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In mathematics, Zolotarev polynomials are polynomials used in approximation theory . They are sometimes used as an alternative to the Chebyshev polynomials where accuracy of approximation near the origin is of less importance. Zolotarev polynomials differ from the Chebyshev polynomials in that two of the coefficients are fixed in advance rather than allowed to take on any value. The Chebyshev polynomials of the first kind are a special case of Zolotarev polynomials. These polynomials were introduced by Russian mathematician Yegor Ivanovich Zolotarev in 1868.
Zolotarev polynomials of degree n {\displaystyle n} in x {\displaystyle x} are of the form
where σ {\displaystyle \sigma } is a prescribed value for a n − 1 {\displaystyle a_{n-1}} and the a k ∈ R {\displaystyle a_{k}\in \mathbb {R} } are otherwise chosen such that the deviation of Z n ( x ) {\displaystyle Z_{n}(x)} from zero is minimum in the interval [ − 1 , 1 ] {\displaystyle [-1,1]} . [ 1 ]
A subset of Zolotarev polynomials can be expressed in terms of Chebyshev polynomials of the first kind, T n ( x ) {\displaystyle T_{n}(x)} . For
then
For values of σ {\displaystyle \sigma } greater than the maximum of this range, Zolotarev polynomials can be expressed in terms of elliptic functions . For σ = 0 {\displaystyle \sigma =0} , the Zolotarev polynomial is identical to the equivalent Chebyshev polynomial. For negative values of σ {\displaystyle \sigma } , the polynomial can be found from the polynomial of the positive value, [ 2 ]
The Zolotarev polynomial can be expanded into a sum of Chebyshev polynomials using the relationship [ 3 ]
The original solution to the approximation problem given by Zolotarev was in terms of Jacobi elliptic functions . Zolotarev gave the general solution where the number of zeroes to the left of the peak value ( q {\displaystyle q} ) in the interval [ − 1 , 1 ] {\displaystyle [-1,1]} is not equal to the number of zeroes to the right of this peak ( p {\displaystyle p} ). The degree of the polynomial is n = p + q {\displaystyle n=p+q} . For many applications, p = q {\displaystyle p=q} is used and then only n {\displaystyle n} need be considered. The general Zolotarev polynomials are defined as [ 5 ]
The variation of the function within the interval [−1,1] is equiripple except for one peak which is larger than the rest. The position and width of this peak can be set independently. The position of the peak is given by [ 3 ]
The height of the peak is given by [ 3 ]
The Jacobi eta function can be defined in terms of a Jacobi auxiliary theta function , [ 7 ]
The polynomials were introduced by Yegor Ivanovich Zolotarev in 1868 as a means of uniformly approximating polynomials of degree x n + 1 {\displaystyle x^{n+1}} on the interval [−1,1]. Pafnuty Chebyshev had shown in 1858 that x n + 1 {\displaystyle x^{n+1}} could be approximated in this interval with a polynomial of degree at most n {\displaystyle n} with an error of 2 − n {\displaystyle 2^{-n}} . In 1868, Zolotarev showed that x n + 1 − σ x n {\displaystyle x^{n+1}-\sigma x^{n}} could be approximated with a polynomial of degree at most n − 1 {\displaystyle n-1} , two degrees lower. The error in Zolotarev's method is given by, [ 9 ]
The procedure was further developed by Naum Achieser in 1956. [ 10 ]
Zolotarev polynomials are used in the design of Achieser-Zolotarev filters . They were first used in this role in 1970 by Ralph Levy in the design of microwave waveguide filters . [ 11 ] Achieser-Zolotarev filters are similar to Chebyshev filters in that they have an equal ripple attenuation through the passband , except that the attenuation exceeds the preset ripple for the peak closest to the origin. [ 12 ]
Zolotarev polynomials can be used to synthesise the radiation patterns of linear antenna arrays , first suggested by D.A. McNamara in 1985. The work was based on the filter application with beam angle used as the variable instead of frequency. The Zolotarev beam pattern has equal-level sidelobes. [ 11 ]
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https://en.wikipedia.org/wiki/Zolotarev_polynomials
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A zombie satellite is a satellite that begins communicating again after an extended period of inactivity. It is a type of space debris , which describes all defunct human-made objects in outer space . At the end of their service life , the majority of satellites suffer from orbital decay and are destroyed by the heat of atmospheric entry . Zombie satellites, however, maintain a stable orbit but are either partially or completely inoperable, preventing operators from communicating with them consistently.
One of the oldest known zombie satellites is Transit 5B-5. [ 1 ] It was launched in 1965 as part of the Transit system, one of the first satellite navigation systems. [ 2 ] Transit 5B-5 is solar powered and still in a stable polar orbit , though operators are unable to control it.
LES-1 , also known as Lincoln Experimental Satellite 1, was a communications satellite launched by the United States Air Force on February 11, 1965, to study the use of Super High Frequency radio transmissions. It never achieved optimal orbit and was out of contact for more than 40 years before spontaneously resuming transmissions in 2012. [ 3 ] [ 4 ]
AMSAT-OSCAR 7 is an amateur-radio communications satellite which was launched into Low Earth Orbit on November 15, 1974, and remained operational until a battery failure in 1981. Then after 21 years of apparent silence, the satellite was heard again on June 21, 2002 – 27 years after launch.
Galaxy 15 is a U.S. telecommunications satellite launched in 2005. In April 2010, only five years into a planned 15-year mission, its operator, Intelsat , lost control of the satellite and it drifted out of its orbital slot . Several months later, on December 27, 2010, the satellite rebooted itself and began responding to commands again. [ 5 ] Intelsat re-positioned it back to its original orbital slot in April 2011.
Launched in 2000, IMAGE (Imager for Magnetopause-to-Aurora Global Exploration), a NASA spacecraft studying the Earth's magnetosphere , unexpectedly ceased operations in December 2005. It was a zombie satellite until Scott Tilley, an amateur radio operator living in Canada tracked it down in January 2018. [ 6 ] On February 25, contact with IMAGE was again lost. It was reestablished in March but lost again in August. NASA is currently evaluating a recovery mission. [ 7 ]
On March 24, 2020, contact with another lost Lincoln Experimental Satellite, LES-5, was made by Scott Tilley . [ 8 ] The satellite is only in operation when its solar panels are receiving sunlight.
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https://en.wikipedia.org/wiki/Zombie_satellite
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In paleontology , a zombie taxon [ 1 ] [ 2 ] (plural zombie taxa ) or the zombie effect refers to a fossil that was washed out of sediments and re-deposited in rocks and/or sediments millions of years younger. [ 3 ] That basic mistake in the interpretation of the age of the fossil leads to its title, [ 4 ] in that the discovered fossil was at some point mobile (or "walking") despite the original organism having been long dead. When that occurs, the fossil is described as a " reworked fossil ".
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https://en.wikipedia.org/wiki/Zombie_taxon
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A zome is a building designed using geometries different from of a series of rectangular boxes, used in a typical house or building. [ 1 ] The word zome was coined in 1968 by Nooruddeen Durkee (then Steve Durkee), combining the words dome and zonohedron . [ 2 ] One of the earliest models became a large climbing structure at the Lama Foundation . [ citation needed ]
Following his education at Amherst College and UCLA , Steve Baer studied mathematics at Eidgenössische Technische Hochschule ( Zurich , Switzerland ). Here he became interested in the possibilities of building innovative structures using polyhedra . Baer and his wife, Holly, moved back to the U.S. , settling in Albuquerque , New Mexico in the early 1960s. In New Mexico, he experimented with constructing buildings of unusual geometries (calling them by his friend Steve Durkee's term: "zomes" — see " Drop City ") — buildings intended to be appropriate to their environment, notably to utilize solar energy well. [ 3 ] He was fascinated with the dome geometry popularized by architect R. Buckminster Fuller . Baer was an occasional guest at Drop City, an arts and experimental community near Trinidad , CO. He wanted to design and construct buildings that didn't suffer from some of the limitations of the smaller, owner-built versions of geodesic domes (of the 'pure Fuller' design). [ citation needed ]
In recent years, the unconventional "zome" building-design approach with its multi-faceted geometric lines has been taken up by French builders in the Pyrenees. Home Work , a book published in 2004 and edited by Lloyd Kahn , has a section featuring these buildings. While many zomes built in the last couple decades have been wood-framed and made use of wood sheathing, much of what Baer himself originally designed and constructed involved metal framing with a sheet-metal outer skin. [ citation needed ]
Zomes have also been used in art , sculpture, and furniture. Zomadic, based in San Francisco, CA and founded by Rob Bell, incorporates zome geometry into artistic structures constructed primarily from CNC machined plywood components. Bell is a frequent attendee at Burning Man , a yearly artistic showcase event located in the Black Rock Desert of Nevada. [ citation needed ]
Richie Duncan of Kodama Zomes, based in southern Oregon has invented a structural system based on a hanging zome geometry, suspended from an overhead anchor point. Constructed of metal compressive elements and webbing tensile elements, the structures are able to be assembled and disassembled. This suspended zome system has been used in furniture, performing arts, and treehouse applications. [ citation needed ]
Yann Lipnick of Zomadic Concepts in France has an extensive study of, and multiple project construction of zomes in many different materials. He highlights the universal appeal and healing atmosphere that zomes provide and has training classes and reference books on zome construction. [ citation needed ]
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https://en.wikipedia.org/wiki/Zome_(architecture)
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Zometool is a construction set toy that had been created by a collaboration of Steve Baer (the creator of Zome architecture) , artist Clark Richert , Paul Hildebrandt (the present CEO of Zometool), and co-inventor Marc Pelletier. [ 1 ] [ 2 ] [ 3 ] It is manufactured by Zometool, Inc. According to the company, Zometool was primarily designed for kids. Zometool has also been used in other fields including mathematics and physics. For example, aperiodic tilings such as Penrose tilings can be modeled using Zometool. The learning tool was designed by inventor-designer Steve Baer, his wife Holly and others.
The Zometool plastic construction set toy is produced by a privately owned company of the same name, based outside of Longmont, Colorado , and which evolved out of Baer's company ZomeWorks. Its elements consist of small connector nodes and struts of various colors. The overall shape of a connector node is that of a non-uniform small rhombicosidodecahedron with each face replaced by a small hole. The ends of the struts are designed to fit in the holes of the connector nodes, allowing for syntheses of a variety of structures. The idea of shape-coding the three types of struts was developed by Marc Pelletier and Paul Hildebrandt. To create the "balls," or nodes, Pelletier and Hildebrandt invented a system of 62 hydraulic pins that came together to form a mold. The first connector node emerged from their mold on April 1, 1992. [ 3 ]
In the years since 1992, Zometool has extended its product line, though the basic design of the connector node has not changed so all parts to date are compatible with each-other. From 1992 until 2000, Zometool produced kits with connector nodes and blue, yellow, and red struts. In 2000, Zometool introduced green struts, prompted by French architect Fabien Vienne , which can be used to construct the regular tetrahedron and octahedron. In 2003, Zometool changed the style of the struts slightly. The struts "with clicks" have a different surface texture and they also have longer nibs which allow for a more robust connection between connector node and strut. [ citation needed ]
The color of a Zometool strut is associated with its cross section and also with the shape of the hole of the connector node in which it fits. Each blue strut has a rectangular cross section, each yellow strut has a triangular cross section, and each red strut has a pentagonal cross section. The cross section of a green strut is a rhombus of √2 aspect ratio, but as the connector nodes do not include holes at the required positions, the green struts instead fit into any of the 12 pentagonal holes with 5 possible orientations per hole, 60 possible orientations in all; using them is not as straightforward as the other struts.
At their midpoints, each of the yellow and red struts has a twist where the cross-sectional shape reverses. This design feature forces the connector nodes on the ends of the strut to have the same orientation. Similarly, the cross section of the blue strut is a non-square rectangle, again ensuring that the two nodes on the ends have the same orientation. Instead of a twist, the green struts have two bends which allow them to fit into the pentagonal holes of the connector node which are at a slight offset from the strut's axis. [ citation needed ]
Among other places, the word zome comes from the term zone. The zome system allows no more than 61 zones. The cross-sectional shapes correspond to colors, and in turn these correspond to zone colors. Hence the zome system has 15 blue zones, 10 yellow zones, 6 red zones, and 30 green zones. Two shapes are associated with blue. The blue struts with a rectangular cross section are designed to lie in the same zones as the blue struts, but they are half the length of a blue strut; hence these struts are often called "half-blue" (and were originally made in a light blue color). The blue-green struts with a rhombic cross section lie in the same zones as the green struts, but they are designed so that the ratio of a rhombic blue-green strut to a blue strut is 1:1 (as opposed to the green strut's √2:1). Due to this length ratio, the blue-green struts that have a rhombic cross section do not mathematically belong to the zome system. [ citation needed ]
The strut lengths follow a mathematical pattern: For any color, there exists lengths such that they increase by a constant factor of approximately 1.618, a number that is yield of what is called the “ golden ratio " which is represented by Greek letter phi ( φ {\displaystyle \varphi } or ϕ {\displaystyle \phi } ). [ 4 ] The golden ratio is a ratio such that the sum of two quantities is equal to the ratio of the same quantities, based on the largest value of the two numbers.
Thus,
An application of the golden ratio for the zome system is that for each color,
there exists a length such that a long strut length equals the length of a medium strut connected to a short strut.
In other words, the length of the long strut equals the sum of the medium strut length and the a short strut length.
A zome is defined in terms of the vector space R 3 {\displaystyle \mathbb {R} ^{3}} , equipped with the standard inner product, also known as 3-dimensional Euclidean space. [ citation needed ]
Let φ {\displaystyle \varphi } denote the golden ratio and let H 3 {\displaystyle H_{3}} denote the symmetry group of the configuration of vectors ( 0 , ± φ , ± 1 ) {\displaystyle (0,\pm \varphi ,\pm 1)} , ( ± φ , ± 1 , 0 ) {\displaystyle (\pm \varphi ,\pm 1,0)} , and ( ± 1 , 0 , ± φ ) {\displaystyle (\pm 1,0,\pm \varphi )} . The group H 3 {\displaystyle H_{3}} , an example of a Coxeter group , is known as the icosahedral group because it is the symmetry group of a regular icosahedron having these vectors as its vertices. The subgroup of H 3 {\displaystyle H_{3}} consisting of the elements with determinant 1 (i.e. the rotations) is isomorphic to A 5 {\displaystyle A_{5}} .
Define the "standard blue vectors" as the A 5 {\displaystyle A_{5}} -orbit of the vector ( 2 , 0 , 0 ) {\displaystyle (2,0,0)} . Define the "standard yellow vectors" as the A 5 {\displaystyle A_{5}} -orbit of the vector ( 1 , 1 , 1 ) {\displaystyle (1,1,1)} . Define the "standard red vectors" as the A 5 {\displaystyle A_{5}} -orbit of the vector ( 0 , φ , 1 ) {\displaystyle (0,\varphi ,1)} . A "strut" of the zome system is any vector which can be obtained from the standard vectors described above by scaling by any power φ n {\displaystyle \varphi ^{n}} , where n {\displaystyle n} is an integer. A "node" of the zome system is any element of the subgroup of R 3 {\displaystyle \mathbb {R} ^{3}} generated by the struts. Finally, the "zome system" is the set of all pairs ( N , S ) {\displaystyle (N,S)} , where N {\displaystyle N} is a set of nodes and S {\displaystyle S} is a set of pairs ( v , w ) {\displaystyle (v,w)} such that v {\displaystyle v} and w {\displaystyle w} are in N {\displaystyle N} and the difference v − w {\displaystyle v-w} is a strut.
There are then 30, 20, and 12 standard vectors having the colors blue, yellow, and red, respectively. Correspondingly, the stabilizer subgroup of a blue, yellow, or red strut is isomorphic to the cyclic group of order 2, 3, or 5, respectively. Hence, one may also describe the blue, yellow, and red struts as "rectangular", "triangular", and "pentagonal", respectively.
The zome system may be extended by adjoining green vectors. The "standard green vectors" comprise the A 5 {\displaystyle A_{5}} -orbit of the vector ( 2 , 2 , 0 ) {\displaystyle (2,2,0)} and a "green strut" as any vector which can be obtained by scaling a standard green vector by any integral power φ n {\displaystyle \varphi ^{n}} . As above, one may check that there are | A 5 | {\displaystyle |A_{5}|} =60 standard green vectors. One may then enhance the zome system by including these green struts. Doing this does not affect the set of nodes.
The abstract zome system defined above is significant because of the following fact: Every connected zome model has a faithful image in the zome system. The converse of this fact is only partially true, but this is due only to the laws of physics. For example, the radius of a zometool node is positive (as opposed to a node being a single point mathematically), so one cannot make a zometool model where two nodes are separated by an arbitrarily small, prescribed distance. Similarly, only a finite number of lengths of struts will ever be manufactured, and a green strut cannot be placed directly adjacent to a red strut or another green strut with which it shares the same hole (even though they are mathematically distinct). [ citation needed ]
The zome system is especially useful for modeling 1-dimensional skeletons of highly symmetric objects in 3- and 4-dimensional Euclidean space. The most prominent among these are the five Platonic Solids , and the 4-dimensional polytopes related to the 120-cell and the 600-cell . However, many other mathematical objects may be modeled using the zome system, including: [ citation needed ]
The uses of zome are not restricted to pure mathematics. Other uses include the study of engineering problems, especially steel-truss structures, the study of some molecular , nanotube , and viral structures, and to make soap film surfaces . [ citation needed ]
Software
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https://en.wikipedia.org/wiki/Zometool
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Zonal and meridional flow are directions and regions of fluid flow on a globe . Zonal flow follows a pattern along latitudinal lines, latitudinal circles or in the west–east direction. [ 1 ] Meridional flow follows a pattern from north to south, or from south to north, along the Earth's longitude lines, longitudinal circles ( meridian ) or in the north–south direction. [ 2 ] These terms are often used in the atmospheric and earth sciences to describe global phenomena, such as "meridional wind", or "zonal average temperature".
In the context of physics, zonal flow connotes a tendency of flux to conform to a pattern parallel to the equator of a sphere. In meteorological term regarding atmospheric circulation , zonal flow brings a temperature contrast along the Earth's longitude. Extratropical cyclones in zonal flows tend to be weaker, moving faster and producing relatively little impact on local weather.
Extratropical cyclones in meridional flows tend to be stronger and move slower. This pattern is responsible for most instances of extreme weather , as not only are storms stronger in this type of flow regime, but temperatures can reach extremes as well, producing heat waves and cold waves depending on the equator -ward or poleward direction of the flow.
For vector fields (such as wind velocity ), the zonal component (or x - coordinate ) is denoted as u , while the meridional component (or y -coordinate) is denoted as v .
In plasma physics , " zonal flow " means poloidal , which is the opposite from the meaning in planetary atmospheres and weather/climate studies.
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https://en.wikipedia.org/wiki/Zonal_and_meridional_flow
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In magnetic confinement fusion the zonal direction primarily connotes the poloidal direction (i.e. the short way around the torus ), the corresponding coordinate being denoted by y in the slab approximation or θ in magnetic coordinates. However, in the fusion context, usage is restricted to the context of zonal plasma flows and there will in general be a toroidal component in such flows as well. Thus, although the term zonal has come into use in plasma physics to emphasize an analogy with zonal flows in geophysics , it does not uniquely identify the direction of flow, unlike the case in geophysics.
This plasma physics –related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Zonal_and_poloidal
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In mathematics , a zonal polynomial is a multivariate symmetric homogeneous polynomial . The zonal polynomials form a basis of the space of symmetric polynomials. Zonal polynomials appear in special functions with matrix argument which on the other hand appear in matrixvariate distributions such as the Wishart distribution when integrating over compact Lie groups . The theory was started in multivariate statistics in the 1960s and 1970s in a series of papers by Alan Treleven James and his doctoral student Alan Graham Constantine . [ 1 ] [ 2 ] [ 3 ]
They appear as zonal spherical functions of the Gelfand pairs ( S 2 n , H n ) {\displaystyle (S_{2n},H_{n})} (here, H n {\displaystyle H_{n}} is the hyperoctahedral group) and ( G l n ( R ) , O n ) {\displaystyle (Gl_{n}(\mathbb {R} ),O_{n})} , which means that they describe canonical basis of the double class
algebras C [ H n ∖ S 2 n / H n ] {\displaystyle \mathbb {C} [H_{n}\backslash S_{2n}/H_{n}]} and C [ O d ( R ) ∖ M d ( R ) / O d ( R ) ] {\displaystyle \mathbb {C} [O_{d}(\mathbb {R} )\backslash M_{d}(\mathbb {R} )/O_{d}(\mathbb {R} )]} .
The zonal polynomials are the α = 2 {\displaystyle \alpha =2} case of the C normalization of the Jack function .
This algebra -related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Zonal_polynomial
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Zone Routing Protocol, or ZRP is a hybrid wireless networking routing protocol that uses both proactive and reactive routing protocols when sending information over the network. ZRP was designed to speed up delivery and reduce processing overhead by selecting the most efficient type of protocol to use throughout the route.
If a packet's destination is in the same zone as the origin, the proactive protocol using an already stored routing table is used to deliver the packet immediately.
If the route extends outside the packet's originating zone, a reactive protocol takes over to check each successive zone in the route to see whether the destination is inside that zone. This reduces the processing overhead for those routes. Once a zone is confirmed as containing the destination node, the proactive protocol, or stored route-listing table, is used to deliver the packet.
In this way packets with destinations within the same zone as the originating zone are delivered immediately using a stored routing table . Packets delivered to nodes outside the sending zone avoid the overhead of checking routing tables along the way by using the reactive protocol to check whether each zone encountered contains the destination node.
Thus ZRP reduces the control overhead for longer routes that would be necessary if using proactive routing protocols throughout the entire route, while eliminating the delays for routing within a zone that would be caused by the route-discovery processes of reactive routing protocols.
What is called the Intra-zone Routing Protocol (IARP), or a proactive routing protocol , is used inside routing zones. What is called the Inter-zone Routing Protocol (IERP), or a reactive routing protocol , is used between routing zones. IARP uses a routing table. Since this table is already stored, this is considered a proactive protocol. IERP uses a reactive protocol.
Any route to a destination that is within the same local zone is quickly established from the source's proactively cached routing table by IARP. Therefore, if the source and destination of a packet are in the same zone, the packet can be delivered immediately.
Most existing proactive routing algorithms can be used as the IARP for ZRP.
In ZRP a zone is defined around each node, called the node's k-neighborhood , which consists of all nodes within k hops of the node. Border nodes are nodes which are exactly k hops away from a source node.
For routes beyond the local zone, route discovery happens reactively. The source node sends a route request to the border nodes of its zone, containing its own address, the destination address and a unique sequence number. Each border node checks its local zone for the destination. If the destination is not a member of this local zone, the border node adds its own address to the route request packet and forwards the packet to its own border nodes. If the destination is a member of the local zone, it sends a route reply on the reverse path back to the source. The source node uses the path saved in the route reply packet to send data packets to the destination.
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https://en.wikipedia.org/wiki/Zone_Routing_Protocol
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Zone axis , a term sometimes used to refer to "high-symmetry" orientations in a crystal, most generally refers to any direction referenced to the direct lattice (as distinct from the reciprocal lattice ) of a crystal in three dimensions. It is therefore indexed with direct lattice indices, instead of with Miller indices .
High-symmetry zone axes through a crystal lattice, in particular, often lie in the direction of tunnels through the crystal between planes of atoms. This is because, as we see below, such zone axis directions generally lie within more than one plane of atoms in the crystal.
The translational invariance of a crystal lattice is described by a set of unit cell , direct lattice basis vectors ( contravariant [ 1 ] or polar ) called a , b , and c , or equivalently by the lattice parameters , i.e. the magnitudes of the vectors, called a , b and c , and the angles between them, called α (between b and c ), β (between c and a ), and γ (between a and b ). [ 2 ] [ 3 ] Direct lattice vectors have components measured in distance units, like meters (m) or angstroms (Å).
A lattice vector is indexed by its coordinates in the direct lattice basis system { a , b , c } {\displaystyle \{{\bf {a}},{\bf {b}},{\bf {c}}\}} and is generally placed between square brackets []. Thus a direct lattice vector s u v w {\displaystyle {\bf {s}}_{uvw}} , or [ u v w ] {\displaystyle [uvw]} , is defined as u a + v b + w c {\displaystyle u{\bf {a}}+v{\bf {b}}+w{\bf {c}}} . Angle brackets ⟨⟩ are used to refer to a symmetrically equivalent class of lattice vectors (i.e. the set of vectors generated by an action of the lattice's symmetry group ). In the case of a cubic lattice , for instance, ⟨100⟩ represents [100], [010], [001], [ 1 00], [0 1 0] and [00 1 ] because each of these vectors is symmetrically equivalent under a 90 degree rotation along an axis. A bar over a coordinate is equivalent to a negative sign (e.g., [ 1 ¯ 00 ] = − a {\displaystyle [{\overline {1}}00]=-{\bf {a}}} ).
The term "zone axis" more specifically refers to the direction of a direct-space lattice vector. For example, since the [120] and [240] lattice vectors are parallel, their orientations both correspond the ⟨120⟩ zone of the crystal. Just as a set of lattice planes in direct space corresponds to a reciprocal lattice vector in the complementary space of spatial frequencies and momenta, a "zone" is defined [ 4 ] [ 5 ] as a set of reciprocal lattice planes in frequency space that corresponds to a lattice vector in direct space.
The reciprocal space analog to a zone axis is a "lattice plane normal " or "g-vector direction". Reciprocal lattice vectors ( one-form [ 6 ] or axial ) are Miller-indexed using coordinates in the reciprocal lattice basis { a ∗ , b ∗ , c ∗ } {\displaystyle \{{\bf {a}}^{*},{\bf {b}}^{*},{\bf {c}}^{*}\}} instead, generally between round brackets () (similar to square brackets [] for direct lattice vectors). Curly brackets {} (not to be confused with a mathematical set ) are used to refer to a symmetrically equivalent class of reciprocal lattice vectors, similar to angle brackets ⟨⟩ for classes of direct lattice vectors.
Here, a ∗ ≡ ( b × c ) / V c {\displaystyle {\bf {a}}^{*}\equiv (b\times c)/V_{c}} , b ∗ ≡ ( c × a ) / V c {\displaystyle {\bf {b}}^{*}\equiv (c\times a)/V_{c}} , and c ∗ ≡ ( a × b ) / V c {\displaystyle {\bf {c}}^{*}\equiv (a\times b)/V_{c}} , where the unit cell volume is V c = a ⋅ ( b × c ) {\displaystyle V_{c}={\bf {a}}\cdot ({\bf {b}}\times {\bf {c}})} ( ⋅ {\displaystyle \cdot } denotes a dot product and × {\displaystyle \times } a cross product ). Thus a reciprocal lattice vector g h k l {\displaystyle {\bf {g}}_{hkl}} or ( h k l ) = h a ∗ + k b ∗ + l c ∗ {\displaystyle (hkl)=h{\bf {a}}^{*}+k{\bf {b}}^{*}+l{\bf {c}}^{*}} has a direction perpendicular to a crystallographic plane and a magnitude g h k l = 1 / d h k l {\displaystyle g_{hkl}=1/d_{hkl}} equal to the reciprocal of the spacing d h k l {\displaystyle d_{hkl}} between those ( h k l ) {\displaystyle (hkl)} planes, measured in spatial frequency units, e.g. of cycles per angstrom (cycles/Å).
A useful and quite general rule of crystallographic " dual vector spaces in 3D", e.g. reciprocal lattices, is that the condition for a direct lattice vector [ uvw ] (or zone axis) to be perpendicular to a reciprocal lattice vector ( hkl ) can be written with a dot product as [ u v w ] ⋅ ( h k l ) = u h + v k + w l = 0 {\displaystyle [uvw]\cdot (hkl)=uh+vk+wl=0} . This is true even if, as is often the case, the basis vector set used to describe the lattice is not Cartesian .
By extension, a [ uvw ] zone-axis pattern (ZAP) is a diffraction pattern taken with an incident beam, e.g. of electrons , X-rays or neutrons traveling along a lattice direction specified by the zone-axis indices [ uvw ]. Because of their small wavelength λ , high energy electrons used in electron microscopes have a very large Ewald sphere radius (1/λ), so that electron diffraction generally "lights up" diffraction spots with g-vectors ( hkl ) that are perpendicular to [ uvw ]. [ 7 ]
One result of this, as illustrated in the figure above, is that "low-index" zones are generally perpendicular to "low- Miller index " lattice planes, which in turn have small spatial frequencies (g-values) and hence large lattice periodicities (d-spacings). A possible intuition behind this is that in electron microscopy, for electron beams to be directed down wide (i.e. easily visible) tunnels between columns of atoms in a crystal, directing the beam down a low-index (and by association high-symmetry) zone axis may help. [ 8 ] [ 9 ] [ 10 ] [ 11 ]
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https://en.wikipedia.org/wiki/Zone_axis
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A zone valve is a specific type of valve used to control the flow of water or steam in a hydronic heating or cooling system.
In the interest of improving efficiency and occupant comfort, such systems are commonly divided up into multiple zones. [ 1 ] For example, in a house, the main floor may be served by one heating zone while the upstairs bedrooms are served by another. In this way, the heat can be directed principally to the main floor during the day and principally to the bedrooms at night, allowing the unoccupied areas to cool down.
This zoning can be accomplished in one of two ways:
Zone valves as used in home hydronic systems are usually electrically powered. In large commercial installations, vacuum or compressed air may be used instead. In either case, the motor is usually connected to the water valve via a mechanical coupling.
For electrical zone valves, the motor is often a small shaded-pole synchronous motor combined with a rotary switch that can disconnect the motor at either of the two stopping points ("valve open" or "valve closed"). In this way, applying power to the "open valve" terminal causes the motor to run until the valve is open while applying power at the "close valve" terminal causes the motor to run until the valve is closed. The motor is commonly powered from the same 24 volt ac power source that is used for the rest of the control system. This allows the zone valves to be directly controlled by low-voltage thermostats and wired with low-voltage wiring. This style of valve requires the use of an SPDT thermostat or relay .
A simpler variant of the motorized design omits the switch that detects the valve position. The motor is simply driven until the valve hits a mechanical stop, which stalls the motor. In an alternative design, the motor continues to turn, while a slip clutch allows the valve to be pushed against a mechanical stop. Usually, the valve remains open as long as power is supplied, and a strong spring closes it when power is cut. This simpler design consumes electrical power whenever the valve is open. There is no feedback to verify the state of the valve, which is assumed to do what has been commanded.
Zone valves can also be constructed using wax motors and a spring-return mechanism. In this case, the valve is normally closed by the force of the spring but can be opened by the force of the wax motor. Removal of electrical power re-closes the valve. This style of zone valve operates with a perfectly ordinary SPST thermostat.
For vacuum- or pneumatically operated zone valves, the thermostat usually switches the pressure or vacuum on or off, causing a spring-loaded rubber diaphragm or ball valve to move and actuate the valve. [ 2 ] Unlike the switch-monitored electrical zone valves, these valves automatically return to the default position without the application of any power, and the default position is usually "open", allowing heat to flow.
Highly sophisticated systems may use some form of building automation such as BACnet or LonWorks to control the zone valves.
Multiple zones can be implemented using either multiple, individually controlled circulator pumps or a single pump and multiple zone valves. Each approach has advantages and disadvantages.
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https://en.wikipedia.org/wiki/Zone_valve
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A zoo (short for zoological garden ; also called an animal park or menagerie ) is a facility in which animals are kept within enclosures for public exhibition and often bred for conservation purposes. [ 1 ]
The term zoological garden refers to zoology , the study of animals. The term is derived from the Ancient Greek ζῷον , zōion , 'animal', and the suffix -λογία , -logia , 'study of'. The abbreviation zoo was first used of the London Zoological Gardens , which was opened for scientific study in 1828, and to the public in 1847. [ 2 ] The first modern zoo was the Tierpark Hagenbeck by Carl Hagenbeck in Germany .
In the United States alone, zoos are visited by over 181 million people annually. [ 3 ]
The London Zoo , which was opened in 1828, was initially known as the "Gardens and Menagerie of the Zoological Society of London", and it described itself as a menagerie or "zoological forest". [ 4 ] The abbreviation "zoo" first appeared in print in the United Kingdom around 1847, when it was used for the Clifton Zoo , but it was not until some 20 years later that the shortened form became popular in the rhyming song " Walking in the Zoo " by music-hall artist Alfred Vance . [ 4 ] The term "zoological park" was used for more expansive facilities in Halifax, Nova Scotia , Washington, D.C. , and the Bronx in New York, which opened in 1846, 1891 and 1899 respectively. [ 5 ]
Relatively new terms for zoos, in the late 20th century are " conservation park" or "bio park". Adopting a new name is a strategy used by some zoo professionals to distance their institutions from the stereotypical and nowadays criticized zoo concept of the 19th century. [ 6 ] The term "bio park" was first coined and developed by the National Zoo in Washington D.C. in the late 1980s. [ 7 ] In 1993, the New York Zoological Society changed its name to the Wildlife Conservation Society and re branded the zoos under its jurisdiction as "wildlife conservation parks". [ 8 ]
The predecessor of the zoological garden is the menagerie , which has a long history from the ancient world to modern times. The oldest known zoological collection was revealed during excavations at Hierakonpolis , Egypt in 2009, of a c. 3500 BCE menagerie. The exotic animals included hippos , hartebeest , elephants , baboons and wildcats . [ 9 ] King Ashur-bel-kala of the Middle Assyrian Empire created zoological and botanical gardens in the 11th century BCE. In the 2nd century BCE, the Chinese Empress Tanki had a "house of deer" built, and King Wen of Zhou kept a 1,500-acre (6.1 km 2 ) zoo called Ling-Yu, or the Garden of Intelligence. Other well-known collectors of animals included King Solomon of the Kingdom of Israel and Judah , Queen Semiramis and King Ashurbanipal of Assyria , and King Nebuchadnezzar of Babylonia . [ 10 ] By the 4th century BCE, zoos existed in most of the Greek city states; Alexander the Great is known to have sent animals that he found on his military expeditions back to Greece. The Roman emperors kept private collections of animals for study or for use in the arena, [ 10 ] the latter faring notoriously poorly. The 19th-century historian W. E. H. Lecky wrote of the Roman games , first held in 366 BCE:
At one time, a bear and a bull , chained together, rolled in fierce combat across the sand ... Four hundred bears were killed in a single day under Caligula ... Under Nero , four hundred tigers fought with bulls and elephants. In a single day, at the dedication of the Colosseum by Titus , five thousand animals perished. Under Trajan ... lions , tigers, elephants, rhinoceroses , hippopotami, giraffes, bulls, stags, even crocodiles and serpents were employed to give novelty to the spectacle. [ 11 ]
Charlemagne had an elephant named Abul-Abbas that was given to him by the Abbasid caliph.
King Henry I of England kept a collection of animals at his palace in Woodstock which reportedly included lions, leopards, and camels. [ 12 ] The most prominent collection in medieval England was in the Tower of London , created as early as 1204 by King John I . Henry III received a wedding gift in 1235 of three leopards from Frederick II, Holy Roman Emperor , and in 1264, the animals were moved to the Bulwark, renamed the Lion Tower, near the main western entrance of the Tower. It was opened to the public during the reign of Elizabeth I in the 16th century. [ 13 ] During the 18th century, the price of admission was three half-pence, or the supply of a cat or dog for feeding to the lions. [ 12 ] The animals were moved to the London Zoo when it opened.
Aztec emperor Moctezuma had in his capital city of Tenochtitlan a "house of animals" with a large collection of birds, mammals and reptiles in a garden tended by more than 600 employees. The garden was described by several Spanish conquerors, including Hernán Cortés in 1520. After the Aztec revolt against the Spanish rule, and during the subsequent battle for the city, Cortés reluctantly ordered the zoo to be destroyed. [ 14 ]
The oldest zoo in the world still in existence is the Tiergarten Schönbrunn in Vienna , Austria. It was constructed by Adrian van Stekhoven in 1752 at the order of Emperor Francis I , to serve as an imperial menagerie as part of Schönbrunn Palace . The menagerie was initially reserved for the viewing pleasure of the imperial family and the court, but was made accessible to the public in 1765. [ 15 ] In 1775, a zoo was founded in Madrid, and in 1795, the zoo inside the Jardin des Plantes in Paris was founded by Jacques-Henri Bernardin , with animals from the royal menagerie at Versailles, primarily for scientific research and education. The planning about a space for the conservation and observation of animals was expressed in connection with the political construction of republican citizenship. [ 16 ]
The Kazan Zoo , the first zoo in Russia was founded in 1806 by the Professor of Kazan State University Karl Fuchs .
Until the early 19th century, the function of the zoo was often to symbolize royal power, like King Louis XIV 's menagerie at Versailles . Major cities in Europe set up zoos in the 19th century, usually using London and Paris as models. The transition was made from princely menageries designed to entertain high society with strange novelties into public zoological gardens. The new goal was to educate the entire population with information along modern scientific lines. Zoos were supported by local commercial or scientific societies.
The modern zoo that emerged in the 19th century in the United Kingdom , [ 17 ] was focused on providing scientific study and later educational exhibits to the public for entertainment and inspiration. [ 18 ]
A growing fascination for natural history and zoology , coupled with the tremendous expansion in the urbanization of London, led to a heightened demand for a greater variety of public forms of entertainment to be made available. The need for public entertainment, as well as the requirements of scholarly research, came together in the founding of the first modern zoos. Whipsnade Park Zoo in Bedfordshire , England, opened in 1931. It allowed visitors to drive through the enclosures and come into close proximity with the animals.
The Zoological Society of London was founded in 1826 by Stamford Raffles and established the London Zoo in Regent's Park two years later in 1828. [ 19 ] At its founding, it was the world's first scientific zoo. [ 10 ] [ 20 ] Originally intended to be used as a collection for scientific study , it was opened to the public in 1847. [ 20 ] The Zoo was located in Regent's Park —then undergoing development at the hands of the architect John Nash . What set the London zoo apart from its predecessors was its focus on society at large. The zoo was established in the middle of a city for the public, and its layout was designed to cater for the large London population. The London zoo was widely copied as the archetype of the public city zoo. [ 21 ] In 1853, the Zoo opened the world's first public aquarium .
Dublin Zoo was opened in 1831 by members of the medical profession interested in studying animals while they were alive and more particularly getting hold of them when they were dead. [ 22 ]
Downs' Zoological Gardens created by Andrew Downs and opened to the Nova Scotia public in 1847. It was originally intended to be used as a collection for scientific study. By the early 1860s, the zoo grounds covered 40 hectares with many fine flowers and ornamental trees, picnic areas, statues, walking paths, The Glass House (which contained a greenhouse with an aviary, aquarium, and museum of stuffed animals and birds), a pond, a bridge over a waterfall, an artificial lake with a fountain, a wood-ornamented greenhouse, a forest area, and enclosures and buildings. [ 23 ] [ 24 ] [ 25 ]
The first zoological garden in Australia was Melbourne Zoo in 1860.
In German states leading roles came Berlin (1841), Frankfurt (1856), and Hamburg (1863). In 1907, the entrepreneur Carl Hagenbeck founded the Tierpark Hagenbeck in Stellingen, now a quarter of Hamburg . His zoo was a radical departure from the layout of the zoo that had been established in 1828. It was the first zoo to use open enclosures surrounded by moats, rather than barred cages, to better approximate animals' natural environments. [ 26 ] He also set up mixed-species exhibits and based the layout on the different organizing principle of geography, as opposed to taxonomy. [ 27 ]
The Wrocław Zoo ( Polish : Ogród Zoologiczny we Wrocławiu ) is the oldest zoo in Poland, opened in 1865 when the city was part of Prussia , and was home to about 10,500 animals representing about 1,132 species (in terms of the number of animal species, it is the third largest in the world [ 28 ] ). In 2014 the Wrocław Zoo opened the Africarium , the only themed oceanarium devoted solely to exhibiting the fauna of Africa , comprehensively presenting selected ecosystems from the continent of Africa . Housing over 10 thousand animals, the facility's breadth extends from housing insects such cockroaches to large mammals like elephants on an area of over 33 hectares . [ 29 ]
In the United States, the Philadelphia Zoo , opened on July 1, 1874, earning its motto "America's First Zoo." The Lincoln Park Zoological Gardens in Chicago and the Cincinnati Zoo opened in 1875. In the 1930s, federal relief programs provided financial aid to most local zoos. The Works Progress Administration and similar New Deal government agencies helped greatly in the construction, renovation, and expansion of zoos when the Great Depression severely reduced local budgets. It was "a new deal for animals." [ 30 ]
The Atlanta Zoo , founded in 1886, suffered neglect. By 1984 it was ranked among the ten worst zoos in the United States. Systematic reform by 2000 put it on the list of the ten best. [ 31 ]
By 2020, the United States featured 230 accredited zoos and aquariums across 45 states, accommodating 800,000 animals, and 6,000 species out of which about 1,000 are endangered. The zoos provide 208,000 jobs, and with an annual
budget of $230 million for wildlife conservation . They attract over 200 million visits a year and have special programs for schools. They are organized by the Association of Zoos and Aquariums . [ 32 ] [ 33 ]
Japan's first modern zoo, Tokyo's Ueno Imperial Zoological Gardens , opened in 1882 based on European models. In World War II it was used to teach the Japanese people about the lands recently conquered by the Army. In 1943, fearing American bombing attacks, the government ordered the zoo to euthanize dangerous animals that might escape. [ 34 ] [ 35 ]
When ecology emerged as a matter of public interest in the 1970s, a few zoos began to consider making conservation their central role, with Gerald Durrell of the Jersey Zoo , George Rabb of Brookfield Zoo , and William Conway of the Bronx Zoo ( Wildlife Conservation Society ) leading the discussion. From then on, zoo professionals became increasingly aware of the need to engage themselves in conservation programs, and the American Zoo Association soon said that conservation was its highest priority. [ 36 ] In order to stress conservation issues, many large zoos stopped the practice of having animals perform tricks for visitors. The Detroit Zoo , for example, stopped its elephant show in 1969, and its chimpanzee show in 1983, acknowledging that the trainers had probably abused the animals to get them to perform. [ 37 ]
Mass destruction of wildlife habitat has yet to cease all over the world and many species such as elephants , big cats, penguins , tropical birds, primates, rhinos , exotic reptiles, and many others are in danger of dying out. Many of today's zoos hope to stop or slow the decline of many endangered species and see their primary purpose as breeding endangered species in captivity and reintroducing them into the wild. Modern zoos also aim to help teach visitors the importance of animal conservation, often through letting visitors witness the animals firsthand. [ 38 ] Some critics, and the majority of animal rights activists, say that zoos, no matter their intentions, or how noble these intentions, are immoral and serve as nothing but to fulfill human leisure at the expense of the animals (an opinion that has spread over the years). However, zoo advocates argue that their efforts make a difference in wildlife conservation and education. [ 38 ]
Humans were occasionally displayed in cages at zoos along with non-human animals, to illustrate the differences between people of European and non-European origin. In September 1906, William Hornaday , director of the Bronx Zoo in New York—with the agreement of Madison Grant , head of the New York Zoological Society —had Ota Benga , a Congolese pygmy , displayed in a cage with the chimpanzees, then with an orangutan named Dohong, and a parrot. The exhibit was intended as an example of the "missing link" between the orangutan and white man. It triggered protests from the city's clergymen, but the public reportedly flocked to see Benga. [ 39 ] [ 40 ]
Humans were also displayed at various events, especially colonial expositions such as the 1931 Paris Colonial Exposition , with the practice continuing in Belgium at least to as late as 1958 in a "Congolese village" display at Expo '58 in Brussels. These displays, while sometimes called "human zoos", usually did not take place in zoos or use cages. [ 41 ]
Zoo animals live in enclosures that often attempt to replicate their natural habitats or behavioral patterns, for the benefit of both the animals and visitors. Nocturnal animals are often housed in buildings with a reversed light-dark cycle, i.e. only dim white or red lights are on during the day so the animals are active during visitor hours, and brighter lights on at night when the animals sleep. Special climate conditions may be created for animals living in extreme environments, such as penguins. Special enclosures for birds , mammals , insects , reptiles , fish , and other aquatic life forms have also been developed. Some zoos have walk-through exhibits where visitors enter enclosures of non-aggressive species, such as lemurs , marmosets , birds, lizards , and turtles . Visitors are asked to keep to paths and avoid showing or eating foods that the animals might snatch.
Some zoos keep animals in larger, outdoor enclosures, confining them with moats and fences, rather than in cages. Safari parks , also known as zoo parks and lion farms, allow visitors to drive through them and come in close proximity to the animals. [ 10 ] Sometimes, visitors are able to feed animals through the car windows.
The first safari park was Whipsnade Park in Bedfordshire, England, opened by the Zoological Society of London in 1931 which today (2014) covers 600 acres (2.4 km 2 ). Since the early 1970s, an 1,800 acre (7 km 2 ) park in the San Pasqual Valley near San Diego has featured the San Diego Zoo Safari Park , run by the Zoological Society of San Diego. One of two state-supported zoo parks in North Carolina is the 2,000-acre (8.1 km 2 ) North Carolina Zoo in Asheboro. [ 42 ] The 500-acre (2.0 km 2 ) Werribee Open Range Zoo in Melbourne, Australia, displays animals living in an artificial savannah .
The first public aquarium was opened at the London Zoo in 1853. This was followed by the opening of public aquaria in continental Europe (e.g. Paris in 1859, Hamburg in 1864, Berlin in 1869, and Brighton in 1872) and the United States (e.g. Boston in 1859, Washington in 1873, San Francisco Woodward's Garden in 1873, and the New York Aquarium at Battery Park in 1896).
Roadside zoos are found throughout North America , particularly in remote locations. They are often small, for-profit zoos, often intended to attract visitors to some other facility, such as a gas station. The animals may be trained to perform tricks, and visitors are able to get closer to them than in larger zoos. [ 43 ] Since they are sometimes less regulated, roadside zoos are often subject to accusations of neglect [ 44 ] and cruelty . [ 45 ]
In June 2014 the Animal Legal Defense Fund filed a lawsuit against the Iowa-based roadside Cricket Hollow Zoo for violating the Endangered Species Act by failing to provide proper care for its animals. [ 46 ] Since filing the lawsuit, ALDF has obtained records from investigations conducted by the USDA's Animal and Plant Health Inspection Services; these records show that the zoo is also violating the Animal Welfare Act. [ 47 ]
A petting zoo, also called petting farms or children's zoos, features a combination of domestic animals and wild species that are docile enough to touch and feed. To ensure the animals' health, the food is supplied by the zoo, either from vending machines or a kiosk nearby.
An animal theme park is a combination of an amusement park and a zoo, mainly for entertaining and commercial purposes. Marine mammal parks such as Sea World and Marineland are more elaborate dolphinariums keeping whales , and containing additional entertainment attractions. Another kind of animal theme park contains more entertainment and amusement elements than the classical zoo, such as stage shows, roller coasters, and mythical creatures. Some examples are Busch Gardens Tampa Bay in Tampa, Florida , both Disney's Animal Kingdom and Gatorland in Orlando, Florida , Flamingo Land in North Yorkshire, England , and Six Flags Discovery Kingdom in Vallejo, California .
By 2000 most animals being displayed in zoos were the offspring of other zoo animals. [ citation needed ] This trend, however was and still is somewhat species-specific. When animals are transferred between zoos, they usually spend time in quarantine, and are given time to acclimatize to their new enclosures which are often designed to mimic their natural environment. For example, some species of penguins may require refrigerated enclosures. Guidelines on necessary care for such animals is published in the International Zoo Yearbook . [ 48 ] Animal exchanges between facilities are usually made voluntarily, based on a model of cooperation for conservation. Loaned animals usually remain the property of the original park, and any offspring yielded by loaned animals are usually divided between the lending and holding institutions. For decades the capture of wild animals or purchasing of animals has been broadly considered unethical and has not been practiced by reputable zoos.
Especially in large animals, a limited number of spaces are available in zoos. As a consequence, various management tools are used to preserve the space for the genetically most important individuals and to reduce the risk of inbreeding . Management of animal populations is typically through international organizations such as AZA and EAZA . [ 49 ] Zoos have several different ways of managing the animal populations, such as moves between zoos, contraception , sale of excess animals and euthanization (culling). [ 50 ]
Contraception can be an effective way to limit a population's breeding. However it may also have health repercussions and can be difficult or even impossible to reverse in some animals. [ 51 ] Additionally, some species may lose their reproductive capability entirely if prevented from breeding for a period (whether through contraceptives or isolation), but further study is needed on the subject. [ 49 ] Sale of surplus animals from zoos was once common and in some cases animals have ended up in substandard facilities. In recent decades the practice of selling animals from certified zoos has declined. [ 50 ] A large number of animals are culled each year in zoos, but this is controversial. [ 52 ] A highly publicized culling as part of population management was that of a healthy giraffe at Copenhagen Zoo in 2014. The zoo argued that his genes already were well-represented in captivity, making the giraffe unsuitable for future breeding. There were offers to adopt him and an online petition to save him had many thousand signatories, but the culling proceeded. [ 53 ] Although zoos in some countries have been open about culling, the controversy of the subject and pressure from the public has resulted in others being closed. [ 50 ] This stands in contrast to most zoos publicly announcing animal births. [ 50 ] Furthermore, while many zoos are willing to cull smaller and/or low-profile animals, fewer are willing to do it with larger high-profile species. [ 50 ] [ 52 ]
Many animals breed readily in captivity. Zoos frequently are forced to intentionally limit captive breeding because of a lack of natural wild habitat in which to reintroduce animals. [ 54 ] This highlights the importance of in situ conservation, or preservation of natural spaces, in addition to the utility of zoo captive breeding and reintroduction programs. In situ conservation and reintroduction programs are key elements to obtaining certification by reputable organisations such as the Association of Zoos and Aquariums (AZA). [ 55 ] Efforts to clone endangered species in the United States, Europe, and Asia are frequently embedded in zoos and zoological parks. [ 56 ]
The position of most modern zoos in Australasia , Asia , Europe , and North America , particularly those with scientific societies, is that they display wild animals primarily for the conservation of endangered species , as well as for research purposes and education, and secondarily for the entertainment of visitors. [ 57 ] [ 58 ] The Zoological Society of London states in its charter that its aim is "the advancement of Zoology and Animal Physiology and the introduction of new and curious subjects of the Animal Kingdom." It maintains two research institutes, the Nuffield Institute of Comparative Medicine and the Wellcome Institute of Comparative Physiology. In the United States, the Penrose Research Laboratory of the Philadelphia Zoo focuses on the study of comparative pathology . [ 10 ] The World Association of Zoos and Aquariums produced its first conservation strategy in 1993, and in November 2004, it adopted a new strategy that sets out the aims and mission of zoological gardens of the 21st century. [ 59 ] When studying behaviour of captive animals, several things should however be taken into account before drawing conclusions about wild populations. Including that captive populations are often smaller than wild ones and that the space available to each animal is often less than in the wild. [ 60 ]
Conservation programs all over the world fight to protect species from going extinct , but many conservation programs are underfunded and under-represented. Conservation programs can struggle to fight bigger issues like habitat loss and illness. It often takes significant funding and long time periods to rebuild degraded habitats, both of which are scarce in conservation efforts. The current state of conservation programs cannot rely solely in situ (on-site conservation) plans alone, ex situ (off-site conservation) may therefore provide a suitable alternative. Off-site conservation relies on zoos, national parks, or other care facilities to support the rehabilitation of the animals and their populations. Zoos benefit conservation by providing suitable habitats and care to endangered animals. When properly regulated, they present a safe, clean environment for the animals to increase populations sizes. A study on amphibian conservation and zoos addressed these problems by writing,
Whilst addressing in situ threats, particularly habitat loss, degradation and fragmentation, is of primary importance; for many amphibian species in situ conservation alone will not be enough, especially in light of current un-mitigatable threats that can impact populations very rapidly such as chytridiomycosis [an infectious fungal disease]. Ex situ programmes can complement in situ activities in a number of ways including maintaining genetically and demographically viable populations while threats are either better understood or mitigated in the wild [ 61 ]
The breeding of endangered species is coordinated by cooperative breeding programmes containing international studbooks and coordinators, who evaluate the roles of individual animals and institutions from a global or regional perspective, and there are regional programmes all over the world for the conservation of endangered species . In Africa, conservation is handled by the African Preservation Program (APP); [ 62 ] in the U.S. and Canada by Species Survival Plans; [ 63 ] in Australasia, by the Australasian Species Management Program; [ 64 ] in Europe, by the European Endangered Species Program; [ 65 ] and in Japan, South Asia, and South East Asia, by the Japanese Association of Zoos and Aquariums, the South Asian Zoo Association for Regional Cooperation , and the South East Asian Zoo Association.
Besides conservation of captive species, large zoos may form a suitable environment for wild native animals such as herons to live in or visit. A colony of black-crowned night herons has regularly summered at the National Zoo in Washington, D.C. for more than a century. [ 66 ] Some zoos may provide information to visitors on wild animals visiting or living in the zoo, or encourage them by directing them to specific feeding or breeding platforms. [ 67 ] [ 68 ]
In modern, well-regulated zoos, breeding is controlled to maintain a self-sustaining, global captive population. This is not the case in some less well-regulated zoos, often based in poorer regions. Overall "stock turnover" of animals during a year in a select group of poor zoos was reported as 20%-25% with 75% of wild caught apes dying in captivity within the first 20 months. [ 69 ] The authors of the report stated that before successful breeding programs, the high mortality rate was the reason for the "massive scale of importations."
One 2-year study indicated that of 19,361 mammals that left accredited zoos in the U.S. between 1992 and 1998, 7,420 (38%) went to dealers, auctions, hunting ranches, unaccredited zoos and individuals, and game farms. [ 70 ]
The welfare of zoo animals varies widely. Many zoos work to improve their animal enclosures and make it fit the animals' needs, but constraints such as size and expense can complicate this. [ 71 ] [ 72 ] The type of enclosure and the husbandry are of great importance in determining the welfare of animals. Substandard enclosures can lead to decreased lifespans, caused by factors as human diseases, unsafe materials in the cages and possible escape attempts (Bendow 382). However, when zoos take time to think about the animal's welfare, zoos can become a place of refuge . Today, many zoos are improving enclosures by including tactile and sensory features in the habitat that allow animals to encourage natural behaviors. These additions can prove to be effective in improving the lives of animals in captivity. The tactile and sensory features will vary depending on the species of animal. [ 73 ] There are animals that are injured in the wild and are unable to survive on their own, but in the zoos they can live out the rest of their lives healthy and happy (McGaffin). In recent years, some zoos have chosen to move out some larger animals because they do not have the space available to provide an adequate enclosure for them (Lemonic, McDowell, and Bjerklie 50).
An issue with animal welfare in zoos is that best animal husbandry practices are often not completely known, especially for species that are only kept in a small number of zoos. [ 60 ] To solve this organizations like EAZA and AZA have begun to develop husbandry manuals. [ 74 ] [ 75 ]
Many modern zoos attempt to improve animal welfare by providing more space and behavioural enrichments . This often involves housing the animals in naturalistic enclosures that allow the animals to express more of their natural behaviours, such as roaming and foraging. Whilst many zoos have been working hard on this change, in some zoos, some enclosures still remain barren concrete enclosures or other minimally enriched cages. [ 76 ]
Sometimes animals are unable to perform certain behaviors in zoos, like seasonal migration or traveling over large distances. Whether these behaviors are necessary for good welfare however is unclear. Some behaviors are seen as essential for an animal's welfare whilst others are not. [ 77 ] It is however shown that even in limited spaces, certain natural behaviors can still be performed. A study in 2014 for example found that Asian elephants in zoos covered similar or higher walking distances when compared to sedentary wild populations. [ 78 ] Migration in the wild can also be related to food scarcity or other unfavorable environmental problems. [ 79 ] However a proper zoo enclosure never runs out of food or water, and in case of unfavorable temperatures or weather animals are provided with (indoor) shelter.
Animals in zoos can exhibit behaviors that are abnormal in their frequency, intensity, or would not normally be part of their behavioural repertoire . Whilst these types of behaviors can be a sign of bad welfare and stress, this is not necessarily the case. Other measurements or behavioral research is advised before determining whether an animal performing stereotypical behavior is living in bad welfare or not. [ 80 ] Examples of stereotypical behaviors are pacing, head-bobbing, obsessive grooming and feather-plucking [ 81 ] A study examining data collected over four decades found that polar bears , lions, tigers and cheetahs can display stereotypical behaviors in many older exhibits. However they also noted that in more modern naturalistic exhibits, these behaviors could completely disappear. [ 82 ] Elephants have also been recorded displaying stereotypical behaviours in the form of swaying back and forth, trunk swaying or route tracing. This has been observed in 54% of individuals in UK zoos. [ 83 ] However it has been shown that modern facilities and modern husbandry can greatly decrease or even entirely remove abnormal behaviors. A study of a group of elephants in Planckendael showed that the older wild-caught animals displayed many stereotypical behaviors. These elephants had spent part of their lives either in a circus or in other substandard enclosures. On the other hand, the elephants born in the modern facilities that had lived in a herd their whole life barely displayed any stereotypical behaviors at all. [ 84 ] The life history of an animal is thus extremely important when analyzing the causes of stereotypical behavior, as this can be a historical relict instead of a result of present-day husbandry.
Some zoos have used psychoactive drugs , such as Prozac , in attempting to stop animals from exhibiting the behaviors. [ 85 ]
The influence on a zoological environment on animal's longevity is not straightforward. A study of 50 mammal species found that 84% of them lived longer in zoos than they would in the wild on average. [ 86 ] On the other hand, some research claims that elephants in Japanese zoos would live shorter than their wild counterparts at just 17 years. This has been refuted by other studies however. [ 87 ] Such studies might not yet fully represent recent improvements in husbandry. For example, studies show that captive-bred elephants already have a lower mortality risk then wild-caught ones. [ 88 ]
Climatic conditions can make it difficult to keep some animals in zoos in some locations. For example, Alaska Zoo had an elephant named Maggie. She was housed in a small, indoor enclosure because the outdoor temperature was too low. [ 89 ] [ 90 ]
Tsetse flies have invaded zoos that have been established in the tsetse zone. More concerning, tsetse-borne species of trypanosomes have entered zoos outside the traditional tsetse zone in infected animals imported and added to their collections. Whether these can be controlled depends on several factors: Vale 1998 found that the technique used in placing attractants was important; and Green 1988, Torr 1994, Torr et al. 1995, and Torr et al. 1997 found the availability for specifically needed attractants for the specific job to also vary widely. [ 91 ] [ 92 ]
Some critics and many animal rights activists argue that zoo animals are treated as voyeuristic objects, rather than living creatures, and often suffer due to the transition from being free and wild to captivity. [ 93 ] Ever since imports of wild-caught animals can became more regulated by organizations like CITES and national laws, zoos have started sustaining their populations via breeding. This change started around the 1970s. Many corporations in the form of breeding programs have been set up since, for both common and endangered species. [ 94 ] [ 95 ] [ 96 ] Emma Marris , writing an opinion piece for The New York Times , suggested zoos "stopped breeding all their animals, with the possible exception of any endangered species with a real chance of being released back into the wild ... Eventually, the only animals on display would be a few ancient holdovers from the old menageries, animals in active conservation breeding programs and perhaps a few rescues. Such zoos might even be merged with sanctuaries." [ 97 ]
In 2017, activist travel company Responsible Travel and anti-captive animal charity the Born Free Foundation conducted an independent survey of 1,000 members of the UK public who had visited a zoo in the previous five years, to gauge public understanding of zoos' contribution to conservation . The results showed that zoos spend on average ten times less than visitors expect on conservation. It also emerged that three-quarters of visitors would expect at least one-fifth of the animals in a zoo to be endangered. The actual figure, according to the Born Free Foundation, is 10%. [ 98 ]
In light of these findings and ongoing animal welfare concerns, [ 99 ] in 2017, Responsible Travel became the first travel company to stop promoting holidays that include visits to a zoo. [ 100 ]
In some countries, feeding live vertebrates to zoo animals is illegal under most circumstances. The UK Animal Welfare Act of 2006, for example, states that prey must be killed for feeding, unless this threatens the health of the predator. [ 101 ] Some zoos had already adopted such practices prior to the implementation of such policies. London Zoo, for example, stopped feeding live vertebrates in the 20th century, long before the Animal Welfare Act. [ 101 ] Despite being illegal in China, some zoos have been found to still feed live vertebrates to their predators. In some parks like Xiongsen Bear and Tiger Mountain Village, live chickens and other livestock were found to be thrown into the enclosures of tigers and other predators. In Guilin, in south-east China, live cows and pigs are thrown to tigers to amuse visitors. Other Chinese parks like Shenzhen Safari Park have already stopped this practice after facing heavy criticism. [ 102 ]
In the United States, any public animal exhibit must be licensed and inspected by the Department of Agriculture , the Environmental Protection Agency , and the Occupational Safety and Health Administration . Depending on the animals they exhibit, the activities of zoos are regulated by laws including the Endangered Species Act , the Animal Welfare Act , the Migratory Bird Treaty Act of 1918 and others. [ 103 ]
Additionally, zoos in several countries may choose to pursue accreditation by the Association of Zoos and Aquariums (AZA), which originated in the U.S. To achieve accreditation, a zoo must pass an application and inspection process and meet or exceed the AZA's standards for animal health and welfare, fundraising, zoo staffing, and involvement in global conservation efforts. Inspection is performed by three experts (typically one veterinarian, one expert in animal care, and one expert in zoo management and operations) and then reviewed by a panel of twelve experts before accreditation is awarded. This accreditation process is repeated once every five years. The AZA estimates that there are approximately 2,400 animal exhibits operating under USDA license as of February 2007; fewer than 10% are accredited. [ 104 ]
The European Union introduced a directive to strengthen the conservation role of zoos, making it a statutory requirement that they participate in conservation and education, and requiring all member states to set up systems for their licensing and inspection. [ 105 ] Zoos are regulated in the UK by the Zoo Licensing Act of 1981, which came into effect in 1984. A zoo is defined as any "establishment where wild animals are kept for exhibition [...] to which members of the public have access, with or without charge for admission, seven or more days in any period of twelve consecutive months", excluding circuses and pet shops. The Act requires that all zoos be inspected and licensed, and that animals kept in enclosures are provided with a suitable environment in which they can express most normal behavior. [ 105 ]
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zoo is a data compression program and format developed by Rahul Dhesi in the mid-1980s. The format is based on the LZW compression algorithm and compressed files are identified by the .zoo file extension. It is no longer widely used. Program source code was originally published on the comp.sources.misc Usenet newsgroup, and was compatible with a variety of Unix-like operating systems. Binaries were also published for the MS-DOS and AmigaOS user communities. [ 1 ]
Zoo archives can store multiple "generations" of a file; if files are added to an archive with the same pathname yet more recent date, if generations are enabled for the archive the older version(s) will be retained (with a semicolon and version number, similar to version numbers in the VMS and RT-11 operating systems) as the new file is added. This allows files that are frequently modified to be backed up in such a way as to allow access to previous versions (up to the version limit chosen) from one archive.
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A zoo blot or garden blot is a type of Southern blot that demonstrates the similarity between specific, usually protein-coding, DNA sequences of different species. A zoo blot compares animal species while a garden blot compares plant species. The purpose of the zoo blot is to detect the conservation of the gene(s) of interest throughout the evolution of different species. [ 1 ]
In order to understand the degree to which a particular gene is similar from species to species, DNA extracts from a set of species are isolated and spread over a surface. Then, a gene probe specific to one of the species is labeled and allowed to hybridize to the prepared DNA. Usually, the probe is marked with a radioactive isotope of phosphorus . Following the hybridization, autoradiography or other imaging techniques are used to identify successfully hybridized probes, proof of similarity between species' genomes. [ 2 ]
The hybridization between a probe and a segment of DNA will happen even when the strands are similar but not identical. As a result, zoo blotting is used to detect similar or exact relationships between the DNA in question and other organisms. It can also help establish the locations of introns and exons, as the latter will be far more conserved than the former. [ 3 ]
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The zoo hypothesis speculates on the assumed behavior and existence of technologically advanced extraterrestrial life and the reasons they refrain from contacting Earth . It is one of many theoretical explanations for the Fermi paradox . The hypothesis states that extraterrestrial life intentionally avoids communication with Earth to allow for natural evolution and sociocultural development , and avoiding interplanetary contamination , similar to people observing animals at a zoo. The hypothesis seeks to explain the apparent absence of extraterrestrial life despite its generally accepted plausibility and hence the reasonable expectation of its existence. [ 1 ] [ 2 ]
Extraterrestrial life forms might, for example, choose to allow contact once the human species has passed certain technological, political, and/or ethical standards. Alternatively, they may withhold contact until humans force contact upon them, possibly by sending a spacecraft to an extraterrestrial-inhabited planet. In this regard, reluctance to initiate contact could reflect a sensible desire to minimize risk. An extraterrestrial society with advanced remote-sensing technologies may conclude that direct contact with neighbors confers added risks to itself without an added benefit. A variant on the zoo hypothesis suggested by former MIT Haystack Observatory scientist John Allen Ball is the "laboratory" hypothesis, in which humanity is being subjected to experiments, with Earth serving as a giant laboratory. [ 3 ] Ball describes this hypothesis as "morbid" and "grotesque", [ 3 ] simultaneously overlooking the possibility that such experiments may be altruistic , i.e., designed to accelerate the pace of civilization to overcome a tendency for intelligent life to destroy itself , until a species is sufficiently developed to establish contact. [ 4 ] [ 5 ] [ 6 ]
The zoo hypothesis assumes, first, that whenever the conditions are such that life can exist and evolve, it will, and secondly, there are many places where life can exist and a large number of extraterrestrial cultures in existence. [ 3 ] It also assumes that these extraterrestrials have great reverence for independent, natural evolution and development. In particular, assuming that intelligence is a physical process that acts to maximize the diversity of a system's accessible futures, [ 7 ] a fundamental motivation for the zoo hypothesis would be that premature contact would "unintelligently" reduce the overall diversity of paths the universe itself could take.
These ideas are perhaps most plausible if there is a relatively universal cultural or legal policy among a plurality of extraterrestrial civilizations necessitating isolation with respect to civilizations at Earth-like stages of development. In a universe without a hegemonic power, random single civilizations with independent principles would make contact. This makes a crowded universe with clearly defined rules seem more plausible. [ 8 ]
If there is a plurality of extraterrestrial cultures, however, this theory may break down under the uniformity of motive concept because it would take just a single extraterrestrial civilization, or simply a small group within any given civilisation, to decide to act contrary to the imperative within human range of detection for it to be undone, and the probability of such a violation of hegemony increases with the number of civilizations. [ 9 ] [ 10 ] This idea, however, becomes more plausible if all civilizations tend to evolve similar cultural standards and values with regard to contact much like convergent evolution on Earth has independently evolved eyes on numerous occasions, [ 11 ] or all civilizations follow the lead of some particularly distinguished civilization, such as the first civilization among them. [ 12 ]
In this hypothesis, the problem of universal ethical homogeneity is solved because the acquisition of a persistent advanced level of civilization requires overcoming many problems, such as self-destruction, war, overpopulation, pollution, and scarcity. Managing to solve these problems could guide a civilization to adopt a responsible and wise behavior, otherwise they would disappear (involving other solutions to the Fermi paradox). In the zoo hypothesis, no contact would be possible until humanity had acquired a certain level of civilization and maturity (responsibility and wisdom), otherwise it would become a potential threat. [ citation needed ]
One estimate for when humanity might be able to test the zoo hypothesis, essentially by eliminating ways technological extraterrestrials within the galaxy may be able to hide, is some time within the next half century. [ 2 ]
A modified zoo hypothesis is a possible solution to the Fermi paradox. The time between the emergence of the first civilization within the Milky Way and all subsequent civilizations could be enormous. Monte Carlo simulation shows the first few inter-arrival times between emergent civilizations would be similar in length to geologic epochs on Earth. The zoo hypothesis assumes a civilization may have a ten-million, one-hundred-million, or half-billion-year head start on humanity, [ 13 ] i.e., it may have the capability to completely negate our best attempts to detect it.
The zoo hypothesis relies in part on applying the concept of hegemonic power to the Fermi paradox. Even if a first hegemonic non-interventionist grand civilization ( first civilization ) is long gone, their initial legacy could persist in the form of a passed-down tradition, or perhaps in an artificial lifeform ( artificial superintelligence ) dedicated to a non-interventionist hegemonic goal without the risk of death. Thus, the hegemonic power does not even have to be the first civilization, but simply the first to spread its non-interventionist doctrine and control over a large volume of the galaxy. If just one civilization acquired hegemony in the distant past, it could form an unbroken chain of taboo against rapacious colonization in favour of non-interference in any civilizations that follow. The uniformity of motive concept previously mentioned would become moot in such a situation. The main problem would be how a galaxy-wide civilization would block Earth from receiving all intentional or unintentional communications. [ 1 ]
Nonetheless, if the oldest civilization still present in the Milky Way has, for example, a 100-million-year time advantage over the next oldest civilization, then it is conceivable that they could be in the singular position of being able to control, monitor, influence or isolate the emergence of every civilization that follows within their sphere of influence. This is analogous to what happens on Earth within our own civilization on a daily basis, in that everyone born on this planet is born into a pre-existing system of familial associations, customs, traditions and laws that were already long established before our birth and which we have little or no control over. [ 14 ]
Overcoming the zoo hypothesis is one of the goals of METI, an organization created in 2015 to communicate with extraterrestrials , an active form of the search for extraterrestrials (SETI). [ 1 ] METI, however, has been criticized for not representing humanity's collective will and for potentially endangering humanity.
Some critics of the hypothesis say that only a single dissident group in an extraterrestrial civilization, or alternatively the existence of galactic cliques instead of a unified galactic club, would be enough to break the pact of no contact. [ 10 ] [ 15 ] To Stephen Webb and others, it seems unlikely, taking humans and human intercivilizational politics as reference, that such prohibition would be in effect for millions of years or at least human existence without a single breach thereof. [ 16 ] [ 17 ] Others say that the zoo hypothesis, along with its planetarium variation, is highly speculative and more aligned with theological theories. [ 18 ] One possible counterargument to the dissident (rogue) group argument is that extraterrestrial artificial superintelligences dominate space, including space occupied by biological intelligences; moreoever, separate artificial superintelligences are assumed to tend towards a network of merged superintelligencies, thereby dissuading rogue behaviour. [ 19 ]
The zoo hypothesis is a common theme in science fiction.
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Zooarchaeology or archaeozoology merges the disciplines of zoology and archaeology , focusing on the analysis of animal remains within archaeological sites. This field, managed by specialists known as zooarchaeologists or faunal analysts, examines remnants such as bones, shells, hair, chitin , scales, hides, and proteins , such as DNA , to derive insights into historical human-animal interactions and environmental conditions. [ 1 ] While bones and shells tend to be relatively more preserved in archaeological contexts, the survival of faunal remains is generally infrequent. [ 2 ] The degradation or fragmentation of faunal remains presents challenges in the accurate analysis and interpretation of data. [ 2 ]
Characterized by its interdisciplinary nature, zooarchaeology bridges the studies of ancient human societies and the animal kingdom. [ 3 ] Practitioners, from various scientific backgrounds including anthropology , paleontology , and ecology , aim primarily to identify and understand human interactions with animals and their environments. [ 4 ] Through the analysis of faunal remains, zooarchaeologists can gain insight into past diets, domestication practices, tool usage, and ritualistic behaviors, thus contributing to a comprehensive view of human-environment interactions and the sub-field of environmental archaeology .
The development of zooarchaeology in eastern North America can be broken up into three different periods. [ 5 ] The first being the Formative period starting around the 1860s, the second being the Systematization period beginning in the early 1950s, and lastly the Integration period which began about 1969. [ 5 ] Full-time zooarchaeologists came to be during the Systematization period. [ 5 ] Prior to the Systemization period, it was just a technique that was applied but not specifically studied.
Zooarchaeological specialists started to come about partly because of a new approach to archaeology known as processual archaeology . [ 6 ] This approach puts more emphasis on explaining why things happened, not just what happened. [ 6 ] Archaeologists began to specialize in zooarchaeology, and their numbers increased. [ 6 ]
One important aspect of zooarchaeology is using morphological and genetic evidence to answer questions zooarchaeologists have about the relationship between animals and humans. [ 7 ] : 172 These questions include:
Another important aspect of zooarchaeology is its application to the migration patterns of humans. In areas where people are either closely tied to animal as companions or regularly follow the migrations of herds, the data collected from these animals can help give context to human movement as well. [ 9 ] : 103 Studying animal remains can also give context to other remains and artifacts found in association with them. [ 10 ] : 1
Faunal remains are parts of animals that have been left in the material record, which archaeologists study. These remains are important to the record because they can show cultural practices, such as what food they were eating, based on the remains left behind. [ 11 ] Zooarcheologists can find out information like the species the animal is, the age the animal was when it died, and what its sex was. [ 11 ]
Some common faunal remains found at sites include, as stated above, bones, shells, hair, chitin, scales, hides, proteins and DNA. These are often found in piles of waste left behind. This means zooarchaeology is part of the general study of waste or garbology . Archaeologists may have to sort through and identify the species and body region of faunal remains. [ 12 ] The types of fauna that leave behind these remains will depend on where the archaeological site is located. These animals can be domesticated or wild, and sometimes they find both types of remains at sites. [ 12 ]
In addition to helping us understand the past, zooarchaeology can also help us to improve the present and the future. [ 13 ] Studying how people dealt with animals, and their effects can help avoid many potential ecological problems. [ 13 ] This specifically includes problems involving wildlife management. [ 13 ] For example, one of the questions that wildlife preservationists ask is whether they should keep animals facing extinction in several smaller areas, or in one larger area. [ 13 ] Based on zooarchaeological evidence, they found that animals that are split up into several smaller areas are more likely to go extinct. [ 13 ]
One of the issues to which zooarchaeologists pay close attention is taphonomy . [ 5 ] Techniques used in the study of taphonomy include researching how items are buried and deposited at an archaeological site, what the conditions are that aid in the preservation of these items, and how these items get destroyed, all a part of what is referred to by archaeologist Michael Brian Schiffer as behavioral archaeology . [ 5 ] One important aspect of taphonomy is assessing how a specimen became damaged; understanding the taphonomy of a faunal assemblage can explain how and why bones were damaged. [ 10 ] One source of damage to animal bones is humans. [ 10 ] : 169 Cut marks on animal bones provide evidence for butchering . [ 10 ] : 169 Fractures, such as by percussion impact and spiral fracture on a bone can suggest that it was processed by humans for its marrow, minerals, and nutrients. [ 10 ] : 170 Other human processes that affect bones include burning [ 10 ] : 171 and damage from archaeological excavations. [ 10 ] : 178 Non-human damage to bones includes interspecies damage, [ 10 ] : 173 damage from raptors and scavengers , [ 10 ] : 173 damage from rodents , [ 10 ] : 175 damage from fungi , [ 10 ] : 176 environmental weathering , [ 10 ] : 176 and polishing . [ 10 ] : 176 Distinguishing different types of damage to animal bones is a tedious and complex process that requires background in multiple scientific fields. [ 10 ] : 169 Some of the physical damage on bones can be seen with the naked eye, but a lens with 10x magnification and good lighting is necessary for seeing most damage. [ 10 ] : 169
Identification is integral to the archaeological analysis of animal remains. [ 10 ] : 1 Identification of animal remains requires a combination of anatomy , taxonomy , and studies of archaeological context. [ 10 ] : 1 The ability to identify a piece of bone requires knowing what element (bone in the body) it is, and to what animal the bone belongs. [ 10 ] : 1 The latter is referred to as taxonomy , which is used to sort animals into different groups. [ 10 ] : 1 Zooarchaeology uses Linnean nomenclature, which includes varying degrees of specificity in regards to the species. [ 10 ] : 2 Linnaean nomenclature ( Linnaean taxonomy ) is used because it allows archaeologists to identify and show the genetic and morphological relationships between species. [ 10 ] : 2 These relationships are based on species evolution , which can often be subject to interpretation. [ 10 ] : 4 While more specific identification is preferable, it is better to be less specific in the identification rather than identify a specimen incorrectly. [ 10 ] : 2 When examining animal remains, it is common that there are bones that are too small or too damaged to be able to accurately identify it. [ 10 ] : 3 Archaeological context can be used to help with assumptions about species identification. [ 10 ] : 3 Skeletal classification is the other half of properly identifying animal remains. [ 10 ] : 1 Zoological osteology is useful to zooarchaeology because certain morphological aspects of a bone are associated with particular periods of growth, which can help narrow down the age the specimen was at death. [ 10 ] : 9 The analysis of teeth require a slightly different approach than bone, but retain the same level of importance when it comes to analysis. [ 10 ] : 9 The wear pattern and tooth morphology provides information about a species diet and age; the enamel also has biochemical remains of what the animal ate. [ 10 ] : 9 While animal remains can include more than just bones and teeth, the nature of things like hair and muscle cause it to deteriorate quickly after death, leaving the skeleton behind; this is why most of zooarchaeology revolves around skeletal morphology. [ 10 ] : 6 Laboratory analysis can include comparing the skeletons found on site with previously identified lab specimens. [ 5 ] This not only helps to identify what the animal is, but also whether the animal was domesticated or not. [ 5 ]
Genetic analysis using ancient DNA is an important tool used by zooarchaeologists. Genetic history of an animal can give information on population movement over time and environmental adaptations necessary to live in an area. [ 9 ] : 103 It can also give context to how animals may or may not have been domesticated over time by a group of people. [ 9 ] : 104 Ancient DNA is critical to the genetic analysis of animals remains. Whereas modern DNA has very long fragments in samples, ancient DNA has very short fragments, making it very easily contaminated. [ 9 ] : 94 The extraction and sampling of ancient DNA requires highly specialized training, as well as intensive protocol to prevent it from being contaminated by modern DNA. [ 14 ] : 5 The paper :Ancient DNA Analysis of the Oldest Canid Species from the Siberian Arctic and Genetic Contribution to the Domestic Dog" by Lee et al. gives a description of claws and teeth were sampled for ancient DNA. In a facility specially designed for ancient DNA extraction, with the use of personal protective equipment and regular bleaching of surfaces and tools, the claws and teeth were wiped with bleach to destroy all modern DNA on the surface, and were then drilled into a powder. The DNA fragments were extracted from the bone powder using an ancient DNA extraction protocol. After using several processes to replicate the DNA fragments and verify the results ( PCR and gel electrophoresis ), the ancient DNA from the bone powder was sequenced and then analyzed. [ 14 ] : 5
With ZooMS analysis (Zooarchaeology by Mass Spectrometry), the animal species behind a bone fragment or bone artifact can be determined even when no morphological traits survive. The method makes use of interspecies differences in the structure of collagen . [ citation needed ]
Yet another technique zooarchaeologists use is quantification . [ 5 ] They make interpretations based on the number and size of the faunal remains. [ 5 ] These interpretations include how important different animals might have been to the diet. [ 5 ]
Human-animal relationships and interactions were diverse during prehistory from being a food source to playing a more intimate role in society. [ 15 ] Animals have been used in non-economical ways such as being part of a human burial. However, the majority of zooarchaeology has focused on who was eating what by looking at various remains such as bones, teeth, and fish scales. [ 15 ] In the twenty-first century researchers have begun to interpret animals in prehistory in wider cultural and social patterns, focusing on how the animals have affected humans and possible animal agency. [ 15 ] There is evidence of animals such as the mountain lion or the jaguar being used for ritualistic purposes, but not being eaten as a food source. [ 15 ]
Analyses of faunal remains are important to show how prehistoric and hunter-gatherer civilizations interacted with the animals in their environment. [ 11 ] This information can be used to help reconstruct Paleolithic environments. Faunal remains with cut marks, teeth marks, burns, or butchering can signify human interaction which can be important to archaeological data. [ 16 ] Sometimes these analyses can be difficult due to decomposition and weathering, which can cause damage to the remains. Not only do faunal remains help reconstruct environments from the past they can show other cultural practices as well. These remains are not always from food, but can be found in jewelry, tools, spiritual practices, and more. [ 16 ] This information can show the fauna located in the area of analyses, as well as cultural significance. [ citation needed ]
Animal burials date back to prehistory with examples emerging from the Mesolithic period. In Sweden at the site of Skateholm I , dogs were found buried with children under eight years old or were found buried by themselves. Some of the dogs who were buried alone have grave goods similar to their human contemporaries such as flint weapons and deer antlers. [ 15 ] Meanwhile, during the same time period Skateholm II emerged and was very different from Skateholm I, as dogs were buried along on the North and West boundaries of the grave area. [ 15 ] Another burial site in Siberia near Lake Baikal known as the "Lokomotiv" cemetery had a wolf burial among human graves. [ 15 ] [ 17 ] Buried together with, but slightly beneath the wolf was a male human skull. [ 17 ] The wolf breed was not native to this area as it was warm and other research for the area shows no other wolf habitation. [ 17 ] Bazaliiskiy and Savelyev suggests that the presence and significance of the wolf could possibly reflect human interaction. [ 17 ] Another example occurred in 300 B.C. in Pazyryk known as the Pazyryk burials where ten horses were buried alongside a human male, the horses were fully adorned with saddles, pendants, among other valuables. [ 15 ] The oldest horse as also the horse with the grandest attachments. Erica Hill, a professor in archaeology, suggests that the burials of prehistory animals can shed light on human-animal relationships. [ 15 ]
Zooarchaeology overlaps significantly with other areas of study. These include:
Such analyses provide the basis by which further interpretations can be made. Topics that have been addressed by zooarchaeologists include:
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Zooflagellates are single-celled eukaryotes with flagella (i.e., flagellates ). They are heterotrophic flagellates, as opposed to phytoflagellates , which are photosynthetic . [ 1 ] The term "zooflagellate" is also used to refer to reproductive cells or zoospores belonging to multicellular organisms , such as fungi . [ 2 ]
In historical systems of classification during the 20th century, zooflagellates were grouped as a single taxon Zoomastigophora or Zoomastigophorea within the kingdom Protista . [ 3 ] It included protists that lack chloroplasts and cell walls and have one or more flagella , but not many as in ciliates or opalines , [ 4 ] [ 5 ] namely:
Over time, with the advancements in phylogenetics and ultrastructure studies, the term "zooflagellate" became obsolete as a formal taxon. [ 1 ] Instead, it was adopted as an informal name to refer to any given group of heterotrophic flagellates, regardless of evolutionary relationships. [ 10 ] [ 11 ] [ 12 ]
This eukaryote -related article is a stub . You can help Wikipedia by expanding it .
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Zoogeography is the branch of the science of biogeography that is concerned with geographic distribution (present and past) of animal species . [ 1 ]
As a multifaceted field of study, zoogeography incorporates methods of molecular biology, genetics, morphology, phylogenetics , and Geographic Information Systems (GIS) to delineate evolutionary events within defined regions of study around the globe. As proposed by Alfred Russel Wallace , known as the father of zoogeography, phylogenetic affinities can be quantified among zoogeographic regions, further elucidating the phenomena surrounding geographic distributions of organisms and explaining evolutionary relationships of taxa. [ 2 ]
Advancements in molecular biology and theory of evolution within zoological research has unraveled questions concerning speciation events and has expanded phylogenic relationships amongst taxa. [ 3 ] Integration of phylogenetics with GIS provides a means for communicating evolutionary origins through cartographic design. Related research linking phylogenetics and GIS has been conducted in areas of the southern Atlantic, Mediterranean, and Pacific Oceans. Recent innovations in DNA bar-coding, for example, have allowed for explanations of phylogenetic relationships within two families of marine venomous fishes, scorpaenidae and tetraodontidae , residing in the Andaman Sea. [ 4 ] Continued efforts to understand species evolutionary divergence articulated in the geologic time scale based on fossil records for killifish ( Aphanius and Aphanolebias ) in locales of the Mediterranean and Paratethys areas revealed climatological influences during the Miocene [ 5 ] Further development of research within zoogeography has expanded upon knowledge of the productivity of South Atlantic ocean regions and distribution of organisms in analogous regions, providing both ecological and geographic data to supply a framework for the taxonomic relationships and evolutionary branching of benthic polychaetes. [ 6 ]
Modern-day zoogeography also places a reliance on GIS to integrate a more precise understanding and predictive model of the past, current, and future population dynamics of animal species both on land and in the ocean. Through employment of GIS technology, linkages between abiotic factors of habitat such as topography, latitude, longitude, temperatures, and sea level can serve to explain the distribution of species populations through geologic time. Understanding correlations of habitat formation and the migration patterns of organisms at an ecological level allows for explanations of speciation events that may have arisen due to physical geographic isolation events or the incorporation of new refugia to survive unfavorable environmental conditions [ 7 ]
Schmarda (1853) proposed 21 regions, [ 8 ] [ 9 ] while Woodward proposed 27 terrestrial and 18 marine, [ 10 ] Murray (1866) proposed 4, [ 11 ] Blyth (1871) proposed 7, [ 12 ] Allen (1871) 8 regions, [ 13 ] Heilprin (1871) proposed 6, [ 14 ] Newton (1893) proposed 6, [ 15 ] Gadow (1893) proposed 4. [ 16 ]
Philip Sclater (1858) and Alfred Wallace (1876) identified the main zoogeographic regions of the world used today: Palaearctic , Aethiopian (today Afrotropic ), India (today Indomalayan ), Australasian , Nearctic and Neotropical . [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ]
Marine regionalization began with Ortmann (1896). [ 22 ] [ 23 ]
In a similar way to geobotanic divisions, our planet is divided in zoogeographical (or faunal) regions (further divided as provinces, territories and districts), sometimes including the categories Empire and Domain.
The current trend is to classify the floristic kingdoms of botany or zoogeographic regions of zoology as biogeographic realms .
Following, some examples of regionalizations:
Creatio Palaeogeana
Creatio Neogeana
Huxley (1868) scheme: [ 24 ]
Scheme by Trouessart (1890): [ 25 ]
First scheme:
Second scheme:
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The Zoological Survey of India ( ZSI ), founded on 1 July 1916 by the Ministry of Environment, Forest and Climate Change of the Government of India as a premier Indian organisation in zoological research and studies to promote the survey, exploration and research of the Indian wildlife .
The annals of (ZSI) [ 2 ] reflect an eventful beginning for the Survey even before its formal birth and growth.
The establishment of the Zoological Survey of India (ZSI) was the fulfillment of the dream [ citation needed ] of Sir William Jones , who in 1784 founded the Asiatic Society of Bengal , which was also the mother institution to the Indian Museum (1875). The Asiatic Society had started collecting zoological and geological specimens since 1796 and set up a museum in 1814. Nathaniel Wallich , the first Superintendent of the "Museum of the Asiatic Society", was in charge of the increasing collections of Geological and Zoological specimens; he had augmented the animal collections to the Zoological Galleries of the Museum.
The genesis of the ZSI was in 1875 with the opening of the Indian Museum. The new museum on its inception comprised only three sections: the Zoological, the Archaeological and the Geological. The zoological collections of the Asiatic Society of Bengal were formally handed over to the board of trustees of the Indian Museum in 1875.
Zoological Section of the Museum during the period from 1875 to 1916 steadily expanded, growing to the greatest collection of natural history in Asia. By the care and activity of the Curators of the Asiatic society of Bengal and the Superintendents of the Indian Museum, viz., John McClelland , Edward Blyth , John Anderson , James Wood-Mason , Alfred William Alcock and finally Thomas Nelson Annandale and his colleagues, the museum was richly endowed with a magnificent collection of animals, especially of the larger vertebrate groups. Further additions of both land and aquatic fauna to the valuable collections came through during several political and military expeditions, including a number of collections purchased, notably those of Francis Day of Indian Fishes, Lionel de Nicéville of butterflies, Dudgeon and Edward Ernest Green of moths, Jacob R. H. Neervoort van de Poll of beetles and Godwin Austen of mollusks. [ 3 ]
The Zoological Gallery at the Asiatic society Museum under the care and charge of Nathaniel Wallich served the impetus for the formation of the Zoological Survey of India, which was later born as an independent organization on 1 July 1916. The excerpt from the ‘Constitution of the Zoological Survey of India’, released by the Government of India, Department of Education, Resolution no. 19-Museum, dated Shimla , 20 June 1916, states: " In March 1913, the Chairman of the Trustees of the Indian Museum forwarded a representation from the Superintendent of the Zoological and Anthropological Section of the Museum regarding the recognition of the Zoological Section as Zoological Survey. The Government of India, who had already under consideration the desirability of establishing on a sound basis a Zoological Survey of India, informed the Trustees of the Museum that they would be prepared to consider a scheme for such a survey on lines somewhat similar to the existing Botanical Survey of India and asked to furnish with the necessary details. The trustees accordingly submitted their proposals at the end of September 1913 ."
Thomas Nelson Annandale , who joined the Indian museum as Deputy Superintendent (1904), and later as the Superintendent (1907), after years-old struggle, achieved his aim in establishing the Zoological survey of India, and became its founder director and continued until his premature death in April 1924. Dr. Annandale was Honorary Secretary to the Trustees of the Indian Museum for several years; he was also the President of the Asiatic Society of Bengal in 1923. [ 4 ]
In 2021, entomologist Dhriti Banerjee became the first woman director of the ZSI since its inception in 1916. [ 5 ]
The Survey acquired the zoological collections of more than a century old from the former museum of the Asiatic Society of Bengal and the zoological section of the Indian Museum (1814–1875) in Calcutta .
The library in Kolkata and regional centers have a total collection of approximately 1,35,000 volumes, which includes books, journals, monographs, reports of expeditions and fauna surveys, periodicals and other archaic literature on Zoology. [ 20 ] The Kolkata library has around 400 titles of rare books. Some of the notable documents include the original publications of Carl Linnaeus and Fabricius, original paintings and drawings of renowned scientists, biogeographers and naturalists. [ 21 ]
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A zoological specimen is an animal or part of an animal preserved for scientific use.
Various uses are: to verify the identity of a ( species ), to allow study, increase public knowledge of zoology .
Zoological specimens are extremely diverse. Examples are bird and mammal study skins, mounted specimens , skeletal material, casts, pinned insects, dried material, animals preserved in liquid preservatives, and microscope slides. Natural history museums are repositories of zoological specimens
Bird and mammal specimens are conserved as dry study skins , a form of taxidermy. [ 1 ] The skin is removed from the animal's carcass, treated with absorbents, and filled with cotton or polyester batting (In the past plant fibres or sawdust were used). Bird specimens have a long, thin, wooden dowel wrapped in batting at their center. The dowel is often intentionally longer than the bird's body and exits at the animal's vent. This exposed dowel provides a place to handle the bird without disturbing the feathers. Mammal study skins do not normally utilize wooden dowels, instead preparators use wire to support the legs and tail of mammals. Labels are attached to a leg of the specimen with thread or string. Heat and chemicals are sometimes used to aid the drying of study skins.
Osteological collections consist of cleaned, complete and partial skeletons, crania of Vertebrates , mainly birds and mammals. They are used in studies of comparative anatomy and to identify bones from archaeological sites. Human bones are used in medical and forensic studies.
In museum collections it is common for the dry material to greatly exceed the amount of material that is preserved in alcohol. The shells minus their soft parts are kept in card trays within drawers or in glass tubes, often as lots (a lot is a collection of a single species taken from a single locality on a single occasion). Shell collections sometimes suffer from Byne's disease which also affects birds eggs. The study of dry mollusc shells is called conchology as distinct from malacology (wet specimens).
Most hard-bodied insect specimens and some other hard-bodied invertebrates such as certain Arachnida , are preserved as pinned specimens. Either while still fresh, or after rehydrating them if necessary because they had dried out, specimens are transfixed by special stainless steel entomological pins . As the insect dries the internal tissues solidify and, possibly aided to some extent by the integument, they grip the pin and secure the specimen in place on the pin. Very small, delicate specimens may instead be secured by fine steel points driven into slips of card, or glued to card points or similar attachments that in turn are pinned in the same way as entire mounted insects. The pins offer a means of handling the specimens without damage, and they also bear labels for descriptive and reference data.
Once dried, the specimens may be kept in conveniently sized open trays. The bottoms of the trays are lined with a material suited to receiving and holding entomological pins securely and conveniently. Cork and foam plastics are convenient examples. However, open trays are very vulnerable to attack by museum beetle and similar pests, so such open trays are stored in turn inside glass-topped, insect-proof drawers, commonly protected by suitable pesticides or repellents or barriers. Alternatively, some museums store the pinned specimens directly in larger trays or drawers that are glass-topped and stored in cabinets.
In contrast to such dried specimens, soft-bodied specimens most commonly are kept in "wet collections", meaning that they are stored in alcohol or similar preservative or fixative liquids, according to the intended function.
Small specimens, whether hard or soft bodied, and whether entire, dissected , or sectioned , may be stored as microscope slide preparations.
"Wet" specimen collections are stored in different solutions. A very old method is to store the specimen in 70% ethanol with various additives after fixing with formalin [ 2 ] or in these days sometimes with a salt-solution. [ 3 ] Some methods are very useful, because the color can be preserved. (Salt-)Solutions like this are Jores, [ 4 ] Kaiserling [ 5 ] and Romhányi. [ 6 ] Modern specimens are stored in borosilicate glass due to its chemical and thermal resistance and good optical clarity.
Minimum data associated with zoological specimens is the place and date of collection, attached to the specimen by a label. Additional information is the name of the collector and the habitat. Tissue from specimens may be saved for genetic studies (molecular data, DNA ). Depending on the animal group , other data may be included, for instance in bird collections the bird’s breeding condition, weight, colours of its eyes, bills and legs and nature of the stomach contents.
A single specimen may be a composite of preparations sharing a unique number. An example would be a vertebrate with an alcohol-preserved skin and viscera, a cleared and stained head, the post-cranial dried skeleton, histological , glass slides of various organs, and frozen tissue samples. This specimen could also be a voucher for a publication, or photographs and audiotape.
A voucher is a representative specimen of the animal used in a study, such as a specimen collected as part of an ecological survey or a specimen which was the source of DNA for a molecular study. Voucher specimens confirm the identity of the species referred to in the study. They are a backup against misidentification, changing species concepts which mislead results. Type specimens are a special type of voucher specimen used in taxonomy .
Museum zoological specimens may have historic significance . For example, the specimens collected by Johann Baptist von Spix and Carl Friedrich Philipp von Martius during their Brazil Expedition (1817–1820) are housed in the Munich Zoology Museum .
Museums make extensive use of models. When these are accurate they are considered to be specimens in their own right. Examples are the glass invertebrates of Leopold and Rudolf Blaschka . [ 7 ]
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Zoology ( UK : / z u ˈ ɒ l ə dʒ i / zoo- OL -ə-jee , US : / z oʊ ˈ ɒ l ə dʒ i / zoh- OL -ə-jee ) [ 1 ] is the scientific study of animals . Its studies include the structure , embryology , classification , habits , and distribution of all animals, both living and extinct , and how they interact with their ecosystems . Zoology is one of the primary branches of biology . The term is derived from Ancient Greek ζῷον , zōion ('animal'), and λόγος , logos ('knowledge', 'study'). [ 2 ]
Although humans have always been interested in the natural history of the animals they saw around them, and used this knowledge to domesticate certain species, the formal study of zoology can be said to have originated with Aristotle . He viewed animals as living organisms, studied their structure and development, and considered their adaptations to their surroundings and the function of their parts. Modern zoology has its origins during the Renaissance and early modern period, with Carl Linnaeus , Antonie van Leeuwenhoek , Robert Hooke , Charles Darwin , Gregor Mendel and many others.
The study of animals has largely moved on to deal with form and function, adaptations, relationships between groups, behaviour and ecology. Zoology has increasingly been subdivided into disciplines such as classification , physiology , biochemistry and evolution . With the discovery of the structure of DNA by Francis Crick and James Watson in 1953, the realm of molecular biology opened up, leading to advances in cell biology , developmental biology and molecular genetics .
The history of zoology traces the study of the animal kingdom from ancient to modern times. Prehistoric people needed to study the animals and plants in their environment to exploit them and survive. Cave paintings, engravings and sculptures in France dating back 15,000 years show bison, horses, and deer in carefully rendered detail. Similar images from other parts of the world illustrated mostly the animals hunted for food and the savage animals. [ 3 ]
The Neolithic Revolution , which is characterized by the domestication of animals , continued throughout Antiquity. Ancient knowledge of wildlife is illustrated by the realistic depictions of wild and domestic animals in the Near East, Mesopotamia, and Egypt, including husbandry practices and techniques, hunting and fishing. The invention of writing is reflected in zoology by the presence of animals in Egyptian hieroglyphics. [ 4 ]
Although the concept of zoology as a single coherent field arose much later, the zoological sciences emerged from natural history reaching back to the biological works of Aristotle and Galen in the ancient Greco-Roman world . In the fourth century BC, Aristotle looked at animals as living organisms, studying their structure, development and vital phenomena. He divided them into two groups: animals with blood, equivalent to our concept of vertebrates , and animals without blood, invertebrates . He spent two years on Lesbos , observing and describing the animals and plants, considering the adaptations of different organisms and the function of their parts. [ 5 ] Four hundred years later, Roman physician Galen dissected animals to study their anatomy and the function of the different parts, because the dissection of human cadavers was prohibited at the time. [ 6 ] This resulted in some of his conclusions being false, but for many centuries it was considered heretical to challenge any of his views, so the study of anatomy stultified. [ 7 ]
During the post-classical era , Middle Eastern science and medicine was the most advanced in the world, integrating concepts from Ancient Greece, Rome, Mesopotamia and Persia as well as the ancient Indian tradition of Ayurveda , while making numerous advances and innovations. [ 8 ] In the 13th century, Albertus Magnus produced commentaries and paraphrases of all Aristotle's works; his books on topics like botany , zoology, and minerals included information from ancient sources, but also the results of his own investigations. His general approach was surprisingly modern, and he wrote, "For it is [the task] of natural science not simply to accept what we are told but to inquire into the causes of natural things." [ 9 ] An early pioneer was Conrad Gessner , whose monumental 4,500-page encyclopedia of animals, Historia animalium , was published in four volumes between 1551 and 1558. [ 10 ]
In Europe, Galen's work on anatomy remained largely unsurpassed and unchallenged up until the 16th century. [ 11 ] [ 12 ] During the Renaissance and early modern period, zoological thought was revolutionized in Europe by a renewed interest in empiricism and the discovery of many novel organisms. Prominent in this movement were Andreas Vesalius and William Harvey , who used experimentation and careful observation in physiology , and naturalists such as Carl Linnaeus , Jean-Baptiste Lamarck , and Buffon who began to classify the diversity of life and the fossil record , as well as studying the development and behavior of organisms. Antonie van Leeuwenhoek did pioneering work in microscopy and revealed the previously unknown world of microorganisms , laying the groundwork for cell theory . [ 13 ] van Leeuwenhoek's observations were endorsed by Robert Hooke ; all living organisms were composed of one or more cells and could not generate spontaneously. Cell theory provided a new perspective on the fundamental basis of life. [ 14 ]
Having previously been the realm of gentlemen naturalists, over the 18th, 19th and 20th centuries, zoology became an increasingly professional scientific discipline . Explorer-naturalists such as Alexander von Humboldt investigated the interaction between organisms and their environment, and the ways this relationship depends on geography, laying the foundations for biogeography , ecology and ethology . Naturalists began to reject essentialism and consider the importance of extinction and the mutability of species . [ 15 ]
These developments, as well as the results from embryology and paleontology , were synthesized in the 1859 publication of Charles Darwin 's theory of evolution by natural selection ; in this Darwin placed the theory of organic evolution on a new footing, by explaining the processes by which it can occur, and providing observational evidence that it had done so. [ 16 ] Darwin's theory was rapidly accepted by the scientific community and soon became a central axiom of the rapidly developing science of biology. The basis for modern genetics began with the work of Gregor Mendel on peas in 1865, although the significance of his work was not realized at the time. [ 17 ]
Darwin gave a new direction to morphology and physiology , by uniting them in a common biological theory: the theory of organic evolution. The result was a reconstruction of the classification of animals upon a genealogical basis, fresh investigation of the development of animals, and early attempts to determine their genetic relationships. The end of the 19th century saw the fall of spontaneous generation and the rise of the germ theory of disease , though the mechanism of inheritance remained a mystery. In the early 20th century, the rediscovery of Mendel's work led to the rapid development of genetics , and by the 1930s the combination of population genetics and natural selection in the modern synthesis created evolutionary biology . [ 18 ]
Research in cell biology is interconnected to other fields such as genetics, biochemistry , medical microbiology , immunology , and cytochemistry . With the determination of the double helical structure of the DNA molecule by Francis Crick and James Watson in 1953, [ 19 ] the realm of molecular biology opened up, leading to advances in cell biology , developmental biology and molecular genetics . The study of systematics was transformed as DNA sequencing elucidated the degrees of affinity between different organisms. [ 20 ]
Zoology is the branch of science dealing with animals . A species can be defined as the largest group of organisms in which any two individuals of the appropriate sex can produce fertile offspring; about 1.5 million species of animal have been described and it has been estimated that as many as 8 million animal species may exist. [ 21 ] An early necessity was to identify the organisms and group them according to their characteristics, differences and relationships, and this is the field of the taxonomist . Originally it was thought that species were immutable, but with the arrival of Darwin's theory of evolution, the field of cladistics came into being, studying the relationships between the different groups or clades . Systematics is the study of the diversification of living forms, the evolutionary history of a group is known as its phylogeny , and the relationship between the clades can be shown diagrammatically in a cladogram . [ 22 ]
Although someone who made a scientific study of animals would historically have described themselves as a zoologist, the term has come to refer to those who deal with individual animals, with others describing themselves more specifically as physiologists, ethologists, evolutionary biologists, ecologists, pharmacologists, endocrinologists or parasitologists. [ 23 ]
Although the study of animal life is ancient, its scientific incarnation is relatively modern. This mirrors the transition from natural history to biology at the start of the 19th century. Since Hunter and Cuvier , comparative anatomical study has been associated with morphography , shaping the modern areas of zoological investigation: anatomy , physiology , histology , embryology , teratology and ethology . [ 24 ] Modern zoology first arose in German and British universities. In Britain, Thomas Henry Huxley was a prominent figure. His ideas were centered on the morphology of animals. Many consider him the greatest comparative anatomist of the latter half of the 19th century. Similar to Hunter , his courses were composed of lectures and laboratory practical classes in contrast to the previous format of lectures only.
Scientific classification in zoology , is a method by which zoologists group and categorize organisms by biological type , such as genus or species . Biological classification is a form of scientific taxonomy . Modern biological classification has its root in the work of Carl Linnaeus , who grouped species according to shared physical characteristics. These groupings have since been revised to improve consistency with the Darwinian principle of common descent . Molecular phylogenetics , which uses nucleic acid sequence as data, has driven many recent revisions and is likely to continue to do so. Biological classification belongs to the science of zoological systematics . [ 25 ]
Many scientists now consider the five-kingdom system outdated. Modern alternative classification systems generally start with the three-domain system : Archaea (originally Archaebacteria); Bacteria (originally Eubacteria); Eukaryota (including protists , fungi , plants , and animals ) [ 26 ] These domains reflect whether the cells have nuclei or not, as well as differences in the chemical composition of the cell exteriors. [ 26 ]
Further, each kingdom is broken down recursively until each species is separately classified. The order is: Domain ; kingdom ; phylum ; class ; order ; family ; genus ; species . The scientific name of an organism is generated from its genus and species. For example, humans are listed as Homo sapiens . Homo is the genus, and sapiens the specific epithet, both of them combined make up the species name. When writing the scientific name of an organism, it is proper to capitalize the first letter in the genus and put all of the specific epithet in lowercase. Additionally, the entire term may be italicized or underlined. [ 27 ]
The dominant classification system is called the Linnaean taxonomy . It includes ranks and binomial nomenclature . The classification, taxonomy , and nomenclature of zoological organisms is administered by the International Code of Zoological Nomenclature . A merging draft, BioCode, was published in 1997 in an attempt to standardize nomenclature, but has yet to be formally adopted. [ 28 ]
Vertebrate zoology is the biological discipline that consists of the study of vertebrate animals, that is animals with a backbone , such as fish , amphibians , reptiles , birds and mammals . The various taxonomically oriented disciplines i.e. mammalogy , biological anthropology , herpetology , ornithology , and ichthyology seek to identify and classify species and study the structures and mechanisms specific to those groups. The rest of the animal kingdom is dealt with by invertebrate zoology , a vast and very diverse group of animals that includes sponges , echinoderms , tunicates , worms , molluscs , arthropods and many other phyla , but single-celled organisms or protists are not usually included. [ 22 ]
Cell biology studies the structural and physiological properties of cells , including their behavior , interactions, and environment . This is done on both the microscopic and molecular levels for single-celled organisms such as bacteria as well as the specialized cells in multicellular organisms such as humans . Understanding the structure and function of cells is fundamental to all of the biological sciences. The similarities and differences between cell types are particularly relevant to molecular biology.
Anatomy considers the forms of macroscopic structures such as organs and organ systems. [ 29 ] It focuses on how organs and organ systems work together in the bodies of humans and other animals, in addition to how they work independently. Anatomy and cell biology are two studies that are closely related, and can be categorized under "structural" studies. Comparative anatomy is the study of similarities and differences in the anatomy of different groups. It is closely related to evolutionary biology and phylogeny (the evolution of species). [ 30 ]
Physiology studies the mechanical, physical, and biochemical processes of living organisms by attempting to understand how all of the structures function as a whole. The theme of "structure to function" is central to biology. Physiological studies have traditionally been divided into plant physiology and animal physiology , but some principles of physiology are universal, no matter what particular organism is being studied. For example, what is learned about the physiology of yeast cells can also apply to human cells. The field of animal physiology extends the tools and methods of human physiology to non-human species. Physiology studies how, for example, the nervous , immune , endocrine , respiratory , and circulatory systems function and interact. [ 31 ]
Developmental biology is the study of the processes by which animals and plants reproduce and grow. The discipline includes the study of embryonic development , cellular differentiation , regeneration , asexual and sexual reproduction , metamorphosis , and the growth and differentiation of stem cells in the adult organism. [ 32 ] Development of both animals and plants is further considered in the articles on evolution , population genetics , heredity , genetic variability , Mendelian inheritance , and reproduction .
Evolutionary biology is the subfield of biology that studies the evolutionary processes (natural selection, common descent, speciation) that produced the diversity of life on Earth. Evolutionary research is concerned with the origin and descent of species , as well as their change over time, and includes scientists from many taxonomically oriented disciplines. For example, it generally involves scientists who have special training in particular organisms such as mammalogy , ornithology , herpetology , or entomology , but use those organisms as systems to answer general questions about evolution. [ 33 ]
Evolutionary biology is partly based on paleontology , which uses the fossil record to answer questions about the mode and tempo of evolution, [ 34 ] and partly on the developments in areas such as population genetics [ 35 ] and evolutionary theory. Following the development of DNA fingerprinting techniques in the late 20th century, the application of these techniques in zoology has increased the understanding of animal populations. [ 36 ] In the 1980s, developmental biology re-entered evolutionary biology from its initial exclusion from the modern synthesis through the study of evolutionary developmental biology . Related fields often considered part of evolutionary biology are phylogenetics , systematics , and taxonomy . [ 37 ]
Ethology is the scientific and objective study of animal behavior under natural conditions, [ 38 ] as opposed to behaviorism , which focuses on behavioral response studies in a laboratory setting. Ethologists have been particularly concerned with the evolution of behavior and the understanding of behavior in terms of the theory of natural selection . In one sense, the first modern ethologist was Charles Darwin , whose book, The Expression of the Emotions in Man and Animals , influenced many future ethologists. [ 39 ]
A subfield of ethology is behavioral ecology which attempts to answer Nikolaas Tinbergen 's four questions with regard to animal behavior: what are the proximate causes of the behavior, the developmental history of the organism, the survival value and phylogeny of the behavior? [ 40 ] Another area of study is animal cognition , which uses laboratory experiments and carefully controlled field studies to investigate an animal's intelligence and learning. [ 41 ]
Biogeography studies the spatial distribution of organisms on the Earth , [ 42 ] focusing on topics like dispersal and migration , plate tectonics , climate change , and cladistics . It is an integrative field of study, uniting concepts and information from evolutionary biology , taxonomy , ecology , physical geography , geology , paleontology and climatology . [ 43 ] The origin of this field of study is widely accredited to Alfred Russel Wallace , a British biologist who had some of his work jointly published with Charles Darwin . [ 44 ]
Molecular biology studies the common genetic and developmental mechanisms of animals and plants, attempting to answer the questions regarding the mechanisms of genetic inheritance and the structure of the gene . In 1953, James Watson and Francis Crick described the structure of DNA and the interactions within the molecule, and this publication jump-started research into molecular biology and increased interest in the subject. [ 45 ] While researchers practice techniques specific to molecular biology, it is common to combine these with methods from genetics and biochemistry . Much of molecular biology is quantitative, and recently a significant amount of work has been done using computer science techniques such as bioinformatics and computational biology .
Molecular genetics , the study of gene structure and function, has been among the most prominent sub-fields of molecular biology since the early 2000s. Other branches of biology are informed by molecular biology, by either directly studying the interactions of molecules in their own right such as in cell biology and developmental biology , or indirectly, where molecular techniques are used to infer historical attributes of populations or species , as in fields in evolutionary biology such as population genetics and phylogenetics . There is also a long tradition of studying biomolecules "from the ground up", or molecularly, in biophysics . [ 46 ]
Animals generally reproduce by sexual reproduction , a process involving the union of a male and female haploid gamete , each gamete formed by meiosis . Ordinarily, gametes produced by separate individuals unite by a process of fertilization to form a diploid zygote that can then develop into a genetically unique individual progeny. However, some animals are also capable, as an alternative reproductive process, to reproduce parthenogenetically. Parthenogenesis has been described in snakes and lizards (see Wikipedia Parthenogenesis in squamates ), in amphibians (see Wikipedia Parthenogenesis in amphibians ) and in numerous other species (see Wikipedia Parthenogenesis ). Generally, meiosis in parthanogenetically reproducing animals occurs by a similar process to that in sexually reproducing animals, but the diploid zygote nucleus is generated by the union of two haploid genomes from the same individual rather than from different individuals.
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Zoombak Inc was a U.S.-based company which developed GPS tracking devices for people and items. [ 1 ] It used satellite-enabled GPS and a location network server for tracking. In 2011, Securus, Inc. acquired Zoombak , LLC from TruePosition, Inc., a subsidiary of Liberty Media . [ 2 ]
In March 2015 it was announced that BrickHouse Security acquired Securus, including Zoombak and related brands. [ 3 ]
This United States corporation or company article is a stub . You can help Wikipedia by expanding it .
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Zoombombing or Zoom raiding [ 1 ] is the unwanted, disruptive intrusion, generally by Internet trolls , into a video-conference call. In a typical Zoombombing incident, a teleconferencing session is hijacked by the insertion of material that is lewd , obscene , or offensive in nature, typically resulting in the shutdown of the session or the removal of the troll. The term is especially associated with and is derived from, the name of the Zoom videoconferencing software program; however, it has also been used to refer to the phenomenon on other video conferencing platforms. The term became popularized in 2020 when the COVID-19 pandemic forced many people to stay at home , and videoconferencing came to be used on a large scale by businesses, schools, and social groups.
Zoombombing has caused significant issues in particular for schools, companies, and organizations worldwide. Such incidents have resulted in increased scrutiny on Zoom as well as restrictions on usage of the platform by educational, corporate, and governmental institutions globally. In response, Zoom, citing the sudden influx of new users due to the COVID-19 pandemic, took measures to increase security of its teleconferencing application. Incidents of Zoombombing have prompted law enforcement officers in various countries to investigate such cases and file criminal charges against those responsible.
The term Zoombombing is a neologism derived from the teleconferencing application Zoom and influenced by the word photobombing . [ 2 ] The term had appeared in mid-March 2020 on technology and news websites. [ 3 ] [ 4 ] [ 5 ] Zoombombing has also been used in reference to similar incidents on other teleconferencing platforms, such as WebEx or Skype . [ 6 ]
The increased use of Zoom during the COVID-19 pandemic as an alternative to face-to-face meetings resulted in widespread exposure to hackers and Internet trolls , who exploit and work around the application's security features. [ 7 ] In various forums such as Discord and Reddit , efforts have been coordinated to disrupt Zoom sessions, while certain Twitter accounts advertise meeting IDs and passwords or meeting links (allowing users to instantly join a Zoom meeting instead of entering the credentials required to access a meeting) for sessions that were vulnerable to being joined without authorization. [ 8 ] At educational institutions, some students were "actively asking strangers to Zoombomb or 'Zoom raid' their virtual classrooms to spice up their isolated lessons" and facilitating the raids by sharing passwords with the raiders. [ 9 ] CNET pointed out that simple Google searches for URLs that include "Zoom.us" could bring up conferences that are not password protected, and that links within public pages can allow anyone to join. [ 10 ] Hackers and trolls also look for easy targets such as unprotected or underprotected "check-in" meetings in which organizations meet with their employers or clients remotely. [ 11 ] While a Zoom session is in progress, unfamiliar users show up and hijack the session by saying or showing things that are lewd, obscene, or racist in nature. [ 12 ] [ 13 ] The compromised Zoom session is then typically shut down by the host. [ 7 ] [ 5 ] Many of those successful in disrupting sessions have posted video footage of those incidents to social media and video sharing platforms such as TikTok and YouTube . [ 12 ]
While it is believed Zoombombing attacks are mainly orchestrated by external hackers and trolls, many are also orchestrated internally from within their respective organization or entity. [ 14 ] Some view Zoombombing as a continuation of cyberbullying by teenagers, particularly after schools were shut down due to the pandemic. [ 15 ]
Zoombombings would frequently make the local news for how disruptive they are. [ 13 ]
The trolling has caused a number of problems for schools and educators, with unwanted participants posting lewd content to interrupt learning sessions. [ 5 ] [ 16 ] [ 17 ] Some schools had to suspend using video conferencing altogether. [ 18 ] The University of Southern California called Zoombombing a type of trolling and apologized for "vile" events that interrupted "lectures and learning." [ 19 ] Zoombombing has prompted colleges and universities to publish guides and resources to educate and bring awareness to their students and staff about the phenomenon. [ 20 ] Zoombombing has left online lectures vulnerable to the intrusion of people looking to inflict harm. These crimes have brought attention not only to the lack of security on videoconferencing platforms, but also the lack in the universities. According to an article from The Guardian , the University of Warwick , in the midst of a rape-chat scandal, received criticisms for its weak cybersecurity. [ 21 ]
Zoombombing affected twelve-step programs such as Alcoholics Anonymous and Narcotics Anonymous and other substance abuse and addiction recovery programs who were forced to switch to online meetings. Concerns arise from causing undue stress to an already vulnerable population and video recording which can break anonymity . [ 22 ] [ 23 ] Some bombers reference the drug-of-choice for recovery members, such as alcohol, in an attempt to emotionally trigger the participants of the meeting. [ 22 ]
The problem reached such prominence that the United States Federal Bureau of Investigation (FBI) warned of video-teleconferencing and online classroom hijacking, which it called "Zoom-bombing." [ 24 ] [ 25 ] The FBI advised users of teleconferencing software to keep meetings private, require passwords or other forms of access control such as "waiting rooms" to limit access only to specific people, and limiting screen-sharing access to the meeting host only. [ 24 ] Given the number of incidents of Zoombombing, New York's attorney general initiated an inquiry into Zoom's data privacy and security policies. [ 26 ] U.S. Senator Sherrod Brown ( D - OH ) asked the Federal Trade Commission to investigate into the matter, accusing Zoom of engaging in deceptive practices regarding user privacy and security. [ 27 ]
Amid concerns about Zoombombing, various organizations banned the use of Zoom . In April 2020, Google banned the use of Zoom on its corporate computers, directing employees to instead use its video chat app Google Duo . [ 28 ] The use of Zoom was also banned by SpaceX , Smart Communications , NASA , and the Australian Defence Force . [ 28 ] The Taiwanese and Canadian governments banned Zoom for all government use. [ 29 ] The New York City Department of Education prohibited all its teachers from using the platform with students, and the Clark County School District in Nevada disabled access to Zoom to its staff. [ 30 ] Singapore 's Ministry of Education briefly banned all teachers within the country from using Zoom [ 31 ] [ 32 ] before lifting the ban three days later, adding extra security features. [ 33 ] Some Zoombombers have shared their side of the story, claiming they aren't trying to cause harm. They claim it is a form of protest in response to the extensive amount of work given from teachers. Not all incidents are malicious, as many have shared some new pop culture, such as memes and TikToks, to bring some relief and fun during the pandemic. [ 1 ]
Zoom CEO Eric Yuan made a public apology, saying that the teleconferencing company had not anticipated the sudden influx of new consumer users and stating that "this is a mistake and lesson learned." [ 34 ] [ 35 ] In response to the concerns, Zoom has published a guide on their blog on how to avoid these types of incidents. [ 36 ] On April 7, 2020, Zoom implemented user experience and security updates to the application. Such updates include a more visible "Security" icon for users to see and use, suppression of meeting ID numbers, [ 35 ] and a change in the default settings to require passwords and waiting rooms for sessions. [ 37 ] On April 8, 2020, Zoom announced that it had formed a council of chief information security officers from other companies to share ideas on best practices, and that it had hired Alex Stamos , former chief security officer of Facebook , as an adviser. [ 38 ] Zoom released its 5.0 version in April 2020 with security features that include AES 256-bit GCM encryption , passwords by default, and a feature to report suspicious users to its Trust and Safety Team for possible misuse. [ 39 ] [ 40 ] In May 2020, Zoom announced it had temporarily disabled its Giphy (frequently used as a tactic in Zoombombing) integration until security concerns could be properly and fully addressed. [ 41 ] On July 1, 2020, Zoom stated it had released 100 new safety features over the past 90 days, including end-to-end encryption for all users, turning on meeting passwords by default, giving users the ability to choose which data centers calls are routed from, consulting with security experts, forming a CISO council, an improved bug bounty program, and working with third parties to help test security. [ 42 ] [ 43 ]
National authorities worldwide warned of possible charges against people engaging with Zoombombing. [ 44 ] [ 45 ] On April 8, 2020, a teen in Madison, Connecticut , was arrested for computer crime , conspiracy , and disturbing the peace following a Zoombombing incident involving online classes at Daniel Hand High School ; police also identified another teen involved in the incident. [ 46 ] In San Francisco , a man was arrested after being traced to pornographic videos that were streamed on Zoom. [ 47 ] As of May 2020, the FBI has received 195 incidents of Zoombombing involving child abuse , [ 48 ] while the United Kingdom 's National Crime Agency has reported more than 120 such cases. [ 49 ]
St. Paulus Lutheran Church in San Francisco filed a class-action lawsuit against Zoom after one of its Bible study classes was "Zoombombed" with pornographic videos on May 6, 2020. [ 50 ] The church alleged that Zoom "did nothing" when it tried to reach out to the company. [ 51 ]
In November 2020, a Dutch journalist for RTL Nieuws managed to gain access to a secret Zoom meeting of European Union defence ministers. The EU's foreign affairs representative Josep Borrell told him that it was criminal offense and he should sign off before the police arrived. The Zoombomb was revealed to have been the result of the Dutch defence minister Ank Bijleveld posting a picture of herself that showed the login and the partial PIN number. [ 52 ]
In 2022, an online event hosted by the Italian Senate 's Movimento 5 Stelle and broadcast live to Senato della Repubblica was interrupted by roughly a minute of a 3D animated Final Fantasy VII pornographic parody, displaying the character Tifa Lockhart in the middle of sexual intercourse. [ 53 ] [ 54 ] Overlapping the content's original audio was a man speaking English with a thick Italian accent stating, "I used to be a sex offender, but now I am a kindergarten teacher." [ 55 ]
Brian Adams, a man from Paintsville , Kentucky , faced multiple federal charges after he interrupted an elementary school's video conference class during the COVID-19 pandemic with a digital racist threat. He allegedly crashed a class Zoom conference on October 14, 2020, and targeted the Laureate Academy Charter School, whose student population is about 67% Black, because of its racial demographics. [ 56 ]
In 2020, livestreamer Muudea Sedik, better known as twomad , gained popularity for his Zoom bombings. Sedik would request Zoom meeting links or passwords from his followers on social media, and would broadcast the subsequent invasions live. Sedik's antics made him a popular subject for various internet memes , particularly among Generation Z . [ 57 ]
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Zooniverse is a citizen science web portal owned and operated by the Citizen Science Alliance. It is home to some of the Internet's largest, most popular and most successful citizen science projects . [ 3 ] The organization grew from the original Galaxy Zoo project and now hosts dozens of projects which allow volunteers to participate in crowdsourced scientific research. It has headquarters at Oxford University and the Adler Planetarium . [ 4 ] Unlike many early internet-based citizen science projects (such as SETI@home ) which used spare computer processing power to analyse data, known as volunteer computing , Zooniverse projects require the active participation of human volunteers to complete research tasks. Projects have been drawn from disciplines including astronomy , ecology , cell biology , humanities , and climate science . [ 5 ]
As of 14 February 2014 [update] , the Zooniverse community consisted of more than 1 million registered volunteers. [ 6 ] By March 2019, that number had reportedly risen to 1.6 million. [ 7 ] The volunteers are often collectively referred to as "Zooites". [ 8 ] [ 9 ] The data collected from the various projects has led to the publication of more than 100 scientific papers. [ 10 ] A daily news website called 'The Daily Zooniverse' provides information on the different projects under the Zooniverse umbrella, and has a presence on social media .
The founder and former principal investigator (P.I.) of the project, Chris Lintott , published a book called The Crowd & the Cosmos: Adventures in the Zooniverse in 2019. [ 11 ] In September 2023 the role of P.I. was taken over by Laura Trouille, VP of Science Engagement at the Adler Planetarium, who was co-P.I. for Zooniverse from 2015-2023. [ 12 ]
The Zooniverse is hosted by the Citizen Science Alliance, which is governed by a board of directors from seven institutions in the United Kingdom and the United States . The partners are the Adler Planetarium , Johns Hopkins University , University of Minnesota , National Maritime Museum , University of Nottingham , Oxford University and Vizzuality. [ 13 ]
date
2022
This data will become part of the Minnesota Biodiversity Atlas , the permanent digital record of the Bell Museum of Natural History's collections.
Zooniverse supports Project Builder, a tool that allows anyone to create their own project by uploading a dataset of images, video files or sound files. In Project Builder a Project Owner creates a workflow for the projects, a tutorial, a field guide and the talk forum of the Project and can add collaborators, researchers and moderators to their project. The moderators for example will have partial administrator rights in the talk, but cannot change anything concerning the workflow. [ 122 ]
Only certain kinds of projects can be enabled on Zooniverse mobile app (Android & iOS). [ 123 ] [ 124 ] [ 125 ] [ 126 ]
Media related to Zooniverse at Wikimedia Commons
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Zoopark-1 ( Russian : Зоопарк , lit. 'zoo') 1L219 is a counter-battery radar system developed by Almaz-Antey for the Soviet Armed Forces . It is a mobile active electronically scanned array radar (based on a tracked MT-LBu chassis) for the purpose of enemy field-artillery acquisition. The system can detect mortar shells at a distance of up to 20 kilometers, up to 30 kilometers for artillery shells and up to 50 kilometers for ground-to-air rockets, determining location of origin of a fire. Moving ground targets can be detected at a distance of up to 40 kilometers. [ 1 ] It reached initial operating status in 1989. [ 2 ]
The later 1L260 / 1L261 variant was designated Zoopark-1M . [ 3 ]
This Russian military article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Zoopark-1
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A zoophyte (animal-plant) is an obsolete term for an organism thought to be intermediate between animals and plants, or an animal with plant-like attributes or appearance. In the 19th century they were reclassified as Radiata which included various taxa, a term superseded by Coelenterata referring more narrowly to the animal phyla Cnidaria ( coral animals, true jellies, sea anemones, sea pens , and their allies), sponges , and Ctenophora (comb jellies).
A group of strange creatures that exist somewhere on, or between, the boundaries of plants and animals kingdoms were the subject of considerable debate in the eighteenth century. Some naturalists believed that they were a blend of plant and animal; other naturalists considered them to be entirely either plant or animal (such as sea anemones). [ 1 ]
In Eastern cultures such as Ancient China fungi were classified as plants in the Traditional Chinese Medicine texts, and cordyceps , and in particular Ophiocordyceps sinensis , were considered zoophytes. [ 2 ]
Zoophytes are common in medieval and renaissance era herbals , notable examples including the Tartar Lamb , a legendary plant which grew sheep as fruit. [ 3 ] Zoophytes appeared in many influential early medical texts, such as Dioscorides's De Materia Medica and subsequent adaptations and commentaries on that work, notably Mattioli's Discorsi . Zoophytes are frequently seen as medieval attempts to explain the origins of exotic, unknown plants with strange properties (such as cotton , in the case of the Tartar Lamb as theorized by Henry Lee , Fellow of the Linnean Society in the book The Vegetable Lamb of Tartary ). [ 4 ] [ 5 ] [ 6 ]
Reports of zoophytes continued into the seventeenth century and were commented on by many influential thinkers of the time period, including Francis Bacon . It was not until 1646 that claims of zoophytes began to be concretely refuted, and skepticism towards claims of zoophytes mounted throughout the seventeenth and eighteenth centuries. [ 3 ]
As natural history and natural philosophy developed in the 18th century, there was considerable debate and disagreements between naturalists about organisms on or near the boundary between the animal and plant kingdoms , and how to relate them in taxonomy . Interest in the topic began in the 1730s with the research by Abraham Trembley into polyps. [ 7 ]
When Carl Linnaeus published the 10th edition of Systema Naturae in 1758, marking the start of zoological nomenclature , he set out three divisions of the Kingdom of Nature: rocks, plants and animals, "though all three exist in the lithophytes", the corals. He defined zoophytes as "a composite small organism, with both animal and plant characteristics". He acknowledged contributions from the coralline expert Ellis by describing him as a "lynx-eyed discoverer of zoophytes". In 1761 he wrote to Ellis that "zoophytes have a mere vegetable life, and are increased every year under their bark, like trees" as shown by growth rings on the trunk of Gorgonia , they are "therefore vegetables, with flowers like small animals. As zoophytes are, many of them, covered with a stony coat, the Creator has been pleased that they should receive nourishment by their naked flowers. He has therefore furnished each with a pore, which we call a mouth." After wide research, in 1786 Ellis was still unconvinced "what or where the link is that divides the animal and vegetable kingdoms of Nature", and pressed Linnaeus to classify most as animals. He subsequently proposed that the animals of the corals construct their own structures, in a book completed by Daniel Solander . [ 8 ]
Georges Cuvier in his Le Règne Animal of 1817 titled one of his four divisions ( Embranchements ) of the animal kingdom "Les Zoophytes ou Animaux Rayonnés". [ 9 ] An 1834 English translation uses the term Radiata , and titles the division "The Zoophytes, or Animalia Radiata", [ 10 ] an expanded 1840 translation notes that "Neither of these names is literally applicable, for all the animals in the division are not radiated; and the very name Zoophyte, 'plant - animal,' is a contradiction. In England, the term Zoophyte is much more restricted than in France, but it is equally inapplicable, excepting, perhaps, to those species, about which there are still disputes as to whether they are animals or vegetables." [ 11 ] Despite its scientific obsolescence, Charles Darwin continued to use the term throughout his studies.
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A zoospore is a motile asexual spore that uses a flagellum for locomotion in aqueous or moist environments. [ 1 ] Also called a swarm spore, these spores are created by some protists , bacteria , and fungi to propagate themselves. Certain zoospores are infectious and transmittable, [ 1 ] such as Batrachochytrium dendrobatidis , a fungal zoospore that causes high rates of mortality in amphibians .
Zoospores are composed of a microtubular cytoskeleton base which extends from the base of the flagellum. The complexity and structure of this cytoskeleton is variable and is largely dependent on volume and size. [ 2 ] One common feature of zoospores is their asymmetrical shape; a result of the ventral grove housing the flagella base. Certain zoospores progress through different phases, the first phase commonly referred to as 'the initial'. [ 2 ] Others form cysts that vary tremendously in volume (14-4905 cubic micrometers) and shape, each with distinctive hair structures. [ 2 ]
Zoospores may possess one or more distinct types of flagella - tinsel or "decorated", and whiplash, in various combinations.
Both tinsel and whiplash flagella beat in a sinusoidal wave pattern, but when both are present, the tinsel beats in the opposite direction of the whiplash, to give two axes of control of motility .
Attachment to the base of the zoospore is variable between taxa and may help with identification of species. [ 2 ]
In eukaryotes , the four main types of zoospore are [ 3 ] illustrated in Fig. 1 at right:
A zoosporangium is the asexual structure ( sporangium ) in which the zoospores develop in plants, fungi, or protists (such as the Oomycota ). Developing sporangia of oomycetes go through a process of cleavage in which a protein kinase , in the case of Phytophthora infestans , induces the sporangial cytoplasm to split and release the various zoospores. [ 4 ] Release of the spores can occur either inside of the zoosporangium (intrasporangial zoosporogenesis) or exteriorly (extrasporangial zoosporogenesis). [ 2 ] Spores absorb water and travel through the cell membrane for excretion. [ 2 ]
Different fungal zoospores may infect different taxa of organisms. Due to zoospores' aquatic lifestyle, [ 1 ] fish and amphibians are ideal hosts. Some colonize exposed injuries in fish which may cause epidermal damage, leading to death in certain cases. [ 5 ] Others may utilize species of frogs (such as Bufo marinus and Rana catesbieana ) as carriers, allowing extended ranges of travel. [ 1 ]
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Zoothamnium niveum is a species of ciliate protozoan which forms feather-shaped colonies in marine coastal environments. The ciliates form a symbiosis with sulfur-oxidizing chemosynthetic bacteria of the species " Candidatus Thiobios zoothamnicoli", which live on the surface of the colonies and give them their unusual white color.
The conspicuously white and feather-shaped colonies are composed of individual bell-shaped cells known as zooids . The stalks of individual cells grow from a single central stalk. Colonies can reach a length of up to 15 mm, formed from hundreds of single zooids, each with a length of only 120 μm. An entire colony can contract into a ball-shaped bunch through the contraction of myonemes in their stalks. [ 2 ] [ 3 ]
The white color is produced by chemolithoautotrophic sulfur-oxidizing bacteria, which cover the entire surface of the Z. niveum colony. [ 4 ] In most other species of Zoothamnium , bacteria are only known to cover the stalks. The bacteria contain elemental sulfur , which appear white. Z. niveum appears colorless when the bacteria are absent. [ 3 ]
Like in other ciliates, a contractile vacuole maintains osmotic balance for the cell, and allows it to survive the salt concentrations in both marine and brackish water. The vacuole is located in Z. niveum directly below the lip of the peristome . [ 2 ]
Most ciliates live as single-celled organisms in aquatic environments, and the single cell carries out all functions of life, such as nutrition, metabolism, and reproduction. Colonies of Z. niveum are composed of numerous individual cells that form a feather-like colonial unit , with several different cell types. Old branches of the colony illustrate the polymorphism of the zooids when viewed under the microscope. Three different forms of the individual ciliate cells are present, which are distinct in both form and function. The large macrozooids can transform into swarmers and leave the colony. They settle on suitable surfaces and develop into new colonies. The microzooids are small cells specialized for feeding, which the colony does by consumption of their symbiotic bacteria and other organic particles. At the terminal ends of the colony are specialized zooids that can elongate and facilitate the asexual reproduction of the colony. [ 2 ]
The bacteria on different parts of a host have different shapes despite belonging to the same species ( polymorphism ). Those on the stalks are shaped like rods, but those in the region of the ciliated oral apparatus of the microzooids are shaped like small spheres (coccoid). Intermediate forms are also found in between. [ 4 ]
The sessile colonies of Z. niveum were first described from the shallow waters of the Red Sea . [ 5 ] They were later also found in the Florida Keys in the Gulf of Mexico , and at the Belize Barrier Reef in the Caribbean Sea . [ 3 ]
The colonies settle in environments that contain sulfide . Hydrogen sulfide , sulfide , and related sulfur-containing compounds like thiosulfate are produced during the decomposition and remineralization of organic material. For example, plant material like the torn-off leaves of Posidonia oceanica in seagrass meadows of the Mediterranean accumulate in depressions of rocky ledges and decompose. In mangrove forests of the Caribbean , organic material can form peat and release sulfide. [ 6 ] Hydrogen sulfide can also originate from geological phenomena such as at underwater hydrothermal vents , e.g. off the Canary Islands .
Extreme ecological conditions prevail at these sources of sulfide close to which colonies of Z. niveum settle. Because there is little water current under mangrove roots and at seagrass deposits under rock ledges, these decomposition hot-spots are extremely poor in oxygen and rich in sulfide. In mangrove forests off the coast of Belize, they have been found around small holes in the mangrove peat which form when the mangrove rootlets decompose. [ 6 ] These openings have been called sulfide "microvent[s]", [ 7 ] because they resemble in miniature the hydrothermal vents of the deep sea, the so-called black smokers , although the temperatures in shallow waters are much lower (28 °C in the Caribbean, 21 °C-25 °C in the Mediterranean (summer)), compared to the gradient between >300 °C and 2 °C in the deep sea because of volcanic activity. The Zoothamnium colonies do not settle directly over the decomposing material, but nearby e.g. on overhanging rocks, leaves of seagrass or seaweed, or mangrove roots. [ 3 ]
The symbiotic benefits provided by the colonies of Z. niveum for its attached ectosymbiotic bacteria Candidatus Thiobios zoothamnicoli (a member of the Gammaproteobacteria [ 4 ] ), which are vertically transmitted to its host, [ 8 ] are its active alternation between oxygen-rich and sulfide-rich conditions. This alternation can occur through the regular contraction and extension of the colonies and through the water currents set up by the beating of the cilia in the region of the oral opening of the ciliates. [ 9 ]
The rapid contraction and slow re-extension of the colonies causes a flow of both sulfide-rich water for the feeding of the bacteria and normal oxygenated seawater for the respiration of Z. niveum . Through the beating of its cilia at the oral apparatus of Zoothamnium is the mixing regulated. When there is a low supply of sulfur compounds, the bacteria use the sulfur that is stored inside their cells. They eventually appear pale and transparent after four hours because the stored sulfur has been consumed. However, if the sulfide concentration is too high, it can be toxic to the Zoothamnium colonies and kill the ciliates despite the bacteria. [ 9 ]
Bacteria close to the oral end of the microzooids have a coccoid form, a larger volume, and a higher division rate than the rod-shaped bacteria on the stalks, despite both belonging to the same species. This is because the mixing of water by the beating of the oral cilia result in a more optimal concentration of both oxygen and sulfide in the water there. [ 9 ] The bacteria at the oral region can thus be used as a food source and are swirled into the mouth ( cytostome ) of the ciliate and digested.
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Zootope is the total habitat available for colonisation within any certain ecotope or biotope by animal life. The community of animals so established constitutes the zoocoenosis of that ecotope.
All these words (ecotope, biotope, zootope and others) describe environmental niches at very small scales of consideration. The rabbits and squirrels and mosquitoes of any suburban garden or village park , or the deer and wolves and birds of a wilderness ravine would each be deserving of the label.
This ecoregion article is a stub . You can help Wikipedia by expanding it .
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Zooxanthellae ( / ˌ z oʊ ə z æ n ˈ θ ɛ l iː / ; sg. zooxanthella ) is a colloquial term for single-celled photosynthetic organisms that are able to live in symbiosis with diverse marine invertebrates including corals , jellyfish , demosponges , and nudibranchs . Most known zooxanthellae are in the dinoflagellate genus Symbiodinium , [ 1 ] but some are known from the genus Amphidinium , and other taxa , as yet unidentified, may have similar endosymbiont affinities. [ 2 ] "Zooxanthella" was originally a genus name (meaning literally "little yellow animal") given in 1881 by Karl Brandt to Zooxanthella nutricula (a mutualist of the radiolarian Collozoum inerme ) [ 3 ] which has been placed in the Peridiniales . [ 4 ] [ a ] Another group of unicellular eukaryotes that partake in similar endosymbiotic relationships in both marine and freshwater habitats are green algae zoochlorellae . [ 6 ]
Zooxanthellae are photosynthetic organisms, which contain chlorophyll a and chlorophyll c , as well as the dinoflagellate pigments peridinin and diadinoxanthin . These provide the yellowish and brownish colours typical of many of the host species. [ 2 ] During the day, they provide their host with the organic carbon products of photosynthesis, sometimes providing up to 90% of their host's energy needs for metabolism, growth and reproduction. In return, they receive nutrients, carbon dioxide, and an elevated position with access to sunshine. [ 7 ] [ 8 ]
Zooxanthellae can be grouped in the classes of Bacillariophyceae , Cryptophyceae , Dinophyceae , and Rhodophycaeae and of the genera Amphidinium , Gymnodinium , Aureodinium , Gyrodinium , Prorocentrum , Scrippsiella , Gloeodinium , and most commonly, Symbiodinium . [ 9 ] Zooxanthellae of genus Symbiodinium belong to a total of eight phylogenetic clades A-H, differentiated via their nuclear ribosomal DNA and chloroplast DNA. [ 10 ]
Zooxanthellae are autotrophs containing chloroplasts composed of thylakoids present in clusters of three. [ 9 ] A pyrenoid protrudes from each chloroplast and is encased along with the chloroplast by a thick, starchy covering. Within the cell’s cytoplasm also exists lipid vacuoles, calcium oxalate crystals, dictyosomes, and mitochondria . [ 9 ] The cell wall of zooxanthellae varies in structure across species. One structure consists of an outer membrane, middle layer compact with electrons, and a thin inner layer. In other species, the characteristics of this low-density inner layer make up the cell wall’s entire structure. [ 9 ] Beneath the cell wall is the cell membrane, and beneath the cell membrane are thecal vesicles. [ 9 ]
DNA in the cell exists in the form of chromatin coils tightly compacted together. [ 9 ] It is condensed in the nucleus alongside an atypical histone complement. [ 11 ] [ 12 ] [ 13 ] The DNA possesses ribosomal RNA (rRNA) that is folded and of similar morphology to rRNA in archaeobacteria. This indicates that RNA is important for DNA packaging in zooxanthellae. [ 11 ] Zooxanthellae, in addition to all other dinoflagellates, possess 5-hydroxymethyluracil and thymidine in their genomes, unlike any other eukaryotic genome. [ 11 ]
Zooxanthellae alternate between life phases expressed as cysts and as motile organisms in the water column. [ 14 ] [ 15 ] In zooxanthellae of the genus Gymnodinium , one possible life cycle of the cell begins as an immature cyst which reaches maturity then divides to form an immature cyst once more. Once growing into an older cell, it becomes no longer useful. In the life cycle of a motile zooxanthellae cell, its youngest stage is known as a zoosporangium, which matures into a zoospore capable of motility. This motile cell produces and releases gametes for reproduction. [ 15 ]
The vegetative phase in the life cycle of a zooxanthellae is the predominant form of the organism. [ 14 ] In this form, the single-celled organism has a thin cell wall. As opposed to the zoospore, the zooxanthella contains numerous chloroplasts. Once the cell continues growing, however, chloroplasts decrease in abundance. [ 14 ] The vegetative cell will either divide into two separate daughter cells or transition into a cyst stage. [ 14 ]
The most common phases in the life history of zooxanthellae following the vegetative phase are cysts, dividing cysts, and degenerate cysts. [ 15 ] Cysts possess a thick cell wall yet retain the composition of the cytoplasm and constitute the majority of clustered zooxanthellae in host tissues. This stage of the cell provides the host with a reddish-brown hue. [ 15 ] Dividing cysts make up a fourth of the composition of zooxanthellae clusters in host tissues and are expressed as cell stages where two daughter cells remain adjoined but possess individual cell walls. Degenerate cysts are present in clusters, though rare, and lose much of their mutualistic benefit to the host they reside in due to a decrease in photosynthetic efficiency. [ 15 ] The young zoosporangium and motile zoospore stages, though seen in zooxanthellae life cycles, are much rarer amongst clades. The zoospore resides in the zoosporangium until the cell wall of the cyst bursts. Zooxanthellae is only motile if it originates as a zoospore. [ 15 ]
Zooxanthellae in the zoospore stage exhibit motility as forward movement or gyratory movement. [ 15 ] In moving forward, the organism rotates on the posterior flagellum’s axis whilst simultaneously propelling through the water column. The zoospore gyrates through the water column via attachment of the posterior flagellum to a substrate. [ 15 ]
Zooxanthellae are particularly associated with reef-building corals but they also inhabit other invertebrates and protists ; their hosts include many sea anemones , jellyfish , nudibranchs , certain bivalve molluscs like the giant clam Tridacna , sponges and flatworms as well as some species of radiolarians and foraminiferans . [ 16 ] Many different species of zooxanthellae are present in host organisms, each species with its own adaptive capabilities and degree of tolerance of varying environmental factors. [ 2 ]
A juvenile organism or newly established colony can acquire its zooxanthellae via sexual reproduction or directly from the environment. The egg from which the individual developed may have already been infected by zooxanthellae at the time of fertilization, or cells of the symbiont may have been transferred from the mother in a period during which the larva was brooded by its parent. Alternatively, the new individual may acquire the zooxanthellae direct from sea water in which the dinoflagellates freely live at some stages of their life cycle. Some stony corals use chemotaxis , with infection occurring as a result of the emission by the coral of a chemical attractant. Infection may also occur after ingestion of infected faecal matter by the host, or of prey that already houses the symbionts. Such indirect acquisition can result in the new host being infected by a species of zooxanthella different from that present in its parent. [ 2 ]
A zooxanthella in symbiosis with coral is contained in vacuoles of the host’s gastrodermal cells and is of the genus Symbiodinium . [ 17 ] Zooxanthellae provide nutrients to their host cnidarians in the form of sugars, glycerol, and amino acids and in return gain carbon dioxide, phosphates, and nitrogen compounds. [ 18 ] [ 17 ] A coral exposed to environmental stressors can result in expulsion of zooxanthellae from host tissues. This in turn strips the coral of its color, in this phenomenon known as coral bleaching , where the now-transparent tissues of the coral reveal its white internal skeletal structure. [ 17 ] Variations in salinity, light intensity, temperature, pollution, sedimentation, and disease can all impact the photosynthetic efficiency of zooxanthellae or result in expulsion from their mutualistic relationships. [ 17 ]
The physiological mechanisms behind endosymbiont expulsion remain under research but are speculated to involve various means of detachment of zooxanthellae or gastrodermal cells from host corals. [ 17 ] During a bleaching event, entire gastrodermal cells containing zooxanthellae may leave the host. In other cases, gastrodermal cells will remain in the host tissues, but zooxanthellae contained in vacuoles may separately undergo damage or may physically leave the cells and enter the surrounding environment. [ 17 ]
Coral is not the only aquatic organism to be affected by bleaching and the expulsion of zooxanthellae; clams have also been found to undergo a similar process when temperatures become too high. [ 19 ] However, clams discard zooxanthellae that are still alive and have been observed being able to recover them. [ 19 ] This not only has positive indications for the clams themselves, but also the surrounding ecosystem. [ 19 ] For many organisms, clams are a vital part of the food chain. Not only can they themselves be eaten, but excrement from giant clams contains live zooxanthellae. [ 19 ] Opportunistic feeders and clams alike use excreted zooxanthellae as a nutrient source. [ 19 ] The consumption of zooxanthellae is especially vital for a clam in its veliger stage as it encourages growth. [ 19 ] Zooxanthellae are not only found in clam excrement, but in the mantle tissue as well where they take up ammonia and nitrate. [ 20 ] They are also found in the eyes of clams like Tridacna where they act as a lens. [ 21 ] Different clades of zooxanthellae have an impact on clam morphology. [ 22 ] Clade E1 of zooxanthellae seems to influence or favor smaller offspring from clams when compared to clams harboring other clades and all five clades appear to be needed in order for larval settlement to occur. [ 22 ]
Jellyfish and zooxanthellae have a history together in the scientific world as Symbiodinium was first cultured from the jellyfish Cassiopea, a model jellyfish species. [ 23 ] Many different types of zooxanthellae have been observed forming relationships with jellyfish across many different phylogenetic branches, and the roles they play will change throughout the jellyfish’s life cycle. [ 23 ] However, as the jellyfishes ages, the diversity of zooxanthellae attaching to them decreases, suggesting that zooxanthellae compete with each other to form relationships with the jellyfish. [ 23 ] Not all jellyfish form relationships with these microbes and for the most part the ones that do are found in tropic and subtropic waters. [ 23 ] The relationship between jellyfish and zooxanthellae is affected a little differently than coral in terms of climate change despite both of them being a part of the cnidaria family. [ 23 ] One study suggested that certain species of jellyfish and their symbiotic zooxanthellae may have some type of resistance to decreasing pH caused by climate change to a certain point. [ 24 ] Although, jellyfish bleaching events have been documented during extreme heat events. [ 23 ] While the causal factors that normally seem to affect the relationship between zooxanthellae and their host may not apply to jellyfish, light intensity does. [ 25 ] Light availability can affect the lipid production of zooxanthellae that the jellyfish then utilize. [ 25 ] To maximize their light uptake, jellyfish will both swim near the surface and do very specific migrations. [ 23 ] The migration patterns also assist with helping the zooxanthellae access specific nutrients. [ 23 ] Many of these jellyfish appear to be mixotrophic consuming both live prey and utilizing phototrophy. [ 23 ] This may be what helps jellyfish survive climate change and bleaching as they could switch feeding methods rather than attempting to recover lost zooxanthellae quickly. [ 23 ] There are many unknowns in when it comes to the relationship between zooxanthellae and jellyfish that scientists look to answer. [ 23 ]
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A Zores section (also: Z-section ) was a railway beam section designed by French engineer, Charles Ferdinand Zores [ fr ] , in the second half of the 19th century for use in the supporting frames of various railway structures. [ 1 ] They were very common in France. In other countries, such as Germany, the originally designated fer arrondi ( rounded profile ) became a standardised rolling mill profile for wrought iron , its shape resembling an upside down rain gutter. It was used as surfacing on steel bridges, covering the deck girders and forming the base on which gravel, concrete or plaster for the actual trackbed was laid. It was spaced 2 to 3 centimetres apart in order to improved drainage. [ 2 ] [ 3 ] For the same purpose, usually for smaller loads, buckled plate was used.
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In mathematical analysis , Zorich's theorem was proved by Vladimir A. Zorich in 1967. [ 1 ] The result was conjectured by M. A. Lavrentev in 1938. [ 2 ]
Every locally homeomorphic quasiregular mapping f : R n → R n {\displaystyle f:R^{n}\rightarrow R^{n}} for n ≥ 3 {\displaystyle n\geq 3} , is a homeomorphism of R n {\displaystyle R^{n}} . [ 3 ]
The fact that there is no such result for n = 2 {\displaystyle n=2} is easily shown using the exponential function . [ 4 ]
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it .
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Zorn's lemma , also known as the Kuratowski–Zorn lemma , is a proposition of set theory . It states that a partially ordered set containing upper bounds for every chain (that is, every totally ordered subset ) necessarily contains at least one maximal element .
The lemma was proved (assuming the axiom of choice ) by Kazimierz Kuratowski in 1922 and independently by Max Zorn in 1935. [ 2 ] It occurs in the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis , the theorem that every vector space has a basis , [ 3 ] Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that in a ring with identity every proper ideal is contained in a maximal ideal and that every field has an algebraic closure . [ 4 ]
Zorn's lemma is equivalent to the well-ordering theorem and also to the axiom of choice , in the sense that within ZF ( Zermelo–Fraenkel set theory without the axiom of choice) any one of the three is sufficient to prove the other two. [ 5 ] An earlier formulation of Zorn's lemma is the Hausdorff maximal principle which states that every totally ordered subset of a given partially ordered set is contained in a maximal totally ordered subset of that partially ordered set. [ 6 ]
To prove the existence of a mathematical object that can be viewed as a maximal element in some partially ordered set in some way, one can try proving the existence of such an object by assuming there is no maximal element and using transfinite induction and the assumptions of the situation to get a contradiction. Zorn's lemma tidies up the conditions a situation needs to satisfy in order for such an argument to work and enables mathematicians to not have to repeat the transfinite induction argument by hand each time, but just check the conditions of Zorn's lemma.
If you are building a mathematical object in stages and find that (i) you have not finished even after infinitely many stages, and (ii) there seems to be nothing to stop you continuing to build, then Zorn’s lemma may well be able to help you.
Preliminary notions:
Zorn's lemma can then be stated as:
Zorn's lemma — [ 8 ] [ 9 ] Let P {\displaystyle P} be a partially ordered set that satisfies the following two properties:
Then P {\displaystyle P} has at least one maximal element .
In fact, property (1) is redundant, since property (2) says, in particular, that the empty chain has an upper bound in P {\displaystyle P} , implying P {\displaystyle P} is nonempty. However, in practice, one often checks (1) and then verifies (2) only for nonempty chains, since the case of the empty chain is taken care by (1).
In the terminology of Bourbaki, a partially ordered set is called inductive if each chain has an upper bound in the set (in particular, the set is then nonempty). [ 10 ] Then the lemma can be stated as:
Zorn's lemma — [ 11 ] Each inductive set has a maximal element.
For some applications, the following variant may be useful.
Corollary — [ 12 ] Let P {\displaystyle P} be a partially ordered set in which every chain has an upper bound and a {\displaystyle a} an element in P {\displaystyle P} . Then there exists a maximal element b {\displaystyle b} in P {\displaystyle P} such that b ≥ a {\displaystyle b\geq a} .
Indeed, let Q = { x ∈ P ∣ x ≥ a } {\displaystyle Q=\{x\in P\mid x\geq a\}} with the partial ordering from P {\displaystyle P} . Then, for a chain in Q {\displaystyle Q} , an upper bound in P {\displaystyle P} is in Q {\displaystyle Q} and so Q {\displaystyle Q} satisfies the hypothesis of Zorn's lemma and a maximal element in Q {\displaystyle Q} is a maximal element in P {\displaystyle P} as well.
Zorn's lemma can be used to show that every vector space V has a basis . [ 13 ]
If V = { 0 }, then the empty set is a basis for V . Now, suppose that V ≠ { 0 }. Let P be the set consisting of all linearly independent subsets of V . Since V is not the zero vector space , there exists a nonzero element v of V , so P contains the linearly independent subset { v }. Furthermore, P is partially ordered by set inclusion (see inclusion order ). Finding a maximal linearly independent subset of V is the same as finding a maximal element in P .
To apply Zorn's lemma, take a chain T in P (that is, T is a subset of P that is totally ordered). If T is the empty set, then { v } is an upper bound for T in P . Suppose then that T is non-empty. We need to show that T has an upper bound, that is, there exists a linearly independent subset B of V containing all the members of T .
Take B to be the union of all the sets in T . We wish to show that B is an upper bound for T in P . To do this, it suffices to show that B is a linearly independent subset of V .
Suppose otherwise, that B is not linearly independent. Then there exists vectors v 1 , v 2 , ..., v k ∈ B and scalars a 1 , a 2 , ..., a k , not all zero, such that
Since B is the union of all the sets in T , there are some sets S 1 , S 2 , ..., S k ∈ T such that v i ∈ S i for every i = 1, 2, ..., k . As T is totally ordered, one of the sets S 1 , S 2 , ..., S k must contain the others, so there is some set S i that contains all of v 1 , v 2 , ..., v k . This tells us there is a linearly dependent set of vectors in S i , contradicting that S i is linearly independent (because it is a member of P ).
The hypothesis of Zorn's lemma has been checked, and thus there is a maximal element in P , in other words a maximal linearly independent subset B of V .
Finally, we show that B is indeed a basis of V . It suffices to show that B is a spanning set of V . Suppose for the sake of contradiction that B is not spanning. Then there exists some v ∈ V not covered by the span of B . This says that B ∪ { v } is a linearly independent subset of V that is larger than B , contradicting the maximality of B . Therefore, B is a spanning set of V , and thus, a basis of V .
Zorn's lemma can be used to show that every nontrivial ring R with unity contains a maximal ideal .
Let P be the set consisting of all proper ideals in R (that is, all ideals in R except R itself). Since R is non-trivial, the set P contains the trivial ideal {0}. Furthermore, P is partially ordered by set inclusion. Finding a maximal ideal in R is the same as finding a maximal element in P .
To apply Zorn's lemma, take a chain T in P . If T is empty, then the trivial ideal {0} is an upper bound for T in P . Assume then that T is non-empty. It is necessary to show that T has an upper bound, that is, there exists an ideal I ⊆ R containing all the members of T but still smaller than R (otherwise it would not be a proper ideal, so it is not in P ).
Take I to be the union of all the ideals in T . We wish to show that I is an upper bound for T in P . We will first show that I is an ideal of R . For I to be an ideal, it must satisfy three conditions:
#1 - I is a nonempty subset of R .
Because T contains at least one element, and that element contains at least 0, the union I contains at least 0 and is not empty. Every element of T is a subset of R , so the union I only consists of elements in R .
#2 - For every x , y ∈ I , the sum x + y is in I .
Suppose x and y are elements of I . Then there exist two ideals J , K ∈ T such that x is an element of J and y is an element of K . Since T is totally ordered, we know that J ⊆ K or K ⊆ J . Without loss of generality , assume the first case. Both x and y are members of the ideal K , therefore their sum x + y is a member of K , which shows that x + y is a member of I .
#3 - For every r ∈ R and every x ∈ I , the product rx is in I .
Suppose x is an element of I . Then there exists an ideal J ∈ T such that x is in J . If r ∈ R , then rx is an element of J and hence an element of I . Thus, I is an ideal in R .
Now, we show that I is a proper ideal. An ideal is equal to R if and only if it contains 1. (It is clear that if it is R then it contains 1; on the other hand, if it contains 1 and r is an arbitrary element of R , then r 1 = r is an element of the ideal, and so the ideal is equal to R .) So, if I were equal to R , then it would contain 1, and that means one of the members of T would contain 1 and would thus be equal to R – but R is explicitly excluded from P .
The hypothesis of Zorn's lemma has been checked, and thus there is a maximal element in P , in other words a maximal ideal in R .
A sketch of the proof of Zorn's lemma follows, assuming the axiom of choice . Suppose the lemma is false. Then there exists a partially ordered set, or poset, P such that every totally ordered subset has an upper bound, and that for every element in P there is another element bigger than it. For every totally ordered subset T we may then define a bigger element b ( T ), because T has an upper bound, and that upper bound has a bigger element. To actually define the function b , we need to employ the axiom of choice (explicitly: let B ( T ) = { b ∈ P : ∀ t ∈ T , b ≥ t } {\displaystyle B(T)=\{b\in P:\forall t\in T,b\geq t\}} , that is, the set of upper bounds for T . The axiom of choice furnishes b : b ( T ) ∈ B ( T ) {\displaystyle b:b(T)\in B(T)} ).
Using the function b , we are going to define elements a 0 < a 1 < a 2 < a 3 < ... < a ω < a ω+1 <…, in P . This uncountable sequence is really long : the indices are not just the natural numbers , but all ordinals . In fact, the sequence is too long for the set P ; there are too many ordinals (a proper class ), more than there are elements in any set (in other words, given any set of ordinals, there exists a larger ordinal), and the set P will be exhausted before long and then we will run into the desired contradiction.
The a i are defined by transfinite recursion : we pick a 0 in P arbitrary (this is possible, since P contains an upper bound for the empty set and is thus not empty) and for any other ordinal w we set a w = b ({ a v : v < w }). Because the a v are totally ordered, this is a well-founded definition.
The above proof can be formulated without explicitly referring to ordinals by considering the initial segments { a v : v < w } as subsets of P . Such sets can be easily characterized as well-ordered chains S ⊆ P where each x ∈ S satisfies x = b ({ y ∈ S : y < x }). Contradiction is reached by noting that we can always find a "next" initial segment either by taking the union of all such S (corresponding to the limit ordinal case) or by appending b ( S ) to the "last" S (corresponding to the successor ordinal case). [ 14 ]
This proof shows that actually a slightly stronger version of Zorn's lemma is true:
Lemma — If P is a poset in which every well-ordered subset has an upper bound, and if x is any element of P , then P has a maximal element greater than or equal to x . That is, there is a maximal element which is comparable to x .
Alternatively, one can use the same proof for the Hausdorff maximal principle . This is the proof given for example in Halmos' Naive Set Theory or in § Proof below.
Finally, the Bourbaki–Witt theorem can also be used to give a proof.
The basic idea of the proof is to reduce the proof to proving the following weak form of Zorn's lemma:
Lemma — Let F {\displaystyle F} be a set consisting of subsets of some fixed set such that F {\displaystyle F} satisfies the following properties:
Then F {\displaystyle F} has a maximal element with respect to set inclusion.
(Note that, strictly speaking, (1) is redundant since (2) implies the empty set is in F {\displaystyle F} .) Note the above is a weak form of Zorn's lemma since Zorn's lemma says in particular that any set of subsets satisfying the above (1) and (2) has a maximal element ((3) is not needed). The point is that, conversely, Zorn's lemma follows from this weak form. [ 15 ] Indeed, let F {\displaystyle F} be the set of all chains in P {\displaystyle P} . Then it satisfies all of the above properties (it is nonempty since the empty subset is a chain.) Thus, by the above weak form, we find a maximal element C {\displaystyle C} in F {\displaystyle F} ; i.e., a maximal chain in P {\displaystyle P} . By the hypothesis of Zorn's lemma, C {\displaystyle C} has an upper bound x {\displaystyle x} in P {\displaystyle P} . Then this x {\displaystyle x} is a maximal element since if y ≥ x {\displaystyle y\geq x} , then C ~ = C ∪ { y } {\displaystyle {\widetilde {C}}=C\cup \{y\}} is larger than or equal to C {\displaystyle C} and so C ~ = C {\displaystyle {\widetilde {C}}=C} . Thus, y = x {\displaystyle y=x} .
The proof of the weak form is given in Hausdorff maximal principle#Proof . Indeed, the existence of a maximal chain is exactly the assertion of the Hausdorff maximal principle.
The same proof also shows the following equivalent variant of Zorn's lemma: [ 16 ]
Lemma — Let P {\displaystyle P} be a partially ordered set in which each chain has a least upper bound in P {\displaystyle P} . Then P {\displaystyle P} has a maximal element.
Indeed, trivially, Zorn's lemma implies the above lemma. Conversely, the above lemma implies the aforementioned weak form of Zorn's lemma, since a union gives a least upper bound.
A proof that Zorn's lemma implies the axiom of choice illustrates a typical application of Zorn's lemma. [ 17 ] (The structure of the proof is exactly the same as the one for the Hahn–Banach theorem .)
Given a set X {\displaystyle X} of nonempty sets and its union U := ⋃ X {\displaystyle U:=\bigcup X} (which exists by the axiom of union ), we want to show there is a function
such that f ( S ) ∈ S {\displaystyle f(S)\in S} for each S ∈ X {\displaystyle S\in X} . For that end, consider the set
It is partially ordered by extension; i.e., f ≤ g {\displaystyle f\leq g} if and only if f {\displaystyle f} is the restriction of g {\displaystyle g} . If f i : X i → U {\displaystyle f_{i}:X_{i}\to U} is a chain in P {\displaystyle P} , then we can define the function f {\displaystyle f} on the union X ′ = ∪ i X i {\displaystyle X'=\cup _{i}X_{i}} by setting f ( x ) = f i ( x ) {\displaystyle f(x)=f_{i}(x)} when x ∈ X i {\displaystyle x\in X_{i}} . This is well-defined since if i < j {\displaystyle i<j} , then f i {\displaystyle f_{i}} is the restriction of f j {\displaystyle f_{j}} . The function f {\displaystyle f} is also an element of P {\displaystyle P} and is a common extension of all f i {\displaystyle f_{i}} 's. Thus, we have shown that each chain in P {\displaystyle P} has an upper bound in P {\displaystyle P} . Hence, by Zorn's lemma, there is a maximal element f {\displaystyle f} in P {\displaystyle P} that is defined on some X ′ ⊂ X {\displaystyle X'\subset X} . We want to show X ′ = X {\displaystyle X'=X} . Suppose otherwise; then there is a set S ∈ X − X ′ {\displaystyle S\in X-X'} . As S {\displaystyle S} is nonempty, it contains an element s {\displaystyle s} . We can then extend f {\displaystyle f} to a function g {\displaystyle g} by setting g | X ′ = f {\displaystyle g|_{X'}=f} and g ( S ) = s {\displaystyle g(S)=s} . (Note this step does not need the axiom of choice.) The function g {\displaystyle g} is in P {\displaystyle P} and f < g {\displaystyle f<g} , a contradiction to the maximality of f {\displaystyle f} . ◻ {\displaystyle \square }
Essentially the same proof also shows that Zorn's lemma implies the well-ordering theorem : take P {\displaystyle P} to be the set of all well-ordered subsets of a given set X {\displaystyle X} and then shows a maximal element of P {\displaystyle P} is X {\displaystyle X} . [ 18 ]
The Hausdorff maximal principle is an early statement similar to Zorn's lemma.
Kazimierz Kuratowski proved in 1922 [ 19 ] a version of the lemma close to its modern formulation (it applies to sets ordered by inclusion and closed under unions of well-ordered chains). Essentially the same formulation (weakened by using arbitrary chains, not just well-ordered) was independently given by Max Zorn in 1935, [ 20 ] who proposed it as a new axiom of set theory replacing the well-ordering theorem, exhibited some of its applications in algebra, and promised to show its equivalence with the axiom of choice in another paper, which never appeared.
The name "Zorn's lemma" appears to be due to John Tukey , who used it in his book Convergence and Uniformity in Topology in 1940. Bourbaki 's Théorie des Ensembles of 1939 refers to a similar maximal principle as "le théorème de Zorn". [ 21 ] The name " Kuratowski–Zorn lemma " prevails in Poland and Russia.
Zorn's lemma is equivalent (in ZF ) to three main results:
A well-known joke alluding to this equivalency (which may defy human intuition) is attributed to Jerry Bona :
"The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" [ 22 ]
Zorn's lemma is also equivalent to the strong completeness theorem of first-order logic. [ 23 ]
Moreover, Zorn's lemma (or one of its equivalent forms) implies some major results in other mathematical areas. For example,
In this sense, Zorn's lemma is a powerful tool, applicable to many areas of mathematics.
A weakened form of Zorn's lemma can be proven from ZF + DC (Zermelo–Fraenkel set theory with the axiom of choice replaced by the axiom of dependent choice ). Zorn's lemma can be expressed straightforwardly by observing that the set having no maximal element would be equivalent to stating that the set's ordering relation would be entire, which would allow us to apply the axiom of dependent choice to construct a countable chain. As a result, any partially ordered set with exclusively finite chains must have a maximal element. [ 28 ]
More generally, strengthening the axiom of dependent choice to higher ordinals allows us to generalize the statement in the previous paragraph to higher cardinalities. [ 28 ] In the limit where we allow arbitrarily large ordinals, we recover the proof of the full Zorn's lemma using the axiom of choice in the preceding section.
The 1970 film Zorns Lemma is named after the lemma.
The lemma was referenced on The Simpsons in the episode " Bart's New Friend ". [ 29 ]
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Zirconium tungstate is the zirconium salt of tungstic acid with the formula Zr(WO 4 ) 2 . The phase formed at ambient pressure by reaction of ZrO 2 and WO 3 is a metastable cubic phase , which has negative thermal expansion characteristics, namely it shrinks over a wide range of temperatures when heated. [ 2 ] In contrast to most other ceramics exhibiting negative CTE (coefficient of thermal expansion), the CTE of ZrW 2 O 8 is isotropic and has a large negative magnitude (average CTE of −7.2 × 10 −6 K −1 ) over a wide range of temperature (−273 °C to 777 °C). [ 3 ] A number of other phases are formed at high pressures.
Cubic zirconium tungstate (alpha-ZrW 2 O 8 ), one of the several known phases of zirconium tungstate (ZrW 2 O 8 ) is perhaps one of the most studied materials to exhibit negative thermal expansion . It has been shown to contract continuously over a previously unprecedented temperature range of 0.3 to 1050 K (at higher temperatures the material decomposes). Since the structure is cubic, as described below, the thermal contraction is isotropic - equal in all directions. There is much ongoing research attempting to elucidate why the material exhibits such dramatic negative thermal expansion. [ citation needed ]
This phase is thermodynamically unstable at room temperature with respect to the binary oxides ZrO 2 and WO 3 , but may be synthesised by heating stoichiometric quantities of these oxides together and then quenching the material by rapidly cooling it from approximately 900 °C to room temperature.
The structure of cubic zirconium tungstate consists of corner-sharing ZrO 6 octahedral and WO 4 tetrahedral structural units. Its unusual expansion properties are thought to be due to vibrational modes known as Rigid Unit Modes (RUMs), which involve the coupled rotation of the polyhedral units that make up the structure, and lead to contraction.
The arrangement of the groups in the structure of cubic ZrW 2 O 8 is analogous to the simple NaCl structure , with ZrO 6 octahedra at the Na sites, and W 2 O 8 groups at the Cl sites. The unit cell consists of 44 atoms aligned in a primitive cubic Bravais lattice , with unit cell length 9.15462 Angstroms .
The ZrO 6 octahedra are only slightly distorted from a regular conformation, and all oxygen sites in a given octahedron are related by symmetry. The W 2 O 8 unit is made up of two crystallographically distinct WO 4 tetrahedra, which are not formally bonded to each other. These two types of tetrahedra differ with respect to the W-O bond lengths and angles. The WO 4 tetrahedra are distorted from a regular shape since one oxygen is unconstrained (an atom that is bonded only to the central tungsten (W) atom), and the three other oxygens are each bonded to a zirconium atom ( i.e. the corner-sharing of polyhedra).
The structure has P2 1 3 space group symmetry at low temperatures. At higher temperatures, a centre of inversion is introduced by the disordering of the orientation of tungstate groups, and the space group above the phase transition temperature (~180C) is Pa 3 ¯ {\displaystyle {\bar {3}}} .
Octahedra and tetrahedra are linked together by sharing an oxygen atom. In the image, note the corner-touching between octahedra and tetrahedra; these are the location of the shared oxygen . The vertices of the tetrahedra and octahedra represent the oxygen, which are spread about the central zirconium and tungsten . Geometrically, the two shapes can "pivot" around these corner-sharing oxygens, without a distortion of the polyhedra themselves. This pivoting is what is thought to lead to the negative thermal expansion , as in certain low frequency normal modes this leads to the contracting 'RUMs' mentioned above.
At high pressure , zirconium tungstate undergoes a series of phase transitions , first to an amorphous phase, and then to a U 3 O 8 -type phase, in which the zirconium and tungsten atoms are disordered.
Through hot-isostatically pressing (HIP) a ZrW 2 O 8 -Cu composite (system) can be realized. Work done by C. Verdon and D.C. Dunand in 1997 used similarly sized zirconium tungstate and copper powder in a low carbon steel can coated with Cu, and they were HIPed under 103MPa pressure for 3 hours at 600 °C. A control experiment was also conducted, with only a heat treatment (i.e., no pressing) for the same powder mixture also under 600 °C for 3 hours in a quartz tube gettered with titanium.
The results from X-ray diffraction (XRD) in the graph in Verdon & Dunand's paper shows expected products. (a) is from the as received zirconium tungstate powder, (b) is the result from the control experiment , and (c) is the ceramic product from the HIP process. Apparently there are new phases formed according to Spectrum (c) with no ZrW 2 O 8 left. While for the control experiment only partial amount of ZrW 2 O 8 was decomposed.
While complex oxides containing Cu, Zr, and W were believed to be created, selected area diffraction (SAD) of the ceramic product has proven the existence of Cu 2 O as precipitates after reaction. A model consisted of two concurrent processes were surmised (as presented): (b) the decomposition of the ceramic and loss of oxygen under low oxygen partial pressure at high temperature leads to Cu 2 O formation; (c) copper diffuses into the ceramic and forms new oxides that absorb some oxygen upon cooling.
Since only very few oxides, those of noble metals which are very expensive, are less stable than Cu 2 O and Cu 2 O was believed to be more stable than ZrW 2 O 8 , kinetic control of the reaction must be taken into account. For example, reducing reaction time and temperature helps alleviate the residual stress caused by different phases of the ceramic during reaction, which could lead to a delamination of the ceramic particles from the matrix and an increase in the CTE. [ 4 ]
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Zirconium(IV) bromide is the inorganic compound with the formula ZrBr 4 . This colourless solid is the principal precursor to other Zr–Br compounds.
ZrBr 4 is prepared by the action of bromine on zirconium oxide via a carbothermic reaction : [ 1 ]
Like many related tetrahalides, it is purified by sublimation .
It can also be prepared by treatment of the borohydride complex with hydrogen bromide : [ 2 ]
Like related tetrabromides of Ti and Hf, ZrBr 4 hydrolyzes readily to give the oxybromide , with release of hydrogen bromide .
No single crystal X-ray study of ZrBr 4 has been described. Some reports suggest that it is isostructural with TiCl 4 and TiBr 4 , featuring tetrahedral metal centers. [ 3 ] Other studies indicate a polymeric structure. [ 4 ] ZrCl 4 is polymeric in the solid state, featuring octahedral Zr centers. [ 5 ]
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Zirconium(III) chloride is an inorganic compound with formula ZrCl 3 . It is a blue-black solid that is highly sensitive to air .
The material was first claimed by Ruff and Wallstein who reduced zirconium tetrachloride with aluminium to give impure samples. [ 4 ] Subsequently, the problem with aluminium contamination was solved when it was prepared by reduction using zirconium metal: [ 5 ]
When aluminium is used as the reducing agent with zirconium tetrachloride, a series of choloroaluminates are formed, for example [Zr(AlCl 4 ) 2 (AlCl 4 ) 2 ] and Zr(AlCl 4 ) 3 . [ 6 ]
Since the trihalides, such as zirconium trichloride, are comparatively nonvolatile, contamination can be avoided by using a gaseous reductant. For example, zirconium trichloride can be prepared by reduction of zirconium tetrachloride with hydrogen. [ 7 ]
Some zirconium halides (ZrCl 3 , ZrBr 3 , and ZrI 3 ) have structures similar to HfI 3 . They also have similar space group (P6 3 /mcm) and hexagonal structure with 2 molecules in the cell. [ 2 ] The magnetic susceptibility of zirconium trichloride suggests metal-metal interactions of the unpaired electron on each Zr(III) center. The magnetic moment of ZrCl 3 (0.4 BM ) indicates considerable overlap of metal orbitals. [ 8 ]
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Zirconium(IV) chloride , also known as zirconium tetrachloride , ( Zr Cl 4 ) is an inorganic compound frequently used as a precursor to other compounds of zirconium. This white high-melting solid hydrolyzes rapidly in humid air.
Unlike molecular TiCl 4 , solid ZrCl 4 adopts a polymeric structure wherein each Zr is octahedrally coordinated. This difference in structures is responsible for the disparity in their properties: TiCl 4 is distillable, but ZrCl 4 is a solid. In the solid state, ZrCl 4 adopts a tape-like linear polymeric structure—the same structure adopted by HfCl 4 . This polymer degrades readily upon treatment with Lewis bases , which cleave the Zr-Cl-Zr linkages. [ 4 ]
This conversion entails treatment of zirconium oxide with carbon in the presence of chlorine at high temperature:
A laboratory scale process uses carbon tetrachloride in place of carbon and chlorine: [ 5 ]
ZrCl 4 is an intermediate in the conversion of zirconium minerals to metallic zirconium by the Kroll process . In nature, zirconium minerals usually exist as oxides (reflected also by the tendency of all zirconium chlorides to hydrolyze). For their conversion to bulk metal, these refractory oxides are first converted to the tetrachloride, which can be distilled at high temperatures. The purified ZrCl 4 can be reduced with Zr metal to produce zirconium(III) chloride .
ZrCl 4 is the most common precursor for chemical vapor deposition of zirconium dioxide and zirconium diboride . [ 6 ]
In organic synthesis zirconium tetrachloride is used as a weak Lewis acid for the Friedel-Crafts reaction , the Diels-Alder reaction and intramolecular cyclisation reactions. [ 7 ] It is also used to make water-repellent treatment of textiles and other fibrous materials.
Hydrolysis of ZrCl 4 gives the hydrated hydroxy chloride cluster called zirconyl chloride . This reaction is rapid and virtually irreversible, consistent with the high oxophilicity of zirconium(IV). For this reason, manipulations of ZrCl 4 typically require air-free techniques .
ZrCl 4 is the principal starting compound for the synthesis of many organometallic complexes of zirconium. [ 8 ] Because of its polymeric structure, ZrCl 4 is usually converted to a molecular complex before use. It forms a 1:2 complex with tetrahydrofuran : CAS [21959-01-3], mp 175–177 °C. [ 9 ] Sodium cyclopentadienide (NaC 5 H 5 ) reacts with ZrCl 4 (THF) 2 to give zirconocene dichloride , ZrCl 2 (C 5 H 5 ) 2 , a versatile organozirconium complex. [ 10 ] One of the most curious properties of ZrCl 4 is its high solubility in the presence of methylated benzenes, such as durene . This solubilization arises through the formation of π-complexes. [ 11 ]
The log (base 10) of the vapor pressure of zirconium tetrachloride (from 480 to 689 K) is given by the equation: log 10 (P) = −5400/T + 11.766, where the pressure is measured in torrs and temperature in kelvins . The log (base 10) of the vapor pressure of solid zirconium tetrachloride (from 710 to 741 K) is given by the equation log 10 (P) = −3427/T + 9.088. The pressure at the melting point is 14,500 torrs. [ 12 ]
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Zirconium(IV) fluoride describes members of a family inorganic compounds with the formula Zr F 4 (H 2 O) x . All are colorless, diamagnetic solids. Anhydrous Zirconium(IV) fluoride is a component of ZBLAN fluoride glass . [ 2 ]
Three crystalline phases of ZrF 4 have been reported, α ( monoclinic ), β ( tetragonal , Pearson symbol tP40, space group P42/m, No 84) and γ (unknown structure). β and γ phases are unstable and irreversibly transform into the α phase at 400 °C. [ 3 ]
Zirconium(IV) fluoride forms several hydrates. The trihydrate has the structure (μ−F) 2 [ZrF 3 (H 2 O) 3 ] 2 . [ 4 ]
Zirconium fluoride can be produced by several methods. Zirconium dioxide reacts with hydrogen fluoride and hydrofluoric acid to afford the anhydrous and monohydrates:
The reaction of Zr metal reacts at high temperatures with HF as well:
Zirconium dioxide reacts at 200 °C with solid ammonium bifluoride to give the heptafluorozirconate salt, which can be converted to the tetrafluoride at 500 °C:
Addition of hydrofluoric acid to solutions of zirconium nitrate precipitates solid monohydrate. Hydrates of zirconium tetrafluoride can be dehydrated by heating under a stream of hydrogen fluoride.
Zirconium fluoride can be purified by distillation or sublimation . [ 2 ]
Zirconium fluoride forms double salts with other fluorides . The most prominent is potassium hexafluorozirconate , formed by fusion of potassium fluoride and zirconium tetrafluoride: [ 5 ]
The major and perhaps only commercial application of zirconium fluoride is as a precursor to ZBLAN glasses. [ 2 ]
Mixture of sodium fluoride, zirconium fluoride, and uranium tetrafluoride (53-41-6 mol.%) was used as a coolant in the Aircraft Reactor Experiment . A mixture of lithium fluoride , beryllium fluoride , zirconium fluoride, and uranium-233 tetrafluoride was used in the Molten-Salt Reactor Experiment . ( Uranium-233 is used in the thorium fuel cycle reactors.) [ citation needed ]
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Zirconium(II) hydride is a molecular chemical compound with the chemical formula Zr H 2 . It is a grey crystalline solid or dark gray to black powder. [ 4 ] It has been prepared by laser ablation and isolated at low temperature. [ 6 ]
Zirconium(II) hydride has repeatedly been the subject of Dirac – Hartree–Fock relativistic calculation studies , which investigate the stabilities, geometries, and relative energies of hydrides of the formula MH 4 , MH 3 , MH 2 , or MH.
Zirconium(II) hydride has a dihedral (C 2v ) structure. In zirconium(II) hydride, the formal oxidation states of zirconium and hydrogen are +2 and −1, respectively, because the electronegativity of zirconium is lower than that of hydrogen. The stability of metal hydrides with the formula MH 2 (M = Ti , Zr , Hf ) decreases from Ti to Hf.
Zirconium(II) hydride is used as a thermal neutron moderator in nuclear reactors and as a material for neutron reflectors in fast reactors . [ 5 ]
Zirconium(II) hydride in the form of a powder is used in powder metallurgy as a hydrogenation catalyst , vacuum tube getter , foaming agent in the production of metal foams and as a reducing agent . [ 5 ]
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Zirconium(IV) iodide is the chemical compound with the formula Zr I 4 . It is the most readily available iodide of zirconium. It is an orange-coloured solid that degrades in the presence of water. The compound was once prominent as an intermediate in the purification of zirconium metal.
Like most binary metal halides, zirconium(IV) iodide adopts a polymeric structure. As characterized by X-ray crystallography , the compound consists of octahedral Zr(IV) centers interconnected by four doubly bridging iodide ligands. The Zr-I distances of 2.692 (terminal) and 3.030 Å [ 2 ] [ 3 ]
This compound can be prepared by heating zirconium metal and an excess of iodine. [ 1 ] The solid is purified by sublimation (400 °C, 10-4 mm Hg). [ 4 ]
Pyrolysis of zirconium(IV) iodide gas by contact with a hot wire was the first industrial process for the commercial production of pure ductile metallic zirconium. This crystal bar process was developed by Anton Eduard van Arkel and Jan Hendrik de Boer in 1925. [ 5 ]
Heating the tetraiodide with zirconium metal gives zirconium triiodide : [ 4 ]
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Zirconium dioxide ( ZrO 2 ), sometimes known as zirconia (not to be confused with zirconium silicate or zircon ), is a white crystalline oxide of zirconium . Its most naturally occurring form, with a monoclinic crystalline structure , is the mineral baddeleyite . A dopant [ clarification needed ] stabilized cubic structured zirconia, cubic zirconia , is synthesized in various colours for use as a gemstone and a diamond simulant . [ 1 ]
Zirconia is produced by calcining zirconium compounds, exploiting its high thermostability . [ 2 ]
Three phases are known: monoclinic below 1170 °C, tetragonal between 1170 °C and 2370 °C, and cubic above 2370 °C. [ 3 ] The trend is for higher symmetry at higher temperatures, as is usually the case. A small percentage of the oxides of calcium or yttrium stabilize in the cubic phase. [ 2 ] The very rare mineral tazheranite , (Zr,Ti,Ca)O 2 , is cubic . Unlike TiO 2 , which features six-coordinated titanium in all phases, monoclinic zirconia consists of seven-coordinated zirconium centres. This difference is attributed to the larger size of the zirconium atom relative to the titanium atom. [ 4 ]
Zirconia is chemically unreactive. It is slowly attacked by concentrated hydrofluoric acid and sulfuric acid . When heated with carbon, it converts to zirconium carbide . When heated with carbon in the presence of chlorine, it converts to zirconium(IV) chloride . This conversion is the basis for the purification of zirconium metal and is analogous to the Kroll process .
Zirconium dioxide is one of the most studied ceramic materials. ZrO 2 adopts a monoclinic crystal structure at room temperature and transitions to tetragonal and cubic at higher temperatures. The change of volume caused by the structure transitions from tetragonal to monoclinic to cubic induces large stresses, causing it to crack upon cooling from high temperatures. [ 5 ] When the zirconia is blended with some other oxides, the tetragonal and/or cubic phases are stabilized. Effective dopants include magnesium oxide (MgO), yttrium oxide ( Y 2 O 3 , yttria), calcium oxide ( CaO ), and cerium(III) oxide ( Ce 2 O 3 ). [ 6 ]
Zirconia is often more useful in its phase 'stabilized' state. Upon heating, zirconia undergoes disruptive phase changes. By adding small percentages of yttria, these phase changes are eliminated, and the resulting material has superior thermal, mechanical, and electrical properties. In some cases, the tetragonal phase can be metastable . If sufficient quantities of the metastable tetragonal phase is present, then an applied stress, magnified by the stress concentration at a crack tip, can cause the tetragonal phase to convert to monoclinic, with the associated volume expansion. This phase transformation can then put the crack into compression, retarding its growth, and enhancing the fracture toughness . This mechanism, known as transformation toughening , significantly extends the reliability and lifetime of products made with stabilized zirconia. [ 6 ] [ 7 ]
The ZrO 2 band gap is dependent on the phase (cubic, tetragonal, monoclinic, or amorphous) and preparation methods, with typical estimates from 5–7 eV. [ 8 ]
A special case of zirconia is that of tetragonal zirconia polycrystal , or TZP, which is indicative of polycrystalline zirconia composed of only the metastable tetragonal phase.
When ZrO₂ is stabilised by adding 3 mol% of yttrium oxide (3Y-ZrO₂) at high temperatures (~1500 °C), its mechanical properties such as fracture toughness , flexural strength , and hardness are significantly improved. This is because 3Y-ZrO₂ retains a metastable tetragonal phase at room temperature, which undergoes a stress-induced transformation to the monoclinic phase, leading to phase transformation toughening mechanism under high stress intensity.
In contrast, when ZrO₂ is stabilised with 5 mol% of yttrium oxide (5Y-ZrO₂), it is primarily in the cubic phase, and does not undergo transformation toughening mechanism when stress is applied. As a result, while 5Y-ZrO₂ exhibits better optical properties i.e, enhanced translucency due to fewer grain boundaries to scatter light , its mechanical properties ( fracture toughness , strength , and hardness ) do not improve in the same way as 3Y-ZrO₂. [ 9 ] [ 10 ]
The main use of zirconia is in the production of hard ceramics, such as in dentistry, [ 11 ] with other uses including as a protective coating on particles of titanium dioxide pigments, [ 2 ] as a refractory material, in insulation , abrasives , and enamels .
Stabilized zirconia is used in oxygen sensors and fuel cell membranes because it has the ability to allow oxygen ions to move freely through the crystal structure at high temperatures. This high ionic conductivity (and a low electronic conductivity) makes it one of the most useful electroceramics . [ 2 ] Zirconium dioxide is also used as the solid electrolyte in electrochromic devices .
Zirconia is a precursor to the electroceramic lead zirconate titanate ( PZT ), which is a high-κ dielectric, which is found in myriad components.
The very low thermal conductivity of cubic phase of zirconia also has led to its use as a thermal barrier coating , or TBC, in jet and diesel engines to allow operation at higher temperatures. [ 12 ] Thermodynamically, the higher the operation temperature of an engine, the greater the possible efficiency . Another low-thermal-conductivity use is as a ceramic fiber insulation for crystal growth furnaces, fuel-cell stacks, and infrared heating systems.
This material is also used in dentistry in the manufacture of subframes for the construction of dental restorations such as crowns and bridges , which are then veneered with a conventional feldspathic porcelain for aesthetic reasons, or of strong, extremely durable dental prostheses constructed entirely from monolithic zirconia, with limited but constantly improving aesthetics. [ 13 ] [ 14 ] [ 15 ] Zirconia stabilized with yttria (yttrium oxide), known as yttria-stabilized zirconia , can be used as a strong base material in some full ceramic crown restorations. [ 14 ] [ 16 ]
Transformation-toughened zirconia is used to make ceramic knives . [ 17 ] Because of the hardness, ceramic-edged cutlery stays sharp longer than steel edged products. [ 18 ]
Due to its infusibility and brilliant luminosity when incandescent , it was used as an ingredient of sticks for limelight . [ citation needed ]
Zirconia has been proposed to electrolyze carbon monoxide and oxygen from the atmosphere of Mars to provide both fuel and oxidizer that could be used as a store of chemical energy for use with surface transportation on Mars. Carbon monoxide/oxygen engines have been suggested for early surface transportation use, as both carbon monoxide and oxygen can be straightforwardly produced by zirconia electrolysis without requiring use of any of the Martian water resources to obtain hydrogen, which would be needed for the production of methane or any hydrogen-based fuels. [ 19 ]
Zirconia can be used as photocatalyst [ 20 ] since its high band gap (~ 5 eV) [ 21 ] allows the generation of high-energy electrons and holes. Some studies demonstrated the activity of doped zirconia (in order to increase visible light absorption) in degrading organic compounds [ 22 ] [ 23 ] and reducing Cr(VI) from wastewaters. [ 24 ]
Zirconia is also a potential high-κ dielectric material with potential applications as an insulator in transistors .
Zirconia is also employed in the deposition of optical coatings ; it is a high-index material usable from the near-UV to the mid-IR , due to its low absorption in this spectral region. In such applications, it is typically deposited by PVD . [ 25 ]
In jewelry making, some watch cases are advertised as being "black zirconium oxide". [ 26 ] In 2015 Omega released a fully ZrO 2 watch named "The Dark Side of The Moon" [ 27 ] with ceramic case, bezel, pushers, and clasp, advertising it as four times harder than stainless steel and therefore much more resistant to scratches during everyday use.
In gas tungsten arc welding , tungsten electrodes containing 1% zirconium oxide (a.k.a. zirconia ) instead of 2% thorium have good arc starting and current capacity, and are not radioactive. [ 28 ]
Single crystals of the cubic phase of zirconia are commonly used as diamond simulant in jewellery . Like diamond, cubic zirconia has a cubic crystal structure and a high index of refraction . Visually discerning a good quality cubic zirconia gem from a diamond is difficult, and most jewellers will have a thermal conductivity tester to identify cubic zirconia by its low thermal conductivity (diamond is a very good thermal conductor). This state of zirconia is commonly called cubic zirconia , CZ , or zircon by jewellers , but the last name is not chemically accurate. Zircon is actually the mineral name for naturally occurring zirconium(IV) silicate ( ZrSiO 4 ).
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Zirconyl chloride is the inorganic compound with the formula of [Zr 4 (OH) 8 (H 2 O) 16 ]Cl 8 (H 2 O) 12 , more commonly written ZrOCl 2 ·8H 2 O, and referred to as zirconyl chloride octahydrate. It is a white solid and is the most common water-soluble derivative of zirconium . A compound with the formula ZrOCl 2 has not been characterized. [ 1 ]
The salt is produced by hydrolysis of zirconium tetrachloride or treating zirconium oxide with hydrochloric acid . [ 2 ] It adopts a tetrameric structure, consisting of the cation [Zr 4 (OH) 8 ] 8+ . features four pairs of hydroxide bridging ligands linking four Zr 4+ centers. The chloride anions are not ligands , consistent with the high oxophilicity of Zr(IV). [ 1 ] The salt crystallizes as tetragonal crystals. [ 3 ]
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Zirconium(IV) sulfide is the inorganic compound with the formula Zr S 2 . It is a violet-brown solid. It adopts a layered structure similar to that of cadmium iodide .
Like the closely related titanium disulfide , ZrS 2 is prepared by heating sulfur and zirconium metal. It can be purified by vapor transport using iodine. [ 2 ]
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Zirconium(4+) orthosilicate
Zirconium silicate , also zirconium orthosilicate , ZrSiO 4 , is a chemical compound , a silicate of zirconium . It occurs in nature as zircon , a silicate mineral . Powdered zirconium silicate is also known as zircon flour.
Zirconium silicate is usually colorless, but impurities induce various colorations. It is insoluble in water, acids, alkali and aqua regia . Hardness is 7.5 on the Mohs scale . [ 1 ]
Zircon consists of 8-coordinated Zr 4+ centers linked to tetrahedral orthosilicate SiO 4 4- sites. The oxygen atoms are all triply bridging, each with the environment OZr 2 Si. Given its highly crosslinked structure, the material is hard, and hence prized as gemstone and abrasive.
Zr(IV) is a d 0 ion. Consequently the material is colorless and diamagnetic.
Zirconium silicate occurs in nature as mineral zircon . Concentrated sources of zircon are rare. It is mined from sand deposits and separated by gravity. Some sands contain a few percent of zircon. [ 2 ]
It can also be synthesized by fusion of SiO 2 and ZrO 2 in an arc furnace, or by reacting a zirconium salt with sodium silicate in an aqueous solution.
As of 1995, the annual consumption of zirconium silicate was nearly 1M tons. The major applications exploit its refractory nature and resistance to corrosion by alkali materials. [ 2 ] Two end-uses are for enamels , and ceramic glazes . In enamels and glazes it serves as an opacifier . It can be also present in some cements .
Another use of zirconium silicate is as beads for milling and grinding .
Thin films of zirconium silicate and hafnium silicate produced by chemical vapor deposition , most often MOCVD , can be used as a high-k dielectric as a replacement for silicon dioxide in semiconductors. [ 3 ]
Zirconium silicates have also been studied for potential use in medical applications. For example, ZS-9 is a zirconium silicate that was designed specifically to trap potassium ions over other ions throughout the gastrointestinal tract. [ 4 ]
Zirconium silicate is also used as foundry sands due to its high thermal stability. [ 5 ] t is also the primary source of zirconium , which is used in various applications, including in nuclear reactors , due to its high resistance to corrosion and low neutron absorption. [ 6 ]
Zirconium silicate is an abrasive irritant for skin and eyes. Chronic exposure to dust can cause pulmonary granulomas , skin inflammation, and skin granuloma. [ 7 ] However, there are no known adverse effects for normal, incidental ingestion. [ 8 ]
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Zirconium silicon sulfide ( ZrSiS ) is a crystalline layered Dirac semi-metal compound of zirconium , silicon and sulfur . [ 1 ] Its crystals are made from planes of five single-atom layers of each element in the order S-Zr-Si-Zr-S, with the single element planes connected to their neighbors by van der Waals forces . [ 1 ] [ 2 ]
Semi-Dirac fermions were first observed within ZrSiS. [ 3 ] [ 4 ]
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Zirconium tungstate is the zirconium salt of tungstic acid with the formula Zr(WO 4 ) 2 . The phase formed at ambient pressure by reaction of ZrO 2 and WO 3 is a metastable cubic phase , which has negative thermal expansion characteristics, namely it shrinks over a wide range of temperatures when heated. [ 2 ] In contrast to most other ceramics exhibiting negative CTE (coefficient of thermal expansion), the CTE of ZrW 2 O 8 is isotropic and has a large negative magnitude (average CTE of −7.2 × 10 −6 K −1 ) over a wide range of temperature (−273 °C to 777 °C). [ 3 ] A number of other phases are formed at high pressures.
Cubic zirconium tungstate (alpha-ZrW 2 O 8 ), one of the several known phases of zirconium tungstate (ZrW 2 O 8 ) is perhaps one of the most studied materials to exhibit negative thermal expansion . It has been shown to contract continuously over a previously unprecedented temperature range of 0.3 to 1050 K (at higher temperatures the material decomposes). Since the structure is cubic, as described below, the thermal contraction is isotropic - equal in all directions. There is much ongoing research attempting to elucidate why the material exhibits such dramatic negative thermal expansion. [ citation needed ]
This phase is thermodynamically unstable at room temperature with respect to the binary oxides ZrO 2 and WO 3 , but may be synthesised by heating stoichiometric quantities of these oxides together and then quenching the material by rapidly cooling it from approximately 900 °C to room temperature.
The structure of cubic zirconium tungstate consists of corner-sharing ZrO 6 octahedral and WO 4 tetrahedral structural units. Its unusual expansion properties are thought to be due to vibrational modes known as Rigid Unit Modes (RUMs), which involve the coupled rotation of the polyhedral units that make up the structure, and lead to contraction.
The arrangement of the groups in the structure of cubic ZrW 2 O 8 is analogous to the simple NaCl structure , with ZrO 6 octahedra at the Na sites, and W 2 O 8 groups at the Cl sites. The unit cell consists of 44 atoms aligned in a primitive cubic Bravais lattice , with unit cell length 9.15462 Angstroms .
The ZrO 6 octahedra are only slightly distorted from a regular conformation, and all oxygen sites in a given octahedron are related by symmetry. The W 2 O 8 unit is made up of two crystallographically distinct WO 4 tetrahedra, which are not formally bonded to each other. These two types of tetrahedra differ with respect to the W-O bond lengths and angles. The WO 4 tetrahedra are distorted from a regular shape since one oxygen is unconstrained (an atom that is bonded only to the central tungsten (W) atom), and the three other oxygens are each bonded to a zirconium atom ( i.e. the corner-sharing of polyhedra).
The structure has P2 1 3 space group symmetry at low temperatures. At higher temperatures, a centre of inversion is introduced by the disordering of the orientation of tungstate groups, and the space group above the phase transition temperature (~180C) is Pa 3 ¯ {\displaystyle {\bar {3}}} .
Octahedra and tetrahedra are linked together by sharing an oxygen atom. In the image, note the corner-touching between octahedra and tetrahedra; these are the location of the shared oxygen . The vertices of the tetrahedra and octahedra represent the oxygen, which are spread about the central zirconium and tungsten . Geometrically, the two shapes can "pivot" around these corner-sharing oxygens, without a distortion of the polyhedra themselves. This pivoting is what is thought to lead to the negative thermal expansion , as in certain low frequency normal modes this leads to the contracting 'RUMs' mentioned above.
At high pressure , zirconium tungstate undergoes a series of phase transitions , first to an amorphous phase, and then to a U 3 O 8 -type phase, in which the zirconium and tungsten atoms are disordered.
Through hot-isostatically pressing (HIP) a ZrW 2 O 8 -Cu composite (system) can be realized. Work done by C. Verdon and D.C. Dunand in 1997 used similarly sized zirconium tungstate and copper powder in a low carbon steel can coated with Cu, and they were HIPed under 103MPa pressure for 3 hours at 600 °C. A control experiment was also conducted, with only a heat treatment (i.e., no pressing) for the same powder mixture also under 600 °C for 3 hours in a quartz tube gettered with titanium.
The results from X-ray diffraction (XRD) in the graph in Verdon & Dunand's paper shows expected products. (a) is from the as received zirconium tungstate powder, (b) is the result from the control experiment , and (c) is the ceramic product from the HIP process. Apparently there are new phases formed according to Spectrum (c) with no ZrW 2 O 8 left. While for the control experiment only partial amount of ZrW 2 O 8 was decomposed.
While complex oxides containing Cu, Zr, and W were believed to be created, selected area diffraction (SAD) of the ceramic product has proven the existence of Cu 2 O as precipitates after reaction. A model consisted of two concurrent processes were surmised (as presented): (b) the decomposition of the ceramic and loss of oxygen under low oxygen partial pressure at high temperature leads to Cu 2 O formation; (c) copper diffuses into the ceramic and forms new oxides that absorb some oxygen upon cooling.
Since only very few oxides, those of noble metals which are very expensive, are less stable than Cu 2 O and Cu 2 O was believed to be more stable than ZrW 2 O 8 , kinetic control of the reaction must be taken into account. For example, reducing reaction time and temperature helps alleviate the residual stress caused by different phases of the ceramic during reaction, which could lead to a delamination of the ceramic particles from the matrix and an increase in the CTE. [ 4 ]
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In number theory , Zsigmondy's theorem , named after Karl Zsigmondy , states that if a > b > 0 {\displaystyle a>b>0} are coprime integers , then for any integer n ≥ 1 {\displaystyle n\geq 1} , there is a prime number p (called a primitive prime divisor ) that divides a n − b n {\displaystyle a^{n}-b^{n}} and does not divide a k − b k {\displaystyle a^{k}-b^{k}} for any positive integer k < n {\displaystyle k<n} , with the following exceptions:
This generalizes Bang's theorem, [ 1 ] which states that if n > 1 {\displaystyle n>1} and n {\displaystyle n} is not equal to 6, then 2 n − 1 {\displaystyle 2^{n}-1} has a prime divisor not dividing any 2 k − 1 {\displaystyle 2^{k}-1} with k < n {\displaystyle k<n} .
Similarly, a n + b n {\displaystyle a^{n}+b^{n}} has at least one primitive prime divisor with the exception 2 3 + 1 3 = 9 {\displaystyle 2^{3}+1^{3}=9} .
Zsigmondy's theorem is often useful, especially in group theory , where it is used to prove that various groups have distinct orders except when they are known to be the same. [ 2 ] [ 3 ]
The theorem was discovered by Zsigmondy working in Vienna from 1894 until 1925.
Let ( a n ) n ≥ 1 {\displaystyle (a_{n})_{n\geq 1}} be a sequence of nonzero integers.
The Zsigmondy set associated to the sequence is the set
i.e., the set of indices n {\displaystyle n} such that every prime dividing a n {\displaystyle a_{n}} also divides some a m {\displaystyle a_{m}} for some m < n {\displaystyle m<n} . Thus Zsigmondy's theorem implies that Z ( a n − b n ) ⊂ { 1 , 2 , 6 } {\displaystyle {\mathcal {Z}}(a^{n}-b^{n})\subset \{1,2,6\}} , and Carmichael's theorem says that the Zsigmondy set of the Fibonacci sequence is { 1 , 2 , 6 , 12 } {\displaystyle \{1,2,6,12\}} , and that of the Pell sequence is { 1 } {\displaystyle \{1\}} . In 2001 Bilu, Hanrot, and Voutier [ 4 ] proved that in general, if ( a n ) n ≥ 1 {\displaystyle (a_{n})_{n\geq 1}} is a Lucas sequence or a Lehmer sequence , then Z ( a n ) ⊆ { 1 ≤ n ≤ 30 } {\displaystyle {\mathcal {Z}}(a_{n})\subseteq \{1\leq n\leq 30\}} (see OEIS : A285314 , there are only 13 such n {\displaystyle n} s, namely 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 18, 30).
Lucas and Lehmer sequences are examples of divisibility sequences .
It is also known that if ( W n ) n ≥ 1 {\displaystyle (W_{n})_{n\geq 1}} is an elliptic divisibility sequence , then its Zsigmondy
set Z ( W n ) {\displaystyle {\mathcal {Z}}(W_{n})} is finite . [ 5 ] However, the result is ineffective in the sense that the proof does not give an explicit upper bound for the largest element in Z ( W n ) {\displaystyle {\mathcal {Z}}(W_{n})} ,
although it is possible to give an effective upper bound for the number of elements in Z ( W n ) {\displaystyle {\mathcal {Z}}(W_{n})} . [ 6 ]
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Zstandard is a lossless data compression algorithm developed by Yann Collet at Facebook . Zstd is the corresponding reference implementation in C , released as open-source software on 31 August 2016. [ 3 ] [ 4 ]
The algorithm was published in 2018 as RFC 8478 , which also defines an associated media type "application/zstd", filename extension "zst", and HTTP content encoding "zstd". [ 5 ]
Zstandard was designed to give a compression ratio comparable to that of the DEFLATE algorithm (developed in 1991 and used in the original ZIP and gzip programs), but faster, especially for decompression. It is tunable with compression levels ranging from negative 7 (fastest) [ 6 ] to 22 (slowest in compression speed, but best compression ratio).
Starting from version 1.3.2 (October 2017), zstd optionally implements very-long-range search and deduplication ( --long , 128 MiB window) similar to rzip or lrzip . [ 7 ]
Compression speed can vary by a factor of 20 or more between the fastest and slowest levels, while decompression is uniformly fast, varying by less than 20% between the fastest and slowest levels. [ 8 ] The Zstandard command-line has an "adaptive" ( --adapt ) mode that varies compression level depending on I/O conditions, mainly how fast it can write the output.
Zstd at its maximum compression level gives a compression ratio close to lzma , lzham , and ppmx , and performs better [ vague ] than lza or bzip2 . [ improper synthesis? ] [ 9 ] [ 10 ] Zstandard reaches the current Pareto frontier , as it decompresses faster than any other currently available algorithm with similar or better compression ratio. [ as of? ] [ 11 ] [ 12 ]
Dictionaries can have a large impact on the compression ratio of small files, so Zstandard can use a user-provided compression dictionary. It also offers a training mode, able to generate a dictionary from a set of samples. [ 13 ] [ 14 ] In particular, one dictionary can be loaded to process large sets of files with redundancy between files, but not necessarily within each file, such as for log files .
Zstandard combines a dictionary-matching stage ( LZ77 ) with a large search window and a fast entropy-coding stage. It uses both Huffman coding (used for entries in the Literals section) [ 15 ] and finite-state entropy (FSE) – a fast tabled version of ANS, tANS , used for entries in the Sequences section. Because of the way that FSE carries over state between symbols, decompression involves processing symbols within the Sequences section of each block in reverse order (from last to first).
The Linux kernel has included Zstandard since November 2017 (version 4.14) as a compression method for the btrfs and squashfs filesystems. [ 17 ] [ 18 ] [ 19 ]
In 2017, Allan Jude integrated Zstandard into the FreeBSD kernel, [ 20 ] and it was subsequently integrated as a compressor option for core dumps (both user programs and kernel panics). It was also used to create a proof-of-concept OpenZFS compression method [ 8 ] which was integrated in 2020. [ 21 ]
The AWS Redshift and RocksDB databases include support for field compression using Zstandard. [ 22 ]
In March 2018, Canonical tested [ 23 ] the use of zstd as a deb package compression method by default for the Ubuntu Linux distribution. Compared with xz compression of deb packages, zstd at level 19 decompresses significantly faster, but at the cost of 6% larger package files. Support was added to Debian (and subsequently, Ubuntu) in April 2018 (in version 1.6~rc1). [ 24 ] [ 23 ] [ 25 ]
Fedora added ZStandard support to RPM in May 2018 (Fedora release 28) and used it for packaging the release in October 2019 (Fedora 31). [ 26 ] In Fedora 33, the filesystem is compressed by default with zstd. [ 27 ] [ 28 ]
Arch Linux added support for zstd as a package compression method in October 2019 with the release of the pacman 5.2 package manager [ 29 ] and in January 2020 switched from xz to zstd for the packages in the official repository. Arch uses zstd -c -T0 --ultra -20 - ; the size of all compressed packages combined increased by 0.8% (compared to xz), the decompression speed is 14 times faster, decompression memory increased by 50 MiB when using multiple threads, and compression memory increased but scales with the number of threads used. [ 30 ] [ 31 ] [ 32 ] Arch Linux later also switched to zstd as the default compression algorithm for mkinitcpio initial ramdisk generator. [ 33 ]
A full implementation of the algorithm with an option to choose the compression level is used in the .NSZ/.XCZ [ 34 ] file formats developed by the homebrew community for the Nintendo Switch hybrid game console. [ 35 ] It is also one of many supported compression algorithms in the .RVZ Wii and GameCube disc image file format.
On 15 June 2020, Zstandard was implemented in version 6.3.8 of the zip file format with codec number 93, deprecating the previous codec number of 20 as it was implemented in version 6.3.7, released on 1 June. [ 36 ] [ 37 ]
In March 2024, Google Chrome version 123 (and Chromium -based browsers such as Brave or Microsoft Edge ) added zstd support in the HTTP header Content-Encoding . [ 38 ] In May 2024, Firefox release 126.0 added zstd support in the HTTP header Content-Encoding . [ 39 ]
The reference implementation is licensed under the BSD license , published at GitHub . [ 40 ] Since version 1.0, published 31 August 2016, [ 41 ] it had an additional Grant of Patent Rights. [ 42 ]
From version 1.3.1, released 20 August 2017, [ 43 ] this patent grant was dropped and the license was changed to a BSD + GPLv2 dual license. [ 44 ]
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In mathematics , L 2 cohomology is a cohomology theory for smooth non-compact manifolds M with Riemannian metric . It is defined in the same way as de Rham cohomology except that one uses square-integrable differential forms . The notion of square-integrability makes sense because the metric on M gives rise to a norm on differential forms and a volume form .
L 2 cohomology, which grew in part out of L 2 d-bar estimates from the 1960s, was studied cohomologically, independently by Steven Zucker (1978) and Jeff Cheeger (1979). It is closely related to intersection cohomology ; indeed, the results in the preceding cited works can be expressed in terms of intersection cohomology.
Another such result is the Zucker conjecture , which states that for a Hermitian locally symmetric variety the L 2 cohomology is isomorphic to the intersection cohomology (with the middle perversity ) of its Baily–Borel compactification (Zucker 1982). This was proved in different ways by Eduard Looijenga (1988) and by Leslie Saper and Mark Stern (1990).
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Zuclopenthixol (brand names Cisordinol , Clopixol and others), also known as zuclopentixol , is a medication used to treat schizophrenia and other psychoses . It is classed, pharmacologically, as a typical antipsychotic . Chemically it is a thioxanthene . It is the cis - isomer of clopenthixol (Sordinol, Ciatyl). [ 3 ] Clopenthixol was introduced in 1961, while zuclopenthixol was introduced in 1978. [ citation needed ]
Zuclopenthixol is a D 1 and D 2 antagonist, α 1 -adrenergic and 5-HT 2 antagonist. [ 4 ] While it is approved for use in Australia, Canada, Ireland, India, New Zealand, Singapore, South Africa and the UK, it is not approved for use in the United States. [ 5 ] [ 6 ]
Zuclopenthixol is available in three major preparations :
It is also used in the treatment of acute bipolar mania .
As a long-acting injection, zuclopenthixol decanoate comes in a 200 mg and 500 mg ampoule. Doses can vary from 50 mg weekly to the maximum licensed dose of 600 mg weekly. In general, the lowest effective dose to prevent relapse is preferred. The interval may be shorter as a patient starts on the medication before extending to 3 weekly intervals subsequently. The dose should be reviewed and reduced if side effects occur, though in the short-term an anticholinergic medication benztropine may be helpful for tremor and stiffness, while diazepam may be helpful for akathisia. 100 mg of zuclopenthixol decanoate is roughly equivalent to 20 mg of flupentixol decanoate or 12.5 mg of fluphenazine decanoate.
In oral form zuclopenthixol is available in 2, 10, 25 and 40 mg tablets, with a dose range of 20–60 mg daily. [ 11 ]
Chronic administration of zuclopenthixol (30 mg/kg/day for two years) in rats resulted in small, but significant, increases in the incidence of thyroid parafollicular carcinomas and, in females, of mammary adenocarcinomas and of pancreatic islet cell adenomas and carcinomas. An increase in the incidence of mammary adenocarcinomas is a common finding for D 2 antagonists which increase prolactin secretion when administered to rats. An increase in the incidence of pancreatic islet cell tumours has been observed for some other D 2 antagonists. The physiological differences between rats and humans with regard to prolactin make the clinical significance of these findings unclear.
Withdrawal syndrome : Abrupt cessation of therapy may cause acute withdrawal symptoms (eg, nausea, vomiting, or insomnia). Symptoms usually begin in 1 to 4 days of withdrawal and subside within 1 to 2 weeks. [ 12 ] [ 13 ]
Other permanent side effects are similar to many other typical antipsychotics, namely extrapyramidal symptoms as a result of dopamine blockade in subcortical areas of the brain. This may result in symptoms similar to those seen in Parkinson's disease and include a restlessness and inability to sit still known as akathisia , a slow tremor and stiffness of the limbs. [ 10 ] Zuclopenthixol is thought to be more sedating than the related flupentixol , though possibly less likely to induce extrapyramidal symptoms than other typical depots. [ 7 ] As with other dopamine antagonists, zuclopenthixol may sometimes elevate prolactin levels; this may occasionally result in amenorrhoea or galactorrhoea in severe cases. Neuroleptic malignant syndrome is a rare but potentially fatal side effect. Any unexpected deterioration in mental state with confusion and muscle stiffness should be seen by a physician.
Zuclopenthixol decanoate induces a transient dose-dependent sedation. However, if the patient is switched to maintenance treatment with zuclopenthixol decanoate from oral zuclopenthixol or from i.m. zuclopenthixol acetate the sedation will be no problem. Tolerance to the unspecific sedative effect develops rapidly. [ 14 ]
Zuclopenthixol antagonises both dopamine D 1 and D 2 receptors, α 1 -adrenoceptors and 5-HT 2 receptors with a high affinity, but has no affinity for muscarinic acetylcholine receptors . It weakly antagonises the histamine (H 1 ) receptor but has no α 2 -adrenoceptor blocking activity [ citation needed ] .
Evidence from in vitro work and clinical sources (i.e. therapeutic drug monitoring databases) suggests that both CYP2D6 and CYP3A4 play important roles in zuclopenthixol metabolism. [ 16 ]
Zuclopenthixol was introduced by Lundbeck in 1978. [ 27 ]
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Zuhair Fayez Partnership ( ZFP ) ( Arabic : شركة زهير فايز ومشاركوه ), formerly Zuhair Fayez and Associates (ZFA), is an Architectural, Engineering, Project Management, Construction Management, and Engineering Information System consultancy firm in the Kingdom of Saudi Arabia .
Zuhair Fayez Partnership was established in 1975 as Zuhair Fayez and Associates by Zuhair H. Fayez and started with a small number of professional architects, engineers, planners, and support staff. The growing number of commissions and projects eventually prompted the organization to open an office in London to meet the demand.
Eight departments were initially formed: Design, Architectural Production, Structural Engineering, Civil Engineering, HVAC, Specifications, and Quantity Surveying departments. However, the demand for professional management and supervision of large scale projects led to the creation of the Project Management and Construction Management departments to effectively monitor and control all contractors and subcontractors' work on any construction project.
In 1991, the organization launched its Information Technology division to provide clients with software and hardware. The division handled the software integration of Maintenance Management Systems (MMS), Geographical Information Systems (GIS), and Facilities Management Systems (FMS) into a single graphical user interface (GUI). In the same year, the Engineering Information Systems division was formed and is responsible for on-site implementation and provision of GIS, MMS, and FMS based on the clients' needs and requirements.
ZFP partnered with Avaya in May 2011 to create a virtual computing environment (VCE). The purpose is to enable the organization to provide virtual services in a cloud-based environment that would serve 3000 users in 5 branches and 20 remote sites and maximize the efficiency of its existing IT resources. [ 1 ]
In July 2012, SNC-Lavalin acquired ZFP's industrial division in Khobar to form SNC-Lavalin Fayez Engineering, a joint-venture with ZFP, in response to Saudi Aramco's General Engineering Services Plus (GES+) initiative. [ 2 ]
In 2014, Zuhair Fayez Partnership was assigned to build a new campus for the American International School of Jeddah to accommodate 1,700 students. The announcement was made at ZFP's main headquarters during the groundbreaking ceremony. [ 3 ]
Saudi Arabia : Jeddah, Riyadh, Madinah, Makkah, Dammam
Middle East : Cairo
Asia Pacific : Philippines (closed)
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Zuzanna Stefania Siwy (born 1972) is a Polish–American chemist at the University of California, Irvine . Her research considers synthetic nanopores and their application in ionic devices. She is a Fellow of the American Physical Society , American Association for the Advancement of Science and Foundation for Polish Science.
Siwy is from Poland . [ 1 ] She studied chemistry at the Silesian University of Technology in Poland . She graduated with a master's degree in polymer technology in 1995, before completing a doctorate in chemical sciences in 1997. Siwy was a postdoctoral scholar at the University of Florida . [ 1 ]
Siwy joined the faculty at the University of California, Irvine in 2005. In 2012 she was made Professor of Chemical Physics. She studies synthetic nanopores , which she looks to use as templates for biomimetic channels as well as ionic diodes and transistors. [ 1 ]
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The Zwanzig projection operator is a mathematical device used in statistical mechanics . [ 1 ] This projection operator acts in the linear space of phase space functions and projects onto the linear subspace of "slow" phase space functions. It was introduced by Robert Zwanzig to derive a generic master equation . It is mostly used in this or similar context in a formal way to derive equations of motion for some "slow" collective variables . [ 2 ]
The Zwanzig projection operator operates on functions in the 6 N {\displaystyle 6N} -dimensional phase space Γ = { q i , p i } {\displaystyle \Gamma =\{\mathbf {q} _{i},\mathbf {p} _{i}\}} of N {\displaystyle N} point particles with coordinates q i {\displaystyle \mathbf {q} _{i}} and momenta p i {\displaystyle \mathbf {p} _{i}} .
A special subset of these functions is an enumerable set of "slow variables" A ( Γ ) = { A n ( Γ ) } {\displaystyle A(\Gamma )=\{A_{n}(\Gamma )\}} . Candidates for some of these variables might be the long-wavelength Fourier components ρ k ( Γ ) {\displaystyle \rho _{k}(\Gamma )} of the mass density and the long-wavelength Fourier components π k ( Γ ) {\displaystyle \mathbf {\pi } _{\mathbf {k} }(\Gamma )} of the momentum density with the wave vector k {\displaystyle \mathbf {k} } identified with n {\displaystyle n} . The Zwanzig projection operator relies on these functions but does not tell how to find the slow variables of a given Hamiltonian H ( Γ ) {\displaystyle H(\Gamma )} .
A scalar product [ 3 ] between two arbitrary phase space functions f 1 ( Γ ) {\displaystyle f_{1}(\Gamma )} and f 2 ( Γ ) {\displaystyle f_{2}(\Gamma )} is defined by the equilibrium correlation
where
denotes the microcanonical equilibrium distribution. "Fast" variables, by definition, are orthogonal to all functions G ( A ( Γ ) ) {\displaystyle G(A(\Gamma ))} of A ( Γ ) {\displaystyle A(\Gamma )} under this scalar product. This definition states that fluctuations of fast and slow variables are uncorrelated, and according to the ergodic hypothesis this also is true for time averages. If a generic function f ( Γ ) {\displaystyle f(\Gamma )} is correlated with some slow variables, then one may subtract functions of slow variables until there remains the uncorrelated fast part of f ( Γ ) {\displaystyle f(\Gamma )} . The product of a slow and a fast variable is a fast variable.
Consider the continuous set of functions Φ a ( Γ ) = δ ( A ( Γ ) − a ) = ∏ n δ ( A n ( Γ ) − a n ) {\displaystyle \Phi _{a}(\Gamma )=\delta (A(\Gamma )-a)=\prod _{n}\delta (A_{n}(\Gamma )-a_{n})} with a = a n {\displaystyle a=a_{n}} constant. Any phase space function G ( A ( Γ ) ) {\displaystyle G(A(\Gamma ))} depending on Γ {\displaystyle \Gamma } only through A ( Γ ) {\displaystyle A(\Gamma )} is a function of the Φ a {\displaystyle \Phi _{a}} , namely
A generic phase space function f ( Γ ) {\displaystyle f(\Gamma )} decomposes according to
where R ( Γ ) {\displaystyle R(\Gamma )} is the fast part of f ( Γ ) {\displaystyle f(\Gamma )} . To get an expression for the slow part F ( Γ ) {\displaystyle F(\Gamma )} of f {\displaystyle f} take the scalar product with the slow function δ ( A ( Γ ) − a ) {\displaystyle \delta (A(\Gamma )-a)} ,
This gives an expression for F ( Γ ) {\displaystyle F(\Gamma )} , and thus for the operator P {\displaystyle P} projecting an arbitrary function f ( Γ ) {\displaystyle f(\Gamma )} to its "slow" part depending on Γ {\displaystyle \Gamma } only through A ( Γ ) {\displaystyle A(\Gamma )} ,
This expression agrees with the expression given by Zwanzig, [ 1 ] except that Zwanzig subsumes H ( Γ ) {\displaystyle H(\Gamma )} in the slow variables. The Zwanzig projection operator fulfills P G ( A ( Γ ) ) = G ( A ( Γ ) ) {\displaystyle PG(A(\Gamma ))=G(A(\Gamma ))} and P 2 = P {\displaystyle P^{2}=P} . The fast part of f ( Γ ) {\displaystyle f(\Gamma )} is ( 1 − P ) f ( Γ ) {\displaystyle (1-P)f(\Gamma )} . Functions of slow variables and in particular products of slow variables are slow variables. The space of slow variables thus is an algebra. The algebra in general is not closed under the Poisson bracket, including the Poisson bracket with the Hamiltonian .
The ultimate justification for the definition of P {\displaystyle P} as given above is that
it allows to derive a master equation for the time dependent probability
distribution p ( a , t ) {\displaystyle p(a,t)} of the slow variables (or Langevin equations for the slow variables themselves).
To sketch the typical steps, let ρ ( Γ , t ) = ρ 0 ( Γ ) σ ( Γ , t ) {\displaystyle \rho (\Gamma ,t)=\rho _{0}(\Gamma )\sigma (\Gamma ,t)} denote the time-dependent probability distribution in phase space.
The phase space density σ ( Γ , t ) {\displaystyle \sigma (\Gamma ,t)} (as well as ρ ( Γ , t ) {\displaystyle \rho (\Gamma ,t)} ) is a solution of the Liouville equation
The crucial step then is to write ρ 1 = P σ {\displaystyle \rho _{1}=P\sigma } , ρ 2 = ( 1 − P ) σ {\displaystyle \rho _{2}=(1-P)\sigma } and to project the Liouville equation onto the slow and
the fast subspace, [ 1 ]
Solving the second equation for ρ 2 {\displaystyle \rho _{2}} and inserting ρ 2 ( Γ , t ) {\displaystyle \rho _{2}(\Gamma ,t)} into the first
equation gives a closed equation for ρ 1 {\displaystyle \rho _{1}} (see Nakajima–Zwanzig equation ).
The latter equation finally gives an equation for p ( A ( Γ ) , t ) = p 0 ( A ( Γ ) ) ρ 1 ( Γ , t ) , {\displaystyle p(A(\Gamma ),t)=p_{0}(A(\Gamma ))\rho _{1}(\Gamma ,t),} where p 0 ( a ) {\displaystyle p_{0}(a)} denotes the equilibrium distribution of the slow variables.
The starting point for the standard derivation of a Langevin equation is the identity 1 = P + Q {\displaystyle 1=P+Q} , where Q {\displaystyle Q} projects onto the fast subspace.
Consider discrete small time steps τ {\displaystyle \tau } with evolution operator U ≅ 1 + i τ L {\displaystyle U\cong 1+i\tau L} , where L {\displaystyle L} is the Liouville operator . The goal is to express U n {\displaystyle U^{n}} in terms of U k P {\displaystyle U^{k}P} and Q ( U Q ) m {\displaystyle Q(UQ)^{m}} . The motivation is that U k P {\displaystyle U^{k}P} is a functional of slow variables and that Q ( U Q ) m {\displaystyle Q(UQ)^{m}} generates expressions which are fast variables at every time step. The expectation is that fast variables isolated in this way can be represented by some model data, for instance by a Gaussian white noise. The decomposition is achieved by multiplying 1 = P + Q {\displaystyle 1=P+Q} from the left with U {\displaystyle U} , except for the last term, which is multiplied with U = P U + Q U {\displaystyle U=PU+QU} . Iteration gives
The last line can also be proved by induction. Assuming U = 1 + i t L / n {\displaystyle U=1+itL/n} and performing the limit n → ∞ {\displaystyle n\rightarrow \infty } directly leads to the operator identity of Kawasaki [ 2 ]
A generic Langevin equation is obtained by applying this equation to the time derivative of a slow variable A {\displaystyle A} , d A ( Γ , t ) / d t = e i t L ( d A ( Γ , t ) / d t ) t = 0 {\displaystyle dA(\Gamma ,t)/dt=e^{itL}(dA(\Gamma ,t)/dt)_{t=0}} ,
Here R {\displaystyle R} is the fluctuating force (it only depends on fast variables). Mode coupling term V {\displaystyle V} and damping term K {\displaystyle K} are functionals of A ( t ) {\displaystyle A(t)} and A ( t − s ) {\displaystyle A(t-s)} and can be simplified considerably. [ 1 ] [ 2 ] [ 4 ]
Instead of expanding the slow part of f ( Γ ) {\displaystyle f(\Gamma )} in the continuous set Φ a ( Γ ) = δ ( A ( Γ ) − a ) {\displaystyle \Phi _{a}(\Gamma )=\delta (A(\Gamma )-a)} of functions one also might use some enumerable set of functions Φ n ( A ( Γ ) ) {\displaystyle \Phi _{n}(A(\Gamma ))} . If these functions constitute a complete orthonormal function set then the projection operator simply reads
A special choice for Φ n ( A ( Γ ) ) {\displaystyle \Phi _{n}(A(\Gamma ))} are orthonormalized linear combinations of the slow variables A ( Γ ) {\displaystyle A(\Gamma )} . This leads to the Mori projection operator. [ 3 ] However, the set of linear functions is not complete, and the orthogonal variables are not fast or random if nonlinearity in A {\displaystyle A} comes into play.
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The Zwikker reagent is used as a simple spot-test to presumptively identify barbiturates . It is composed of a mixture of two solutions. Part A is 0.5 g of copper (II) sulfate in 100 ml of distilled water . Part B consists of 5% pyridine (v/v) in chloroform. [ 1 ] [ 2 ] One drop of each is added to the substance to be tested and any change in colour is observed.
The test turns phenobarbital , pentobarbital and secobarbital light purple. Tea and tobacco turn yellow-green. [ 1 ]
The test's lack of specificity and tendency to produce false positives means it is not widely used for presumptive drug testing, although it does still play a role as a thin layer chromatography stain. [ 3 ]
It is named after the Dutch scientist Cornelis Zwikker . [ 4 ]
This article about analytical chemistry is a stub . You can help Wikipedia by expanding it .
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In coding theory , the Zyablov bound is a lower bound on the rate r {\displaystyle r} and relative distance δ {\displaystyle \delta } that are achievable by concatenated codes .
The bound states that there exists a family of q {\displaystyle q} -ary (concatenated, linear) codes with rate r {\displaystyle r} and relative distance δ {\displaystyle \delta } whenever
r ⩽ max 0 ⩽ r ′ ⩽ 1 − H q ( δ ) r ′ ⋅ ( 1 − δ H q − 1 ( 1 − r ′ ) ) {\displaystyle r\leqslant \max \limits _{0\leqslant r'\leqslant 1-H_{q}(\delta )}r'\cdot \left(1-{\delta \over {H_{q}^{-1}(1-r')}}\right)} ,
where H q {\displaystyle H_{q}} is the q {\displaystyle q} -ary entropy function
H q ( x ) = x log q ( q − 1 ) − x log q ( x ) − ( 1 − x ) log q ( 1 − x ) {\displaystyle H_{q}(x)=x\log _{q}(q-1)-x\log _{q}(x)-(1-x)\log _{q}(1-x)} .
The bound is obtained by considering the range of parameters that are obtainable by concatenating a "good" outer code C o u t {\displaystyle C_{out}} with a "good" inner code C i n {\displaystyle C_{in}} . Specifically, we suppose that the outer code meets the Singleton bound , i.e. it has rate r o u t {\displaystyle r_{out}} and relative distance δ o u t {\displaystyle \delta _{out}} satisfying r o u t + δ o u t = 1 {\displaystyle r_{out}+\delta _{out}=1} . Reed Solomon codes are a family of such codes that can be tuned to have any rate r o u t ∈ ( 0 , 1 ) {\displaystyle r_{out}\in (0,1)} and relative distance 1 − r o u t {\displaystyle 1-r_{out}} (albeit over an alphabet as large as the codeword length). We suppose that the inner code meets the Gilbert–Varshamov bound , i.e. it has rate r i n {\displaystyle r_{in}} and relative distance δ i n {\displaystyle \delta _{in}} satisfying r i n + H q ( δ i n ) ≥ 1 {\displaystyle r_{in}+H_{q}(\delta _{in})\geq 1} . Random linear codes are known to satisfy this property with high probability, and an explicit linear code satisfying the property can be found by brute-force search (which requires time polynomial in the size of the message space).
The concatenation of C o u t {\displaystyle C_{out}} and C i n {\displaystyle C_{in}} , denoted C o u t ∘ C i n {\displaystyle C_{out}\circ C_{in}} , has rate r = r i n ⋅ r o u t {\displaystyle r=r_{in}\cdot r_{out}} and relative distance δ = δ o u t ⋅ δ i n ≥ ( 1 − r o u t ) ⋅ H q − 1 ( 1 − r i n ) . {\displaystyle \delta =\delta _{out}\cdot \delta _{in}\geq (1-r_{out})\cdot H_{q}^{-1}(1-r_{in}).}
Expressing r o u t {\displaystyle r_{out}} as a function of δ , r i n {\displaystyle \delta ,r_{in}} ,
Then optimizing over the choice of r i n {\displaystyle r_{in}} , we see it is possible for the concatenated code to satisfy,
See Figure 1 for a plot of this bound.
Note that the Zyablov bound implies that for every δ > 0 {\displaystyle \delta >0} , there exists a (concatenated) code with positive rate and positive relative distance.
We can construct a code that achieves the Zyablov bound in polynomial time. In particular, we can construct explicit asymptotically good code (over some alphabets) in polynomial time.
Linear Codes will help us complete the proof of the above statement since linear codes have polynomial representation. Let Cout be an [ N , K ] Q {\displaystyle [N,K]_{Q}} Reed–Solomon error correction code where N = Q − 1 {\displaystyle N=Q-1} (evaluation points being F Q ∗ {\displaystyle \mathbb {F} _{Q}^{*}} with Q = q k {\displaystyle Q=q^{k}} , then k = θ ( log N ) {\displaystyle k=\theta (\log N)} .
We need to construct the Inner code that lies on Gilbert-Varshamov bound . This can be done in two ways
Thus we can construct a code that achieves the Zyablov bound in polynomial time.
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The term zygoma generally refers to the zygomatic bone , a bone of the human skull that is commonly referred to as the cheekbone or malar bone, but it may also refer to:
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A zygospore is a diploid reproductive stage in the life cycle of many fungi and protists . Zygospores are created by the nuclear fusion of haploid cells. In fungi, zygospores are formed in zygosporangia after the fusion of specialized budding structures, from mycelia of the same (in homothallic fungi) or different mating types (in heterothallic fungi), and may be chlamydospores . [ 1 ] In many eukaryotic algae , including many species of the Chlorophyta , zygospores are formed by the fusion of unicellular gametes of different mating types.
A zygospore remains dormant while it waits for environmental cues, such as light, moisture, heat, or chemicals secreted by plants . When the environment is favorable, the zygospore germinates, meiosis occurs, and haploid vegetative cells are released.
In fungi, a sporangium is produced at the end of a sporangiophore that sheds spores . A fungus that forms zygospores is called a zygomycete , indicating that the class is characterized by this evolutionary development.
This mycology -related article is a stub . You can help Wikipedia by expanding it .
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A zygote ( / ˈ z aɪ ˌ ɡ oʊ t / ⓘ ; from Ancient Greek ζυγωτός (zygōtós) ' joined, yoked ' , from ζυγοῦν (zygoun) ' to join, to yoke ' ) [ 1 ] is a eukaryotic cell formed by a fertilization event between two gametes . The zygote's genome is a combination of the DNA in each gamete, and contains all of the genetic information of a new individual organism. The sexual fusion of haploid cells is called karyogamy , the result of which is the formation of a diploid cell called the zygote or zygospore.
German zoologists Oscar and Richard Hertwig made some of the first discoveries on animal zygote formation in the late 19th century. [ citation needed ]
The zygote is the earliest developmental stage. In humans and most other anisogamous organisms, a zygote is formed when an egg cell and sperm cell come together to create a new unique organism. [ citation needed ]
The formation of a totipotent zygote with the potential to produce a whole organism depends on epigenetic reprogramming. DNA demethylation of the paternal genome in the zygote appears to be an important part of epigenetic reprogramming. [ 2 ] In the paternal genome of the mouse, demethylation of DNA, particularly at sites of methylated cytosines, is likely a key process in establishing totipotency. Demethylation involves the processes of base excision repair and possibly other DNA-repair–based mechanisms. [ 2 ]
In human fertilization , a released ovum (a haploid secondary oocyte with replicate chromosome copies) and a haploid sperm cell ( male gamete) combine to form a single diploid cell called the zygote. Once the single sperm fuses with the oocyte, the latter completes the division of the second meiosis forming a haploid daughter with only 23 chromosomes, almost all of the cytoplasm, and the male pronucleus . The other product of meiosis is the second polar body with only chromosomes but no ability to replicate or survive. In the fertilized daughter, DNA is then replicated in the two separate pronuclei derived from the sperm and ovum, making the zygote's chromosome number temporarily 4n diploid . After approximately 30 hours from the time of fertilization, a fusion of the pronuclei and immediate mitotic division produce two 2n diploid daughter cells called blastomeres . [ 3 ] Between the stages of fertilization and implantation , the developing embryo is sometimes termed as a preimplantation- conceptus . This stage has also been referred to as the pre-embryo in legal discourses including relevance to the use of embryonic stem cells. [ 4 ] In the US the National Institutes of Health has determined that the traditional classification of pre-implantation embryo is still correct. [ 5 ]
After fertilization, the conceptus travels down the fallopian tube towards the uterus while continuing to divide [ 6 ] without actually increasing in size, in a process called cleavage . [ 7 ] After four divisions, the conceptus consists of 16 blastomeres, and it is known as the morula . [ 8 ] Through the processes of compaction, cell division, and blastulation, the conceptus takes the form of the blastocyst by the fifth day of development, just as it approaches the site of implantation. [ 9 ] When the blastocyst hatches from the zona pellucida , it can implant in the endometrial lining of the uterus and begin the gastrulation stage of embryonic development. [ citation needed ]
The human zygote has been genetically edited in experiments designed to cure inherited diseases. [ 10 ]
In fungi, this cell may then enter meiosis or mitosis depending on the life cycle of the species. [ citation needed ]
In plants, the zygote may be polyploid if fertilization occurs between meiotically unreduced gametes. [ citation needed ]
In land plants , the zygote is formed within a chamber called the archegonium . In seedless plants, the archegonium is usually flask-shaped, with a long hollow neck through which the sperm cell enters. As the zygote divides and grows, it does so inside the archegonium. [ citation needed ]
The zygote can divide asexually by mitosis to produce identical offspring. [ citation needed ]
A Chlamydomonas zygote contains chloroplast DNA (cpDNA) from both parents; such cells are generally rare, since normally cpDNA is inherited uniparentally from the mt+ mating type parent. These rare biparental zygotes allowed mapping of chloroplast genes by recombination. [ citation needed ]
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Zygotene (from greek "paired threads" [ 1 ] ) is the second stage of prophase I during meiosis , the specialized cell division that reduces the chromosome number by half to produce haploid gametes. It follows the Leptotene stage and is followed by Pachytene stage.
The key event during zygotene is the completion of synapsis between homologous chromosomes . Synapsis began during the previous leptotene stage, with the homologous chromosomes starting to pair together and associate lengthwise, facilitated by the synaptonemal complex protein structure. [ 2 ]
In zygotene, the synaptonemal complex forms more extensively between the paired chromosomes. It zips the homologs together along their entire length, with the lateral elements of the complex associated with each chromosome and the central region holding them together. This allows intimate pairing and genetic recombination events. [ 3 ] [ 4 ]
The chromosomes continue condensing during zygotene into distinct threadlike structures. Each chromosome now appears thicker as the sister chromatids are closely aligned. [ 5 ]
As synapsis completes, proteinaceous recombination nodules begin to appear along the synaptonemal complex between the homologous chromosomes. These represent sites of genetic crossover events, where exchange of chromosomal segments occurs between the non-sister chromatids. [ 6 ] [ 7 ]
Key recombination proteins like MLH1/3 and MSH4/5 mark the sites of crossover formation. The number and positioning of these crossovers is regulated to ensure at least one crossover per chromosome arm for proper segregation in later meiotic stages. [ 8 ]
Once synapsis and crossing over are complete, the cell transitions to the pachytene stage of prophase I. Pachytene features fully condensed and paired chromosomes along their length, with distinctly visible recombination nodules. [ 9 ] [ 10 ]
The zygotene stage is crucial for genetic recombination and proper chromosome segregation in meiosis. [ 1 ] Defects in synapsis, recombination, or crossover regulation can lead to aneuploidy and chromosomal abnormalities in gametes. [ 11 ]
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Zymoblot is the fastest available microtechnique to detect gene expression or enzyme activity in any biological specimen. The technique was invented by Professor Elsayed Elsayed Wagih in collaboration with Professor Jacqueline Fletcher of the Department of Plant Pathology, Noble Research Centre , Oklahoma State University , US in 1993. [ 1 ]
Physiological phenomena whether at the cellular or molecular level in living organisms are driven either directly or indirectly by enzyme reactions . The assay of enzyme activities in living organisms is therefore one of the most commonly performed activities in modern physiology laboratories. Numerous methods of enzyme assays are available to quantitatively follow enzyme reactions. These methods which have been grouped in six categories, namely, spectrophotometric , fluorescence , nanometric , electrode , polarimetric , [ 2 ] radiobiochemical [ 3 ] are with no drawbacks. Recently, a new qualitative or rather semi quantitative micro-technique, first described by Wagih and Fletcher (1993), [ 1 ] and termed 'zymoblot' has been introduced to detect enzyme activities in spiroplasmas and bacteria and many other biological systems . [ 4 ] [ 5 ] Later, the technique was made quantitative by densitometry and successfully used to monitor peroxidase activity in virus infected plants. [ 6 ]
As little as 1 μL, or less, of a sample is enough to detect enzyme activity by the zymoblot technique as the coloured product being insoluble , accumulates at a confined area over the spotting site. The other techniques, based on colorimetry , may require larger aliquots of a sample so that the amount of the coloured soluble products produced is large enough to colour the content of the assay cuvette to a colorimetrically readable level.
The technique has advantages not shared by any other technique. Samples to be analysed by zymoblot require no dialysis (a process that may take days) as washing blots in Tris-buffered saline (TBS) before marinating them in the reaction mixture does remove inhibitors . In contrast to the other techniques where samples are assayed individually, samples to be analysed by zymoblot are spotted on the same blot and enzyme activity is assayed with the same reaction mixture at the same time minimising experimental errors and allowing quick qualitative comparisons. Additionally, several enzymes can be assayed in a sequential order on the same blot. That is to say, if a blot proves negative for a certain enzyme, it can be washed in TBS and reused for another enzyme and so on until a positive reaction for an enzyme is obtained. Unlike wet assays (e.g. colorimetry), results obtained by the zymoblot are always in a recorded from. This allows zymoblots to be carried out in one place, where a densitometer may not be available, and taken or sent to another place to be quantitatively assayed by densitometry. Taking a zymoblot in a researcher's wallet to a meeting facilitates discussions and exchange of ideas with other scientists. While immunologically -based enzyme assays [ 3 ] which uses enzyme specific antibodies to directly detect enzymes suffers from the major disadvantage of measuring the "total enzyme content" and not the total enzyme activity, zymoblot, being not a serological technique , uses no antibodies and measures enzyme activity as it detects only the active (functional) portion of the total enzyme content in a sample.
Zymoblot is an end-point type of assay where an enzyme reaction is allowed to proceed for a fixed period of time before being stopped by rapid elimination of its specific substrate . However, the technique could be adapted for the continuous enzyme assay when colour intensity is monitored over time by incubating sister blots for progressively increasing periods of time. When different samples are compared on the same blot, the reaction should be stopped sometime during the linear part of the course of the reaction. This could be judged upon visually and the reaction is stopped when differences in colour intensity among spots are evident, taking into consideration that the duration of linearity in some enzyme reactions may be very short indeed.
The Zymoblot technique is simpler, cheaper, more reliable and less time-consuming than all known procedures for enzyme assays. It is probably the quickest available technique to detect enzyme activity in any biological or even non-biological specimen. The technique is highly competitive in price with all commercially available kits. Such advantages should qualify the Zymoblot technique for wide potential uses in medicine , agriculture and industrial biotechnology and, more broadly, in general biotechnology application. It is useful in studies including physiology of humans, animals, plants and microorganisms, differential diagnosis of diseases and identification of pathogens , biotaxonomy of organisms, stress and pathogenesis physiology, physiological basis for disease resistance , developmental physiology and screening for commercially important enzymes and many other applications. The technique is particularly useful when initial testing for enzyme activity is required. It can be used in investigations involving screening a living organism for large numbers of enzymes. It can also be very handy in studying enzyme distribution or tissue-specific gene expression in terms of enzyme activity throughout the body or across an organ . Samples taken from different parts of an organism or an organ can simultaneously be analysed and compared, on the same blot, giving a clear picture of the distribution of enzyme activity. With the same simplicity, corresponding tissues taken from normally and biotically- or abiotically-stressed individuals can be compared for enzyme stimulation or induction. Furthermore, zymoblots can be very helpful in cytochemodissection studies aiming at localising enzymes within cells. Cell fractions representing different parts of the cell ( nuclei , mitochondria , lysosomes , peroxisomes , Golgi bodies , cytosol ,... etc.) can be tested for a host of enzymes in a relatively short time.
Qualitative zymoblot is of great potential use in diagnosis of human, animal and plant diseases . If a pathogen demonstrates a specific enzyme that is not shared by its host, the technique can be a definitive diagnostic tool. The detection of an enzyme not known to be normally present in a sample of body fluid (e.g. blood serum , CSF , synovial fluid , milk, tears...etc.) using qualitative zymoblot is an indication of a physiological disorder , inflammatory reaction or pathogenic infection . In all these situations, quantitative zymoblot can be used to determine the severity of the problem. Similarly, replacing biological fluids with non-biological fluids taken from water bodies (or prepared from similar environmental sources) at different locations or depths at different times will allow zymoblot, through detecting enzyme activities, to reveal or monitor microbial load and consequently determine the level of contamination in these sources.
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Zymography is an electrophoretic technique for the detection of hydrolytic enzymes , based on the substrate repertoire of the enzyme. Three types of zymography are used; in gel zymography, in situ zymography and in vivo zymography. [ 2 ] For instance, gelatin embedded in a polyacrylamide gel will be digested by active gelatinases run through the gel. After Coomassie staining , areas of degradation are visible as clear bands against a darkly stained background. [ 3 ]
Modern usage of the term zymography has been adapted to define the study and cataloging of fermented products, such as beer or wine, often by specific brewers or winemakers or within an identified category of fermentation such as with a particular strain of yeast or species of bacteria. [ citation needed ] Zymography also refers to a collection of related, fermented products, considered as a body of work. For example, all of the beers produced by a particular brewery could collectively be referred to as its zymography. [ citation needed ]
See also Zymology or the applied science of zymography. Zymology relates to the biochemical processes of fermentation, especially the selection of fermenting yeast and bacteria in brewing, winemaking, and other fermented foods. For example, beer-making involves the application of top (ale) or bottom fermenting yeast (lager), to produce the desired variety of beer. The synthesis of the yeast can impact the flavor profile of the beer, i.e. diacetyl (taste or aroma of buttery, butterscotch).
Samples are prepared in a standard, non-reducing loading buffer for SDS-PAGE . No reducing agent or boiling are necessary since these would interfere with refolding of the enzyme. A suitable substrate (e.g. gelatin or casein for protease detection) is embedded in the resolving gel during preparation of the acrylamide gel . Following electrophoresis , the SDS is removed from the gel (or zymogram ) by incubation in unbuffered Triton X-100 , followed by incubation in an appropriate digestion buffer, for an optimized length of time at 37 °C. The zymogram is subsequently stained (commonly with Amido Black or Coomassie brilliant blue ), and areas of digestion appear as clear bands against a darkly stained background where the substrate has been degraded by the enzyme.
The standard protocol may require modifications depending on the sample enzyme; for instance, D. melanogaster digestive glycosidases generally survive reducing conditions (i.e. the presence of 2-mercaptoethanol or DTT ), and to an extent, heating. Indeed, the separations following heating to 50 °C tend to exhibit a substantial increase in band resolution, without appreciable loss of activity. [ 4 ] [ 5 ]
A common protocol used in the past for zymography of α-amylase activity was the so-called starch film protocol of W.W. Doane. Here a native PAGE gel was run to separate the proteins in a homogenate. Subsequently, a thin gel with starch dissolved (or more properly, suspended) in it was overlaid for a period of time on top of the original gel. [ 6 ] The starch was then stained with Lugol's iodine.
Gel zymography is often used for the detection and analysis of enzymes produced by microorganisms. [ 7 ] This has led to variations on the standard protocol e.g. mixed-substrate zymography. [ 2 ]
Reverse zymography copolymerizes both the substrate and the enzyme with the acrylamide, and is useful for the demonstration of enzyme inhibitor activity. Following staining, areas of inhibition are visualized as dark bands against a clear (or lightly stained) background.
In imprint technique, the enzyme is separated by native gel electrophoresis and the gel is laid on top of a substrate treated agarose . [ 1 ]
Zymography can also be applied to other types of enzymes, including xylanases , lipases and chitinases.
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Zymology , also known as zymurgy , [ a ] is an applied science that studies the biochemical process of fermentation and its practical uses. Common topics include the selection of fermenting yeast and bacteria species and their use in brewing , wine making , fermenting milk , and the making of other fermented foods .
Fermentation can be simply defined, in the context of brewing, as the conversion of sugar molecules into ethanol and carbon dioxide by yeast .
Fermentation practices have led to the discovery of ample microbial and antimicrobial cultures on fermented foods and products. [ 1 ] [ 2 ]
French chemist Louis Pasteur was the first 'zymologist' when in 1857 he connected yeast to fermentation. Pasteur originally defined fermentation as "respiration without air".
Pasteur performed careful research and concluded:
Je pense que la fermentation alcoolique ne se produit jamais sans une organization simultanée, une développement, une multiplication de cellules … . Si l'on me demandai en quoi consiste la réaction chimique par laquelle le sucre et décomposé … je l'ignore complètement.
I am of the opinion that alcoholic fermentation never occurs without simultaneous organization, development and multiplication of cells … . If asked, in what consists the chemical act whereby the sugar is decomposed … I am completely ignorant of it.
The German Eduard Buchner , winner of the 1907 Nobel Prize in chemistry, later determined that fermentation was actually caused by a yeast secretion, which he termed ' zymase '.
The research efforts undertaken by the Danish Carlsberg scientists greatly accelerated understanding of yeast and brewing. The Carlsberg scientists are generally acknowledged [ by whom? ] as having jump-started the entire field of molecular biology .
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https://en.wikipedia.org/wiki/Zymology
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Read the Wiktionary entry "zymoscope"
You can also:
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Ádám István Mechler is a materials scientist and academic most known for his research on intermolecular interactions in physical chemistry , as well as on molecular machines , hierarchical metamaterials , and self-assembling systems inspired by biology . [ 1 ] He is a professor of Chemistry at La Trobe University , Australia, where he leads the Bioinspired self-assembling nanostructures research group. [ 2 ] He is also the Academic Program Director of the IIT Kanpur - La Trobe University Research Academy
and the BITS Pilani - La Trobe University joint PhD program. [ 3 ]
Mechler earned a Diploma (BSc and MSc) in Chemistry and Physics in 1996, followed by a PhD in physics at the University of Szeged in 2001. Subsequently, he worked at the University of California, Santa Barbara , for three years, during which his research focus shifted to bioinspired materials and biomolecule interactions. In 2004, he moved to Australia to Monash University, where he established his independent research program focusing on biomolecule self-assembly, membrane biophysics, and peptide-membrane interactions while continuing to explore bioinspired materials and bioactive natural products. [ 4 ] [ 5 ]
In 2009, Mechler joined La Trobe University as a Senior Lecturer in the Department of Chemistry, was later appointed associate professor in 2016, and has held the position of Professor since 2021. [ 6 ]
For his work, Mechler was honored with the Government of Australia Office of Learning and Teaching National Citation For Outstanding Student Learning in 2013 [ 7 ] and was elected Fellow of the Royal Society of Chemistry in 2016.
Mechler has contributed to the field of materials science through his work on self-assembling systems, lipid membranes, biophysical chemistry , antimicrobial peptides , and metallosupramolecular systems. [ 1 ]
Mechler's research on biomolecular interactions has focused on lipid membranes, their phase and domain dynamics, and membrane disruption by antimicrobial peptides. He utilized spectroscopic imaging and near-field microscopy to show that cholesterol-rich domains in bilayer membranes form optimally at a 15:85 lipid-cholesterol ratio, with specific domain separation occurring at lower concentrations. [ 8 ] Additionally, he found that the structure of supported phospholipid bilayers varies with liposome size, composition, and substrate, as shown by quartz crystal microbalance and atomic force microscopy. [ 9 ]
Working with Imad Younus Hasan, Mechler employed QCM-based measurements to show cholesterol induces phase separation in single bilayer lipid membranes [ 10 ] and demonstrated that partially suspended DMPC-based bilayer membranes can form on functionalized gold surfaces in a way that allows natural membrane movement, providing a truly Biomimetic platform for membrane studies and protein insertion. [ 11 ] They also mapped thermodynamic phase transitions of lipid membranes, through nanoviscosity measurements, in single bilayer lipid membranes, revealing that domain separation occurs only in planar membranes and that phase transitions are due to the breaking of van der Waals interactions. [ 12 ]
Using quartz crystal microbalance and atomic force microscopy, Mechler and his research group investigated how specific antimicrobial peptides secreted by insects such as honeybees and amphibians such as Australian tree frogs disrupt bacterial membranes. [ 13 ] Among other contributions, his research introduced oncocin, a novel antimicrobial peptide optimized for treating Gram-negative bacteria, showing effective activity and improved stability in mouse serum without causing lysis or toxicity. [ 14 ] Later, he showed that LL-37 acts through pore formation in membranes made of unsaturated lipids whereas it yields membrane modulation in saturated lipids, suggesting new design strategies for antimicrobial peptide drugs. [ 15 ]
Mechler engaged in the design and characterization of biomaterials, nanostructures as well as in the development of novel nanotechnologies throughout his career. He used multimodal atomic force microscopy to map charge transfer properties of the conductive copolymer poly(ethyldioxythiophene)–poly(styrenesulfonic acid), showing that efficient charge injection occurs at lamellar edges and can be improved by controlling lamellar orientation. [ 16 ] In a collaborative project, he also presented a method utilizing surface acoustic waves to produce monodispersed submicron poly-ε-caprolactone particles, demonstrating how acoustic forces and evaporative processes influence particle size and morphology. [ 17 ]
In a joint study, Mechler established that 14-helical N-acetyl β3-peptides self-assemble into nanofibers and that their morphology, such as nano-beams and dendritic structures, can be tuned by adjusting the solvent and inter-fibril interactions, enabling new bio- and nanomaterial applications. [ 18 ] [ 19 ] By using far-IR spectroscopy and DFT modeling, he confirmed the structure of self-assembled fibrous nano-materials from unnatural tripeptides, showing that far-IR spectroscopy can effectively characterize bioinspired materials where crystallographic methods fall short. [ 20 ] He further showcased that using two binding motifs in supramolecular assemblies creates metallosupramolecular frameworks with controlled nanorod and two-dimensional structures, with copper ions forming polynuclear metal complexes. [ 21 ] In 2023, his work highlighted that substituted beta oligoamides self-assemble into metallosupramolecular frameworks with varied structures, including thin films and three-dimensional networks, by coordinating with different transition metals and metalates. [ 22 ]
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Ágnes Szendrei is a Hungarian-American mathematician whose research concerns clones , the congruence lattice problem , and other topics in universal algebra . She is a professor of mathematics at the University of Colorado Boulder , [ 1 ] and the author of the well-cited book Clones in Universal Algebra (1986). [ 2 ] In May 2022 [ 3 ] [ 4 ] , Dr. Szendrei was elected as an external member of the Hungarian Academy of Sciences [ 5 ] ; such external memberships are for Hungarian scientists who live outside of Hungary and who have made exceptional contributions to scientific research.
Szendrei earned a doctorate from the Hungarian Academy of Sciences in 1982, and a habilitation in 1993. [ 6 ] Her 1982 dissertation was Clones of Linear Operations and Semi-Affine Algebras , supervised by Béla Csákány [ hu ] . [ 7 ] She was on the faculty of the University of Szeged from 1982 until 2003, when she moved to the University of Colorado. [ 6 ]
Szendrei is a Humboldt Fellow . She won the Kató Rényi Award for undergraduate research in 1975, the Géza Grünwald Commemorative Prize for young researchers of the János Bolyai Mathematical Society in 1978, and the Golden Ring of the Republic in 1979. She was the 1992 winner of the Paul Erdős Prize of the Hungarian Academy of Sciences, and the 2000 winner of the Academy's Farkas Bolyai Award. [ 6 ]
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Álvaro Ríos Poveda (born 3 February 1974, Cali , Colombia ) is a Colombian electronic engineer, university professor, and researcher who specializes in biomedical engineering and mechatronics . He has performed research on myoelectric prostheses, sensory feedback, and bionic vision technologies. [ 1 ]
He began his studies at San Juan Berchmans school in Cali , Colombia. [ 2 ]
Ríos earned an undergraduate degree in Electronic Engineering at Pontifical Xavierian University and completed his master's at Simon Bolivar University and doctorate studies at USF in Biomedical Engineering. [ 3 ] Along with that, he obtained an MBA from ISEAD. [ 4 ] His professional career began with research in neural prostheses and bionics systems. Ríos researched biomedical engineering, artificial intelligence, and robotics in control systems.
Ríos is a researcher and university professor in undergraduate and postgraduate studies in Europe and Mexico. From a young age, his interest had grown into motor limitations.
In 1996, he developed prosthetic systems that allow patients to have greater limb functionality while ensuring accessibility for these systems in developing countries. [ 5 ] [ 6 ] [ 7 ]
In 1997, a sensory feedback system for prostheses was presented at France's World Congress on Biomedical Engineering. Ríos's public work includes myoelectric prosthesis with sensory feedback, presented at MEC'02: The Next Generation . His work mainly aims of his work is to control prosthetics more naturally, utilizing artificial intelligence, neural control, machine learning, and gesture control. [ 8 ] [ 9 ] [ 10 ]
He has remained a member of the Publications Committee of the International Federation of Medical and Biological Engineering and a founding member of the Colombian Association of Biomedical Engineering. Since its inception in 2017, Ríos has been participating at every CBS IEEE International Conference on Bionic Systems and Cyborg and giving guest participation at IEEE 's CBS 2017. Later in 2018, he represented the Latin American region at a conference on Upper Limb Prosthesis. Since then, Ríos has remained Chairman for the region of the Americas at the 2020 IEEE CBS and has also been working with World Health Organization, a member of Global Cooperation on Assistive Technology. He also established HAT (Human Assistive Technologies), [ 11 ] [ 12 ] [ 13 ] a bionics company based in Mexico City. [ 14 ] [ 15 ] [ 16 ] [ 17 ] At HAT, a C-Hand was developed, which is a bionic prosthesis with sensory feedback and gesture control, and is a bionic arm designed for smart cities.
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The ÄKTA explorer was the first high end FPLC ( Fast Protein Liquid Chromatography ) system that was developed for Life Science research by the Swedish company Pharmacia in 1994. Its purpose was to simplify and automatize protein purification. It was followed by a line of similar devices (the "Äkta" line). [ 1 ] The product line name was transferred together with the sale of Pharmacia first to Amersham and then to GE Healthcare . Although protein purification is possible with a large range of chromatographic devices, the Äkta line represents together with BioRad's NGC line [ 2 ] the only devices that were specifically designed for this purpose both from the hardware and software perspective. Main users of these devices are the pharmaceutical industry and academic researchers.
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ÉLECTRE is a family of multi-criteria decision analysis (MCDA) methods that originated in Europe in the mid-1960s. The acronym ÉLECTRE stands for: ÉLimination Et Choix Traduisant la REalité ("Elimination and Choice Translating Reality").
The method was first proposed by Bernard Roy and his colleagues at SEMA consultancy company. A team at SEMA was working on the concrete, multiple criteria, real-world problem of how firms could decide on new activities and had encountered problems using a weighted sum technique . Roy was called in as a consultant and the group devised the ELECTRE method. As it was first applied in 1965, the ELECTRE method was to choose the best action(s) from a given set of actions, but it was soon applied to three main problems: choosing, ranking and sorting. The method became more widely known when a paper by B. Roy appeared in a French operations research journal. [ 1 ] It evolved into ELECTRE I ( electre one ) and the evolutions have continued with ELECTRE II, ELECTRE III, ELECTRE IV, ELECTRE IS and ELECTRE TRI ( electre tree ), to mention a few. [ 2 ] They are used in the fields of business, development, [ 3 ] design, [ 4 ] and small hydropower. [ 5 ]
Roy is widely recognized as the father of the ELECTRE method, which was one of the earliest approaches in what is sometimes known as the French school of decision making . It is usually classified as an "outranking method" of decision making.
There are two main parts to an ELECTRE application: first, the construction of one or several outranking relations, which aims at comparing in a comprehensive way each pair of actions; second, an exploitation procedure that elaborates on the recommendations obtained in the first phase. The nature of the recommendation depends on the problem being addressed: choosing, ranking or sorting.
Criteria in ELECTRE methods have two distinct sets of parameters: the importance coefficients and the veto thresholds. ELECTRE method cannot determine the weights of the criteria. In this regard, it can be combined with other approaches such as Ordinal Priority Approach , Analytic Hierarchy Process , etc.
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The École Nationale Supérieure d'Électrochimie et d'Électrométallurgie de Grenoble , or ENSEEG , was one of the French Grandes écoles of engineering (engineering schools). It has been created in 1921 under the name Institut d’électrochimie et d’électrométallurgie (IEE) (Institute of Electrochemistry and Electrometallurgy). The name ENSEEG has been chosen in 1948 and ENSEEG has been part of Grenoble Institute of Technology (INPG or GIT) since its creation in 1971. Therefore, the name INPG-ENSEEG has also been commonly used.
ENSEEG delivered a multidisciplinary education in physical chemistry . The ENSEEG engineers are especially competent in materials science , process engineering and electrochemistry . From September 2008, ENSEEG merged with two other Grandes écoles to create Phelma .
This electrochemistry -related article is a stub . You can help Wikipedia by expanding it .
This French school-related article is a stub . You can help Wikipedia by expanding it .
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The National School of Applied Sciences Sciences in Khouribga(ENSA Khouribga)' is a Moroccan public engineering school within the Sultan Moulay Souliman University of Beni Mellal . It was created in 2007 to support the government's commitment under the National Training Initiative of 10,000 engineers by 2010. It trains state engineers to be qualified scientifically, technically in modeling, and communication management. It is part of the National Schools of the Applied Sciences network .
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https://en.wikipedia.org/wiki/École_nationale_des_sciences_appliquées_de_Khouribga
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The École nationale des sciences appliquées de Kénitra ( Arabic : المدرسة الوطنية للعلوم التطبيقية القنيطرة ) is a Moroccan engineering school founded in 2008 by a partnership between the University Ibn Tofail in Kenitra ( جامعة ابن طفيل ) and the Institut national des sciences appliquées de Lyon .
It is a Moroccan public institution, training engineers with specializations in;
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https://en.wikipedia.org/wiki/École_nationale_des_sciences_appliquées_de_Kénitra
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The École nationale supérieure d'ingénieurs de constructions aéronautiques ( French pronunciation: [ekɔl nɑsjɔnal sypeʁjœʁ dɛ̃ʒenjœʁ də kɔ̃stʁyksjɔ̃ aeʁɔnotik] ; meaning "National Higher School of aeronautical constructions"), or ENSICA , was a French engineering school founded in 1945. It was located in Toulouse . In 2007, Ensica merged with Supaéro to form the Institut supérieur de l'aéronautique et de l'espace (ISAE).
Ensica recruited its students from the French "Concours des Grandes Écoles", a competitive examination which requires studies at the "classes préparatoires". Classes préparatoires last two years where students are to work intensively on mathematics and physics.
Studies at Ensica lasted for 3 years where students eventually got a Master in Aeronautics.
Area of studies cover all the fundamentals of aeronautics, including: aerodynamics, structures, fluid dynamics, thermal power, electronics, control theory, airframe systems, IT, etc. Students are also trained in management, manufacturing, certification, and foreign languages.
Main employers are Airbus , Thales , Dassault , Safran ( Sagem , Snecma), Rolls-Royce, Astrium , Eurocopter . [ citation needed ]
The decree giving birth to the "Ecole Nationale des Travaux Aéronautiques" (ENTA) was signed in 1945. The text was then ratified by Charles de Gaulle, president of the temporary government, and by René Pleven, Finance Minister. There were 25 students in the first class and 24 of them joined the "Ingénieurs Militaires des Travaux de l'Air" (IMTA).
In 1957, the school changed its name to the "Ecole Nationale d'Ingénieurs des Constructions Aéronautiques" (ENICA).The course was extended to three years and the school embarked on its new civil vocation welcoming a higher proportion of civil students.
In 1961, ENICA was transferred to Toulouse, the director at that time being Emile Blouin. It then took on a new dimension and established its identity. In 1969, the school joined the competitive entrance examination system organised by the Ecoles Nationales Supérieures d'Ingénieurs (ENSI). It thus increased its recruitment standards to become one of the leading French schools. This excellence was rewarded in 1979 when it received the Médaille de l'Aéronautique from Général Georges Bousquet: ENICA then became ENSICA, Ecole Nationale Supérieure d'Ingénieurs de Constructions Aéronautiques.
The eighties were marked by a profound diversification in the training courses offered: opening of a "Mastère" degree and an Advanced Studies degree (DEA) in automatic control and mechanics, specialisations in aircraft maintenance and helicopter techniques. ENSICA became the top-listed school for students with pass marks in ENSI competitive entrance examinations and continuously increased the part set aside for research. It also internationalised its training by implementing exchange programmes with English, American and German institutes and universities. In 1994, ENSICA became a public establishment and can now sign, in its own name, agreements and conventions with other organisations and receive research contracts.
Today, ENSICA has a staff of 150 people including 25 scientific directors and almost 700 part-time lecturers. The school can accommodate more than 400 students on the initial training courses and the same number of persons doing further training. The 50th class recently graduated. It included a total of 98 graduates 11 students of which did their third year of studies in a foreign university (USA, Great Britain, Germany and Sweden) and a high number of students who carried out their end of study projects abroad.
A public establishment under the auspices of the Ministry of Defence, ENSICA gives technological teaching courses for civil and military engineering students and offers a range of training:
The engineer's course lasts three years.
At ENSICA, research and training are integrated into the four training and research departments: avionics and systems, mechanical engineering, fluid mechanics, applied mathematics and computer science.
All the departments are composed with a scientific staff. The staff is composed by lecturers-researchers with Ph.D's, lecturers and senior lecturers from universities and full professors. They are responsible for the research work and pedagogical engineering, as well as the coordination of the lecturers' teams. By this way, they actively participate in international actions and in industrial relations.
The lecturers come, for one third, from the university and research world, for one fourth from industry and one fourth from the DGA.
Human, economics, social, linguistics and multi-cultural training is under the responsibility of three departments: human and social sciences, sports and languages.
Main departments are Avionics, Mechanical Engineering, Fluid Dynamics and Mathematics
The Avionics & Systems Department develop :
- In the first year a basic training in: Signal processing, Automatic System and Electrical Engineering.
- In the third year, two advanced itineraries are proposed into the field :
The Department trains at these multidisciplinary itineraries :
Preparation for the post-graduate diplomas DEA (Advanced Studies Diploma) :
These two itineraries allow, respectively, the preparation for the postgraduate diplomas signals-images-acoutics and automatic systems.
The aim of the Mechanical engineering Department's curriculum is to provide the students with basic knowledge in mechanics indispensable for their future jobs as engineers and this within a multidisciplinary aerospace training framework.
The Mechanical Engineering courses lasts three years and includes :
- basic training including fundamental knowledge mainly concerning calculation of structures and technological knowledge of mechanisms, manufacturing and materials, - training applied to aeronautics and space; this part increasing progressively throughout the three years.
This common core is complemented, within the scope the third-year optional modules, by courses given at ENSICA for the Mechanical Engineering advanced studies degree and more specialised courses related to aeronautics and space.
The Mechanical Engineering Department also coordinates the school's space activities: this specific space training corresponds to around 250 hours and development is oriented both towards ultralight systems and crewed flight engineering.
The courses given by the Fluid Mechanics Department concern the thermodynamics of irreversible processes and continuum mechanics. The courses in these two disciplines are given in the first year and are completed by a basic fluid mechanics course (general equations of the movement of a Newtonian fluid and inviscid fluid movements). In the second year, the studies concern the flow of incompressible viscous fluids and compressible inviscid fluids dealing with the boundary layer, shock wave and turbulence phenomena with complements in unsteady fluid hypersonic and mechanical phenomena.
From these theoretical bases, aeronautical applications are introduced in the second year. They mainly concern:
external aerodynamics plus flight mechanics and handling qualities.
aeronautical turbine engines.
The goals of CS training are:
(1) to study the methods for developing programs (specification methods, object-oriented design, structured programming algorithms, testing);
(2) to learn the basics of algorithmics
(3) in-depth study of object programming, and learning an object-oriented methodology that uses UML as modeling notation;
(4) to study the specific features of "Real-Time" applications and systems and of new-generation network architectures in close association with the research work carried out in the department. Practical implementations of theoretical concepts are based on Java language;
ENSICA is co-accredited for issuing the Toulouse Systems Postgraduate School's Computer-based Systems DEAs (Advanced Studies Degrees) in cooperation with UPS science university, INSA and SUPAERO engineering schools, and the Toulouse CS and Telecommunications Postgraduate School's Networks and Telecommunications DEAs in cooperation with INPT engineering school, UPS science university, SUPAERO , INSA, ENST and ENAC engineering schools.
During the 3 years, students of Ensica have the opportunity of studying for one semester or one year abroad, or make a one-year additional training period in a company.
Foreign partnerships include:
Australia
Belgium
Canada
China
Germany
Italy
Mexico
Netherlands
Poland
Romania
Russia
Singapore
Spain
Sweden
United Kingdom
USA
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The network of Écoles nationales des sciences appliquées (ENSA, lit. ' National Schools of Applied Sciences ' ) is a group of higher education Moroccan public schools delivering engineering courses under the system of French grandes écoles . [ 1 ] It is the largest network of engineering schools in Morocco. The network includes 11 ENSA throughout the Kingdom; Agadir, Al Hoceima, El Jadida, Fes, Kenitra, Khouribga, Marrakech, Oujda, Safi, Tangier and Tetouan. The Forum "ENSA Maroc", organized by engineering students of ENSA Agadir, is the first high-level meeting between engineering students, professors and administrators of the network of National Schools of Applied Sciences throughout the Kingdom.
ENSA training lasts 5 years. After two years of preparatory integrated education these schools offer many courses in the engineering cycle
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https://en.wikipedia.org/wiki/Écoles_nationales_des_sciences_appliquées
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Éleuthère Irénée du Pont de Nemours ( / dj uː ˈ p ɒ n t , ˈ dj uː p ɒ n t / dew- PONT , DEW -pont , [ 1 ] French: [eløtɛʁ iʁene dy pɔ̃ d(ə) nəmuʁ] ; 24 June 1771 – 31 October 1834) was a French-American chemist and industrialist who founded the gunpowder manufacturer E. I. du Pont de Nemours and Company . His descendants, the du Pont family , have been one of the richest and most prominent American families since the 19th century, with generations of influential businessmen, politicians and philanthropists. In 1807, du Pont was elected a member of the American Philosophical Society in his adopted hometown of Philadelphia . [ 2 ]
Du Pont was born 24 June 1771, in Paris , the son of Pierre Samuel du Pont de Nemours and Nicole-Charlotte Marie-Louise le Dée de Rencourt. His father was a political economist who had been elevated to the nobility in 1784 by letters patent granted by King Louis XVI , allowing him to carry the honorable de Nemours suffix. Growing up on his father's estate, "Bois des Fossés", near Égreville , young du Pont was enthusiastic about his studies in most subjects, and showed particular interest in explosives.
Du Pont was a Huguenot . [ 3 ]
In the fall of 1785, du Pont entered Collège de France in Paris. Two years later, he was accepted by the friend of his father and noted chemist Antoine Lavoisier as a student in the Régie des poudres , the government agency responsible for the manufacture of gunpowder. It was from Lavoisier that he gained his expertise in nitrate extraction and manufacture. [ 4 ] He studied "advanced explosives production techniques". [ 5 ]
After a brief apprenticeship, he took a position at the government -owned powder works in Essonne but quit after Lavoisier left. [ 6 ]
Du Pont eventually sailed before his family and landed at Newport, Rhode Island on 1 January 1800, along with his father and his brother's family. By 1802, he had established both his business and his family home, Eleutherian Mills , on the Brandywine Creek in Delaware . Du Pont's 1 January 1800 arrival in the United States is still celebrated annually by his descendants. [ 7 ]
In 1791, du Pont began to help his father manage their small publishing house in Paris, where they published a republican newspaper in support of governmental reforms in France. Du Pont was a member of the pro-Revolution national guard and supported the Jacobins . However, on 20 August 1792, both du Pont and his father participated in protecting the escape of Louis XVI and Marie Antoinette when the Tuileries Palace was stormed. His father angered fellow revolutionaries by refusing to go along with the guillotine execution of Louis XVI, and the two men's moderate political views proved to be a liability in revolutionary France.
His father was arrested in 1794, only avoiding execution because of the end of the Reign of Terror . In September 1797, du Pont and his father spent a night in La Force prison while their home and presses were ransacked. These events led his father to lose hope in the political situation in France, and so he began making plans to move their family to America and aspired to create a model community of French émigrés. On 2 October 1799, the du Pont family sold their publishing house and set sail for the United States. They reached Rhode Island on 1 January 1800 and began to settle in the home the eldest du Pont had secured in Bergen Point, New Jersey.
They soon set up an office in New York City to decide what their new line of business would be, but Éleuthère Irénée was not included in much of these plans. However, he saw the possibilities that his earlier apprenticeship with Lavoisier would allow him and his family in America. [ 8 ]
Du Pont had no thought of becoming involved with gunpowder manufacture again upon his arrival in the United States, but he brought with him an expertise in chemistry and gunpowder making, during a time when the quality of American-made gunpowder was very poor. Delaware legend holds that he decided to go into the gunpowder business during a fateful hunting trip with Major Louis de Tousard , a former French artillery officer then employed by the United States Army to procure gunpowder supplies. Du Pont's gun misfired as he attempted to shoot a bird, which caused him to reflect on his powder-making apprenticeship with Lavoisier as a youth in France. Du Pont commented on the inferior quality of the American-made powder they were using for hunting despite its high price.
At du Pont's request, Tousard arranged a tour of an American powder plant. He quickly deduced that the saltpeter being used was of good enough quality; however, the American refining process was poor and inefficient compared with the techniques he had learned in France. He began to think that he could use his experience from France to manufacture gunpowder of a higher quality in the United States and reform the current industry standard for refinery. With his father's blessing, he began to assemble capital for the construction of the first powder mills, and returned to France in the beginning of 1801 to procure the necessary financing and equipment.
The act of association was signed on 21 April 1801, and the company was christened E.I. du Pont de Nemours & Company since it was its namesake's ingenuity that had created this venture. [ 8 ] His gunpowder company was capitalized at $36,000 with 18 shares at $2,000 each. He purchased a site on Brandywine Creek for $6,740. There were several small buildings and a dam with foundations for a cotton-spinning mill which had been destroyed by fire. The first gunpowder was produced in April 1804. [ 6 ]
Du Pont married Sophie Dalmas (1775–1828) in 1791, and they had eight children.
Du Pont died on 31 October 1834 in Philadelphia , aged 63. [ 9 ] The cause of death was not definitively specified due to "conflicting reports of either cholera or a heart attack " as its cause. [ 8 ] He was buried in the Du Pont de Nemours Cemetery on the family property in Wilmington, Delaware .
The company du Pont founded would become one of the largest and most successful American corporations. By the mid-19th century it was the largest supplier of gunpowder to the U.S. military, and supplied as much as 40 percent of the powder used by the Union Army during the American Civil War . [ 10 ]
Du Pont's sons, Alfred V. du Pont (1798–1856) and Henry du Pont (1812–1889), managed the plant after his death, following three years of tutelage by his son-in-law, Jacques Antoine Bidermann . His grandson, Lammot du Pont I (1831–1884), was the first president of the United States Gunpowder Trade Association , popularly known as the Powder Trust . [ 6 ]
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https://en.wikipedia.org/wiki/Éleuthère_Irénée_du_Pont
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Émile P. Torres (born 2 July 1982), formerly known as Phil Torres , is an American philosopher, intellectual historian , and activist. Their research focuses on eschatology , existential risk , and human extinction . Along with computer scientist Timnit Gebru , Torres coined the acronym neologism " TESCREAL " to criticize what they see as a group of related philosophies: transhumanism , extropianism , singularitarianism , cosmism , rationalism , effective altruism , and longtermism .
Torres grew up in Maryland . They were raised in a fundamentalist evangelical Christian family, but later left the religion and became an atheist . [ 3 ] [ 4 ] They attribute their interest in eschatology to their fundamentalist upbringing, which exposed them to substantial discussion of the Rapture . [ 5 ]
Torres attended the University of Maryland, College Park and earned a Bachelor of Science with honors in philosophy in 2007. In 2009, they earned a Master of Science in neuroscience from Brandeis University . Simultaneously, from 2008–2009, they were a special student at Harvard University in the philosophy department. [ 5 ] In 2020, Torres began a philosophy Ph.D . program at the Leibniz University Hannover . [ 6 ]
Much of Torres's work focused on existential risk, the study of potential catastrophic events that could result in human extinction. More recently, they have focused on "existential ethics", which they define as "questions about whether our extinction would be right or wrong to bring about if it happened". [ 7 ]
In 2016, Torres published a book titled The End: What Science and Religion Tell Us About the Apocalypse , which discusses both religious and secular eschatology, and describes threats from technologies such as nuclear weapons , biological engineering , nanotechnology , and artificial intelligence . [ 5 ] In 2017 they published another book, titled Morality, Foresight, and Human Flourishing: An Introduction to Existential Risks . Like their first book, it discusses a range of existential threats, but also delves into what they term "agential risk": the roles of outside agents in existential risk. Morality, Foresight, and Human Flourishing was positively reviewed in Futures as a "current and timely" introduction to existential risk. [ 8 ]
From 2023 to 2024, Torres was a visiting postdoctoral researcher at Case Western Reserve University's Inamori International Center for Ethics and Excellence. [ 9 ] [ 10 ] Also in 2023, Routledge published Torres's Human Extinction: A History of the Science and Ethics of Annihilation. [ 3 ] The book posits that the rise of Christianity, along with Christianity's focus on salvation, removed the topic of human extinction from public discourse. [ 3 ] : 1 They argue that concerns around human extinction have re-emerged amid increasing secularism. [ 3 ] [ 11 ] While Torres does not in practice "wish to see or promote" human extinction, they contend that it would not be inherently bad if it were to occur without violence, such as through declining birthrates. [ 12 ]
Torres has published articles in popular media including The Washington Post and Current Affairs , [ 13 ] [ 14 ] and is a contributing writer to Salon and Truthdig . [ 15 ] [ 16 ]
Torres runs a reading group devoted to "The Ethics of Human Extinction." [ 17 ]
The Guardian reported in 2023 that there were "accounts of Torres harassing the philosopher Peter Boghossian and the British cultural theorist Helen Pluckrose ." In the same article, Torres disputed these accounts as being part of a coordinated campaign to undermine Torres's critiques of "radical far-right views". [ 3 ] : 1
For the first decade of their career, Torres identified as a transhumanist , longtermist , and effective altruist . [ 3 ] [ 18 ] Before 2017, Torres contributed writing to the Future of Life Institute , a non-profit organization focused on technology and existential risk. After turning against the organization and opposing techno-optimism with ideas such as a need for a moratorium on the development of artificial intelligence, Torres says they were ousted and their writing removed from the website. [ 19 ]
Torres later left the longtermist, transhumanist, and effective altruist communities, and became a vocal critic. [ 6 ] [ 20 ] Torres claims that longtermism and related ideologies stem from eugenics , and could be used to justify "dangerous" consequentialist thinking. [ 20 ] Along with Timnit Gebru, Torres coined the acronym neologism " TESCREAL " to refer to what they see as a group of related philosophies: transhumanism, extropianism, singularitarianism, cosmism, rationalism, effective altruism, and longtermism. [ 21 ] They first publicized the term in a paper on artificial general intelligence (AGI). Torres argued that a race towards developing AGI would instead produce systems that harm marginalized groups and concentrate power. [ 6 ]
Torres continued to write extensively about the philosophies, and about how they intersect with respect to artificial intelligence. [ 22 ] They have criticized adherents of those philosophies for treating AGI as a technological solution to issues like climate change and access to education, while ignoring other political, social, or economic factors. [ 23 ] They have also expressed concern over their belief that longtermism is prominent in the tech industry. [ 24 ] Torres has also been described as a critic of techno-optimism. [ 25 ]
Ozy Brennan, writing in the journal Asterisk , has criticized Torres's approach of grouping different philosophies as if they were a "monolithic" movement. They argue Torres has misunderstood these different philosophies, and has taken philosophical thought experiments out of context. [ 26 ] James Hughes and Eli Sennesh have argued that Torres's approach is characterized by a "conspiracy style of argumentation", which they contend represents "bad intellectual history and bad politics." [ 27 ]
Torres has also written about artificial intelligence, and has advocated for more focus on AI harms including intellectual property theft , algorithmic bias , and concentration of wealth in technology corporations. [ 20 ] Although effective altruism and a newer philosophy known as effective accelerationism have been described by most observers, including members of both groups, as opposing sides of the argument on how to approach developing artificial intelligence, Torres has opined that the two groups are in fact very similar, and characterized the conflict as a "family dispute". "What's missing is all of the questions that AI ethicists are asking about algorithmic bias, discrimination, the environmental impact of [AI systems], and so on," Torres told The Independent . [ 28 ]
Andrew Anthony , writing in The Observer , has described Torres as longtermism's "most vehement critic". [ 3 ]
Torres is non-binary and uses they/them pronouns. [ 3 ]
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https://en.wikipedia.org/wiki/Émile_P._Torres
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The Étard reaction is a chemical reaction that involves the direct oxidation of an aromatic or heterocyclic bound methyl group to an aldehyde using chromyl chloride . [ 1 ] [ 2 ] [ 3 ] For example, toluene can be oxidized to benzaldehyde .
It is named for the French chemist Alexandre Léon Étard (5 January 1852, Alençon – 1 May 1910).
The reaction mechanism proceeds via an ene reaction with chromyl chloride , forming the precipitated Étard complex. The Étard complex is then decomposed by a [2,3] sigmatropic rearrangement under reducing conditions to prevent further oxidation to a carboxylic acid. Reducing conditions for the decomposition of the Étard complex are provided by saturated aqueous sodium sulphite . Typical solvents for the reaction include carbon disulfide , dichloromethane , [ 4 ] chloroform , and carbon tetrachloride , with carbon tetrachloride being the most common. To obtain a highly purified aldehyde product, the Étard complex precipitate is often purified before decomposition in order to prevent reaction with any unreacted reagent. The reaction is normally carried out for a few days to several weeks and the yields are high. [ 5 ] [ 6 ]
The Étard reaction is most commonly used as a relatively easy method of converting toluene into benzaldehyde . Obtaining specific aldehyde products from reagents other than toluene tends to be difficult due to rearrangements. For example, n -propylbenzene is oxidized to propiophenone , benzyl methyl ketone , and several chlorinated products, with benzyl methyl ketone being the major product. [ 7 ] [ 8 ] Another example arises from the Étard reaction of trans- decalin which results in a mixture of trans-9-decalol, spiro [4.5]decan-6-one, trans-1-decalone, cis-1-decalone, 9,10-octal-1-one, and 1-tetralone . [ 9 ]
Other oxidation reagents like potassium permanganate or potassium dichromate oxidize to the more stable carboxylic acids.
Oxidation of toluene to benzaldehyde is quite a useful conversion. Benzaldehyde is routinely used for its almond flavor. The aldehyde is comparatively reactive and readily participates in aldol condensations . Benzaldehyde can serve as a precursor for various compounds, including dyes, perfumes, and pharmaceuticals. For example, the first step in the synthesis of ephedrine is condensation of benzaldehyde with nitroethane [ citation needed ] . Additionally, benzaldehyde is instrumental in the synthesis of phentermine . [ 10 ] Unlike other oxidising agents (like KMnO 4 or CrO 3 etc.), chromyl chloride does not oxidise aldehyde to carboxylic acid.
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https://en.wikipedia.org/wiki/Étard_reaction
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Étienne Bézout ( French: [bezu] ; 31 March 1730 – 27 September 1783) was a French mathematician who was born in Nemours , Seine-et-Marne , France , and died in Avon (near Fontainebleau ), France.
In 1758 Bézout was elected an adjoint in mechanics of the French Academy of Sciences . Besides numerous minor works, he wrote a Théorie générale des équations algébriques , published at Paris in 1779, which in particular contained much new and valuable matter on the theory of elimination and symmetrical functions of the roots of an equation : he used determinants in a paper in the Histoire de l'académie royale , 1764, but did not treat the general theory.
After his death, a statue was erected in his birth town, Nemours, to commemorate his achievements. [ 1 ]
In 2000, the minor planet 17285 Bezout was named after him. [ 2 ]
This article about a French mathematician is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Étienne_Bézout
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Étienne Henri Gilson ( French: [ʒilsɔ̃] ; 13 June 1884 – 19 September 1978) was a French philosopher and historian of philosophy . A scholar of medieval philosophy , he originally specialised in the thought of Descartes ; he also philosophized in the tradition of Thomas Aquinas , although he did not consider himself a neo-Thomist philosopher. In 1946 he attained the distinction of being elected an "Immortal" (member) of the Académie française . He was nominated for the Nobel Prize in Literature . [ 4 ]
In 2009, the International Étienne Gilson Society was created “to promote the thought of Étienne Gilson and classical philosophy in the academy and culture.” It publishes a journal, Studia Gilsoniana . [ 5 ]
Born in Paris to a Roman Catholic family originally from Burgundy , Gilson attended the minor seminary at Notre-Dame-des-Champs, then finished his secondary education at the Lycée Henri IV . After finishing his military service, during which he began to read René Descartes , he studied for his licence (bachelor's degree), focusing on the influence of scholasticism on Cartesian thought. After studying at the Sorbonne under Victor Delbos (1862–1916), and Lucien Lévy-Bruhl and at the Collège de France under Henri Bergson , he finished his degree in philosophy in 1906.
In 1908, he married Thérèse Ravisé of Melun, and he taught in the high schools of Bourg-en-Bresse , Rochefort , Tours , Saint-Quentin and Angers . In 1913, while employed in teaching at the University of Lille , he defended his doctoral dissertation at the University of Paris on "Liberty in Descartes and Theology" ("La Liberté chez Descartes et la Théologie").
His career was interrupted by the outbreak of World War I , as he was drafted into the French Army as a sergeant. He served on the front and took part in the Battle of Verdun as second lieutenant. He was captured in February 1916 and spent two years in captivity. During this time he devoted himself to new areas of study, including the Russian language and St. Bonaventure . He was later awarded the Croix de Guerre for bravery in action. [ 6 ]
In 1919, he became professor of the history of philosophy at the University of Strasbourg . From 1921 to 1932, he taught the history of medieval philosophy at the University of Paris . At the invitation of the Congregation of St. Basil , in 1929, he set up the Pontifical Institute of Medieval Studies in Toronto in conjunction with St. Michael's College at the University of Toronto , which now hosts an annual Étienne Gilson Lecture. He was elected to the American Academy of Arts and Sciences in 1929. [ 7 ] As an internationally renowned thinker, Gilson was first, along with Jacques Maritain , to receive an honorary doctorate in philosophy from the Pontifical University of Saint Thomas Aquinas ( Angelicum ) in 1930. [ 8 ] [ 9 ]
He taught as a Visiting Professor of Philosophy at Indiana University for 1939-1940.
He also taught for three years at Harvard . He was elected to the Académie française in 1946. In 1948, he was elected an International Member of the American Philosophical Society . [ 10 ]
With the death of his wife, Thérèse Ravisé, on 12 November 1949, Gilson endured a considerable emotional shock. [ 11 ]
In 1951, he relinquished his chair to Martial Gueroult at the Collège de France to devote himself completely to the Pontifical Institute of Mediaeval Studies until 1968. He knew the Jesuit theologian and cardinal Henri de Lubac . Their correspondence has been published. Although Gilson was primarily a historian of philosophy, he was also at the forefront of the 20th century revival of Thomism , along with Jacques Maritain . His work has received critical praise from Richard McKeon .
Gilson undertook an in-depth analysis of Thomism from a historical perspective. To Gilson, Thomism is certainly not identical with scholasticism in the pejorative sense, but rather a revolt against it. [ 12 ] Gilson considered the philosophy of his own era to be deteriorating into a discipline which would signal humanity's abdication of the right to judge and rule nature, relegating humanity into a mere part of nature, which in turn would give the green light for the most reckless of social adventures to play havoc with human lives and institutions. Against "systems" of philosophy, Gilson was convinced that a revival of the philosophy of Thomas Aquinas would lead to the way out of that danger zone. [ citation needed ]
In his time, Gilson was the leading scholar of the history of medieval philosophy as well as a highly regarded philosopher in his own right. [ citation needed ] His works continue to be reprinted and studied today – perhaps alone among "Thomist" philosophers, his work and reputation have not suffered from the general decline of interest in and regard for medieval philosophy since the 1960s. [ citation needed ]
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https://en.wikipedia.org/wiki/Étienne_Gilson
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The Överkalix study ( Swedish : Överkalixstudien ) was a study conducted on the physiological effects of various environmental factors on transgenerational epigenetic inheritance. The study was called " Cardiovascular and diabetes mortality determined by nutrition during parents’ and grandparents’ slow growth period " and was published in the journal European Journal of Human Genetics in 2002. [ 1 ] The study was conducted utilizing historical records, including harvests and food prices , in Överkalix , a small isolated municipality in northeast Sweden . Mortality risk ratios (RR) on children and grandchildren were determined based on available food supply , as indicated by these historical data.
The study started with 320 probands , 164 men and 139 women, born in 1890, 1905, or 1920, and their 1,818 children and grandchildren. 44 were still alive in 1995 when mortality follow-up stopped and other issues (eg. missing birthyear, cause of death unknown) reduced the final analysis to 239 probands. Between 7-22% of these were further removed from each ancestor-specific analysis due to the ancestor experiencing both "good" and "bad" years during the sample period.
The study found that a severe increase/decrease in food supply in male ancestors shortly before puberty was linked to a change in death rates from cardiovascular disease (CVD) and diabetes rates in their descendants. In particular children of a father who suffered a deficit of food had lower rates of deaths from CVD, and a paternal grandfather who suffered a similar deficit saw a reduction in deaths from diabetes in their grandchildren. Conversely a surplus in food supply for a paternal grandfather saw a 4-fold increase in the number of diabetes-related deaths in their grandchildren.
These effects were observed correlating with food surplus/deficit during the slow growth period (SGP). The SGP is the time before the start of puberty , when environmental factors have a larger impact on the body. The ancestors' SGP in this study, was set between the ages of 9-12 for boys and 8–10 years for girls. This occurred in the SGP of both grandparents, or during the gestation period/infant life of the grandmothers, but not during either grandparent's puberty.
The study notes a number of potential issues, including small sample sizes, borderline statistical significance , progeny size effects, puberty estimation, regional food access and environmental effects. [ 1 ] A 2018 study attempted to replicate these findings using a much larger sample of over 11,500 grandchildren using data from the Uppsala Multigeneration Study. It failed to replicate the association with either cardiovascular or diabetes mortality, but did report an increased all-cause mortality correlated to SGP food intake, mostly due to cancer . [ 2 ]
Sex-specific effects can be due to parental imprinting, a process that results in allele-specific differences in transcription, DNA methylation , and DNA replication timing . Imprinting is an important process in human development, and its deregulation can cause certain defined disease states of other imprinted human disease loci. The establishment of parental imprints occurs during gametogenesis as homologous DNA passes through sperm or egg ; subsequently during embryogenesis and into adulthood, alleles of imprinted genes are maintained in two "conformational"/epigenetic states: paternal or maternal . Thus, genomic imprints template their own replication, are heritable, can be identified by molecular analysis, and serve as markers of the parental origin of genomic regions.
The estimation of percentage of human genes subject to parental imprinting is approximately one to two percent, currently parental imprinting has been identified in fewer than 100 distinct named genes. [ 3 ]
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https://en.wikipedia.org/wiki/Överkalix_study
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Øystein Linnebo (born 1971) is a Norwegian philosopher . As of 2020 he is currently employed in the Department of Philosophy at the University of Oslo , having earlier held a position as Professor of Philosophy at Birkbeck College , University of London . He is a fellow of the Norwegian Academy of Science and Letters . [ 1 ]
Linnebo earned his MA in Mathematics from the University of Oslo in 1995 and his PhD in Philosophy at Harvard University in June 2002.
Linnebo's primary areas of concentration are philosophy of logic , philosophy of mathematics , metaphysics , as well as philosophy of language and philosophy of science . He is known for his numerous publications in many top international journals in his field including: The Review of Symbolic Logic , Dialectica , The Journal of Philosophy , Notre Dame Journal of Formal Logic as well as editing a special edition of Synthese . [ 2 ] Additionally, he is the author of the articles "Plural Quantification" and "Platonism in the Philosophy of Mathematics" in the Stanford Encyclopedia of Philosophy . [ 3 ] [ 4 ] He is also an "Area Editor" for philosophy of mathematics on PhilPapers . [ 5 ]
In addition to being a Professorial fellow at the Northern Institute of Philosophy, University of Aberdeen he has also been awarded many grants. Most recently he led a research project as part of a European Research Council Starting Grant entitled "Plurals, Predicates, and Paradox: Towards a Type-Free Account" which ran from January 2010 until December 2013. [ 6 ]
In 2018, he published Thin Objects: An Abstractionist Account , an abstractionist approach to thin objects .
Since 2022, he is visiting professor at the University of Italian Switzerland .
This biography of a Norwegian philosopher is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Øystein_Linnebo
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Āryabhata's sine table is a set of twenty-four numbers given in the astronomical treatise Āryabhatiya composed by the fifth century Indian mathematician and astronomer Āryabhata (476–550 CE), for the computation of the half-chords of a certain set of arcs of a circle. The set of numbers appears in verse 12 in Chapter 1 Dasagitika of Aryabhatiya and is the first table of sines. [ 1 ] [ 2 ] It is not a table in the modern sense of a mathematical table; that is, it is not a set of numbers arranged into rows and columns. [ 3 ] [ 4 ] [ 5 ] Āryabhaṭa's table is also not a set of values of the trigonometric sine function in a conventional sense; it is a table of the first differences of the values of trigonometric sines expressed in arcminutes , and because of this the table is also referred to as Āryabhaṭa's table of sine-differences . [ 6 ] [ 7 ]
Āryabhaṭa's table was the first sine table ever constructed in the history of mathematics . [ 8 ] The now lost tables of Hipparchus (c. 190 BC – c. 120 BC) and Menelaus (c. 70–140 CE) and those of Ptolemy (c. AD 90 – c. 168) were all tables of chords and not of half-chords. [ 8 ] Āryabhaṭa's table remained as the standard sine table of ancient India. There were continuous attempts to improve the accuracy of this table. These endeavors culminated in the eventual discovery of the power series expansions of the sine and cosine functions by Madhava of Sangamagrama (c. 1350 – c. 1425), the founder of the Kerala school of astronomy and mathematics , and the tabulation of a sine table by Madhava with values accurate to seven or eight decimal places.
Some historians of mathematics have argued that the sine table given in Āryabhaṭiya was an adaptation of earlier such tables constructed by mathematicians and astronomers of ancient Greece. [ 9 ] David Pingree , one of America's foremost historians of the exact sciences in antiquity, was an exponent of such a view. Assuming this hypothesis, G. J. Toomer [ 10 ] [ 11 ] [ 12 ] writes, "Hardly any documentation exists for the earliest arrival of Greek astronomical models in India, or for that matter what those models would have looked like. So it is very difficult to ascertain the extent to which what has come down to us represents transmitted knowledge, and what is original with Indian scientists. ... The truth is probably a tangled mixture of both." [ 13 ]
The values encoded in Āryabhaṭa's Sanskrit verse can be decoded using the numerical scheme explained in Āryabhaṭīya , and the decoded numbers are listed in the table below. In the table, the angle measures relevant to Āryabhaṭa's sine table are listed in the second column. The third column contains the list the numbers contained in the Sanskrit verse given above in Devanagari script. For the convenience of users unable to read Devanagari, these word-numerals are reproduced in the fourth column in ISO 15919 transliteration. The next column contains these numbers in the Hindu-Arabic numerals . Āryabhaṭa's numbers are the first differences in the values of sines. The corresponding value of sine (or more precisely, of jya ) can be obtained by summing up the differences up to that difference. Thus the value of jya corresponding to
18° 45′ is the sum 225 + 224 + 222 + 219 + 215 = 1105. For assessing the accuracy of Āryabhaṭa's computations, the modern values of jya s are given in the last column of the table.
In the Indian mathematical tradition, the sine ( or jya ) of an angle is not a ratio of numbers. It is the length of a certain line segment, a certain half-chord. The radius of the base circle is basic parameter for the construction of such tables. Historically, several tables have been constructed using different values for this parameter. Āryabhaṭa has chosen the number 3438 as the value of radius of the base circle for the computation of his sine table. The rationale of the choice of this parameter is the idea of measuring the circumference of a circle in angle measures. In astronomical computations distances are measured in degrees , minutes , seconds , etc. In this measure, the circumference of a circle is 360° = (60 × 360) minutes = 21600 minutes. The radius of the circle, the measure of whose circumference is 21600 minutes, is 21600 / 2π minutes. Computing this using the value π = 3.1416 known to Aryabhata one gets the radius of the circle as 3438 minutes approximately. Āryabhaṭa's sine table is based on this value for the radius of the base circle. It has not yet been established who is the first ever to use this value for the base radius. But Aryabhatiya is the earliest surviving text containing a reference to this basic constant. [ 14 ]
The second section of Āryabhaṭiya, titled Ganitapādd, a contains a stanza indicating a method for the computation of the sine table. There are several ambiguities in correctly interpreting the meaning of this verse. For example, the following is a translation of the verse given by Katz wherein the words in square brackets are insertions of the translator and not translations of texts in the verse. [ 14 ]
This may be referring to the fact that the second derivative of the sine function is equal to the negative of the sine function.
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https://en.wikipedia.org/wiki/Āryabhaṭa's_sine_table
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Ćmielów figurines [ 1 ] are objects of small-scale (decorative) ceramic sculpture created in Poland during the 1950s and 1960s, reflecting the style of the so-called New Look or the Post-Sevastopol Thaw, cast in porcelain or porcelainite . They were designed by artists employed at the Institute of Industrial Design [ pl ] , particularly Henryk Jędrasiak, Mieczysław Naruszewicz [ pl ] , Hanna Orthwein [ pl ] , and Lubomir Tomaszewski , and produced in various ceramic manufacturing facilities across Poland. In 1964, the production of figurines designed by the Institute of Industrial Design was (with a few exceptions) moved to the Ćmielów Porcelain Works in Ćmielów .
Ćmielów figurines represent an important phenomenon in the applied arts of their time, with significance comparable to that of Nymphenburg and Meissen figurines in the 18th century and Copenhagen figurines in the era of modernism . [ 2 ]
In 2021, the first biography of Lubomir Tomaszewski was published by Agora , [ 3 ] authored by Katarzyna Rij and Jerzy A. Wlazło. The book explores the broader context associated with Ćmielów figurines.
In the 1950s, a four-member team of artists was established at the Institute of Industrial Design in Warsaw under the leadership of Henryk Jędrasiak. The team included young graduates of the Warsaw Academy of Fine Arts – Mirosław Naruszewicz, Hanna Orthwein, and Lubomir Tomaszewski. [ 4 ] Their task was to create a new collection of porcelain sculptures, representing a contemporary take on decorative figurines. [ 5 ] Work on the designs began in 1955, [ 6 ] initially as experimental efforts due to the need to break away from traditional approaches to small-scale sculpture. Moreover, apart from Naruszewicz, the artists had no prior experience working with this type of material and needed to familiarize themselves with its properties. [ 7 ]
The first design was completed in mid-1956. It was Akt – Końska Wenus by Henryk Jędrasiak. This figurine still bore features of the earlier style, characterized by numerous angular details and a decorative base. [ 8 ] However, subsequent designs – Jędrasiak's Jeleń and Naruszewicz's Dzik – increasingly showcased new trends. These included simplified forms and a synthesis of the object's silhouette, with deliberate deformations emphasizing specific distinctive elements. [ 8 ]
The production of the figurines was entrusted to several factories: the Bogucice Porcelain Works, the Porcelain and Porcelainite Works in Chodzież , the Ćmielów Porcelain Works , the Karolina Porcelain Works [ pl ] in Jaworzyna Śląska , the Tułowice Porcelainite Works, the Krzysztof Porcelain Works in Wałbrzych , and the Wałbrzych Porcelain Works. [ 6 ] The figurines were produced under the supervision of their creators, though this oversight was rarely enforced. [ 6 ] Designs were often adjusted locally for production, resulting in variations of the same project in different factories. For example, Sowa , designed by Hanna Orthwein, differs in claw shapes between the versions from Ćmielów and Karolina works. [ 9 ]
In 1964, the production of all small-scale sculpture designs was taken over by the Świt division of the Ćmielów Porcelain Works. [ 1 ] However, Tułowice retained the rights to produce most of the Institute of Industrial Design's figurines, while Bogucice did not transfer the original molds created in their facility. [ 1 ]
Already in 1956, Ćmielów figurines achieved exhibition success at the Poznań International Fair . [ 6 ] Until 1964, they were featured attractions at nearly all domestic and international exhibitions and trade fairs. [ 10 ] They were showcased at the Leipzig Trade Fair , in New York and Chicago , at the Second Polish Industrial Exhibition in Moscow in 1959, and at the Polish Exhibition of Glass and Ceramics in Berlin . [ 2 ]
The English magazine The Studio highlighted them in its annual special editions dedicated to the best designs in applied arts: in 1959 ( Dzik and Batalion by M. Naruszewicz), 1960 ( Gibbon by H. Orthwein and Kura by L. Tomaszewski), 1961 ( Gołębie and Gazela by H. Jędrasiak), and 1962 ( Bawół afrykański by L. Tomaszewski). [ 11 ]
The design of these figurines continued at the Institute of Industrial Design until about 1965. During the late 1950s and early 1960s, they were widely available consumer goods. [ 10 ] By the late 1970s, the Ćmielów Porcelain Works attempted to reintroduce them into production under a new program, [ 12 ] but this effort met resistance and was not pursued further until the 1990s. [ 10 ] In 1991, the Ćmielów factories declared bankruptcy, but their new owner initiated a reissue of the Institute of Industrial Design patterns. [ 1 ]
The new owner, Adam Spała [ pl ] , purchased the Ćmielów Porcelain Works in 1996 and 1997. Along with the factory, he acquired the original molds and models of the figurines. Over four years, damaged designs were restored, a new design studio was established, and production resumed in 2000. [ 13 ] Ćmielów figurines are now made from English porcelain, with each figurine accompanied by a certificate of authenticity, a serial number, a trademark (AS Ćmielów), the year of production, and, in some cases, a limited-edition label. [ 13 ] In 2004, Adam Spała published a catalog featuring the figurines listed by their catalog names. The catalog includes photographs of the figurines, each labeled with a consecutive number, as well as information about the designer and the year the design was created. [ 13 ]
The catalog also explains how to interpret the markings on the figurines. For numbered figurines, the markings follow this format: 1/13/02 [ 13 ]
For items in a limited edition series, the marking would be: 13/500 [ 13 ]
The first figurines sold were numbered 13. Figurines numbered 1 to 12 were given a gold certificate and reserved for the owner of the AS Porcelain Factory and his friends. [ 13 ]
Ćmielów figurines represent the style known as the New Look or the Post-Sevastopol Thaw, [ 14 ] characterized by biomorphic lines, asymmetry, and abstract patterns. [ 15 ] The shapes of the figurines simplify the silhouettes of the objects depicted, omitting details except for a few distinctive elements, which are emphasized and define the overall expression of the figurine, reflecting the essence of the object. [ 8 ] This approach was based on the observation of nature and a deep understanding of the subject being portrayed. [ 2 ] Transparency, lightness, and a sense of openness were used, evoking associations with the work of Henry Moore , as seen in Jędrasiak’s Sziedząca Dziewczyna [ 16 ] and, particularly, in the works of Lubomir Tomaszewski (e.g., Dama z lustrem ). [ 17 ] Typically, the objects are depicted in a static pose, though some figurines suggest movement, such as Naruszewicz's Jeździec meksykański and Bizon . [ 16 ]
Researchers have identified around 130 designs of Ćmielów figurines, though incomplete project documentation has led to challenges in attributing some of them. [ 6 ] The thematic scope of the designs was inspired by the animal world, [ 2 ] with an emphasis on domestic, farm, forest, exotic animals, and a few prehistoric creatures (e.g., Brontozaurus and Ichtiozaurus by H. Jędrasiak, Mamut by L. Tomaszewski), as well as birds. Human figures made up a smaller group. [ 18 ]
Figurine models typically came in one size, with some exceptions, such as H. Orthwein's Pingwin , which was available in three sizes, and L. Tomaszewski's Pocałunek , which was produced in two sizes. [ 19 ] There were also designs featuring group compositions, the first being H. Jędrasiak’s Gołąbki , which consisted of two figurines. [ 20 ] A unique case was the two-part sculptures by Jędrasiak – Pawian , Marabut , and Bażant – which consisted of two separate pieces that formed a complete figurine when assembled. These were not introduced into mass production and remained in the prototype stage. [ 16 ]
An important element influencing the final form of the figurines was their painting. [ 16 ] In addition to glaze painting, spray painting and selective spraying techniques were used. These techniques enhanced the realism of the design, mimicking the feathers or fur of animals (as in Naruszewicz's Czapla ), or emphasized the sculptural qualities with an abstract character. [ 21 ] Although bold and expressive colors were used (e.g., Arabka by L. Tomaszewski), [ 16 ] the most common palette was a range of greys, based on contrasts of white and black, [ 2 ] [ 22 ] reflecting the existentialist fashion prevailing in the culture. [ 2 ] Multiple painting designs were created for one model, sometimes changing the entire expression of the figurine (e.g., Śpiewaczka by L. Tomaszewski). [ 17 ]
The painters involved in the decoration of these figurines included designers from the Institute of Industrial Design, such as Zofia Palowa [ pl ] , Barbara Frybes, Zofia Przybyszewska, Zofia Galińska, Jadwiga Adamczewska-Miklaszewska [ pl ] , and Danuta Duszniak [ pl ] . [ 2 ] According to Barbara Banaś, some of the painting designs were also created within the factories that produced the figurines. [ 6 ]
The main designers of Ćmielów figurines were members of the team formed at the Institute of Industrial Design: Henryk Jędrasiak, Mieczysław Naruszewicz, Hanna Orthwein, and Lubomir Tomaszewski:
In the 1950s and 1960s, small-scale sculptural works were created that were not directly considered Ćmielów figurines by researchers, but they fit the aesthetic created by them. [ 27 ] These works came from other designers associated with the Institute of Industrial Design, as well as from designers employed in modeling centers established by a 1952 directive at porcelain factories. [ 27 ]
Other designers at the Institute of Industrial Design involved in the creation of figurines include Zdana Kosicka, who created models of Kotek/Kotek Siedzący and Konik/Konik mały in the early 1950s, [ 27 ] and Liliana Borenowska-Ziemka, who created a Kotek model in the 1950s. Kosicka’s Kotek was realized at the Bogucice factory, [ 28 ] while the other two models were produced in Ćmielów. [ 29 ] In Ćmielów, Wincenty Potacki [ pl ] designed Wesoły byczek (Fernando) and Kazimierz Czuba designed Zajączek/Zajączek ze stojącymi słuchami . [ 30 ]
At the Bogucice factory, Paweł Karasek designed Dziewczyna z gitarą/Dziewczyna z mandoliną , and Eryka Trzewik-Drost [ pl ] created five designs, including Pierwszy bal . [ 30 ] For the Krzysztof factories in Wałbrzych, Stanisław Olszamowski designed Biały niedźwiedź and Panna plażowa , while Zbigniewa Śliwowska-Wawrzyniak created Grzybiarka/Dama z koszykiem . [ 31 ] Jan Kwinta, head of the modeling center at Krzysztof, designed Mrówkojad . [ 30 ]
In addition to the models mentioned above, there are several figurine designs created in Chodzież, Karolina, and Krzysztof factories whose designers remain unidentified. [ 30 ] Some of them are attributed to Jędrasiak, Naruszewicz, Orthwein, or Tomaszewski. [ 30 ]
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https://en.wikipedia.org/wiki/Ćmielów_figurines
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In real algebraic geometry , the Łojasiewicz inequality , named after Stanisław Łojasiewicz , gives an upper bound for the distance of a point to the nearest zero of a given real analytic function . Specifically, let ƒ : U → R be a real analytic function on an open set U in R n , and let Z be the zero locus of ƒ. Assume that Z is not empty. Then for any compact set K in U , there exist positive constants α and C such that, for all x in K
Here, α {\displaystyle \alpha } can be large.
The following form of this inequality is often seen in more analytic contexts: with the same assumptions on f , for every p ∈ U there is a possibly smaller open neighborhood W of p and constants θ ∈ (0,1) and c > 0 such that
A special case of the Łojasiewicz inequality, due to Polyak [ ru ] , is commonly used to prove linear convergence of gradient descent algorithms. This section is based on Karimi, Nutini & Schmidt (2016) and Liu, Zhu & Belkin (2022) .
f {\textstyle f} is a function of type R d → R {\textstyle \mathbb {R} ^{d}\to \mathbb {R} } , and has a continuous derivative ∇ f {\displaystyle \nabla f} .
X ∗ {\displaystyle X^{*}} is the subset of R d {\displaystyle \mathbb {R} ^{d}} on which f {\displaystyle f} achieves its global minimum (if one exists). Throughout this section we assume such a global minimum value f ∗ {\displaystyle f^{*}} exists, unless otherwise stated. The optimization objective is to find some point x {\displaystyle x} in X ∗ {\displaystyle X^{*}} .
μ , L > 0 {\textstyle \mu ,L>0} are constants.
∇ f {\textstyle \nabla f} is L {\displaystyle L} - Lipschitz continuous iff
‖ ∇ f ( x ) − ∇ f ( y ) ‖ ≤ L ‖ x − y ‖ , ∀ x , y {\displaystyle \|\nabla f(x)-\nabla f(y)\|\leq L\|x-y\|,\quad \forall x,y}
f {\textstyle f} is μ {\textstyle \mu } - strongly convex iff f ( y ) ≥ f ( x ) + ∇ f ( x ) T ( y − x ) + μ 2 ‖ y − x ‖ 2 ∀ x , y {\displaystyle f(y)\geq f(x)+\nabla f(x)^{T}(y-x)+{\frac {\mu }{2}}\lVert y-x\rVert ^{2}\quad \forall x,y}
f {\textstyle f} is μ {\textstyle \mu } -PL (where "PL" means "Polyak-Łojasiewicz") iff 1 2 ‖ ∇ f ( x ) ‖ 2 ≥ μ ( f ( x ) − f ( x ∗ ) ) , ∀ x {\displaystyle {\frac {1}{2}}\|\nabla f(x)\|^{2}\geq \mu \left(f(x)-f(x^{*})\right),\quad \forall x}
Theorem — 1. If f {\textstyle f} is μ {\textstyle \mu } -PL, then it is invex .
2. If ∇ f {\textstyle \nabla f} is L-Lipschitz continuous, then f ( y ) ≤ f ( x ) + ⟨ ∇ f ( x ) , y − x ⟩ + L 2 ‖ y − x ‖ 2 {\displaystyle f(y)\leq f(x)+\langle \nabla f(x),y-x\rangle +{\frac {L}{2}}\|y-x\|^{2}}
3. If f {\textstyle f} is μ {\textstyle \mu } -strongly convex then it is μ {\textstyle \mu } -PL.
4. If g {\textstyle g} is μ {\textstyle \mu } -strongly convex, and A {\textstyle A} is linear, then f := g ∘ A {\textstyle f:=g\circ A} is ( μ σ 2 ) {\textstyle (\mu \sigma ^{2})} -PL, where σ {\textstyle \sigma } is the smallest nonzero singular value of A {\textstyle A} .
5. (quadratic growth) If f {\textstyle f} is μ {\textstyle \mu } -PL, x {\textstyle x} is a point, and x ∗ {\textstyle x^{*}} is the point on the optimum set that is closest to x {\textstyle x} in L2-norm, then f ( x ) ≥ f ( x ∗ ) + μ 2 ‖ x − x ∗ ‖ 2 2 {\displaystyle f(x)\geq f\left(x^{*}\right)+{\frac {\mu }{2}}\left\|x-x^{*}\right\|_{2}^{2}}
1. By definition, every stationary point is a global minimum.
2. Set g ( t ) = f ( x + t ( y − x ) ) {\textstyle g(t)=f(x+t(y-x))} for t ∈ [ 0 , 1 ] {\textstyle t\in [0,1]} and use the L {\textstyle L} -Lipschitz continuity to show that f ( y ) − f ( x ) = g ( 1 ) − g ( 0 ) = ∫ 0 1 g ′ ( t ) = ⟨ ∫ 0 1 ∇ f ( x + t ( y − x ) ) d t , y − x ⟩ ≤ ⟨ ∇ f ( x ) , y − x ⟩ + L 2 ‖ y − x ‖ 2 {\textstyle f(y)-f(x)=g(1)-g(0)=\int _{0}^{1}g'(t)=\langle \int _{0}^{1}\nabla f(x+t(y-x))dt,y-x\rangle \leq \langle \nabla f(x),y-x\rangle +{\frac {L}{2}}\|y-x\|^{2}} .
3. By definition, f ( y ) ≥ f ( x ) + ∇ f ( x ) T ( y − x ) + μ 2 ‖ y − x ‖ 2 {\textstyle f(y)\geq f(x)+\nabla f(x)^{T}(y-x)+{\frac {\mu }{2}}\lVert y-x\rVert ^{2}} . Now, minimize the left side, we have f ( x ∗ ) ≥ f ( x ) + ∇ f ( x ) T ( x ∗ − x ) + μ 2 ‖ x ∗ − x ‖ 2 {\displaystyle f(x^{*})\geq f(x)+\nabla f(x)^{T}(x^{*}-x)+{\frac {\mu }{2}}\lVert x^{*}-x\rVert ^{2}} then minimize the right side, we have f ( x ) + ∇ f ( x ) T ( x ∗ − x ) + μ 2 ‖ x ∗ − x ‖ 2 ≥ f ( x ) − 1 2 μ ‖ ∇ f ( x ) ‖ 2 {\displaystyle f(x)+\nabla f(x)^{T}(x^{*}-x)+{\frac {\mu }{2}}\lVert x^{*}-x\rVert ^{2}\geq f(x)-{\frac {1}{2\mu }}\|\nabla f(x)\|^{2}} Combining the two, we have the μ {\textstyle \mu } -PL inequality.
f ( x k ) − f ( x ∗ ) ≤ ( 1 − μ / L ) k ( f ( x 0 ) − f ( x ∗ ) ) {\displaystyle f\left(x_{k}\right)-f\left(x^{*}\right)\leq \left(1-\mu /L\right)^{k}\left(f\left(x_{0}\right)-f\left(x^{*}\right)\right)}
4. g ( A y ) ≥ g ( A x ) + ⟨ ∇ g ( A x ) , A y − A x ⟩ + μ 2 ‖ A y − A x ‖ 2 {\displaystyle g(Ay)\geq g(Ax)+\langle \nabla g(Ax),Ay-Ax\rangle +{\frac {\mu }{2}}\|Ay-Ax\|^{2}}
Now, since ∇ f ( x ) = A T ∇ g ( A x ) {\textstyle \nabla f(x)=A^{T}\nabla g(Ax)} , we have f ( y ) ≥ f ( x ) + ⟨ ∇ f ( x ) , y − x ⟩ + μ 2 ‖ A ( y − x ) ‖ 2 {\displaystyle f(y)\geq f(x)+\langle \nabla f(x),y-x\rangle +{\frac {\mu }{2}}\|A(y-x)\|^{2}}
Set y {\textstyle y} to be the projection of x {\textstyle x} to the optimum subspace, then we have ‖ A ( y − x ) ‖ ≥ σ ‖ y − x ‖ {\textstyle \|A(y-x)\|\geq \sigma \|y-x\|} . Thus, we have f ( y ) − f ( x ) ≥ ⟨ ∇ f ( x ) , y − x ⟩ + μ σ 2 2 ‖ y − x ‖ 2 {\displaystyle f(y)-f(x)\geq \langle \nabla f(x),y-x\rangle +{\frac {\mu \sigma ^{2}}{2}}\|y-x\|^{2}} Vary the y {\textstyle y} on the right side to minimize the right side, we have the desired result.
5. Let g ( x ) := f ( x ) − f ∗ {\textstyle g(x):={\sqrt {f(x)-f^{*}}}} . For any x ∉ X ∗ {\textstyle x\not \in X^{*}} , we have ∇ g ( x ) = ∇ f ( x ) 2 f ( x ) − f ∗ {\displaystyle \nabla g(x)={\frac {\nabla f(x)}{2{\sqrt {f(x)-f^{*}}}}}} so by μ {\textstyle \mu } -PL, ‖ ∇ g ( x ) ‖ 2 ≥ μ / 2 {\displaystyle \|\nabla g(x)\|^{2}\geq \mu /2}
In particular, we see that ∇ g {\textstyle \nabla g} is a vector field on R d ∖ X ∗ {\textstyle \mathbb {R} ^{d}\setminus X^{*}} with size at least μ / 2 {\textstyle {\sqrt {\mu /2}}} . Define a gradient flow along ∇ g {\textstyle \nabla g} with constant unit velocity, starting at x ( 0 ) = x {\textstyle x(0)=x} : x ( 0 ) = x , x ˙ ( t ) = ∇ g ‖ ∇ g ‖ {\displaystyle x(0)=x,\quad {\dot {x}}(t)={\frac {\nabla g}{\|\nabla g\|}}}
Because g {\textstyle g} is bounded below by 0 {\textstyle 0} , and ‖ ∇ g ‖ ≥ μ / 2 {\textstyle \|\nabla g\|\geq {\sqrt {\mu /2}}} , the gradient flow terminates on the zero set X ∗ {\textstyle X^{*}} at a finite time T ≤ g ( x ) / μ / 2 {\displaystyle T\leq g(x)/{\sqrt {\mu /2}}} The path length is T {\textstyle T} , since the velocity is constantly 1.
Since x ( T ) {\textstyle x(T)} is on the zero set, and x ∗ {\textstyle x^{*}} is the point closest to x {\textstyle x} , we have ‖ x ∗ − x ‖ ≤ T ≤ g ( x ) / μ / 2 {\displaystyle \|x^{*}-x\|\leq T\leq g(x)/{\sqrt {\mu /2}}} which is the desired result.
Theorem (linear convergence of gradient descent) — If f {\textstyle f} is μ {\textstyle \mu } -PL and ∇ f {\textstyle \nabla f} is L {\textstyle L} -Lipschitz, then gradient descent with constant step size η {\textstyle \eta } x k + 1 = x k − η ∇ f ( x k ) {\displaystyle x_{k+1}=x_{k}-\eta \nabla f(x_{k})} converges linearly as f ( x k ) − f ( x ∗ ) ≤ ( 1 − 2 μ η ( 1 − L η / 2 ) ) k ( f ( x 0 ) − f ( x ∗ ) ) , η ∈ ( 0 , 2 / L ) {\displaystyle f\left(x_{k}\right)-f\left(x^{*}\right)\leq \left(1-2\mu \eta (1-L\eta /2)\right)^{k}\left(f\left(x_{0}\right)-f\left(x^{*}\right)\right),\quad \eta \in (0,2/L)}
The convergence is the fastest when η = 1 / L {\textstyle \eta =1/L} , at which point f ( x k ) − f ( x ∗ ) ≤ ( 1 − μ / L ) k ( f ( x 0 ) − f ( x ∗ ) ) {\displaystyle f\left(x_{k}\right)-f\left(x^{*}\right)\leq \left(1-\mu /L\right)^{k}\left(f\left(x_{0}\right)-f\left(x^{*}\right)\right)}
Since ∇ f {\textstyle \nabla f} is L {\textstyle L} -Lipschitz, we have the parabolic upper bound f ( x k + 1 ) ≤ f ( x k ) + ⟨ ∇ f ( x k ) , x k + 1 − x k ⟩ + L 2 ‖ x k + 1 − x k ‖ 2 {\displaystyle f(x_{k+1})\leq f(x_{k})+\langle \nabla f(x_{k}),x_{k+1}-x_{k}\rangle +{\frac {L}{2}}\|x_{k+1}-x_{k}\|^{2}}
Plugging in the gradient descent step, f ( x k + 1 ) − f ( x k ) ≤ ⟨ ∇ f ( x k ) , − η ∇ f ( x k ) ⟩ + L 2 ‖ − η ∇ f ( x k ) ‖ 2 = ( L η 2 / 2 − η ) ‖ ∇ f ( x k ) ‖ 2 ≤ 2 μ ( L η 2 / 2 − η ) ( f ( x k ) − f ( x ∗ ) ) {\displaystyle {\begin{aligned}f(x_{k+1})-f(x_{k})&\leq \langle \nabla f(x_{k}),-\eta \nabla f(x_{k})\rangle +{\frac {L}{2}}\|-\eta \nabla f(x_{k})\|^{2}\\&=(L\eta ^{2}/2-\eta )\|\nabla f(x_{k})\|^{2}\\&\leq 2\mu (L\eta ^{2}/2-\eta )\left(f(x_{k})-f(x^{*})\right)\end{aligned}}}
Thus, f ( x k ) − f ( x ∗ ) ≤ ( 1 − 2 μ η ( 1 − L η / 2 ) ) k ( f ( x 0 ) − f ( x ∗ ) ) {\displaystyle f\left(x_{k}\right)-f\left(x^{*}\right)\leq \left(1-2\mu \eta (1-L\eta /2)\right)^{k}\left(f\left(x_{0}\right)-f\left(x^{*}\right)\right)}
Corollary — 1. x k {\textstyle x_{k}} converges to the optimum set X ∗ {\textstyle X^{*}} at a rate of ( 1 − μ η ( 2 − L η ) ) {\textstyle \left(1-\mu \eta (2-L\eta )\right)} .
2. If f {\textstyle f} is μ {\textstyle \mu } -PL, not constant, and ∇ f {\textstyle \nabla f} is L {\textstyle L} -Lipschitz, then L ≥ μ {\textstyle L\geq \mu } .
3. Under the same conditions, gradient descent with optimal step size (which might be found by line-searching ) satisfies
f ( x k ) − f ( x ∗ ) ≤ ( 1 − μ / L ) k ( f ( x 0 ) − f ( x ∗ ) ) {\displaystyle f\left(x_{k}\right)-f\left(x^{*}\right)\leq \left(1-\mu /L\right)^{k}\left(f\left(x_{0}\right)-f\left(x^{*}\right)\right)}
The coordinate descent algorithm first samples a random coordinate i k {\textstyle i_{k}} uniformly, then perform gradient descent by x k + 1 = x k − η ∂ i k f ( x k ) e i k {\displaystyle x_{k+1}=x_{k}-\eta \partial _{i_{k}}f(x_{k})e_{i_{k}}}
Theorem — Assume that f {\textstyle f} is μ {\textstyle \mu } -PL, and that ∇ f {\textstyle \nabla f} is L {\textstyle L} -Lipschitz at each coordinate, meaning that | ∂ i f ( x + t e i ) − ∂ i f ( x ) | ≤ L | t | {\displaystyle |\partial _{i}f(x+te_{i})-\partial _{i}f(x)|\leq L|t|} Then, E [ f ( x k ) − f ( x ∗ ) ] {\textstyle \mathbb {E} [f(x_{k})-f(x^{*})]} converges linearly for all η ∈ ( 0 , 2 / L ) {\textstyle \eta \in (0,2/L)} by E [ f ( x k ) − f ( x ∗ ) ] ≤ ( 1 − μ η ( 2 − L η ) d ) k ( f ( x 0 ) − f ( x ∗ ) ) {\displaystyle \mathbb {E} [f(x_{k})-f(x^{*})]\leq \left(1-{\frac {\mu \eta (2-L\eta )}{d}}\right)^{k}(f(x_{0})-f(x^{*}))}
By the same argument, f ( x k + 1 ) ≤ f ( x k ) + ( L η 2 / 2 − η ) ( ∂ i k f ( x k ) ) 2 {\displaystyle f(x_{k+1})\leq f(x_{k})+(L\eta ^{2}/2-\eta )(\partial _{i_{k}}f(x_{k}))^{2}}
Take expectation with respect to i k {\textstyle i_{k}} , we have E [ f ( x k + 1 ) ] ≤ f ( x k ) + L η 2 / 2 − η d ‖ ∇ f ( x k ) ‖ 2 {\displaystyle \mathbb {E} [f(x_{k+1})]\leq f(x_{k})+{\frac {L\eta ^{2}/2-\eta }{d}}\|\nabla f(x_{k})\|^{2}}
Plug in the μ {\textstyle \mu } -PL inequality, we have E [ f ( x k ) − f ( x ∗ ) ] ≤ ( 1 − μ η ( 2 − L η ) d ) ( f ( x k ) − f ( x ∗ ) ) {\displaystyle \mathbb {E} [f(x_{k})-f(x^{*})]\leq \left(1-{\frac {\mu \eta (2-L\eta )}{d}}\right)(f(x_{k})-f(x^{*}))} Iterating the process, we have the desired result.
In stochastic gradient descent , we have a function to minimize f ( x ) {\textstyle f(x)} , but we cannot sample its gradient directly. Instead, we sample a random gradient ∇ f i ( x ) {\textstyle \nabla f_{i}(x)} , where f i {\textstyle f_{i}} are such that f ( x ) = E i [ f i ( x ) ] {\displaystyle f(x)=\mathbb {E} _{i}[f_{i}(x)]} For example, in typical machine learning, x {\textstyle x} are the parameters of the neural network, and f i ( x ) {\textstyle f_{i}(x)} is the loss incurred on the i {\textstyle i} -th training data point, while f ( x ) {\textstyle f(x)} is the average loss over all training data points.
The gradient update step is x k + 1 = x k − η k ∇ f i k ( x k ) {\displaystyle x_{k+1}=x_{k}-\eta _{k}\nabla f_{i_{k}}(x_{k})} where η k > 0 {\textstyle \eta _{k}>0} are a sequence of learning rates (the learning rate schedule).
Theorem — If each ∇ f i {\textstyle \nabla f_{i}} is L {\textstyle L} -Lipschitz, f {\textstyle f} is μ {\textstyle \mu } -PL, and f {\textstyle f} has global minimum f ∗ {\textstyle f^{*}} , then E [ f ( x k + 1 ) − f ∗ ] ≤ ( 1 − 2 η k μ ) [ f ( x k ) − f ∗ ] + L η k 2 2 E i [ ‖ ∇ f i ( x k ) ‖ 2 ] {\displaystyle \mathbb {E} \left[f\left(x_{k+1}\right)-f^{*}\right]\leq \left(1-2\eta _{k}\mu \right)\left[f\left(x_{k}\right)-f^{*}\right]+{\frac {L\eta _{k}^{2}}{2}}\mathbb {E} _{i}[\|\nabla f_{i}(x_{k})\|^{2}]} We can also write it using the variance of gradient L2 norm: E [ f ( x k + 1 ) − f ∗ ] ≤ ( 1 − μ ( 2 η k − L η k 2 ) ) [ f ( x k ) − f ∗ ] + L η k 2 2 E i [ ‖ ∇ f i ( x k ) − ∇ f ( x k ) ‖ 2 ] {\displaystyle \mathbb {E} \left[f\left(x_{k+1}\right)-f^{*}\right]\leq \left(1-\mu (2\eta _{k}-L\eta _{k}^{2})\right)\left[f\left(x_{k}\right)-f^{*}\right]+{\frac {L\eta _{k}^{2}}{2}}\mathbb {E} _{i}[\|\nabla f_{i}(x_{k})-\nabla f(x_{k})\|^{2}]}
Because all ∇ f i {\textstyle \nabla f_{i}} are L {\textstyle L} -Lipschitz, so is ∇ f {\textstyle \nabla f} . We thus have f ( x k + 1 ) ≤ f ( x k ) − η k ⟨ ∇ f ( x k ) , ∇ f i k ( x k ) ⟩ + L η k 2 2 ‖ ∇ f i k ( x k ) ‖ 2 {\displaystyle f(x_{k+1})\leq f(x_{k})-\eta _{k}\langle \nabla f(x_{k}),\nabla f_{i_{k}}(x_{k})\rangle +{\frac {L\eta _{k}^{2}}{2}}\|\nabla f_{i_{k}}(x_{k})\|^{2}}
Now, take the expectation over i k {\textstyle i_{k}} , and use the fact that f {\textstyle f} is μ {\textstyle \mu } -PL. This gives the first equation.
The second equation is shown similarly by noting that E i [ ‖ ∇ f i ( x k ) ‖ 2 ] = E i [ ‖ ∇ f i ( x k ) − ∇ f ( x k ) ‖ 2 ] + ‖ ∇ f ( x k ) ‖ 2 {\displaystyle \mathbb {E} _{i}[\|\nabla f_{i}(x_{k})\|^{2}]=\mathbb {E} _{i}[\|\nabla f_{i}(x_{k})-\nabla f(x_{k})\|^{2}]+\|\nabla f(x_{k})\|^{2}}
As it is, the proposition is difficult to use. We can make it easier to use by some further assumptions.
The second-moment on the right can be removed by assuming a uniform upper bound. That is, if there exists some C > 0 {\textstyle C>0} such that during the SG process, we have E i [ ‖ ∇ f i ( x k ) ‖ 2 ] ≤ C {\displaystyle \mathbb {E} _{i}[\|\nabla f_{i}(x_{k})\|^{2}]\leq C} for all k = 0 , 1 , … {\textstyle k=0,1,\dots } , then E [ f ( x k + 1 ) − f ∗ ] ≤ ( 1 − 2 η k μ ) [ f ( x k ) − f ∗ ] + L C η k 2 2 {\displaystyle \mathbb {E} \left[f\left(x_{k+1}\right)-f^{*}\right]\leq \left(1-2\eta _{k}\mu \right)\left[f\left(x_{k}\right)-f^{*}\right]+{\frac {LC\eta _{k}^{2}}{2}}} Similarly, if ∀ k , E i [ ‖ ∇ f i ( x k ) − ∇ f ( x k ) ‖ 2 ] ≤ C {\displaystyle \forall k,\quad \mathbb {E} _{i}[\|\nabla f_{i}(x_{k})-\nabla f(x_{k})\|^{2}]\leq C} then E [ f ( x k + 1 ) − f ∗ ] ≤ ( 1 − μ ( 2 η k − L η k 2 ) ) [ f ( x k ) − f ∗ ] + L C η k 2 2 {\displaystyle \mathbb {E} \left[f\left(x_{k+1}\right)-f^{*}\right]\leq \left(1-\mu (2\eta _{k}-L\eta _{k}^{2})\right)\left[f\left(x_{k}\right)-f^{*}\right]+{\frac {LC\eta _{k}^{2}}{2}}}
For constant learning rate schedule , with η k = η = 1 / L {\textstyle \eta _{k}=\eta =1/L} , we have E [ f ( x k + 1 ) − f ∗ ] ≤ ( 1 − μ / L ) [ f ( x k ) − f ∗ ] + C 2 L {\displaystyle \mathbb {E} \left[f\left(x_{k+1}\right)-f^{*}\right]\leq \left(1-\mu /L\right)\left[f\left(x_{k}\right)-f^{*}\right]+{\frac {C}{2L}}} By induction, we have E [ f ( x k ) − f ∗ ] ≤ ( 1 − μ / L ) k [ f ( x 0 ) − f ∗ ] + C 2 μ {\displaystyle \mathbb {E} \left[f\left(x_{k}\right)-f^{*}\right]\leq \left(1-\mu /L\right)^{k}\left[f\left(x_{0}\right)-f^{*}\right]+{\frac {C}{2\mu }}} We see that the loss decreases in expectation first exponentially, but then stops decreasing, which is caused by the C / ( 2 L ) {\textstyle C/(2L)} term. In short, because the gradient descent steps are too large, the variance in the stochastic gradient starts to dominate, and x k {\textstyle x_{k}} starts doing a random walk in the vicinity of X ∗ {\textstyle X^{*}} .
For decreasing learning rate schedule with η k = O ( 1 / k ) {\textstyle \eta _{k}=O(1/k)} , we have E [ f ( x k ) − f ∗ ] = O ( 1 / k ) {\displaystyle \mathbb {E} \left[f\left(x_{k}\right)-f^{*}\right]=O(1/k)} .
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https://en.wikipedia.org/wiki/Łojasiewicz_inequality
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The Łoś–Tarski theorem is a theorem in model theory , a branch of mathematics , that states that the set of formulas preserved under taking substructures is exactly the set of universal formulas. [ 1 ] The theorem was discovered by Jerzy Łoś and Alfred Tarski .
Let T {\displaystyle T} be a theory in a first-order logic language L {\displaystyle L} and Φ ( x ¯ ) {\displaystyle \Phi ({\bar {x}})} a set of formulas of L {\displaystyle L} .
(The sequence of variables x ¯ {\displaystyle {\bar {x}}} need not be
finite.) Then the following are equivalent:
A formula is ∀ 1 {\displaystyle \forall _{1}} if and only if it is of the form ∀ x ¯ [ ψ ( x ¯ ) ] {\displaystyle \forall {\bar {x}}[\psi ({\bar {x}})]} where ψ ( x ¯ ) {\displaystyle \psi ({\bar {x}})} is quantifier-free.
In more common terms, this states that
every first-order formula is preserved under induced substructures if and only if it is ∀ 1 {\displaystyle \forall _{1}} , i.e. logically equivalent to a first-order universal formula.
As substructures and embeddings are dual notions, this theorem is sometimes stated in its dual form:
every first-order formula is preserved under embeddings on all structures if and only if it is ∃ 1 {\displaystyle \exists _{1}} , i.e. logically equivalent to a first-order existential formula. [ 2 ]
Note that this property fails for finite models .
This mathematical logic -related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Łoś–Tarski_preservation_theorem
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In model theory , a branch of mathematical logic , the Łoś–Vaught test is a criterion for a theory to be complete , unable to be augmented without becoming inconsistent. For theories in classical logic , this means that for every sentence , the theory contains either the sentence or its negation but not both.
A theory T {\displaystyle T} with signature σ is κ {\displaystyle \kappa } -categorical for an infinite cardinal κ {\displaystyle \kappa } if T {\displaystyle T} has exactly one model (up to isomorphism) of cardinality κ . {\displaystyle \kappa .}
The Łoś–Vaught test states that if a satisfiable theory is κ {\displaystyle \kappa } -categorical for some κ ≥ | σ | {\displaystyle \kappa \geq |\sigma |} and has no finite model, then it is complete.
This theorem was proved independently by Jerzy Łoś ( 1954 ) and Robert L. Vaught ( 1954 ), after whom it is named.
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https://en.wikipedia.org/wiki/Łoś–Vaught_test
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In the Babylonian magico-medical tradition , Šulak is the lurker of the bathroom or the demon of the privy . Šulak appears in the Babylonian Diagnostic Handbook (Tablet XXVII), in which various diseases are described and attributed to the hand of a god , goddess , or spirit. A lurker is a type of demon who lies in wait in places where a potential victim is likely to be alone. When a man attends to excretory functions or elimination , he is exposed and hence vulnerable: "Šulak will hit him!" The "hit" may be a type of stroke ( mišittu ).
Ancient folk etymology held that the name Šulak derived from a phrase meaning "dirty hands", due to his dwelling in the bīt musâti - literally "house of rinse-water", i.e. lavatory . [ 1 ] Šulak is described in Akkadian sources as a rampant or bipedal but otherwise normal looking lion. [ 1 ]
The demon referred to as "The Hitter" or "Striker" elsewhere in the handbook may be Šulak identified by an epithet . A much earlier reference to this demon is found in a Hittite diagnostic text. [ 2 ]
Ancient Mesopotamian medical texts attribute cases of paralysis and stroke to the action of Šulak, a connection possibly due to fears that excessive strain on the toilet could cause such maladies. Protective amulets in the form of the Lion Centaur Urmahlullu , or cuneiform tablets inscribed with spells to ward off Šulak, were often buried in the doorways of lavatories, or in the foundations of the house, or deposited in drainage pipes. [ 1 ]
A similar lavatory demon takes the form of a goat in the Talmud ( Shabbat 67a, Berachot 62a). [ 3 ] This "demon of the privy" (Sheid beit ha-Kisset) appears also in the Babylonian Talmud :
The Rabbis taught: On coming from a privy a man should not have sexual intercourse till he has waited long enough to walk half a mil ,
Stroke and epilepsy were closely related in ancient medicine. This law is not included in the Mishneh Torah . [ 6 ]
The "demon of the privy" is the type of unclean spirit that in the early Christian era was regarded as causing both physical and spiritual affliction. [ 7 ]
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Ștefan Emilian (August 8, 1819 – November 1899) was an Imperial Austrian -born Romanian mathematician and architect.
Born in Bonchida, Kolozs County (now Bonțida , Cluj County ), in the Principality of Transylvania , he was given the surname Kertész as a child, although his birth name was Emilian . He attended high school in Sibiu . Then, from 1841 to 1845, he studied at the Academy of Fine Arts Vienna , graduating with an architect's degree. Additionally, from 1841 to 1843, he took courses at the Vienna Polytechnic Institute . Emilian returned home shortly before 1848, in time for the Transylvanian Revolution . Pursued by the authorities, he sought refuge in Wallachia . By 1850, he was back in Transylvania, where he taught mathematics at Brașov 's Greek Orthodox High School . He remained there until 1858, a period during which he designed the new school building. Additionally, he was the architect for the first paper factory in Zărnești . [ 1 ]
In 1858, he was invited to Iași , the capital of Moldavia , in order to teach drawing and geometry to the upper classes of Academia Mihăileană . Emilian remained there for two years, until the founding of the University of Iași . Additionally, he taught at the military officers' school and the technical school of arts and professions. At the new university, he was named full professor of descriptive geometry and linear perspective, remaining from October 1860 to October 1892, when he had to retire. Meanwhile, he designed the Iași anatomy institute, the Lipovan Church , and the church in Bosia . A single published book of his is known: the 1886 Curs practic de perspectivă liniară . Emilian's funeral eulogy was delivered by Alexandru Dimitrie Xenopol . [ 1 ]
He married Cornelia Ederlly de Medve . [ 2 ]
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α,β-Unsaturated carbonyl compounds are organic compounds with the general structure (O=CR)−C α =C β −R. [ 1 ] [ 2 ] Such compounds include enones and enals , but also carboxylic acids and the corresponding esters and amides. In these compounds, the carbonyl group is conjugated with an alkene (hence the adjective unsaturated ). Unlike the case for carbonyls without a flanking alkene group, α,β-unsaturated carbonyl compounds are susceptible to attack by nucleophiles at the β-carbon. This pattern of reactivity is called vinylogous . Examples of unsaturated carbonyls are acrolein (propenal), mesityl oxide , acrylic acid , and maleic acid . Unsaturated carbonyls can be prepared in the laboratory in an aldol reaction and in the Perkin reaction .
α,β-Unsaturated carbonyl compounds can be subclassified according to the nature of the carbonyl and alkene groups.
α,β-Unsaturated carbonyl compounds featuring a carbonyl conjugated to an alkene that is terminal, or vinylic , contain the acryloyl group ( H 2 C =CH−C(= O )− ); it is the acyl group derived from acrylic acid . The preferred IUPAC name for the group is prop-2-enoyl , and it is also known as acrylyl or simply (and incorrectly) as acryl . Compounds containing an acryloyl group can be referred to as "acrylic compounds".
An α,β-unsaturated acid is a type of α,β-unsaturated carbonyl compound that consists of an alkene conjugated to a carboxylic acid . [ 3 ] The simplest example is acrylic acid ( CH 2 =CHCO 2 H ). These compounds are prone to polymerization, giving rise to the large area of polyacrylate plastics. Acrylate polymers are derived from but do not contain the acrylate group. [ 4 ] The carboxyl group of acrylic acid can react with ammonia to form acrylamide , or with an alcohol to form an acrylate ester . Acrylamide and methyl acrylate are commercially important examples of α,β-unsaturated amides and α,β-unsaturated esters, respectively. They also polymerize readily. Acrylic acid, its esters, and its amide derivatives feature the acryloyl group.
α,β-Unsaturated dicarbonyls are also common. The parent compounds are maleic acid and the isomeric fumaric acid . Maleic acid forms esters, an imide, and an anhydride, i.e. diethyl maleate , maleimide , and maleic anhydride . Fumaric acid, as fumarate, is an intermediate in the Krebs citric acid cycle , which is of great importance in bioenergy.
An enone (or alkenone ) is an organic compound containing both alkene and ketone functional groups. In an α,β-unsaturated enone, the alkene is conjugated to the carbonyl group of the ketone. [ 3 ] The simplest enone is methyl vinyl ketone (butenone, CH 2 =CHCOCH 3 ). Enones are typically produced using an aldol condensation or Knoevenagel condensation . Some commercially significant enones produced by condensations of acetone are mesityl oxide ( dimer of acetone) and phorone and isophorone ( trimers ). [ 5 ] In the Meyer–Schuster rearrangement , the starting compound is a propargyl alcohol . Another method to access α,β-unsaturated carbonyls is via selenoxide elimination . Cyclic enones can be prepared via the Pauson–Khand reaction .
The cyclic enones include cyclopropenone , cyclobutenone, [ 6 ] cyclopentenone , cyclohexenone , and cycloheptenone. [ 7 ]
An enal (or alkenal ) is an organic compound containing both alkene and aldehyde functional groups. In an α,β-unsaturated enal, the alkene is conjugated to the carbonyl group of the aldehyde (formyl group). [ 3 ] The simplest enal is acrolein ( CH 2 =CHCHO ). Other examples include cis -3-hexenal (essence of mowed lawns) and cinnamaldehyde (essence of cinnamon).
α,β-Unsaturated carbonyls are electrophilic at both the carbonyl carbon as well as the β-carbon. Depending on conditions, either site is attacked by nucleophiles . Additions to the alkene are called conjugate additions . One type of conjugate addition is the Michael addition , which is used commercially in the conversion of mesityl oxide into isophorone . Owing to their extended conjugation, α,β-unsaturated carbonyls are prone to polymerization. In terms of industrial scale, polymerization dominates the use of α,β-unsaturated carbonyls. Again because of their electrophilic character, the alkene portion of α,β-unsaturated carbonyls is good dienophiles in Diels–Alder reactions . They can be further activated by Lewis acids, which bind to the carbonyl oxygen. α,β-Unsaturated carbonyls are good ligands for low-valent metal complexes, examples being (bda)Fe(CO) 3 and tris(dibenzylideneacetone)dipalladium(0) .
α,β-Unsaturated carbonyls are readily hydrogenated. Hydrogenation can target the carbonyl or the alkene ( conjugate reduction ) selectively, or both functional groups.
Enones undergo the Nazarov cyclization reaction and in the Rauhut–Currier reaction (dimerization).
α,β-Unsaturated thioesters are intermediates in several enzymatic processes. Two prominent examples are coumaroyl-coenzyme A and crotonyl-coenzyme A . They arise by the action of acyl-CoA dehydrogenases . [ 8 ] Flavin adenine dinucleotide (FAD) is a required co-factor.
Since α,β-unsaturated compounds are electrophiles and alkylating agents, many α,β-unsaturated carbonyl compounds are toxic. The endogenous scavenger compound glutathione naturally protects from toxic electrophiles in the body. Some drugs (amifostine, N -acetylcysteine ) containing thiol groups may protect from such harmful alkylation.
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The α-aminoadipate pathway is a biochemical pathway for the synthesis of the amino acid L - lysine . In the eukaryotes , this pathway is unique to several species of yeast , higher fungi (containing chitin in their cell walls), and the euglenids . [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] It has also been reported from bacteria of the genus Thermus [ 6 ] and also in Pyrococcus horikoshii , [ 7 ] potentially suggesting a wider distribution than previously thought. This uniqueness of the pathway makes it a potentially interesting target for antimycotics . [ 3 ]
This pathway is a part of the glutamate family of amino acid biosynthetic pathways. [ 2 ] The reaction steps in the pathway are similar to the citric acid cycle .
The first step in the pathway is condensation of acetyl-CoA with α-ketoglutarate , which gives homocitrate . This reaction is catalyzed by homocitrate synthase . Homocitrate is then converted to homoaconitate by homoaconitase and then to homoisocitrate . This is then decarboxylated by homoisocitrate dehydrogenase , which results in α-ketoadipate . A nitrogen atom is added from glutamate by aminoadipate aminotransferase to form the α-aminoadipate , from which this pathway gets its name. This is then reduced by aminoadipate reductase via an acyl-enzyme intermediate to a semialdehyde. Reaction with glutamate by one class of saccharopine dehydrogenase yields saccharopine which is then cleaved by a second saccharopine dehydrogenase to yield lysine and oxoglutarate. [ 2 ]
Conversion of lysine to α-ketoadipate during degradation of lysine proceeds via the same steps, but in reverse. [ 8 ]
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α-Endopsychosin is a putative antagonist of the phencyclidine site of the NMDA receptor which was discovered in extracts of porcine brain and may also be endogenous in humans. [ 1 ] [ 2 ] [ 3 ] The compound appears to be a peptide , but has yet to be purified and fully characterized. [ 1 ] [ 3 ]
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α-Galactosylceramide ( α-GalCer , KRN7000 ) is a synthetic glycolipid derived from structure-activity relationship studies of galactosylceramides isolated from the marine sponge Agelas mauritianus . α-GalCer is a strong immunostimulant and shows potent anti-tumour activity in many in vivo models. [ 1 ]
α-GalCer is a potent activator of iNKT cells , and a model CD1d antigen. The invariant T cell receptor of the iNKT cell is able to bind the CD1d:glycolipid complex leading to iNKT cell activation in both mice and humans. [ 2 ]
In combination with a peptide antigen, α-GalCer is able to stimulate a strong immune response against the epitope. The CD1d:glycolipid:TCR interaction activates the iNKT cell which can then activate the dendritic cell. This causes the release of a range of cytokines and licenses the dendritic cell to activate a peptide-specific T cell response. This adjuvant acts through this cellular interaction, rather than through classic pattern recognition receptor pathways. [ 3 ]
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https://en.wikipedia.org/wiki/Α-Galactosylceramide
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α-Halo carboxylic acids and esters are organic compounds with the respective formulas RCHXCO 2 H and RCHXCO 2 R' where R and R' are organic substituents. The X in these compounds is a halide, usually chloride and bromide . These compounds are often used as intermediates in the preparation of more elaborate derivatives. They are often potent alkylating agents . The mono halide derivatives are chiral .
They are often prepared by reaction of the acid or the ester with halogen:
A related method is the Hell-Volhard-Zelinsky halogenation .
Amino acids are susceptible to diazotization in the presence of chloride, a process that affords chiral 2-chloro carboxylic acids and esters. [ 1 ]
Consistent with these compounds being alkylating agents, the α-halide is readily substituted, e.g. by azide . [ 2 ] Similarly, the α-bromocarboxylic acid undergo nucleophilic substitution with ammonia to give the amino acid, [ 3 ]
The Darzens reaction involves a ketone or aldehyde with an α-haloester in the presence of a base to form an α,β- epoxy ester , also called a "glycidic ester". [ 4 ] The reaction process begins with deprotonation at the halogenated position. In a related reaction, α-halo carboxylic esters can be reduced by lithium aluminium hydride to the α-halo alcohols, which can be converted to the α- epoxides . [ 5 ]
α-Halo-esters can be converted to vinyl halides. upon reaction with ketones and chromous chloride . [ 6 ]
A prominent α-halo carboxylic acid is chloroacetic acid , which is used to produce carboxymethyl cellulose , carboxymethyl starch , as well as several phenoxy herbicides . [ 7 ] 2,2-Dichloropropionic acid ("Dalapon") is an herbicide. [ 8 ]
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In organic chemistry , an α-halo ketone is a functional group consisting of a ketone group or more generally a carbonyl group with an α- halogen substituent . α-Halo ketones are alkylating agents . Prominent α-halo ketones include phenacyl bromide and chloroacetone . [ 1 ]
The general structure is RR′C(X)C(=O)R where R is an alkyl or aryl residue and X any one of the halogens.
The preferred conformation of a halo ketone is that of a cisoid with the halogen and carbonyl sharing the same plane as the steric hindrance with the carbonyl alkyl group is generally larger. [ 2 ]
Halo ketones and halo carbonyl compounds in general are synthesized by reaction of carbonyl compounds with sources of X + (X = halogen), which is provided using halogens : [ 1 ]
Specialized sources of electrophilic halogenating agents include N -Bromosuccinimide and 1,3-dibromo-5,5-dimethylhydantoin (DBDMH). In the Nierenstein reaction an acyl chloride reacts with diazomethane
Efforts are reported in asymmetric synthesis of halo carbonyls through organocatalysis . In one study an acid chloride is converted into an α-halo ester with a strong base ( sodium hydride ), a bromine donor and an organocatalyst based on proline and quinine : [ 3 ]
In the proposed reaction mechanism the base first converts the acid chloride to the ketene , the organocatalyst then introduces chirality through its quinonoid tertiary amine , forming a ketene adduct.
Illustrative of their alkylating activity are reactions with potassium iodide in acetone , chloroacetone reacts faster than 1-chloropropane by a factor of 36,000. Halo ketones react with phosphites in the Perkow reaction .
The halo group can be removed in reductive dehalogenation of halo ketones . α-Halo ketones can also be converted to alkenes by treatment with hydrazine.
Due to the presence of two electron withdrawing groups (carbonyl and halide), the α-hydrogen is acidic. This property is exploited in the Favorskii rearrangement , where base abstracts first an acidic α-hydrogen and the resulting carbanion then displaces the halogen.
In crossed aldol reactions between halo ketones and aldehydes , the initial reaction product is a halohydrin which can subsequently form an oxirane in the presence of base.
α-Halo ketones can react with amines to form an α-halo imine, which can be converted back to the parent halo ketone by hydrolysis , so that halo imines may be used as masked versions of halo ketones. This allows some chemical transformations to be achieved that are not possible with the parent halo ketones directly. [ 4 ]
Halo ketones take part in several reaction types, especially since they are bifunctional, with two electrophilic sites (α-carbon and carbonyl carbon). In one manifestation of this duality, they are precursors to heterocycles. Thiazoles arise from reaction of chloroacetone with thioamides. 2-Aminothiazoles are similarly produced by reaction of 2-chloroketones with thioureas . [ 5 ] [ 6 ] Pyrroles may be synthesized by reaction of halo ketones with dicarbonyls and ammonia in the Hantzsch pyrrole synthesis .
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α-Hexachlorocyclohexane ( α-HCH ) is an organochloride which is one of the isomers of hexachlorocyclohexane (HCH). [ 1 ] It is a byproduct of the production of the insecticide lindane (γ-HCH) and it is typically still contained in commercial grade lindane used as insecticide. Lindane, however, has not been produced or used in the United States for more than 20 years. [ 1 ] At ambient temperatures it is a stable, white, powdery solid substance. As of 2009, the Stockholm Convention on Persistent Organic Pollutants classified (α-HCH) and (β-HCH) as persistent organic pollutants (POPs) , due to the chemical's ability to persistence in the environment, bioaccumulative , biomagnifying, and long-range transport capacity.
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α-Ketovaleric acid is a keto acid that is found in human blood. [ 1 ] [ 2 ] [ 3 ] Unlike related keto acids, it is not an intermediate or metabolite associated with amino acids and its origin is unknown. [ 4 ]
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α-Neoendorphin is an endogenous opioid peptide with a decapeptide structure and the amino acid sequence Tyr - Gly -Gly- Phe - Leu - Arg - Lys -Tyr- Pro -Lys. [ 1 ]
α-Neoendorphin is a neuropeptide . Prodynorphin or Proenkephalin B is its precursor. Researchers and anatomists have not yet studied the distribution of α-neoendorphin in the human in detail. However, some studies have been done which supports the presence of α-neoendorphin immunoreactive fibers throughout the human brainstem. According to a study done by Duque, Ewing, Arturo Mangas, Pablo Salinas, Zaida Díaz-cabiale, José Narváez, and Rafael Coveñas; α-neoendorphin immunoreactive fibers can be found in the caudal part of the solitary nucleus, in the caudal and the gelatinosa parts of the spinal trigeminal nucleus, and only low density was found in the central grey matter of medulla. [ 2 ]
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β-Carbon elimination ( beta -carbon elimination) is a type of reaction in organometallic chemistry wherein an allyl ligand bonded to a metal center is broken into the corresponding metal-bonded alkyl (aryl) ligand and an alkene . [ 1 ] It is a subgroup of elimination reactions. Though less common and less understood than β-hydride elimination , it is an important step involved in some olefin polymerization processes and transition-metal-catalyzed organic reactions. [ 2 ]
Like β-hydride elimination, β-carbon elimination requires the metal to have an open coordination site cis to the alkyl group for this reaction to occur. β-carbon elimination is usually less favored than hydride elimination because the metal–hydride bond is stronger than the metal–carbon bond for most metals in catalytic reactions . The principles governing β-alkyl elimination are not well-established experimentally. One reason for this is that breaking C−C bonds in the presence of other reactive C−H bonds is a rare event, and systems designed to interrogate the reaction are more difficult to devise. [ 2 ]
β-alkyl elimination is the most common and useful type among all β-carbon elimination reactions.
In terms of thermodynamics , more electron-deficient metal centers increase the likelihood of β-alkyl elimination. For example, β-alkyl elimination is more favorable than β-hydride elimination when it is bonded to electron-deficient early transition metals (Hf, Ti, Zr, Nb, etc.) with d 0 configuration. Computational studies show a thermodynamic preference for β-Me elimination over β-H elimination in these complexes due to additional stability for the metal–alkyl species. [ 3 ] The origin of the additional bonding interaction comes from an orbital centered on the CH 3 weakly π-donating to the LUMO of the d 0 of the metal center which is analogous to the hyperconjugation effect (see figure on the right), thus increasing the stability of M−CH 3 over M−H species. Their calculations predict that a more electrophilic metal ion enhances the −CH 3 π-donation, which consequently increases the stability of M−CH 3 over M−H species. Conversely, a more electron-rich metal ion will favor M−H formation (for example, using the more electron-donating Cp* ligand in Cp* 2 MX 2 ).
In terms of kinetics , steric effects of ligands could play a role in increasing the energy barrier of β-H elimination relative to β-alkyl elimination, specifically when the ligand is Cp*. A model was proposed to illustrate this effect: [ 4 ] In both β-methyl elimination (A) and β-hydride elimination (B), the transferring group aligns perpendicular to the Cp*(centroid)−Zr−Cp*(centroid), allowing the σ C−C or σ C−H bond to overlap with the metal d-orbital. However, to achieve the prerequisite geometry for β-H elimination (B), the adjacent methyl group experiences a significant steric repulsion from the Cp* ligand, thereby elevating the barrier to hydride transfer. By contrast, transition state A for β-Me elimination experiences less steric interaction with the Cp* ligand.
In middle and late transition metal complexes, there is larger thermodynamic preference for β-H elimination over β-alkyl elimination, where the difference is usually >15 kcal/mol. [ 2 ] Examples involved middle and late transition metal complexes are either absent of β-hydrogens or use ring strain relief and aromaticity as driving forces to favor β-alkyl elimination over β-hydride elimination. [ 5 ]
Ring-opening polymerization that involves β-alkyl elimination can be catalyzed by Ti, [ 6 ] Zr, [ 7 ] [ 8 ] Pd [ 9 ] -based catalyst, and some Lanthanide-based metallocene catalyst, [ 10 ] [ 11 ] where different polymerization patterns vary when catalysts are different. Examples of copolymerization with alkene [ 10 ] or carbon monoxide [ 12 ] [ 13 ] were also reported. The key step of this kind of ROP is string-driven β-alkyl elimination, which provides linear polymer with unsaturation in the polymer chain.
There is enormous amount of catalytic processes involving β-alkyl elimination that are synthetically useful. β-alkyl elimination in this case, however, is often considered as an alternative way of C–C bond cleavage while oxidative addition is the direct way. [ 14 ] One of the examples is β-alkyl elimination of tert -alcoholates which can generate from either addition of an organometallic reagent or ligand exchange. [ 15 ] [ 16 ] [ 17 ] The consequent organometallic species can undergo various downstream reactivities (reductive elimination, carbonyl insertion, etc.) to generate useful building blocks.
In addition to ring strain, aromaticity-driven β-Me elimination can be effectively employed to dealkylate steroid derivatives and some other cyclohexyl compounds. [ 18 ] [ 19 ]
β-aryl elimination is much less common and understood than β-alkyl elimination. Examples are reported to occur from metal alkoxide and amido complexes. [ 20 ] [ 21 ] [ 22 ] A theoretical study showed that these reactions are driven by consequent extensive conjugation system. [ 23 ] A very recent example of catalytic β-aryl elimination which leads to enantioselective synthesis of biaryl atropisomers is driven by release of distorted ring string. [ 24 ]
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β-Galactosidase (EC 3.2.1.23, beta-gal or β-gal ; systematic name β- D -galactoside galactohydrolase ) is a glycoside hydrolase enzyme that catalyzes hydrolysis of terminal non-reducing β- D -galactose residues in β- D -galactosides. (This enzyme digests many β-Galactosides, not just lactose. It is sometimes loosely referred to as lactase but that name is generally reserved for mammalian digestive enzymes that breaks down lactose specifically.)
β-Galactosides include carbohydrates containing galactose where the glycosidic bond lies above the galactose molecule. Substrates of different β-galactosidases include ganglioside GM1, lactosylceramides, lactose , and various glycoproteins . [ 1 ]
β-Galactosidase is an exoglycosidase which hydrolyzes the β- glycosidic bond formed between a galactose and its organic moiety. It may also cleave fucosides and arabinosides but at a much lower rate. It is an essential enzyme in the human body. Deficiencies in the protein can result in galactosialidosis or Morquio B syndrome . In E. coli , the lacZ gene is the structural gene for β-galactosidase; which is present as part of the inducible system lac operon which is activated in the presence of lactose when glucose level is low. β-Galactosidase synthesis stops when glucose levels are sufficient. [ 2 ]
β-Galactosidase has many homologues based on similar sequences. A few are evolved β-galactosidase (EBG), β-glucosidase , 6-phospho-β-galactosidase, β-mannosidase, and lactase-phlorizin hydrolase. Although they may be structurally similar, they all have different functions. [ 3 ] Beta-gal is inhibited by L -ribose and by competitive inhibitors 2-phenylethyl 1-thio-β- D -galactopyranoside (PETG), D -galactonolactone, isopropyl thio-β- D -galactoside (IPTG) , and galactose. [ 4 ]
β-Galactosidase is important for organisms as it is a key provider in the production of energy and a source of carbons through the break down of lactose to galactose and glucose. It is also important for lactose-intolerant people as it is responsible for making lactose-free milk and other dairy products. Many adult humans lack the lactase enzyme, which has the same function as β-galactosidase, so they are not able to properly digest dairy products. β-Galactose is used in such dairy products as yogurt, sour cream, and some cheeses which are treated with the enzyme to break down any lactose before human consumption. In recent years, β-galactosidase has been researched as a potential treatment for lactose intolerance through gene replacement therapy where it could be placed into the human DNA so individuals can break down lactose on their own. [ 5 ] [ 6 ]
The 1,023 amino acids of E. coli β-galactosidase were sequenced in 1983, [ 7 ] and its structure determined eleven years later in 1994. The protein is a 464- kDa homotetramer with 2,2,2-point symmetry . [ 8 ] Each unit of β-galactosidase consists of five domains ; domain 1 is a jelly-roll type β-barrel , domain 2 and 4 are fibronectin type III -like barrels, domain 5 a novel β-sandwich, while the central domain 3 is a distorted TIM-type barrel , lacking the fifth helix with a distortion in the sixth strand. [ 8 ]
The third domain contains the active site. [ 9 ] The active site is made up of elements from two subunits of the tetramer, and disassociation of the tetramer into dimers removes critical elements of the active site. The amino-terminal sequence of β-galactosidase, the α-peptide involved in α-complementation, participates in a subunit interface. Its residues 22–31 help to stabilize a four-helix bundle which forms the major part of that interface, and residue 13 and 15 also contributing to the activating interface. [ citation needed ] These structural features provide a rationale for the phenomenon of α-complementation, where the deletion of the amino-terminal segment results in the formation of an inactive dimer.
β-Galactosidase can catalyze three different reactions in organisms. In one, it can go through a process called transgalactosylation to make allolactose , creating a positive feedback loop for the production of β-galactose. Allolactose can also be cleaved to form monosaccharides. It can also hydrolyze lactose into galactose and glucose which will proceed into glycolysis . [ 3 ] The active site of β-galactosidase catalyzes the hydrolysis of its disaccharide substrate via "shallow" (nonproductive site) and "deep" (productive site) binding. Galactosides such as PETG and IPTG will bind in the shallow site when the enzyme is in "open" conformation while transition state analogs such as L -ribose and D -galactonolactone will bind in the deep site when the conformation is "closed". [ 4 ]
The enzymatic reaction consists of two chemical steps, galactosylation and degalactosylation. Galactosylation is the first chemical step in the reaction where Glu461 donates a proton to a glycosidic oxygen, resulting in galactose covalently bonding with Glu537. In the second step, degalactosylation, the covalent bond is broken when Glu461 accepts a proton, replacing the galactose with water. Two transition states occur in the deep site of the enzyme during the reaction, once after each step. When water participates in the reaction, galactose is formed, otherwise, when D -glucose acts as the acceptor in the second step, transgalactosylation occurs . [ 4 ] It has been kinetically measured that single tetramers of the protein catalyze reactions at a rate of 38,500 ± 900 reactions per minute. [ 10 ] Monovalent potassium ions (K + ) as well as divalent magnesium ions (Mg 2+ ) are required for the enzyme's optimal activity. The β-linkage of the substrate is cleaved by a terminal carboxyl group on the side chain of a glutamic acid .
In E. coli , Glu-461 was thought to be the nucleophile in the substitution reaction. [ 11 ] However, it is now known that Glu-461 is an acid catalyst. Instead, Glu-537 is the actual nucleophile, [ 12 ] binding to a galactosyl intermediate. In humans , the nucleophile of the hydrolysis reaction is Glu-268. [ 13 ] Gly794 is important for β-galactosidase activity. It is responsible for putting the enzyme in a "closed", ligand bounded, conformation or "open" conformation, acting like a "hinge" for the active site loop. The different conformations ensure that only preferential binding occurs in the active site. In the presence of a slow substrate, Gly794 activity increased as well as an increase in galactosylation and decrease in degalactosylation. [ 4 ]
The β-galactosidase assay is used frequently in genetics , molecular biology , and other life sciences . [ 14 ] An active enzyme may be detected using artificial chromogenic substrate 5-bromo-4-chloro-3-indolyl-β- D -galactopyranoside, X-gal . β-galactosidase will cleave the glycosidic bond in X-gal and form galactose and 5-bromo-4-chloro-3-hydroxyindole which dimerizes and oxidizes to 5,5'-dibromo-4,4'-dichloro-indigo, an intense blue product that is easy to identify and quantify. [ 15 ] It is used for example in blue white screen . [ 16 ] Its production may be induced by a non-hydrolyzable analog of allolactose , IPTG , which binds and releases the lac repressor from the lac operator, thereby allowing the initiation of transcription to proceed.
It is commonly used in molecular biology as a reporter marker to monitor gene expression. It also exhibits a phenomenon called α-complementation which forms the basis for the blue/white screening of recombinant clones. This enzyme can be split in two peptides, LacZ α and LacZ Ω , neither of which is active by itself but when both are present together, spontaneously reassemble into a functional enzyme. This property is exploited in many cloning vectors where the presence of the lacZα gene in a plasmid can complement in trans another mutant gene encoding the LacZΩ in specific laboratory strains of E. coli . However, when DNA fragments are inserted in the vector, the production of LacZα is disrupted, the cells therefore show no β-galactosidase activity. The presence or absence of an active β-galactosidase may be detected by X-gal , which produces a characteristic blue dye when cleaved by β-galactosidase, thereby providing an easy means of distinguishing the presence or absence of cloned product in a plasmid. In studies of leukaemia chromosomal translocations, Dobson and colleagues used a fusion protein of LacZ in mice, [ 17 ] exploiting β-galactosidase's tendency to oligomerise to suggest a potential role for oligomericity in MLL fusion protein function. [ 18 ]
A recent study conducted in 2020–2021 determined that Beta-Galactosidase activity correlates with senescence of the cells. Senescence of the cells can be interpreted as cells that do not divide, but cells that do not die. Beta-Galactosidase activity can be overexpressed, and this can lead to various diseases afflicting a wide range of body systems. These systems include the cardiovascular system, skeletal system, and many more. Detecting senescence cells can be achieved by measuring the lysosomal Beta-Galactosidase activity. [ 19 ]
A new isoform for beta-galactosidase with optimum activity at pH 6.0 (Senescence Associated beta-gal or SA-beta-gal ) [ 20 ] which is specifically expressed in senescence (the irreversible growth arrest of cells). Specific quantitative assays were even developed for its detection. [ 21 ] [ 15 ] [ 22 ] However, it is now known that this is due to an overexpression and accumulation of the lysosomal endogenous beta-galactosidase, [ 23 ] and its expression is not required for senescence. Nevertheless, it remains the most widely used biomarker for senescent and aging cells, because it is reliable and easy to detect.
Some species of bacteria, including E. coli , have additional β-galactosidase genes. A second gene, called evolved β-galactosidase ( ebgA ) gene was discovered when strains with the lacZ gene deleted (but still containing the gene for galactoside permease, lacY ), were plated on medium containing lactose (or other 3-galactosides) as sole carbon source. After a time, certain colonies began to grow. However, the EbgA protein is an ineffective lactase and does not allow growth on lactose. Two classes of single point mutations dramatically improve the activity of ebg enzyme toward lactose. [ 24 ] [ 25 ] and, as a result, the mutant enzyme is able to replace the lacZ β-galactosidase. [ 26 ] EbgA and LacZ are 50% identical on the DNA level and 33% identical on the amino acid level. [ 27 ] The active ebg enzyme is an aggregate of ebgA -gene and ebgC-gene products in a 1:1 ratio with the active form of ebg enzymes being an α 4 β4 hetero-octamer. [ 28 ]
Much of the work done on β-galactosidase is derived from E. coli. However the enzyme can be found in many plants (especially fruits), mammals, yeast, bacteria, and fungi. [ 29 ] β-galactosidase genes can differ in the length of their coding sequence and the length of proteins formed by amino acids. [ 30 ] This separates the β-galactosidases into four families: GHF-1, GHF-2, GHF-35, and GHF- 42. [ 31 ] E. Coli belongs to GHF-2, all plants belong to GHF-35, and Thermus thermophilus belongs to GHF-42. [ 31 ] [ 30 ] Various fruits can express multiple β-galactosidase genes. There are at least seven β-galactosidase genes expressed in tomato fruit development, that have amino acid similarity between 33% and 79%. [ 32 ] A study targeted at identifying fruit softening of peaches found 17 different gene expressions of β-galactosidases. [ 30 ] The only other known crystal structure of β-galactosidase is from Thermus thermophilus . [ 31 ]
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https://en.wikipedia.org/wiki/Β-Galactosidase
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β-Glucosidase ( EC 3.2.1.21 ; systematic name β- D -glucoside glucohydrolase ) is an enzyme that catalyses the following reaction: [ 2 ]
β-Glucosidase is composed of two polypeptide chains. [ 3 ] Each chain is made up of 438 amino acids and constitute a subunit of the enzyme. [ 4 ] Each of these subunits contains an active site. The active site has three potential components: the pocket, the cleft, and the tunnel. [ 5 ] The pocket structure is beneficial for recognition of monosaccharide like glucose. The cleft allows for binding of sugars to form polysaccharides. The tunnel allows for the enzyme to attach to polysaccharide and then release product while still attached to the sugar. [ 5 ]
The function of the enzyme is to perform hydrolysis of various glycosides and oligosaccharides. The most significant oligosaccharide β-glucosidase reacts with is cellulose. Cellulose is a polymer composed of β-1,4-linked glucosyl residues. β-glucosidases, cellulases ( endoglucanases ), cellobiosidases (exoglucanases ) are required by a number of organisms to consume it. These enzymes are powerful tools for degradation of plant cell walls by pathogens and other organisms consuming plant biomass. β‑glucosidases are essential for many organisms to digest a variety of nutrients. This enzyme completes double-displacement reaction, meaning that the enzyme is changed to an intermediate form when the first substrate enters the active site, it then releases the product before another substrate binds, and reverts to its original form by the end of the reaction. [ 6 ] In the case of β-glucosidase, two carboxylate residues of glucosides, cellobiose, cellotriose, cellotetraose are involved at the active site. The purpose of the reaction is to remove the residues from disaccharide cellobiose to produce glucose during the hydrolysis of biomass. [ 7 ] Depending on what the enzyme is reacting with the end product will be one or two glucose molecules.
In humans, tissues within the liver, small intestine, spleen and kidney contain a cytosolic β-glucosidase (CBG) that hydrolyses various β-d-glycosides. This human enzyme shows significant activity towards many xenobiotics commonly found in the human diet including glycosides of phytoestrogens , flavonoids , simple phenolics and cyanogens and human CBG hydrolyses a broad range of dietary glucosides, possibly playing a critical role in xenobiotic metabolism. [ 8 ]
Liposomal β-glucosidase ( glucocerebrosidas ), found in human lysosomes , plays an important role in the degradation of glycosphingolipids, breaking down glucosylceramide into ceramide and glucose. [ 9 ] Gaucher's disease is characterised by an accumulation of glucosylceramide in bodily tissues due to a lack of, or impaired activity of liposomal β-glucosidase, leading to weakened bones, liver damage, and enlargement of the spleen and impairment to its normal function. [ 10 ]
Beyond β-glucosidases expressed in human tissues, bacterial β-glucosidases are also found in human saliva and inside the intestine produced by the bacterial microbiota of the mouth and gastro-intestinal tract, with various implications to normal human health, drug and hormone metabolism, and involvement in certain diseases. [ 11 ] [ 12 ]
Bonnethead sharks are found in tropical and subtropical water living in estuaries with muddy or sandy bottoms, rich with seagrass . They were once thought of as being solely carnivores. It was known that bonnethead did consume seagrass, but it was viewed as incidental and dismissed as not helping the benefitting the shark. [ 13 ] However, recent studies of the shark's hindgut has found that it has a high activity level of β-glucosidase. [ 14 ] During the digestive process of the bonnethead shark, the acidic stomach weakens the cell walls of the seagrass and allows for β-glucosidase to enter the cell and digest the cellulose. The activity level is on par with the monkeyface eel . The monkeyface eel is a herbivore, meaning that the bonnethead is able to perform the same digestive activity as a herbivore. Therefore, the bonnethead shark is now classified as an omnivore.
The Christmas Island red crab is a species of crab located solely in the Christmas Island of the Indian Ocean. Land crabs such as these possess multiple varieties of β-glucosidase as they are terrestrial herbivores. In the case of the Christmas Island red crab β-glucosidase not only produces glucose, but also removes cellobiose. [ 15 ] This is important as cellobiose is an inhibitor for a number of enzymes including endo-β-1,4-glucanase and cellobiohydrolase. β-Glucosidase is also capable of hydrolysis on small oligomers that are produced by other enzymes without the assistance of an intermediate enzyme. [ 15 ] This in turn makes β-glucosidase a very efficient enzyme in not only the digestive tract of the Christmas Island red crab, but other crustaceans as well.
Synonyms, derivatives, and related enzymes include gentiobiase , cellobiase , emulsin , [ 16 ] elaterase , aryl-β-glucosidase , β- D -glucosidase , β-glucoside glucohydrolase , arbutinase , amygdalinase , p -nitrophenyl β-glucosidase , primeverosidase , amygdalase , linamarase , salicilinase , and β-1,6-glucosidase .
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https://en.wikipedia.org/wiki/Β-Glucosidase
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β-Hexachlorocyclohexane ( β-HCH ) is an organochloride which is one of the isomers of hexachlorocyclohexane (HCH). [ 1 ] It is a byproduct of the production of the insecticide lindane (γ-HCH). It is typically constitutes 5–14% of technical-grade lindane, [ 2 ] though it has not been produced or used in the United States since 1985. [ 1 ] As of 2009, the Stockholm Convention on Persistent Organic Pollutants classified α-hexachlorocyclohexane and β-HCH as persistent organic pollutants (POPs) , due to the chemical's ability to persist in the environment, bioaccumulative , biomagnifying , and long-range transport capacity.
This pesticide was widely used during the 1960s and 1970s, particularly on cotton plants . Although banned as a pesticide more than 30 years ago, traces of beta-HCH can still be found in water and soil. Animal studies show that organochlorine pesticides, including beta-HCH, are neurotoxic , cause oxidative stress , and damage the brain's dopaminergic system . Human studies show that exposure to beta-HCH is linked to Parkinson's and Alzheimer's disease . [ 3 ] β-HCH was present in elevated levels in some patients as recently as 2009.
It was manufactured by exhausting chlorination of benzene and for this reason was called erroneously β-BHC. This synonym still persists.
In March 2005, the Italian National Monitoring System on Chemical Residuals in Food of Animal Origin detected levels of the pesticide β-HCH that were 20 times higher than the legal limit of 0.003 mg/kg in bulk milk from a dairy farm in the Sacco River valley. β-HCH, a lindane isomer and possible human carcinogen , was subsequently found in milk from several neighboring farms. A study was therefore undertaken to evaluate the extent and risk factors for contamination. [ 4 ] [ 5 ]
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https://en.wikipedia.org/wiki/Β-Hexachlorocyclohexane
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