionistic logic. This is shown below.
Firstly, from P → Q {\displaystyle P\to Q} follows the equivalence P ↔ ( P ∧ Q ) {\displaystyle P\leftrightarrow (P\land Q)} , and so ( P → Q ) → P {\displaystyle (P\to Q)\to P} is equivalent to ( P → Q ) → ( P ∧ Q ) {\displaystyle (P\to Q)\to (P\land Q)} . With this, one can also establish Peirce's law by establishing the equivalent form ( ( P → Q ) → ( P ∧ Q ) ) → P {\displaystyle ((P\to Q)\to (P\land Q))\to P} . Considering the case Q = ⊥ {\displaystyle Q=\bot } likewise also shows how double-negation elimination ¬ ¬ P → P {\displaystyle \neg \neg P\to P} implies consequentia mirabilis, and this direction even only uses minimal logic. Now in intuitionistic logic, explosion can be used for ⊥ → ( P ∧ ⊥ ) {\displaystyle \bot \to (P\land \bot )} , and so here consequentia mirabilis also implies double-negation elimination.
As the double-negated excluded middle is always already valid even in minimal logic, it thus further also implies excluded middle, over intuitionistic logic. In the other direction, one can intuitionistically also show that excluded middle implies the full Peirce's law directly. To this end, note that using the principle of explosion , excluded middle may be expressed as P ∨ ( P → Q ) {\displaystyle P\lor (P\to Q)} . In words, this may be expressed as: "Every proposition P {\displaystyle P} either holds or implies any other proposition."
Now to prove the law, note that ( P ∨ R ) → ( ( R → P ) → P ) {\displaystyle (P\lor R)\to ((R\to P)\to P)} is derivable from just implication introduction on the one hand and modus ponens on the other. Finally, in place of R {\displaystyle R} consider P → Q {\displaystyle P\to Q} .
Another proof of the law in classical logic proceeds by passing through the classically valid reverse disjunctive syllogism twice:
First note that ¬ ¬ P {\displaystyle \neg \neg P} is implied by ( ¬ ¬ P ∧ ¬ Q ) ∨ P {\displaystyle (\neg \neg P\land \neg Q)\lor P} , which is intuitionistically equivalent to ¬ ( ¬ P ∨ Q ) ∨ P {\displaystyle \neg (\neg P\lor Q)\lor P} . Now explosion entails that ¬ A ∨ B {\displaystyle \neg A\lor B} implies A → B {\displaystyle A\to B} , and using excluded middle for A {\displaystyle A} here entails that these two are in fact equivalent. Taken together, this means that in classical logic P {\displaystyle P} is equivalent to ( P → Q ) → P {\displaystyle (P\to Q)\to P} .
Intuitionistically, not even the constraint ¬ Q → P {\displaystyle \neg Q\to P} always implies Pierce's law for two propositions. Postulating the latter to be valid in its propositional form results in Smetanich's intermediate logic .
Peirce's law allows one to enhance the technique of using the deduction theorem to prove theorems. Suppose one is given a set of premises Γ and one wants to deduce a proposition Z from them. With Peirce's law, one can add (at no cost) additional premises of the form Z → P to Γ. For example, suppose we are given P → Z and ( P → Q )→ Z and we wish to deduce Z so that we can use the deduction theorem to conclude that ( P → Z )→((( P → Q )→ Z )→ Z ) is a theorem. Then we can add another premise Z → Q . From that and P → Z , we get P → Q . Then we apply modus ponens with ( P → Q )→ Z as the major premise to get Z . Applying the deduction theorem, we get that ( Z → Q )→ Z follows from the original premises. Then we use Peirce's law in the form (( Z → Q )→ Z )→ Z and modus ponens to derive Z from the original premises. Then we can finish off proving the theorem as we originally intended.
( P → Z )→((( P → Q )→ Z )→ Z )
One reason that Peirce's law is important is that it can substitute for the law of excluded middle in the logic which only uses implication. The sentences which can be deduced from the axiom schemas:
(where P , Q , R contain only "→" as a connective) are all the tautologies which use only "→" as a connective.
Since Peirce's law implies the law of the excluded middle, it must always fail in non-classical intuitionistic logics. A simple explicit counterexample is that of Gödel many valued logics , which are a fuzzy logic where truth values are real numbers between 0 and 1, with material implication defined by:
and where Peirce's law as a formula can be simplified to:
where it always being true would be equivalent to the statement that u > v implies u = 1, which is true only if 0 and 1 are the only allowed values. At the same time however, the expression cannot ever be equal to the bottom truth value of the logic and its double negation is always true. | https://en.wikipedia.org/wiki/Peirce's_law |
In the theory of dynamical systems , Peixoto's theorem , proved by Maurício Peixoto , states that among all smooth flows on surfaces , i.e. compact two-dimensional manifolds , structurally stable systems may be characterized by the following properties:
Moreover, they form an open set in the space of all flows endowed with C 1 topology.
This mathematical physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peixoto's_theorem |
The pelB leader sequence is a sequence of amino acids which, when attached to a protein , directs the protein to the bacterial periplasm , where the sequence is removed by a signal peptidase . [ 1 ] Specifically, pelB refers to pectate lyase B of Erwinia carotovora CE. The leader sequence consists of the 22 N-terminal amino acid residues. This leader sequence can be attached to any other protein (on the DNA level) resulting in a transfer of such a fused protein to the periplasmic space of Gram-negative bacteria , such as Escherichia coli , often used in genetic engineering .
Protein secretion can increase the stability of cloned gene products. For instance it was shown that the half-life of the recombinant proinsulin is increased 10-fold when the protein is secreted to the periplasmic space. (vijji. Narne, R.S.Ramya)
One of pelB's possible applications is to direct coat protein-antigen fusions to the cell surface for the construction of engineered bacteriophages for the purpose of phage display .
The Pectobacterium carotovorum pelB leader sequence commonly used in molecular biology has the sequence MKYLLPTAAAGLLLLAAQPAMA ( UniProt Q04085).
This genetics article is a stub . You can help Wikipedia by expanding it .
This article about biological engineering is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/PelB_leader_sequence |
Pellets are a processed form of iron ore utilized in the steel industry, specifically designed for direct application in blast furnaces or direct reduction plants. These pellets are spherical in shape, with diameters ranging from 8 to 18 millimeters.
The production of iron ore pellets involves several steps, including grinding the ore, mixing it with binders, and then forming and heating the pellets. The iron content of the pellets generally ranges from 62% to 66%. This enrichment process improves the iron concentration and imparts specific chemical and mechanical properties that enhance the efficiency of steel production.
The pelletizing of powdered iron ores was first introduced at the end of the nineteenth century, utilizing tar as a binding agent, comprising 1% by weight. [ 1 ] This method involved firing the mixture in a rotating drum to create pellets suitable for blast furnaces, while also facilitating the removal of undesirable elements such as sulfur and arsenic through the emitted fumes. [ 2 ]
During this period, pellet sintering developed alongside grate sintering as an alternative process to address the agglomeration challenges faced by high-quality iron ore products. [ 1 ] The concept of pellet agglomeration was initially patented by A. Anderson in Sweden in 1912, followed by a similar patent in Germany in 1913. [ 3 ] The resultant product was named "GEROELL", derived from the German word for "rolling." Pellets produced through this method demonstrated faster reduction rates compared to calibrated ores and agglomerates made from the same feedstock. In 1926, an industrial pilot plant was constructed by Krupp in Rheinhausen to explore the potential of this pelletizing technology. However, the plant was later dismantled to make way for the installation of a large-scale grate sintering line, which emerged as a competing process in the industry. [ 4 ]
Pellet sintering has remained a viable method for processing iron ore. In the United States, this technique was employed to process fine concentrates from the Mesabi Range during World War II. [ 5 ] This was necessary as naturally rich iron ores (containing over 50% iron) were being depleted. The development of pelletizing fine magnetite ores, which typically have less than 44 mm in size and are around 85% iron, began around 1943 with support from the University of Minnesota. The process was later adopted in Europe, particularly in Sweden, to facilitate the production of pre-reduced iron ore. [ 4 ]
Pellet production saw substantial growth between 1960 and 1980 but eventually plateaued at approximately 300 million tons annually. The following data illustrates pellet production over several years: [ 5 ]
Pellets are produced directly at the extraction site by mining companies and are marketed as a distinct product, unlike agglomerates which are typically manufactured at blast furnace sites through the mixing of iron ores from various sources. [ 8 ] Pellets are generally more robust and better suited to handling compared to agglomerates, which are relatively fragile. The production process for pellets can vary significantly depending on the local characteristics of the iron ore, and some facilities may include additional stages, such as arsenic removal. [ 9 ] The pellet production process involves several key stages: [ 9 ]
These processes ensure that the pellets are produced to meet specific quality standards and can withstand the demands of handling and transportation. [ 8 ]
The ore concentrate is formed into pellets through a compaction process. This can be performed using various types of mixing equipment, though saucers are the most commonly employed tool. Before being subjected to sintering , the pellets are referred to as "green" or "raw" pellets, and their typical diameter ranges from 5 to 20 mm. [ 6 ]
Following pellet formation, they are either sent to a consumption plant or directed to a cooking oven. Due to their inherent fragility, which persists despite the binder used, pellets are generally more suitable for processing in a cooking oven rather than a consumption plant. After cooking, the pellets are cooled. [ 6 ]
The cooking process involves passing the pellets through a chain of contiguous ovens, where they are heated to temperatures of up to 1,200°C. This can be achieved using different methods: a straight grate process for a single, uninterrupted chain or a grate kiln process that includes a rotating cooling tray at the end of the chain. [ 10 ] The required heat for this process is supplied by burners, which can either add fuel to the ore concentrate or facilitate the oxidation of the ore, depending on the specific type of ore being processed. [ 9 ]
Pelletizing ore enhances the efficiency of blast furnaces and direct reduction plants by providing several advantages over raw iron ore: [ 11 ] [ 12 ] [ 13 ]
Pellets generally contain a higher iron content than agglomerated ore, leading to increased plant productivity and reduced fuel consumption. [ 13 ] They are also more durable and capable of withstanding repeated handling. Despite their higher cost—typically about 70% more than raw ore—the benefits they offer in terms of efficiency and performance justify the expense. In steelmaking , pellets are often mixed with sinter in varying proportions to optimize the process. [ 7 ] [ 14 ]
Similar to sinter, the high-temperature roasting and sintering of pellets effectively eliminate undesirable elements such as sulfur. It is also an efficient method for removing zinc, which can otherwise hinder the operation of blast furnaces. With a vaporization temperature of 907°C, zinc is effectively removed during the roasting process, making pelletizing a suitable method for this application. [ 12 ] [ a ]
Pellets are vulnerable to sulfur-induced damage during the reduction process in blast furnaces. Even low levels of sulfur dioxide (SO₂) can interfere with furnace operations, with effects observed at concentrations as low as 5 to 50 parts per million ( ppm ) in the reduction gas. The detailed mechanism behind this issue was only fully understood towards the end of the 20th century. [ 15 ] Initially, sulfur accelerates the extraction of oxygen from the iron oxide, but this effect reverses once metallic iron begins to form, significantly slowing the oxygen extraction process. [ 3 ] This unusual behavior is attributed to sulfur's strong affinity for the metallic iron that forms on the pellet surface, which inhibits the penetration of carbon. [ 3 ]
Furthermore, the reaction between wustite ( FeO ) and carbon monoxide ( CO ) occurs not only on the surface of FeO but also beneath the surface of the reduced iron. [ 16 ] Due to iron's superior absorption characteristics, a substantial portion of gas transport happens at the iron/iron oxide phase boundary. This process depends on the iron's ability to absorb sufficient carbon (carburization). If sulfur obstructs carbon absorption, reduction is limited to the surface of the iron oxide. [ 3 ] This restriction results in the formation of elongated, fibrous iron crystals, as iron crystallization can only proceed in the direction of the reducing iron oxide. Consequently, the structure of the granules becomes reinforced and can expand to two or three times their original volume. This expansion, or "swelling," of the granules can lead to blockage or significant damage to the blast furnace , highlighting the challenges associated with using pellets in blast furnace operations. [ 15 ]
Pellets, similar to agglomerates, are classified based on their chemical properties as either acidic or basic. To determine the basicity index ( i c ), the following ratio of mass concentrations is used: [ 17 ]
i c = [ C a O ] + [ M g O ] [ S i O 2 ] + [ A l 2 O 3 ] {\displaystyle i_{c}={\frac {[CaO]+[MgO]}{[SiO_{2}]+[Al_{2}O_{3}]}}}
This ratio helps in assessing the relative basicity of the pellets, which is important for optimizing their use in blast furnaces and other metallurgical processes. [ 17 ]
In practice, a simplified basicity index ( i ) is commonly used to classify pellets based on their chemical properties. This index is calculated using the ratio of calcium oxide (CaO) to silicon dioxide ( SiO 2 ): [ 6 ]
i = CaO SiO 2 {\displaystyle {\ce {i={\frac {CaO}{SiO2}}}}}
Pellets can contain high levels of hematite , but the proportion must be controlled. Excessive hematite can weaken the pellet structure during reduction, leading to the pellets breaking down into dust under the weight of stacked charges. This is due to the fact that a high hematite content can cause the pellets to disintegrate, compromising their integrity and usability in the reduction process. [ 15 ]
Acid pellets are produced without the addition of additives, resulting in a specific chemical composition. Typically, the composition of acid pellets is as follows: 2.2% SiO 2 and 0.2% CaO. In the United States during the 1990s, the typical characteristics of acid pellets were: [ 6 ]
Unlike agglomerated ores, which may include basic fluxes like silicates in the binder during pelletizing, acid pellets maintain their acidic composition due to their solid spherical shape. This design helps preserve their mechanical properties and reduces the risk of disintegration. [ 15 ]
Acid pellets exhibit notable mechanical strength with a crush resistance exceeding 250 kg per pellet. However, their reducibility could be improved. Additionally, they are prone to swelling when exposed to lime, especially when the basicity index ( i = CaO / SiO 2 ) exceeds 0.25, which may potentially cause issues in a blast furnace. [ 18 ]
Self-melting pellets, also known as basic pellets, are a type of iron ore pellet that was developed in the United States in the 1990s. These pellets are designed for use in blast furnaces and are produced by adding lime (calcium oxide) and magnesia (magnesium oxide) to iron ore concentrate, enhancing their metallurgical properties. Self-melting pellets typically have the following properties: [ 6 ]
These pellets are recognized for their high compressive strength and ease of reduction, making them well-suited for blast furnace operations. The production process of self-melting pellets involves incorporating limestone into the iron ore concentrate. This inclusion affects the productivity of pellet plants due to the calcination process, which involves the endothermic process of limestone. As a result, the overall productivity of the pellet plant can decrease by approximately 10 to 15% compared to the production of acid pellets, which do not include lime. Self-melting pellets are appreciated for their enhanced performance in blast furnaces but require consideration of the trade-offs in production efficiency. [ 18 ]
These pellets are designed for use in direct reduction plants. The typical composition of the pellets includes: 67.8% iron (Fe), 1.7% silicon dioxide (SiO 2 ), 0.40% aluminum oxide (Al 2 O 3 ), 0.50% calcium oxide (CaO), 0.30% magnesium oxide (MgO), and 0.01% phosphorus (P). [ 6 ]
Low-silica pellets, when doped with lime, can self-fuse. A typical composition for these self-fusing pellets is: 65.1% iron (Fe), 2.5% silicon dioxide (SiO 2 ), 0.45% aluminum oxide (Al 2 O 3 ), 2.25% calcium oxide (CaO), 1.50% magnesium oxide (MgO), and 0.01% phosphorus (P). [ 6 ]
To cater to specific customer needs, manufacturers have developed alternative pellet types that offer distinct properties and performance characteristics: [ 6 ]
These alternative pellet types are designed to address different operational requirements and enhance the flexibility of iron-making processes. [ 6 ] | https://en.wikipedia.org/wiki/Pellet_(steel_industry) |
Pelletizing is the process of compressing or molding a material into the shape of a pellet. A wide range of different materials are pelletized including chemicals , iron ore , animal compound feed , plastics ( nurdles ), waste materials, and more. The process is considered an excellent option for the storage and transport of said materials. [ 1 ] The technology is widely used in the powder metallurgy engineering and medicine industries. [ 2 ]
Edward W Davis of the University of Minnesota is credited for devising the process of pelletizing iron ore.
Pelletizing iron ore is undertaken due to the excellent physical and metallurgical properties of iron ore pellets. [ 1 ] Iron ore pellets are spheres of typically 6–16 mm (0.24–0.63 in) to be used as raw material for blast furnaces . They typically contain 64–72% Fe and various additional material adjusting the chemical composition and the metallurgic properties of the pellets. [ 3 ] Typically limestone , dolomite and olivine is added and Bentonite is used as binder.
The process of pelletizing combines mixing of the raw material, forming the pellet and a thermal treatment baking the soft raw pellet to hard spheres. The raw material is rolled into a ball, then fired in a kiln or in travelling grate to sinter the particles into a hard sphere. [ 4 ]
The configuration of iron ore pellets as packed spheres in the blast furnace allows air to flow between the pellets, decreasing the resistance to the air that flows up through the layers of material during the smelting. The configuration of iron ore powder in a blast furnace is more tightly-packed and restricts the air flow. This is the reason that iron ore is preferred in the form of pellets rather than in the form of finer particles. [ 5 ] The quality of the iron ore pellets depends on different factors, which include feed particle size, amount of water used, disc rotating speed, inclination angle of the disc bottom, residence time in the disc as well as the quality and quantity of the binder(s) used. [ 1 ]
Additional materials are added to the iron ore (pellet feed) to meet the requirements of the final pellets. This is done by placing the mixture in the pelletizer, which can hold different types of ores and additives, and mixing to adjust the chemical composition and the metallurgic properties of the pellets. In general, the following stages are included in this period of processing: concentration / separation, homogenization of the substance ratios, milling, classification, increasing thickness, homogenization of the pulp and filtering.
The formation of raw iron ore pellets, also known as pelletizing, has the objective of producing pellets in an appropriate band of sizes and with mechanical properties high usefulness during the stresses of transference, transport, and use. For example, waste materials are ground before being heated and introduced into a press for compression. [ 6 ] Both mechanical force and thermal processes are used to produce the correct pellet properties. From an equipment point of view there are two alternatives for industrial production of iron ore pellets: the drum and the pelletizing disk.
In order to confer to the pellets high resistance metallurgic mechanics and appropriate characteristics, the pellets are subjected to thermal processing, which involves stages of drying, preheating, firing, after-firing and cooling. The duration of each stage and the temperature that the pellets are subjected to have a strong influence on the final product quality.
In the field of medicine, pelletization is referred to as the agglomeration process that converts fine powders or granules into more or less spherical pellets. [ 7 ] The use of the technology increased because it allows for the controlled release of dosage form, which also lead to a uniform absorption with less mucosal irritation within the gastrointestinal tract. [ 7 ] There are different pelletization processes applied in the pharmaceutical industry and these typically vary according to the bonding forces. [ 8 ] Some examples of the processes include balling, compression, and spray congealing. [ 8 ] Balling is similar to the wet (or green) pelletization used in the iron ore industry. [ 9 ]
Pelletizing of animal feeds can result in pellets from 1.2 mm (0.047 in) (shrimp feeds), through to 3–4 mm (0.12–0.16 in) (poultry feeds) up to 8–10 mm (0.31–0.39 in) (stock feeds). The pelletizing of stock feed is done with the pellet mill machinery, which is done in a feed mill .
Feed ingredients are normally first hammered to reduce the particle size of the ingredients. Ingredients are then batched, and then combined and mixed thoroughly by a feed mixer . Once the feed has been prepared to this stage the feed is ready to be pelletized.
Pelletizing is done in a pellet mill , where feed is normally conditioned and thermal-treated in the fitted conditioners of a pellet mill. The feed is then pushed through the holes and exit the pellet mill as pelleted feed.
Wood pellets made by compressing sawdust or other ground woody materials are used in a variety of energy and non-energy applications. In the energy sector, wood pellets are often used to replace coal with power plants such as Drax , in England, replacing most of their coal use with woody pellet. As sustainably harvested wood does not lead to a long-term increase in atmospheric carbon dioxide levels, wood fuels are considered to be a low-carbon form of energy. [ 10 ] Wood pellets are also used for domestic and commercial heating either in the form of automated boilers or pellet stoves. Compared to other fuels made from wood, pellets have the advantage of higher energy density, simpler handling as it flows similar to grain, and low moisture.
Concerns have been raised about the short-term carbon balance of wood pellet production, particularly if it is driving the harvesting of old or mature harvests that would otherwise not be logged. [ 11 ] Areas of concern include the inland rainforests of British Columbia These claims are contested by the pellet and forest industries.
After pelleting, the pellets are cooled with a cooler to bring the temperature of the feed down. Other post pelleting applications include post-pelleting conditioning, sorting via a screen, and maybe coating if required. | https://en.wikipedia.org/wiki/Pelletizing |
The term pellis refers to the cellular cortical layers of a mushroom . The term was introduced by Dutch mycologist Cornelis Bas in 1969, who distinguished different layers of the pellis as suprapellis, mediopellis and subpellis. [ 1 ] He also distinguished various topographies of the pellis. For example, pileipellis refers to the cuticle of the mushroom pileus (or cap), while stipitipellis is the cuticle of the stipe (the stem).
This mycology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pellis |
The Pellizzari reaction was discovered in 1911 by Guido Pellizzari, and is the organic reaction of an amide and a hydrazide to form a 1,2,4-triazole . [ 1 ]
The product is similar to that of the Einhorn-Brunner reaction , but the mechanism itself is not regioselective .
The mechanism begins by the nitrogen in the hydrazide attacking the carbonyl carbon on the amide to form compound 3 . The negatively charged oxygen then abstracts two hydrogens from neighboring nitrogens in order for a molecule of water to be released to form compound 5 . The nitrogen then performs an intramolecular attack on the carbonyl group to form the five-membered ring of compound 6 . After another proton migration from the nitrogens to the oxygen, another water molecule is released to form the 1,2,4-triazole 8 . [ 2 ]
The synthesis of the 1,2,4-triazole has a wide range of biological functions. [ citation needed ] 1,2,4-triazoles have antibacterial , antifungal , antidepressant and hypoglycemic properties. 3-benzylsulfanyl derivates of the triazole also show slight to moderate antimycobacterial activity, but are considered moderately toxic. [ 3 ]
The Pellizzari reaction is limited in the number of substituents that can be on the ring, so other methods have been developed to incorporate three elements of diversity. Liquid-phase synthesis of 3-alkylamino-4,5-disubstituted-1,2,4-triazoles by PEG support has given moderate yields with excellent purity. [ 4 ] In practice, the Pellizzari reaction requires high temperatures, long reaction times, and has an overall low yield. However, adding microwave irradiation shortens the reaction time and increases its yield. [ 5 ] | https://en.wikipedia.org/wiki/Pellizzari_reaction |
In marine navigation , a pelorus is a reference tool for maintaining bearing of a vessel at sea. It is a "simplified compass" without a directive element, suitably mounted and provided with vanes to permit observation of relative bearings. [ 1 ]
The instrument was named for one Pelorus, said to have been the pilot for Hannibal , circa 203 BC.
Harold Gatty described the use of a pelorus by Polynesians before the use of a compass. In equatorial waters the nightly course of stars overhead is nearly uniform during the year. This regularity simplified navigation for the Polynesians using a pelorus, or dummy compass:
[Arabs] divided the horizon into 32 points. These points were derived from fifteen stars which rose at approximately equally spaced points of the eastern horizon. The setting points of these stars on the western horizon gave them another fifteen points and north and south brought the total to thirty two.
These accomplished navigators [Polynesians] had names for one hundred and fifty stars. They knew the point on the horizon where each of these rose, and the time at which it did so. They knew the islands which each passed over.
Many of the peoples in the Pacific used the thirty two point dummy compass…I consider this…proof of the Indo-Malayan origin of the Polynesians.
Reading from North to South, in their rising and setting positions, these stars are: [ 3 ]
The true position of these stars is only approximate to their theoretical equidistant rhumbs on the sidereal compass. Over time, the elaboration of the pelorus points led to the modern compass rose .
In appearance and use, a pelorus resembles a compass or compass repeater , with sighting vanes or a sighting telescope attached, but it has no directive properties. That is, it remains at any relative direction to which it is set. It is generally used by setting 000° at the lubber's line . Relative bearings are then observed. They can be converted to bearings true, magnetic, grid, etc., by adding the appropriate heading. The direct use of relative bearings is sometimes of value. A pelorus is useful, for instance, in determining the moment at which an aid to navigation is broad on the beam. It is also useful in measuring pairs of relative bearings which can be used to determine distance off and distance abeam of a navigational aid.
If the true heading is set at the lubber's line, true bearings are observed directly. Similarly, compass bearings can be observed if the compass heading is set at the lubber's line, etc. However, the vessel must be on the heading to which the pelorus is set if accurate results are to be obtained, or else a correction must be applied to the observed results. Perhaps the easiest way of avoiding error is to have the steersman indicate when the vessel is on course. This is usually done by calling out "mark, mark, mark" as long as the vessel is within a specified fraction of a degree of the desired heading. The observer, who is watching a distant object across the pelorus, selects an instant when the vessel is steady and is on course. An alternative method is to have the observer call out "mark" when the relative bearing is steady, and the steersman note the heading. If the compass is swinging at the moment of observation, the observation should be rejected. The number of degrees between the desired and actual headings is added if the vessel is to the right of the course, and subtracted if to the left . Thus, if the course is 060° and the heading is 062° at the moment of observation, a correction of 2° is added to the bearing. | https://en.wikipedia.org/wiki/Pelorus_(instrument) |
The pelvic thrust is the thrusting motion of the pelvic region, which is used for a variety of activities, such as dance, exercise, or sexual activity .
The pelvic thrust is used during copulation by many species of mammals , [ 1 ] [ 2 ] [ 3 ] including humans, [ 4 ] or for other sexual activities (such as non-penetrative sex ). In 2007, German scientists noted that female monkeys could increase the vigor and number of pelvic thrusts made by the male by shouting during intercourse . [ 5 ] In whitetail deer , copulation consists of a single pelvic thrust. [ 6 ]
One of the first to perform this move on stage was Elvis Presley . It was quite controversial due to its obvious sexual connotations. Due to this controversy, he was sometimes shown (as seen on his third appearance on The Ed Sullivan Show ) from the waist up on TV. [ 7 ] Later, the pelvic thrust also became one of the signature moves of Michael Jackson . [ 8 ] It is also mentioned in " Time Warp ", a song from The Rocky Horror Show , as a part of the choreography associated with the warp itself. Twerking , a reverse and sometimes passive form of pelvic thrust dance move, is also a very popular form of hip-hop dance move. The sideways pelvic thrust is a famous female dance move in India and Bangladesh and known as thumka . It appears in the lyrics of various Bollywood songs. [ citation needed ]
Hip thrusts can be used as an exercise to train the gluteus maximus muscle. The athlete will get into a reclined position and thrust their hips upward to lift weights balanced on their lap. [ 9 ] [ 10 ]
Pelvic thrusting is observed in infant monkeys, apes, and humans. These observations led ethologist John Bowlby (1969) to suggest that infantile sexual behavior may be the rule in mammals, not the exception. Thrusting has been observed in humans at eight to 10 months of age and may be an expression of affection. Typically, the infant clings to the parent, then nuzzles, thrusts, and rotates the pelvis for several seconds. [ 11 ] | https://en.wikipedia.org/wiki/Pelvic_thrust |
Pelvic tilt is the orientation of the pelvis in respect to the thighbones and the rest of the body. The pelvis can tilt towards the front, back, or either side of the body. [ 1 ]
Anterior pelvic tilt and posterior pelvic tilt are very common abnormalities in regard to the orientation of the pelvis.
Anterior Pelvic Tilt (APT) : Treatment focuses on strengthening the glutes, core, and lower back muscles while stretching the hip flexors. Exercises such as glute bridges, planks, and hip thrusts help restore alignment and counteract muscle imbalances. [ 3 ]
Posterior Pelvic Tilt (PPT) : For PPT, strengthening the lower back and hip extensors is crucial, along with stretching the hip flexors and abdominal muscles. Exercises like back extensions and glute bridges are often recommended for restoring neutral pelvic alignment. [ 4 ]
Lateral Pelvic Tilt (LPT) : LPT treatment involves addressing the root cause, such as scoliosis or leg length discrepancies. Balancing exercises for the hips and improving spinal posture, along with orthotics, may help correct imbalances. [ 5 ] | https://en.wikipedia.org/wiki/Pelvic_tilt |
Pempidine is a nicotinic antagonist drug, first reported in 1958 by two research groups working independently, and introduced as an oral treatment for hypertension . [ 1 ]
Reports on the "classical" pharmacology of pempidine have been published. [ 2 ] [ 3 ] The Spinks group, at ICI , compared pempidine, its N -ethyl analogue, and mecamylamine in considerable detail, with additional data related to several structurally simpler compounds. [ 2 ]
LD 50 for the HCl salt of pempidine in mice: 74 mg/kg ( intravenous ); 125 mg/kg ( intraperitoneal ); 413 mg/kg ( oral ). [ 2 ]
Pempidine is an aliphatic , sterically hindered , cyclic, tertiary amine , which is a weak base : in its protonated form it has a p K a of 11.25. [ 4 ]
Pempidine is a liquid with a boiling point of 187–188 °C and a density of 0.858 g/cm 3 . [ 2 ]
Two early syntheses of this compound are those of Leonard and Hauck, [ 5 ] and Hall. [ 4 ] These are very similar in principle: Leonard and Hauck reacted phorone with ammonia , to produce 2,2,6,6-tetramethyl-4-piperidone , which was then reduced by means of the Wolff–Kishner reduction to 2,2,6,6-tetramethylpiperidine . This secondary amine was then N - methylated using methyl iodide and potassium carbonate . [ 6 ]
Hall's method involved reacting acetone with ammonia in the presence of calcium chloride to give 2,2,6,6-tetramethyl-4-piperidone, which was then reduced under Wolff–Kishner conditions, followed by N -methylation of the resulting 2,2,6,6-tetramethylpiperidine with methyl p -toluenesulfonate . | https://en.wikipedia.org/wiki/Pempidine |
Pencil beam scanning is the practice of steering a beam of radiation or charged particles across an object. It is often used in proton therapy , to reduce unnecessary radiation exposure to surrounding non-cancerous cells.
Ionizing radiation photons or x-rays ( IMRT ) use pencil beam scanning to precisely target a tumor. [ 1 ] Photon pencil beam scans are defined as crossing of two beams to a fine point.
Several charged particles devices used with Proton therapy cancer centers use pencil beam scanning. [ 2 ] The newer proton therapy machines use a pencil beam scanning technology. [ 3 ] This technique is also called spot scanning. [ 4 ] The Paul Scherrer Institute was the developer of spot beam. [ 5 ]
Varian's IMPT system uses all pencil-beam controlled protons where the beam intensity can also be controlled at this small level. This can be done by going back and forth over a previously radiated area during the same radiation session. [ citation needed ] | https://en.wikipedia.org/wiki/Pencil-beam_scanning |
Pendant group Side-group An offshoot, neither oligomeric nor polymeric, from a chain. [ 1 ]
In IUPAC nomenclature of chemistry , a pendant group (sometimes spelled pendent ) or side group is a group of atoms attached to a backbone chain of a long molecule , usually a polymer . Pendant groups are different from pendant chains , as they are neither oligomeric nor polymeric. [ 2 ]
For example, the phenyl groups are the pendant groups on a polystyrene chain.
Large, bulky pendant groups such as adamantyl usually raise the glass transition temperature ( T g ) of a polymer by preventing the chains from sliding past each other easily. Short alkyl pendant groups may lower the T g by a lubricant effect.
This article about polymer science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pendant_group |
The Pendellösung effect or phenomenon is seen in diffraction in which there is a beating in the intensity of electromagnetic waves travelling within a crystal lattice . It was predicted by P. P. Ewald in 1916 [ 1 ] and first observed in electron diffraction of magnesium oxide in 1942 by Robert D. Heidenreich [ 2 ] and in X-ray diffraction by Norio Kato and Andrew Richard Lang in 1959. [ 3 ]
At the exit surface of a photonic crystal (PhC), the intensity of the diffracted wave can be periodically modulated, showing a maximum in the "positive" (forward diffracted) or in the "negative" (diffracted) direction, depending on the crystal slab thickness.
The Pendellösung effect in photonic crystals can be understood as a beating phenomenon due to the phase modulation between coexisting plane wave components, propagating in the same direction. [ 4 ] [ 5 ]
This thickness dependence is a direct result of the so-called Pendellösung phenomenon, consisting of the periodic exchange inside the crystal of the energy between direct and diffracted beams. [ 6 ]
The Pendellösung interference effect was predicted by dynamical diffraction and also by its fellow theories developed for visible light.
This condensed matter physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Pendellösung |
Pendimethalin is an herbicide of the dinitroaniline class [ 2 ] used premergently and postemergently to control annual grasses and certain broadleaf weeds . It inhibits cell division and cell elongation. Pendimethalin is a K1-group (in Australia group D, or numerically group 3) according to the Herbicide Resistance Action Committee (HRAC) classification and is approved in Europe, North America, South America, Africa, Asia and Oceania for different crops including cereals (wheat, barley, rye, triticale), corn, soybeans, rice, potato, legumes, fruits, vegetables, and nuts, plus lawns and ornamental plants.
Pendimethalin protects crops like wheat, corn, soybeans, potatoes, cabbage, peas, carrots, and asparagus. It is used to control annual grasses and certain broadleaf weeds which interfere with growth, development, yield and quality of agricultural and horticultural crops by competing on nutrients, water and light.
Where weed infestation is particularly bad, yield loss can render wheat production uneconomical. [ 3 ] Many other crops are grown in Europe that make a fraction of total agriculture. Herbicide options are limited for these minor crops, particularly in the vegetable sector. [ 4 ] Long-term field studies performed by the German government and institutions together with farmers call pendimethalin efficient for controlling blackgrass, regarding weed control efficacy, crop yield, treatment costs and environmental impact. [ 5 ] [ 6 ] [ 7 ]
There is some control of Johnsongrass , but other dinitrolaniline herbicides, such as trifluralin and profluralin , showed much stronger effect. [ 8 ]
In 2012, 6–12 million pounds (2,700–5,400 t) of pendimethalin was used in the US. [ 9 ]
Pendimethalin acts in both pre-weed-emergence and early post-emergence. Pendimethalin is absorbed into roots and shoots, inhibits cell division and prevents growth, [ 10 ] to prevent weeds from emerging, particularly during the development phase of the crop. Its primary mode of action is to prevent plant cell division and elongation in susceptible species. In the HRAC classification of herbicides according their mode of action, pendimethalin is listed in group K1, also called group D (Australia) or group 3 (numeric).
A study in the International Journal of Cancer suggests that Pendimethalin exposure is associated with higher incidence of pancreatic cancer . [ 11 ] Mechanistic studies linking Pendimethalin to pancreatic cancer are lacking, warranting additional research. A French study found no association with lung cancer. [ 12 ]
Pendimethalin exposure can reduce apoptosis . [ 13 ]
Herbicide resistance increases production costs and limits herbicide options, cultivations and rotations. Up to 2009 pendimethalin did not show resistance. It is not cross-resistant with other grass weed herbicides. So pendimethalin supports other supplementary grass weed herbicides using other modes of action. [ 14 ] Lolium rigidum has evolved resistance to pendimethalin, at least in part due to increased cytochrome P450 activity. [ 2 ] This resistance mechanism in ryegrass (shared with other dinitroanilines like trifluralin , see for longer explanation) is by an opposing mutation to resistance to prosulfocarb , a thiocarbamate herbicide. By evolving resistance to one, the weed devolves its resistance to the other. [ 15 ]
Pendimethalin is registered globally for a wide range of crops, according to human and environmental safety standards by the European Commission, US-EPA, Canada-PMRA, Japan, Brazil-ANVISA and others.
Pendimethalin is not toxic to mammals, though interestingly the oral LD 50 for rats and mice is 1050-1620 mg/kg, yet for dogs and rabbits it is much less harmful, at over 5000 mg/kg. For comparison, table salt 's LD 50 is 3000 mg/kg. There may be chronic effects however; repeated or prolonged skin exposure may cause eczema , hives or Quincke's oedema . Prolonged exposure by other routes may affect changes to the liver . [ 16 ]
Pendimethalin is highly persistent in soil and water. It has high potential for bioaccumulation, and it is moderately mobile in soil, [ 17 ] despite it adsorbing strongly into soil. [ 18 ]
Tradenames include Pendimethalin 440, Satellite, Halts, Prowl, PRE-M, Stomp, Stealth and Pendulum, Hilpendi etc. | https://en.wikipedia.org/wiki/Pendimethalin |
Pendular water is the moisture clinging to particles, such as soil particles or sand, because of surface tension . [ 1 ] [ 2 ]
At the moisture content of a specific yield , gravity drainage will cease. This term relates to hydrology and groundwater flow . | https://en.wikipedia.org/wiki/Pendular_water |
A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back towards the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging it back and forth. The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allow the equations of motion to be solved analytically for small-angle oscillations.
A simple gravity pendulum [ 1 ] is an idealized mathematical model of a real pendulum. [ 2 ] [ 3 ] [ 4 ] It is a weight (or bob ) on the end of a massless cord suspended from a pivot , without friction . Since in the model there is no frictional energy loss, when given an initial displacement it swings back and forth with a constant amplitude . The model is based on the assumptions:
The differential equation which governs the motion of a simple pendulum is
where g is the magnitude of the gravitational field , ℓ is the length of the rod or cord, and θ is the angle from the vertical to the pendulum.
Consider Figure 1 on the right, which shows the forces acting on a simple pendulum. Note that the path of the pendulum sweeps out an arc of a circle. The angle θ is measured in radians , and this is crucial for this formula. The blue arrow is the gravitational force acting on the bob, and the violet arrows are that same force resolved into components parallel and perpendicular to the bob's instantaneous motion. The direction of the bob's instantaneous velocity always points along the red axis, which is considered the tangential axis because its direction is always tangent to the circle. Consider Newton's second law , F = m a {\displaystyle F=ma} where F is the sum of forces on the object, m is mass, and a is the acceleration. Newton's equation can be applied to the tangential axis only. This is because only changes in speed are of concern and the bob is forced to stay in a circular path. The short violet arrow represents the component of the gravitational force in the tangential axis, and trigonometry can be used to determine its magnitude. Thus, F = − m g sin θ = m a , so a = − g sin θ , {\displaystyle {\begin{aligned}F&=-mg\sin \theta =ma,\qquad {\text{so}}\\a&=-g\sin \theta ,\end{aligned}}} where g is the acceleration due to gravity near the surface of the earth. The negative sign on the right hand side implies that θ and a always point in opposite directions. This makes sense because when a pendulum swings further to the left, it is expected to accelerate back toward the right.
This linear acceleration a along the red axis can be related to the change in angle θ by the arc length formulas; s is arc length: s = ℓ θ , v = d s d t = ℓ d θ d t , a = d 2 s d t 2 = ℓ d 2 θ d t 2 , {\displaystyle {\begin{aligned}s&=\ell \theta ,\\v&={\frac {ds}{dt}}=\ell {\frac {d\theta }{dt}},\\a&={\frac {d^{2}s}{dt^{2}}}=\ell {\frac {d^{2}\theta }{dt^{2}}},\end{aligned}}} thus: ℓ d 2 θ d t 2 = − g sin θ , d 2 θ d t 2 + g ℓ sin θ = 0. {\displaystyle {\begin{aligned}\ell {\frac {d^{2}\theta }{dt^{2}}}&=-g\sin \theta ,\\{\frac {d^{2}\theta }{dt^{2}}}+{\frac {g}{\ell }}\sin \theta &=0.\end{aligned}}}
Equation (1) can be obtained using two definitions for torque. τ = r × F = d L d t . {\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} ={\frac {d\mathbf {L} }{dt}}.}
First start by defining the torque on the pendulum bob using the force due to gravity. τ = l × F g , {\displaystyle {\boldsymbol {\tau }}=\mathbf {l} \times \mathbf {F} _{\mathrm {g} },} where l is the length vector of the pendulum and F g is the force due to gravity.
For now just consider the magnitude of the torque on the pendulum. | τ | = − m g ℓ sin θ , {\displaystyle |{\boldsymbol {\tau }}|=-mg\ell \sin \theta ,} where m is the mass of the pendulum, g is the acceleration due to gravity, l is the length of the pendulum, and θ is the angle between the length vector and the force due to gravity.
Next rewrite the angular momentum. L = r × p = m r × ( ω × r ) . {\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} =m\mathbf {r} \times ({\boldsymbol {\omega }}\times \mathbf {r} ).} Again just consider the magnitude of the angular momentum. | L | = m r 2 ω = m ℓ 2 d θ d t . {\displaystyle |\mathbf {L} |=mr^{2}\omega =m\ell ^{2}{\frac {d\theta }{dt}}.} and its time derivative d d t | L | = m ℓ 2 d 2 θ d t 2 , {\displaystyle {\frac {d}{dt}}|\mathbf {L} |=m\ell ^{2}{\frac {d^{2}\theta }{dt^{2}}},}
The magnitudes can then be compared using τ = d L / dt
− m g ℓ sin θ = m ℓ 2 d 2 θ d t 2 , {\displaystyle -mg\ell \sin \theta =m\ell ^{2}{\frac {d^{2}\theta }{dt^{2}}},} thus: d 2 θ d t 2 + g ℓ sin θ = 0 , {\displaystyle {\frac {d^{2}\theta }{dt^{2}}}+{\frac {g}{\ell }}\sin \theta =0,} which is the same result as obtained through force analysis.
It can also be obtained via the conservation of mechanical energy principle: any object falling a vertical distance h {\displaystyle h} would acquire kinetic energy equal to that which it lost to the fall. In other words, gravitational potential energy is converted into kinetic energy. Change in potential energy is given by Δ U = m g h . {\displaystyle \Delta U=mgh.}
The change in kinetic energy (body started from rest) is given by Δ K = 1 2 m v 2 . {\displaystyle \Delta K={\tfrac {1}{2}}mv^{2}.}
Since no energy is lost, the gain in one must be equal to the loss in the other 1 2 m v 2 = m g h . {\displaystyle {\tfrac {1}{2}}mv^{2}=mgh.}
The change in velocity for a given change in height can be expressed as v = 2 g h . {\displaystyle v={\sqrt {2gh}}.}
Using the arc length formula above, this equation can be rewritten in terms of dθ / dt : v = ℓ d θ d t = 2 g h , so d θ d t = 2 g h ℓ , {\displaystyle {\begin{aligned}v=\ell {\frac {d\theta }{dt}}&={\sqrt {2gh}},\quad {\text{so}}\\{\frac {d\theta }{dt}}&={\frac {\sqrt {2gh}}{\ell }},\end{aligned}}} where h is the vertical distance the pendulum fell. Look at Figure 2, which presents the trigonometry of a simple pendulum. If the pendulum starts its swing from some initial angle θ 0 , then y 0 , the vertical distance from the screw, is given by y 0 = ℓ cos θ 0 . {\displaystyle y_{0}=\ell \cos \theta _{0}.}
Similarly, when y 1 , then y 1 = ℓ cos θ . {\displaystyle y_{1}=\ell \cos \theta .}
Then h is the difference of the two h = ℓ ( cos θ − cos θ 0 ) . {\displaystyle h=\ell \left(\cos \theta -\cos \theta _{0}\right).}
In terms of dθ / dt gives
This equation is known as the first integral of motion , it gives the velocity in terms of the location and includes an integration constant related to the initial displacement ( θ 0 ). Next, differentiate by applying the chain rule , with respect to time to get the acceleration d d t d θ d t = d d t 2 g ℓ ( cos θ − cos θ 0 ) , d 2 θ d t 2 = 1 2 − 2 g ℓ sin θ 2 g ℓ ( cos θ − cos θ 0 ) d θ d t = 1 2 − 2 g ℓ sin θ 2 g ℓ ( cos θ − cos θ 0 ) 2 g ℓ ( cos θ − cos θ 0 ) = − g ℓ sin θ , d 2 θ d t 2 + g ℓ sin θ = 0 , {\displaystyle {\begin{aligned}{\frac {d}{dt}}{\frac {d\theta }{dt}}&={\frac {d}{dt}}{\sqrt {{\frac {2g}{\ell }}\left(\cos \theta -\cos \theta _{0}\right)}},\\{\frac {d^{2}\theta }{dt^{2}}}&={\frac {1}{2}}{\frac {-{\frac {2g}{\ell }}\sin \theta }{\sqrt {{\frac {2g}{\ell }}(\cos \theta -\cos \theta _{0})}}}{\frac {d\theta }{dt}}\\&={\frac {1}{2}}{\frac {-{\frac {2g}{\ell }}\sin \theta }{\sqrt {{\frac {2g}{\ell }}(\cos \theta -\cos \theta _{0})}}}{\sqrt {{\frac {2g}{\ell }}(\cos \theta -\cos \theta _{0})}}=-{\frac {g}{\ell }}\sin \theta ,\\{\frac {d^{2}\theta }{dt^{2}}}&+{\frac {g}{\ell }}\sin \theta =0,\end{aligned}}}
which is the same result as obtained through force analysis.
Equation 1 can additionally be obtained through Lagrangian Mechanics . More specifically, using the Euler–Lagrange equations (or Lagrange's equations of the second kind) by identifying the Lagrangian of the system ( L {\displaystyle {\mathcal {L}}} ), the constraints ( q {\displaystyle q} ) and solving the following system of equations
d d t ( ∂ L ∂ q j ˙ ) = ∂ L ∂ q j . {\displaystyle {\frac {d}{dt}}\left({\frac {\partial {\mathcal {L}}}{\partial {\dot {q_{j}}}}}\right)={\frac {\partial {\mathcal {L}}}{\partial q_{j}}}.}
If the origin of the Cartesian coordinate system is defined as the point of suspension (or simply pivot), then the bob is at
x = ℓ sin θ , {\displaystyle x=\ell \sin {\theta },} y = − ℓ cos θ , {\displaystyle y=-\ell \cos {\theta },}
and the velocity of the bob, calculated via differentiating the coordinates with respect to time (using dot notation to indicate the time derivatives)
x ˙ = ℓ θ ˙ cos θ , {\displaystyle {\dot {x}}=\ell {\dot {\theta }}\cos {\theta },} y ˙ = ℓ θ ˙ sin θ . {\displaystyle {\dot {y}}=\ell {\dot {\theta }}\sin {\theta }.}
Thus, the Lagrangian is
L = E k − E p = 1 2 m v 2 − m g h = 1 2 m ( x ˙ 2 + y ˙ 2 ) − m g ℓ ( 1 − cos θ ) = 1 2 m ℓ 2 θ ˙ 2 − m g ℓ + m g ℓ cos θ . {\displaystyle {\begin{aligned}{\mathcal {L}}&=E_{k}-E_{p}\\&={\frac {1}{2}}mv^{2}-mgh\\&={\frac {1}{2}}m({\dot {x}}^{2}+{\dot {y}}^{2})-mg\ell (1-\cos {\theta })\\&={\frac {1}{2}}m\ell ^{2}{\dot {\theta }}^{2}-mg\ell +mg\ell \cos {\theta }.\end{aligned}}}
The Euler-Lagrange equation (singular as there is only one constraint, q = θ {\displaystyle q=\theta } ) is thus
d d t ( ∂ L ∂ θ ˙ ) = ∂ L ∂ θ d d t ( m ℓ 2 θ ˙ ) = − m g ℓ sin θ m ℓ 2 θ ¨ = − m g ℓ sin θ θ ¨ = − g ℓ sin θ . {\displaystyle {\begin{aligned}{\frac {d}{dt}}\left({\frac {\partial {\mathcal {L}}}{\partial {\dot {\theta }}}}\right)&={\frac {\partial {\mathcal {L}}}{\partial \theta }}\\{\frac {d}{dt}}(m\ell ^{2}{\dot {\theta }})&=-mg\ell \sin {\theta }\\m\ell ^{2}{\ddot {\theta }}&=-mg\ell \sin {\theta }\\{\ddot {\theta }}&=-{\frac {g}{\ell }}\sin {\theta }.\\\end{aligned}}}
Which can then be rearranged to match Equation 1 , obtained through force analysis.
d 2 θ d t 2 + g ℓ sin θ = 0. {\displaystyle {\frac {d^{2}\theta }{dt^{2}}}+{\frac {g}{\ell }}\sin {\theta }=0.}
Deriving via Lagrangian Mechanics, while excessive with a single pendulum, is useful for more complicated, chaotic systems , such as a double pendulum .
The differential equation given above is not easily solved, and there is no solution that can be written in terms of elementary functions. However, adding a restriction to the size of the oscillation's amplitude gives a form whose solution can be easily obtained. If it is assumed that the angle is much less than 1 radian (often cited as less than 0.1 radians, about 6°), or θ ≪ 1 , {\displaystyle \theta \ll 1,} then substituting for sin θ into Eq. 1 using the small-angle approximation , sin θ ≈ θ , {\displaystyle \sin \theta \approx \theta ,} yields the equation for a harmonic oscillator , d 2 θ d t 2 + g ℓ θ = 0. {\displaystyle {\frac {d^{2}\theta }{dt^{2}}}+{\frac {g}{\ell }}\theta =0.}
The error due to the approximation is of order θ 3 (from the Taylor expansion for sin θ ).
Let the starting angle be θ 0 . If it is assumed that the pendulum is released with zero angular velocity , the solution becomes
θ ( t ) = θ 0 cos ( g ℓ t ) θ 0 ≪ 1. {\displaystyle \theta (t)=\theta _{0}\cos \left({\sqrt {\frac {g}{\ell }}}\,t\right)\quad \quad \quad \quad \theta _{0}\ll 1.}
The motion is simple harmonic motion where θ 0 is the amplitude of the oscillation (that is, the maximum angle between the rod of the pendulum and the vertical). The corresponding approximate period of the motion is then
T 0 = 2 π ℓ g θ 0 ≪ 1 {\displaystyle T_{0}=2\pi {\sqrt {\frac {\ell }{g}}}\quad \quad \quad \quad \quad \theta _{0}\ll 1}
which is known as Christiaan Huygens 's law for the period. Note that under the small-angle approximation, the period is independent of the amplitude θ 0 ; this is the property of isochronism that Galileo discovered.
T 0 = 2 π ℓ g {\displaystyle T_{0}=2\pi {\sqrt {\frac {\ell }{g}}}} gives ℓ = g π 2 T 0 2 4 . {\displaystyle \ell ={\frac {g}{\pi ^{2}}}{\frac {T_{0}^{2}}{4}}.}
If SI units are used (i.e. measure in metres and seconds), and assuming the measurement is taking place on the Earth's surface, then g ≈ 9.81 m/s 2 , and g / π 2 ≈ 1 m/s 2 (0.994 is the approximation to 3 decimal places).
Therefore, relatively reasonable approximations for the length and period are: ℓ ≈ T 0 2 4 , T 0 ≈ 2 ℓ {\displaystyle {\begin{aligned}\ell &\approx {\frac {T_{0}^{2}}{4}},\\T_{0}&\approx 2{\sqrt {\ell }}\end{aligned}}} where T 0 is the number of seconds between two beats (one beat for each side of the swing), and l is measured in metres.
For amplitudes beyond the small angle approximation , one can compute the exact period by first inverting the equation for the angular velocity obtained from the energy method ( Eq. 2 ), d t d θ = ℓ 2 g 1 cos θ − cos θ 0 {\displaystyle {\frac {dt}{d\theta }}={\sqrt {\frac {\ell }{2g}}}{\frac {1}{\sqrt {\cos \theta -\cos \theta _{0}}}}} and then integrating over one complete cycle, T = t ( θ 0 → 0 → − θ 0 → 0 → θ 0 ) , {\displaystyle T=t(\theta _{0}\rightarrow 0\rightarrow -\theta _{0}\rightarrow 0\rightarrow \theta _{0}),} or twice the half-cycle T = 2 t ( θ 0 → 0 → − θ 0 ) , {\displaystyle T=2t(\theta _{0}\rightarrow 0\rightarrow -\theta _{0}),} or four times the quarter-cycle T = 4 t ( θ 0 → 0 ) , {\displaystyle T=4t(\theta _{0}\rightarrow 0),} which leads to T = 4 ℓ 2 g ∫ 0 θ 0 d θ cos θ − cos θ 0 . {\displaystyle T=4{\sqrt {\frac {\ell }{2g}}}\int _{0}^{\theta _{0}}{\frac {d\theta }{\sqrt {\cos \theta -\cos \theta _{0}}}}.}
Note that this integral diverges as θ 0 approaches the vertical lim θ 0 → π T = ∞ , {\displaystyle \lim _{\theta _{0}\to \pi }T=\infty ,} so that a pendulum with just the right energy to go vertical will never actually get there. (Conversely, a pendulum close to its maximum can take an arbitrarily long time to fall down.)
This integral can be rewritten in terms of elliptic integrals as T = 4 ℓ g F ( π 2 , sin θ 0 2 ) {\displaystyle T=4{\sqrt {\frac {\ell }{g}}}F\left({\frac {\pi }{2}},\sin {\frac {\theta _{0}}{2}}\right)} where F is the incomplete elliptic integral of the first kind defined by F ( φ , k ) = ∫ 0 φ d u 1 − k 2 sin 2 u . {\displaystyle F(\varphi ,k)=\int _{0}^{\varphi }{\frac {du}{\sqrt {1-k^{2}\sin ^{2}u}}}\,.}
Or more concisely by the substitution sin u = sin θ 2 sin θ 0 2 {\displaystyle \sin {u}={\frac {\sin {\frac {\theta }{2}}}{\sin {\frac {\theta _{0}}{2}}}}} expressing θ in terms of u ,
T = 2 T 0 π K ( k ) , where k = sin θ 0 2 . {\displaystyle T={\frac {2T_{0}}{\pi }}K(k),\qquad {\text{where}}\quad k=\sin {\frac {\theta _{0}}{2}}.} Eq. 3
Here K is the complete elliptic integral of the first kind defined by
K ( k ) = F ( π 2 , k ) = ∫ 0 π 2 d u 1 − k 2 sin 2 u . {\displaystyle K(k)=F\left({\frac {\pi }{2}},k\right)=\int _{0}^{\frac {\pi }{2}}{\frac {du}{\sqrt {1-k^{2}\sin ^{2}u}}}\,.}
For comparison of the approximation to the full solution, consider the period of a pendulum of length 1 m on Earth ( g = 9.806 65 m/s 2 ) at an initial angle of 10 degrees is 4 1 m g K ( sin 10 ∘ 2 ) ≈ 2.0102 s . {\displaystyle 4{\sqrt {\frac {1{\text{ m}}}{g}}}\ K\left(\sin {\frac {10^{\circ }}{2}}\right)\approx 2.0102{\text{ s}}.} The linear approximation gives
2 π 1 m g ≈ 2.0064 s . {\displaystyle 2\pi {\sqrt {\frac {1{\text{ m}}}{g}}}\approx 2.0064{\text{ s}}.}
The difference between the two values, less than 0.2%, is much less than that caused by the variation of g with geographical location.
From here there are many ways to proceed to calculate the elliptic integral.
Given Eq. 3 and the Legendre polynomial solution for the elliptic integral: K ( k ) = π 2 ∑ n = 0 ∞ ( ( 2 n − 1 ) ! ! ( 2 n ) ! ! k n ) 2 {\displaystyle K(k)={\frac {\pi }{2}}\sum _{n=0}^{\infty }\left({\frac {(2n-1)!!}{(2n)!!}}k^{n}\right)^{2}} where n !! denotes the double factorial , an exact solution to the period of a simple pendulum is: T = 2 π ℓ g ( 1 + ( 1 2 ) 2 sin 2 θ 0 2 + ( 1 ⋅ 3 2 ⋅ 4 ) 2 sin 4 θ 0 2 + ( 1 ⋅ 3 ⋅ 5 2 ⋅ 4 ⋅ 6 ) 2 sin 6 θ 0 2 + ⋯ ) = 2 π ℓ g ⋅ ∑ n = 0 ∞ ( ( ( 2 n ) ! ( 2 n ⋅ n ! ) 2 ) 2 ⋅ sin 2 n θ 0 2 ) . {\displaystyle {\begin{alignedat}{2}T&=2\pi {\sqrt {\frac {\ell }{g}}}\left(1+\left({\frac {1}{2}}\right)^{2}\sin ^{2}{\frac {\theta _{0}}{2}}+\left({\frac {1\cdot 3}{2\cdot 4}}\right)^{2}\sin ^{4}{\frac {\theta _{0}}{2}}+\left({\frac {1\cdot 3\cdot 5}{2\cdot 4\cdot 6}}\right)^{2}\sin ^{6}{\frac {\theta _{0}}{2}}+\cdots \right)\\&=2\pi {\sqrt {\frac {\ell }{g}}}\cdot \sum _{n=0}^{\infty }\left(\left({\frac {(2n)!}{(2^{n}\cdot n!)^{2}}}\right)^{2}\cdot \sin ^{2n}{\frac {\theta _{0}}{2}}\right).\end{alignedat}}}
Figure 4 shows the relative errors using the power series. T 0 is the linear approximation, and T 2 to T 10 include respectively the terms up to the 2nd to the 10th powers.
Another formulation of the above solution can be found if the following Maclaurin series: sin θ 0 2 = 1 2 θ 0 − 1 48 θ 0 3 + 1 3 840 θ 0 5 − 1 645 120 θ 0 7 + ⋯ . {\displaystyle \sin {\frac {\theta _{0}}{2}}={\frac {1}{2}}\theta _{0}-{\frac {1}{48}}\theta _{0}^{3}+{\frac {1}{3\,840}}\theta _{0}^{5}-{\frac {1}{645\,120}}\theta _{0}^{7}+\cdots .} is used in the Legendre polynomial solution above.
The resulting power series is: [ 5 ]
T = 2 π ℓ g ( 1 + 1 16 θ 0 2 + 11 3 072 θ 0 4 + 173 737 280 θ 0 6 + 22 931 1 321 205 760 θ 0 8 + 1 319 183 951 268 147 200 θ 0 10 + 233 526 463 2 009 078 326 886 400 θ 0 12 + ⋯ ) , {\displaystyle T=2\pi {\sqrt {\frac {\ell }{g}}}\left(1+{\frac {1}{16}}\theta _{0}^{2}+{\frac {11}{3\,072}}\theta _{0}^{4}+{\frac {173}{737\,280}}\theta _{0}^{6}+{\frac {22\,931}{1\,321\,205\,760}}\theta _{0}^{8}+{\frac {1\,319\,183}{951\,268\,147\,200}}\theta _{0}^{10}+{\frac {233\,526\,463}{2\,009\,078\,326\,886\,400}}\theta _{0}^{12}+\cdots \right),} more fractions available in the On-Line Encyclopedia of Integer Sequences with OEIS : A223067 having the numerators and OEIS : A223068 having the denominators.
Given Eq. 3 and the arithmetic–geometric mean solution of the elliptic integral: K ( k ) = π 2 M ( 1 − k , 1 + k ) , {\displaystyle K(k)={\frac {\pi }{2M(1-k,1+k)}},} where M ( x , y ) is the arithmetic-geometric mean of x and y .
This yields an alternative and faster-converging formula for the period: [ 6 ] [ 7 ] [ 8 ] T = 2 π M ( 1 , cos θ 0 2 ) ℓ g . {\displaystyle T={\frac {2\pi }{M\left(1,\cos {\frac {\theta _{0}}{2}}\right)}}{\sqrt {\frac {\ell }{g}}}.}
The first iteration of this algorithm gives T 1 = 2 T 0 1 + cos θ 0 2 . {\displaystyle T_{1}={\frac {2T_{0}}{1+\cos {\frac {\theta _{0}}{2}}}}.}
This approximation has the relative error of less than 1% for angles up to 96.11 degrees. [ 6 ] Since 1 2 ( 1 + cos ( θ 0 2 ) ) = cos 2 θ 0 4 , {\textstyle {\frac {1}{2}}\left(1+\cos \left({\frac {\theta _{0}}{2}}\right)\right)=\cos ^{2}{\frac {\theta _{0}}{4}},} the expression can be written more concisely as T 1 = T 0 sec 2 θ 0 4 . {\displaystyle T_{1}=T_{0}\sec ^{2}{\frac {\theta _{0}}{4}}.}
The second order expansion of sec 2 ( θ 0 / 4 ) {\displaystyle \sec ^{2}(\theta _{0}/4)} reduces to T ≈ T 0 ( 1 + θ 0 2 16 ) . {\textstyle T\approx T_{0}\left(1+{\frac {\theta _{0}^{2}}{16}}\right).}
A second iteration of this algorithm gives T 2 = 4 T 0 1 + cos θ 0 2 + 2 cos θ 0 2 = 4 T 0 ( 1 + cos θ 0 2 ) 2 . {\displaystyle T_{2}={\frac {4T_{0}}{1+\cos {\frac {\theta _{0}}{2}}+2{\sqrt {\cos {\frac {\theta _{0}}{2}}}}}}={\frac {4T_{0}}{\left(1+{\sqrt {\cos {\frac {\theta _{0}}{2}}}}\right)^{2}}}.}
This second approximation has a relative error of less than 1% for angles up to 163.10 degrees. [ 6 ]
Though the exact period T {\displaystyle T} can be determined, for any finite amplitude θ 0 < π {\displaystyle \theta _{0}<\pi } rad, by evaluating the corresponding complete elliptic integral K ( k ) {\displaystyle K(k)} , where k ≡ sin ( θ 0 / 2 ) {\displaystyle k\equiv \sin(\theta _{0}/2)} , this is often avoided in applications because it is not possible to express this integral in a closed form in terms of elementary functions. This has made way for research on simple approximate formulae for the increase of the pendulum period with amplitude (useful in introductory physics labs, classical mechanics, electromagnetism, acoustics, electronics, superconductivity, etc. [ 9 ] The approximate formulae found by different authors can be classified as follows:
Of course, the increase of T {\displaystyle T} with amplitude is more apparent when π / 2 < θ 0 < π {\displaystyle \pi /2<\theta _{0}<\pi } , as has been observed in many experiments using either a rigid rod or a disc. [ 12 ] As accurate timers and sensors are currently available even in introductory physics labs, the experimental errors found in ‘very large-angle’ experiments are already small enough for a comparison with the exact period, and a very good agreement between theory and experiments in which friction is negligible has been found. Since this activity has been encouraged by many instructors, a simple approximate formula for the pendulum period valid for all possible amplitudes, to which experimental data could be compared, was sought. In 2008, Lima derived a weighted-average formula with this characteristic: [ 9 ] T ≈ r a 2 T Lima + k 2 T Cromer r a 2 + k 2 , {\displaystyle T\approx {\frac {r\,a^{2}\,T_{\text{Lima}}+k^{2}\,T_{\text{Cromer}}}{r\,a^{2}+k^{2}}},} where r = 7.17 {\displaystyle r=7.17} , which presents a maximum error of only 0.6% (at θ 0 = 95 ∘ {\displaystyle \theta _{0}=95^{\circ }} ).
The Fourier series expansion of θ ( t ) {\displaystyle \theta (t)} is given by [ 13 ] [ 14 ]
θ ( t ) = 8 ∑ n ≥ 1 odd ( − 1 ) ⌊ n / 2 ⌋ n q n / 2 1 + q n cos ( n ω t ) {\displaystyle \theta (t)=8\sum _{n\geq 1{\text{ odd}}}{\frac {(-1)^{\left\lfloor {n/2}\right\rfloor }}{n}}{\frac {q^{n/2}}{1+q^{n}}}\cos(n\omega t)}
where q {\displaystyle q} is the elliptic nome , q = exp ( − π K ( 1 − k 2 ) / K ( k ) ) , {\displaystyle q=\exp \left({-\pi K{\bigl (}{\sqrt {\textstyle 1-k^{2}}}{\bigr )}{\big /}K(k)}\right),} k = sin ( θ 0 / 2 ) , {\displaystyle k=\sin(\theta _{0}/2),} and ω = 2 π / T {\displaystyle \omega =2\pi /T} the angular frequency.
If one defines ε = 1 2 ⋅ 1 − cos ( θ 0 / 2 ) 1 + cos ( θ 0 / 2 ) {\displaystyle \varepsilon ={\frac {1}{2}}\cdot {\frac {1-{\sqrt {\cos(\theta _{0}/2)}}}{1+{\sqrt {\cos(\theta _{0}/2)}}}}} q {\displaystyle q} can be approximated using the expansion q = ε + 2 ε 5 + 15 ε 9 + 150 ε 13 + 1707 ε 17 + 20910 ε 21 + ⋯ {\displaystyle q=\varepsilon +2\varepsilon ^{5}+15\varepsilon ^{9}+150\varepsilon ^{13}+1707\varepsilon ^{17}+20910\varepsilon ^{21}+\cdots } (see OEIS : A002103 ). Note that ε < 1 2 {\displaystyle \varepsilon <{\tfrac {1}{2}}} for θ 0 < π {\displaystyle \theta _{0}<\pi } , thus the approximation is applicable even for large amplitudes.
Equivalently, the angle can be given in terms of the Jacobi elliptic function cd {\displaystyle \operatorname {cd} } with modulus k {\displaystyle k} [ 15 ] θ ( t ) = 2 arcsin ( k cd ( g ℓ t ; k ) ) , k = sin θ 0 2 . {\displaystyle \theta (t)=2\arcsin \left(k\operatorname {cd} \left({\sqrt {\frac {g}{\ell }}}t;k\right)\right),\quad k=\sin {\frac {\theta _{0}}{2}}.}
For small x {\displaystyle x} , sin x ≈ x {\displaystyle \sin x\approx x} , arcsin x ≈ x {\displaystyle \arcsin x\approx x} and cd ( t ; 0 ) = cos t {\displaystyle \operatorname {cd} (t;0)=\cos t} , so the solution is well-approximated by the solution given in Pendulum (mechanics)#Small-angle approximation .
The animations below depict the motion of a simple (frictionless) pendulum with increasing amounts of initial displacement of the bob, or equivalently increasing initial velocity. The small graph above each pendulum is the corresponding phase plane diagram; the horizontal axis is displacement and the vertical axis is velocity. With a large enough initial velocity the pendulum does not oscillate back and forth but rotates completely around the pivot.
A compound pendulum (or physical pendulum ) is one where the rod is not massless, and may have extended size; that is, an arbitrarily shaped rigid body swinging by a pivot O {\displaystyle O} . In this case the pendulum's period depends on its moment of inertia I O {\displaystyle I_{O}} around the pivot point.
The equation of torque gives: τ = I α {\displaystyle \tau =I\alpha } where: α {\displaystyle \alpha } is the angular acceleration. τ {\displaystyle \tau } is the torque
The torque is generated by gravity so: τ = − m g r ⊕ sin θ {\displaystyle \tau =-mgr_{\oplus }\sin \theta } where:
Hence, under the small-angle approximation, sin θ ≈ θ {\displaystyle \sin \theta \approx \theta } (or equivalently when θ m a x ≪ 1 {\displaystyle \theta _{\mathrm {max} }\ll 1} ), α = θ ¨ = m g r ⊕ I O sin θ ≈ − m g r ⊕ I O θ {\displaystyle \alpha ={\ddot {\theta }}={\frac {mgr_{\oplus }}{I_{O}}}\sin \theta \approx -{\frac {mgr_{\oplus }}{I_{O}}}\theta } where I O {\displaystyle I_{O}} is the moment of inertia of the body about the pivot point O {\displaystyle O} .
The expression for α {\displaystyle \alpha } is of the same form as the conventional simple pendulum and gives a period of [ 2 ] T = 2 π I O m g r ⊕ {\displaystyle T=2\pi {\sqrt {\frac {I_{O}}{mgr_{\oplus }}}}}
And a frequency of f = 1 T = 1 2 π m g r ⊕ I O {\displaystyle f={\frac {1}{T}}={\frac {1}{2\pi }}{\sqrt {\frac {mgr_{\oplus }}{I_{O}}}}}
If the initial angle is taken into consideration (for large amplitudes), then the expression for α {\displaystyle \alpha } becomes: α = θ ¨ = − m g r ⊕ I O sin θ {\displaystyle \alpha ={\ddot {\theta }}=-{\frac {mgr_{\oplus }}{I_{O}}}\sin \theta } and gives a period of: T = 4 K ( sin 2 θ m a x 2 ) I O m g r ⊕ {\displaystyle T=4\operatorname {K} \left(\sin ^{2}{\frac {\theta _{\mathrm {max} }}{2}}\right){\sqrt {\frac {I_{O}}{mgr_{\oplus }}}}} where θ m a x {\displaystyle \theta _{\mathrm {max} }} is the maximum angle of oscillation (with respect to the vertical) and K ( k ) {\displaystyle \operatorname {K} (k)} is the complete elliptic integral of the first kind .
An important concept is the equivalent length , ℓ e q {\displaystyle \ell ^{\mathrm {eq} }} , the length of a simple pendulums that has the same angular frequency ω 0 {\displaystyle \omega _{0}} as the compound pendulum: ω 0 2 = g ℓ e q := m g r ⊕ I O ⟹ ℓ e q = I O m r ⊕ {\displaystyle {\omega _{0}}^{2}={\frac {g}{\ell ^{\mathrm {eq} }}}:={\frac {mgr_{\oplus }}{I_{O}}}\implies \ell ^{\mathrm {eq} }={\frac {I_{O}}{mr_{\oplus }}}}
Consider the following cases:
ω 0 2 = m g r ⊕ I O = ( m b o b ℓ + m r o d ℓ 2 ) g m b o b ℓ 2 + 1 3 m r o d ℓ 2 = g ℓ m b o b + m r o d 2 m b o b + m r o d 3 = g ℓ 1 + m r o d 2 m b o b 1 + m r o d 3 m b o b {\displaystyle {\omega _{0}}^{2}={\frac {mgr_{\oplus }}{I_{O}}}={\frac {\left(m_{\mathrm {bob} }\ell +m_{\mathrm {rod} }{\frac {\ell }{2}}\right)g}{m_{\mathrm {bob} }\ell ^{2}+{\frac {1}{3}}m_{\mathrm {rod} }\ell ^{2}}}={\frac {g}{\ell }}{\frac {m_{\mathrm {bob} }+{\frac {m_{\mathrm {rod} }}{2}}}{m_{\mathrm {bob} }+{\frac {m_{\mathrm {rod} }}{3}}}}={\frac {g}{\ell }}{\frac {1+{\frac {m_{\mathrm {rod} }}{2m_{\mathrm {bob} }}}}{1+{\frac {m_{\mathrm {rod} }}{3m_{\mathrm {bob} }}}}}} Where ℓ e q = ℓ 1 + m r o d 3 m b o b 1 + m r o d 2 m b o b {\displaystyle \ell ^{\mathrm {eq} }=\ell {\frac {1+{\frac {m_{\mathrm {rod} }}{3m_{\mathrm {bob} }}}}{1+{\frac {m_{\mathrm {rod} }}{2m_{\mathrm {bob} }}}}}} . Notice these formulae can be particularized into the two previous cases studied before just by considering the mass of the rod or the bob to be zero respectively. Also notice that the formula does not depend on both the mass of the bob and the rod, but actually on their ratio, m r o d m b o b {\displaystyle {\frac {m_{\mathrm {rod} }}{m_{\mathrm {bob} }}}} . An approximation can be made for m r o d m b o b ≪ 1 {\displaystyle {\frac {m_{\mathrm {rod} }}{m_{\mathrm {bob} }}}\ll 1} :
ω 0 2 ≈ g ℓ ( 1 + 1 6 m r o d m b o b + ⋯ ) {\displaystyle {\omega _{0}}^{2}\approx {\frac {g}{\ell }}\left(1+{\frac {1}{6}}{\frac {m_{\mathrm {rod} }}{m_{\mathrm {bob} }}}+\cdots \right)}
Notice how similar it is to the angular frequency in a spring-mass system with effective mass .
The above discussion focuses on a pendulum bob only acted upon by the force of gravity. Suppose a damping force, e.g. air resistance, as well as a sinusoidal driving force acts on the body. This system is a damped, driven oscillator , and is chaotic .
Equation (1) can be written as
m l 2 d 2 θ d t 2 = − m g l sin θ {\displaystyle ml^{2}{\frac {d^{2}\theta }{dt^{2}}}=-mgl\sin \theta }
(see the Torque derivation of Equation (1) above).
A damping term and forcing term can be added to the right hand side to get
m l 2 d 2 θ d t 2 = − m g l sin θ − b d θ d t + a cos ( Ω t ) {\displaystyle ml^{2}{\frac {d^{2}\theta }{dt^{2}}}=-mgl\sin \theta -b{\frac {d\theta }{dt}}+a\cos(\Omega t)}
where the damping is assumed to be directly proportional to the angular velocity (this is true for low-speed air resistance, see also Drag (physics) ). a {\displaystyle a} and b {\displaystyle b} are constants defining the amplitude of forcing and the degree of damping respectively. Ω {\textstyle \Omega } is the angular frequency of the driving oscillations.
Dividing through by m l 2 {\textstyle ml^{2}} :
d 2 θ d t 2 + b m l 2 d θ d t + g l sin θ − a m l 2 cos ( Ω t ) = 0. {\displaystyle {\frac {d^{2}\theta }{dt^{2}}}+{\frac {b}{ml^{2}}}{\frac {d\theta }{dt}}+{\frac {g}{l}}{\sin \theta }-{\frac {a}{ml^{2}}}\cos(\Omega t)=0.}
For a physical pendulum:
d 2 θ d t 2 + b I d θ d t + m g r ⊕ I sin θ − a I cos ( Ω t ) = 0. {\displaystyle {\frac {d^{2}\theta }{dt^{2}}}+{\frac {b}{I}}{\frac {d\theta }{dt}}+{\frac {mgr_{\oplus }}{I}}{\sin \theta }-{\frac {a}{I}}\cos(\Omega t)=0.}
This equation exhibits chaotic behaviour . The exact motion of this pendulum can only be found numerically and is highly dependent on initial conditions, e.g. the initial velocity and the starting amplitude. However, the small angle approximation outlined above can still be used under the required conditions to give an approximate analytical solution.
The Jacobian elliptic function that expresses the position of a pendulum as a function of time is a doubly periodic function with a real period and an imaginary period. The real period is, of course, the time it takes the pendulum to go through one full cycle. Paul Appell pointed out a physical interpretation of the imaginary period: [ 16 ] if θ 0 is the maximum angle of one pendulum and 180° − θ 0 is the maximum angle of another, then the real period of each is the magnitude of the imaginary period of the other.
Coupled pendulums can affect each other's motion, either through a direction connection (such as a spring connecting the bobs) or through motions in a supporting structure (such as a tabletop). The equations of motion for two identical simple pendulums coupled by a spring connecting the bobs can be obtained using Lagrangian mechanics .
The kinetic energy of the system is: E K = 1 2 m L 2 ( θ ˙ 1 2 + θ ˙ 2 2 ) {\displaystyle E_{\text{K}}={\frac {1}{2}}mL^{2}\left({\dot {\theta }}_{1}^{2}+{\dot {\theta }}_{2}^{2}\right)} where m {\displaystyle m} is the mass of the bobs, L {\displaystyle L} is the length of the strings, and θ 1 {\displaystyle \theta _{1}} , θ 2 {\displaystyle \theta _{2}} are the angular displacements of the two bobs from equilibrium.
The potential energy of the system is: E p = m g L ( 2 − cos θ 1 − cos θ 2 ) + 1 2 k L 2 ( θ 2 − θ 1 ) 2 {\displaystyle E_{\text{p}}=mgL(2-\cos \theta _{1}-\cos \theta _{2})+{\frac {1}{2}}kL^{2}(\theta _{2}-\theta _{1})^{2}}
where g {\displaystyle g} is the gravitational acceleration , and k {\displaystyle k} is the spring constant . The displacement L ( θ 2 − θ 1 ) {\displaystyle L(\theta _{2}-\theta _{1})} of the spring from its equilibrium position assumes the small angle approximation .
The Lagrangian is then L = 1 2 m L 2 ( θ ˙ 1 2 + θ ˙ 2 2 ) − m g L ( 2 − cos θ 1 − cos θ 2 ) − 1 2 k L 2 ( θ 2 − θ 1 ) 2 {\displaystyle {\mathcal {L}}={\frac {1}{2}}mL^{2}\left({\dot {\theta }}_{1}^{2}+{\dot {\theta }}_{2}^{2}\right)-mgL(2-\cos \theta _{1}-\cos \theta _{2})-{\frac {1}{2}}kL^{2}(\theta _{2}-\theta _{1})^{2}} which leads to the following set of coupled differential equations: θ ¨ 1 + g L sin θ 1 + k m ( θ 1 − θ 2 ) = 0 θ ¨ 2 + g L sin θ 2 − k m ( θ 1 − θ 2 ) = 0 {\displaystyle {\begin{aligned}{\ddot {\theta }}_{1}+{\frac {g}{L}}\sin \theta _{1}+{\frac {k}{m}}(\theta _{1}-\theta _{2})&=0\\{\ddot {\theta }}_{2}+{\frac {g}{L}}\sin \theta _{2}-{\frac {k}{m}}(\theta _{1}-\theta _{2})&=0\end{aligned}}}
Adding and subtracting these two equations in turn, and applying the small angle approximation, gives two harmonic oscillator equations in the variables θ 1 + θ 2 {\displaystyle \theta _{1}+\theta _{2}} and θ 1 − θ 2 {\displaystyle \theta _{1}-\theta _{2}} : θ ¨ 1 + θ ¨ 2 + g L ( θ 1 + θ 2 ) = 0 θ ¨ 1 − θ ¨ 2 + ( g L + 2 k m ) ( θ 1 − θ 2 ) = 0 {\displaystyle {\begin{aligned}{\ddot {\theta }}_{1}+{\ddot {\theta }}_{2}+{\frac {g}{L}}(\theta _{1}+\theta _{2})&=0\\{\ddot {\theta }}_{1}-{\ddot {\theta }}_{2}+\left({\frac {g}{L}}+2{\frac {k}{m}}\right)(\theta _{1}-\theta _{2})&=0\end{aligned}}} with the corresponding solutions θ 1 + θ 2 = A cos ( ω 1 t + α ) θ 1 − θ 2 = B cos ( ω 2 t + β ) {\displaystyle {\begin{aligned}\theta _{1}+\theta _{2}&=A\cos(\omega _{1}t+\alpha )\\\theta _{1}-\theta _{2}&=B\cos(\omega _{2}t+\beta )\end{aligned}}} where ω 1 = g L ω 2 = g L + 2 k m {\displaystyle {\begin{aligned}\omega _{1}&={\sqrt {\frac {g}{L}}}\\\omega _{2}&={\sqrt {{\frac {g}{L}}+2{\frac {k}{m}}}}\end{aligned}}}
and A {\displaystyle A} , B {\displaystyle B} , α {\displaystyle \alpha } , β {\displaystyle \beta } are constants of integration .
Expressing the solutions in terms of θ 1 {\displaystyle \theta _{1}} and θ 2 {\displaystyle \theta _{2}} alone: θ 1 = 1 2 A cos ( ω 1 t + α ) + 1 2 B cos ( ω 2 t + β ) θ 2 = 1 2 A cos ( ω 1 t + α ) − 1 2 B cos ( ω 2 t + β ) {\displaystyle {\begin{aligned}\theta _{1}&={\frac {1}{2}}A\cos(\omega _{1}t+\alpha )+{\frac {1}{2}}B\cos(\omega _{2}t+\beta )\\\theta _{2}&={\frac {1}{2}}A\cos(\omega _{1}t+\alpha )-{\frac {1}{2}}B\cos(\omega _{2}t+\beta )\end{aligned}}}
If the bobs are not given an initial push, then the condition θ ˙ 1 ( 0 ) = θ ˙ 2 ( 0 ) = 0 {\displaystyle {\dot {\theta }}_{1}(0)={\dot {\theta }}_{2}(0)=0} requires α = β = 0 {\displaystyle \alpha =\beta =0} , which gives (after some rearranging): A = θ 1 ( 0 ) + θ 2 ( 0 ) B = θ 1 ( 0 ) − θ 2 ( 0 ) {\displaystyle {\begin{aligned}A&=\theta _{1}(0)+\theta _{2}(0)\\B&=\theta _{1}(0)-\theta _{2}(0)\end{aligned}}} | https://en.wikipedia.org/wiki/Pendulum_(mechanics) |
Penetrance in genetics is the proportion of individuals carrying a particular variant (or allele ) of a gene ( genotype ) that also expresses an associated trait ( phenotype ). In medical genetics , the penetrance of a disease -causing mutation is the proportion of individuals with the mutation that exhibit clinical symptoms among all individuals with such mutation. [ 1 ] For example: If a mutation in the gene responsible for a particular autosomal dominant disorder has 95% penetrance, then 95% of those with the mutation will go on to develop the disease, showing its phenotype, whereas 5% will not.
Penetrance only refers to whether an individual with a specific genotype exhibits any phenotypic signs or symptoms, and is not to be confused with variable expressivity which is to what extent or degree the symptoms for said disease are shown (the expression of the phenotypic trait). Meaning that, even if the same disease-causing mutation affects separate individuals, the expressivity will vary. [ 1 ] [ 2 ] [ 3 ]
If 100% of individuals carrying a particular genotype express the associated trait, the genotype is said to show complete penetrance. [ 1 ] Neurofibromatosis type 1 (NF1) , is an autosomal dominant condition which shows complete penetrance, consequently everyone who inherits the disease-causing variant of this gene will develop some degree of symptoms for NF1. [ 4 ]
The penetrance is said to be reduced if less than 100% of individuals carrying a particular genotype express associated traits, and is likely to be caused by a combination of genetic, environmental and lifestyle factors. [ 1 ] [ 3 ] BRCA1 is an example of a genotype with reduced penetrance. By age 70, the mutation is estimated to have a breast cancer penetrance of around 65% in women. Meaning that about 65% of women carrying the gene will develop breast cancer by the time they turn 70. [ 5 ]
Many factors such as age, sex, environment, epigenetic modifiers, and modifier genes are linked to penetrance. These factors can help explain why certain individuals with a specific genotype exhibit symptoms or signs of disease, whilst others do not. [ 1 ] [ 3 ]
If clinical signs associated with a specific genotype appear more frequently with increasing age, the penetrance is said to be age dependent. Some diseases are non-penetrant up until a certain age and then the penetrance starts to increase drastically, whilst others exhibit low penetrance at an early age and continue to increase with time. For this reason, many diseases have a different estimated penetrance dependent on the age. [ 1 ]
A specific hexanucleotide repeat expansion within the C9orf72 gene said to be a major cause for developing amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) is an example of a genotype with age dependent penetrance. The genotype is said to be non-penetrant until the age of 35, 50% penetrant by the age of 60, and almost completely penetrant by age 80. [ 1 ] [ 7 ]
For some mutations, the phenotype is more frequently present in one sex and in rare cases mutations appear completely non-penetrant in a particular gender. This is called gender-related penetrance or sex-dependent penetrance and may be the result of allelic variation, disorders in which the expression of the disease is limited to organs only found in one sex such as testis or ovaries, or sex steroid-responsive genes. [ 1 ] [ 3 ] [ 9 ] Breast cancer caused by the BRCA2 mutation is an example of a disease with gender-related penetrance. The penetrance is determined to be much higher in women than men. By age 70, around 86% of females in contrast to 6% of males with the same mutation is estimated to develop breast cancer. [ 9 ]
In cases where clinical symptoms or the phenotype related to a genetic mutation are present only in one sex, the disorder is said to be sex-limited. Familial male-limited precocious puberty (FMPP) caused by a mutation in the LHCGR gene, is an example of a genotype only penetrant in males. Meaning that males with this particular genotype exhibit symptoms of the disease whilst the same genotype is nonpenetrant in females. [ 3 ] [ 9 ] [ 10 ]
Genetic modifiers are genetic variants or mutations able to modify a primary disease-causing variant's phenotypic outcome without being disease causing themselves. [ 11 ] For instance, in single gene disorders there is one gene primarily responsible for development of the disease, but modifier genes inherited separately can affect the phenotype. Meaning that the presence of a mutation located on a loci different from the one with the disease-causing mutation, may either hinder manifestation of the phenotype or alter the mutations effects, and thereby influencing the penetrance. [ 1 ] [ 3 ]
Exposure to environmental and lifestyle factors such as chemicals , diet , alcohol intake , drugs and stress are some of the factors that might influence disease penetrance. [ 1 ] [ 12 ] For example, several studies of BRCA1 and BRCA2 mutations, associated with an elevated risk of breast and ovarian cancer in women, have examined associations with environmental and behavioral modifiers such as pregnancies , history of breast feeding , smoking , diet, and so forth. [ 13 ]
Sometimes, genetic alterations which can cause genetic disease and phenotypic traits, are not from changes related directly to the DNA sequence, but from epigenetic alterations such as DNA methylation or histone modifications . Epigenetic differences may therefore be one of the factors contributing to reduced penetrance. [ 1 ] [ 6 ] [ 14 ] A study done on a pair of genetically identical monozygotic twins , where one twin got diagnosed with leukemia and later on thyroid carcinoma whilst the other had no registered illnesses, showed that the affected twin had increased methylation levels of the BRCA 1 gene. The research concluded that the family had no known DNA-repair syndrome or any other hereditary diseases in the last four generations, and no genetic differences between the studied pair of monozygotic twins were detected in the BRCA1 regulatory region. This indicates that epigenetic changes caused by environmental or behavioral factors had a key role in the cause of promotor hypermethylation of the BRCA1 gene in the affected twin, which caused the cancer. [ 15 ]
It can be challenging to estimate the penetrance of a specific genotype due to all the influencing factors. In addition to the factors mentioned above there are several other considerations that must be taken into account when penetrance is determined:
Penetrance estimates can be affected by ascertainment bias if the sampling is not systematic. [ 16 ] Traditionally a phenotype-driven approach focusing on individuals with a given condition and their family members has been used to determine penetrance. However, it may be difficult to transfer these estimates over to the general population because family members may share other genetic and/or environmental factors that could influence manifestation of said disease, leading to ascertainment bias and an overestimation of the penetrance. Large-scale population-based studies, which use both genetic sequencing and phenotype data from large groups of people, is a different method for determining penetrance. This method offers less upward bias compared to family-based studies and is more accurate the larger the sample population is. However, these studies may contain a healthy-participant-bias which can lead to lower penetrance estimates. [ 16 ] [ 17 ] [ 18 ]
A genotype with complete penetrance will always display the clinical phenotypic traits related to its mutation (taking into consideration the expressivity), but the signs or symptoms displayed by a specific affected individual can often be similar to other unrelated phenotypical traits. Taking into consideration the effect that environmental or behavioral modifiers have, and how they can impact the cause of a mutation or epigenetic alteration, we now have the cause as to how different paths lead to the same phenotypic display. When similar phenotypes can be observed but by different causes, it is called phenocopies . Phenocopies is when environmental and/or behavioral modifiers causes an illness which mimics the phenotype of a genetic inherited disease. Because of phenocopies, determining the degree of penetrance for a genetic disease requires full knowledge of the individuals attending the studies, and the factors that may or may not have caused their illness. [ 6 ]
For example, new research on Hypertrophic Cardiomyopathy ( HCM ) based on a technique called Cardiac Magnetic Resonance (CMR), describes how various genetic illnesses that showcase the same phenotypic traits as HCM, are actually phenocopies. Previously these phenocopies were all diagnosed and treated, thought to arrive from the same cause, but because of new diagnostic methods, they can now be separated and treated more efficiently. [ 19 ] | https://en.wikipedia.org/wiki/Penetrance |
A biochemical penetrant is a chemical that increases the ability of a poison to apply its toxic effect to a living organism.
Typically, the term penetrant when used for a biochemical agent, relates to an agrichemical that is used with a weedkiller or fungicide . [ 1 ] The term seems to be used in relation to agrichemicals within English speaking countries rather than North American.
When mixed with a weedkiller (normally as an aqua solution) the penetrant chemical causes a plant to absorb the poison in a more effective manner and so succumb more readily. Penetrants are most often used against plants that would otherwise be able to resist the weedkiller . Often such plants have tough leaves or shiny leaves that shed water easily.
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Penetrant_(biochemical) |
Penetrants , or penetrating items , are the mechanical, electrical or structural items that pass through an opening in a wall or floor, such as pipes , electrical conduits , ducting , electrical cables and cable trays , or structural steel beams and columns. When these items pierce a wall or floor assembly, they create a space between the penetrant and the surrounding structure which can become an avenue for the spread of fire between rooms or floors. Building codes require a firestop to seal the openings around penetrants. | https://en.wikipedia.org/wiki/Penetrant_(mechanical,_electrical,_or_structural) |
Penetrating oil , also known as penetrating fluid , is a low-viscosity oil . It can be used to free rusted mechanical parts (such as nuts and bolts) so that they can be removed, because it can penetrate into the narrow space between the threads of two parts. It can also be used as a cleaner; however, it should not be used as a general-purpose lubricant or a corrosion stopper. Using penetrating fluids as general-purpose lubricants is not advisable, because such oils are relatively volatile . As a result, much of the penetrating oil will evaporate in a short amount of time, leaving little residual lubricant.
Other uses include removing chewing gum and adhesive stickers, and lessening friction on metal-stringed musical instruments.
This material -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Penetrating_oil |
A penetration , in firestopping , is an opening, such as one created by the use of a cast-in-place sleeve , in a wall or floor assembly required to have a fire-resistance rating , for the purpose of accommodating the passage of a mechanical, electrical, or structural penetrant . [ 1 ]
The penetration may or may not contain a firestop system. A penetration (opening) may or may not include a penetrant (something passing through the opening). | https://en.wikipedia.org/wiki/Penetration_(firestop) |
Penetration depth is a measure of how deep light or any electromagnetic radiation can penetrate into a material. It is defined as the depth at which the intensity of the radiation inside the material falls to 1/ e (about 37%) of its original value at (or more properly, just beneath) the surface.
When electromagnetic radiation is incident on the surface of a material, it may be (partly) reflected from that surface and there will be a field containing energy transmitted into the material. This electromagnetic field interacts with the atoms and electrons inside the material. Depending on the nature of the material, the electromagnetic field might travel very far into the material, or may die out very quickly. For a given material, penetration depth will generally be a function of wavelength .
According to Beer–Lambert law , the intensity of an electromagnetic wave inside a material falls off exponentially from the surface as
If δ p {\displaystyle \delta _{p}} denotes the penetration depth, we have
Penetration depth is one term that describes the decay of electromagnetic waves inside of a material. The above definition refers to the depth δ p {\displaystyle \delta _{p}} at which the intensity or power of the field decays to 1/e of its surface value. In many contexts one is concentrating on the field quantities themselves: the electric and magnetic fields in the case of electromagnetic waves. Since the power of a wave in a particular medium is proportional to the square of a field quantity, one may speak of a penetration depth at which the magnitude of the electric (or magnetic) field has decayed to 1/e of its surface value, and at which point the power of the wave has thereby decreased to 1 / e 2 {\displaystyle 1/e^{2}} or about 13% of its surface value:
Note that δ e {\displaystyle \delta _{e}} is identical to the skin depth , the latter term usually applying to metals in reference to the decay of electrical currents (which follow the decay in the electric or magnetic field due to a plane wave incident on a bulk conductor). The attenuation constant α / 2 {\displaystyle \alpha /2} is also identical to the (negative) real part of the propagation constant , which may also be referred to as α {\displaystyle \alpha } using a notation inconsistent with the above use. When referencing a source one must always be careful to note whether a number such as α {\displaystyle \alpha } or δ {\displaystyle \delta } refers to the decay of the field itself, or of the intensity (power) associated with that field. It can also be ambiguous as to whether a positive number describes attenuation (reduction of the field) or gain ; this is usually obvious from the context.
The attenuation constant for an electromagnetic wave at normal incidence on a material is also proportional to the imaginary part of the material's refractive index n . Using the above definition of α {\displaystyle \alpha } (based on intensity) the following relationship holds:
where n ~ {\displaystyle {\tilde {n}}} denotes the complex index of refraction , ω {\displaystyle \omega } is the radian frequency of the radiation, c is the speed of light in vacuum and λ {\displaystyle \lambda } is the wavelength. Note that n ~ ( ω ) {\displaystyle {\tilde {n}}(\omega )} is very much a function of frequency, as is its imaginary part which is often not mentioned (it is essentially zero for transparent dielectrics). The complex refractive index of metals is also infrequently mentioned but has the same significance, leading to a penetration depth (or skin depth δ e {\displaystyle \delta _{e}} ) accurately given by a formula which is valid up to microwave frequencies.
Relationships between these and other ways of specifying the decay of an electromagnetic field can be expressed by mathematical descriptions of opacity .
This is only specifying the decay of the field which may be due to absorption of the electromagnetic energy in a lossy medium or may simply describe the penetration of the field in a medium where no loss occurs (or a combination of the two). For instance, a hypothetical substance may have a complex index of refraction n ~ = 1 + .01 j {\displaystyle {\tilde {n}}=1+.01j} . A wave will enter that medium without significant reflection and will be totally absorbed in the medium with a penetration depth (in field strength) of δ e ≈ 16 λ {\displaystyle \delta _{e}\approx 16\lambda } , where λ {\displaystyle \lambda } is the vacuum wavelength. A different hypothetical material with a complex index of refraction n ~ = 0 + .01 j {\displaystyle {\tilde {n}}=0+.01j} will also have a penetration depth of 16 wavelengths, however in this case the wave will be perfectly reflected from the material! No actual absorption of the radiation takes place, however the electric and magnetic fields extend well into the substance. In either case the penetration depth is found directly from the imaginary part of the material's refractive index as is detailed above. | https://en.wikipedia.org/wiki/Penetration_depth |
Penetration enhancers (also called chemical penetration enhancers, absorption enhancers or sorption promotors) are chemical compounds that can facilitate the penetration of active pharmaceutical ingredients (API) into or through the poorly permeable biological membranes. These compounds are used in some pharmaceutical formulations to enhance the penetration of APIs in transdermal drug delivery and transmucosal drug delivery (for example, ocular, nasal, oral and buccal). [ 1 ] They typically penetrate into the biological membranes and reversibly decrease their barrier properties.
Human skin is a very impermeable membrane that protects the body from ingress of harmful substances and prevents water loss from underlying organs. However, this seriously limits the use of skin as a site for drug administration. One of the approaches to facilitate transdermal drug delivery is the use of penetration enhancers. Many different compounds have been explored as potential penetration enhancers to facilitate transdermal drug delivery. These include dimethylsulphoxide , azones (such as laurocapram ), pyrrolidones (for example 2-pyrrolidone ), alcohols ( ethanol and decanol ), glycols (for example propylene glycol ), surfactants, urea , various hydrocarbons and terpenes. [ 2 ] [ 3 ] [ 4 ] Different potential skin site and modes of action were identified for penetration enhancement through the skin. In some cases, penetration enhancers may disrupt the packing motif of the intercellular lipid matrix or keratin domains. In other cases, drug penetration to the skin is facilitated because the penetration enhancer saturates the tissue and becomes a better system to dissolve the molecules of API.
Topical administration to the eye is usually characterised by very poor drug bioavailability due to several natural defence mechanisms, including nasolacrymal drainage , blinking , and poor permeability of the cornea . Enhancement of the corneal permeability to drug molecules is one of the strategies to improve the efficiency of topical drug delivery to the eye. Several classes of compounds have been researched as potential penetration enhancers through ocular membranes. These include chelating agents , cyclodextrins , surfactants, bile acids and salts, and crown ethers . [ 5 ] There are also reports on the use of cell penetrating peptides and chitosan as penetration enhancers in ocular drug delivery. [ 6 ] The most commonly used penetration enhancers in ocular formulations are benzalkonium chloride and ethylenediamine tetraacetate (EDTA). Benzalkonium chloride is often used as an antimicrobial preservative in eye drops [ 7 ] and EDTA is used as a chelating agent.
Cyclodextrins, chitosan , some surfactants , bile acids and salts, sodium tauro-24,25-dihydro-fusidate , and phospholipids were reported as penetration enhancers in nasal drug delivery both for humans and equines. [ 8 ] Chitosan is one of the most widely researched penetration enhancers in nasal drug delivery and it enhances the penetration of drugs by opening the tight junctions in the cell membranes. [ 9 ]
Penetration enhancers have been applied to improve the absorption of poorly permeable, hydrophilic drugs or macromolecules. [ 10 ] Permeation enhancers that have been used successfully for oral drug development include medium-chain fatty acids such as caprylic acid (caprate) [ 11 ] or one of its amino acid esters such as salcaprozate sodium (SNAC). [ 12 ] The above-mentioned permeation/penetration enhancers have a surfactant-like activity where they perturb the intestinal epithelium, promoting transcellular or paracellular absorption. [ 13 ] | https://en.wikipedia.org/wiki/Penetration_enhancer |
A penetrometer is a device to test the strength of a material .
There are many types of penetrometer designed to be used on soil. They are usually round or cone shaped. The penetrometer is dropped on the test subject or pressed against it and the depth of the resulting hole is measured. The measurements find whether the soil is strong enough to build a road on. Scientists also use a penetrometer to measure how much moisture is in soil. Penetrometers are used by space probes such as the Cassini–Huygens probe, to measure the amount of moisture in soil on other planets. [ citation needed ] Penetrometers are furthermore used in glaciology to measure the strength and nature of materials underlying a glacier at its bed.
A penetrometer is also used in longer professional cricket matches, to measure how the pitch is holding up over the course of a multi-day match.
British horse racing courses have been required, since 2009, to report the readings obtained using a penetrometer, [ 1 ] on each day of a race meeting.
A penetrometer may be used in botany to find the toughness of a leaf by measuring the force needed to punch a hole of a certain size through the leaf.
Penetrometers are also used to measure the firmness of apples and other hard fruit. [ 2 ]
Penetrometers equipped with a known needle and mass are used to determine the hardness of bitumen and thus its efficacy and material properties when applied to roads as asphalt concrete .
Penetrometers are used for objective evaluation of food products. Penetrometers, equipped with a plunger and a needle or cone, penetrate food samples through gravitational force for a selected period of time. The distance the test device penetrates into the sample is measured to determine the relative tenderness of the samples such as baked products and gels. [ 3 ] | https://en.wikipedia.org/wiki/Penetrometer |
The Penex process is a continuous catalytic process used in the refining of crude oil . It isomerizes light naphtha (C 5 /C 6 ) into higher-octane, branched C 5 /C 6 molecules . It also reduces the concentration of benzene in the gasoline pool. [ 1 ] It was first used commercially in 1958. [ 2 ] Ideally, the isomerization catalyst converts normal pentane (nC5) to isopentane (iC5) and normal hexane (nC6) to 2,2- and 2,3-dimethylbutane. The thermodynamic equilibrium is more favorable at low temperature. [ 3 ]
In the petroleum industry , much research has been done on the upgrading of light hydrocarbons . The realisation that normal pentane is one of the most important remaining components of naphtha that can be easily upgraded prompted Phillips Petroleum to investigate the various processes for converting normal (linear) pentane into (branched) isopentane. The decisive factor in the isomerisation of normal pentane is an increase in the total octane number. This improvement in quality makes the result more valuable for blending with today's high-octane fuels. In addition, like other isoparaffins, isopentane has a low sensitivity (research octane minus engine octane) which means improved performance at street octane. Increasing the octane number also allows larger quantities of pentanes to be blended into premium petrol. [ 4 ]
In a refinery, light naphtha can come from the distillation column ("straight-run naphtha") or from other processes, for example the cracking units.
During isomerisation, the low-octane normal hydrocarbons are converted into their higher-octane isomers. For this purpose, the feed material is passed over a fixed bed catalyst in the presence of hydrogen. The hydrogen is continuously circulated in the reactor circuit. [ 5 ] The Penex process uses fixed-bed catalysts containing chlorides. [ 6 ]
As this is an equilibrium reaction, 100% conversion of the normal isomers is not achieved. The maximum octane number of the product is achieved by separating the unconverted normals using a molecular sieve (Molex technology) and returning them to the reactor. [ 5 ]
A single pass of feedstock with an octane rating of 50-60 through such a bed typically produces an end product rated at 82-86. If the feedstock is subsequently passed through a DIH (deisohexanizer) column, the end product typically has an octane rating of 87-90.5. If the feedstock is subsequently passed through a Molex-technology column, the end product typically has an octane rating of 88-91. If the feedstock is first passed through a DIP (deisopentanizer) column to remove iso-pentanes, then through the Penex bed, and subsequently through the DIH column, the end product typically has an octane rating of 91-93.
The Penex Process is licensed by the UOP corporation and currently utilized at more than 120 units at petroleum refineries and natural gas liquids plants throughout the world. [ 7 ]
This article related to natural gas, petroleum or the petroleum industry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Penex |
Peng Sixun ( Chinese : 彭司勛 ; 28 July 1919 – 9 December 2018) was a Chinese medicinal chemist.
A native of Baojing County , Peng was of Tujia descent. He graduated from the National College of Pharmacy in 1942, and completed a master's degree at Columbia University in 1950. Peng returned to teach at his alma mater, which had been renamed China Pharmaceutical University , and was elected to the Chinese Academy of Engineering in February 1996. Peng died at the age of 99 on 9 December 2018. [ 1 ]
This biographical article about a chemist is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Peng_Sixun |
A peniche (or stand-off [ 1 ] ) is material inserted between a half-model, often of an airplane , and the wall of a wind tunnel . Péniche is a French nautical term meaning barge. The purpose of the peniche is to remove or reduce the influence of the boundary layer on the half-model. [ 2 ] The effect of the peniche itself in fluid dynamics is not fully understood.
Half-models are used in wind-tunnel testing in aerodynamics , as larger scale half-models in constant pressure tunnels operate at increased Reynolds numbers closer to those of real aircraft. One trade-off is the interaction between the central part of the half-model and the wall boundary layer. [ 2 ] Inserting a peniche between the centre line of the half-model and the wall of the wind tunnel attempts to eliminate or reduce that boundary layer effect by creating distance between the model and the wall. Varying widths and shapes of peniches have been used; a peniche that follows the longitudinal cross section contour of the half-model is the simplest. [ 2 ]
The peniche itself affects the fluid dynamics around the half-model. It increases the local angle of attack on an inboard wing, while having no influence on an outboard wing. [ 3 ] The blocking of the peniche in the flow field leads to further displacement of the flow, which in turn leads to higher flow speeds and local angles of attack. [ 3 ] How strong of an effect the peniche has is a function of the angle of attack, with the effect present at all angles. [ 3 ] | https://en.wikipedia.org/wiki/Peniche_(fluid_dynamics) |
Penicillamine , sold under the brand name of Cuprimine among others, is a medication primarily used for the treatment of Wilson's disease . [ 1 ] It is also used for people with kidney stones who have high urine cystine levels , rheumatoid arthritis , and various heavy metal poisonings . [ 1 ] [ 2 ] It is taken by mouth. [ 2 ]
Penicillamine was approved for medical use in the United States in 1970. [ 1 ] It is on the World Health Organization's List of Essential Medicines . [ 3 ]
It is used as a chelating agent:
In cystinuria , a hereditary disorder in which high urine cystine levels lead to the formation of cystine stones, penicillamine binds with cysteine to yield a mixed disulfide which is more soluble than cystine. [ 8 ]
Penicillamine has been used to treat scleroderma . [ 9 ]
Penicillamine can be used as a disease-modifying antirheumatic drug (DMARD) to treat severe active rheumatoid arthritis in patients who have failed to respond to an adequate trial of conventional therapy, [ 10 ] although it is rarely used today due to availability of TNF inhibitors and other agents, such as tocilizumab and tofacitinib . Penicillamine works by reducing numbers of T-lymphocytes , inhibiting macrophage function, decreasing IL-1 , decreasing rheumatoid factor , and preventing collagen from cross-linking.
Common side effects include rash, loss of appetite, nausea, diarrhea, and low white blood cell levels . [ 1 ] Other serious side effects include liver problems , obliterative bronchiolitis , and myasthenia gravis . [ 1 ] It is not recommended in people with lupus erythematosus . [ 2 ] Use during pregnancy may result in harm to the baby. [ 2 ] Penicillamine works by binding heavy metals ; the resulting penicillamine–metal complexes are then removed from the body in the urine . [ 1 ]
Bone marrow suppression , dysgeusia , anorexia , vomiting , and diarrhea are the most common side effects , occurring in ~20–30% of the patients treated with penicillamine. [ 11 ] [ 12 ]
Other possible adverse effects include:
Penicillamine is a tri functional organic compound, consisting of a thiol , an amine , and a carboxylic acid . It is an amino acid structurally similar to cysteine , but with geminal dimethyl substituents α to the thiol. Like most amino acids, it is a colorless solid that exists in the zwitterionic form at physiological pH .
Penicillamine is a chiral molecule with one stereogenic center ; the two enantiomers have distinct physiological effects. ( S )-penicillamine ( D -penicillamine , having (–) optical rotation ) is used as aa drug (a chiral drug ). [ 19 ] ( R )-penicillamine ( L -penicillamine , having (+) optical rotation) is toxic because it inhibits the action of pyridoxine (also known as vitamin B 6 ). [ 20 ] D -penicillamine is a metabolite of penicillin but has no antibiotic properties itself. A variety of penicillamine–copper complexes are known. [ 21 ]
John Walshe first described the use of penicillamine in Wilson's disease in 1956. [ 22 ] He had discovered the compound in the urine of patients (including himself) who had taken penicillin , and experimentally confirmed that it increased urinary copper excretion by chelation . He had initial difficulty convincing several world experts of the time (Denny-Brown and Cumings) of its efficacy, as they held that Wilson's disease was not primarily a problem of copper homeostasis but of amino acid metabolism, and that dimercaprol should be used as a chelator. Later studies confirmed both the copper-centered theory and the efficacy of D -penicillamine. Walshe also pioneered other chelators in Wilson's such as triethylene tetramine and tetrathiomolybdate . [ 23 ]
Penicillamine was first synthesized by John Cornforth under supervision of Robert Robinson . [ 24 ]
Penicillamine has been used in rheumatoid arthritis since the first successful case in 1964. [ 25 ] | https://en.wikipedia.org/wiki/Penicillamine |
The Penman equation describes evaporation ( E ) from an open water surface, and was developed by Howard Penman in 1948. Penman's equation requires daily mean temperature , wind speed , air pressure , and solar radiation to predict E. Simpler Hydrometeorological equations continue to be used where obtaining such data is impractical, to give comparable results within specific contexts, e.g. humid vs arid climates.
Numerous variations of the Penman equation are used to estimate evaporation from water, and land. Specifically the Penman–Monteith equation refines weather based potential evapotranspiration (PET) estimates of vegetated land areas. [ 1 ] It is widely regarded as one of the most accurate models, in terms of estimates. [ citation needed ]
The original equation was developed by Howard Penman at the Rothamsted Experimental Station , Harpenden, UK.
The equation for evaporation given by Penman is:
where:
which (if the SI units in parentheses are used) will give the evaporation E mass in units of kg/(m 2 ·s), kilograms of water evaporated every second for each square meter of area.
Remove λ to obviate that this is fundamentally an energy balance. Replace λ v with L to get familiar precipitation units ET vol , where L v = λ v ρ water . This has units of m/s, or more commonly mm/day, because it is flux m 3 /s per m 2 =m/s.
This equation assumes a daily time step so that net heat exchange with the ground is insignificant, and a unit area surrounded by similar open water or vegetation so that net heat & vapor exchange with the surrounding area cancels out. Some times people replace R n with and A for total net available energy when a situation warrants account of additional heat fluxes.
Temperature , wind speed , relative humidity impact the values of m , g , c p , ρ , and δ e .
In 1993, W.Jim Shuttleworth modified and adapted the Penman equation to use SI , which made calculating evaporation simpler. [ 2 ] The resultant equation is:
where:
Therefore m = Δ = d e s d T a = 5336 T a 2 e ( 21.07 − 5336 T a ) {\displaystyle m=\Delta ={\frac {de_{s}}{dT_{a}}}={\frac {5336}{T_{a}^{2}}}e^{\left(21.07-{\frac {5336}{T_{a}}}\right)}} , mmHg/K | https://en.wikipedia.org/wiki/Penman_equation |
The Penman-Monteith equation approximates net evapotranspiration (ET) from meteorological data as a replacement for direct measurement of evapotranspiration. The equation is widely used, and was derived by the United Nations Food and Agriculture Organization for modeling reference evapotranspiration ET 0 . [ 1 ]
Evapotranspiration contributions are significant in a watershed's water balance , yet are often not emphasized in results because the precision of this component is often weak relative to more directly measured phenomena, e.g., rain and stream flow. In addition to weather uncertainties, the Penman-Monteith equation is sensitive to vegetation-specific parameters, e.g., stomatal resistance or conductance. [ 2 ]
Various forms of crop coefficients (K c ) account for differences between specific vegetation modeled and a reference evapotranspiration (RET or ET 0 ) standard. Stress coefficients (K s ) account for reductions in ET due to environmental stress (e.g. soil saturation reduces root -zone O 2 , low soil moisture induces wilt , air pollution effects, and salinity). Models of native vegetation cannot assume crop management to avoid recurring stress.
Per Monteith's Evaporation and Environment , [ 3 ] the equation is:
Note: Often, resistances are used rather than conductivities.
where r c refers to the resistance to flux from a vegetation canopy to the extent of some defined boundary layer.
The atmospheric conductance g a accounts for aerodynamic effects like the zero plane displacement height and the roughness length of the surface. The stomatal conductance g s accounts for the effect of leaf density (Leaf Area Index), water stress, and CO 2 concentration in the air, that is to say plant reaction to external factors. Different models exist to link the stomatal conductance to these vegetation characteristics, like the ones from P.G. Jarvis (1976) [ 4 ] or Jacobs et al. (1996). [ 5 ]
While the Penman-Monteith method is widely considered accurate for practical purposes and is recommended by the Food and Agriculture Organization of the United Nations, [ 1 ] errors when compared to direct measurement or other techniques can range from -9 to 40%. [ 6 ]
To avoid the inherent complexity of determining stomatal and atmospheric conductance, the Food and Agriculture Organization proposed in 1998 [ 1 ] a simplified equation for the reference evapotranspiration ET 0 . It is defined as the evapotranpiration for "[an] hypothetical reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s m-1 and an albedo of 0.23." This reference surface is defined to represent "an extensive surface of green grass of uniform height, actively growing, completely shading the ground and with adequate water".
The corresponding equation is:
N.B.: The coefficients 0.408 and 900 are not unitless but account for the conversion from energy values to equivalent water depths: radiation [mm day −1 ] = 0.408 radiation [MJ m −2 day −1 ].
This reference evapotranspiration ET 0 can then be used to evaluate the evapotranspiration rate ET from unstressed plants through crop coefficients K c : ET = K c * ET 0 . [ 1 ]
The standard methods of the American Society of Civil Engineers modify the standard Penman-Monteith equation for use with an hourly time step. The SWAT model is one of many GIS -integrated hydrologic models estimating ET using Penman-Monteith equations. [ 7 ]
The Priestley–Taylor equation was developed as a substitute for the Penman-Monteith equation to remove dependence on observations. For Priestley–Taylor, only radiation (irradiance) observations are required. This is done by removing the aerodynamic terms from the Penman-Monteith equation and adding an empirically derived constant factor, α {\displaystyle \alpha } .
The underlying concept behind the Priestley–Taylor model is that an air mass moving above a vegetated area with abundant water would become saturated with water. In these conditions, the actual evapotranspiration would match the Penman rate of reference evapotranspiration. However, observations revealed that actual evaporation was 1.26 times greater than reference evaporation. Therefore, the equation for actual evaporation was found by taking reference evapotranspiration and multiplying it by α {\displaystyle \alpha } . [ 8 ] The assumption here is for vegetation with an abundant water supply (i.e. the plants have low moisture stress). Areas like arid regions with high moisture stress are estimated to have higher α {\displaystyle \alpha } values. [ 9 ]
The assumption that an air mass moving over a vegetated surface with abundant water saturates has been questioned later. The atmosphere's lowest and most turbulent part, the atmospheric boundary layer , is not a closed box but constantly brings in dry air from higher up in the atmosphere towards the surface. As water evaporates more readily into a dry atmosphere, evapotranspiration is enhanced. This explains the larger-than-unity value of the Priestley-Taylor parameter α {\displaystyle \alpha } . The proper equilibrium of the system has been derived. It involves the characteristics of the interface of the atmospheric boundary layer and the overlying free atmosphere. [ 10 ] [ 11 ]
The equation is named after Howard Penman and John Monteith . Penman published his equation in 1948, and Monteith revised it in 1965. [ 3 ] | https://en.wikipedia.org/wiki/Penman–Monteith_equation |
A Penning mixture is a mixture of gases that is used in electric gas-discharge lamps . It is defined as a mixture of one inert gas with a minute amount of another gas, one that has lower ionization voltage than the main constituent. It is named after Frans Michel Penning . [ 1 ] [ 2 ]
The well-known neon lighting and neon lamps and displays are filled not with pure neon , but with a Penning mixture.
The other gas, called a quenching gas , has to have a lower ionization energy than the first excited state of the noble gas. The energy of the excited, but neutral, noble gas atoms then can ionize the quench gas particles by energy transfer via collisions; known as the Penning effect .
A very common Penning mixture of about 98–99.5% of neon with 0.5–2% argon is used in some neon lamps, especially those rated for 120 volts. The mixture is easier to ionize than either neon or argon alone, and lowers the breakdown voltage at which the tube becomes conductive and starts producing light. The optimal level of argon is about 0.25%, but some of it gets adsorbed onto the borosilicate glass used for the tubes, so higher concentrations are used to take the losses into account; higher argon content is used in higher-power tubes, as hotter glass adsorbs more argon. The argon changes the color of the "neon light", making it slightly more yellowish. The neon gas used in some nixie tubes includes a small amount of mercury vapor (for various reasons), which glows blue.
A Penning mixture of neon and argon is also used as a starter gas in sodium vapor lamps , where it is responsible for the faint pinkish glow before the sodium emission begins.
The Penning mixture used in plasma displays is usually helium or neon with small percentage of xenon , at several hundred torr .
Penning mixtures with the formulas of argon–xenon, neon–argon, argon– acetylene , and xenon– TMA are used as filler gases in gaseous ionization detectors .
Other kinds of Penning mixture include helium –xenon. | https://en.wikipedia.org/wiki/Penning_mixture |
A Penning trap is a device for the storage of charged particles using a homogeneous magnetic field and a quadrupole electric field . It is mostly found in the physical sciences and related fields of study for precision measurements of properties of ions and stable subatomic particles , like for example mass, [ 1 ] fission yields and isomeric yield ratios . One initial object of study was the so-called geonium atoms , which represent a way to measure the electron magnetic moment by storing a single electron. These traps have been used in the physical realization of quantum computation and quantum information processing by trapping qubits . Penning traps are in use in many laboratories worldwide, including CERN , to store and investigate anti-particles such as antiprotons . [ 2 ] The main advantages of Penning traps are the potentially long storage times and the existence of a multitude of techniques to manipulate and non-destructively detect the stored particles. [ 3 ] [ 4 ] This makes Penning traps versatile for the investigation of stored particles, but also for their selection, preparation or mere storage.
The Penning trap was named after F. M. Penning (1894–1953) by Hans Georg Dehmelt (1922–2017) who built the first trap. Dehmelt got inspiration from the vacuum gauge built by F. M. Penning where a current through a discharge tube in a magnetic field is proportional to the pressure. Citing from H. Dehmelt's autobiography: [ 5 ]
"I began to focus on the magnetron/Penning discharge geometry, which, in the Penning ion gauge, had caught my interest already at Göttingen and at Duke. In their 1955 cyclotron resonance work on photoelectrons in vacuum Franken and Liebes had reported undesirable frequency shifts caused by accidental electron trapping. Their analysis made me realize that in a pure electric quadrupole field the shift would not depend on the location of the electron in the trap. This is an important advantage over many other traps that I decided to exploit. A magnetron trap of this type had been briefly discussed in J.R. Pierce's 1949 book, and I developed a simple description of the axial, magnetron, and cyclotron motions of an electron in it. With the help of the expert glassblower of the Department, Jake Jonson, I built my first high vacuum magnetron trap in 1959 and was soon able to trap electrons for about 10 sec and to detect axial, magnetron and cyclotron resonances ." – H. Dehmelt
H. Dehmelt shared the Nobel Prize in Physics in 1989 for the development of the ion trap technique.
Penning traps use a strong homogeneous axial magnetic field to confine particles radially and a quadrupole electric field to confine the particles axially. [ 6 ] The static electric potential can be generated using a set of three electrodes : a ring and two endcaps. In an ideal Penning trap the ring and endcaps are hyperboloids of revolution. For trapping of positive (negative) ions, the endcap electrodes are kept at a positive (negative) potential relative to the ring. This potential produces a saddle point in the centre of the trap, which traps ions along the axial direction. The electric field causes ions to oscillate (harmonically in the case of an ideal Penning trap) along the trap axis. The magnetic field in combination with the electric field causes charged particles to move in the radial plane with a motion which traces out an epitrochoid .
The orbital motion of ions in the radial plane is composed of two modes at frequencies which are called the magnetron ω − {\displaystyle \omega _{-}} and the modified cyclotron ω + {\displaystyle \omega _{+}} frequencies. These motions are similar to the deferent and epicycle , respectively, of the Ptolemaic model of the solar system.
The sum of these two frequencies is the cyclotron frequency, which depends only on the ratio of electric charge to mass and on the strength of the magnetic field . This frequency can be measured very accurately and can be used to measure the masses of charged particles. Many of the highest-precision mass measurements (masses of the electron , proton , 2 H , 20 Ne and 28 Si ) come from Penning traps.
Buffer gas cooling, resistive cooling, and laser cooling are techniques to remove energy from ions in a Penning trap. Buffer gas cooling relies on collisions between the ions and neutral gas molecules that bring the ion energy closer to the energy of the gas molecules. In resistive cooling, moving image charges in the electrodes are made to do work through an external resistor, effectively removing energy from the ions. Laser cooling can be used to remove energy from some kinds of ions in Penning traps. This technique requires ions with an appropriate electronic structure . Radiative cooling is the process by which the ions lose energy by creating electromagnetic waves by virtue of their acceleration in the magnetic field. This process dominates the cooling of electrons in Penning traps, but is very small and usually negligible for heavier particles.
Using the Penning trap can have advantages over the radio frequency trap ( Paul trap ). Firstly, in the Penning trap only static fields are applied and therefore there is no micro-motion and resultant heating of the ions due to the dynamic fields, even for extended 2- and 3-dimensional ion Coulomb crystals. Also, the Penning trap can be made larger whilst maintaining strong trapping. The trapped ion can then be held further away from the electrode surfaces. Interaction with patch potentials on the electrode surfaces can be responsible for heating and decoherence effects and these effects scale as a high power of the inverse distance between the ion and the electrode.
Fourier-transform ion cyclotron resonance mass spectrometry (also known as Fourier-transform mass spectrometry) is a type of mass spectrometry used for determining the mass-to-charge ratio (m/z) of ions based on the cyclotron frequency of the ions in a fixed magnetic field. [ 7 ] The ions are trapped in a Penning trap where they are excited to a larger cyclotron radius by an oscillating electric field perpendicular to the magnetic field. The excitation also results in the ions moving in phase (in a packet). The signal is detected as an image current on a pair of plates which the packet of ions passes close to as they cyclotron. The resulting signal is called a free induction decay (fid), transient or interferogram that consists of a superposition of sine waves . The useful signal is extracted from this data by performing a Fourier transform to give a mass spectrum .
Single ions can be investigated in a Penning trap held at a temperature of 4 K. For this the ring electrode is segmented and opposite electrodes are connected to a superconducting coil and the source and the gate of a field-effect transistor . The coil and the parasitic capacitances of the circuit form a LC circuit with a Q of about 50 000. The LC circuit is excited by an external electric pulse. The segmented electrodes couple the motion of the single electron to the LC circuit. Thus the energy in the LC circuit in resonance with the ion slowly oscillates between the many electrons (10000) in the gate of the field effect transistor and the single electron. This can be detected in the signal at the drain of the field effect transistor.
A geonium atom is a pseudo-atomic system that consists of a single electron or ion stored in a Penning trap which is 'bound' to the remaining Earth, hence the term 'geonium'. [ 6 ] The name was coined by H.G. Dehmelt . [ 8 ]
In the typical case, the trapped system consists of only one particle or ion . Such a quantum system is determined by quantum states of one particle , like in the hydrogen atom . Hydrogen consists of two particles, the nucleus and electron, but the electron motion relative to the nucleus is equivalent to one particle in an external field, see center-of-mass frame .
The properties of geonium are different from a typical atom. The charge undergoes cyclotron motion around the trap axis and oscillates along the axis. An inhomogeneous magnetic "bottle field" is applied to measure the quantum properties by the "continuous Stern-Gerlach " technique. Energy levels and g-factor of the particle can be measured with high precision. [ 8 ] Van Dyck, et al. explored the magnetic splitting of geonium spectra in 1978 and in 1987 published high-precision measurements of electron and positron g-factors, which constrained the electron radius. [ citation needed ]
In November 2017, an international team of scientists isolated a single proton in a Penning trap in order to measure its magnetic moment to the highest precision to date. [ 9 ] It was found to be 2.792 847 344 62 (82) nuclear magnetons . The CODATA 2018 value matches this. [ 10 ] | https://en.wikipedia.org/wiki/Penning_trap |
The Penning–Malmberg trap ( PM trap ), named after Frans Penning and John Malmberg , is an electromagnetic device used to confine large numbers of charged particles of a single sign of charge. Much interest in Penning–Malmberg (PM) traps arises from the fact that if the density of particles is large and the temperature is low, the gas will become a single-component plasma. [ 1 ] While confinement of electrically neutral plasmas is generally difficult, single-species plasmas (an example of a non-neutral plasma ) can be confined for long times in PM traps. They are the method of choice to study a variety of plasma phenomena. They are also widely used to confine antiparticles such as positrons (i.e., anti-electrons) and antiprotons for use in studies of the properties of antimatter and interactions of antiparticles with matter. [ 2 ]
A schematic design of a PM trap is shown in Fig. 1. [ 1 ] [ 2 ] Charged particles of a single sign of charge are confined in a vacuum inside an electrode structure consisting of a stack of hollow, metal cylinders. A uniform axial magnetic field B {\displaystyle B} is applied to inhibit positron motion radially, and voltages are imposed on the end electrodes to prevent particle loss in the magnetic field direction. This is similar to the arrangement in a Penning trap , but with an extended confinement electrode to trap large numbers of particles (e.g., N ≥ 10 10 {\displaystyle N\geq 10^{10}} ).
Such traps are renowned for their good confinement properties. This is due to the fact that, for a sufficiently strong magnetic field, the canonical angular momentum L z {\displaystyle L_{z}} of the charge cloud (i.e., including angular momentum due to the magnetic field B) in the direction z {\displaystyle z} of the field is approximately [ 3 ]
where r j {\displaystyle r_{j}} is the radial position of the j {\displaystyle j} th particle, N {\displaystyle N} is the total number of particles, and ω c = e B / m {\displaystyle {\omega _{c}}=eB/m} is the cyclotron frequency , with particle mass m and charge e. If the system has no magnetic or electrostatic asymmetries in the plane perpendicular to B {\displaystyle B} , there are no torques on the plasma; thus L z {\displaystyle L_{z}} is constant, and the plasma cannot expand. As discussed below, these plasmas do expand due to magnetic and/or electrostatic asymmetries thought to be due to imperfections in trap construction.
The PM traps are typically filled using sources of low energy charged particles. In the case of electrons, this can be done using a hot filament or electron gun . [ 4 ] For positrons, a sealed radioisotope source and "moderator" (the latter used to slow the positrons to electron-volt energies) can be used. [ 2 ] Techniques have been developed to measure the plasma length, radius, temperature, and density in the trap, and to excite plasma waves and oscillations. [ 2 ] It is frequently useful to compress plasmas radially to increase the plasma density and/or to combat asymmetry-induced transport. [ 5 ] This can be accomplished by applying a torque on the plasma using rotating electric fields [the so-called "rotating wall" (RW) technique ], [ 6 ] [ 7 ] [ 8 ] or in the case of ion plasmas, using laser light. [ 9 ] Very long confinement times (hours or days) can be achieved using these techniques.
Particle cooling is frequently necessary to maintain good confinement (e.g., to mitigate the heating from RW torques). This can be accomplished in a number of ways, such as using inelastic collisions with molecular gases, [ 2 ] or in the case of ions, using lasers. [ 9 ] [ 10 ] In the case of electrons or positrons, if the magnetic field is sufficiently strong, the particles will cool by cyclotron radiation . [ 11 ]
The confinement and properties of single species plasmas in (what are now known as) PM traps was first studied by John Malmberg and John DeGrassie. [ 4 ] Confinement was shown to be excellent as compared to that for neutral plasmas. It was also shown that, while good, confinement is not perfect and there are particle losses.
Penning–Malmberg traps have been used to study a variety of transport mechanisms. Figure 2 shows an early study of confinement in a PM trap as a function of a background pressure of helium gas . At higher pressures, transport is due to electron-atom collisions, while at lower pressures, there is a pressure-independent particle loss mechanism. The latter (“anomalous transport”) mechanism has been shown to be due to inadvertent magnetic and electrostatic asymmetries and the effects of trapped particles. [ 5 ] There is evidence that confinement in PM traps is improved if the main confinement electrode (blue in Fig. 1) is replaced by a series of coaxial cylinders biased to create a smoothly varying potential well (a “multi-ring PM trap”). [ 12 ]
One fruitful area of research arises from the fact that plasmas in PM traps can be used to model the dynamics of inviscid two-dimensional fluid flows. [ 14 ] [ 15 ] [ 16 ] [ 17 ] PM traps are also the device of choice to accumulate and store anti-particles such as positrons and antiprotons. [ 2 ] One has been able to create positron and antiproton plasmas [ 18 ] and to study electron-beam positron plasma dynamics. [ 19 ]
Pure ion plasmas can be laser-cooled into crystalline states. [ 20 ] Cryogenic pure-ion plasmas are used to study quantum entanglement . [ 21 ] The PM traps also provide an excellent source for cold positron beams. They have been used to study with precision positronium (Ps) atoms (the bound state of a positron and an electron, lifetime ≤ 0.1 μs) and to create and study the positronium molecule (Ps 2 {\displaystyle _{2}} , e + e − e + e − {\displaystyle e^{+}e^{-}e^{+}e^{-}} ). [ 22 ] [ 23 ] Recently PM-trap-based positron beams have been used to produce practical Ps-atom beams. [ 24 ] [ 25 ] [ 26 ]
Antihydrogen is the bound state of an antiproton and a positron and the simplest antiatom. Nested PM traps (one for antiprotons and another for positrons) have been central to the successful efforts to create, trap and to compare the properties of antihydrogen with those of hydrogen. [ 27 ] [ 28 ] [ 29 ] The antiparticle plasmas (and electron plasmas used to cool the antiprotons) are carefully tuned with an array of recently developed techniques to optimize the production antihydrogen atoms. [ 30 ] These neutral antiatoms are then confined in a minimum-magnetic-field trap. [ 31 ] | https://en.wikipedia.org/wiki/Penning–Malmberg_trap |
The Pennsylvania State University Applied Research Laboratory (short: Penn State ARL or simply ARL ), is a specialized research unit dedicated to interdisciplinary scientific research at the Penn State University Park campus. The ARL is a DoD designated U.S. Navy University Affiliated Research Center . It is the university's largest research unit with over 1,000 faculty and staff. [ 1 ] The Laboratory ranks 2nd in DoD and 10th in NASA funding to universities. [ 2 ]
ARL maintains a long-term relationship with the Naval Sea Systems Command and the Office of Naval Research .
The ARL was established in 1945 by the U.S. Navy when the Harvard Underwater Sound Laboratory (USL) was terminated and its torpedo division was moved to Penn State. Eric Walker , the USL's assistant director, moved to Penn State to become its first director from 1945 until 1951, when he became Dean of the College of Engineering and Architecture. He would later become the Vice President for Research and then the President of the university, both in 1951.
Today, ARL operates over a dozen facilities ranging from acoustic research to fluid and nuclear.
The ARL is made of six distinct research divisions:
The Applied Research Laboratory operates a number of locations and off-site facilities. [ 3 ]
ARL operates the Structural Acoustics Laboratory which houses an array of tanks including an Acoustic Reverberant Tank and an Acoustic Test Tank for acoustic research projects. The facilities include complete instrumentation for measuring and calibrating transducers and transducer arrays. The Acoustic Test Tank is equipped with the instrumentation required for determining the acoustic characteristics of sonar devices designed for frequency response calibrations, radiation pattern plots, and impedance and admittance characterizations. [ 4 ]
Additionally, ARL operates a Large Anechoic Chamber with the "mission is to increase the knowledge and understanding of applied electromagnetics in key areas of defense and commercial systems utilizing communications, navigation, and sensor-based systems such as direction finding, for example." The facility is stationed in Warminster , Pennsylvania at the former Naval Air Warfare Center. [ 5 ]
The Garfield Thomas Water Tunnel was constructed shortly after the establishment of the ARL at Penn State in cooperation with the U.S. Navy for further torpedo research. The facility operates one of the largest circulating water tunnels in the world. It also operates an array of wind tunnels, glycerin tunnels, and anechoic chamber for used in many physics problems and experiments.
ARL operates the Advanced Nuclear Fuel Test Facility (ANFTF) [ 6 ] which is a Westinghouse-funded facility to test advanced power reactors and fuel component designs. The facility entered operation in 1996 with a fully functional 600 MWe nuclear power plant, the Westinghouse AP600 . The facility's objective is to characterize the effect of different fuel grid spacers on the onset of the departure from nucleate boiling (DNB) phenomenon and to quantify the critical heat flux (CHF) as the DNB event occurs. [ 7 ] [ 8 ]
On September 4, 2013 an agreement has been reached between the Applied Research Laboratory and NASA's Lyndon B. Johnson Space Center. [ 9 ] The laboratory created the Space Systems Initiative which would allow the space center to provide bipropellant rockets and liquid methane/liquid oxygen control engines with the university to enabling students to gain a better understanding of rocket performance. Data and results would be shared with NASA.
The Penn State Lunar Lion is a team within the Applied Research Laboratory as part of the Space Systems Initiative which has joined the Google Lunar X Prize . The team is expected to build a robotic spacecraft that is four feet in diameter and weighs 500 pounds. The team hopes to land the craft on the moon in December 2015. [ 10 ] The project includes over 500 students and 50 faculty members. | https://en.wikipedia.org/wiki/Pennsylvania_State_University_Applied_Research_Laboratory |
The penny battery is a voltaic pile which uses various coinage as the metal disks (pennies) of a traditional voltaic pile. The coins are stacked with pieces of electrolyte soaked paper in between (see diagram at right). The penny battery experiment is common during electrochemistry units in an educational setting.
Each cell in a penny battery can produce up to 0.8 volt , and many can be stacked together to produce higher voltages. Since the battery is a wet cell , the effectiveness will be reduced when the electrolyte evaporates.
As the name implies, Canadian pennies from 1997 to 1999 may serve the zinc electrode and 1942-1996 pennies as the copper . Alternatively, American pennies from 1982–present may be used as the zinc electrodes and 1944-1982 pennies as the copper electrodes. A variety of other coins can also be used, with varying results. [ 1 ] [ 2 ]
Batteries convert the chemical energy of the two metals (electrodes) interacting with the acid on the matboard (electrolyte) into electrical energy. In this situation, the metal surface serves as the electrode and an electric current (movement of electrons from one metal to the other) is created when the wire connects both metal surfaces. In the first hour, a five cell penny battery is able to provide about 5 × 10 −4 watts. Each cell is defined as a stack of a zinc penny, matboard, and a copper penny. Each cell can provide about 0.6 volts. Indicating that to power an LED light, needing 1.7 volts, only three cells need to be used. As time goes on the amount of energy that the battery can provide decreases. A five cell penny battery can last up to 6 + 1 ⁄ 2 hours providing minimal voltage. The stack of cells is also known as a voltaic pile. [ 3 ] [ 4 ] [ 5 ]
A penny battery functions as a standard voltaic pile , and is powered by a redox reaction between zinc and acid. Electrons flow through the electrolyte solution from zinc toward copper because zinc has a higher activity than copper. [ 6 ] The acid releases positively charged hydrogen ions that combine with these electrons to form hydrogen gas, which escapes to the atmosphere. The release of gas corresponds with a large increase in entropy , making the reaction irreversible .
The reaction can be written as two separate reactions in different regions of the cell, or as one overall reaction. The reactions shown here use acetic acid , but a variety of other acids can also be used.
Despite often being made of similar materials, this is not the same mechanism that powers a galvanic cell . Both types of cell can use acid as an electrolyte, copper as a cathode, and zinc as both an anode and as a substance to be oxidized. However they cause different substances to be reduced: voltaic piles reduce acid, and galvanic cells reduce copper. This is because galvanic cells contain dissolved copper ions, which can be reduced to form the more stable copper metal. Voltaic piles such as the penny battery start with all of their metal in solid form, so they don't contain any dissolved copper ions that can be reduced. | https://en.wikipedia.org/wiki/Penny_battery |
In mathematics and physics , Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions or tensors proposed by Roger Penrose in 1971. [ 1 ] A diagram in the notation consists of several shapes linked together by lines.
The notation widely appears in modern quantum theory , particularly in matrix product states and quantum circuits . In particular, categorical quantum mechanics (which includes ZX-calculus ) is a fully comprehensive reformulation of quantum theory in terms of Penrose diagrams.
The notation has been studied extensively by Predrag Cvitanović , who used it, along with Feynman's diagrams and other related notations in developing "birdtracks", a group-theoretical diagram to classify the classical Lie groups . [ 2 ] Penrose's notation has also been generalized using representation theory to spin networks in physics, and with the presence of matrix groups to trace diagrams in linear algebra .
In the language of multilinear algebra , each shape represents a multilinear function . The lines attached to shapes represent the inputs or outputs of a function, and attaching shapes together in some way is essentially the composition of functions .
In the language of tensor algebra , a particular tensor is associated with a particular shape with many lines projecting upwards and downwards, corresponding to abstract upper and lower indices of tensors respectively. Connecting lines between two shapes corresponds to contraction of indices . One advantage of this notation is that one does not have to invent new letters for new indices. This notation is also explicitly basis -independent. [ 3 ]
Each shape represents a matrix, and tensor multiplication is done horizontally, and matrix multiplication is done vertically.
The metric tensor is represented by a U-shaped loop or an upside-down U-shaped loop, depending on the type of tensor that is used.
The Levi-Civita antisymmetric tensor is represented by a thick horizontal bar with sticks pointing downwards or upwards, depending on the type of tensor that is used.
The structure constants ( γ a b c {\displaystyle {\gamma _{ab}}^{c}} ) of a Lie algebra are represented by a small triangle with one line pointing upwards and two lines pointing downwards.
Contraction of indices is represented by joining the index lines together.
Symmetrization of indices is represented by a thick zigzag or wavy bar crossing the index lines horizontally.
Antisymmetrization of indices is represented by a thick straight line crossing the index lines horizontally.
The determinant is formed by applying antisymmetrization to the indices.
The covariant derivative ( ∇ {\displaystyle \nabla } ) is represented by a circle around the tensor(s) to be differentiated and a line joined from the circle pointing downwards to represent the lower index of the derivative.
The diagrammatic notation is useful in manipulating tensor algebra. It usually involves a few simple " identities " of tensor manipulations.
For example, ε a . . . c ε a . . . c = n ! {\displaystyle \varepsilon _{a...c}\varepsilon ^{a...c}=n!} , where n is the number of dimensions, is a common "identity".
The Ricci and Bianchi identities given in terms of the Riemann curvature tensor illustrate the power of the notation
The notation has been extended with support for spinors and twistors . [ 4 ] [ 5 ] | https://en.wikipedia.org/wiki/Penrose_graphical_notation |
In the mathematical theory of games , the Penrose square root law , originally formulated by Lionel Penrose , concerns the distribution of the voting power in a voting body consisting of N members. [ 1 ] [ 2 ] [ 3 ] It states that the a priori voting power of any voter, measured by the Penrose–Banzhaf index ψ {\displaystyle \psi } scales like 1 / N {\displaystyle 1/{\sqrt {N}}} .
This result was used to design the Penrose method for allocating the voting weights of representatives in a decision-making bodies proportional to the square root of the population represented.
To estimate the voting index of any player one needs to estimate the number of the possible winning coalitions in which his vote is decisive. Assume for simplicity that the number of voters is odd, N = 2 j + 1, and the body votes according to the standard majority rule. Following Penrose one concludes that a given voter will be able to effectively influence the outcome of the voting only if the votes split half and half: if j players say 'Yes' and the remaining j players vote 'No', the last vote is decisive.
Assuming that all members of the body vote independently (the votes are uncorrelated)
and that the probability of each vote 'Yes' is equal to p = 1/2 one can estimate likelihood of such an event using the Bernoulli trial . The probability to obtain j votes 'Yes' out of 2 j votes reads
For large N we may use the Stirling's approximation for the factorial j ! and obtain the probability ψ {\displaystyle \psi } that the vote of a given voter is decisive
The same approximation is obtained for an even number N .
A mathematical investigation of the influence of possible correlations between the voters for the Penrose square root law was presented by Kirsch. [ 3 ]
Penrose law is applied to construct Penrose-like systems of two-tier voting, including the Jagiellonian Compromise designed for the Council of the European Union . | https://en.wikipedia.org/wiki/Penrose_square_root_law |
The Penrose triangle , also known as the Penrose tribar , the impossible tribar , [ 1 ] or the impossible triangle , [ 2 ] is a triangular impossible object , an optical illusion consisting of an object which can be depicted in a perspective drawing. It cannot exist as a solid object in ordinary three-dimensional Euclidean space, although its surface can be embedded isometrically (bent but not stretched) in five-dimensional Euclidean space. [ 3 ] It was first created by the Swedish artist Oscar Reutersvärd in 1934. [ 4 ] Independently from Reutersvärd, the triangle was devised and popularized in the 1950s by psychiatrist Lionel Penrose and his son, the mathematician and Nobel Prize laureate Roger Penrose , who described it as "impossibility in its purest form". [ 5 ] It is featured prominently in the works of artist M. C. Escher , whose earlier depictions of impossible objects partly inspired it.
The tribar/triangle appears to be a solid object, made of three straight beams of square cross-section which meet pairwise at right angles at the vertices of the triangle they form. The beams may be broken, forming cubes or cuboids.
This combination of properties cannot be realized by any three-dimensional object in ordinary Euclidean space . Such an object can exist in certain Euclidean 3-manifolds . [ 6 ] A surface with the same geodesic distances as the depicted surface of the tribar, but without its flat shape and right angles, are to be preserved, can also exist in 5-dimensional Euclidean space, which is the lowest-dimensional Euclidean space within which this surface can be isometrically embedded. [ 3 ] There also exist three-dimensional solid shapes each of which, when viewed from a certain angle, appears the same as the 2-dimensional depiction of the Penrose triangle, such as the sculpture "Impossible Triangle" in East Perth , Australia. [ 7 ] The term "Penrose Triangle" can refer to the 2-dimensional depiction or the impossible object itself.
If a line is traced around the Penrose triangle, a 4-loop Möbius strip is formed. [ 8 ]
M.C. Escher 's lithograph Waterfall (1961) depicts a watercourse that flows in a zigzag along the long sides of two elongated Penrose triangles, so that it ends up two stories higher than it began. The resulting waterfall, forming the short sides of both triangles, drives a water wheel . Escher points out that in order to keep the wheel turning, some water must occasionally be added to compensate for evaporation . A third Penrose triangle lies between the other two, formed by two segments of waterway and a support tower. [ 9 ] | https://en.wikipedia.org/wiki/Penrose_triangle |
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