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The Y Chromosome Consortium ( YCC ) was [ 1 ] a collection of scientists who worked toward the understanding of human Y chromosomal phylogenetics and evolution. The consortium had the following objective: web resources that communicate information relating to the non-recombinant region of the Y-chromosome including new variants and changes in the nomenclature . [ 2 ] The consortium sponsored literature regarding updates in the phylogenetics and nomenclature . [ 3 ] [ 4 ]
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A Yagi–Uda antenna , or simply Yagi antenna , is a directional antenna consisting of two or more parallel resonant antenna elements in an end-fire array ; [ 1 ] these elements are most often metal rods (or discs) acting as half-wave dipoles . [ 2 ] Yagi–Uda antennas consist of a single driven element connected to a radio transmitter or receiver (or both) through a transmission line , and additional passive radiators with no electrical connection, usually including one so-called reflector and any number of directors . [ 2 ] [ 3 ] [ 4 ] It was invented in 1926 by Shintaro Uda of Tohoku Imperial University , Japan , [ 5 ] with a lesser role played by his boss Hidetsugu Yagi . [ 5 ] [ 6 ]
Reflector elements (usually only one is used) are slightly longer than the driven dipole and placed behind the driven element, opposite the direction of intended transmission. Directors, on the other hand, are a little shorter and placed in front of the driven element in the intended direction. [ 4 ] These parasitic elements are typically off-tuned short-circuited dipole elements, that is, instead of a break at the feedpoint (like the driven element) a solid rod is used. They receive and reradiate the radio waves from the driven element but in a different phase determined by their exact lengths. Their effect is to modify the driven element's radiation pattern . The waves from the multiple elements superpose and interfere to enhance radiation in a single direction, increasing the antenna's gain in that direction.
Also called a beam antenna [ 4 ] and parasitic array , the Yagi is widely used as a directional antenna on the HF , VHF and UHF bands. [ 3 ] [ 4 ] It has moderate to high gain of up to 20 dBi , [ 3 ] depending on the number of elements used, and a front-to-back ratio of up to 20 dB. It radiates linearly polarized [ 3 ] radio waves and is usually mounted for either horizontal or vertical polarization. It is relatively lightweight, inexpensive and simple to construct. [ 3 ] The bandwidth of a Yagi antenna, the frequency range over which it maintains its gain and feedpoint impedance , is narrow, just a few percent of the center frequency, decreasing for models with higher gain, [ 3 ] [ 4 ] making it ideal for fixed-frequency applications. The largest and best-known use is as rooftop terrestrial television antennas , [ 3 ] but it is also used for point-to-point fixed communication links, [ 2 ] radar, [ 4 ] and long-distance shortwave communication by broadcasting stations and radio amateurs . [ 2 ]
The antenna was invented by Shintaro Uda of Tohoku Imperial University , Japan , [ 5 ] in 1926, with a lesser role played by Hidetsugu Yagi . [ 6 ] [ 7 ]
However, the name Yagi has become more familiar, while the name of Uda, who applied the idea in practice or established the conception through experiment, is often omitted. This appears to have been due to the fact that Yagi based his work on Uda's pre-announcement [ 5 ] and developed the principle of the absorption phenomenon Yagi had announced earlier. [ 8 ] Yagi filed a patent application in Japan on the new idea, without Uda's name in it, and later transferred the patent to the Marconi Company in the UK. [ 9 ] Incidentally, in the US, the patent was transferred to RCA Corporation . [ 10 ]
Yagi antennas were first widely used during World War II in radar systems by Japan, Germany, the United Kingdom, and the United States. [ 7 ] After the war, they saw extensive development as home television antennas .
The Yagi–Uda antenna typically consists of a number of parallel thin rod elements, each approximately a half wave in length. Rarely, the elements are discs rather than rods. Often they are supported on a perpendicular crossbar or "boom" along their centers. [ 2 ] Usually there is a single dipole driven element consisting of two collinear rods each connected to one side of the transmission line, and a variable number of parasitic elements , reflectors on one side and optionally one or more directors on the other side. [ 2 ] [ 3 ] [ 4 ] The parasitic elements are not electrically connected to the transmission line and serve as passive radiators , reradiating the radio waves to modify the radiation pattern . [ 2 ] Typical spacings between elements vary from about 1 ⁄ 10 to 1 ⁄ 4 of a wavelength, depending on the specific design. The directors are slightly shorter than the driven element, while the reflector(s) are slightly longer. [ 4 ] The radiation pattern is unidirectional, with the main lobe along the axis perpendicular to the elements in the plane of the elements, off the end with the directors. [ 3 ]
Conveniently, the dipole parasitic elements have a node (point of zero RF voltage ) at their centre, so they can be attached to a conductive metal support at that point without need of insulation, without disturbing their electrical operation. [ 4 ] They are usually bolted or welded to the antenna's central support boom. [ 4 ] The most common form of the driven element is one fed at its centre so its two halves must be insulated where the boom supports them.
The gain increases with the number of parasitic elements used. [ 4 ] Only one reflector is normally used since the improvement of gain with additional reflectors is small, but more reflectors may be employed for other reasons such as wider bandwidth. Yagis have been built with 40 directors [ 3 ] and more. [ 11 ]
The bandwidth of an antenna is, by one definition, the width of the band of frequencies having a gain within 3 dB (one-half the power) of its maximum gain. The Yagi–Uda array in its basic form has a narrow bandwidth, 2–3 percent of the centre frequency. [ 4 ] There is a tradeoff between gain and bandwidth, with the bandwidth narrowing as more elements are used. [ 4 ] For applications that require wider bandwidths, such as terrestrial television , Yagi–Uda antennas commonly feature trigonal reflectors, and larger diameter conductors, in order to cover the relevant portions of the VHF and UHF bands. [ 12 ] Wider bandwidth can also be achieved by the use of "traps", as described below.
Yagi–Uda antennas used for amateur radio are sometimes designed to operate on multiple bands. These elaborate designs create electrical breaks along each element (both sides) at which point a parallel LC ( inductor and capacitor ) circuit is inserted. This so-called trap has the effect of truncating the element at the higher frequency band, making it approximately a half wavelength in length. At the lower frequency, the entire element (including the remaining inductance due to the trap) is close to half-wave resonance, implementing a different Yagi–Uda antenna. Using a second set of traps, a "triband" antenna can be resonant at three different bands. Given the associated costs of erecting an antenna and rotator system above a tower, the combination of antennas for three amateur bands in one unit is a practical solution. The use of traps is not without disadvantages, however, as they reduce the bandwidth of the antenna on the individual bands and reduce the antenna's electrical efficiency and subject the antenna to additional mechanical considerations (wind loading, water and insect ingress).
Consider a Yagi–Uda consisting of a reflector, driven element, and a single director as shown here. The driven element is typically a 1 ⁄ 2 λ dipole or folded dipole and is the only member of the structure that is directly excited (electrically connected to the feedline ). All the other elements are considered parasitic . That is, they reradiate power which they receive from the driven element. They also interact with each other, but this mutual coupling is neglected in the following simplified explanation, which applies to far-field conditions.
One way of thinking about the operation of such an antenna is to consider a parasitic element to be a normal dipole element of finite diameter fed at its centre, with a short circuit across its feed point. The principal part of the current in a loaded receiving antenna is distributed as in a center-driven antenna. It is proportional to the effective length of the antenna and is in phase with the incident electric field if the passive dipole is excited exactly at its resonance frequency. [ 13 ] Now we imagine the current as the source of a power wave at the (short-circuited) port of the antenna. As is well known in transmission line theory, a short circuit reflects the incident voltage 180 degrees out of phase. So one could as well model the operation of the parasitic element as the superposition of a dipole element receiving power and sending it down a transmission line to a matched load, and a transmitter sending the same amount of power up the transmission line back toward the antenna element. If the transmitted voltage wave were 180 degrees out of phase with the received wave at that point, the superposition of the two voltage waves would give zero voltage, equivalent to shorting out the dipole at the feedpoint (making it a solid element, as it is). However, the current of the backward wave is in phase with the current of the incident wave. This current drives the reradiation of the (passive) dipole element. At some distance, the reradiated electric field is described by the far-field component of the radiation field of a dipole antenna . Its phase includes the propagation delay (relating to the current) and an additional 90 degrees lagging phase offset. Thus, the reradiated field may be thought as having a 90 degrees lagging phase with respect to the incident field.
Parasitic elements involved in Yagi–Uda antennas are not exactly resonant but are somewhat shorter (or longer) than 1 ⁄ 2 λ so that the phase of the element's current is modified with respect to its excitation from the driven element. The so-called reflector element, being longer than 1 ⁄ 2 λ , has an inductive reactance , which means the phase of its current lags the phase of the open-circuit voltage that would be induced by the received field. The phase delay is thus larger than 90 degrees and, if the reflector element is made sufficiently long, the phase delay may be imagined to approach 180 degrees, so that the incident wave and the wave reemitted by the reflector interfere destructively in the forward direction (i.e. looking from the driven element towards the passive element). The director element, on the other hand, being shorter than 1 ⁄ 2 λ , has a capacitive reactance with the voltage phase lagging that of the current. [ 14 ] The phase delay is thus smaller than 90 degrees and, if the director element is made sufficiently short, the phase delay may be imagined to approach zero and the incident wave and the wave reemitted by the reflector interfere constructively in the forward direction.
Interference also occurs in the backward direction. This interference is influenced by the distance between the driven and the passive element, because the propagation delays of the incident wave (from the driven element to the passive element) and of the reradiated wave (from the passive element back to the driven element) have to be taken into account. To illustrate the effect, we assume zero and 180 degrees phase delay for the reemission of director and reflector, respectively, and assume a distance of a quarter wavelength between the driven and the passive element. Under these conditions the wave reemitted by the director interferes destructively with the wave emitted by the driven element in the backward direction (away from the passive element), and the wave reemitted by the reflector interferes constructively.
In reality, the phase delay of passive dipole elements does not reach the extreme values of zero and 180 degrees. Thus, the elements are given the correct lengths and spacings so that the radio waves radiated by the driven element and those re-radiated by the parasitic elements all arrive at the front of the antenna in-phase, so they superpose and add, increasing signal strength in the forward direction. In other words, the crest of the forward wave from the reflector element reaches the driven element just as the crest of the wave is emitted from that element. These waves reach the first director element just as the crest of the wave is emitted from that element, and so on. The waves in the reverse direction interfere destructively , cancelling out, so the signal strength radiated in the reverse direction is small. Thus the antenna radiates a unidirectional beam of radio waves from the front (director end) of the antenna.
While the above qualitative explanation is useful for understanding how parasitic elements can enhance the driven elements' radiation in one direction at the expense of the other, the assumption of an additional 90 degrees (leading or lagging) phase shift of the reemitted wave is not valid. Typically, the phase shift in the passive element is much smaller. Moreover, to increase the effect of the passive radiators, they should be placed close to the driven element, so that they can collect and reemit a significant part of the primary radiation.
A more realistic model of a Yagi–Uda array using just a driven element and a director is illustrated in the accompanying diagram. The wave generated by the driven element (green) propagates in both the forward and reverse directions (as well as other directions, not shown). The director receives that wave slightly delayed in time (amounting to a phase delay of about 45° which will be important for the reverse direction calculations later). Due to the director's shorter length, the current generated in the director is advanced in phase (by about 20°) with respect to the incident field and emits an electromagnetic field, which lags (under far-field conditions) this current by 90°. The net effect is a wave emitted by the director (blue) which is about 70° (20° - 90°) retarded with respect to that from the driven element (green), in this particular design. These waves combine to produce the net forward wave (bottom, right) with an amplitude somewhat larger than the individual waves.
In the reverse direction, on the other hand, the additional delay of the wave from the director (blue) due to the spacing between the two elements (about 45° of phase delay traversed twice) causes it to be about 160° (70° + 2 × 45°) out of phase with the wave from the driven element (green). The net effect of these two waves, when added (bottom, left), is partial cancellation. The combination of the director's position and shorter length has thus obtained a unidirectional rather than the bidirectional response of the driven (half-wave dipole) element alone.
When a passive radiator is placed close (less than a quarter wavelength distance) to the driven dipole, it interacts with the near field , in which the phase-to-distance relation is not governed by propagation delay, as would be the case in the far field. Thus, the amplitude and phase relation between the driven and the passive element cannot be understood with a model of successive collection and reemission of a wave that has become completely disconnected from the primary radiating element. Instead, the two antenna elements form a coupled system, in which, for example, the self-impedance (or radiation resistance ) of the driven element is strongly influenced by the passive element. A full analysis of such a system requires computing the mutual impedances between the dipole elements [ 15 ] which implicitly takes into account the propagation delay due to the finite spacing between elements and near-field coupling effects. We model element number j as having a feedpoint at the centre with a voltage V j and a current I j flowing into it. Just considering two such elements we can write the voltage at each feedpoint in terms of the currents using the mutual impedances Z ij :
Z 11 and Z 22 are simply the ordinary driving point impedances of a dipole, thus 73 + j43 ohms for a half-wave element (or purely resistive for one slightly shorter, as is usually desired for the driven element). Due to the differences in the elements' lengths Z 11 and Z 22 have a substantially different reactive component. Due to reciprocity we know that Z 21 = Z 12 . Now the difficult computation is in determining that mutual impedance Z 21 which requires a numerical solution. This has been computed for two exact half-wave dipole elements at various spacings in the accompanying graph.
The solution of the system then is as follows. Let the driven element be designated 1 so that V 1 and I 1 are the voltage and current supplied by the transmitter. The parasitic element is designated 2, and since it is shorted at its "feedpoint" we can write that V 2 = 0. Using the above relationships, then, we can solve for I 2 in terms of I 1 :
and so
This is the current induced in the parasitic element due to the current I 1 in the driven element. We can also solve for the voltage V 1 at the feedpoint of the driven element using the earlier equation:
where we have substituted Z 12 = Z 21 . The ratio of voltage to current at this point is the driving point impedance Z dp of the 2-element Yagi:
With only the driven element present the driving point impedance would have simply been Z 11 , but has now been modified by the presence of the parasitic element. And now knowing the phase (and amplitude) of I 2 in relation to I 1 as computed above allows us to determine the radiation pattern (gain as a function of direction) due to the currents flowing in these two elements. Solution of such an antenna with more than two elements proceeds along the same lines, setting each V j = 0 for all but the driven element, and solving for the currents in each element (and the voltage V 1 at the feedpoint). [ 16 ] Generally the mutual coupling tends to lower the impedance of the primary radiator and thus, folded dipole antennas are frequently used because of their large radiation resistance, which is reduced to the typical 50 to 75 Ohm range by coupling with the passive elements.
There are no simple formulas for designing Yagi–Uda antennas due to the complex relationships between physical parameters such as
However using the above kinds of iterative analysis, one can calculate the performance of a given a set of parameters and adjust them to optimize the gain (perhaps subject to some constraints). Since with an n element Yagi–Uda antenna, there are 2 n − 1 parameters to adjust (the element lengths and relative spacings), this iterative analysis method is not straightforward. The mutual impedances plotted above only apply to λ /2 length elements, so these might need to be recomputed to get good accuracy.
The current distribution along a real antenna element is only approximately given by the usual assumption of a classical standing wave, requiring a solution of Hallen's integral equation taking into account the other conductors. Such a complete exact analysis, considering all of the interactions mentioned, is rather overwhelming, and approximations are inevitable on the path to finding a usable antenna. Consequently, these antennas are often empirical designs using an element of trial and error , often starting with an existing design modified according to one's hunch. The result might be checked by direct measurement or by computer simulation.
A well-known reference employed in the latter approach is a report published by the United States National Bureau of Standards (NBS) (now the National Institute of Standards and Technology (NIST)) that provides six basic designs derived from measurements conducted at 400 MHz and procedures for adapting these designs to other frequencies. [ 17 ] These designs, and those derived from them, are sometimes referred to as "NBS yagis."
By adjusting the distance between the adjacent directors it is possible to reduce the back lobe of the radiation pattern.
The Yagi–Uda antenna was invented in 1926 by Shintaro Uda of Tohoku Imperial University , [ 5 ] Sendai , Japan , with the guidance of Hidetsugu Yagi , also of Tohoku Imperial University. [ 6 ] Yagi and Uda published their first report on the wave projector directional antenna. Yagi demonstrated a proof of concept , but the engineering problems proved to be more onerous than conventional systems. [ 18 ]
Yagi published the first English-language reference on the antenna in a 1928 survey article on short wave research in Japan and it came to be associated with his name. However, Yagi who provided the conception which was originally vague expression to Uda, always acknowledged Uda's principal contribution towards the design which will currently be recognized as the reduction to practice , and if the novelty is not considered, the proper name for the antenna is, as above, the Yagi–Uda antenna (or array).
The Yagi was first widely used during World War II for airborne radar sets, because of its simplicity and directionality. [ 18 ] [ 19 ] Despite its being invented in Japan, many Japanese radar engineers were unaware of the design until late in the war, partly due to rivalry between the Army and Navy. The Japanese military authorities first became aware of this technology after the Battle of Singapore when they captured the notes of a British radar technician that mentioned "yagi antenna". Japanese intelligence officers did not even recognise that Yagi was a Japanese name in this context. When questioned, the technician said it was an antenna named after a Japanese professor. [ 20 ] [ 21 ] [ N 1 ]
A horizontally polarized array can be seen on many different types of WWII aircraft, particularly those types engaged in maritime patrol, or night fighters, commonly installed on the lower surface of each wing. Two types that often carried such equipment are the Grumman TBF Avenger carrier-based US Navy aircraft and the Consolidated PBY Catalina long range patrol seaplane. Vertically polarized arrays can be seen on the cheeks of the P-61 and on the nose cones of many WWII aircraft, notably the Lichtenstein radar -equipped examples of the German Junkers Ju 88 R-1 fighter-bomber , and the British Bristol Beaufighter night-fighter and Short Sunderland flying-boat. Indeed, the latter had so many antenna elements arranged on its back – in addition to its formidable turreted defensive armament in the nose and tail, and atop the hull – it was nicknamed the fliegendes Stachelschwein , or "Flying Porcupine" by German airmen. [ 22 ] The experimental Morgenstern German AI VHF-band radar antenna of 1943–44 used a "double-Yagi" structure from its 90° angled pairs of Yagi antennas formed from six discrete dipole elements, making it possible to fit the array within a conical, rubber-covered plywood radome on an aircraft's nose, with the extreme tips of the Morgenstern's antenna elements protruding from the radome's surface, with an NJG 4 Ju 88 G-6 of the wing's staff flight using it late in the war for its Lichtenstein SN-2 AI radar. [ 23 ]
After World War II, the advent of television broadcasting motivated extensive adaptation of the Yagi–Uda design for rooftop television reception in the VHF band (and later for UHF television) and also as an FM radio antenna in fringe areas. A major drawback was the Yagi's inherently narrow bandwidth, eventually solved by the adoption of the wideband log-periodic dipole array (LPDA). Yet the Yagi's higher gain compared to the LPDA makes it the best for fringe reception , and complicated Yagi designs and combination with other antenna technologies have been developed to permit its operation over the broad television bands .
The Yagi–Uda antenna was named an IEEE Milestone in 1995. [ 10 ]
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Yair Nathan Minsky (born in 1962) is an Israeli - American mathematician whose research concerns three-dimensional topology , differential geometry , group theory and holomorphic dynamics . He is a professor at Yale University . [ 1 ] He is known for having proved Thurston 's ending lamination conjecture and as a student of curve complex geometry .
Minsky obtained his Ph.D. from Princeton University in 1989 under the supervision of William Paul Thurston , with the thesis Harmonic Maps and Hyperbolic Geometry . [ 2 ]
His Ph.D. students include Jason Behrstock , Erica Klarreich , Hossein Namazi and Kasra Rafi . [ 2 ]
He received a Sloan Fellowship in 1995. [ 3 ] [ 4 ]
He was a speaker at the ICM (Madrid) 2006.
He was named to the 2021 class of fellows of the American Mathematical Society "for contributions to hyperbolic 3-manifolds, low-dimensional topology, geometric group theory and Teichmuller theory". [ 5 ] He was elected to the American Academy of Arts and Sciences in 2023. [ 6 ]
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Yajnavalkya's 95-year cycle is a method of harmonizing the lunar and solar calendars. It was proposed by the ancient Indian sage Yajnavalkya , who is believed to have lived around the 9th - 8th century BCE. [ citation needed ] He was described as the greatest Brahmajnyani by all the sages at the philosophical function organised by king Janaka . [ 1 ] This cycle of reconciliation is also known as Yajnavalkya Cycle . [ citation needed ]
Yajnavalkya was Indian astronomer who studied about the motion of Sun and mentioned these theories in his work Shatapatha Brahmana . [ 2 ] He invented a method of reconciliating the lunar calendar and the solar calendar . [ citation needed ] He described the 95-year cycle to synchronize the motions of the sun and the moon . [ 3 ] [ 4 ] It is mentioned as 95 year “Agnichayana” in the 6th Kānda of Shatapatha Brahmana . [ 4 ]
The lunar calendar is based on the cycle of the Moon and consists of 12 months of 29.5 days each. This means that the lunar calendar is about 11 days shorter than the solar calendar, which is based on the Earth's orbit around the Sun. [ citation needed ]
The Yajnavalkya 95-year cycle corrects this difference by adding an extra month (Adhik Maasa) to the lunar calendar every 32.5 years. This means that there will be 71 lunar years and 70 solar years in a 95-year cycle. [ 5 ]
There is a logic behind this cycle that if the year is counted as 360 Tithis , then this leads to exactly 35 intercalary months (with a residual small error) in 95 years. [ citation needed ]
Yajnavalkya 95-years cycle consisted of five sub cycles of 19 years. The sub cycle of 19 years is called as Metonic Cycle in the modern times. The cycle of 19 years had been derived from the cycle of 95 years. [ 4 ]
As of this edit , this article uses content from "Yajnavalkya's 95 Years Cycle of Synchronisation" , which is licensed in a way that permits reuse under the Creative Commons Attribution-ShareAlike 3.0 Unported License , but not under the GFDL . All relevant terms must be followed.
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Yak Bak was a line of handheld electronic voice recorder toys developed by Ralph Osterhout at Team Machina for Yes! Gear (a.k.a. Yes! Entertainment) in the mid-to-late 1990s. Several versions of the toy were developed, including the Yak Bak, Yak Bak 2, Yak Bak 2k, Yak Bak WarpR, Yak Wakky, Yak Bak SFX, and the Yak Bakwards. Some of these models also came in pen form as part of the "Power Penz" series. The Yak Bak was intended to be a compact, more affordable competitor to the Talkboy introduced by Tiger Electronics in 1992. [ 1 ]
In December 1994, YES! launched its YES! Gear product line with the introduction of Yak Bak, [ 2 ] a simple device consisting of a single speaker and two buttons. One button was marked "Say" and the other, "Play." By holding down the "Say" button, a person could record six seconds of sound , during which a light would shine to indicate that the Yak Bak was recording. Afterwards, the "Play" button would enable the person to hear what was just recorded. This was the basic premise for all subsequent models of the toy, each one adding a slight variance to the original. The television commercial for it showed a boy sitting in a living room recliner while his sister came by and started fussing at him. Then he kept playing his "Is not!" quote using the Yak Bak at his sister, while his sister kept saying "Is too!".
Following encouraging sales of its 1995 line of miniature recorders, YES! introduced four new Yak Bak products for 1996 and lowered the products' prices to a more affordable range. [ 3 ] The original Yak Bak would be re-released in 1997 as Yak Bak Classic and again in 2000 as Yak Bak 2k.
This was identical to the original, but added a locking mechanism which prevented the user from accidentally hitting the "Say" button and thereby erasing the stored recording. This locking mechanism became a staple of some of the future models. The most notable function of this version is the WarpR, which changes the pitch of the recording. Later models of this series had incorporated the WarpR design and function. It came in many colors. One of the toys of the year during the Sixth Annual CBS This Morning Toy Test and the Seventh Annual Sesame Street Parents' Toy Test.
To cash in on the hysteria regarding the turn of the millennium , the Yak Bak 2k was released. [ 4 ]
The Yak Bak WarpR provided users with the ability to alter the recording via a pitch dial that would speed up or slow down the sound, thereby making the voice sound higher or deeper. This model was more popular than previous ones as the novelty of voice recording became more enticing once users could "warp" their voices. This "warping" option also became a staple of all future models. As was the case with the Yak Bak 2, the Yak Bak WarpR also contained a lockout mechanism which disabled the Say button.
The Yak Guard was a motion-triggered device capable of guarding rooms and belongings, or to "pull gags on friends and family members," as suggested in company advertisements. A personally recorded "alarm" could be placed on door knobs or drawers, for example, alerting the owner of trespass.
The Yak Time was a combination of the original Yak Bak and a wrist watch .
The Yak Wakky allowed users to change the pitch and speed of the recording by way of light sensitive sensors on the body of the device. When activated by a switch on the right hand side of the toy, the sensors would, depending on how much light shone on them, increase the pitch of the recording. By using the palm of his/her hand, the user could alter the pitch of the recordings dramatically.
The Yak Bak SFX provided the same function as the Yak Bak WarpR but with additional buttons that added six sound effects before or after the recording.
Retail priced at $19.99, [ 5 ] the Yak Bakwards was essentially the Yak Bak WarpR with an additional "Yalp" button. This button literally reversed the "Play" function, causing the recording to be reversed.
Yak Bak Ball is in the shape of a small football. The user holds down the button and record; toss it and after catching it, squeezes or hit it and hear the message. The grips are designed to be easy to catch. It was made to get children active outdoors.
The Yak Maniak allowed the user to alter the pitch of the recording as was the case with past models. It also included five sound effects, not too dissimilar to the previous Yak Baks, but the most notable difference between this model and others in the series were its three extra voice effects.
The Yak Maniak enabled the user to cause their recordings to stutter, echo or warble. These effects were activated by a trigger on the left hand side of the toy.
A three-position dial was turned either all the way to the right for stutter, to the central position for echo, or to the left for warble. During playback, the trigger had to be held down to activate the stutter, held down for a certain length of the recording then released to enable the echo or held down to activate the warble effect. Hitting play mid-way through the echo effect could delete the remainder of the recording.
The Yak Bak Power Pens combined working ink pens with the Yak Bak toy. Marketed for children in school, the Power Penz came in both the Yak Write SFX and the Yak Bak 2 models. It was made to compete against the Talkboy FX Plus by Tiger Electronics .
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Yakovlevian torque (also known as occipital bending ( OB ) [ 2 ] or counterclockwise brain torque [ 3 ] ) is the tendency of the right side of the human brain to be warped slightly forward relative to the left and the left side of the human brain to be warped slightly backward relative to the right. This is responsible for certain asymmetries , such as how the lateral sulcus of the human brain is often longer and less curved on the left side of the brain relative to the right. Stated in another way, Yakovlevian torque can be defined by the existence of right-frontal and left-occipital petalias , which are protrusions of the surface of one hemisphere relative to the other. It is named for Paul Ivan Yakovlev (1894–1983), a Russian-American neuroanatomist from Harvard Medical School . [ 1 ] [ 4 ]
A 2012 literature review showed that morphometry studies had consistently found that handedness-related effects corresponded to the extent of the Yakovlevian torque; [ 5 ] increased torque, as measured by increased size of the right-frontal petalia and the left-occipital petalia, tends to be more common in right-handed individuals. [ 6 ] Individuals with mixed-handedness or left-handedness show reduced levels of Yakovlevian torque. [ 7 ]
Reduced right-frontal and left-occipital petalias and reversed petalia asymmetries (that is, left-frontal and right occipital petalias) have been associated with developmental stuttering in both adults and pre-adolescent boys. [ 3 ] This may be tied to the lateral sulcus housing Broca's area , [ 5 ] which plays a significant role in production of language .
Increased size of the left-occipital petalia, resulting from an abnormally high degree of Yakovlevian torque has been associated with bipolar disorder . [ 2 ] Maller et al. 2015 found that increased asymmetry of the occipital lobe, or occipital bending, was four times more prevalent in subjects with bipolar disorder than in healthy controls. [ 2 ] This applied both to patients with bipolar disorder type I and type II .
There is some evidence suggesting that the Yakovlevian torque is related to the aurofacial asymmetry and the contralateral organization of the brain and is due to a not quite complete twist of the anterior part of the head . [ 8 ] According to the Axial Twist theory , each side of the brain represents the opposite body side due to a developmental twist along the body axis. [ 9 ]
Yakovlevian torque is found in modern humans and fossil hominids , appearing reliably as early as Homo erectus . [ 6 ] The patterning of petalias in extinct human ancestors is examined via endocasts , wherein a cast is made of the cranial vault : the asymmetries of human ancestors can be measured from these casts because petalias leave impressions inside the cranial vault. [ 6 ]
Some authors have reported that similar petalia patterns are found in a number of primates including Old World monkeys , New World monkeys and Great apes , [ 10 ] but others report different protrusions; [ 11 ] [ 12 ] these differences seem to be tied to which techniques are used to measure the petalia, so it is not well-understood if all primates demonstrate Yakovlevian torque. [ 6 ]
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Yalo (formerly Yalochat ) is an artificial intelligence platform specializing in emerging markets. Its headquerters were formerly in San Francisco with offices in Mexico City, Mumbai, Shanghai, Bogotá, and São Paulo. [ 1 ] It subsequently relocated to Mexico City [ when? ] .
Yalo enables companies to interact with their customers in conversational commerce on messaging apps including WhatsApp , Facebook Messenger , and WeChat . [ 1 ]
Customers include Walmart , Nike , Volkswagen , Aeroméxico , appliance and electronics retailer Elektra , Mexico's largest department store, Coppel , and Mexico's largest theme resort Xcaret . [ 1 ]
The company was founded in Mexico by CEO Javier Mata and was formerly based in San Francisco, but subsequently moved to Mexico. As at 2021 its board of directors includes Mark Fernandes and Rashmi Gopinath. [ 2 ]
In February 2018, the company announced the opening of its office in Shanghai, China, in alliance with venture capitalist Michael Kuan's company Strategic Impact Group.
In May 2021, Yalo raised $50 million in new funding led by B Capital , for a total of $75 million in total funding. [ 3 ]
Yalochat introduced a variety of services on Facebook Messenger in 2016, shortly after Facebook launched its chatbot platform. [ 4 ] [ 5 ]
In April 2017, it announced that its chatbot with Aeroméxico had added an artificial intelligence component to the Facebook Messenger bot. [ 6 ] [ 7 ] [ 8 ]
In October 2017, Aeroméxico announced that together with Yalochat it would launch services on the new enterprise platform of WhatsApp , the world's most popular messaging platform, and that it would be the first airline in The Americas to do so. Services available via WhatsApp include shopping for and purchasing flights, making changes, checking in and obtaining a boarding pass, and tracking a flight. It includes both an artificial intelligence -powered chatbot, and chat with the airline's human agents. [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ]
In February 2018 Yalochat announced the opening of its office in Shanghai, China and that it had begun offering services on WeChat , China's most popular messaging app. [ 1 ]
In an interview, Yalochat CEO Javier Mata said that the company was planning to offer services on Line messenger, popular in Japan, Korea and Thailand. [ 15 ]
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https://en.wikipedia.org/wiki/Yalo_(company)
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The Yamabe problem refers to a conjecture in the mathematical field of differential geometry , which was resolved in the 1980s. It is a statement about the scalar curvature of Riemannian manifolds :
Let ( M , g ) be a closed smooth Riemannian manifold. Then there exists a positive and smooth function f on M such that the Riemannian metric fg has constant scalar curvature.
By computing a formula for how the scalar curvature of fg relates to that of g , this statement can be rephrased in the following form:
Let ( M , g ) be a closed smooth Riemannian manifold. Then there exists a positive and smooth function φ on M , and a number c , such that
Here n denotes the dimension of M , R g denotes the scalar curvature of g , and ∆ g denotes the Laplace-Beltrami operator of g .
The mathematician Hidehiko Yamabe , in the paper Yamabe (1960) , gave the above statements as theorems and provided a proof; however, Trudinger (1968) discovered an error in his proof. The problem of understanding whether the above statements are true or false became known as the Yamabe problem. The combined work of Yamabe, Trudinger, Thierry Aubin , and Richard Schoen provided an affirmative resolution to the problem in 1984.
It is now regarded as a classic problem in geometric analysis , with the proof requiring new methods in the fields of differential geometry and partial differential equations . A decisive point in Schoen's ultimate resolution of the problem was an application of the positive energy theorem of general relativity , which is a purely differential-geometric mathematical theorem first proved (in a provisional setting) in 1979 by Schoen and Shing-Tung Yau .
There has been more recent work due to Simon Brendle , Marcus Khuri, Fernando Codá Marques , and Schoen, dealing with the collection of all positive and smooth functions f such that, for a given Riemannian manifold ( M , g ) , the metric fg has constant scalar curvature. Additionally, the Yamabe problem as posed in similar settings, such as for complete noncompact Riemannian manifolds, is not yet fully understood.
Here, we refer to a "solution of the Yamabe problem" on a Riemannian manifold ( M , g ¯ ) {\displaystyle (M,{\overline {g}})} as a Riemannian metric g on M for which there is a positive smooth function φ : M → R , {\displaystyle \varphi :M\to \mathbb {R} ,} with g = φ − 2 g ¯ . {\displaystyle g=\varphi ^{-2}{\overline {g}}.}
Let ( M , g ¯ ) {\displaystyle (M,{\overline {g}})} be a smooth Riemannian manifold. Consider a positive smooth function φ : M → R , {\displaystyle \varphi :M\to \mathbb {R} ,} so that g = φ − 2 g ¯ {\displaystyle g=\varphi ^{-2}{\overline {g}}} is an arbitrary element of the smooth conformal class of g ¯ . {\displaystyle {\overline {g}}.} A standard computation shows
Taking the g -inner product with φ ( Ric − 1 n R g ) {\displaystyle \textstyle \varphi (\operatorname {Ric} -{\frac {1}{n}}Rg)} results in
If g ¯ {\displaystyle {\overline {g}}} is assumed to be Einstein, then the left-hand side vanishes. If M {\displaystyle M} is assumed to be closed, then one can do an integration by parts , recalling the Bianchi identity div Ric = 1 2 ∇ R , {\displaystyle \textstyle \operatorname {div} \operatorname {Ric} ={\frac {1}{2}}\nabla R,} to see
If g has constant scalar curvature, then the right-hand side vanishes. The consequent vanishing of the left-hand side proves the following fact, due to Obata (1971):
Every solution to the Yamabe problem on a closed Einstein manifold is Einstein.
Obata then went on to prove that, except in the case of the standard sphere with its usual constant-sectional-curvature metric, the only constant-scalar-curvature metrics in the conformal class of an Einstein metric (on a closed manifold ) are constant multiples of the given metric. The proof proceeds by showing that the gradient of the conformal factor is actually a conformal Killing field. If the conformal factor is not constant, following flow lines of this gradient field, starting at a minimum of the conformal factor, then allows one to show that the manifold is conformally related to the cylinder S n − 1 × R {\displaystyle S^{n-1}\times \mathbb {R} } , and hence has vanishing Weyl curvature.
A closely related question is the so-called "non-compact Yamabe problem", which asks: Is it true that on every smooth complete Riemannian manifold ( M , g ) which is not compact, there exists a metric that is conformal to g , has constant scalar curvature and is also complete? The answer is no, due to counterexamples given by Jin (1988) . Various additional criteria under which a solution to the Yamabe problem for a non-compact manifold can be shown to exist are known (for example Aviles & McOwen (1988) ); however, obtaining a full understanding of when the problem can be solved in the non-compact case remains a topic of research.
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https://en.wikipedia.org/wiki/Yamabe_problem
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The Yamada–Watanabe theorem is a result from probability theory saying that for a large class of stochastic differential equations a weak solution with pathwise uniqueness implies a strong solution and uniqueness in distribution . In its original form, the theorem was stated for n {\displaystyle n} -dimensional Itô equations and was proven by Toshio Yamada and Shinzo Watanabe in 1971. [ 1 ] Since then, many generalizations appeared particularly one for general semimartingales by Jean Jacod from 1980. [ 2 ]
Jean Jacod generalized the result to SDEs of the form
where ( Z t ) t ≥ 0 {\displaystyle (Z_{t})_{t\geq 0}} is a semimartingale and the coefficient u {\displaystyle u} can depend on the path of Z {\displaystyle Z} . [ 2 ]
Further generalisations were done by Hans-Jürgen Engelbert (1991 [ 3 ] ) and Thomas G. Kurtz (2007 [ 4 ] ). For SDEs in Banach spaces there is a result from Martin Ondrejat (2004 [ 5 ] ), one by Michael Röckner , Byron Schmuland and Xicheng Zhang (2008 [ 6 ] ) and one by Stefan Tappe (2013 [ 7 ] ).
The converse of the theorem is also true and called the dual Yamada–Watanabe theorem . The first version of this theorem was proven by Engelbert (1991 [ 3 ] ) and a more general version by Alexander Cherny (2002 [ 8 ] ).
Let n , r ∈ N {\displaystyle n,r\in \mathbb {N} } and C ( R + , R n ) {\displaystyle C(\mathbb {R} _{+},\mathbb {R} ^{n})} be the space of continuous functions. Consider the n {\displaystyle n} -dimensional Itô equation
where
We say uniqueness in distribution (or weak uniqueness ), if for two arbitrary solutions ( X ( 1 ) , W ( 1 ) ) {\displaystyle (X^{(1)},W^{(1)})} and ( X ( 2 ) , W ( 2 ) ) {\displaystyle (X^{(2)},W^{(2)})} defined on (possibly different) filtered probability spaces ( Ω 1 , F 1 , F 1 , P 1 ) {\displaystyle (\Omega _{1},{\mathcal {F}}_{1},\mathbf {F} _{1},P_{1})} and ( Ω 2 , F 2 , F 2 , P 2 ) {\displaystyle (\Omega _{2},{\mathcal {F}}_{2},\mathbf {F} _{2},P_{2})} , we have for their distributions P X ( 1 ) = P X ( 2 ) {\displaystyle P_{X^{(1)}}=P_{X^{(2)}}} , where P X ( 1 ) := Law ( X t 1 , t ≥ 0 ) {\displaystyle P_{X^{(1)}}:=\operatorname {Law} (X_{t}^{1},t\geq 0)} .
We say pathwise uniqueness (or strong uniqueness ) if any two solutions ( X ( 1 ) , W ) {\displaystyle (X^{(1)},W)} and ( X ( 2 ) , W ) {\displaystyle (X^{(2)},W)} , defined on the same filtered probability spaces ( Ω , F , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbf {F} ,P)} with the same F {\displaystyle \mathbf {F} } -Brownian motion, are indistinguishable processes, i.e. we have P {\displaystyle P} -almost surely that { X t ( 1 ) = X t ( 2 ) , t ≥ 0 } {\displaystyle \{X_{t}^{(1)}=X_{t}^{(2)},t\geq 0\}}
Assume the described setting above is valid, then the theorem is:
Jacod's result improved the statement with the additional statement that
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The Yamaguchi esterification is the chemical reaction of an aliphatic carboxylic acid and 2,4,6-trichlorobenzoyl chloride ( TCBC, Yamaguchi reagent ) to form a mixed anhydride which, upon reaction with an alcohol in the presence of stoichiometric amount of DMAP , produces the desired ester . It was first reported by Masaru Yamaguchi et al. in 1979. [ 1 ] [ 2 ]
It is especially useful in the synthesis of macro- lactones and highly functionalised esters.
The aliphatic carboxylate adds to the carbonyl carbon of Yamaguchi reagent, forming a mixed anhydride, which is then attacked by DMAP regioselectively at the less hindered carbon, producing acyl-substituted DMAP. This highly electrophilic agent is then attacked by the alcohol to form the product ester.
The in situ formation of the symmetric [ clarification needed ] aliphatic anhydride is proposed to explain the regioselectivity observed in the reactions of aliphatic acids, based on the fact that aliphatic carboxylates are more nucleophilic, and aliphatic anhydrides are more electrophilic towards DMAP and alcohol than their counterparts. [ clarification needed ]
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https://en.wikipedia.org/wiki/Yamaguchi_esterification
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The Yamaha M7CL is a digital mixer that was introduced by Yamaha Pro Audio in 2005. [ 1 ] Two models with onboard analog input exist: the M7CL-32 and M7CL-48. These models have 40 (32 microphone and 4 stereo line)- and 56 (48 microphone and 4 stereo line)-input channels respectively, counting mono channels. Mixes, masters, groups, DCAs and individual channels can then be routed to an output via any number of the board's 16 configurable output XLR ports. The eight faders of the master control section can control multiple functions by way of "layers" in the same manner as the Yamaha PM5D . The board features Yamaha's "Selected Channel" technology, and Centralogic, unique to the M7CL. It can be augmented with more inputs or outputs via expansion cards, and can be fitted with third-party cards such as ones made by Aviom (A-Net), AuviTran ( EtherSound ), Audinate ( Dante networking), AudioService ( MADI ), Dan Dugan ( automixer ), Riedel Communications (RockNet), Waves Audio (SoundGrid interface, DSP plugins ), and Optocore (optical network). In 2010, the M7CL-48ES joined the line-up with built-in EtherSound for digital networking using EtherSound stage boxes. [ 1 ]
In 2006, the M7CL was recognized at the TEC Awards ceremony for best sound reinforcement console technology. [ 2 ] In 2011, a wireless app to control the M7CL with an iPad was nominated but did not win the TEC Award for best wireless technology. [ 3 ]
The selected channel interface allows for quick and easy access to every parameter of any channel on the board quickly and easily. Selecting a channel will pull up all available parameters into the Centralogic section for adjustment.
Centralogic is a technology new and unique to the M7CL. It employs a touch screen, rotary encoders, and faders that dynamically map to whatever function or parameter is selected for adjustment. The control software has only 3 main screens, Overview, Selected Channel, and Effects Rack views. There are no additional layers to navigate through. It is possible to control the mixer from the Centralogic section only and is designed to keep the user at the center section.
The M7CL features a virtual signal processing "rack" which allows for the use of many different effects or Graphic EQs. Effects are from Yamaha's library of digital effects developed for other digital mixers. Of note is Graphic EQ operation, where the individual bands of EQ can be mapped to faders for precision control.
The M7CL is becoming popular in both broadcasting and live sound reinforcement applications. Broadcast companies like the console primarily for parameter recall, which is useful in daily news broadcasts. Live sound companies often use the mixer for stage monitoring purposes, but have also used it for Front of House environments.
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https://en.wikipedia.org/wiki/Yamaha_M7CL
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The Yamaneko Group of Comet Observers (YGCO) is a famous group of astronomical observers based in Japan. Founded by K. Ichikawa in 1980, the members have obtained approximately 12,300 astronomic and 6,300 photometric observations. [ 1 ] This group maintains the YGCO Chiyoda Station , also based in Japan.
This article about an organization or institute connected with astronomy is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Yamaneko_Group_of_Comet_Observers
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In probability theory , Yan's theorem is a separation and existence result. It is of particular interest in financial mathematics where one uses it to prove the Kreps-Yan theorem .
The theorem was published by Jia-An Yan . [ 1 ] It was proven for the L 1 space and later generalized by Jean-Pascal Ansel to the case 1 ≤ p < + ∞ {\displaystyle 1\leq p<+\infty } . [ 2 ]
Notation:
Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} be a probability space , 1 ≤ p < + ∞ {\displaystyle 1\leq p<+\infty } and B + {\displaystyle B_{+}} be the space of non-negative and bounded random variables . Further let K ⊆ L p ( Ω , F , P ) {\displaystyle K\subseteq L^{p}(\Omega ,{\mathcal {F}},P)} be a convex subset and 0 ∈ K {\displaystyle 0\in K} .
Then the following three conditions are equivalent:
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YaneuraOu ( やねうら王 , lit. ' King Yaneura ' ) ) is a free and open source shogi engine . Being one of the first shogi engines to implement an efficiently updatable neural network , it won the 29th annual World Computer Shogi Championship in 2019. [ 3 ] It supports the Universal Shogi Interface communication protocol [ 1 ] (a dialect of the Universal Chess Interface used by most chess engines ), which gives it compatibility with most shogi programs . Lishogi , an open source online shogi server, primarily uses YaneuraOu for its analysis and AI opponent features. [ 4 ]
This software article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/YaneuraOu
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Private spaceflight companies include non-governmental or privately-owned entities focused on developing and/or offering equipment and services geared towards spaceflight , both robotic and human . This list includes both inactive and active entities.
LEO : Low Earth orbit GTO : Geostationary transfer orbit HCO : Heliocentric orbit VTOL : Vertical take-off and landing SSTO : Single-stage-to-orbit TSTO : Two-stage-to-orbit SSTSO : Single-stage-to- sub-orbit
(1/3)
(Uncrewed: April 29, 2015)
[ 268 ]
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In physics , the Yang–Baxter equation (or star–triangle relation ) is a consistency equation which was first introduced in the field of statistical mechanics . It depends on the idea that in some scattering situations, particles may preserve their momentum while changing their quantum internal states. It states that a matrix R {\displaystyle R} , acting on two out of three objects, satisfies
where R ˇ {\displaystyle {\check {R}}} is R {\displaystyle R} followed by a swap of the two objects. In one-dimensional quantum systems, R {\displaystyle R} is the scattering matrix and if it satisfies the Yang–Baxter equation then the system is integrable . The Yang–Baxter equation also shows up when discussing knot theory and the braid groups where R {\displaystyle R} corresponds to swapping two strands. Since one can swap three strands in two different ways, the Yang–Baxter equation enforces that both paths are the same.
According to Michio Jimbo , [ 1 ] the Yang–Baxter equation (YBE) manifested itself in the works of J. B. McGuire [ 2 ] in 1964 and C. N. Yang [ 3 ] in 1967. They considered a quantum mechanical many-body problem on a line having c ∑ i < j δ ( x i − x j ) {\displaystyle c\sum _{i<j}\delta (x_{i}-x_{j})} as the potential. Using the Bethe ansatz techniques, they found that the scattering matrix factorized to that of the two-body problem, and determined it exactly. Here YBE arises as the consistency condition for the factorization.
In statistical mechanics , the source of YBE probably goes back to Onsager's star-triangle relation, briefly mentioned in the introduction to his solution of the Ising model [ 4 ] in 1944. The hunt for solvable lattice models has been actively pursued since then, culminating in Rodney Baxter 's solution of the eight vertex model [ 5 ] in 1972.
Another line of development was the theory of factorized S -matrix in two dimensional quantum field theory. [ 6 ] Alexander B. Zamolodchikov pointed out [ 7 ] that the algebraic mechanics working here is the same as that in the Baxter's and others' works.
The YBE has also manifested itself in a study of Young operators in the group algebra C [ S n ] {\displaystyle \mathbb {C} [S_{n}]} of the symmetric group in the work of A. A. Jucys [ 8 ] in 1966.
Let A {\displaystyle A} be a unital associative algebra . In its most general form, the parameter-dependent Yang–Baxter equation is an equation for R ( u , u ′ ) {\displaystyle R(u,u')} , a parameter-dependent element of the tensor product A ⊗ A {\displaystyle A\otimes A} (here, u {\displaystyle u} and u ′ {\displaystyle u'} are the parameters, which usually range over the real numbers ℝ in the case of an additive parameter, or over positive real numbers ℝ + in the case of a multiplicative parameter).
Let R i j ( u , u ′ ) = ϕ i j ( R ( u , u ′ ) ) {\displaystyle R_{ij}(u,u')=\phi _{ij}(R(u,u'))} for 1 ≤ i < j ≤ 3 {\displaystyle 1\leq i<j\leq 3} , with algebra homomorphisms ϕ i j : A ⊗ A → A ⊗ A ⊗ A {\displaystyle \phi _{ij}:A\otimes A\to A\otimes A\otimes A} determined by
The general form of the Yang–Baxter equation is
for all values of u 1 {\displaystyle u_{1}} , u 2 {\displaystyle u_{2}} and u 3 {\displaystyle u_{3}} .
Let A {\displaystyle A} be a unital associative algebra. The parameter-independent Yang–Baxter equation is an equation for R {\displaystyle R} , an invertible element of the tensor product A ⊗ A {\displaystyle A\otimes A} . The Yang–Baxter equation is
where R 12 = ϕ 12 ( R ) {\displaystyle R_{12}=\phi _{12}(R)} , R 13 = ϕ 13 ( R ) {\displaystyle R_{13}=\phi _{13}(R)} , and R 23 = ϕ 23 ( R ) {\displaystyle R_{23}=\phi _{23}(R)} .
Often the unital associative algebra is the algebra of endomorphisms of a vector space V {\displaystyle V} over a field k {\displaystyle k} , that is, A = End ( V ) {\displaystyle A={\text{End}}(V)} . With respect to a basis { e i } {\displaystyle \{e_{i}\}} of V {\displaystyle V} , the components of the matrices R ∈ End ( V ) ⊗ End ( V ) ≅ End ( V ⊗ V ) {\displaystyle R\in {\text{End}}(V)\otimes {\text{End}}(V)\cong {\text{End}}(V\otimes V)} are written R i j k l {\displaystyle R_{ij}^{kl}} , which is the component associated to the map e i ⊗ e j ↦ e k ⊗ e l {\displaystyle e_{i}\otimes e_{j}\mapsto e_{k}\otimes e_{l}} . Omitting parameter dependence, the component of the Yang–Baxter equation associated to the map e a ⊗ e b ⊗ e c ↦ e d ⊗ e e ⊗ e f {\displaystyle e_{a}\otimes e_{b}\otimes e_{c}\mapsto e_{d}\otimes e_{e}\otimes e_{f}} reads
Let V {\displaystyle V} be a module of A {\displaystyle A} , and P i j = ϕ i j ( P ) {\displaystyle P_{ij}=\phi _{ij}(P)} . Let P : V ⊗ V → V ⊗ V {\displaystyle P:V\otimes V\to V\otimes V} be the linear map satisfying P ( x ⊗ y ) = y ⊗ x {\displaystyle P(x\otimes y)=y\otimes x} for all x , y ∈ V {\displaystyle x,y\in V} . The Yang–Baxter equation then has the following alternate form in terms of R ˇ ( u , u ′ ) = P ∘ R ( u , u ′ ) {\displaystyle {\check {R}}(u,u')=P\circ R(u,u')} on V ⊗ V {\displaystyle V\otimes V} .
Alternatively, we can express it in the same notation as above, defining R ˇ i j ( u , u ′ ) = ϕ i j ( R ˇ ( u , u ′ ) ) {\displaystyle {\check {R}}_{ij}(u,u')=\phi _{ij}({\check {R}}(u,u'))} , in which case the alternate form is
In the parameter-independent special case where R ˇ {\displaystyle {\check {R}}} does not depend on parameters, the equation reduces to
and (if R {\displaystyle R} is invertible) a representation of the braid group , B n {\displaystyle B_{n}} , can be constructed on V ⊗ n {\displaystyle V^{\otimes n}} by σ i = 1 ⊗ i − 1 ⊗ R ˇ ⊗ 1 ⊗ n − i − 1 {\displaystyle \sigma _{i}=1^{\otimes i-1}\otimes {\check {R}}\otimes 1^{\otimes n-i-1}} for i = 1 , … , n − 1 {\displaystyle i=1,\dots ,n-1} . This representation can be used to determine quasi-invariants of braids , knots and links .
Solutions to the Yang–Baxter equation are often constrained by requiring the R {\displaystyle R} matrix to be invariant under the action of a Lie group G {\displaystyle G} . For example, in the case G = G L ( V ) {\displaystyle G=GL(V)} and R ( u , u ′ ) ∈ End ( V ⊗ V ) {\displaystyle R(u,u')\in {\text{End}}(V\otimes V)} , the only G {\displaystyle G} -invariant maps in End ( V ⊗ V ) {\displaystyle {\text{End}}(V\otimes V)} are the identity I {\displaystyle I} and the permutation map P {\displaystyle P} . The general form of the R {\displaystyle R} -matrix is then R ( u , u ′ ) = A ( u , u ′ ) I + B ( u , u ′ ) P {\displaystyle R(u,u')=A(u,u')I+B(u,u')P} for scalar functions A , B {\displaystyle A,B} .
The Yang–Baxter equation is homogeneous in parameter dependence in the sense that if one defines R ′ ( u i , u j ) = f ( u i , u j ) R ( u i , u j ) {\displaystyle R'(u_{i},u_{j})=f(u_{i},u_{j})R(u_{i},u_{j})} , where f {\displaystyle f} is a scalar function, then R ′ {\displaystyle R'} also satisfies the Yang–Baxter equation.
The argument space itself may have symmetry. For example translation invariance enforces that the dependence on the arguments ( u , u ′ ) {\displaystyle (u,u')} must be dependent only on the translation-invariant difference u − u ′ {\displaystyle u-u'} , while scale invariance enforces that R {\displaystyle R} is a function of the scale-invariant ratio u / u ′ {\displaystyle u/u'} .
A common ansatz for computing solutions is the difference property, R ( u , u ′ ) = R ( u − u ′ ) {\displaystyle R(u,u')=R(u-u')} , where R depends only on a single (additive) parameter. Equivalently, taking logarithms, we may choose the parametrization R ( u , u ′ ) = R ( u / u ′ ) {\displaystyle R(u,u')=R(u/u')} , in which case R is said to depend on a multiplicative parameter. In those cases, we may reduce the YBE to two free parameters in a form that facilitates computations:
for all values of u {\displaystyle u} and v {\displaystyle v} . For a multiplicative parameter, the Yang–Baxter equation is
for all values of u {\displaystyle u} and v {\displaystyle v} .
The braided forms read as:
In some cases, the determinant of R ( u ) {\displaystyle R(u)} can vanish at specific values of the spectral parameter u = u 0 {\displaystyle u=u_{0}} . Some R {\displaystyle R} matrices turn into a one dimensional projector at u = u 0 {\displaystyle u=u_{0}} . In this case a quantum determinant can be defined [ clarification needed ] .
Then the parametrized Yang-Baxter equation (in braided form) with the multiplicative parameter is satisfied:
There are broadly speaking three classes of solutions: rational, trigonometric and elliptic. These are related to quantum groups known as the Yangian , affine quantum groups and elliptic algebras respectively.
Set-theoretic solutions were studied by Drinfeld . [ 9 ] In this case, there is an R {\displaystyle R} -matrix invariant basis X {\displaystyle X} for the vector space V {\displaystyle V} in the sense that the R {\displaystyle R} -matrix maps the induced basis of V ⊗ V {\displaystyle V\otimes V} to itself. This then induces a map r : X × X → X × X {\displaystyle r:X\times X\rightarrow X\times X} given by restriction of the R {\displaystyle R} -matrix to the basis. The set-theoretic Yang–Baxter equation is then defined using the 'twisted' alternate form above, asserting ( i d × r ) ( r × i d ) ( i d × r ) = ( r × i d ) ( i d × r ) ( r × i d ) {\displaystyle (id\times r)(r\times id)(id\times r)=(r\times id)(id\times r)(r\times id)} as maps on X × X × X {\displaystyle X\times X\times X} . The equation can then be considered purely as an equation in the category of sets .
Solutions to the classical YBE were studied and to some extent classified by Belavin and Drinfeld. [ 10 ] Given a 'classical r {\displaystyle r} -matrix' r : V ⊗ V → V ⊗ V {\displaystyle r:V\otimes V\rightarrow V\otimes V} , which may also depend on a pair of arguments ( u , v ) {\displaystyle (u,v)} , the classical YBE is (suppressing parameters) [ r 12 , r 13 ] + [ r 12 , r 23 ] + [ r 13 , r 23 ] = 0. {\displaystyle [r_{12},r_{13}]+[r_{12},r_{23}]+[r_{13},r_{23}]=0.} This is quadratic in the r {\displaystyle r} -matrix, unlike the usual quantum YBE which is cubic in R {\displaystyle R} .
This equation emerges from so called quasi-classical solutions to the quantum YBE, in which the R {\displaystyle R} -matrix admits an asymptotic expansion in terms of an expansion parameter ℏ , {\displaystyle \hbar ,} R ℏ = I + ℏ r + O ( ℏ 2 ) . {\displaystyle R_{\hbar }=I+\hbar r+{\mathcal {O}}(\hbar ^{2}).} The classical YBE then comes from reading off the ℏ 2 {\displaystyle \hbar ^{2}} coefficient of the quantum YBE (and the equation trivially holds at orders ℏ 0 , ℏ {\displaystyle \hbar ^{0},\hbar } ).
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https://en.wikipedia.org/wiki/Yang–Baxter_equation
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Yang–Baxter operators are invertible linear endomorphisms with applications in theoretical physics and topology . They are named after theoretical physicists Yang Chen-Ning and Rodney Baxter . These operators are particularly notable for providing solutions to the quantum Yang–Baxter equation , which originated in statistical mechanics , and for their use in constructing invariants of knots , links, and three-dimensional manifolds . [ 1 ] [ 2 ] [ 3 ]
In the category of left modules over a commutative ring k {\displaystyle k} , Yang–Baxter operators are k {\displaystyle k} -linear mappings R : V ⊗ k V → V ⊗ k V {\displaystyle R:V\otimes _{k}V\rightarrow V\otimes _{k}V} . The operator R {\displaystyle R} satisfies the quantum Yang-Baxter equation if
R 12 R 13 R 23 = R 23 R 13 R 12 {\displaystyle R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12}}
where
R 12 = R ⊗ k 1 {\displaystyle R_{12}=R\otimes _{k}1} , R 23 = 1 ⊗ k R {\displaystyle R_{23}=1\otimes _{k}R} , R 13 = ( 1 ⊗ k τ V , V ) ( R ⊗ k 1 ) ( 1 ⊗ k τ V , V ) {\displaystyle R_{13}=(1\otimes _{k}\tau _{V,V})(R\otimes _{k}1)(1\otimes _{k}\tau _{V,V})}
The τ U , V {\displaystyle \tau _{U,V}} represents the "twist" mapping defined for k {\displaystyle k} -modules U {\displaystyle U} and V {\displaystyle V} by τ U , V ( u ⊗ v ) = v ⊗ u {\displaystyle \tau _{U,V}(u\otimes v)=v\otimes u} for all u ∈ U {\displaystyle u\in U} and v ∈ V {\displaystyle v\in V} .
An important relationship exists between the quantum Yang-Baxter equation and the braid equation . If R {\displaystyle R} satisfies the quantum Yang-Baxter equation, then B = τ V , V R {\displaystyle B=\tau _{V,V}R} satisfies B 12 B 23 B 12 = B 23 B 12 B 23 {\displaystyle B_{12}B_{23}B_{12}=B_{23}B_{12}B_{23}} . [ 4 ]
Yang–Baxter operators have applications in statistical mechanics and topology . [ 5 ] [ 6 ] [ 7 ]
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The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics , and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute , which has offered a prize of $1,000,000 USD for its solution.
The problem is phrased as follows: [ 1 ]
In this statement, a quantum Yang–Mills theory is a non-abelian quantum field theory similar to that underlying the Standard Model of particle physics ; R 4 {\displaystyle \mathbb {R} ^{4}} is Euclidean 4-space ; the mass gap Δ is the mass of the least massive particle predicted by the theory.
Therefore, the winner must prove that:
For example, in the case of G=SU(3)—the strong nuclear interaction—the winner must prove that glueballs have a lower mass bound, and thus cannot be arbitrarily light.
The general problem of determining the presence of a mass gap (a special case of a spectral gap ) in a system is known to be undecidable , meaning no computer algorithm exists that can find the answer programmatically. [ 4 ] [ 5 ]
[...] one does not yet have a mathematically complete example of a quantum gauge theory in four-dimensional space-time , nor even a precise definition of quantum gauge theory in four dimensions. Will this change in the 21st century? We hope so!
The problem requires the construction of a QFT satisfying the Wightman axioms and showing the existence of a mass gap. Both of these topics are described in sections below.
The Millennium problem requires the proposed Yang–Mills theory to satisfy the Wightman axioms or similarly stringent axioms. [ 1 ] There are four axioms:
Quantum mechanics is described according to John von Neumann ; in particular, the pure states are given by the rays, i.e. the one-dimensional subspaces, of some separable complex Hilbert space .
The Wightman axioms require that the Poincaré group acts unitarily on the Hilbert space. In other words, a change of reference frame (position, velocity, rotation) must be a unitary operator , or a surjective operator which preserves the inner product, which can be viewed as an isomorphism on a Hilbert space. Among the implications of this is the fact that the probability of an event must not change with a change of reference frame, as the probability of an event occurring is its inner product with itself. This requirement can also be stated in other words to mean that the Wightman axioms have position dependent operators called quantum fields which form covariant representations of the Poincaré group .
The group of space-time translations is commutative , and so the operators can be simultaneously diagonalised. The generators of these groups give us four self-adjoint operators , P j , j = 0 , 1 , 2 , 3 {\displaystyle P_{j},j=0,1,2,3} , which transform under the homogeneous group as a four-vector , called the energy-momentum four-vector.
The second part of the zeroth axiom of Wightman is that the representation U ( a , A ) fulfills the spectral condition—that the simultaneous spectrum of energy-momentum is contained in the forward cone:
The third part of the axiom is that there is a unique state, represented by a ray in the Hilbert space, which is invariant under the action of the Poincaré group. It is called a vacuum.
For each test function f , there exists a set of operators A 1 ( f ) , … , A n ( f ) {\displaystyle A_{1}(f),\ldots ,A_{n}(f)} which, together with their adjoints, are defined on a dense subset of the Hilbert state space, containing the vacuum. The fields A are operator-valued tempered distributions . The Hilbert state space is spanned by the field polynomials acting on the vacuum (cyclicity condition).
The fields are covariant under the action of Poincaré group , and they transform according to some representation S of the Lorentz group , or SL(2, C ) if the spin is not integer:
If the supports of two fields are space-like separated, then the fields either commute or anticommute.
Cyclicity of a vacuum, and uniqueness of a vacuum are sometimes considered separately. Also, there is the property of asymptotic completeness—that the Hilbert state space is spanned by the asymptotic spaces H i n {\displaystyle H^{in}} and H o u t {\displaystyle H^{out}} , appearing in the collision S matrix . The other important property of field theory is the mass gap which is not required by the axioms—that the energy-momentum spectrum has a gap between zero and some positive number.
In quantum field theory , the mass gap is the difference in energy between the vacuum and the next lowest energy state . The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle.
For a given real field ϕ ( x ) {\displaystyle \phi (x)} , we can say that the theory has a mass gap if the two-point function has the property
with Δ 0 > 0 {\displaystyle \Delta _{0}>0} being the lowest energy value in the spectrum of the Hamiltonian and thus the mass gap. This quantity, easy to generalize to other fields, is what is generally measured in lattice computations. It was proved in this way that Yang–Mills theory develops a mass gap on a lattice. [ 6 ] [ 7 ]
Most known and nontrivial (i.e. interacting) quantum field theories in 4 dimensions are effective field theories with a cutoff scale. Since the beta function is positive for most models, it appears that most such models have a Landau pole as it is not at all clear whether or not they have nontrivial UV fixed points . This means that if such a QFT is well-defined at all scales, as it has to be to satisfy the axioms of axiomatic quantum field theory , it would have to be trivial (i.e. a free field theory ).
Quantum Yang–Mills theory with a non-abelian gauge group and no quarks is an exception, because asymptotic freedom characterizes this theory, meaning that it has a trivial UV fixed point . Hence it is the simplest nontrivial constructive QFT in 4 dimensions. ( QCD is a more complicated theory because it involves quarks .)
At the level of rigor of theoretical physics , it has been well established that the quantum Yang–Mills theory for a non-abelian Lie group exhibits a property known as confinement ; though proper mathematical physics has more demanding requirements on a proof. A consequence of this property is that above the confinement scale , the color charges are connected by chromodynamic flux tubes leading to a linear potential between the charges. Hence isolated color charge and isolated gluons cannot exist. In the absence of confinement, we would expect to see massless gluons, but since they are confined, all we would see are color-neutral bound states of gluons, called glueballs . If glueballs exist, they are massive, which is why a mass gap is expected.
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Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special unitary group SU( n ) , or more generally any compact Lie group . A Yang–Mills theory seeks to describe the behavior of elementary particles using these non-abelian Lie groups and is at the core of the unification of the electromagnetic force and weak forces (i.e. U(1) × SU(2) ) as well as quantum chromodynamics , the theory of the strong force (based on SU(3) ). Thus it forms the basis of the understanding of the Standard Model of particle physics.
All known fundamental interactions can be described in terms of gauge theories, but working this out took decades. [ 2 ] Hermann Weyl 's pioneering work on this project started in 1915 when his colleague Emmy Noether proved that every conserved physical quantity has a matching symmetry, and culminated in 1928 when he published his book applying the geometrical theory of symmetry ( group theory ) to quantum mechanics. [ 3 ] : 194 Weyl named the relevant symmetry in Noether's theorem the "gauge symmetry", by analogy to distance standardization in railroad gauges .
Erwin Schrödinger in 1922, three years before working on his equation, connected Weyl's group concept to electron charge. Schrödinger showed that the group U ( 1 ) {\displaystyle U(1)} produced a phase shift e i θ {\displaystyle e^{i\theta }} in electromagnetic fields that matched the conservation of electric charge. [ 3 ] : 198 As the theory of quantum electrodynamics developed in the 1930's and 1940's the U ( 1 ) {\displaystyle U(1)} group transformations played a central role. Many physicists thought there must be an analog for the dynamics of nucleons. Chen Ning Yang in particular was obsessed with this possibility.
Yang's core idea was to look for a conserved quantity in nuclear physics comparable to electric charge and use it to develop a corresponding gauge theory comparable to electrodynamics. He settled on conservation of isospin , a quantum number that distinguishes a neutron from a proton, but he made no progress on a theory. [ 3 ] : 200 Taking a break from Princeton in the summer of 1953, Yang met a collaborator who could help: Robert Mills . As Mills himself describes:
"During the academic year 1953–1954, Yang was a visitor to Brookhaven National Laboratory ... I was at Brookhaven also ... and was assigned to the same office as Yang. Yang, who has demonstrated on a number of occasions his generosity to physicists beginning their careers, told me about his idea of generalizing gauge invariance and we discussed it at some length ... I was able to contribute something to the discussions, especially with regard to the quantization procedures, and to a small degree in working out the formalism; however, the key ideas were Yang's." [ 4 ]
In the summer 1953, Yang and Mills extended the concept of gauge theory for abelian groups , e.g. quantum electrodynamics , to non-abelian groups, selecting the group SU(2) to provide an explanation for isospin conservation in collisions involving the strong interactions. Yang's presentation of the work at Princeton in February 1954 was challenged by Pauli, asking about the mass in the field developed with the gauge invariance idea. [ 3 ] : 202 Pauli knew that this might be an issue as he had worked on applying gauge invariance but chose not to publish it, viewing the massless excitations of the theory to be "unphysical 'shadow particles'". [ 2 ] : 13 Yang and Mills published in October 1954; near the end of the paper, they admit:
We next come to the question of the mass of the b {\displaystyle b} quantum, to which we do not have a satisfactory answer. [ 5 ]
This problem of unphysical massless excitation blocked further progress. [ 3 ]
The idea was set aside until 1960, when the concept of particles acquiring mass through symmetry breaking in massless theories was put forward, initially by Jeffrey Goldstone , Yoichiro Nambu , and Giovanni Jona-Lasinio . This prompted a significant restart of Yang–Mills theory studies that proved successful in the formulation of both electroweak unification and quantum chromodynamics (QCD). The electroweak interaction is described by the gauge group SU(2) × U(1) , while QCD is an SU(3) Yang–Mills theory. The massless gauge bosons of the electroweak SU(2) × U(1) mix after spontaneous symmetry breaking to produce the three massive bosons of the weak interaction ( W + , W − , and Z 0 ) as well as the still-massless photon field. The dynamics of the photon field and its interactions with matter are, in turn, governed by the U(1) gauge theory of quantum electrodynamics. The Standard Model combines the strong interaction with the unified electroweak interaction (unifying the weak and electromagnetic interaction ) through the symmetry group SU(3) × SU(2) × U(1) . In the current epoch the strong interaction is not unified with the electroweak interaction, but from the observed running of the coupling constants it is believed [ citation needed ] they all converge to a single value at very high energies.
Phenomenology at lower energies in quantum chromodynamics is not completely understood due to the difficulties of managing such a theory with a strong coupling. This may be the reason why confinement has not been theoretically proven, though it is a consistent experimental observation. This shows why QCD confinement at low energy is a mathematical problem of great relevance, and why the Yang–Mills existence and mass gap problem is a Millennium Prize Problem .
In 1953, in a private correspondence, Wolfgang Pauli formulated a six-dimensional theory of Einstein's field equations of general relativity , extending the five-dimensional theory of Kaluza, Klein , Fock , and others to a higher-dimensional internal space. [ 6 ] However, there is no evidence that Pauli developed the Lagrangian of a gauge field or the quantization of it. Because Pauli found that his theory "leads to some rather unphysical shadow particles", he refrained from publishing his results formally. [ 6 ] Although Pauli did not publish his six-dimensional theory, he gave two seminar lectures about it in Zürich in November 1953. [ 6 ]
In January 1954 Ronald Shaw , a graduate student at the University of Cambridge also developed a non-Abelian gauge theory for nuclear forces. [ 7 ] However, the theory needed massless particles in order to maintain gauge invariance . Since no such massless particles were known at the time, Shaw and his supervisor Abdus Salam chose not to publish their work. [ 7 ] Shortly after Yang and Mills published their paper in October 1954, Salam encouraged Shaw to publish his work to mark his contribution. Shaw declined, and instead it only forms a chapter of his PhD thesis published in 1956. [ 8 ] [ 9 ]
Yang–Mills theories are special examples of gauge theories with a non-abelian symmetry group given by the Lagrangian
with the generators T a {\displaystyle \ T^{a}\ } of the Lie algebra , indexed by a , corresponding to the F -quantities (the curvature or field-strength form) satisfying
Here, the f abc are structure constants of the Lie algebra (totally antisymmetric if the generators of the Lie algebra are normalised such that tr ( T a T b ) {\displaystyle \ \operatorname {tr} (T^{a}\ T^{b})\ } is proportional to δ a b {\displaystyle \ \delta ^{ab}\ } ), the covariant derivative is defined as
I is the identity matrix (matching the size of the generators), A μ a {\displaystyle \ A_{\mu }^{a}\ } is the vector potential, and g is the coupling constant . In four dimensions, the coupling constant g is a pure number and for a SU( n ) group one has a , b , c = 1 … n 2 − 1 . {\displaystyle \ a,b,c=1\ldots n^{2}-1~.}
The relation
can be derived by the commutator
The field has the property of being self-interacting and the equations of motion that one obtains are said to be semilinear, as nonlinearities are both with and without derivatives. This means that one can manage this theory only by perturbation theory with small nonlinearities. [ citation needed ]
Note that the transition between "upper" ("contravariant") and "lower" ("covariant") vector or tensor components is trivial for a indices (e.g. f a b c = f a b c {\displaystyle \ f^{abc}=f_{abc}\ } ), whereas for μ and ν it is nontrivial, corresponding e.g. to the usual Lorentz signature, η μ ν = d i a g ( + − − − ) . {\displaystyle \ \eta _{\mu \nu }={\rm {diag}}(+---)~.}
From the given Lagrangian one can derive the equations of motion given by
Putting F μ ν = T a F μ ν a , {\displaystyle \ F_{\mu \nu }=T^{a}F_{\mu \nu }^{a}\ ,} these can be rewritten as
A Bianchi identity holds
which is equivalent to the Jacobi identity
since [ D μ , F ν κ a ] = D μ F ν κ a . {\displaystyle \ \left[D_{\mu },F_{\nu \kappa }^{a}\right]=D_{\mu }\ F_{\nu \kappa }^{a}~.} Define the dual strength tensor F ~ μ ν = 1 2 ε μ ν ρ σ F ρ σ , {\displaystyle \ {\tilde {F}}^{\mu \nu }={\tfrac {1}{2}}\varepsilon ^{\mu \nu \rho \sigma }F_{\rho \sigma }\ ,} then the Bianchi identity can be rewritten as
A source J μ a {\displaystyle \ J_{\mu }^{a}\ } enters into the equations of motion as
Note that the currents must properly change under gauge group transformations.
We give here some comments about the physical dimensions of the coupling. In D dimensions, the field scales as [ A ] = [ L ( 2 − D 2 ) ] {\displaystyle \ \left[A\right]=\left[L^{\left({\tfrac {2-D}{2}}\right)}\right]\ } and so the coupling must scale as [ g 2 ] = [ L ( D − 4 ) ] . {\displaystyle \ \left[g^{2}\right]=\left[L^{\left(D-4\right)}\right]~.} This implies that Yang–Mills theory is not renormalizable for dimensions greater than four. Furthermore, for D = 4 , the coupling is dimensionless and both the field and the square of the coupling have the same dimensions of the field and the coupling of a massless quartic scalar field theory . So, these theories share the scale invariance at the classical level.
A method of quantizing the Yang–Mills theory is by functional methods, i.e. path integrals . One introduces a generating functional for n -point functions as
but this integral has no meaning as it is because the potential vector can be arbitrarily chosen due to the gauge freedom . This problem was already known for quantum electrodynamics but here becomes more severe due to non-abelian properties of the gauge group. A way out has been given by Ludvig Faddeev and Victor Popov with the introduction of a ghost field (see Faddeev–Popov ghost ) that has the property of being unphysical since, although it agrees with Fermi–Dirac statistics , it is a complex scalar field, which violates the spin–statistics theorem . So, we can write the generating functional as
being
for the field,
for the gauge fixing and
for the ghost. This is the expression commonly used to derive Feynman's rules (see Feynman diagram ). Here we have c a for the ghost field while ξ fixes the gauge's choice for the quantization. Feynman's rules obtained from this functional are the following
These rules for Feynman's diagrams can be obtained when the generating functional given above is rewritten as
with
being the generating functional of the free theory. Expanding in g and computing the functional derivatives , we are able to obtain all the n -point functions with perturbation theory. Using LSZ reduction formula we get from the n -point functions the corresponding process amplitudes, cross sections and decay rates . The theory is renormalizable and corrections are finite at any order of perturbation theory.
For quantum electrodynamics the ghost field decouples because the gauge group is abelian. This can be seen from the coupling between the gauge field and the ghost field that is c ¯ a f a b c ∂ μ A b μ c c . {\displaystyle \ {\bar {c}}^{a}\ f^{abc}\ \partial _{\mu }A^{b\mu }\ c^{c}~.} For the abelian case, all the structure constants f a b c {\displaystyle \ f^{abc}\ } are zero and so there is no coupling. In the non-abelian case, the ghost field appears as a useful way to rewrite the quantum field theory without physical consequences on the observables of the theory such as cross sections or decay rates.
One of the most important results obtained for Yang–Mills theory is asymptotic freedom . This result can be obtained by assuming that the coupling constant g is small (so small nonlinearities), as for high energies, and applying perturbation theory . The relevance of this result is due to the fact that a Yang–Mills theory that describes strong interaction and asymptotic freedom permits proper treatment of experimental results coming from deep inelastic scattering .
To obtain the behavior of the Yang–Mills theory at high energies, and so to prove asymptotic freedom, one applies perturbation theory assuming a small coupling. This is verified a posteriori in the ultraviolet limit . In the opposite limit, the infrared limit, the situation is the opposite, as the coupling is too large for perturbation theory to be reliable. Most of the difficulties that research meets is just managing the theory at low energies. That is the interesting case, being inherent to the description of hadronic matter and, more generally, to all the observed bound states of gluons and quarks and their confinement (see hadrons ). The most used method to study the theory in this limit is to try to solve it on computers (see lattice gauge theory ). In this case, large computational resources are needed to be sure the correct limit of infinite volume (smaller lattice spacing) is obtained. This is the limit the results must be compared with. Smaller spacing and larger coupling are not independent of each other, and larger computational resources are needed for each. As of today, the situation appears somewhat satisfactory for the hadronic spectrum and the computation of the gluon and ghost propagators, but the glueball and hybrids spectra are yet a questioned matter in view of the experimental observation of such exotic states. Indeed, the σ resonance [ 10 ] [ 11 ] is not seen in any of such lattice computations and contrasting interpretations have been put forward. This is a hotly debated issue.
Yang–Mills theories met with general acceptance in the physics community after Gerard 't Hooft , in 1972, worked out their renormalization, relying on a formulation of the problem worked out by his advisor Martinus Veltman . [ 12 ] Renormalizability is obtained even if the gauge bosons described by this theory are massive, as in the electroweak theory, provided the mass is only an "acquired" one, generated by the Higgs mechanism .
The mathematics of the Yang–Mills theory is a very active field of research, yielding e.g. invariants of differentiable structures on four-dimensional manifolds via work of Simon Donaldson . Furthermore, the field of Yang–Mills theories was included in the Clay Mathematics Institute 's list of " Millennium Prize Problems ". Here the prize-problem consists, especially, in a proof of the conjecture that the lowest excitations of a pure Yang–Mills theory (i.e. without matter fields) have a finite mass-gap with regard to the vacuum state. Another open problem, connected with this conjecture, is a proof of the confinement property in the presence of additional fermions.
In physics the survey of Yang–Mills theories does not usually start from perturbation analysis or analytical methods, but more recently from systematic application of numerical methods to lattice gauge theories .
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A Yankee dryer is a pressure vessel used in the production of machine glazed (MG) and tissue paper . On the Yankee dryer, the paper goes from approximately 42–45% dryness to just over 89% dryness. In industry, MG cylinders or Yankee dryers are primarily used to remove excess moisture from pulp that is about to be converted into paper. The Yankee cylinder can be equipped with a doctor blade and sprayed with adhesives to make the paper stick. Creping is done by the Yankee's doctor blade scraping the dry paper off the cylinder surface thereby crêping the paper. The crinkle (crêping) is controlled by the strength of the adhesive, the geometry of the doctor blade, the speed difference between the yankee and final section of the paper machine, and the paper pulp's characteristics. [ 1 ]
Whereas in other paper productions a series of drying cylinders is used, in tissue production only one cylinder (the yankee cylinder) dries the paper. This is due to the necessity of creping and made possible by the low grammage (gsm = gram per square meter) of the paper sheet for tissue products, which is in the range of 14-45 gsm. For the production of the higher gsm in this range, some machines are nevertheless provided with some (4-10) drying cylinders after the yankee. In this case one speaks of "wet creping", as the creping of the paper done on the yankee is not made on the fully dried paper and the drying is completed after the yankee cylinder.
Yankee cylinders are traditionally made of cast iron and have diameters up to 6 m, therefore much higher than conventional drying cylinders. The width is a bit larger than that of the paper: typical for tissue are paper machine widths 1,74m 2,32m and 2,70m and their multiples (usually nowadays the doubles of these values are typical). Therefore, yankees are very heavy (~100t) and difficult to cast.
Since a couple of decades the production of yankees made of steel is gaining market and new machines are practically always nowadays equipped with a steel yankee, which is much lighter, easier to produce and to transport.
Due to the abrasive effect of the creping blade the surface of the yankee becomes irregular and rough. Therefore, periodically (with very varying frequency: from every 6 months to some years) cast iron yankees have to be ground or polished. This decreases the thickness of the shell, and since the yankee is a pressure vessel, also the maximum pressure which can be used for paper production. A way to avoid this declassing of pressure is to make a metallisation, i.e. to spray onto the surface a special Chrom-Nickel alloy, similar to a high alloyed stainless steel, which is then ground with the foreseen crown of the shell surface, leaving a coated thickness of ca. 0,7–1 mm. The metallised surface is then much more resistant to the abrasion and only a very mild polishing may be necessary ca. every 2 to 4 years.
The thermal conductivity of the metallisation is a bit less than that of the original material, so that cast iron cylinders are metallised after some grindings of the shell, in order to gain, through [ clarification needed ] thickness decrease, some conductivity which is then again lost with the metallisation. Steel yankees are instead always metallised since the beginning.
The big dimension generates a problem with the elimination of the condensate forming inside the cylinders, therefore all yankees use a system with blow through steam which than it is re-compressed by help of a thermocompressor (ejector). In the inner surface of the yankee circular grooves are present which accommodate small pipes (s.c. "straw pipes" or "straws") through which the mixture of steam and condensate is sucked by means of a pressure difference between the yankee and the tank collecting the condensate (separator). The straws are combined in racks and these go to typically 6 collectors which take the condensate-steam mixture towards the center of the cylinder from which then it is taken out into usual piping and brought to the separator. Here the condensate and the blow-through steam separate at a lower pressure than that inside the yankee.
In order not to spoil the blow-through steam, a thermocompressor uses motive steam (at a pressure ca. the double of that in the yankee) in order to increase again the pressure of the blow through steam to the value of the yankee.
Yankee safety is an important issue and TAPPI has a committee (Yankee Dryer Safety Committee) dedicated to it.
The sharper problems are present with cast iron yankee, being this material much more brittle than steel, making the yankee very sensitive to temperature differences. For example, a yankee which is receiving steam while it is not rotating may be damaged by the temperature difference of the bulk to the bottom of the cylinder where the condensate is present. Particular attention shall be taken in case of fire, as direct jets of cold water on the surface of the hot yankee may damage it. Some cases of exploded yankees due to these and other reasons are unfortunately present in the history of tissue production.
The usage of a chemical coating on the surface of the yankee is nowadays the rule. This is constituted by a mixture of usually 2 or more constituents:
The coating is sprayed together with water in the space between the creping blade and the press through a spray bar with nozzles. Only the narrow space between this spray bar and the press is the one in which the water coming with the coating shall be evaporated and the polymer has to cure. For this reason, pre-cured polymers are increasingly used for the base coating.
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Yantrarāja is the Sanskrit name for the ancient astronomical instrument called astrolabe . It is also the title of a Sanskrit treatise on the construction and working of the astrolabe composed by a Jain astronomer Mahendra Sūri in around 1370 CE. [ 1 ]
The ideas leading to the construction of the astrolabe originated in the Hellenistic world. The earliest crude forms of the instrument are believed to have been constructed during second century BCE in Greece. The first person to give a description of the astrolabe was Theon of Alexandria (c.335 - 405 CE). Astrolabes were further developed in the medieval Islamic world where it was widely used as an aid for navigation and as an aid for finding the direction of Mecca . The earliest Arabic treatise on astrolabes was composed sometime around 815 CE. [ 2 ]
It is not known when exactly the astrolabe reached India. al-Biruni (973 – after 1050) has claimed in his Indica that he has composed a manual on astrolabes in Sanskrit. Probably he brought the astrolabe with him to Multan and taught its working principles to the Hindu astronomers there. With the establishment of the Delhi Sultanate , many Muslim scholars migrated to Delhi and they might have popularized the instrument among the astronomers there. It was Fīrūz Shah Tughlaq , the third Sultan of the Tughlaq dynasty who ruled over the Delhi Sultanate during 1351 - 1388, who took an active interest in promoting the study and use of the astrolabe in India. This was the most important contribution of Fīrūz Shah Tughlaq in the field of astronomy. Mahendra Sūri, the astronomer who wrote the first ever Sanskrit manual on astrolabes was a court astronomer of Fīrūz Shah Tughlaq.
The earliest extant astrolabe constructed in India, now in a private collection in Brussels, is dated 1 February 1601. It was manufactured in Ahmedabad during the reign of Jahangir (1569 – 1627), the fourth Mughal emperor .
With the support and patronage of Firuz Shah Tughlaq, Mahendra Sūri, a Jain astronomer composed the first ever Sanskrit manual on astrolabes. It was Sūri who coined the Sanskrit name "Yantrarāja" ("the king of astronomical instruments") for the astrolabe and he also titled his manual on astrolabes as Yantrarāja . Sūri composed the manual in 1370 CE. Mahendra Sūri's student Malayendu Sūri composed a commentary on Yantrarāja in 1382. Two other commentaries on Yantrarāja are known, one by Gopirāja written in 1540 and other by Yajñeśvara in 1842.
The Yantrarāja manual in 128 verses is divided into five chapters. The first chapter Gaṇitādhyāya discusses the theory behind the astrolabe. The second chapter Yantraghatanādhyāya is devoted to descriptions of the various components of the astrolabe. The third chapter Yantraracanādhyāya describes the details of the construction of the astrolabe. The fourth chapter Yantrasodhanādhyāya discusses method for ascertaining whether the astrolabe has been properly constructed. It is in the fifth and final chapter Yantravicāraṇādhyāya one can see descriptions on how to use the instrument for observational and computational purposes. This chapter also dwells on the different types of astronomical and trigonometrical problems that can be solved using the astrolabe.
While Mahendra Sūri's manual is in 128 verses and contains no data in the form of tables, Malayendu Sūri's commentary is interspersed with neatly prepared tables.
Over the centuries since the publication of Mahendra Sūri's Yantrarāja in 1370, several other Sanskrit manuals on the astrolabe have been composed. These include the following: [ 2 ]
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The Yarkovsky effect is a force acting on a rotating body in space caused by the anisotropic emission of thermal photons , which carry momentum . It is usually considered in relation to meteoroids or small asteroids (about 10 cm to 10 km in diameter), as its influence is most significant for these bodies.
The effect was discovered by the Polish-Russian [ 1 ] civil engineer Ivan Osipovich Yarkovsky (1844–1902), who worked in Russia on scientific problems in his spare time. Writing in a pamphlet around the year 1900, Yarkovsky noted that the daily heating of a rotating object in space would cause it to experience a force that, while tiny, could lead to large long-term effects in the orbits of small bodies, especially meteoroids and small asteroids . Yarkovsky's insight would have been forgotten had it not been for the Estonian astronomer Ernst J. Öpik (1893–1985), who read Yarkovsky's pamphlet sometime around 1909. Decades later, Öpik, recalling the pamphlet from memory, discussed the possible importance of the Yarkovsky effect on movement of meteoroids about the Solar System . [ 2 ]
The Yarkovsky effect is a consequence of the fact that change in the temperature of an object warmed by radiation (and therefore the intensity of thermal radiation from the object) lags behind changes in the incoming radiation. That is, the surface of the object takes time to become warm when first illuminated, and takes time to cool down when illumination stops. In general there are two components to the effect:
In general, the effect is size-dependent, and will affect the semi-major axis of smaller asteroids, while leaving large asteroids practically unaffected. For kilometre-sized asteroids, the Yarkovsky effect is minuscule over short periods: the force on asteroid 6489 Golevka has been estimated at 0.25 newtons , for a net acceleration of 10 −12 m/s 2 . But it is steady; over millions of years an asteroid's orbit can be perturbed enough to transport it from the asteroid belt to the inner Solar System.
The mechanism is more complicated for bodies in strongly eccentric orbits.
The effect was first measured in 1991–2003 on the asteroid 6489 Golevka . The asteroid drifted 15 km from its predicted position over twelve years (the orbit was established with great precision by a series of radar observations in 1991, 1995, and 1999 from the Arecibo radio telescope ). [ 4 ]
Without direct measurement, it is very hard to predict the exact result of the Yarkovsky effect on a given asteroid's orbit. This is because the magnitude of the effect depends on many variables that are hard to determine from the limited observational information that is available. These include the exact shape of the asteroid, its orientation, and its albedo . Calculations are further complicated by the effects of shadowing and thermal "reillumination", whether caused by local craters or a possible overall concave shape. The Yarkovsky effect also competes with radiation pressure , whose net effect may cause similar small long-term forces for bodies with albedo variations or non-spherical shapes.
As an example, even for the simple case of the pure seasonal Yarkovsky effect on a spherical body in a circular orbit with 90° obliquity , semi-major axis changes could differ by as much as a factor of two between the case of a uniform albedo and the case of a strong north-south albedo asymmetry. Depending on the object's orbit and spin axis , the Yarkovsky change of the semi-major axis may be reversed simply by changing from a spherical to a non-spherical shape.
Despite these difficulties, using the Yarkovsky effect is one scenario under investigation to alter the course of potentially Earth-impacting near-Earth asteroids . Possible asteroid deflection strategies include "painting" the surface of the asteroid or focusing solar radiation onto the asteroid to alter the intensity of the Yarkovsky effect and so alter the orbit of the asteroid away from a collision with Earth. [ 5 ] The OSIRIS-REx mission, launched in September 2016, studied the Yarkovsky effect on asteroid Bennu . [ 6 ]
In 2020, astronomers confirmed Yarkovsky acceleration of the asteroid 99942 Apophis . The findings are relevant to asteroid impact avoidance as 99942 Apophis was thought to have a very small chance of Earth impact in 2068, and the Yarkovsky effect was a significant source of prediction uncertainty. [ 7 ] [ 8 ] In 2021, a multidisciplinary professional-amateur collaboration combined Gaia satellite and ground-based radar measurements with amateur stellar occultation observations to further refine 99942 Apophis's orbit and measure the Yarkovsky acceleration with high precision, to within 0.5%. With these data, astronomers were able to eliminate the possibility of a collision with the Earth for at least the next 100 years. [ 9 ]
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YASS (Yet Another Similarity Searcher) [ 1 ] [ 2 ] is a free software , [ 3 ] pairwise sequence alignment software for nucleotide sequences, that is, it can search for similarities between DNA or RNA sequences. YASS accepts nucleotide sequences in either plain text or the FASTA format and the output format includes the BLAST tabular output. YASS uses several transition-constrained spaced seed k-mers , which allow considerably improved sensitivity. YASS can be used locally on a user's machine, or as SaaS on the YASS web server , which produces a browser based dot-plot .
This bioinformatics-related article is a stub . You can help Wikipedia by expanding it .
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In differential geometry , Yau's conjecture is a mathematical conjecture which states that any closed Riemannian 3-manifold has infinitely many smooth closed immersed minimal surfaces . It is named after Shing-Tung Yau , who posed it as the 88th entry in his 1982 list of open problems in differential geometry. [ 1 ]
The conjecture was resolved by Kei Irie, Fernando Codá Marques and André Neves in the generic case, [ 2 ] and by Antoine Song in full generality. [ 3 ]
This differential geometry -related article is a stub . You can help Wikipedia by expanding it .
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The yaw string , also known as a slip string , is a simple device for indicating a slip or skid in an aircraft in flight. It performs the same function as the slip-skid indicator ball, but is more sensitive, and does not require the pilot to look down at the instrument panel. [ 1 ] Technically, it measures sideslip angle, not yaw angle , [ 2 ] but this indicates how the aircraft must be yawed to return the sideslip angle to zero.
It is typically constructed from a short piece or tuft of yarn placed in the free air stream where it is visible to the pilot. [ 3 ] In closed-cockpit aircraft, it is usually taped to the aircraft canopy . It may also be mounted on the aircraft's nose, either directly on the skin, or elevated on a mast, in which case it may also be fitted with a small paper cone at the trailing end. [ 4 ] They are commonly used on gliders, but may also be found on jet aircraft (especially fighters ), ultralight aircraft , light-sport aircraft , autogyros , [ 5 ] airplanes and helicopters . Its usefulness on airplanes with a tractor configuration (single propeller at the nose) is limited because the propeller creates turbulence and the spiral slipstream displaces the string to one side. [ 6 ]
The yaw string is considered a primary flight reference instrument on gliders , which must be flown with near zero sideslip angle to reduce drag as much as possible. It is valued for its high sensitivity, and the fact that it is presented in a head-up display . Even the most sophisticated modern racing sailplanes are fitted with yaw strings by their pilots, who reference them constantly throughout the flight.
The yaw string dates from the earliest days of aviation, and actually was the first flight instrument . The Wright Brothers used a yaw string on their 1902 glider tied on their front mounted elevator. [ 7 ] Wilbur Wright is credited with its invention, having applied it concurrently with the movable rudder invented by his brother Orville in October 1902, [ 8 ] although others may have used it before. Glenn Curtiss also used it on his early airplanes.
In flight, pilots are instructed to step on the head of the yaw string; the head is the front of the string, where the string is attached to the aircraft. If the head of the yaw string is to the right of the yaw string tail, then the pilot should apply right rudder pressure. If the head of the yaw string is to the left of the yaw string tail, then the pilot should apply left rudder pressure. Or pilots may be instructed to view the attached point of the yaw string as an arrowhead pointing to the rudder pedal needing application of pressure. According to Helmut Reichmann , "...rudder against the string and/or aileron toward the string."
In a spin the yaw string always points in the direction of spin. Inclinometers do not work in spins because they follow the local centrifugal direction. In a spin, only turn needles and yaw strings are reliable. Turn coordinators work if erect but not when inverted. [ 9 ] [ 10 ] [ 11 ] [ 12 ] [ 13 ]
Yaw strings are also fitted to the Lockheed U-2 high-altitude surveillance aircraft [ 14 ] and variants of the Grumman F-14 Tomcat . [ 15 ] A flat spin , caused by excessive sideslip even in level flight, happens much more easily at high altitudes. Some light twin-engine airplane pilots place yaw strings on their aircraft to help maintain control in the event of an engine failure, because the slip-skid indicator ball is not accurate in this case. [ 16 ] In a multiengine airplane with an inoperative engine,
the centered ball is no longer the indicator of zero
sideslip due to asymmetrical thrust . The yaw string is the only
flight instrument that will directly tell the pilot the
flight conditions for zero sideslip. [ 17 ]
Yaw strings are also used on some (especially smaller) helicopters.
A variation of the yaw string is the side string, used in gliders for a determination of the angle of attack. In this way the speed for best glide angle, the best thermalling speed and the stall speed can be observed independently of other parameters like air speed, aircraft weight, acceleration due to turning, stick movements, and gusts. [ 18 ]
Investigations of the side string and on its use in glider flight were performed by the Akaflieg Köln . [ 19 ]
This article incorporates public domain material from Instrument Flying Handbook . United States government .
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Yaël Nazé is a Belgian astrophysicist , author and professor at the University of Liège . She specializes in massive stars and their interactions with their surroundings. In her research, she has worked with images and data collected from various space telescopes and has worked on creating new observation satellites .
Nazé is also engaged in outreach to educate the general public about space, notably planetary science . She has written several books and articles that connect astronomy to other aspects of human culture, such as archaeology and art ( painting , music ). Her efforts in science communication as well as research have been recognized with awards by several organizations.
Yaël Nazé was born in Baudour , Belgium in 1976. [ 2 ] By the age of 10, she knew that she wanted she wanted to become an astrophysicist after observing constellations from her home in Borinage and reading about the astronomy in the newspapers. Early in her last year of secondary school, Nazé wrote a letter to astrophysicist Jean-Marie Vreux to "find out what...to study to become an astronomer." He became her teacher and mentor. [ 1 ]
Nazé completed a degree in electrical engineering at the Faculté polytechnique de Mons [Faculty of Engineering of UMons] in 1999 and received her PhD in Astrophysics from the University of Liège in March 2004. [ 3 ]
At the astrophysics center of the University of Liège, Yaël Nazé engages in research to create new observation satellites and "analyses data from different international observatories. [ 1 ]
She particularly focuses on massive stars , which start their life as objects with spectral types O and B, and then evolve notably as Wolf-Rayet stars or Luminous Blue Variables . [ 4 ] Her work aims at constraining the properties of these stars, notably their strong stellar winds . Her work was publicized through several press releases.
For example, she led or collaborated to several studies examining the X-ray emission of Zeta Puppis , one of the nearest massive stars to Earth . In 2013, she analyzed XMM-Newton data "spread over a decade to study variability in the X-ray emission." The project confirmed "the winds from massive stars are not simply a uniform breeze,..., but also reveal hundreds of thousands of individual hot and cool pieces." [ 5 ] Collaborating with You-Hua Chu , she also identified wind-blown bubbles in the Magellanic Clouds [ 6 ] and also characterized ultra-hot nebulae ionized by extreme Wolf-Rayet stars [ 7 ] .
Using various X-ray telescopes , she pinpointed the high-energy properties of several classes of massive stars , such as magnetic massive stars, [ 8 ] Be stars , [ 9 ] evolved massive stars, [ 10 ] or massive binaries in which the stellar winds collide. As an example of the latter category, in 2007, she and her colleagues used data collected between 2000 and 2005 from the XMM-Newton observatory and the Chandra X-ray Observatory to "discovered the collision of winds in" the massive system HD 5980 - it was the first extragalactic case securely identified. They examined the binary star again in 2016 and were surprised to find that it "was two and a half times brighter than a decade earlier, and its X-ray emission was even more energetic." The team could understand this surprising observation thanks to a changing cooling regime, a new one having been proposed theoretically just before. The hypothesis is that "when stellar winds collide, the shocked material releases plenty of X-rays. However, if the hot matter radiates too much light, it rapidly cools, the shock becomes unstable and the X-ray emission dims. But by 2016, the shock had relaxed and the instabilities had diminished, allowing the X-ray emission to rise eventually.” [ 11 ] In the same way, in 2011, Nazé led the team that used data from the XMM-Newton observatory and the Neil Gehrels Swift Observatory to examine the x-ray emissions produced by collisions of stellar winds in the Cyg OB2 #9 binary star system in the " Cygnus star-forming region". [ 12 ]
Since October 2019, Yaël Nazé has been a permanent Senior Research Associate at the National Fund for Scientific Research (FNRS) researcher. [ 3 ]
In her role as a professor at the University of Liège, Nazé has taught general physics and astronomy courses, as well as advanced astrophysics such as spectroscopy and astrobiology . She has also taught multidisciplinary courses on the "evolution of ideas in astronomy, critical reasoning , science communication ." [ 3 ] She considers the most important thing about teaching to be passing our knowledge onto the next generation. She aims to make her classes fun and interactive. [ 1 ]
Yaël Nazé shares her knowledge not only in academic settings, but also "gives public lectures during which she hopes to see stars in the eyes of her audience." [ 1 ] In 2012, Nazé was awarded the Prize for Excellence in Public Engagement with Planetary Science by the Europlanet Society for her "outreach activities...in attracting hard to reach audiences", which includes "children, artists and elderly people." [ 13 ] In the 15 years leading up to that honor, "[s]he has been particularly active in highlighting the contribution of women to astronomy and showing opportunities for girls looking at careers in astronomy." [ 13 ]
To further the general public's engagement with information about the cosmos , Yaël Nazé, "together with a colleague, pioneered a service for journalists giving daily summaries of space news translated into French." To interest children in astronomy, "[s]he designed a permanent exhibition on the Solar System for the pediatric ward of the Bruyères Hospital in Belgium [ 13 ] as well as booklets, hands-on activities, and serious games published by the science diffusion office of the university of Liège (Réjouisciences).
In addition to authoring and co-authoring over 180 academic papers in refereed journals [ 14 ] , Yaël Nazé has written 12 general interest books (as of March 2023) "that brilliantly demonstrate the role of astronomy in our history and culture." [ 1 ] Her book L'astronomie des anciens [ The astronomy of the ancients ], "which won the Jean Rostand Prize for the best work of popular science in the French language in 2009" [ 13 ] , draws a connection between astronomy and archaeology. [ 15 ] In her book Art & astronomie: impressions célestes [ Art & Astronomy: celestial impressions ], she juxtaposes art and astronomy [ 16 ] with observations such as " Pollock ...wanted to make the trajectories of stars visible." [ 1 ] Using a play on words for the title, Cahier de (G)astronomie: la cuisine du cosmos [ (G)astronomy notebook: the cuisine of the cosmos ] [ 17 ] is "a cookbook inspired by the planets , which includes a recipe for Io pizza." [ 13 ]
In 2018, in an effort to combat pseudoscience , Yaël Nazé wrote an article for Skeptical Inquirer in which she analyzed the controversy over a Ph.D. thesis proposed by a student at the University of Sfax , which defended a flat earth as well as a geocentric model of the Solar System and Young Earth creationism . The dissertation theme had been approved by the committee overseeing environmental studies theses (but not the final, full dissertation) and its summary had been made public and denounced in 2017 by professor Hafedh Ateb, a co-founder of the Tunisian Astronomical Society, on his Facebook page. [ 18 ]
In 2023 in response to NASA scientists mapping the colors of the images from the James Webb Space Telescope (JWST) "to different pitches of sound", Yaël Nazé wrote an article about "the long love story between music and astronomy." She traced the history of music in astronomy beginning with the Ancient Greek beliefs that "each planet hung on a sphere, which...revolved around the Earth" and that those "moving spheres in the cosmos should also produce sounds" to Johannes Kepler 's "conclusion that planets sung melodies" which he later "abandoned...to concentrate on spelling out his third law on planetary motion in 1619." In modern times, Nazé explains, sounds are mapped to colors produced by celestial objects: "a brighter object produce a louder sound" and "a sound's duration corresponds to the object's appearance: short for a star ..., long for a nebulous cloud. [ 19 ]
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Ytterbium(III) oxide is the chemical compound with the formula Yb 2 O 3 . It is one of the more commonly encountered compounds of ytterbium . It occurs naturally in trace amounts in the mineral gadolinite . It was first isolated from this in 1878 by Jean Charles Galissard de Marignac . [ 3 ]
Ytterbium(III) oxide can be obtained by directly reacting ytterbium with oxygen : [ 4 ]
It can also be obtained by the thermal decomposition of ytterbium carbonate or ytterbium oxalate at temperatures around 700 °C: [ 5 ]
Ytterbium(III) oxide is a white powder. [ 2 ] It reacts with carbon tetrachloride [ 6 ] or hot hydrochloric acid to form ytterbium(III) chloride : [ 7 ]
Like the other trivalent oxides of the heavier lanthanides, ytterbium(III) oxide has the "rare-earth C-type sesquioxide" structure which is related to the fluorite structure with one quarter of the anions removed, leading to ytterbium atoms in two different six coordinate (non-octahedral) environments. [ 8 ]
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Ytterbium(III) bromide ( Yb Br 3 ) is an inorganic chemical compound .
Refer to the adjacent table for the main properties of Ytterbium(III) bromide.
Dissolving ytterbium oxide into 40% hydrobromic acid forms YbBr 3 ·6H 2 O crystals. After mixing the hydrate with ammonium bromide and heating it in a vacuum, anhydrous YbBr 3 can be obtained. [ 2 ]
Ytterbium(III) bromide can also be prepared by directly heating ytterbium oxide and ammonium bromide. [ 3 ]
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Ytterbium(II) chloride ( Yb Cl 2 ) is an inorganic chemical compound . It was first prepared in 1929 by W. K. Klemm and W. Schuth, by reduction of ytterbium(III) chloride, YbCl 3 , using hydrogen .
Like other Yb(II) compounds and other low-valence rare earth compounds, it is a strong reducing agent. It is unstable in aqueous solution, reducing water to hydrogen gas. [ 2 ]
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Ytterbium(III) chloride ( Yb Cl 3 ) is an inorganic chemical compound. It reacts with NiCl 2 to form a very effective catalyst for the reductive dehalogenation of aryl halides . [ 2 ] It is poisonous if injected, and mildly toxic by ingestion. It is an experimental teratogen , known to irritate the skin and eyes.
The synthesis of YbCl 3 was first reported by Jan Hoogschagen in 1946. [ 3 ] It is now a commercially available source of Yb 3+ ions and therefore of significant chemical interest.
The valence electron configuration of Yb +3 (from YbCl 3 ) is 4 f 13 5 s 2 5 p 6 , which has crucial implications for the chemical behaviour of Yb +3 . Also, the size of Yb +3 governs its catalytic behaviour and biological applications. For example, while both Ce +3 and Yb +3 have a single unpaired f electron, Ce +3 is much larger than Yb +3 because lanthanides become much smaller with increasing effective nuclear charge as a consequence of the f electrons not being as well shielded as d electrons. [ 4 ] This behavior is known as the lanthanide contraction. The small size of Yb +3 produces fast catalytic behavior and an atomic radius (0.99 Å) comparable to many biologically important ions. [ 4 ]
The gas-phase thermodynamic properties of this chemical are difficult to determine because the chemical can disproportionate to form [YbCl 6 ] −3 or dimerize. [ 5 ] The Yb 2 Cl 6 species was detected by electron impact (EI) mass spectrometry as (Yb 2 Cl 5 + ). [ 5 ] Additional complications in obtaining experimental data arise from the myriad of low-lying f - d and f - f electronic transitions. [ 6 ] Despite these issues, the thermodynamic properties of YbCl 3 have been obtained and the C 3V symmetry group has been assigned based upon the four active infrared vibrations. [ 6 ]
Anhydrous ytterbium(III) chloride can be produced by the ammonium chloride route . [ 7 ] [ 8 ] [ 9 ] In the first step, ytterbium oxide is heated with ammonium chloride to produce the ammonium salt of the pentachloride:
In the second step, the ammonium chloride salt is converted to the trichlorides by heating in a vacuum at 350-400 °C:
YbCl 3 is a paramagnetic Lewis acid , like many of the lanthanide chlorides . It gives rise to pseudocontact shifted NMR spectra, akin to NMR shift reagents
Membrane biology has been greatly influenced by YbCl 3 , where 39 K + and 23 Na + ion movement is critical in establishing electrochemical gradients. [ 10 ] Nerve signaling is a fundamental aspect of life that may be probed with YbCl 3 using NMR
techniques. YbCl 3 may also be used as a calcium ion probe, in a fashion similar
to a sodium ion probe. [ 11 ]
YbCl 3 is also used to track digestion in animals. Certain additives to swine feed, such as probiotics, may be added to either solid feed or drinking liquids. YbCl 3 travels
with the solid food and therefore helps determine which food phase is ideal to incorporate the food additive. [ 12 ] The YbCl 3 concentration is quantified by inductively coupled plasma mass spectrometry to within 0.0009 μg/mL. [ 4 ] YbCl 3 concentration versus time yields the flow rate of solid particulates in the animal's digestion. The animal is not harmed by the YbCl 3 since YbCl 3 is simply excreted in fecal matter and no change in body weight, organ weight, or hematocrit levels has been observed in mice. [ 11 ]
The catalytic nature of YbCl 3 also has an application in DNA microarrays, or so called DNA “chips”. [ 13 ] YbCl 3 led to a 50–80 fold increase in fluorescein incorporation into target DNA, which could revolutionize infectious disease detection (such as a rapid test for tuberculosis ). [ 13 ]
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Ytterbium(III) fluoride ( YbF 3 ) is an inorganic chemical compound that is insoluble in water. Like other Ytterbium compounds, it is a rather unremarkable white substance. [ 3 ] Ytterbium fluoride has found a niche usage as a radio-opaque agent in the dental industry to aid in the identification of fillings under X-ray examination. [ 4 ]
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Ytterbium(III) phosphide is an inorganic compound of ytterbium and phosphorus with the chemical formula YbP . [ 1 ] This is one of the phosphides of ytterbium. [ 2 ] [ 3 ]
Ytterbium and phosphine reacts in liquid ammonia to form Yb(PH 2 ) 2 ·5NH 3 , which can be decomposed to obtain ytterbium(III) phosphide: [ 4 ]
Ytterbium(III) phosphide decomposes at or above 550 °C:
It is soluble in hydrochloric acid , nitric acid , and aqua regia .
The compound forms black crystals of a cubic system , space group Fm 3 m . [ 5 ]
The ytterbium(III) phosphide compound is a semiconductor used in high power, high frequency applications and in laser and other photo diodes. [ 1 ]
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Ytterbium sulfide may refer to:
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Ytterbium monotelluride is an inorganic compound, one of the tellurides of ytterbium , with the chemical formula YbTe.
Ytterbium monotelluride can be produced by the high-temperature reduction reaction of ytterbium(III) telluride (Yb 2 Te 3 ), [ 1 ] or by the reaction of ytterbium(III) chloride , tellurium and hydrogen : [ 2 ]
The thermal decomposition of [(py) 2 Yb(μ-η 2 -η 2 -PhNNPh)(TePh)] 2 · 2 py will also produce ytterbium monotelluride, but at the same time, ytterbium(III) nitride will be produced. [ 3 ]
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YcaO is a protein found in bacteria which is involved in the synthesis of thiazole/oxazole modified microcin antibiotics, such as bottromycin . YcaO performs ATP dependent cyclodehydration to form the oxazole and thiazole moieties of the microcin. [ 2 ] [ 3 ] [ 4 ]
The YcaO name origin is from a gene naming rubric that was established from the bacterium Escherichia coli . If a gene has an unknown function, it was given a four-letter name starting with the letter Y and the next three letters are given based on the genomic location. [ 5 ]
Methyl coenzyme M reductase (MCR) or Coenzyme-B sulfoethylthiotransferase is a protein known in thioamidation (a posttranslational modification). A Ycao enzyme dependent on ATP is needed for MCR thioamidation as well as a sulfide source. YcaO enzymes are needed to catalyze the ATP-dependent backbone cyclodehydration of polar amino acids such as Cysteine , Serine , and Threonine to the correct thiazoline and (methyl) oxazoline Heterocycle . [ 6 ] The side chains of these amino acids can act as Nucleophiles . The Thiol group in cysteine and the hydroxyl group of serine and threonine are strong nucleophiles.
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In molecular biology, the Ycf4 protein is involved in the assembly of the photosystem I complex which is part of an energy-harvesting process named photosynthesis . [ 1 ] Without Ycf4, photosynthesis would be inefficient affecting plant growth. Ycf4 is located in the thylakoid membrane of the chloroplast . Ycf4 is important for the light dependent reaction of photosynthesis.
To date, three thylakoid proteins involved in the stable accumulation of PSI have been identified, these are as follows:
The Ycf4 protein is firmly associated with the thylakoid membrane, presumably through a transmembrane domain . [ 1 ] Ycf4 co-fractionates with a protein complex larger than PSI upon sucrose density gradient centrifugation of solubilised thylakoids. [ 1 ]
Ycf is an acronym standing for h y pothetical c hloroplast open reading f rame .
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YeTFaSCo (The Yeast Transcription Factor Specificity Compendium) is a database of transcription factors for Saccharomyces cerevisiae . [ 1 ]
This Biological database -related article is a stub . You can help Wikipedia by expanding it .
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A year loss table ( YLT ) is a table that lists historical or simulated years, with financial losses for each year. [ 1 ] [ 2 ] [ 3 ] YLTs are widely used in catastrophe modeling as a way to record and communicate historical or simulated losses from catastrophes. The use of lists of years with historical or simulated financial losses is discussed in many references on catastrophe modelling and disaster risk management, [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] but it is only more recently that the term YLT has been standardized. [ 1 ] [ 2 ] [ 3 ]
In a simulated YLT, each year of simulated loss is considered a possible loss outcome for a single year, defined as the year of interest , which is usually in the future. In insurance industry catastrophe modelling , the year of interest is often this year or next, due to the annual nature of many insurance contracts. [ 1 ]
Many YLTs are event based; that is, they are constructed from historical or simulated catastrophe events, each of which has an associated loss. Each event is allocated to one or more years in the YLT and there may be multiple events in a year. [ 4 ] [ 5 ] [ 6 ] The events may have an associated frequency model, that specifies the distribution for the number of different types of events per year, and an associated severity distribution, that specifies the distribution of loss for each event.
YLTs are widely used in the insurance industry, [ 1 ] [ 2 ] as they are a flexible way to store samples from a distribution of possible losses. Two properties make them particularly useful:
YLTs are often stored in either long-form or short-form.
In a long-form YLT, [ 1 ] each row corresponds to a different loss-causing event. For each event, the YLT records the year, the event, the loss, and any other relevant information about the event.
In this example:
In a short-form YLT, [ 3 ] each row of the YLT corresponds to a different year. For each event, the YLT records the year, the loss, and any other relevant information about that year.
The same YLT above, condensed to a short form, would look like:
The most commonly used frequency model for the events in a YLT is the Poisson distribution with constant parameters. [ 6 ] An alternative frequency model is the mixed Poisson distribution , which allows for the temporal and spatial clustering of events. [ 10 ]
When YLTs are generated from parametrized mathematical models, they may use the same parameter values in each year (fixed parameter YLTs), or different parameter values in each year (stochastic parameter YLTs). [ 3 ]
As an example, the annual frequency of hurricanes hitting the United States might be modelled as a Poisson distribution with an estimated mean of 1.67 hurricanes per year. The estimation uncertainty around the estimate of the mean might considered to be a gamma distribution . In a fixed parameter YLT, the number of hurricanes every year would be simulated using a Poisson distribution with a mean of 1.67 hurricanes per year, and the distribution of estimation uncertainty would be ignored. In a stochastic parameter YLT, the number of hurricanes in each year would be simulated by first simulating the mean number of hurricanes for that year from the gamma distribution, and then simulating the number of hurricanes itself from a Poisson distribution with the simulated mean.
In the fixed parameter YLT the mean of the Poisson distribution used to model the frequency of hurricanes, by year, would be:
In the stochastic parameter YLT the mean of the Poisson distribution used to model the frequency of hurricanes, by year, might be:
It is often of interest to adjust YLTs, perform sensitivity tests, or make adjustments for climate change. Adjustments can be made in several different ways. If a YLT has been created by simulating from a list of events with given frequencies, then one simple way to adjust the YLT is to resimulate but with different frequencies. Resimulation with different frequencies can be made much more accurate by using the incremental simulation approach. [ 11 ]
YLTs can be adjusted by applying weights to the years, which converts a YLT to a WYLT. An example would be adjusting weather and climate risk YLTs to account for the effects of climate variability and change. [ 12 ] [ 13 ]
A general and principled method for applying weights to YLTs is importance sampling , [ 12 ] [ 3 ] in which the weight on the year i {\displaystyle i} is given by the ratio of the probability of year i {\displaystyle i} in the adjusted model to the probability of year i {\displaystyle i} in the unadjusted model. Importance sampling can be applied to both fixed parameter YLTs [ 12 ] and stochastic parameter YLTs. [ 3 ]
WYLTs are less flexible in some ways than YLTs. For instance, two WYLTs with different weights, cannot easily be combined to create a new WYLT. For this reason, it may be useful to convert WYLTs to YLTs. This can be done using the method of repeat-and-delete, [ 12 ] in which years with high weights are repeated one or more times and years with low weights are deleted.
Standard risk metrics can be calculated straightforwardly from YLTs and WYLTs. Some examples are: [ 1 ]
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The Year of the Solar System [ 1 ] is a NASA education/public outreach initiative. [ 2 ] The year runs October 2010 until August 2012, a Martian year . For each month's topic there are resources for clubs, schools and the general public. The months/topics are:
The Year of the Solar System is supported by NASA's Science Mission Directorate and its Planetary Science Division.
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A year zero does not exist in the Anno Domini (AD) calendar year system commonly used to number years in the Gregorian calendar (nor in its predecessor, the Julian calendar ); in this system, the year 1 BC is followed directly by year AD 1 (which is the year of the epoch of the era). However, there is a year zero in both the astronomical year numbering system (where it coincides with the Julian year 1 BC ), and the ISO 8601:2004 system, a data interchange standard for certain time and calendar information (where year zero coincides with the Gregorian year 1 BC ; see: Holocene calendar § Conversion ) . There is also a year zero in most Buddhist and Hindu calendars .
The Anno Domini era was introduced in 525 by Scythian monk Dionysius Exiguus (c. 470 – c. 544), who used it to identify the years on his Easter table . He introduced the new era to avoid using the Diocletian era , based on the accession of Roman emperor Diocletian , as he did not wish to continue the memory of a persecutor of Christians . In the preface to his Easter table, Dionysius stated that the "present year" was "the consulship of Probus Junior " which was also 525 years "since the incarnation of our Lord Jesus Christ ". [ 1 ] How he arrived at that number is unknown. [ 2 ]
Dionysius Exiguus did not use "AD" years to date any historical event. This practice began with the English cleric Bede (c. 672–735), who used AD years in his Historia ecclesiastica gentis Anglorum (731), popularizing the era. Bede also used – only once – a term similar to the modern English term " before Christ ", though the practice did not catch on for nearly a thousand years, when books by Denis Pétau treating calendar science gained popularity. Bede did not sequentially number days of the month , weeks of the year, or months of the year. However, he did number many of the days of the week using the counting origin one in Ecclesiastical Latin . [ citation needed ]
Previous Christian histories used several titles for dating events: anno mundi ("in the year of the world") beginning on the purported first day of creation ; or anno Adami ("in the year of Adam ") beginning at the creation of Adam five days later (or the sixth day of creation according to the Genesis creation narrative ) as used by Africanus ; or anno Abrahami ("in the year of Abraham ") beginning 3,412 years after Creation according to the Septuagint , used by Eusebius of Caesarea ; all of which assigned "one" to the year beginning at Creation, or the creation of Adam, or the birth of Abraham, respectively. Bede continued this earlier tradition relative to the AD era. [ citation needed ]
In chapter II of book I of Ecclesiastical History , Bede stated that Julius Caesar invaded Britain "in the year 693 after the building of Rome, but the sixtieth year before the incarnation of our Lord", while stating in chapter III, "in the year of Rome 798, Claudius " also invaded Britain and "within a very few days ... concluded the war in ... the forty-sixth [year] from the incarnation of our Lord". [ 3 ] Although both dates are wrong, they are sufficient to conclude that Bede did not include a year zero between BC and AD: 798 − 693 + 1 (because the years are inclusive) = 106, but 60 + 46 = 106, which leaves no room for a year zero. The modern English term "before Christ" (BC) is only a rough equivalent, not a direct translation, of Bede's Latin phrase ante incarnationis dominicae tempus ("before the time of the lord's incarnation"), which was itself never abbreviated. Bede's singular use of 'BC' continued to be used sporadically throughout the Middle Ages . [ citation needed ]
Neither the concept of nor a symbol for zero existed in the system of Roman numerals . The Babylonian system of the BC era had used the idea of "nothingness" without considering it a number, and the Romans enumerated in much the same way. Wherever a modern zero would have been used, Bede and Dionysius Exiguus did use Latin number words, or the word nulla (meaning "nothing") alongside Roman numerals. [ 1 ] [ 4 ] [ 5 ] Zero was invented in India in the sixth century, [ 6 ] and was either transferred or reinvented by the Arabs by about the eighth century. The Arabic numeral for zero ( 0 ) did not enter Europe until the thirteenth century. Even then, it was known only to very few, and only entered widespread use in Europe by the seventeenth century. [ citation needed ]
The anno Domini nomenclature was not widely used in Western Europe until the 9th century, and the 1 January to 31 December historical year was not uniform throughout Western Europe until 1752. The first extensive use (hundreds of times) of 'BC' occurred in Fasciculus Temporum by Werner Rolevinck in 1474, alongside years of the world ( anno mundi ). [ 7 ] The terms anno Domini , Dionysian era , Christian era , vulgar era , and common era were used interchangeably between the Renaissance and the 19th century, at least in Latin . But vulgar era fell out of use in English at the beginning of the 20th century after vulgar acquired the meaning of "offensively coarse", replacing its original meaning of "common" or "ordinary". Consequently, historians regard all these eras as equal. [ citation needed ]
Historians have never included a year zero. This means that between, for example, 1 January 500 BC and 1 January AD 500 , there are 999 years: 500 years BC, and 499 years AD preceding 500. In common usage anno Domini 1 is preceded by the year 1 BC , without an intervening year zero. [ 8 ] Neither the choice of calendar system (whether Julian or Gregorian ) nor the name of the era ( Anno Domini or Common Era ) determines whether a year zero will be used. If writers do not use the convention of their group (historians or astronomers), they must explicitly state whether they include a year 0 in their count of years, otherwise their historical dates will be misunderstood. [ 9 ]
In astronomy, for the year AD 1 and later it is common to assign the same numbers as the Anno Domini notation, which in turn is numerically equivalent to the Common Era notation. But the discontinuity between 1 AD and 1 BC makes it cumbersome to compare ancient and modern dates. So the year before 1 AD is designated 0, the year before 0 is −1, and so on.
The letters "AD", "BC", "CE", or "BCE" are omitted. So 1 BC in historical notation is equivalent to 0 in astronomical notation, 2 BC is equivalent to −1, etc. Sometimes positive years are preceded by the + sign. This year numbering notation was introduced by the astronomer Jacques Cassini in 1740. [ 10 ]
In 1627, the German astronomer Johannes Kepler , in his Rudolphine Tables , first used an astronomical year essentially as a year zero. He labeled it Christi and inserted it between years labeled Ante Christum and Post Christum —abbreviated BC and AD today, respectively— on the "mean motion" pages of the Sun, Moon, and planets. [ 11 ] In 1702, the French astronomer Philippe de La Hire labeled a year as Christum 0 and placed it at the end of the years labeled ante Christum (BC), and immediately before the years labeled post Christum (AD), on the mean motion pages in his Tabulæ Astronomicæ , thus adding the number designation 0 to Kepler's Christi . [ 12 ]
Finally, in 1740, the transition was completed by French astronomer Jacques Cassini (Cassini II) , who is traditionally credited with inventing year zero. [ 13 ] In his Tables astronomiques , Cassini labeled the year simply as 0 , and placed it at the end of years labeled avant Jesus-Christ (BC), and immediately before years labeled après Jesus-Christ (AD). [ 14 ]
ISO 8601:2004 (and previously ISO 8601:2000, but not ISO 8601:1988) explicitly uses astronomical year numbering in its date reference systems. (Because it also specifies the use of the proleptic Gregorian calendar for all years before 1582, some readers incorrectly assume that a year zero is also included in that proleptic calendar, but it is not used with the BC/AD era.) The "basic" format for year 0 is the four-digit form 0000, which equals the historical year 1 BC. Several "expanded" formats are possible: −0000 and +0000, as well as five- and six-digit versions. Earlier years are also negative four-, five- or six-digit years, which have an absolute value one less than the equivalent BC year, hence -0001 = 2 BC. Because only ISO 646 (7-bit ASCII ) characters are allowed by ISO 8601, the minus sign is represented by a hyphen-minus .
Programming libraries may implement a year zero, an example being the Perl CPAN module DateTime. [ 15 ]
Most eras used with Hindu and Buddhist calendars , such as the Saka era or the Kali Yuga , begin with the year 0. These calendars mostly use elapsed, expired, or complete years, in contrast with most calendars from other parts of the world which use current years. A complete year had not yet elapsed for any date in the initial year of the epoch, thus the number 1 cannot be used. Instead, during the first year the indication of 0 years (elapsed) is given in order to show that the epoch is less than 1 year old. This is similar to the Western method of stating a person's age – people do not reach age one until one year has elapsed since birth (but their age during the year beginning at birth is specified in months or fractional years, not as age zero). However, if ages were specified in years and months, such a person would be said to be, for example, 0 years and 6 months or 0.5 years old. This is analogous to the way time is shown on a 24-hour clock : during the first hour of a day, the time elapsed is 0 hours, n minutes.
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The Yeast Promoter Atlas ( YPA ) is a repository of promoter features in Saccharomyces cerevisiae . [ 1 ]
This Biological database -related article is a stub . You can help Wikipedia by expanding it .
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https://en.wikipedia.org/wiki/Yeast_Promoter_Atlas
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Yeast artificial chromosomes (YACs) are genetically engineered chromosomes derived from the DNA of the yeast, Saccharomyces cerevisiae [1] , which is then ligated into a bacterial plasmid. By inserting large fragments of DNA, from 100–1000 kb, the inserted sequences can be cloned and physically mapped using a process called chromosome walking . This is the process that was initially used for the Human Genome Project , however due to stability issues, YACs were abandoned for the use of bacterial artificial chromosome [2]
The bakers' yeast S. cerevisiae is one of the most important experimental organisms for studying eukaryotic molecular genetics. [ 1 ]
Beginning with the initial research of the Rankin et al., Strul et al., and Hsaio et al., the inherently fragile chromosome was stabilized by discovering the necessary autonomously replicating sequence (ARS); [ 2 ] a refined YAC utilizing this data was described in 1983 by Murray et al. [ 3 ]
The primary components of a YAC are the ARS, centromere [3] , and telomeres [4] from S. cerevisiae . Additionally, selectable marker genes, such as antibiotic resistance and a visible marker, are utilized to select transformed yeast cells. Without these sequences, the chromosome will not be stable during extracellular replication, and would not be distinguishable from colonies without the vector. [ 4 ]
A YAC is built using an initial circular DNA plasmid , which is typically cut into a linear DNA molecule using restriction enzymes ; DNA ligase is then used to ligate a DNA sequence or gene of interest into the linearized DNA, forming a single large, circular piece of DNA. [ 3 ] [5] The basic generation of linear yeast artificial chromosomes can be broken down into 6 main steps:
Chromosome III is the third smallest chromosome in S. cerevisiae; its size was estimated from pulsed-field gel electro- phoresis studies to be 300–360 kb [ 10 ]
This chromosome has been the subject of intensive study, not least because it contains the three genetic loci involved in mating-type control: MAT, HML and HMR. [ 11 ] In March 2014, Jef Boeke of the Langone Medical Centre at New York University, published that his team has synthesized one of the S. cerevisiae 16 yeast chromosomes, the chromosome III, that he named synIII . [ 12 ] [ 13 ] The procedure involved replacing the genes in the original chromosome with synthetic versions and the finished synthesized chromosome was then integrated into a yeast cell. It required designing and creating 273,871 base pairs of DNA - fewer than the 316,667 pairs in the original chromosome.
Yeast expression vectors, such as YACs, YIps (yeast integrating plasmids), and YEps (yeast episomal plasmids), have an advantage over bacterial artificial chromosomes (BACs) in that they can be used to express eukaryotic proteins that require posttranslational modification . By being able to insert large fragments of DNA, YACs can be utilized to clone and assemble the entire genomes of an organism. [ 14 ] With the insertion of a YAC into yeast cells, they can be propagated as linear artificial chromosomes, cloning the inserted regions of DNA in the process. With this completed, two processes can be used to obtain a sequenced genome, or region of interest:
This is significant in that it allows for the detailed mapping of specific regions of the genome. Whole human chromosomes have been examined, such as the X chromosome, [ 16 ] generating the location of genetic markers for numerous genetic disorders and traits. [ 17 ]
In the United States, the Human Genome Project first took clear form in February of 1988, with the release of the National Research Council (NRC) report Mapping and Sequencing the Human Genome. [ 18 ] YACs are significantly less stable than BACs, producing "chimeric effects" : artifacts where the sequence of the cloned DNA actually corresponds not to a single genomic region but to multiple regions. Chimerism may be due to either co-ligation of multiple genomic segments into a single YAC, or recombination of two or more YACs transformed in the same host Yeast cell. [ 19 ] The incidence of chimerism may be as high as 50%. [ 20 ] Other artifacts are deletion of segments from a cloned region, and rearrangement of genomic segments (such as inversion). In all these cases, the sequence as determined from the YAC clone is different from the original, natural sequence, leading to inconsistent results and errors in interpretation if the clone's information is relied upon. Due to these issues, the Human Genome Project ultimately abandoned the use of YACs and switched to bacterial artificial chromosomes , where the incidence of these artifacts is very low. In addition to stability issues, specifically the relatively frequent occurrence of chimeric events, YACs proved to be inefficient when generating the minimum tiling path covering the entire human genome. Generating the clone libraries is time consuming. Also, due to the nature of the reliance on sequence tagged sites (STS) as a reference point when selecting appropriate clones, there are large gaps that need further generation of libraries to span. It is this additional hindrance that drove the project to utilize BACs instead. [ 21 ] This is due to two factors: [ 22 ]
However, it is possible to utilize both approaches, as was demonstrated when the genome of the nematode, C. elegans . There majority of the genome was tiled with BACs, and the gaps filled in with YACs. [ 21 ]
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The yeast deletion project , formally the Saccharomyces Genome Deletion Project , is a project to create data for a near-complete collection of gene-deletion mutants of the yeast Saccharomyces cerevisiae . Each strain carries a precise deletion of one of the genes in the genome . This allows researchers to determine what each gene does by comparing the mutated yeast to the behavior of normal yeast. Gene deletion, or gene knockout , is one of the main ways in which the function of genes are discovered. Many of the deletion mutations are sold by the biotech firm Invitrogen . [ 1 ] [ 2 ] [ 3 ]
This yeast -related article is a stub . You can help Wikipedia by expanding it .
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The yeast mitochondrial code (translation table 3 ) is a genetic code used by the mitochondrial genome of yeasts, notably Saccharomyces cerevisiae , Candida glabrata , Hansenula saturnus , and Kluyveromyces thermotolerans . [ 1 ]
Bases: adenine (A), cytosine (C), guanine (G) and thymine (T) or uracil (U).
Amino acids: Alanine (Ala, A), Arginine (Arg, R), Asparagine (Asn, N), Aspartic acid (Asp, D), Cysteine (Cys, C), Glutamic acid (Glu, E), Glutamine (Gln, Q), Glycine (Gly, G), Histidine (His, H), Isoleucine (Ile, I), Leucine (Leu, L), Lysine (Lys, K), Methionine (Met, M), Phenylalanine (Phe, F), Proline (Pro, P), Serine (Ser, S), Threonine (Thr, T), Tryptophan (Trp, W), Tyrosine (Tyr, Y), Valine (Val, V).
This article incorporates text from the United States National Library of Medicine , which is in the public domain . [ 3 ]
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YEASTRACT ( Yea st S earch for T ranscriptional R egulators A nd C onsensus T racking) is a curated repository of more than 48000 regulatory associations between transcription factors (TF) and target genes in Saccharomyces cerevisiae , based on more than 1200 bibliographic references. [ 1 ] It also includes the description of about 300 specific DNA binding sites for more than a hundred characterized TFs. Further information about each Yeast gene has been extracted from the Saccharomyces Genome Database (SGD). For each gene the associated Gene Ontology (GO) terms and their hierarchy in GO was obtained from the GO consortium. Currently, YEASTRACT maintains more than 7100 terms from GO. The nucleotide sequences of the promoter and coding regions for Yeast genes were obtained from Regulatory Sequence Analysis Tools (RSAT). All the information in YEASTRACT is updated regularly to match the latest data from SGD, GO consortium, RSA Tools and recent literature on yeast regulatory networks.
YEASTRACT includes DISCOVERER, a set of tools that can be used to identify complex motifs found to be over-represented in the promoter regions of co-regulated genes. [ 2 ] DISCOVERER is based on the MUSA algorithm. These algorithms take as input a list of genes and identify over-represented motifs, which can then be compared with transcription factor binding sites described in the YEASTRACT database.
Facilities are also provided to enable the exploitation of the gathered data when solving a number of biological questions, as exemplified in the Tutorial. YEASTRACT allows the identification of documented or potential transcription regulators of a given gene and of documented or potential regulons for each transcription factor. It also renders possible the comparison between DNA motifs and the transcription factor binding sites described in the literature. The system also provides a useful mechanism for grouping a list of genes (for instance a set of genes with similar expression profiles as revealed by microarray analysis) based on their regulatory associations with known transcription factors.
YEASTRACT provides a set of queries to search and retrieve important biological information from the gathered data and to predict transcription regulation networks in yeast from data emerging from gene-by-gene analysis or global approaches.
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Yellow.ai , formerly Yellow Messenger , is a multinational company headquartered in San Mateo, California focused on customer service automation. [ 2 ] It was founded in 2016 and provides an AI platform for automating customer support experiences across chat and voice. The platform supports more than 135 languages across more than 35 channels. [ 3 ] [ 4 ]
Yellow.ai was founded in 2016 by Raghu Ravinutala, Jaya Kishore Reddy Gollareddy, and Rashid Khan in Bangalore , India. Raghavendra Ravinutala and Jaya Kishore Reddy Gollareddy left their full-time jobs to establish Yellow.ai, and they met Rashid Khan at a college hackathon, where he began working with them. By January 2016, Yellow.ai had acquired 50,000 customers. [ 5 ] The same year, the company rolled out a model of the application for B2B companies. This version of the software and platform was intended to support voice and chat interactions for enterprises. [ 6 ] In 2016, the company joined Microsoft 's accelerator program and SAP Startup Studio. [ 7 ] [ 8 ]
In April 2021, amid the COVID-19 pandemic, the company developed chatbots to assist governments with vaccinations. [ 9 ] It launched Yellow Messenger Care to create omnichannel chatbots related to COVID-19 assistance, which helped NGOs and hospitals in their crisis management efforts. [ 10 ] In June 2021, the company rebranded itself from Yellow Messenger to Yellow.ai. [ 11 ] In 2022, Yellow.ai launched DynamicNLP, which was designed to eliminate the necessity for NLP model training. [ 12 ] In 2023, Yellow.ai announced the launch of its Dynamic Automation Platform (DAP) and revealed a new logo as part of a larger rebranding strategy. [ 13 ] In May 2023, the company also launched a proprietary small language model called as YellowG, a generative AI platform for automation workflows. [ 14 ] [ 15 ] The company deployed over 120 generative AI bots for businesses in 2023. [ 2 ]
In January 2019, the company collaborated with Microsoft to work on transforming its voice automation using Azure Al Speech Services and Natural language processing (NLP) tools. [ 16 ] In February 2022, the company partnered with Tech Mahindra to develop enterprise AI technology. [ 17 ] It partnered with the e-commerce company Unicommerce in July 2020. [ 18 ] In February 2022, Edelweiss General Insurance launched its AI Voice Bot, using Yellow.ai's technology. [ 19 ] Yellow.ai implemented its AI-based customer service technology in Urja, a virtual assistant launched by the public sector company BPCL . [ 20 ] The company has also formed partnerships with Accenture , Infosys , TCS , and Wipro . [ 21 ] [ 22 ]
Its clients include Sony , [ 23 ] Flipkart , Grab , Skoda , Honda , Domino's Pizza , Bajaj Finance , Volkswagen , HDFC Bank , Ferrellgas , Indigo , Adani Capital, [ 24 ] Haldiram , Lulu Group , Bharat Petroleum Corporation Limited , Dr. Reddy's Laboratories and Concentrix . [ 25 ] [ 26 ] [ 27 ]
In June 2019, Yellow.ai completed a series A funding of $4 million led by Lightspeed Venture Partners and angel investors such as Phanindra Sama, founder of RedBus , Anand Swaminathan, senior partner, McKinsey & Company , Limeroad founder Prashant Malik, and Snapdeal founder Kunal Bahl . [ 28 ]
In April 2020, it raised $20 million in a series B round led by Lightspeed Ventures Partners and Lightspeed India Partners . [ 29 ] In August 2021, the company raised $78.15 million in its Series C funding round led by WestBridge Capital, Sapphire Ventures , Salesforce Ventures , and Lightspeed Venture Partners . [ 30 ] The company has raised a total of $102 million so far. [ 31 ]
The company won the Frost & Sullivan Technology Innovation Leadership Award in 2021. [ 32 ] Entrepreneur magazine named Yellow.ai the Best AI Startup of the Year at the Entrepreneur India Startup Awards 2022. [ 33 ] It was awarded Best Chat/Conversational Bot/Tool during the MarTech Leadership Summit 2022. [ 34 ] The Financial Express awarded it the Best Use of Conversational AI – Gold at the Financial Express FuTech Awards in 2022. [ 35 ] The company received an honorable mention in the automation solution of the Year category at the CCW Excellence Awards 2022. [ 36 ]
Forbes magazine added Yellow.ai's co-founder Rashid Khan to Forbes India 30 Under 30 2022 [ 37 ] and Forbes Asia 30 Under 30 2022 [ 38 ] lists, as one of the young game changers disrupting the Enterprise Technology industry. Hurun Research Institute listed the company in its 'Future Unicorn Index 2022' list for India. [ 39 ] In 2023, co-founder & CEO, Raghu Ravinutala was recognized as one of the top 50 SaaS CEOs by The Software Report. [ 40 ] Yellow.ai ranked 13th in the Bay Area and 88th nationally on the 2023 Deloitte Technology Fast 500 for North America . [ 41 ]
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The Yellow Card Scheme is the United Kingdom's system for collecting information on suspected adverse drug reactions (ADRs) to medicines. The scheme allows the safety of the medicines and vaccines that are on the market to be monitored. [ 1 ]
The scheme was founded in 1964 after the thalidomide disaster, and was developed by Bill Inman . It is run by the Medicines and Healthcare products Regulatory Agency (MHRA) and the Commission on Human Medicines . It was extended to hospital pharmacists in 1997, and to community pharmacists in 1999. [ 2 ]
The Yellow Card Centre Scotland is a joint venture between MHRA and the Scottish Government . [ 3 ]
Suspected adverse reactions are collected on all licensed medicines and vaccines, whether issued on prescription or bought over the counter from a pharmacist or supermarket. The scheme also includes all herbal preparations and unlicensed medicines. Adverse reactions can be reported by anyone; this is usually done by healthcare professionals – including doctors, pharmacists and nurses – but patients and carers can also make reports.
The types of adverse reactions that should be reported are:
Reports can be entered through the MHRA's website, or a smartphone app which is available for iOS and Android devices. The app can also provide news and alerts to users. [ 4 ]
Yellow Cards are available from pharmacies and a few are presented near the back of the BNF as tear-off pages; copies may also be obtained by telephoning +44 (0) 808 100 3352. [ 5 ] The scheme provides forms that allow members of the public to report suspected side effects, as well as health professionals. [ 6 ] Children and Young People can also report suspected Adverse Drug Reactions to the Yellow Card scheme, and specific information for them has been developed and tested. [ 7 ] [ 8 ]
NHS Digital publishes an information standard DCB1582 for electronic submission of adverse reactions by IT systems [ 9 ] (until 2014, this was ISB 1582 from the Information Standards Board). [ 10 ] The specification is based on the ICH E2B (R2) international standard format. [ 11 ]
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Yellow rain was a 1981 political incident in which the United States Secretary of State Alexander Haig accused the Soviet Union of supplying T-2 mycotoxin to the communist states in Vietnam , Laos and Cambodia for use in counterinsurgency warfare. [ 1 ] Refugees described many different forms of "attacks", including a sticky yellow liquid falling from planes or helicopters, which was dubbed "yellow rain". The U.S. government alleged that over ten thousand people had been killed in attacks using these supposed chemical weapons . [ 2 ] The Soviets denied these claims and an initial United Nations investigation was inconclusive.
Samples of the supposed chemical agent that were supplied to a group of independent scientists turned out to be honeybee feces, suggesting that the "yellow rain" was due to mass defecation of digested pollen grains from large swarms of bees. [ 3 ] Although the majority of the scientific literature on this topic now regards the hypothesis that yellow rain was a Soviet chemical weapon as disproved, [ 4 ] [ 5 ] the U.S. government has not retracted its allegations, [ 6 ] arguing that the issue has not been fully resolved. [ 2 ] Many of the U.S. documents relating to this incident remain classified. [ 1 ]
The charges stemmed from events in Laos and North Vietnam beginning in 1975, when the two governments, which were allied with and supported by the Soviet Union, fought against Hmong tribes, peoples who had sided with the United States and South Vietnam during the Vietnam War . Refugees described events that they believed to be chemical warfare attacks by low-flying aircraft or helicopters; several of the reports were of a yellow, oily liquid that was dubbed "yellow rain". Those exposed claimed neurological and physical symptoms including seizures, blindness, and bleeding. Similar reports came from the Vietnamese invasion of Cambodia in 1978. [ 7 ]
A 1997 textbook produced by the U.S. Army Medical Department asserted that over ten thousand people were killed in attacks using chemical weapons in Laos, Cambodia and Afghanistan. [ 2 ] The descriptions of the attacks were diverse and included air-dropped canisters and sprays, booby traps, artillery shells, rockets and grenades that produced droplets of liquid, dust, powders, smoke or "insect-like" materials of a yellow, red, green, white or brown color. [ 2 ]
Secretary of State Alexander Haig announced in September 1981 that:
The Soviet Union described these accusations as a " big lie " and said that the US government used chemical weapons during the Vietnam War and supplied them to Afghan rebels and Salvadoran troops. [ 8 ] The American accusations prompted a United Nations investigation in Pakistan and Thailand. This involved five doctors and scientists who interviewed alleged witnesses and collected samples that were purported to come from Afghanistan and Cambodia. However, the interviews produced conflicting testimony and the analyses of the samples were inconclusive. The UN experts also examined two refugees who claimed to be suffering from the after-effects of a chemical attack, but the refugees were instead diagnosed as having fungal skin infections. The team reported that they were unable to verify that chemical weapons had been used but noted that circumstantial evidence "suggestive of the possible use of some sort of toxic chemical substance in some instances." [ 9 ]
The US mycotoxin analyses were reported in the scientific literature in 1983 and 1984 and reported small amounts of mycotoxins called trichothecenes , ranging from the parts per million to traces in the parts per billion range. [ 10 ] [ 11 ] The lowest possible limit of detection in these mycotoxin analyses is in the parts per billion range. [ 12 ] However, several inconsistencies in these reports caused a "prolonged, and at times acrimonious, debate on the validity of the analyses". [ 13 ] A 2003 medical review notes that this debate may have been exacerbated since "Although analytical methods were in their infancy during the controversy, they were still sensitive enough to pick up low levels of environmental trichothecene contamination." [ 14 ]
C. J. Mirocha at the University of Minnesota conducted a biochemical investigation, looking for the presence of trichothecene mycotoxins, including T-2 toxin, diacetoxyscirpenol (DAS), and deoxynivalenol (DON). [ 10 ] This included chemical analyses of blood, urine, and tissue of alleged victims of chemical attacks in February 1982 in Laos and Kampuchea. "The finding of T-2, HT-2, and DAS toxins in blood, urine, and body tissues of alleged victims of chemical warfare in Southeast Asia provides compelling proof of the use of trichothecenes as nonconventional warfare agents. ... Additional significant findings lie in the trichothecenes found in the leaf samples (T-2, DON, nivalenol ) and yellow powder (T-2, DAS). ... The most compelling evidence is the presence of T-2 and DAS in the yellow powder. Both toxins are infrequently found in nature and rarely occur together. In our experience, copious producers of T-2 toxin ( F. tricinctum ) do not produce DAS, and conversely, good producers of DAS ( F. roseum 'Gibbosum') do not produce T-2." [ 10 ]
In 1983, these charges were disputed by Harvard biologist and biological weapons opponent Matthew Meselson and his team, who traveled to Laos and conducted a separate investigation. Meselson's team noted that trichothecene mycotoxins occur naturally in the region and questioned the witness testimony. He suggested an alternate hypothesis that the yellow rain was the harmless fecal matter of honeybees . [ 3 ] The Meselson team offered the following as evidence: separate "yellow rain drops" which occurred on the same leaf, and which were "accepted as authentic", consisted largely of pollen ; each drop contained a different mix of pollen grains, as one would expect if they came from different bees, and the grains showed properties characteristic of pollen digested by bees (the protein inside the pollen grain was gone, while the outer indigestible shell remained). [ 15 ] Further, the pollen mix came from plant species typical of the area where a drop was collected. [ 16 ] [ 17 ]
The US government responded to these findings by arguing that the pollen was added deliberately, in order to make a substance that could be easily inhaled and "ensure the retention of toxins in the human body". [ 18 ] Meselson responded to this idea by stating that it was rather far-fetched to imagine that somebody would produce a chemical weapon by "gathering pollen predigested by honeybees." [ 17 ] The fact that the pollen originated in Southeast Asia meant that the Soviet Union could not have manufactured the substance domestically, and would have had to import tons of pollen from Vietnam. [ 19 ] : 35 Meselson's work was described in an independent medical review as providing "compelling evidence that yellow rain might have a benign natural explanation". [ 14 ]
After the honeybee hypothesis was made public, a literature search turned up an earlier Chinese paper [ 20 ] on the phenomenon of yellow droppings in Jiangsu Province in September 1976. Strikingly, the Chinese villagers had also used the term "yellow rain" to describe this phenomenon. Many villagers believed that the yellow droppings were portents of imminent earthquake activity. Others believed that the droppings were chemical weapons sprayed by the Soviet Union or Taiwan . However, the Chinese scientists also concluded that the droppings came from bees. [ 21 ] : 46
Analyses of putative "yellow rain" samples by the British, French and Swedish governments confirmed the presence of pollen and failed to find any trace of mycotoxins. [ 18 ] [ 22 ] Toxicology studies questioned the reliability of reports stating that mycotoxins had been detected in alleged victims up to two months after exposure, since these compounds are unstable in the body and are cleared from the blood in just a few hours. [ 13 ] An autopsy on a Khmer Rouge fighter named Chan Mann, a victim of a putative yellow rain attack in 1982, turned up traces of mycotoxins, but also aflatoxin , Blackwater fever , and malaria . [ 19 ] : 33
Surveys also showed that both mycotoxin-producing fungi and mycotoxin contamination were common in Southeast Asia, casting doubt on the assertion that detecting these compounds was an unusual occurrence. [ 23 ] [ 24 ] For example, a Canadian military laboratory found mycotoxins in the blood of five people from the area who had never been exposed to yellow rain, out of 270 tested, but none in the blood of ten alleged victims, [ 17 ] [ 25 ] and a 1988 paper reported that illnesses from mycotoxin exposure may pose a serious threat to public health in Malaysia . [ 26 ] It is now recognized that mycotoxin contamination of foods such as wheat and maize is a common problem, particularly in temperate regions of the world. [ 24 ] [ 27 ] As noted in a 2003 medical review, "The government research highlighted, if nothing else, that natural mycotoxicoses were an important health hazard in Southeast Asia." [ 14 ]
In 1987, the New York Times reported that Freedom of Information requests showed that field investigations in 1983–85 by US government teams had produced no evidence to substantiate the initial allegations and instead cast doubt on the reliability of the initial reports, but these critical reports were not released to the public. [ 28 ] A 1989 analysis of the initial reports gathered from Hmong refugees that was published in the Journal of the American Medical Association noted "marked inconsistencies that greatly compromised the validity of the testimony" and criticized the methods used in interviews by the US Army medical team that gathered this information. These issues included the US Army team only interviewing those people who claimed to have knowledge of attacks with chemical weapons and the investigators asking leading questions during interviews. The authors noted that individuals' stories changed over time, were inconsistent with other accounts, and that the people who claimed to have been eyewitnesses when first interviewed later stated that they had been relaying the accounts of others. [ 29 ]
In 1982, Meselson had visited a Hmong refugee camp with samples of bee droppings that he had collected in Thailand. Most of the Hmong he interviewed claimed that these were samples of the chemical weapons that they had been attacked with. One man accurately identified them as insect droppings, but switched to the chemical weapons story after discussion with fellow Hmong. [ 21 ] : 46
Australian military scientist Rod Barton visited Thailand in 1984, and discovered that Thai villagers were blaming yellow rain for a variety of ailments, including scabies. An American doctor in Bangkok explained that the United States had been taking a special interest in yellow rain, and was providing medical care to alleged victims. [ 19 ] : 39–40
A CIA report from the 1960s reported allegations by the Cambodian government that their forces had been attacked with chemical weapons, leaving behind a yellow powder. The Cambodians blamed the United States for these alleged chemical attacks. Some of the samples of "yellow rain" collected from Cambodia in 1983 tested positive for CS , which the United States had used during the Vietnam War. CS is a form of tear gas and is not acutely toxic, but may account for some of the milder symptoms reported by the Hmong villagers. [ 19 ] : 39
Most of the scientific community sees these allegations as supported by insufficient evidence, or as having been completely refuted. For instance, a 1992 review published in Politics and the Life Sciences described the idea of yellow rain as a biological agent as conclusively disproved and called for an assessment by the US government of the mistakes made in this episode, stating that "the present approach of sweeping the matter under the rug and hoping people will forget about it could be counterproductive." [ 25 ] Similarly, a 1997 review of the history of biological warfare published in the Journal of the American Medical Association stated that the yellow rain allegations are "widely regarded as erroneous", [ 5 ] a 2001 review in the Annual Reviews in Microbiology described them as "unsubstantiated for many reasons", [ 30 ] and a 2003 article in Annual Review of Phytopathology described them as "largely discredited". [ 4 ] A 2003 review of the history of biological warfare described these allegations as one of many cases where states have produced propaganda containing false or unsubstantiated accusations of the use of biological weapons by their enemies. [ 31 ]
In contrast, as of 1997 the U.S. Army maintains that some experts believe that "trichothecenes were used as biological weapons in Southeast Asia and Afghanistan" although they write that "it has not been possible for the United States to prove unequivocally that trichothecene mycotoxins were used as biological weapons." They argued that presence of pollen in yellow rain samples is best explained by the idea that "during biological warfare attacks, dispersed trichothecenes landed in pollen-containing areas." [ 2 ] (Essentially the same position is taken in a subsequent volume in the same series of U.S. Army textbooks published in 2007. [ 32 ] ) Similarly, the US Defense Threat Reduction Agency argues that the controversy has not been resolved and states that a CIA report indicated the Soviet Union did possess weapons based on T-2 mycotoxin, although the agency states that "no trace of a trichothecene-containing weapon was ever found in the areas affected by yellow rain" and concludes that the use of such weapons "may never be unequivocally proved." [ 33 ] A 2007 review published in Politics and the Life Sciences concluded that the balance of evidence strongly supported the hypothesis that some type of chemical or biological weapon was used in Southeast Asia in the late 1970s and early 1980s, but noted that they found no definitive proof of this hypothesis and that the evidence could not "identify the specific agents used, the intent, or the root source or sources of the attacks." [ 34 ] The Vietnamese and the Soviets have also reportedly used other chemical weapons in conflict, in Cambodia and Afghanistan, respectively. [ 35 ] [ 36 ] [ 37 ]
An episode of mass pollen release from bees in 2002 in Sangrampur, India , prompted unfounded fears of a chemical weapons attack, although this was in fact due to a mass migration of giant Asian honeybees . This event revived memories of what New Scientist described as "cold war paranoia", and the article noted that the Wall Street Journal had covered these 1980s yellow rain allegations in particular detail. [ 38 ] Indeed, the Wall Street Journal continues to assert that the Soviet Union used yellow rain as a chemical weapon in the 1980s and in 2003 accused Matthew Meselson of "excusing away evidence of Soviet violations." [ 39 ]
In the build-up to the 2003 invasion of Iraq the Wall Street Journal alleged that Saddam Hussein possessed a chemical weapon called "yellow rain". [ 40 ] The Iraqis appear to have investigated trichothecene mycotoxins in 1990, but only purified a total of 20 ml of the agent from fungal cultures and did not manage to scale up the purification or produce any weapons containing these compounds. [ 41 ] Although these toxins are not generally regarded as practical tactical weapons, [ 42 ] the T-2 toxin might be a usable weapon since it can be absorbed through the skin, although it would be very difficult to manufacture it in any reasonable quantity. [ 43 ]
Henry Wilde, a retired US Foreign Service Officer , has drawn parallels between the use of yellow rain allegations by the US government against the Soviet Union and the later exaggerated allegations on the topic of Iraq and weapons of mass destruction . [ 44 ] Wilde considers it likely that states may again "use rumors and false or planted intelligence of such weapons use for propaganda purposes." and calls for the establishment of a more rigorous inspection process to deal with such claims. [ 44 ] Similar concerns were expressed in a 2006 review published by the World Organisation for Animal Health , which compared the American yellow rain accusations to other Cold War-era accusations from the Soviet Union and Cuba , as well as to more recent mistaken intelligence on Iraqi weapons capabilities, concluding that such unjustified accusations have encouraged the development of biological weapons and increased the risk that they might be used, as they have discredited arms-control efforts. [ 45 ]
In 2012 the science-themed show Radiolab aired an interview with Hmong refugee Eng Yang and his niece, author Kao Kalia Yang , to discuss Eng Yang's experience with yellow rain. The hosts took the position that yellow rain was unlikely to have been a chemical agent. The episode prompted a backlash among some listeners, who criticized Robert Krulwich for insensitivity, racism, and their disregard for Yang's personal and professional experience with the region in question. [ 46 ] [ 47 ] The negative response prompted host Krulwich to issue an apology for his handling of the interview. [ 48 ]
On 23 May 2015, just before the national holiday of 24 May (the day of Bulgarian writing and culture), yellow rain fell in Sofia, Bulgaria . Suspicions were raised because the Bulgarian government was criticizing Russian actions in Ukraine at the time. The Bulgarian national academy BAN explained the event as flower pollen. [ 49 ]
American Hmong poet Mai Der Vang published Yellow Rain (Graywolf Press, 2021) to critical acclaim and was a 2022 Finalist for the Pulitzer Prize in Poetry. [ 50 ] [ non-primary source needed ] The book explores yellow rain in Southeast Asia through the use of documentary poetics. [ clarification needed ]
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"Yes, and ...", also referred to as "Yes, and ..." thinking , is a rule-of-thumb in improvisational comedy that suggests that an improviser should accept what another improviser has stated ("yes") and then expand on that line of thinking ("and"). [ 1 ] [ 2 ] [ 3 ] The principle does not forbid disagreements between the improvisers' characters, but states that one should not reject the basic premises introduced by the other person, as this would throw them off and harm the flow of the scene. [ 1 ]
The principle is also used in business and other organizations for improving the effectiveness of the brainstorming process, fosters effective communication, and encourages the free sharing of ideas. [ 4 ]
The "Yes, and ..." rule is complemented by the "No, but ..." technique, which serves to refine and challenge ideas in a constructive manner.
Despite the popularity in recent years of "Yes, and ..." as a sort of slogan among many practitioners, there is hardly universal consensus regarding its authenticity and value. Gary Schwartz argues that it runs counter to the most basic tenets of improvisation. Schwartz states that he never heard Viola Spolin propose anything similar and that in fact she would have been categorically opposed to it. He argues that the slogan "misses the point of total relation needed in improvised theater." To Schwartz, it substantially interferes with the natural flow experience of the group and generally reduces the project of improvisation to "information sharing" and rapid-fire entertainment, led by the wittiest performers, resulting in "uninspired, 'talky' and not very theatrical" work. According to Schwartz, Spolin's formula contrasts completely with the intellectualization and urgent planning involved under "Yes, and ...": "by sharing a deep non-intellectual connection where mind and body work harmoniously as in play, spontaneity and true improvisation appears." He advises replacing "Yes, and ..." with a more elemental mantra frequently used by Spolin: "Follow the follower!" [ 5 ]
The "Yes" portion of the rule encourages the acceptance of the contributions added by others. Participants in an improvisation are encouraged to agree to a proposition, fostering a sense of cooperation [ 2 ] rather than shutting down the suggestion and effectively ending the line of communication.
In an organizational setting, saying "Yes" in theory encourages people to listen and be receptive to the ideas of others. Rather than immediately judging the idea, as judgment has its place later on in the development process, one should initially accept the idea, which enables the discussion to expand on the idea without limitations. [ 4 ] The next step in the process is to add new information into the narrative. The concept of "and" is to sway away from directly changing the suggested material, "and" rather building upon it. [ 2 ] Additionally, and often overlooked, the "And" encourages self-awareness, confidence, and expressive skills which are necessary for setting limits, asking for help, giving feedback, delegating and even the ability to say "No". [ 6 ]
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In chemistry , yield , also known as reaction yield or chemical yield , refers to the amount of product obtained in a chemical reaction . [ 1 ] Yield is one of the primary factors that scientists must consider in organic and inorganic chemical synthesis processes. [ 2 ] In chemical reaction engineering, "yield", " conversion " and "selectivity" are terms used to describe ratios of how much of a reactant was consumed (conversion), how much desired product was formed (yield) in relation to the undesired product (selectivity), represented as X, Y, and S.
The term yield also plays an important role in analytical chemistry , as individual compounds are recovered in purification processes in a range from quantitative yield (100 %) to low yield (< 50 %).
In chemical reaction engineering, "yield", " conversion " and "selectivity" are terms used to describe ratios of how much of a reactant has reacted—conversion, how much of a desired product was formed—yield, and how much desired product was formed in ratio to the undesired product—selectivity, represented as X, S, and Y.
According to the Elements of Chemical Reaction Engineering manual, yield refers to the amount of a specific product formed per mole of reactant consumed. [ 3 ] In chemistry, mole is used to describe quantities of reactants and products in chemical reactions.
The Compendium of Chemical Terminology defined yield as the " ratio expressing the efficiency of a mass conversion process. The yield coefficient is defined as the amount of cell mass (kg) or product formed (kg,mol) [ Notes 1 ] related to the consumed substrate (carbon or nitrogen source or oxygen in kg or moles) or to the intracellular ATP production (moles)." [ 4 ] [ 5 ] : 168
In the section "Calculations of yields in the monitoring of reactions" in the 1996 4th edition of Vogel's Textbook of Practical Organic Chemistry (1978), the authors write that, " theoretical yield in an organic reaction is the weight of product which would be obtained if the reaction has proceeded to completion according to the chemical equation. The yield is the weight of the pure product which is isolated from the reaction." [ 1 ] : 33 [ Notes 2 ] In 'the 1996 edition of Vogel's Textbook , percentage yield is expressed as, [ 1 ] : 33 [ Notes 3 ]
According to the 1996 edition of Vogel's Textbook , yields close to 100% are called quantitative , yields above 90% are called excellent , yields above 80% are very good , yields above 70% are good , yields above 50% are fair , and yields below 40% are called poor . [ 1 ] : 33 In their 2002 publication, Petrucci, Harwood, and Herring wrote that Vogel's Textbook names were arbitrary, and not universally accepted, and depending on the nature of the reaction in question, these expectations may be unrealistically high. Yields may appear to be 100% or above when products are impure, as the measured weight of the product will include the weight of any impurities. [ 6 ] : 125
In their 2016 laboratory manual, Experimental Organic Chemistry , the authors described the "reaction yield" or "absolute yield" of a chemical reaction as the "amount of pure and dry product yielded in a reaction". [ 7 ] They wrote that knowing the stoichiometry of a chemical reaction—the numbers and types of atoms in the reactants and products, in a balanced equation "make it possible to compare different elements through stoichiometric factors." [ 7 ] Ratios obtained by these quantitative relationships are useful in data analysis. [ 7 ]
The percent yield is a comparison between the actual yield—which is the weight of the intended product of a chemical reaction in a laboratory setting—and the theoretical yield—the measurement of pure intended isolated product, based on the chemical equation of a flawless chemical reaction, [ 1 ] and is defined as,
The ideal relationship between products and reactants in a chemical reaction can be obtained by using a chemical reaction equation. Stoichiometry is used to run calculations about chemical reactions, for example, the stoichiometric mole ratio between reactants and products. The stoichiometry of a chemical reaction is based on chemical formulas and equations that provide the quantitative relation between the number of moles of various products and reactants, including yields. [ 8 ] Stoichiometric equations are used to determine the limiting reagent or reactant—the reactant that is completely consumed in a reaction. The limiting reagent determines the theoretical yield—the relative quantity of moles of reactants and the product formed in a chemical reaction. Other reactants are said to be present in excess. The actual yield—the quantity physically obtained from a chemical reaction conducted in a laboratory—is often less than the theoretical yield. [ 8 ] The theoretical yield is what would be obtained if all of the limiting reagent reacted to give the product in question. A more accurate yield is measured based on how much product was actually produced versus how much could be produced. The ratio of the theoretical yield and the actual yield results in a percent yield. [ 8 ]
When more than one reactant participates in a reaction, the yield is usually calculated based on the amount of the limiting reactant , whose amount is less than stoichiometrically equivalent (or just equivalent) to the amounts of all other reactants present. Other reagents present in amounts greater than required to react with all the limiting reagent present are considered excess. As a result, the yield should not be automatically taken as a measure for reaction efficiency. [ citation needed ]
In their 1992 publication General Chemistry , Whitten, Gailey, and Davis described the theoretical yield as the amount predicted by a stoichiometric calculation based on the number of moles of all reactants present. This calculation assumes that only one reaction occurs and that the limiting reactant reacts completely. [ 9 ]
According to Whitten, the actual yield is always smaller (the percent yield is less than 100%), often very much so, for several reasons. [ 9 ] : 95 As a result, many reactions are incomplete and the reactants are not completely converted to products. If a reverse reaction occurs, the final state contains both reactants and products in a state of chemical equilibrium . Two or more reactions may occur simultaneously, so that some reactant is converted to undesired side products. Losses occur in the separation and purification of the desired product from the reaction mixture. Impurities are present in the starting material which do not react to give desired product. [ 9 ]
This is an example of an esterification reaction where one molecule acetic acid (also called ethanoic acid) reacts with one molecule ethanol , yielding one molecule ethyl acetate (a bimolecular second-order reaction of the type A + B → C):
In his 2016 Handbook of Synthetic Organic Chemistry , Michael Pirrung wrote that yield is one of the primary factors synthetic chemists must consider in evaluating a synthetic method or a particular transformation in "multistep syntheses." [ 10 ] : 163 He wrote that a yield based on recovered starting material (BRSM) or (BORSM) does not provide the theoretical yield or the "100% of the amount of product calculated", that is necessary in order to take the next step in the multistep systhesis. : 163
Purification steps always lower the yield, through losses incurred during the transfer of material between reaction vessels and purification apparatus or imperfect separation of the product from impurities, which may necessitate the discarding of fractions deemed insufficiently pure. The yield of the product measured after purification (typically to >95% spectroscopic purity, or to sufficient purity to pass combustion analysis) is called the isolated yield of the reaction. [ citation needed ]
Yields can also be calculated by measuring the amount of product formed (typically in the crude, unpurified reaction mixture) relative to a known amount of an added internal standard, using techniques like Gas chromatography (GC), High-performance liquid chromatography , or Nuclear magnetic resonance spectroscopy (NMR spectroscopy) or magnetic resonance spectroscopy (MRS). [ citation needed ] A yield determined using this approach is known as an internal standard yield . Yields are typically obtained in this manner to accurately determine the quantity of product produced by a reaction, irrespective of potential isolation problems. Additionally, they can be useful when isolation of the product is challenging or tedious, or when the rapid determination of an approximate yield is desired. Unless otherwise indicated, yields reported in the synthetic organic and inorganic chemistry literature refer to isolated yields, which better reflect the amount of pure product one is likely to obtain under the reported conditions, upon repeating the experimental procedure. [ citation needed ]
In their 2010 Synlett article, Martina Wernerova and organic chemist, Tomáš Hudlický, raised concerns about inaccurate reporting of yields, and offered solutions—including the proper characterization of compounds. [ 11 ] After performing careful control experiments, Wernerova and Hudlický said that each physical manipulation (including extraction/washing, drying over desiccant, filtration, and column chromatography) results in a loss of yield of about 2%. Thus, isolated yields measured after standard aqueous workup and chromatographic purification should seldom exceed 94%. [ 11 ] They called this phenomenon "yield inflation" and said that yield inflation had gradually crept upward in recent decades in chemistry literature. They attributed yield inflation to careless measurement of yield on reactions conducted on small scale, wishful thinking and a desire to report higher numbers for publication purposes. [ 11 ]
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In materials science and engineering , the yield point is the point on a stress–strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation .
The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. For most metals, such as aluminium and cold-worked steel , there is a gradual onset of non-linear behavior, and no precise yield point. In such a case, the offset yield point (or proof stress ) is taken as the stress at which 0.2% plastic deformation occurs. Yielding is a gradual failure mode which is normally not catastrophic , unlike ultimate failure .
For ductile materials, the yield strength is typically distinct from the ultimate tensile strength , which is the load-bearing capacity for a given material. The ratio of yield strength to ultimate tensile strength is an important parameter for applications such steel for pipelines , and has been found to be proportional to the strain hardening exponent . [ 1 ]
In solid mechanics , the yield point can be specified in terms of the three-dimensional principal stresses ( σ 1 , σ 2 , σ 3 {\displaystyle \sigma _{1},\sigma _{2},\sigma _{3}} ) with a yield surface or a yield criterion . A variety of yield criteria have been developed for different materials.
It is often difficult to precisely define yielding due to the wide variety of stress–strain curves exhibited by real materials. In addition, there are several possible ways to define yielding: [ 10 ]
Yielded structures have a lower stiffness, leading to increased deflections and decreased buckling strength. The structure will be permanently deformed when the load is removed, and may have residual stresses. Engineering metals display strain hardening, which implies that the yield stress is increased after unloading from a yield state.
Yield strength testing involves taking a small sample with a fixed cross-section area and then pulling it with a controlled, gradually increasing force until the sample changes shape or breaks. This is called a tensile test. Longitudinal and/or transverse strain is recorded using mechanical or optical extensometers.
Indentation hardness correlates roughly linearly with tensile strength for most steels, but measurements on one material cannot be used as a scale to measure strengths on another. [ 17 ] Hardness testing can therefore be an economical substitute for tensile testing, as well as providing local variations in yield strength due to, e.g., welding or forming operations. For critical situations, tension testing is often done to eliminate ambiguity. However, it is possible to obtain stress-strain curves from indentation-based procedures, provided certain conditions are met. These procedures are grouped under the term Indentation plastometry .
There are several ways in which crystalline materials can be engineered to increase their yield strength. By altering dislocation density, impurity levels, grain size (in crystalline materials), the yield strength of the material can be fine-tuned. This occurs typically by introducing defects such as impurities dislocations in the material. To move this defect (plastically deforming or yielding the material), a larger stress must be applied. This thus causes a higher yield stress in the material. While many material properties depend only on the composition of the bulk material, yield strength is extremely sensitive to the materials processing as well.
These mechanisms for crystalline materials include
Where deforming the material will introduce dislocations , which increases their density in the material. This increases the yield strength of the material since now more stress must be applied to move these dislocations through a crystal lattice. Dislocations can also interact with each other, becoming entangled.
The governing formula for this mechanism is:
where σ y {\displaystyle \sigma _{y}} is the yield stress, G is the shear elastic modulus, b is the magnitude of the Burgers vector , and ρ {\displaystyle \rho } is the dislocation density.
By alloying the material, impurity atoms in low concentrations will occupy a lattice position directly below a dislocation, such as directly below an extra half plane defect. This relieves a tensile strain directly below the dislocation by filling that empty lattice space with the impurity atom.
The relationship of this mechanism goes as:
where τ {\displaystyle \tau } is the shear stress , related to the yield stress, G {\displaystyle G} and b {\displaystyle b} are the same as in the above example, C s {\displaystyle C_{s}} is the concentration of solute and ϵ {\displaystyle \epsilon } is the strain induced in the lattice due to adding the impurity.
Where the presence of a secondary phase will increase yield strength by blocking the motion of dislocations within the crystal. A line defect that, while moving through the matrix, will be forced against a small particle or precipitate of the material. Dislocations can move through this particle either by shearing the particle or by a process known as bowing or ringing, in which a new ring of dislocations is created around the particle.
The shearing formula goes as:
and the bowing/ringing formula:
In these formulas, r particle {\displaystyle r_{\text{particle}}\,} is the particle radius, γ particle-matrix {\displaystyle \gamma _{\text{particle-matrix}}\,} is the surface tension between the matrix and the particle, l interparticle {\displaystyle l_{\text{interparticle}}\,} is the distance between the particles.
Where a buildup of dislocations at a grain boundary causes a repulsive force between dislocations. As grain size decreases, the surface area to volume ratio of the grain increases, allowing more buildup of dislocations at the grain edge. Since it requires much energy to move dislocations to another grain, these dislocations build up along the boundary, and increase the yield stress of the material. Also known as Hall-Petch strengthening, this type of strengthening is governed by the formula:
where
The theoretical yield strength of a perfect crystal is much higher than the observed stress at the initiation of plastic flow. [ 18 ]
That experimentally measured yield strength is significantly lower than the expected theoretical value can be explained by the presence of dislocations and defects in the materials. Indeed, whiskers with perfect single crystal structure and defect-free surfaces have been shown to demonstrate yield stress approaching the theoretical value. For example, nanowhiskers of copper were shown to undergo brittle fracture at 1 GPa, [ 19 ] a value much higher than the strength of bulk copper and approaching the theoretical value.
The theoretical yield strength can be estimated by considering the process of yield at the atomic level. In a perfect crystal, shearing results in the displacement of an entire plane of atoms by one interatomic separation distance, b, relative to the plane below. In order for the atoms to move, considerable force must be applied to overcome the lattice energy and move the atoms in the top plane over the lower atoms and into a new lattice site. The applied stress to overcome the resistance of a perfect lattice to shear is the theoretical yield strength, τ max .
The stress displacement curve of a plane of atoms varies sinusoidally as stress peaks when an atom is forced over the atom below and then falls as the atom slides into the next lattice point. [ 18 ]
where b {\displaystyle b} is the interatomic separation distance. Since τ = G γ and dτ/dγ = G at small strains (i.e. Single atomic distance displacements), this equation becomes:
For small displacement of γ=x/a, where a is the spacing of atoms on the slip plane, this can be rewritten as:
Giving a value of τ max {\displaystyle \tau _{\max }} τ max equal to:
The theoretical yield strength can be approximated as τ max = G / 30 {\displaystyle \tau _{\max }=G/30} .
During monotonic tensile testing, some metals such as annealed steel exhibit a distinct upper yield point or a delay in work hardening. [ 20 ] These tensile testing phenomena, wherein the strain increases but stress does not increase as expected, are two types of yield point elongation.
Yield Point Elongation (YPE) significantly impacts the usability of steel. In the context of tensile testing and the engineering stress-strain curve, the Yield Point is the initial stress level, below the maximum stress, at which an increase in strain occurs without an increase in stress. This characteristic is typical of certain materials, indicating the presence of YPE. [ 20 ] The mechanism for YPE has been related to carbon diffusion, and more specifically to Cottrell atmospheres .
YPE can lead to issues such as coil breaks, edge breaks, fluting, stretcher strain, and reel kinks or creases, which can affect both aesthetics and flatness. Coil and edge breaks may occur during either initial or subsequent customer processing, while fluting and stretcher strain arise during forming. Reel kinks, transverse ridges on successive inner wraps of a coil, are caused by the coiling process. [ 20 ]
When these conditions are undesirable, it is essential for suppliers to be informed to provide appropriate materials. The presence of YPE is influenced by chemical composition and mill processing methods such as skin passing or temper rolling, which temporarily eliminate YPE and improve surface quality. However, YPE can return over time due to aging, which is holding at a temperature usually 200-400 °C. [ 20 ]
Despite its drawbacks, YPE offers advantages in certain applications, such as roll forming , and reduces springback . Generally, steel with YPE is highly formable. [ 20 ]
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In computer science , yield is an action that occurs in a computer program during multithreading , of forcing a processor to relinquish control of the current running thread , and sending it to the end of the running queue , of the same scheduling priority.
Different programming languages implement yielding in various ways.
Coroutines are a fine-grained concurrency primitive, which may be required to yield explicitly. They may enable specifying another function to take control. Coroutines that explicitly yield allow cooperative multitasking .
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In materials science , the yield strength anomaly refers to materials wherein the yield strength (i.e., the stress necessary to initiate plastic yielding) increases with temperature. [ 1 ] [ 2 ] [ 3 ] For the majority of materials, the yield strength decreases with increasing temperature. In metals, this decrease in yield strength is due to the thermal activation of dislocation motion, resulting in easier plastic deformation at higher temperatures. [ 4 ]
In some cases, a yield strength anomaly refers to a decrease in the ductility of a material with increasing temperature, which is also opposite the trend in the majority of materials. Anomalies in ductility can be more clear, as an anomalous effect on yield strength can be obscured by its typical decrease with temperature. [ 5 ] In concert with yield strength or ductility anomalies, some materials demonstrate extrema in other temperature dependent properties, such as a minimum in ultrasonic damping, or a maximum in electrical conductivity . [ 6 ]
The yield strength anomaly in β-brass was one of the earliest discoveries such a phenomenon, [ 7 ] and several other ordered intermetallic alloys demonstrate this effect. Precipitation-hardened superalloys exhibit a yield strength anomaly over a considerable temperature range. For these materials, the yield strength shows little variation between room temperature and several hundred degrees Celsius. Eventually, a maximum yield strength is reached. For even higher temperatures, the yield strength decreases and, eventually, drops to zero when reaching the melting temperature , where the solid material transforms into a liquid . For ordered intermetallics , the temperature of the yield strength peak is roughly 50% of the absolute melting temperature . [ 8 ]
A number of alloys with the L1 2 structure ( e.g., Ni 3 Al, Ni 3 Ga, Ni 3 Ge, Ni 3 Si), show yield strength anomalies. [ 9 ] The L1 2 structure is a derivative of the face-centered cubic crystal structure. For these alloys, the active slip system below the peak is ⟨110⟩{111} while the active system at higher temperatures is ⟨110⟩{010}. The hardening mechanism in these alloys is the cross slip of screw dislocations from (111) to (010) crystallographic planes . [ 10 ] This cross slip is thermally activated, and the screw dislocations are much less mobile on the (010) planes, so the material is strengthened as temperatures increases and more screw dislocations are in the (010) plane. A similar mechanism has been proposed for some B2 alloys that have yield strength anomalies ( e.g., CuZn, FeCo, NiTi, CoHf, CoTi, CoZr). [ 8 ]
The yield strength anomaly mechanism in Ni-based superalloys is similar. [ 11 ] In these alloys, screw superdislocations undergo thermally activated cross slip onto {100} planes from {111} planes. This prevents motion of the remaining parts of the dislocations on the (111)[-101] slip system. Again, with increasing temperature, more cross-slip occurs, so dislocation motion is more hindered and yield strength increases.
In superalloys strengthened by metal carbides , increasingly large carbide particles form preferentially at grain boundaries, preventing grain boundary sliding at high temperatures. This leads to an increase in the yield strength, and thus a yield strength anomaly. [ 5 ]
While FeAl is a B2 alloy, the observed yield strength anomaly in FeAl is due to another mechanism. If cross-slip were the mechanism, then the yield strength anomaly would be rate dependent, as expected for a thermally activated process. Instead, yield strength anomaly is state dependent, which is a property that is dependent on the state of the material. As a result, vacancy activated strengthening is the most widely-accepted mechanism. [ 12 ] The vacancy formation energy is low for FeAl, allowing for an unusually high concentration of vacancies in FeAl at high temperatures (2.5% at 1000C for Fe-50Al). The vacancy formed in either aluminum-rich FeAl or through heating is an aluminum vacancy. [ 13 ]
At low temperatures around 300K, the yield strength either decreases or does not change with temperature. At moderate temperatures (0.35-0.45 T m ), yield strength has been observed to increase with an increased vacancy concentration, providing further evidence for a vacancy driven strengthening mechanism. [ 13 ] [ 8 ] The increase in yield strength from increased vacancy concentration is believed to be the result of dislocations being pinned by vacancies on the slip plane, causing the dislocations to bow. Then, above the peak stress temperature, vacancies can migrate as vacancy migration is easier with elevated temperatures. At those temperatures, vacancies no longer hinder dislocation motion but rather aid climb . In the vacancy strengthening model, the increased strength below the peak stress temperature is approximated as proportional to the vacancy concentration to the one-half with the vacancy concentration estimated using Maxwell-Boltzmann statistics . Thus, the strength can be estimated as e − E f / 2 k B T {\displaystyle e^{-E_{f}/2k_{B}T}} , with E f {\displaystyle E_{f}} being the vacancy formation energy and T being the absolute temperature. Above the peak stress temperature, a diffusion-assisted deformation mechanism can be used to describe strength since vacancies are now mobile and assist dislocation motion. Above the peak, the yield strength is strain rate dependent and thus, the peak yield strength is rate dependent. As a result, the peak stress temperature increases with an increased strain rate. Note, this is different than the yield strength anomaly, which is the yield strength below the peak, being rate dependent. The peak yield strength is also dependent on percent aluminum in the FeAl alloy. As the percent aluminum increases, the peak yield strength occurs at lower temperatures. [ 8 ]
The yield strength anomaly in FeAl alloys can be hidden if thermal vacancies are not minimized through a slow anneal at a relatively low temperature (~400 °C for ~5 days). [ 14 ] Further, the yield strength anomaly is not present in systems that use a very low strain rate as the peak yield strength is strain rate dependent and thus, would occur at temperatures too low to observe the yield strength anomaly. Additionally, since the formation of vacancies requires time, the peak yield strength magnitude is dependent on how long the material is held at the peak stress temperature. Also, the peak yield strength has been found not to be dependent on crystal orientation. [ 8 ]
Other mechanisms have been proposed including a cross slip mechanism similar to that for L1 2 , dislocation decomposition into less mobile segments at jogs, dislocation pinning, climb-lock mechanism, and slip vector transition. The slip vector transition from <111> to <100>. At the peak stress temperature, the slip system changes from <111> to <100>. The change is believed to be a result of glide in <111> becoming more difficult as temperature increases due to a friction mechanism. Then, dislocations in <100> have easier movement in comparison. [ 15 ] Another mechanism combines the vacancy strengthening mechanism with dislocation decomposition. FeAl with the addition of a tertiary additive such as Mn has been shown to also exhibit the yield stress anomaly. In contrast to FeAl, however, the peak yield strength or peak stress temperature of Fe 2 MnAl is not dependent on strain rate and thus, may not follow the vacancy activated strengthening mechanism. Instead, there an order-strengthening mechanism has been proposed. [ 8 ]
The yield strength anomaly is exploited in the design of gas turbines and jet engines that operate at high temperatures, where the materials used are selected based on their paramount yield and creep resistance. Superalloys can withstand high temperature loads far beyond the capabilities of steels and other alloys, and allow operation at higher temperatures, which improves efficiency . [ 16 ]
Materials with yield strength anomalies are used in nuclear reactors due to their high temperature mechanical properties and good corrosion resistance. [ 5 ]
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A yield surface is a five-dimensional surface in the six-dimensional space of stresses . The yield surface is usually convex and the state of stress of inside the yield surface is elastic. When the stress state lies on the surface the material is said to have reached its yield point and the material is said to have become plastic . Further deformation of the material causes the stress state to remain on the yield surface, even though the shape and size of the surface may change as the plastic deformation evolves. This is because stress states that lie outside the yield surface are non-permissible in rate-independent plasticity , though not in some models of viscoplasticity . [ 1 ]
The yield surface is usually expressed in terms of (and visualized in) a three-dimensional principal stress space ( σ 1 , σ 2 , σ 3 {\displaystyle \sigma _{1},\sigma _{2},\sigma _{3}} ), a two- or three-dimensional space spanned by stress invariants ( I 1 , J 2 , J 3 {\displaystyle I_{1},J_{2},J_{3}} ) or a version of the three-dimensional Haigh–Westergaard stress space . Thus we may write the equation of the yield surface (that is, the yield function) in the forms:
The first principal invariant ( I 1 {\displaystyle I_{1}} ) of the Cauchy stress ( σ {\displaystyle {\boldsymbol {\sigma }}} ), and the second and third principal invariants ( J 2 , J 3 {\displaystyle J_{2},J_{3}} ) of the deviatoric part ( s {\displaystyle {\boldsymbol {s}}} ) of the Cauchy stress are defined as:
where ( σ 1 , σ 2 , σ 3 {\displaystyle \sigma _{1},\sigma _{2},\sigma _{3}} ) are the principal values of σ {\displaystyle {\boldsymbol {\sigma }}} , ( s 1 , s 2 , s 3 {\displaystyle s_{1},s_{2},s_{3}} ) are the principal values of s {\displaystyle {\boldsymbol {s}}} , and
where I {\displaystyle {\boldsymbol {I}}} is the identity matrix.
A related set of quantities, ( p , q , r {\displaystyle p,q,r\,} ), are usually used to describe yield surfaces for cohesive frictional materials such as rocks, soils, and ceramics. These are defined as
where σ e q {\displaystyle \sigma _{\mathrm {eq} }} is the equivalent stress . However, the possibility of negative values of J 3 {\displaystyle J_{3}} and the resulting imaginary r {\displaystyle r} makes the use of these quantities problematic in practice.
Another related set of widely used invariants is ( ξ , ρ , θ {\displaystyle \xi ,\rho ,\theta \,} ) which describe a cylindrical coordinate system (the Haigh–Westergaard coordinates). These are defined as:
The ξ − ρ {\displaystyle \xi -\rho \,} plane is also called the Rendulic plane . The angle θ {\displaystyle \theta } is called stress angle, the value cos ( 3 θ ) {\displaystyle \cos(3\theta )} is sometimes called the Lode parameter [ 4 ] [ 5 ] [ 6 ] and the relation between θ {\displaystyle \theta } and J 2 , J 3 {\displaystyle J_{2},J_{3}} was first given by Novozhilov V.V. in 1951, [ 7 ] see also [ 8 ]
The principal stresses and the Haigh–Westergaard coordinates are related by
A different definition of the Lode angle can also be found in the literature: [ 9 ]
in which case the ordered principal stresses (where σ 1 ≥ σ 2 ≥ σ 3 {\displaystyle \sigma _{1}\geq \sigma _{2}\geq \sigma _{3}} ) are related by [ 10 ]
There are several different yield surfaces known in engineering, and those most popular are listed below.
The Tresca yield criterion is taken to be the work of Henri Tresca . [ 11 ] It is also known as the maximum shear stress theory (MSST) and the Tresca–Guest [ 12 ] (TG) criterion. In terms of the principal stresses the Tresca criterion is expressed as
Where S s y {\displaystyle S_{sy}} is the yield strength in shear, and S y {\displaystyle S_{y}} is the tensile yield strength.
Figure 1 shows the Tresca–Guest yield surface in the three-dimensional space of principal stresses. It is a prism of six sides and having infinite length. This means that the material remains elastic when all three principal stresses are roughly equivalent (a hydrostatic pressure ), no matter how much it is compressed or stretched. However, when one of the principal stresses becomes smaller (or larger) than the others the material is subject to shearing. In such situations, if the shear stress reaches the yield limit then the material enters the plastic domain. Figure 2 shows the Tresca–Guest yield surface in two-dimensional stress space, it is a cross section of the prism along the σ 1 , σ 2 {\displaystyle \sigma _{1},\sigma _{2}} plane.
The von Mises yield criterion is expressed in the principal stresses as
where S y {\displaystyle S_{y}} is the yield strength in uniaxial tension.
Figure 3 shows the von Mises yield surface in the three-dimensional space of principal stresses. It is a circular cylinder of infinite length with its axis inclined at equal angles to the three principal stresses. Figure 4 shows the von Mises yield surface in two-dimensional space compared with Tresca–Guest criterion. A cross section of the von Mises cylinder on the plane of σ 1 , σ 2 {\displaystyle \sigma _{1},\sigma _{2}} produces the elliptical shape of the yield surface.
This criterion [ 13 ] [ 14 ] reformulated as the function of the hydrostatic nodes with the coordinates 1 / γ 1 {\displaystyle 1/\gamma _{1}} and 1 / γ 2 {\displaystyle 1/\gamma _{2}}
represents the general equation of a second order surface of revolution about the hydrostatic axis. Some special case are: [ 15 ]
The relations compression-tension and torsion-tension can be computed to
The Poisson's ratios at tension and compression are obtained using
For ductile materials the restriction
is important. The application of rotationally symmetric criteria for brittle failure with
has not been studied sufficiently. [ 16 ]
The Burzyński-Yagn criterion is well suited for academic purposes. For practical applications, the third invariant of the deviator in the odd and even power should be introduced in the equation, e.g.: [ 17 ]
The Huber criterion consists of the Beltrami ellipsoid and a scaled von Mises cylinder in the principal stress space, [ 18 ] [ 19 ] [ 20 ] [ 21 ] see also [ 22 ] [ 23 ]
with γ 1 ∈ [ 0 , 1 [ {\displaystyle \gamma _{1}\in [0,1[} . The transition between the surfaces in the cross section I 1 = 0 {\displaystyle I_{1}=0} is continuously differentiable.
The criterion represents the "classical view" with respect to inelastic material behavior:
The Huber criterion can be used as a yield surface with an empirical restriction for Poisson's ratio at tension ν + i n ∈ [ 0.48 , 1 / 2 ] {\displaystyle \nu _{+}^{\mathrm {in} }\in [0.48,1/2]} , which leads to γ 1 ∈ [ 0 , 0.1155 ] {\displaystyle \gamma _{1}\in [0,0.1155]} .
The modified Huber criterion, [ 24 ] [ 23 ] see also, [ 25 ] cf. [ 26 ]
consists of the Schleicher ellipsoid with the restriction of Poisson's ratio at compression
and a cylinder with the C 1 {\displaystyle C^{1}} -transition in the cross section I 1 = − d σ + {\displaystyle I_{1}=-d\,\sigma _{\mathrm {+} }} .
The second setting for the parameters γ 1 ∈ [ 0 , 1 [ {\displaystyle \gamma _{1}\in [0,1[} and γ 2 < 0 {\displaystyle \gamma _{2}<0} follows with the compression / tension relation
The modified Huber criterion can be better fitted to the measured data as the Huber criterion. For setting ν + i n = 0.48 {\displaystyle \nu _{+}^{\mathrm {in} }=0.48} it follows γ 1 = 0.0880 {\displaystyle \gamma _{1}=0.0880} and γ 2 = − 0.0747 {\displaystyle \gamma _{2}=-0.0747} .
The Huber criterion and the modified Huber criterion should be preferred to the von Mises criterion since one obtains safer results in the region I 1 > σ + {\displaystyle I_{1}>\sigma _{\mathrm {+} }} .
For practical applications the third invariant of the deviator I 3 ′ {\displaystyle I_{3}'} should be considered in these criteria. [ 23 ]
The Mohr–Coulomb yield (failure) criterion is similar to the Tresca criterion, with additional provisions for materials with different tensile and compressive yield strengths. This model is often used to model concrete , soil or granular materials . The Mohr–Coulomb yield criterion may be expressed as:
where
and the parameters S y c {\displaystyle S_{yc}} and S y t {\displaystyle S_{yt}} are the yield (failure) stresses of the material in uniaxial compression and tension, respectively. The formula reduces to the Tresca criterion if S y c = S y t {\displaystyle S_{yc}=S_{yt}} .
Figure 5 shows Mohr–Coulomb yield surface in the three-dimensional space of principal stresses. It is a conical prism and K {\displaystyle K} determines the inclination angle of conical surface. Figure 6 shows Mohr–Coulomb yield surface in two-dimensional stress space. In Figure 6 R r {\displaystyle R_{r}} and R c {\displaystyle R_{c}} is used for S y t {\displaystyle S_{yt}} and S y c {\displaystyle S_{yc}} , respectively, in the formula. It is a cross section of this conical prism on the plane of σ 1 , σ 2 {\displaystyle \sigma _{1},\sigma _{2}} . In Figure 6 Rr and Rc are used for Syc and Syt, respectively, in the formula.
The Drucker–Prager yield criterion is similar to the von Mises yield criterion, with provisions for handling materials with differing tensile and compressive yield strengths. This criterion is most often used for concrete where both normal and shear stresses can determine failure. The Drucker–Prager yield criterion may be expressed as
where
and S y c {\displaystyle S_{yc}} , S y t {\displaystyle S_{yt}} are the uniaxial yield stresses in compression and tension respectively. The formula reduces to the von Mises equation if S y c = S y t {\displaystyle S_{yc}=S_{yt}} .
Figure 7 shows Drucker–Prager yield surface in the three-dimensional space of principal stresses. It is a regular cone . Figure 8 shows Drucker–Prager yield surface in two-dimensional space. The elliptical elastic domain is a cross section of the cone on the plane of σ 1 , σ 2 {\displaystyle \sigma _{1},\sigma _{2}} ; it can be chosen to intersect the Mohr–Coulomb yield surface in different number of vertices. One choice is to intersect the Mohr–Coulomb yield surface at three vertices on either side of the σ 1 = − σ 2 {\displaystyle \sigma _{1}=-\sigma _{2}} line, but usually selected by convention to be those in the compression regime. [ 27 ] Another choice is to intersect the Mohr–Coulomb yield surface at four vertices on both axes (uniaxial fit) or at two vertices on the diagonal σ 1 = σ 2 {\displaystyle \sigma _{1}=\sigma _{2}} (biaxial fit). [ 28 ] The Drucker-Prager yield criterion is also commonly expressed in terms of the material cohesion and friction angle .
The Bresler–Pister yield criterion is an extension of the Drucker Prager yield criterion that uses three parameters, and has additional terms for materials that yield under hydrostatic compression.
In terms of the principal stresses, this yield criterion may be expressed as
where c 0 , c 1 , c 2 {\displaystyle c_{0},c_{1},c_{2}} are material constants. The additional parameter c 2 {\displaystyle c_{2}} gives the yield surface an ellipsoidal cross section when viewed from a direction perpendicular to its axis. If σ c {\displaystyle \sigma _{c}} is the yield stress in uniaxial compression, σ t {\displaystyle \sigma _{t}} is the yield stress in uniaxial tension, and σ b {\displaystyle \sigma _{b}} is the yield stress in biaxial compression, the parameters can be expressed as
The Willam–Warnke yield criterion is a three-parameter smoothed version of the Mohr–Coulomb yield criterion that has similarities in form to the Drucker–Prager and Bresler–Pister yield criteria.
The yield criterion has the functional form
However, it is more commonly expressed in Haigh–Westergaard coordinates as
The cross-section of the surface when viewed along its axis is a smoothed triangle (unlike Mohr–Coulomb). The Willam–Warnke yield surface is convex and has unique and well defined first and second derivatives on every point of its surface. Therefore, the Willam–Warnke model is computationally robust and has been used for a variety of cohesive-frictional materials.
Normalized with respect to the uniaxial tensile stress σ e q = σ + {\displaystyle \sigma _{\mathrm {eq} }=\sigma _{+}} , the Podgórski criterion [ 29 ] as function of the stress angle θ {\displaystyle \theta } reads
with the shape function of trigonal symmetry in the π {\displaystyle \pi } -plane
It contains the criteria of von Mises (circle in the π {\displaystyle \pi } -plane, β 3 = [ 0 , 1 ] {\displaystyle \beta _{3}=[0,\,1]} , χ 3 = 0 {\displaystyle \chi _{3}=0} ), Tresca (regular hexagon, β 3 = 1 / 2 {\displaystyle \beta _{3}=1/2} , χ 3 = { 1 , − 1 } {\displaystyle \chi _{3}=\{1,-1\}} ), Mariotte (regular triangle, β 3 = { 0 , 1 } {\displaystyle \beta _{3}=\{0,1\}} , χ 3 = { 1 , − 1 } {\displaystyle \chi _{3}=\{1,-1\}} ), Ivlev [ 30 ] (regular triangle, β 3 = { 1 , 0 } {\displaystyle \beta _{3}=\{1,0\}} , χ 3 = { 1 , − 1 } {\displaystyle \chi _{3}=\{1,-1\}} ) and also the cubic criterion of Sayir [ 31 ] (the Ottosen criterion [ 32 ] ) with β 3 = { 0 , 1 } {\displaystyle \beta _{3}=\{0,1\}} and the isotoxal (equilateral) hexagons of the Capurso criterion [ 30 ] [ 31 ] [ 33 ] with χ 3 = { 1 , − 1 } {\displaystyle \chi _{3}=\{1,-1\}} . The von Mises - Tresca transition [ 34 ] follows with β 3 = 1 / 2 {\displaystyle \beta _{3}=1/2} , χ 3 = [ 0 , 1 ] {\displaystyle \chi _{3}=[0,1]} . The isogonal (equiangular) hexagons of the Haythornthwaite criterion [ 23 ] [ 35 ] [ 36 ] containing the Schmidt-Ishlinsky criterion (regular hexagon) cannot be described with the Podgórski ctiterion.
The Rosendahl criterion [ 37 ] [ 38 ] [ 39 ] reads
with the shape function of hexagonal symmetry in the π {\displaystyle \pi } -plane
It contains the criteria of von Mises (circle, β 6 = [ 0 , 1 ] {\displaystyle \beta _{6}=[0,\,1]} , χ 6 = 0 {\displaystyle \chi _{6}=0} ), Tresca (regular hexagon, β 6 = { 1 , 0 } {\displaystyle \beta _{6}=\{1,0\}} , χ 6 = { 1 , − 1 } {\displaystyle \chi _{6}=\{1,-1\}} ), Schmidt—Ishlinsky (regular hexagon, β 6 = { 0 , 1 } {\displaystyle \beta _{6}=\{0,1\}} , χ 6 = { 1 , − 1 } {\displaystyle \chi _{6}=\{1,-1\}} ), Sokolovsky (regular dodecagon, β 6 = 1 / 2 {\displaystyle \beta _{6}=1/2} , χ 6 = { 1 , − 1 } {\displaystyle \chi _{6}=\{1,-1\}} ), and also the bicubic criterion [ 23 ] [ 37 ] [ 40 ] [ 41 ] with β 6 = 0 {\displaystyle \beta _{6}=0} or equally with β 6 = 1 {\displaystyle \beta _{6}=1} and the isotoxal dodecagons of the unified yield criterion of Yu [ 42 ] with χ 6 = { 1 , − 1 } {\displaystyle \chi _{6}=\{1,-1\}} . The isogonal dodecagons of the multiplicative ansatz criterion of hexagonal symmetry [ 23 ] containing the Ishlinsky-Ivlev criterion (regular dodecagon) cannot be described by the Rosendahl criterion.
The criteria of Podgórski and Rosendahl describe single surfaces in principal stress space without any additional outer contours and plane intersections. Note that in order to avoid numerical issues the real part function R e {\displaystyle Re} can be introduced to the shape function: R e ( Ω 3 ) {\displaystyle Re(\Omega _{3})} and R e ( Ω 6 ) {\displaystyle Re(\Omega _{6})} . The generalization in the form Ω 3 n {\displaystyle \Omega _{3n}} [ 37 ] is relevant for theoretical investigations.
A pressure-sensitive extension of the criteria can be obtained with the linear I 1 {\displaystyle I_{1}} -substitution [ 23 ]
which is sufficient for many applications, e.g. metals, cast iron, alloys, concrete, unreinforced polymers, etc.
The Bigoni–Piccolroaz yield criterion [ 43 ] [ 44 ] is a seven-parameter surface defined by
where F ( p ) {\displaystyle F(p)} is the "meridian" function
describing the pressure-sensitivity and g ( θ ) {\displaystyle g(\theta )} is the "deviatoric" function [ 45 ]
describing the Lode-dependence of yielding. The seven, non-negative material parameters:
define the shape of the meridian and deviatoric sections.
This criterion represents a smooth and convex surface, which is closed both in hydrostatic tension and compression and has a
drop-like shape, particularly suited to describe frictional and granular materials. This criterion has also been generalized to the case of surfaces with corners. [ 46 ]
For the formulation of the strength criteria the stress angle
can be used.
The following criterion of isotropic material behavior
contains a number of other well-known less general criteria, provided suitable parameter values are chosen.
Parameters c 3 {\displaystyle c_{3}} and c 6 {\displaystyle c_{6}} describe the geometry of the surface in the π {\displaystyle \pi } -plane. They are subject to the constraints
which follow from the convexity condition. A more precise formulation of the third constraints is proposed in. [ 47 ] [ 48 ]
Parameters γ 1 ∈ [ 0 , 1 [ {\displaystyle \gamma _{1}\in [0,\,1[} and γ 2 {\displaystyle \gamma _{2}} describe the position of the intersection points of the yield surface with hydrostatic axis (space diagonal in the principal stress space). These intersections points are called hydrostatic nodes.
In the case of materials which do not fail at hydrostatic pressure (steel, brass, etc.) one gets γ 2 ∈ [ 0 , γ 1 [ {\displaystyle \gamma _{2}\in [0,\,\gamma _{1}[} . Otherwise for materials which fail at hydrostatic pressure (hard foams, ceramics, sintered materials, etc.) it follows γ 2 < 0 {\displaystyle \gamma _{2}<0} .
The integer powers l ≥ 0 {\displaystyle l\geq 0} and m ≥ 0 {\displaystyle m\geq 0} , l + m < 6 {\displaystyle l+m<6} describe the curvature of the meridian. The meridian with l = m = 0 {\displaystyle l=m=0} is a straight line and with l = 0 {\displaystyle l=0} – a parabola.
For the anisotropic materials, depending on the direction of the applied process (e.g., rolling) the mechanical properties vary and, therefore, using an anisotropic yield function is crucial. Since 1989 Frederic Barlat has developed a family of yield functions for constitutive modelling of plastic anisotropy. Among them, Yld2000-2D yield criteria has been applied for a wide range of sheet metals (e.g., aluminum alloys and advanced high-strength steels). The Yld2000-2D model is a non-quadratic type yield function based on two linear transformation of the stress tensor:
for principal values of X’ and X”, the model could be expressed as:
and:
where α 1 . . . α 8 {\displaystyle \alpha _{1}...\alpha _{8}} are eight parameters of the Barlat's Yld2000-2D model to be identified with a set of experiments.
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Yip-Wah Chung (born 1950 [ 1 ] ) is a materials scientist at Northwestern University . He is a professor of materials science & engineering , and, by courtesy, of mechanical engineering within the McCormick School of Engineering , [ 2 ] and serves as co-director of the mechanical engineering–materials science & engineering Master of Science program. [ 3 ]
Chung was raised in Hong Kong , [ 4 ] and holds a B.S. and an M.S. in physics from the University of Hong Kong , as well as a Ph.D. in physics from the University of California, Berkeley . [ 2 ] He joined Northwestern, after obtaining his doctorate; at Northwestern, he previously served as department chair of materials science & engineering (1992–1998). [ 5 ]
His research includes work on energy efficiency , surface engineering , and tribology . In 2016, Chung, Jiaxing Huang , and other co-authors published an article in the Proceedings of the National Academy of Sciences describing how a lubricant containing crumpled graphene could provide higher lubrication performance than other lubricant oils. [ 6 ] In 2017, Chung was featured in the Northwestern Engineering magazine for his research on improving energy efficiency. The article describes a development by Chung and others on reducing friction within automobiles. Their development, a lubricant additive, "can reduce friction by up to 70 percent and wear by up to 90 percent compared to conventional lubricant counterparts." [ 7 ] In 2019, Chung was interviewed by Tribology & Lubrication Technology . In his interview, he expressed sentiment that communication skills are a vital part of career tribology, and are not emphasized enough in education. [ 5 ]
In 2002, Chung, Leon M. Keer , and Kornel Ehmann won the Innovative Research Award, conferred by the tribology division of the American Society of Mechanical Engineers . [ 8 ] For his contributions to surface engineering and coatings , Chung received the 2024 R.F. Bunshah Award from the Advanced Surface Engineering Division, American Vacuum Society . [ 9 ] [ 10 ] As of 2024, he is a fellow of ASM International , American Vacuum Society, and the Society of Tribologists and Lubrication Engineers . [ 2 ]
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Yliaster or Iliaster , a term coined by Paracelsus , refers to "prime matter, consisting of body and soul".
Paracelsus described the Iliaster as the "completely healed human being who has burned away all the dross of his lower being and is free to fly as the Phoenix." [ 1 ] It is most likely a portmanteau of the Greek hyle (matter) and Latin astrum (star). To Paracelsus, the Iliaster represented the two basic compounds of the cosmos, matter representing "below", and the stars representing "above". Paracelsus says this of the Yliaster while describing how fossils are trapped in wood:
Accordingly, the first body, the Yliaster, was nothing but a clod which contained all the chaos, all the waters, all minerals, all herbs, all stones, all gems. Only the supreme Master could release them and form them with tender solicitude, so that other things could be created from the rest. [ 2 ]
In this sense, the Yliaster is the same as the Prima Materia . It is the formless base of all matter which is the raw material for the alchemical Great Work .
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An ylide ( / ˈ ɪ l aɪ d / ) [ 1 ] or ylid ( / ˈ ɪ l ɪ d / ) is a neutral dipolar molecule containing a formally negatively charged atom (usually a carbanion ) directly attached to a heteroatom with a formal positive charge (usually nitrogen, phosphorus or sulfur), and in which both atoms have full octets of electrons. The result can be viewed as a structure in which two adjacent atoms are connected by both a covalent and an ionic bond ; normally written X + –Y − . Ylides are thus 1,2- dipolar compounds , and a subclass of zwitterions . [ 2 ] They appear in organic chemistry as reagents or reactive intermediates . [ 3 ]
The class name "ylide" for the compound should not be confused with the suffix "-ylide".
Many ylides may be depicted by a multiply bonded form in a resonance structure , known as the ylene form, while the actual structure lies in between both forms: [ citation needed ]
The actual bonding picture of these types of ylides is strictly zwitterionic (the structure on the right) with the strong Coulombic attraction between the "onium" atom and the adjacent carbon accounting for the reduced bond length. Consequently, the carbon anion is trigonal pyramidal. [ citation needed ]
Phosphonium ylides are used in the Wittig reaction , a method used to convert ketones and especially aldehydes to alkenes. The positive charge in these Wittig reagents is carried by a phosphorus atom with three phenyl substituents and a bond to a carbanion . Ylides can be 'stabilised' or 'non-stabilised'. A phosphonium ylide can be prepared rather straightforwardly. Typically, triphenylphosphine is allowed to react with an alkyl halide in a mechanism analogous to that of an S N 2 reaction . This quaternization forms an alkyltriphenyl phosphonium salt, which can be isolated or treated in situ with a strong base (in this case, butyllithium ) to form the ylide.
Due to the S N 2 mechanism, a less sterically hindered alkyl halide reacts more favorably with triphenylphosphine than an alkyl halide with significant steric hindrance (such as tert-butyl bromide ). Because of this, there will typically be one synthetic route in a synthesis involving such compounds that is more favorable than another.
Phosphorus ylides are important reagents in organic chemistry, especially in the synthesis of naturally occurring products with
biological and pharmacological activities. Much of the interest in the coordination properties of a-keto stabilized phosphorus
ylides stems from their coordination versatility due to the presence of different functional groups in their molecular structure.
The a-keto stabilized ylides derived from bisphosphines like dppe , dppm , etc., viz., [Ph 2 PCH 2 PPh 2 ]C(H)C(O)R and [Ph 2 PCH 2 CH 2 PPh 2 ]C(H)C(O)R (R = Me, Ph or OMe) constitute an important class of hybrid ligands containing both phosphine and ylide functionalities, and can exist in ylidic and enolate forms. These ligands can therefore be engaged in different kinds of bonding with metal ions like palladium and platinum . [ 4 ]
Other common ylides include sulfonium ylides and sulfoxonium ylides ; for instance, the Corey-Chaykovsky reagent used in the preparation of epoxides or in the Stevens rearrangement .
Carbonyl ylides (RR'C=O + C − RR') can form by ring-opening of epoxides or by reaction of carbonyls with electrophilic carbenes , [ 5 ] which are usually prepared from diazo compounds. Oxonium ylides (RR'-O + -C − R'R) are formed by the reaction of ethers with electrophilic carbenes .
Certain nitrogen -based ylides also exist such as azomethine ylides with the general structure:
These compounds can be envisioned as iminium cations placed next to a carbanion . The substituents R 1 , R 2 are electron withdrawing groups . These ylides can be generated by condensation of an α- amino acid and an aldehyde or by thermal ring opening reaction of certain N-substituted aziridines .
The further-unsaturated nitrile ylides are known almost exclusively as unstable intermediates.
A rather exotic family of dinitrogen-based ylides are the isodiazenes (R 1 R 2 N + =N – ), which generally decompose by extrusion of dinitrogen.
Stable carbenes also have a ylidic resonance contributor, e.g. :
Halonium ylides can be prepared from allyl halides and metal carbenoids . After a [2,3]-rearrangement, a homoallylhalide is obtained.
The active form of Tebbe's reagent is often considered a titanium ylide. Like the Wittig reagent, it is able to replace the oxygen atom on carbonyl groups with a methylene group. Compared with the Wittig reagent, it has more functional group tolerance.
An important ylide reaction is of course the Wittig reaction (for phosphorus) but there are more.
Some ylides are 1,3-dipoles and interact in 1,3-dipolar cycloadditions . For instance an azomethine ylide is a dipole in the Prato reaction with fullerenes .
In the presence of the group 3 homoleptic catalyst Y[N(SiMe 3 ) 2 ] 3 , triphenylphosphonium methylide can be coupled with phenylsilane . [ 6 ] This reaction produces H 2 gas as a byproduct, and forms a silyl-stabilised ylide.
Many ylides react in sigmatropic reactions . [ 7 ] The Sommelet-Hauser rearrangement is an example of a [2,3]-sigmatropic reaction. The Stevens rearrangement is a [1,2]-rearrangement.
A [3,3]-sigmatropic reaction has been observed in certain phosphonium ylides. [ 8 ] [ 9 ]
Wittig reagents are found to react as nucleophiles in S N 2' substitution : [ 10 ]
The initial addition reaction is followed by an elimination reaction .
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In organic chemistry , an ynone is an organic compound containing a ketone ( >C=O ) functional group and a C≡C triple bond . Many ynones are α,β-ynones, where the carbonyl and alkyne groups are conjugated. Capillin is a naturally occurring example. Some ynones are not conjugated .
One method for synthesizing ynones is the acyl substitution reaction of an alkynyldimethylaluminum with an acyl chloride . An alkynyldimethylaluminum compound is the reaction product of trimethylaluminum and a terminal alkyne . [ 1 ]
An alternative is the direct coupling of an acyl chloride with a terminal alkyne, using a copper-based nanocatalyst: [ 2 ]
Other methods utilize an oxidative cleavage of an aldehyde , followed by reaction with a hypervalent alkynyl iodide, using a gold catalyst. [ 3 ]
An alternative but longer synthetic method involves the reaction of an alkynyllithium compound with an aldehyde. The reaction produces a secondary alcohol that then can be oxidized via the Swern oxidation .
Terminal alkynes add across α,β-unsaturated ketones in the presence of palladium catalysts. The reaction affords γ,δ-ynones. [ 4 ] Terminal alkynes add across epoxides to given yneols, which can be oxidized to give β,γ-ynones. [ 5 ]
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In software development , the yo-yo problem is an anti-pattern that occurs when a programmer has to read and understand a program whose inheritance graph is so long and complicated that the programmer has to keep flipping between many different class definitions in order to follow the control flow of the program. It is most often seen in the context of object-oriented programming . The term comes from comparing the bouncing attention of the programmer to the up-down movement of a toy yo-yo . Taenzer, Ganti, and Podar described the problem by name, explaining: "Often we get the feeling of riding a yoyo when we try to understand one of these message trees." [ 1 ]
Most practices of object-oriented programming recommend keeping the inheritance graph as shallow as possible, in part to avoid this problem. The use of composition instead of inheritance is also strongly preferred, although this still requires that a programmer keep multiple class definitions in mind at once.
Deep hierarchies are a code smell and a symptom of sub-classification for code reuse . [ 2 ]
More generally, the yo-yo problem can also refer to any situation where a person must keep flipping between different sources of information in order to understand a concept.
There are several code refactor techniques to flatten these hierarchies without compromising the overall behavior.
Object-oriented design techniques such as documenting layers of the inheritance hierarchy can reduce the effect of this problem, as they collect in one place the information that the programmer is required to understand.
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Yohkoh ( Japanese : ようこう , 'Sunbeam'), known before launch as Solar-A , was a Solar observatory spacecraft of the Institute of Space and Astronautical Science (Japan), in collaboration with space agencies in the United States and the United Kingdom . It was launched into Earth orbit on August 30, 1991 by the M-3SII rocket from Kagoshima Space Center . It took its first soft X-ray image on 13 September 1991, 21:53:40, [ 1 ] and movie representations of the X-ray corona over 1991-2001 are available at the Yohkoh Legacy site .
The satellite was three-axis stabilized and in a near-circular orbit. It carried four instruments: a Soft X-ray Telescope (SXT), a Hard X-ray Telescope (HXT), a Bragg Crystal Spectrometer (BCS), and a Wide Band Spectrometer (WBS). About 50 MB were generated each day and stored on board by a 10.5 MB bubble memory recorder.
Because SXT utilized a charge-coupled device (CCD) as its readout device, perhaps being the first X-ray astronomical telescope to do so, its "data cube" of images was both extensive and convenient, and it revealed much interesting detail about the behavior of the solar corona.
Previous solar soft X-ray observations, such as those of Skylab , had been restricted to film as a readout device.
Yohkoh therefore returned many novel scientific results, especially regarding solar flares and other forms of magnetic activity. [ 2 ]
The mission ended after more than ten years of successful observation when it went into its "safehold" mode during an annular eclipse on 14 December 2001, 20:58:33 and the spacecraft lost lock on the Sun. Operational mistakes and other flaws combined in such a way that its solar panels could no longer charge the batteries, which drained irreversibly; several other solar eclipses had successfully been observed. [ citation needed ]
On 12 September 2005, the spacecraft burned up during reentry over South Asia. The time of reentry, as provided by the U.S. Space Surveillance Network , was 6:16 pm Japan Standard Time (JST). [ citation needed ]
Yohkoh carried four instruments : [ 3 ]
The CCD was 1024×1024 pixels with pixel angular size of 2.45″×2.45″, a point-spread function (core width FWHM ) of about 1.5 pixels (i.e. 3.7″), a field of view of 42′×42′, which was a little larger than the whole solar disk. Typical time resolution was 2 s in flare mode and 8 s in quiet (no flare) mode, the maximum time resolution in 0.5 s.
For spectral discrimination, SXT employed wide-band filters installed on a filter wheel. There were five usable filter positions: 1265 Å -thick Al filter (2.5 Å–36 Å pass band), Al/Mg/Mn filter (2.4 Å–32 Å), 2.52 μm Mg filter (2.4 Å–23 Å), 11.6 μm Al filter (2.4 Å–13 Å), 119 μm Be filter (2.3 Å–10 Å). Before the entrance filter failure in November 1992 three more filter positions were available: no analysis filter (2.5 Å–46 Å), Wide band optical filter (4600 Å–4800 Å), Narrow band optical filter (4290 Å–4320 Å).
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In mathematics , the Yoneda lemma is a fundamental result in category theory . [ 1 ] It is an abstract result on functors of the type morphisms into a fixed object . It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only isomorphisms). It also generalizes the information-preserving relation between a term and its continuation-passing style transformation from programming language theory . [ 2 ] It allows the embedding of any locally small category into a category of functors ( contravariant set-valued functors) defined on that category. It also clarifies how the embedded category, of representable functors and their natural transformations , relates to the other objects in the larger functor category. It is an important tool that underlies several modern developments in algebraic geometry and representation theory . It is named after Nobuo Yoneda .
The Yoneda lemma suggests that instead of studying the locally small category C {\displaystyle {\mathcal {C}}} , one should study the category of all functors of C {\displaystyle {\mathcal {C}}} into S e t {\displaystyle \mathbf {Set} } (the category of sets with functions as morphisms ). S e t {\displaystyle \mathbf {Set} } is a category we think we understand well, and a functor of C {\displaystyle {\mathcal {C}}} into S e t {\displaystyle \mathbf {Set} } can be seen as a "representation" of C {\displaystyle {\mathcal {C}}} in terms of known structures. The original category C {\displaystyle {\mathcal {C}}} is contained in this functor category, but new objects appear in the functor category, which were absent and "hidden" in C {\displaystyle {\mathcal {C}}} . Treating these new objects just like the old ones often unifies and simplifies the theory.
This approach is akin to (and in fact generalizes) the common method of studying a ring by investigating the modules over that ring. The ring takes the place of the category C {\displaystyle {\mathcal {C}}} , and the category of modules over the ring is a category of functors defined on C {\displaystyle {\mathcal {C}}} .
Yoneda's lemma concerns functors from a fixed category C {\displaystyle {\mathcal {C}}} to a category of sets , S e t {\displaystyle \mathbf {Set} } . If C {\displaystyle {\mathcal {C}}} is a locally small category (i.e. the hom-sets are actual sets and not proper classes ), then each object A {\displaystyle A} of C {\displaystyle {\mathcal {C}}} gives rise to a functor to S e t {\displaystyle \mathbf {Set} } called a hom-functor . This functor is denoted:
The ( covariant ) hom-functor h A {\displaystyle h_{A}} sends X ∈ C {\displaystyle X\in {\mathcal {C}}} to the set of morphisms H o m ( A , X ) {\displaystyle \mathrm {Hom} (A,X)} and sends a morphism f : X → Y {\displaystyle f\colon X\to Y} (where Y ∈ C {\displaystyle Y\in {\mathcal {C}}} ) to the morphism f ∘ − {\displaystyle f\circ -} (composition with f {\displaystyle f} on the left) that sends a morphism g {\displaystyle g} in H o m ( A , X ) {\displaystyle \mathrm {Hom} (A,X)} to the morphism f ∘ g {\displaystyle f\circ g} in H o m ( A , Y ) {\displaystyle \mathrm {Hom} (A,Y)} . That is,
Yoneda's lemma says that:
Lemma (Yoneda) — Let F {\displaystyle F} be a functor from a locally small category C {\displaystyle {\mathcal {C}}} to S e t {\displaystyle \mathbf {Set} } . Then for each object A {\displaystyle A} of C {\displaystyle {\mathcal {C}}} , the natural transformations N a t ( h A , F ) ≡ H o m ( H o m ( A , − ) , F ) {\displaystyle \mathrm {Nat} (h_{A},F)\equiv \mathrm {Hom} (\mathrm {Hom} (A,-),F)} from h A {\displaystyle h_{A}} to F {\displaystyle F} are in one-to-one correspondence with the elements of F ( A ) {\displaystyle F(A)} . That is,
Moreover, this isomorphism is natural in A {\displaystyle A} and F {\displaystyle F} when both sides are regarded as functors from C × S e t C {\displaystyle {\mathcal {C}}\times \mathbf {Set} ^{\mathcal {C}}} to S e t {\displaystyle \mathbf {Set} } .
Here the notation S e t C {\displaystyle \mathbf {Set} ^{\mathcal {C}}} denotes the category of functors from C {\displaystyle {\mathcal {C}}} to S e t {\displaystyle \mathbf {Set} } .
Given a natural transformation Φ {\displaystyle \Phi } from h A {\displaystyle h_{A}} to F {\displaystyle F} , the corresponding element of F ( A ) {\displaystyle F(A)} is u = Φ A ( i d A ) {\displaystyle u=\Phi _{A}(\mathrm {id} _{A})} ; [ a ] and given an element u {\displaystyle u} of F ( A ) {\displaystyle F(A)} , the corresponding natural transformation is given by Φ X ( f ) = F ( f ) ( u ) {\displaystyle \Phi _{X}(f)=F(f)(u)} which assigns to a morphism f : A → X {\displaystyle f\colon A\to X} a value of F ( X ) {\displaystyle F(X)} .
There is a contravariant version of Yoneda's lemma, [ 3 ] which concerns contravariant functors from C {\displaystyle {\mathcal {C}}} to S e t {\displaystyle \mathbf {Set} } . This version involves the contravariant hom-functor
which sends X {\displaystyle X} to the hom-set H o m ( X , A ) {\displaystyle \mathrm {Hom} (X,A)} . Given an arbitrary contravariant functor G {\displaystyle G} from C {\displaystyle {\mathcal {C}}} to S e t {\displaystyle \mathbf {Set} } , Yoneda's lemma asserts that
The bijections provided in the (covariant) Yoneda lemma (for each A {\displaystyle A} and F {\displaystyle F} ) are the components of a natural isomorphism between two certain functors from C × S e t C {\displaystyle {\mathcal {C}}\times \mathbf {Set} ^{\mathcal {C}}} to S e t {\displaystyle \mathbf {Set} } . [ 4 ] : 61 One of the two functors is the evaluation functor
that sends a pair ( f , Φ ) {\displaystyle (f,\Phi )} of a morphism f : A → B {\displaystyle f\colon A\to B} in C {\displaystyle {\mathcal {C}}} and a natural transformation Φ : F → G {\displaystyle \Phi \colon F\to G} to the map
This is enough to determine the other functor since we know what the natural isomorphism is. Under the second functor
the image of a pair ( f , Φ ) {\displaystyle (f,\Phi )} is the map
that sends a natural transformation Ψ : hom ( A , − ) → F {\displaystyle \Psi \colon \hom(A,-)\to F} to the natural transformation Φ ∘ Ψ ∘ hom ( f , − ) : hom ( B , − ) → G {\displaystyle \Phi \circ \Psi \circ \hom(f,-)\colon \hom(B,-)\to G} , whose components are
The use of h A {\displaystyle h_{A}} for the covariant hom-functor and h A {\displaystyle h^{A}} for the contravariant hom-functor is not completely standard. Many texts and articles either use the opposite convention or completely unrelated symbols for these two functors. However, most modern algebraic geometry texts starting with Alexander Grothendieck 's foundational EGA use the convention in this article. [ b ]
The mnemonic "falling into something" can be helpful in remembering that h A {\displaystyle h_{A}} is the covariant hom-functor. When the letter A {\displaystyle A} is falling (i.e. a subscript), h A {\displaystyle h_{A}} assigns to an object X {\displaystyle X} the morphisms from A {\displaystyle A} into X {\displaystyle X} .
Since Φ {\displaystyle \Phi } is a natural transformation, we have the following commutative diagram :
This diagram shows that the natural transformation Φ {\displaystyle \Phi } is completely determined by Φ A ( i d A ) = u {\displaystyle \Phi _{A}(\mathrm {id} _{A})=u} since for each morphism f : A → X {\displaystyle f\colon A\to X} one has
Moreover, any element u ∈ F ( A ) {\displaystyle u\in F(A)} defines a natural transformation in this way. The proof in the contravariant case is completely analogous. [ 1 ]
An important special case of Yoneda's lemma is when the functor F {\displaystyle F} from C {\displaystyle {\mathcal {C}}} to S e t {\displaystyle \mathbf {Set} } is another hom-functor h B {\displaystyle h_{B}} . In this case, the covariant version of Yoneda's lemma states that
That is, natural transformations between hom-functors are in one-to-one correspondence with morphisms (in the reverse direction) between the associated objects. Given a morphism f : B → A {\displaystyle f\colon B\to A} the associated natural transformation is denoted H o m ( f , − ) {\displaystyle \mathrm {Hom} (f,-)} .
Mapping each object A {\displaystyle A} in C {\displaystyle {\mathcal {C}}} to its associated hom-functor h A = H o m ( A , − ) {\displaystyle h_{A}=\mathrm {Hom} (A,-)} and each morphism f : B → A {\displaystyle f\colon B\to A} to the corresponding natural transformation H o m ( f , − ) {\displaystyle \mathrm {Hom} (f,-)} determines a contravariant functor h ∙ {\displaystyle h_{\bullet }} from C {\displaystyle {\mathcal {C}}} to S e t C {\displaystyle \mathbf {Set} ^{\mathcal {C}}} , the functor category of all (covariant) functors from C {\displaystyle {\mathcal {C}}} to S e t {\displaystyle \mathbf {Set} } . One can interpret h ∙ {\displaystyle h_{\bullet }} as a covariant functor :
The meaning of Yoneda's lemma in this setting is that the functor h ∙ {\displaystyle h_{\bullet }} is fully faithful , and therefore gives an embedding of C o p {\displaystyle {\mathcal {C}}^{\mathrm {op} }} in the category of functors to S e t {\displaystyle \mathbf {Set} } . The collection of all functors { h A | A ∈ C } {\displaystyle \{h_{A}|A\in C\}} is a subcategory of S e t C {\displaystyle \mathbf {Set} ^{\mathcal {C}}} . Therefore, Yoneda embedding implies that the category C o p {\displaystyle {\mathcal {C}}^{\mathrm {op} }} is isomorphic to the category { h A | A ∈ C } {\displaystyle \{h_{A}|A\in C\}} .
The contravariant version of Yoneda's lemma states that
Therefore, h ∙ {\displaystyle h^{\bullet }} gives rise to a covariant functor from C {\displaystyle {\mathcal {C}}} to the category of contravariant functors to S e t {\displaystyle \mathbf {Set} } :
Yoneda's lemma then states that any locally small category C {\displaystyle {\mathcal {C}}} can be embedded in the category of contravariant functors from C {\displaystyle {\mathcal {C}}} to S e t {\displaystyle \mathbf {Set} } via h ∙ {\displaystyle h^{\bullet }} . This is called the Yoneda embedding .
The Yoneda embedding is sometimes denoted by よ, the hiragana Yo . [ 5 ]
The Yoneda embedding essentially states that for every (locally small) category, objects in that category can be represented by presheaves , in a full and faithful manner. That is,
for a presheaf P . Many common categories are, in fact, categories of pre-sheaves, and on closer inspection, prove to be categories of sheaves , and as such examples are commonly topological in nature, they can be seen to be topoi in general. The Yoneda lemma provides a point of leverage by which the topological structure of a category can be studied and understood.
Given two categories C {\displaystyle \mathbf {C} } and D {\displaystyle \mathbf {D} } with two functors F , G : C → D {\displaystyle F,G:\mathbf {C} \to \mathbf {D} } , natural transformations between them can be written as the following end . [ 6 ]
For any functors K : C o p → S e t s {\displaystyle K\colon \mathbf {C} ^{op}\to \mathbf {Sets} } and H : C → S e t s {\displaystyle H\colon \mathbf {C} \to \mathbf {Sets} } the following formulas are all formulations of the Yoneda lemma. [ 7 ]
A preadditive category is a category where the morphism sets form abelian groups and the composition of morphisms is bilinear ; examples are categories of abelian groups or modules. In a preadditive category, there is both a "multiplication" and an "addition" of morphisms, which is why preadditive categories are viewed as generalizations of rings . Rings are preadditive categories with one object.
The Yoneda lemma remains true for preadditive categories if we choose as our extension the category of additive contravariant functors from the original category into the category of abelian groups; these are functors which are compatible with the addition of morphisms and should be thought of as forming a module category over the original category. The Yoneda lemma then yields the natural procedure to enlarge a preadditive category so that the enlarged version remains preadditive — in fact, the enlarged version is an abelian category , a much more powerful condition. In the case of a ring R {\displaystyle R} , the extended category is the category of all right modules over R {\displaystyle R} , and the statement of the Yoneda lemma reduces to the well-known isomorphism
As stated above, the Yoneda lemma may be considered as a vast generalization of Cayley's theorem from group theory . To see this, let C {\displaystyle {\mathcal {C}}} be a category with a single object ∗ {\displaystyle *} such that every morphism is an isomorphism (i.e. a groupoid with one object). Then G = H o m C ( ∗ , ∗ ) {\displaystyle G=\mathrm {Hom} _{\mathcal {C}}(*,*)} forms a group under the operation of composition, and any group can be realized as a category in this way.
In this context, a covariant functor C → S e t {\displaystyle {\mathcal {C}}\to \mathbf {Set} } consists of a set X {\displaystyle X} and a group homomorphism G → P e r m ( X ) {\displaystyle G\to \mathrm {Perm} (X)} , where P e r m ( X ) {\displaystyle \mathrm {Perm} (X)} is the group of permutations of X {\displaystyle X} ; in other words, X {\displaystyle X} is a G-set . A natural transformation between such functors is the same thing as an equivariant map between G {\displaystyle G} -sets: a set function α : X → Y {\displaystyle \alpha \colon X\to Y} with the property that α ( g ⋅ x ) = g ⋅ α ( x ) {\displaystyle \alpha (g\cdot x)=g\cdot \alpha (x)} for all g {\displaystyle g} in G {\displaystyle G} and x {\displaystyle x} in X {\displaystyle X} . (On the left side of this equation, the ⋅ {\displaystyle \cdot } denotes the action of G {\displaystyle G} on X {\displaystyle X} , and on the right side the action on Y {\displaystyle Y} .)
Now the covariant hom-functor H o m C ( ∗ , − ) {\displaystyle \mathrm {Hom} _{\mathcal {C}}(*,-)} corresponds to the action of G {\displaystyle G} on itself by left-multiplication (the contravariant version corresponds to right-multiplication). The Yoneda lemma with F = H o m C ( ∗ , − ) {\displaystyle F=\mathrm {Hom} _{\mathcal {C}}(*,-)} states that
that is, the equivariant maps from this G {\displaystyle G} -set to itself are in bijection with G {\displaystyle G} . But it is easy to see that (1) these maps form a group under composition, which is a subgroup of P e r m ( G ) {\displaystyle \mathrm {Perm} (G)} , and (2) the function which gives the bijection is a group homomorphism. (Going in the reverse direction, it associates to every g {\displaystyle g} in G {\displaystyle G} the equivariant map of right-multiplication by g {\displaystyle g} .) Thus G {\displaystyle G} is isomorphic to a subgroup of P e r m ( G ) {\displaystyle \mathrm {Perm} (G)} , which is the statement of Cayley's theorem.
Yoshiki Kinoshita stated in 1996 that the term "Yoneda lemma" was coined by Saunders Mac Lane following an interview he had with Yoneda in the Gare du Nord station. [ 8 ] [ 9 ]
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In algebra, the Yoneda product (named after Nobuo Yoneda ) is the pairing between Ext groups of modules : Ext n ( M , N ) ⊗ Ext m ( L , M ) → Ext n + m ( L , N ) {\displaystyle \operatorname {Ext} ^{n}(M,N)\otimes \operatorname {Ext} ^{m}(L,M)\to \operatorname {Ext} ^{n+m}(L,N)} induced by Hom ( N , M ) ⊗ Hom ( M , L ) → Hom ( N , L ) , f ⊗ g ↦ g ∘ f . {\displaystyle \operatorname {Hom} (N,M)\otimes \operatorname {Hom} (M,L)\to \operatorname {Hom} (N,L),\,f\otimes g\mapsto g\circ f.}
Specifically, for an element ξ ∈ Ext n ( M , N ) {\displaystyle \xi \in \operatorname {Ext} ^{n}(M,N)} , thought of as an extension ξ : 0 → N → E 0 → ⋯ → E n − 1 → M → 0 , {\displaystyle \xi :0\rightarrow N\rightarrow E_{0}\rightarrow \cdots \rightarrow E_{n-1}\rightarrow M\rightarrow 0,} and similarly ρ : 0 → M → F 0 → ⋯ → F m − 1 → L → 0 ∈ Ext m ( L , M ) , {\displaystyle \rho :0\rightarrow M\rightarrow F_{0}\rightarrow \cdots \rightarrow F_{m-1}\rightarrow L\rightarrow 0\in \operatorname {Ext} ^{m}(L,M),} we form the Yoneda (cup) product ξ ⌣ ρ : 0 → N → E 0 → ⋯ → E n − 1 → F 0 → ⋯ → F m − 1 → L → 0 ∈ Ext m + n ( L , N ) . {\displaystyle \xi \smile \rho :0\rightarrow N\rightarrow E_{0}\rightarrow \cdots \rightarrow E_{n-1}\rightarrow F_{0}\rightarrow \cdots \rightarrow F_{m-1}\rightarrow L\rightarrow 0\in \operatorname {Ext} ^{m+n}(L,N).}
Note that the middle map E n − 1 → F 0 {\displaystyle E_{n-1}\rightarrow F_{0}} factors through the given maps to M {\displaystyle M} .
We extend this definition to include m , n = 0 {\displaystyle m,n=0} using the usual functoriality of the Ext ∗ ( ⋅ , ⋅ ) {\displaystyle \operatorname {Ext} ^{*}(\cdot ,\cdot )} groups.
Given a commutative ring R {\displaystyle R} and a module M {\displaystyle M} , the Yoneda product defines a product structure on the groups Ext ∙ ( M , M ) {\displaystyle {\text{Ext}}^{\bullet }(M,M)} , where Ext 0 ( M , M ) = Hom R ( M , M ) {\displaystyle {\text{Ext}}^{0}(M,M)={\text{Hom}}_{R}(M,M)} is generally a non-commutative ring. This can be generalized to the case of sheaves of modules over a ringed space , or ringed topos.
In Grothendieck's duality theory of coherent sheaves on a projective scheme i : X ↪ P k n {\displaystyle i:X\hookrightarrow \mathbb {P} _{k}^{n}} of pure dimension r {\displaystyle r} over an algebraically closed field k {\displaystyle k} , there is a pairing Ext O X p ( O X , F ) × Ext O X r − p ( F , ω X ∙ ) → k {\displaystyle {\text{Ext}}_{{\mathcal {O}}_{X}}^{p}({\mathcal {O}}_{X},{\mathcal {F}})\times {\text{Ext}}_{{\mathcal {O}}_{X}}^{r-p}({\mathcal {F}},\omega _{X}^{\bullet })\to k} where ω X {\displaystyle \omega _{X}} is the dualizing complex ω X = E x t O P n − r ( i ∗ F , ω P ) {\displaystyle \omega _{X}={\mathcal {Ext}}_{{\mathcal {O}}_{\mathbb {P} }}^{n-r}(i_{*}{\mathcal {F}},\omega _{\mathbb {P} })} and ω P = O P ( − ( n + 1 ) ) {\displaystyle \omega _{\mathbb {P} }={\mathcal {O}}_{\mathbb {P} }(-(n+1))} given by the Yoneda pairing. [ 1 ]
The Yoneda product is useful for understanding the obstructions to a deformation of maps of ringed topoi . [ 2 ] For example, given a composition of ringed topoi X → f Y → S {\displaystyle X\xrightarrow {f} Y\to S} and an S {\displaystyle S} -extension j : Y → Y ′ {\displaystyle j:Y\to Y'} of Y {\displaystyle Y} by an O Y {\displaystyle {\mathcal {O}}_{Y}} -module J {\displaystyle J} , there is an obstruction class ω ( f , j ) ∈ Ext 2 ( L X / Y , f ∗ J ) {\displaystyle \omega (f,j)\in {\text{Ext}}^{2}(\mathbf {L} _{X/Y},f^{*}J)} which can be described as the yoneda product ω ( f , j ) = f ∗ ( e ( j ) ) ⋅ K ( X / Y / S ) {\displaystyle \omega (f,j)=f^{*}(e(j))\cdot K(X/Y/S)} where K ( X / Y / S ) ∈ Ext 1 ( L X / Y , L Y / S ) f ∗ ( e ( j ) ) ∈ Ext 1 ( f ∗ L Y / S , f ∗ J ) {\displaystyle {\begin{aligned}K(X/Y/S)&\in {\text{Ext}}^{1}(\mathbf {L} _{X/Y},\mathbf {L} _{Y/S})\\f^{*}(e(j))&\in {\text{Ext}}^{1}(f^{*}\mathbf {L} _{Y/S},f^{*}J)\end{aligned}}} and L X / Y {\displaystyle \mathbf {L} _{X/Y}} corresponds to the cotangent complex .
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The Yorkshire Mycological Committee is a committee within the Yorkshire Naturalists' Union . [ 1 ] First formed in 1892, it was the first permanent organisation dedicated to the study of fungi in Great Britain . [ 2 ] It was the principal founding organisation of the British Mycological Society . [ 3 ]
The Mycological Committee was first founded in 1892 so that the Yorkshire Naturalists' Union might better organise its recording of fungi across Yorkshire via annual 'fungal forays'. The Rev. William Fowler was appointed as its first Chairman with Charles Crossland being appointed its first secretary. George Edward Massee would succeed Fowler and together with Crossland would run the Committee until 1916. [ 4 ]
The period of Massee's tenure would see the Mycological Committee function completely independently of the British Mycological Society (a national mycological society founded primarily by members of Mycological Committee. [ 5 ] This was primarily due to a disagreement of an unknown nature between Massee and Carleton Rea , a prominent figure in the British Mycological Society. [ 2 ]
By 1903, the Committee was so prominent that it attracted the attention of George Francis Atkinson who attended the 1903 foray as a guest of George Edward Massee . Notably, he did not attend any events hosted by the British Mycological Society . [ 6 ]
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The Yoshimine
sort [ 1 ] is an algorithm that is used in quantum chemistry to order lists of two electron repulsion integrals. It is implemented in the IBM Alchemy program
suite [ 2 ] and in the UK R-matrix package for electron and positron scattering by molecules [ 3 ] which is based on the early versions of the IBM Alchemy program suite.
In quantum chemistry , it is common practice to represent one electron functions in terms of an
expansion over a basis set, χ i {\displaystyle \chi _{i}} . The most common choice for this basis set is Gaussian orbitals (GTOs) however for linear molecules Slater orbitals (STOs) can be
used. [ 4 ]
The Schrödinger equation, for a system with two or more electrons, includes the Coulomb repulsion
operator. In the basis set expansion approach this leads to the requirement to compute two electron
repulsion integrals involving four basis functions. Any given basis set may be ordered so that
each function can assigned a unique index. So, for any given basis set, each two electron
integral can be described by four indices, that is the indices of the four basis functions involved.
It is customary to denote these indices as p,q,r and s and the integral as (pq|rs). Assuming that χ i {\displaystyle \chi _{i}} are real functions, the (pq|rs) are defined by
The number of two electron integrals that must be computed for any basis set depends on the
number of functions in the basis set and on the symmetry point group of the molecule being studied.
The computed two electron integrals are real numbers, ( p q | r s ) ∈ R {\displaystyle (pq|rs)\in \mathbb {R} } ,
and this implies certain permutational symmetry properties on the indices p,q,r
and s. [ 5 ] The exact details depend on whether the part of the basis function representing angular
behavior is real or complex. For Gaussian orbitals real spherical harmonics are
generally used whereas for Slater orbitals the complex spherical harmonics are used.
In the case of real orbitals, p can be swapped with q without changing the integral value,
or independently r with s. in addition pq as a pair can be swapped with rs as a pair without
changing the integral. Putting these interchanges together means that
which is eightfold symmetry. If the molecule has no spatial symmetry, in other words it
belongs to the C 1 {\displaystyle C_{1}} point group which has only one irreducible representation,
then the permutational symmetry of the integrals indices is the only operation
which can be applied. On the other hand, if the molecule has some symmetry operations,
then further ordering is possible. The impact of the above symmetry relationship is that
an integral can be computed once, but corresponds to eight different index combinations.
The Schrödinger Hamiltonian commutes with the operations of the point symmetry group of the
nuclear framework of the molecule. This means that a two electron integral can be non-zero
only if the product of the four functions transforms, or contains a component which transforms,
as the totally symmetric irreducible representation of the symmetry point group to which the
molecule belongs.
This means that a computer program for two electron integral processing can precompute the
list of basis function symmetry combinations ( symmetry blocks ) for which integrals may
be non zero and ignore all other symmetry combinations. The list of symmetry blocks can
also be ordered. Frequently, the totally symmetric irreducible representation is assigned
the lowest index in the list, typically 1 in Fortran or 0 in the C programming language.
Within any given symmetry block, the permutational symmetry of the integrals still
applies and the integrals can be ordered within that block. For example if the
molecule belongs to the C 2 {\displaystyle C_{2}} point group, which has irreducible representations A {\displaystyle A} and B {\displaystyle B} then integral blocks for the following symmetry combinations
are non-zero
and integrals blocks for any other symmetry combination are identically zero
by group theory. Thus two types of ordering can be used:
This means that given the four indices pqrs defining a two electron integral, a unique index may be computed.
This is the essence of the Yoshimine procedure.
When the integrals are computed by the integrals program they are written out to a sequential
file along with the p,q,r,s indices which define them. The order in which the integrals are
computed is defined by the algorithm used in the integration program. The most efficient
algorithms do not compute the integrals in order, that is such that the p,q,r and s indices
are ordered.
This would not be a problem is all of the integrals could be held in CPU memory simultaneously.
In that case the computed integral can be assigned into its position in the array of
two electron integrals by computing the required index from the p,q,r and s indices.
In the 1960s it was essentially impossible to hold all of the two electron integrals in
memory simultaneously. Therefore, M Yoshimine developed a sorting algorithm for
two-electron integrals which reads the unordered list of integrals from a files and transforms
it into an ordered list which is then written to another file. A by-product of this is that the file
storing the ordered integrals does not need to contain the p,q,r,s indices for each integral.
The ordering process uses a direct access file but the input and output files of integrals
are sequential.
At the start of the 21st century, computer memory is much larger and for small molecules
and/or small basis sets it is sometimes possible to hold all two electron integrals in memory.
In general however, the Yoshimine algorithm is still required.
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Yoshimura buckling , named after Japanese researcher Yoshimaru Yoshimura (吉村慶丸), is a triangular mesh buckling pattern found in thin-walled cylinders under compression along the axis of the cylinder that produces corrugated shape resembling the Schwarz lantern . This is the same pattern on found on the sleeves of Mona Lisa . Due to its axial stiffness and origami-like ability it is being researched in applications such as aerospace, civil engineering, and robotics in addressing problems relating to compactness and rapid deployment. However broader use is currently limited by the absence of a general mathematical framework.
Crease patterns in cylindrical shells were first studied by Theodore von Kármán and Hsue-Shen Tsien in 1941 from the California Institute of Technology, and was later independently studied by Yoshimaru Yoshimura in a 1951 Japanese paper, with an English version published in 1955. [ 1 ] [ 2 ] Isolation of Japan during and after World War II made Yoshimura unaware of the earlier work. [ 3 ]
The compatibility condition of the buckling pattern is given by:
1 2 ( 2 ∂ 2 F ∂ x ∂ θ − ∂ 2 E ∂ θ 2 − ∂ 2 G ∂ x 2 ) = L N − M 2 = K H {\displaystyle {\frac {1}{2}}\left(2{\frac {\partial ^{2}F}{\partial x\partial \theta }}-{\frac {\partial ^{2}E}{\partial \theta ^{2}}}-{\frac {\partial ^{2}G}{\partial x^{2}}}\right)=LN-M^{2}=KH}
H 2 = E G − F 2 {\displaystyle H^{2}=EG-F^{2}}
where E , F , G {\displaystyle E,F,G} and L , M , N {\displaystyle L,M,N} represent the first and second fundamental forms of the deflection surface, respectively. [ 4 ] K {\displaystyle K} represents the Gaussian curvature , which is expressed as:
K = 1 R 1 R 2 {\displaystyle K={\frac {1}{R_{1}R_{2}}}}
where R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} are the principal radii of curvature of the cylinder. H {\displaystyle H} is expressed as:
H = 2 ( k 4 + 1 ) {\displaystyle H=2\left(k^{4}+1\right)}
where k {\displaystyle k} is the length of the buckle in the circumferential direction divided by the length of the buckle in the axial direction.
In classical shell theory, the asymptotic formula to predict the critical buckling load σ c r {\displaystyle \sigma _{cr}} in cylindrical shells is expressed as:
σ c r = E h ( 3 − ν 2 ) {\displaystyle \sigma _{cr}={\frac {Eh}{\sqrt {(3-\nu ^{2})}}}}
where h = t R {\displaystyle h={\frac {t}{R}}} represents the ratio of the cylinder wall thickness to the radius, and E {\displaystyle E} and ν {\displaystyle \nu } represent the Young's modulus and Poisson ratio , respectively. [ 6 ] This classical formula is occasionally referred to as Koiter's formula [ 7 ] [ 8 ] after Dutch engineer Warner T. Koiter , who derived it in 1945, [ 9 ] but was first derived by R. Lorenz in 1911. [ 10 ]
Experimental results have shown that this classical formula frequently overestimates the buckling load by a factor of 4 to 5. [ 6 ] This discrepancy is often attributed to the buckling load's high sensitivity to imperfections in the structure's shape and load. [ 11 ] [ 12 ] [ 13 ]
Under a Cartesian coordinate system, the equilibrium conditions for a cylinder under axial compression can be expressed as:
D ∇ 4 ω = 2 h [ ∂ 2 ϕ ∂ y 2 ∂ 2 ω ∂ x 2 − 2 ∂ 2 ϕ ∂ x 2 ∂ y 2 ∂ 2 ω ∂ x ∂ y + ∂ 2 ϕ ∂ x 2 ( ∂ 2 ω ∂ y 2 + 1 r ) ] {\displaystyle D\nabla ^{4}\omega =2h\left[{\frac {\partial ^{2}\phi }{\partial y^{2}}}{\frac {\partial ^{2}\omega }{\partial x^{2}}}-2{\frac {\partial ^{2}\phi }{\partial x^{2}\partial y^{2}}}{\frac {\partial ^{2}\omega }{\partial x\partial y}}+{\frac {\partial ^{2}\phi }{\partial x^{2}}}\left({\frac {\partial ^{2}\omega }{\partial y^{2}}}+{\frac {1}{r}}\right)\right]}
∇ 4 ϕ = E [ ( ∂ 2 ω ∂ y 2 ) 2 − ∂ 2 ω ∂ x 2 ∂ 2 ω ∂ 2 y 2 ] − E r ∂ 2 ω ∂ x 2 {\displaystyle \nabla ^{4}\phi =E\left[\left({\frac {\partial ^{2}\omega }{\partial y^{2}}}\right)^{2}-{\frac {\partial ^{2}\omega }{\partial x^{2}}}{\frac {\partial ^{2}\omega }{\partial ^{2}y^{2}}}\right]-{\frac {E}{r}}{\frac {\partial ^{2}\omega }{\partial x^{2}}}}
where E {\displaystyle E} and D {\displaystyle D} are the Young's modulus and flexural rigidity, respectively. ϕ {\displaystyle \phi } is derived from the second equation, and ω {\displaystyle \omega } can be expressed as:
ω = A cos λ ( y + m x ) cos λ ( y − m x ) + B [ cos λ ( y + m x ) + cos λ ( y − m x ) ] + C {\displaystyle \omega =A\cos \lambda (y+mx)\cos \lambda (y-mx)+B[\cos \lambda (y+mx)+\cos \lambda (y-mx)]+C}
with λ , m , A , B , C {\displaystyle \lambda ,m,A,B,C} as the parameters. This carefully selected method [ 14 ] allows for the following methods of simplication:
The solutions for the equations may be found with these equations, with varying methods of solution. Two significant methods of solution come from Kármán and Hsue-Shen in 1941, [ 1 ] [ 2 ] and D. M. A Leggett in 1953. [ 14 ]
The Yoshimura folding pattern is composed of isosceles triangles that share a single edge at the base, forming repeated rhombuses , as seen in the Schwarz lantern crease pattern. [ 5 ] Slightly different buckling patterns can occur based on manipulating the angles and dimensions of the individual triangles. [ 15 ] The crease pattern for folding the Schwarz lantern from a flat piece of paper, a tessellation of the plane by isosceles triangles , has also been called the Yoshimura pattern based on the same work by Yoshimura. [ 16 ] [ 17 ] The Yoshimura creasing pattern is related to both the Kresling and Hexagonal folds, and can be framed as a special case of the Miura fold . [ 18 ] Unlike the Miura fold which is rigidly deformable, both the Yoshimura and Kresling patterns require panel deformation to be folded to a compact state. [ 19 ]
Cylindrical shells under axial compression have been observed to exhibit local buckling, provided that they are comparatively long. [ 5 ] Local buckling is a phenomenon where a structure undergoes local deformation, as opposed to Euler (global) buckling, which is a deformation of the whole structure. [ 20 ] Consequently, lengthwise along the cylinder, the buckling occurs at over 1.5 times the lobe's axial wavelength. [ 5 ] Circumference-wise, both the cylinder and loading equipment must have complete rotational symmetry to affect the cylinder's entire circumference. [ 6 ]
This phenomenon can be further explained as a loss of total elastic energy. Considering a cylinder with fixed ends under Euler's critical load, the elastic energy decrease of the unbuckled region will overpower the increase in elastic energy of the buckled region when local buckling occurs. This results in a loss of total elastic energy. [ 5 ]
The critical buckling load of cylindrical shells under axial compression is highly sensitive to imperfections in the shape and load. [ 21 ] [ 12 ] [ 15 ] With respect to the asymptotic formula σ c r = E h ( 3 − ν 2 ) {\displaystyle \sigma _{cr}={\frac {Eh}{\sqrt {(3-\nu ^{2})}}}} from classical shell theory, where h = t R {\displaystyle h={\frac {t}{R}}} is the shell's dimensionless thickness, [ 7 ] the buckling load approximately scales in two different ways:
As the thickness of the cylindrical shell decreases, the buckled surface becomes approximately developable . The surface is consequently most developable when the thickness of the shell approaches 0, as it behaves like an ideal membrane. [ 5 ]
Yoshimura buckling and its related origami patterns' possible applications have been researched, but their use in engineering remains limited. [ 22 ] [ 23 ] Current Yoshimura origami designs lack an overarching mathematical theory between the two dimensional (2-D) creases, and three-dimensional (3-D) forms. [ 22 ] The absence of a unified theory makes it difficult for a general design method to be formulated, and current designs are extremely specific to its application.
Additional research for its potential uses in engineering is still in development; researchers are attempting to develop an intuitive parametric method and general numerical theorem to tweak existing Yoshimura designs for engineering efficiency. [ 24 ] Currently, engineering attempts to develop a deployable cylindrical structure with Yoshimura folding have only been made for membrane structures, like soft pneumatic actuators . [ 24 ]
The application of origami-based design, like the Yoshimura pattern, allows for aerospace engineering applications with reduced weight and volumes while also increasing portability and deployability. [ 24 ] For example, a cylinder in a Yoshimura folding pattern has a high stiffness in the axial direction, allowing for structural rigidity. [ 24 ] [ 23 ] Origami flashers self-deploy under the centrifugal force of orbit without requiring additional structural support. [ 24 ] While some other origami patterns have already been utilized and validated (the IKAROS spacecraft). The Yoshimura pattern is being researched in applications like inflatable space habitats that require a portable and structurally rigid solution. [ 22 ]
The Yoshimura buckling pattern allows for uniform thickness of material. Uniform thickness is important in origami used in construction applications, as uniform thickness can transfer compression and tension forces more evenly, allowing for stiffer structures and higher load capacity. [ 5 ] [ 24 ] Research shows that origami with non-uniform thickness has much lower load-carrying performance when subject to axial compression forces. [ 24 ] Similar to aerospace applications, applications in civil engineering and construction can potentially use Yoshimura patterns when portable and quickly deployable structures are required. [ 23 ] For example, emergency shelters in disaster relief infrastructure or rapidly deployable bridges. A large setback is due to the Yoshimura pattern's significant amount of material deformation, which can make it difficult to build with brittle materials such as metals or other composites with high strength typically used in construction. [ 24 ] Instead, researchers are studying using Yoshimura buckling inspired construction using hinges at the creases instead of deformation of the material itself. [ 23 ]
Rotary origami structures provide protection for rigid robotic structures by reducing the peak impact force they experience. This approach shows potential for applications in antenna design and space engineering. [ 25 ] Current applications of the Yoshimura buckling have focused on structures built with soft membranes, such as the casing around pneumatic actuators or protective housing of robotic joints. [ 24 ] [ 26 ] Yoshimura pattern's compliability also makes it applicable in reconfigurable soft robots (RSRs) made from synthesized materials due to its 1800% elongation ratio under paper fabrication. [ 26 ]
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The yotari mouse is an autosomal recessive mutant. [ 1 ] It has a mutated disabled homolog 1 ( Dab1 ) gene. [ 2 ] This mutant mouse is recognized by unstable gait ("Yota-ru" in Japanese means "unstable gait") and tremor and by early deaths around the time of weaning . The cytoarchitectures of cerebellar and cerebral cortices and hippocampal formation of the yotari mouse are abnormal. These malformations resemble those of reeler mouse.
This neuroscience article is a stub . You can help Wikipedia by expanding it .
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The byte is a unit of digital information that most commonly consists of eight bits . Historically, the byte was the number of bits used to encode a single character of text in a computer [ 1 ] [ 2 ] and for this reason it is the smallest addressable unit of memory in many computer architectures . To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as the Internet Protocol ( RFC 791 ) refer to an 8-bit byte as an octet . [ 3 ] Those bits in an octet are usually counted with numbering from 0 to 7 or 7 to 0 depending on the bit endianness .
The size of the byte has historically been hardware -dependent and no definitive standards existed that mandated the size. Sizes from 1 to 48 bits have been used. [ 4 ] [ 5 ] [ 6 ] [ 7 ] The six-bit character code was an often-used implementation in early encoding systems, and computers using six-bit and nine-bit bytes were common in the 1960s. These systems often had memory words of 12, 18, 24, 30, 36, 48, or 60 bits, corresponding to 2, 3, 4, 5, 6, 8, or 10 six-bit bytes, and persisted, in legacy systems, into the twenty-first century. In this era, bit groupings in the instruction stream were often referred to as syllables [ a ] or slab , before the term byte became common.
The modern de facto standard of eight bits, as documented in ISO/IEC 2382-1:1993, is a convenient power of two permitting the binary-encoded values 0 through 255 for one byte, as 2 to the power of 8 is 256. [ 8 ] The international standard IEC 80000-13 codified this common meaning. Many types of applications use information representable in eight or fewer bits and processor designers commonly optimize for this usage. The popularity of major commercial computing architectures has aided in the ubiquitous acceptance of the 8-bit byte. [ 9 ] Modern architectures typically use 32- or 64-bit words, built of four or eight bytes, respectively.
The unit symbol for the byte was designated as the upper-case letter B by the International Electrotechnical Commission (IEC) and Institute of Electrical and Electronics Engineers (IEEE). [ 10 ] Internationally, the unit octet explicitly defines a sequence of eight bits, eliminating the potential ambiguity of the term "byte". [ 11 ] [ 12 ] The symbol for octet, 'o', also conveniently eliminates the ambiguity in the symbol 'B' between byte and bel .
The term byte was coined by Werner Buchholz in June 1956, [ 4 ] [ 13 ] [ 14 ] [ b ] during the early design phase for the IBM Stretch [ 15 ] [ 16 ] [ 1 ] [ 13 ] [ 14 ] [ 17 ] [ 18 ] computer, which had addressing to the bit and variable field length (VFL) instructions with a byte size encoded in the instruction. [ 13 ] It is a deliberate respelling of bite to avoid accidental mutation to bit . [ 1 ] [ 13 ] [ 19 ] [ c ]
Another origin of byte for bit groups smaller than a computer's word size, and in particular groups of four bits , is on record by Louis G. Dooley, who claimed he coined the term while working with Jules Schwartz and Dick Beeler on an air defense system called SAGE at MIT Lincoln Laboratory in 1956 or 1957, which was jointly developed by Rand , MIT, and IBM. [ 20 ] [ 21 ] Later on, Schwartz's language JOVIAL actually used the term, but the author recalled vaguely that it was derived from AN/FSQ-31 . [ 22 ] [ 21 ]
Early computers used a variety of four-bit binary-coded decimal (BCD) representations and the six-bit codes for printable graphic patterns common in the U.S. Army ( FIELDATA ) and Navy . These representations included alphanumeric characters and special graphical symbols. These sets were expanded in 1963 to seven bits of coding, called the American Standard Code for Information Interchange (ASCII) as the Federal Information Processing Standard , which replaced the incompatible teleprinter codes in use by different branches of the U.S. government and universities during the 1960s. ASCII included the distinction of upper- and lowercase alphabets and a set of control characters to facilitate the transmission of written language as well as printing device functions, such as page advance and line feed, and the physical or logical control of data flow over the transmission media. [ 18 ] During the early 1960s, while also active in ASCII standardization, IBM simultaneously introduced in its product line of System/360 the eight-bit Extended Binary Coded Decimal Interchange Code (EBCDIC), an expansion of their six-bit binary-coded decimal (BCDIC) representations [ d ] used in earlier card punches. [ 23 ] The prominence of the System/360 led to the ubiquitous adoption of the eight-bit storage size, [ 18 ] [ 16 ] [ 13 ] while in detail the EBCDIC and ASCII encoding schemes are different.
In the early 1960s, AT&T introduced digital telephony on long-distance trunk lines . These used the eight-bit μ-law encoding . This large investment promised to reduce transmission costs for eight-bit data.
In Volume 1 of The Art of Computer Programming (first published in 1968), Donald Knuth uses byte in his hypothetical MIX computer to denote a unit which "contains an unspecified amount of information ... capable of holding at least 64 distinct values ... at most 100 distinct values. On a binary computer a byte must therefore be composed of six bits". [ 24 ] He notes that "Since 1975 or so, the word byte has come to mean a sequence of precisely eight binary digits...When we speak of bytes in connection with MIX we shall confine ourselves to the former sense of the word, harking back to the days when bytes were not yet standardized." [ 24 ]
The development of eight-bit microprocessors in the 1970s popularized this storage size. Microprocessors such as the Intel 8080 , the direct predecessor of the 8086 , could also perform a small number of operations on the four-bit pairs in a byte, such as the decimal-add-adjust (DAA) instruction. A four-bit quantity is often called a nibble , also nybble , which is conveniently represented by a single hexadecimal digit.
The term octet unambiguously specifies a size of eight bits. [ 18 ] [ 12 ] It is used extensively in protocol definitions.
Historically, the term octad or octade was used to denote eight bits as well at least in Western Europe; [ 25 ] [ 26 ] however, this usage is no longer common. The exact origin of the term is unclear, but it can be found in British, Dutch, and German sources of the 1960s and 1970s, and throughout the documentation of Philips mainframe computers.
The unit symbol for the byte is specified in IEC 80000-13 , IEEE 1541 and the Metric Interchange Format [ 10 ] as the upper-case character B.
In the International System of Quantities (ISQ), B is also the symbol of the bel , a unit of logarithmic power ratio named after Alexander Graham Bell , creating a conflict with the IEC specification. However, little danger of confusion exists, because the bel is a rarely used unit. It is used primarily in its decadic fraction, the decibel (dB), for signal strength and sound pressure level measurements, while a unit for one-tenth of a byte, the decibyte, and other fractions, are only used in derived units, such as transmission rates.
The lowercase letter o for octet is defined as the symbol for octet in IEC 80000-13 and is commonly used in languages such as French [ 27 ] and Romanian , and is also combined with metric prefixes for multiples, for example ko and Mo.
More than one system exists to define unit multiples based on the byte. Some systems are based on powers of 10 , following the International System of Units (SI), which defines for example the prefix kilo as 1000 (10 3 ); other systems are based on powers of two . Nomenclature for these systems has led to confusion. Systems based on powers of 10 use standard SI prefixes ( kilo , mega , giga , ...) and their corresponding symbols (k, M, G, ...). Systems based on powers of 2, however, might use binary prefixes ( kibi , mebi , gibi , ...) and their corresponding symbols (Ki, Mi, Gi, ...) or they might use the prefixes K, M, and G, creating ambiguity when the prefixes M or G are used.
While the difference between the decimal and binary interpretations is relatively small for the kilobyte (about 2% smaller than the kibibyte), the systems deviate increasingly as units grow larger (the relative deviation grows by 2.4% for each three orders of magnitude). For example, a power-of-10-based terabyte is about 9% smaller than power-of-2-based tebibyte.
Definition of prefixes using powers of 10—in which 1 kilobyte (symbol kB) is defined to equal 1,000 bytes—is recommended by the International Electrotechnical Commission (IEC). [ 28 ] The IEC standard defines eight such multiples, up to 1 yottabyte (YB), equal to 1000 8 bytes. [ 29 ] The additional prefixes ronna- for 1000 9 and quetta- for 1000 10 were adopted by the International Bureau of Weights and Measures (BIPM) in 2022. [ 30 ] [ 31 ]
This definition is most commonly used for data-rate units in computer networks , internal bus, hard drive and flash media transfer speeds, and for the capacities of most storage media , particularly hard drives , [ 32 ] flash -based storage, [ 33 ] and DVDs . [ citation needed ] Operating systems that use this definition include macOS , [ 34 ] iOS , [ 34 ] Ubuntu , [ 35 ] and Debian . [ 36 ] It is also consistent with the other uses of the SI prefixes in computing, such as CPU clock speeds or measures of performance .
Prior art, the IBM System 360 and the related tape systems set the byte at 8 bits. [ 37 ] Early 5.25-inch disks used decimal [ dubious – discuss ] even though they used 128-byte and 256-byte sectors. [ 38 ] Hard disks used mostly 256-byte and then 512-byte before 4096-byte blocks became standard. [ 39 ] RAM was always sold in powers of 2. [ citation needed ]
A system of units based on powers of 2 in which 1 kibibyte (KiB) is equal to 1,024 (i.e., 2 10 ) bytes is defined by international standard IEC 80000-13 and is supported by national and international standards bodies ( BIPM , IEC , NIST ). The IEC standard defines eight such multiples, up to 1 yobibyte (YiB), equal to 1024 8 bytes. The natural binary counterparts to ronna- and quetta- were given in a consultation paper of the International Committee for Weights and Measures' Consultative Committee for Units (CCU) as robi- (Ri, 1024 9 ) and quebi- (Qi, 1024 10 ), but have not yet been adopted by the IEC or ISO. [ 40 ]
An alternative system of nomenclature for the same units (referred to here as the customary convention ), in which 1 kilobyte (KB) is equal to 1,024 bytes, [ 41 ] [ 42 ] [ 43 ] 1 megabyte (MB) is equal to 1024 2 bytes and 1 gigabyte (GB) is equal to 1024 3 bytes is mentioned by a 1990s JEDEC standard. Only the first three multiples (up to GB) are mentioned by the JEDEC standard, which makes no mention of TB and larger. While confusing and incorrect, [ 44 ] the customary convention is used by the Microsoft Windows operating system [ 45 ] [ better source needed ] and random-access memory capacity, such as main memory and CPU cache size, and in marketing and billing by telecommunication companies, such as Vodafone , [ 46 ] AT&T , [ 47 ] Orange [ 48 ] and Telstra . [ 49 ]
For storage capacity, the customary convention was used by macOS and iOS through Mac OS X 10.5 Leopard and iOS 10, after which they switched to units based on powers of 10. [ 34 ]
Various computer vendors have coined terms for data of various sizes, sometimes with different sizes for the same term even within a single vendor. These terms include double word , half word , long word , quad word , slab , superword and syllable . There are also informal terms. e.g., half byte and nybble for 4 bits, octal K for 1000 8 .
When I see a disk advertised as having a capacity of one megabyte, what is this telling me? There are three plausible answers, and I wonder if anybody knows which one is correct ... Now this is not a really vital issue, as there is just under 5% difference between the smallest and largest alternatives. Nevertheless, it would [be] nice to know what the standard measure is, or if there is one.
Contemporary [ e ] computer memory has a binary architecture making a definition of memory units based on powers of 2 most practical. The use of the metric prefix kilo for binary multiples arose as a convenience, because 1024 is approximately 1000 . [ 27 ] This definition was popular in early decades of personal computing , with products like the Tandon 5 1 ⁄ 4 -inch DD floppy format (holding 368 640 bytes) being advertised as "360 KB", following the 1024 -byte convention. It was not universal, however. The Shugart SA-400 5 1 ⁄ 4 -inch floppy disk held 109,375 bytes unformatted, [ 51 ] and was advertised as "110 Kbyte", using the 1000 convention. [ 52 ] Likewise, the 8-inch DEC RX01 floppy (1975) held 256 256 bytes formatted, and was advertised as "256k". [ 53 ] Some devices were advertised using a mixture of the two definitions: most notably, floppy disks advertised as "1.44 MB" have an actual capacity of 1440 KiB , the equivalent of 1.47 MB or 1.41 MiB.
In 1995, the International Union of Pure and Applied Chemistry 's (IUPAC) Interdivisional Committee on Nomenclature and Symbols attempted to resolve this ambiguity by proposing a set of binary prefixes for the powers of 1024, including kibi (kilobinary), mebi (megabinary), and gibi (gigabinary). [ 54 ] [ 55 ]
In December 1998, the IEC addressed such multiple usages and definitions by adopting the IUPAC's proposed prefixes (kibi, mebi, gibi, etc.) to unambiguously denote powers of 1024. [ 56 ] Thus one kibibyte (1 KiB) is 1024 1 bytes = 1024 bytes, one mebibyte (1 MiB) is 1024 2 bytes = 1 048 576 bytes, and so on.
In 1999, Donald Knuth suggested calling the kibibyte a "large kilobyte" ( KKB ). [ 57 ]
The IEC adopted the IUPAC proposal and published the standard in January 1999. [ 58 ] [ 59 ] The IEC prefixes are part of the International System of Quantities . The IEC further specified that the kilobyte should only be used to refer to 1000 bytes. [ 60 ]
Lawsuits arising from alleged consumer confusion over the binary and decimal definitions of multiples of the byte have generally ended in favor of the manufacturers, with courts holding that the legal definition of gigabyte or GB is 1 GB = 1 000 000 000 (10 9 ) bytes (the decimal definition), rather than the binary definition (2 30 , i.e., 1 073 741 824 ). Specifically, the United States District Court for the Northern District of California held that "the U.S. Congress has deemed the decimal definition of gigabyte to be the 'preferred' one for the purposes of 'U.S. trade and commerce' [...] The California Legislature has likewise adopted the decimal system for all 'transactions in this state. ' " [ 61 ]
Earlier lawsuits had ended in settlement with no court ruling on the question, such as a lawsuit against drive manufacturer Western Digital . [ 62 ] [ 63 ] Western Digital settled the challenge and added explicit disclaimers to products that the usable capacity may differ from the advertised capacity. [ 62 ] Seagate was sued on similar grounds and also settled. [ 62 ] [ 64 ]
Many programming languages define the data type byte .
The C and C++ programming languages define byte as an "addressable unit of data storage large enough to hold any member of the basic character set of the execution environment" (clause 3.6 of the C standard). The C standard requires that the integral data type unsigned char must hold at least 256 different values, and is represented by at least eight bits (clause 5.2.4.2.1). Various implementations of C and C++ reserve 8, 9, 16, 32, or 36 bits for the storage of a byte. [ 71 ] [ 72 ] [ f ] In addition, the C and C++ standards require that there be no gaps between two bytes. This means every bit in memory is part of a byte. [ 73 ]
Java's primitive data type byte is defined as eight bits. It is a signed data type, holding values from −128 to 127.
.NET programming languages, such as C# , define byte as an unsigned type, and the sbyte as a signed data type, holding values from 0 to 255, and −128 to 127 , respectively.
In data transmission systems, the byte is used as a contiguous sequence of bits in a serial data stream, representing the smallest distinguished unit of data. For asynchronous communication a full transmission unit usually additionally includes a start bit, 1 or 2 stop bits, and possibly a parity bit , and thus its size may vary from seven to twelve bits for five to eight bits of actual data. [ 74 ] For synchronous communication the error checking usually uses bytes at the end of a frame .
Terms used here to describe the structure imposed by the machine design, in addition to bit , are listed below. Byte denotes a group of bits used to encode a character, or the number of bits transmitted in parallel to and from input-output units. A term other than character is used here because a given character may be represented in different applications by more than one code, and different codes may use different numbers of bits (i.e., different byte sizes). In input-output transmission the grouping of bits may be completely arbitrary and have no relation to actual characters. (The term is coined from bite , but respelled to avoid accidental mutation to bit .) A word consists of the number of data bits transmitted in parallel from or to memory in one memory cycle. Word size is thus defined as a structural property of the memory. (The term catena was coined for this purpose by the designers of the Bull GAMMA 60 [ fr ] computer.) Block refers to the number of words transmitted to or from an input-output unit in response to a single input-output instruction. Block size is a structural property of an input-output unit; it may have been fixed by the design or left to be varied by the program.
[...] Most important, from the point of view of editing, will be the ability to handle any characters or digits, from 1 to 6 bits long. Figure 2 shows the Shift Matrix to be used to convert a 60-bit word , coming from Memory in parallel, into characters , or 'bytes' as we have called them, to be sent to the Adder serially. The 60 bits are dumped into magnetic cores on six different levels. Thus, if a 1 comes out of position 9, it appears in all six cores underneath. Pulsing any diagonal line will send the six bits stored along that line to the Adder. The Adder may accept all or only some of the bits. Assume that it is desired to operate on 4 bit decimal digits , starting at the right. The 0-diagonal is pulsed first, sending out the six bits 0 to 5, of which the Adder accepts only the first four (0-3). Bits 4 and 5 are ignored. Next, the 4 diagonal is pulsed. This sends out bits 4 to 9, of which the last two are again ignored, and so on. It is just as easy to use all six bits in alphanumeric work, or to handle bytes of only one bit for logical analysis, or to offset the bytes by any number of bits. All this can be done by pulling the appropriate shift diagonals. An analogous matrix arrangement is used to change from serial to parallel operation at the output of the adder. [...]
byte: A string that consists of a number of bits, treated as a unit, and usually representing a character or a part of a character. NOTES: 1 The number of bits in a byte is fixed for a given data processing system. 2 The number of bits in a byte is usually 8.
We received the following from W Buchholz, one of the individuals who was working on IBM's Project Stretch in the mid 1950s. His letter tells the story. Not being a regular reader of your magazine, I heard about the question in the November 1976 issue regarding the origin of the term "byte" from a colleague who knew that I had perpetrated this piece of jargon [see page 77 of November 1976 BYTE, "Olde Englishe"] . I searched my files and could not locate a birth certificate. But I am sure that "byte" is coming of age in 1977 with its 21st birthday. Many have assumed that byte, meaning 8 bits, originated with the IBM System/360, which spread such bytes far and wide in the mid-1960s. The editor is correct in pointing out that the term goes back to the earlier Stretch computer (but incorrect in that Stretch was the first, not the last, of IBM's second-generation transistorized computers to be developed). The first reference found in the files was contained in an internal memo written in June 1956 during the early days of developing Stretch . A byte was described as consisting of any number of parallel bits from one to six. Thus a byte was assumed to have a length appropriate for the occasion. Its first use was in the context of the input-output equipment of the 1950s, which handled six bits at a time. The possibility of going to 8-bit bytes was considered in August 1956 and incorporated in the design of Stretch shortly thereafter . The first published reference to the term occurred in 1959 in a paper ' Processing Data in Bits and Pieces ' by G A Blaauw , F P Brooks Jr and W Buchholz in the IRE Transactions on Electronic Computers , June 1959, page 121. The notions of that paper were elaborated in Chapter 4 of Planning a Computer System (Project Stretch) , edited by W Buchholz, McGraw-Hill Book Company (1962). The rationale for coining the term was explained there on page 40 as follows: Byte denotes a group of bits used to encode a character, or the number of bits transmitted in parallel to and from input-output units. A term other than character is used here because a given character may be represented in different applications by more than one code, and different codes may use different numbers of bits (ie, different byte sizes). In input-output transmission the grouping of bits may be completely arbitrary and have no relation to actual characters. (The term is coined from bite , but respelled to avoid accidental mutation to bit. ) System/360 took over many of the Stretch concepts, including the basic byte and word sizes, which are powers of 2. For economy, however, the byte size was fixed at the 8 bit maximum, and addressing at the bit level was replaced by byte addressing. Since then the term byte has generally meant 8 bits, and it has thus passed into the general vocabulary. Are there any other terms coined especially for the computer field which have found their way into general dictionaries of English language?
1956 Summer: Gerrit Blaauw , Fred Brooks , Werner Buchholz , John Cocke and Jim Pomerene join the Stretch team. Lloyd Hunter provides transistor leadership. 1956 July [ sic ]: In a report Werner Buchholz lists the advantages of a 64-bit word length for Stretch. It also supports NSA 's requirement for 8-bit bytes. Werner's term "Byte" first popularized in this memo.
NB. This timeline erroneously specifies the birth date of the term "byte" as July 1956 , while Buchholz actually used the term as early as June 1956 .
[...] 60 is a multiple of 1, 2, 3, 4, 5, and 6. Hence bytes of length from 1 to 6 bits can be packed efficiently into a 60-bit word without having to split a byte between one word and the next. If longer bytes were needed, 60 bits would, of course, no longer be ideal. With present applications, 1, 4, and 6 bits are the really important cases. With 64-bit words, it would often be necessary to make some compromises, such as leaving 4 bits unused in a word when dealing with 6-bit bytes at the input and output. However, the LINK Computer can be equipped to edit out these gaps and to permit handling of bytes which are split between words. [...]
[...] The maximum input-output byte size for serial operation will now be 8 bits, not counting any error detection and correction bits. Thus, the Exchange will operate on an 8-bit byte basis, and any input-output units with less than 8 bits per byte will leave the remaining bits blank. The resultant gaps can be edited out later by programming [...]
I came to work for IBM , and saw all the confusion caused by the 64-character limitation. Especially when we started to think about word processing, which would require both upper and lower case. Add 26 lower case letters to 47 existing, and one got 73 -- 9 more than 6 bits could represent. I even made a proposal (in view of STRETCH , the very first computer I know of with an 8-bit byte) that would extend the number of punch card character codes to 256 [1] . Some folks took it seriously. I thought of it as a spoof. So some folks started thinking about 7-bit characters, but this was ridiculous. With IBM's STRETCH computer as background, handling 64-character words divisible into groups of 8 (I designed the character set for it, under the guidance of Dr. Werner Buchholz , the man who DID coin the term "byte" for an 8-bit grouping). [2] It seemed reasonable to make a universal 8-bit character set, handling up to 256. In those days my mantra was "powers of 2 are magic". And so the group I headed developed and justified such a proposal [3]. That was a little too much progress when presented to the standards group that was to formalize ASCII, so they stopped short for the moment with a 7-bit set, or else an 8-bit set with the upper half left for future work. The IBM 360 used 8-bit characters, although not ASCII directly. Thus Buchholz's "byte" caught on everywhere. I myself did not like the name for many reasons. The design had 8 bits moving around in parallel. But then came a new IBM part, with 9 bits for self-checking, both inside the CPU and in the tape drives . I exposed this 9-bit byte to the press in 1973. But long before that, when I headed software operations for Cie. Bull in France in 1965-66, I insisted that 'byte' be deprecated in favor of " octet ". You can notice that my preference then is now the preferred term. It is justified by new communications methods that can carry 16, 32, 64, and even 128 bits in parallel. But some foolish people now refer to a "16-bit byte" because of this parallel transfer, which is visible in the UNICODE set. I'm not sure, but maybe this should be called a " hextet ". But you will notice that I am still correct. Powers of 2 are still magic!
The word byte was coined around 1956 to 1957 at MIT Lincoln Laboratories within a project called SAGE (the North American Air Defense System), which was jointly developed by Rand , Lincoln Labs, and IBM . In that era, computer memory structure was already defined in terms of word size . A word consisted of x number of bits ; a bit represented a binary notational position in a word. Operations typically operated on all the bits in the full word. We coined the word byte to refer to a logical set of bits less than a full word size. At that time, it was not defined specifically as x bits but typically referred to as a set of 4 bits , as that was the size of most of our coded data items. Shortly afterward, I went on to other responsibilities that removed me from SAGE. After having spent many years in Asia, I returned to the U.S. and was bemused to find out that the word byte was being used in the new microcomputer technology to refer to the basic addressable memory unit.
A question-and-answer session at an ACM conference on the history of programming languages included this exchange: [ John Goodenough : You mentioned that the term "byte" is used in JOVIAL . Where did the term come from? ] [ Jules Schwartz (inventor of JOVIAL): As I recall, the AN/FSQ-31 , a totally different computer than the 709 , was byte oriented. I don't recall for sure, but I'm reasonably certain the description of that computer included the word "byte," and we used it. ] [ Fred Brooks : May I speak to that? Werner Buchholz coined the word as part of the definition of STRETCH , and the AN/FSQ-31 picked it up from STRETCH, but Werner is very definitely the author of that word. ] [ Schwartz: That's right. Thank you. ]
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YouMail is an Irvine, CA -based developer of a visual voicemail [ 1 ] and Robocall blocking service for mobile phones , [ 2 ] available in the US and the UK. [ 3 ] Their voicemail mobile app replaces the voicemail service offered by mobile phone service providers, and offers webmail -like voicemail access and voicemail-to-text transcriptions. [ 4 ] The company also compiles the YouMail Robocall index by monitoring automated call patterns and behaviors, and verifying that activity against numbers that its customers block, or report as spam. [ 5 ]
The YouMail brand visual voicemail software was first developed, trademarked, and brought to market in 2006 by communications software developer Zeacom , which is based in Auckland , New Zealand. The service originally started out as a multi-platform visual voicemail solution, with the novel feature of personal greetings, where users could create different greetings for callers based on their incoming caller ID. [ 1 ] Helping combat robocalls their service replaces an ordinary voicemail; it instead plays three notes that create the impression of a non-working number to prevent robocalls from coming in. [ 6 ]
YouMail was spun off as a standalone service in 2007. [ 7 ] In November 2007, YouMail announced a partnership with Salient Media, [ 8 ] to offer a combination of free and subscription-based comedic voicemail greetings.
In 2009, the company saw its first success, with visual voicemail for BlackBerry . [ 7 ] It also launched a free iPhone app, which was considered a loss leader for its voicemail transcription services. [ 4 ]
In 2010, the company announced that YouMail was the standard voicemail that comes with all mobile phones from IMMIX Wireless in Pennsylvania , Cellular One in eastern Central Illinois , Blue Wireless in New York , iSmart Mobile in Montana , VoicePulse in New Jersey , and Windy City Cellular in Adak , Alaska. [ 9 ]
In 2011, the company launched WhoAreYou, an app for Android that provides users with caller's names, and gives them the ability to add specific numbers to a block list, screening out robocalls and telemarketers in the process. [ 10 ]
By 2012, the company reported over 2.5 million registered users of its service. [ 11 ] The company also announced they stopped supporting new updates for BlackBerry devices. [ 12 ]
In November 2015, the company launched the YouMail Robocall Index, to track legal and illegal robocall traffic across the US. The YouMail Robocall Index is a unique online portal which provides a monthly estimate of the volumes and types of robocalls nationwide, and for each specific state, city and area code. The initial report indicated at that time that 1 out of every 6 calls received in the US was generated by a machine. [ 13 ]
The ongoing monthly estimate is created by extrapolating from the behavior of the billions of calls that YouMail has managed for its users. YouMail identifies problematic numbers through its audio fingerprinting technology and analysis of calling patterns, along with direct consumer feedback. In turn, the Index's statistics have been regularly cited [ 14 ] by the Federal Communications Commission (FCC), consumer advocates and many other groups as the national source [ 15 ] [ 16 ] for robocalling data trends.
YouMail won the American Business Awards' Gold Stevie Award for Technical Innovation of the Year, [ 17 ] and the YouMail app was named the nation's best robocall-blocking solution [ 18 ] in a competition organized by Geoffrey Fowler of The Washington Post .
YouMail services have been described in detail by an independent source, with review. [ 19 ]
YouMail develops visual voicemail apps for Android phones [ 20 ] and iPhones . [ 4 ] The app features a voice-to-text feature which automatically transcribes voice messages and displays the text on-screen. This allows users to get their messages without having to listen to them. [ 21 ]
The company also produces WhoAreYou for Android, which enhances their visual voicemail app by adding call and text blocking and real-time reverse lookups on incoming calls and SMS messages. [ 10 ] The app can deter callers by picking up the call, playing a recorded "out of service" message to the caller, and hang back up, making the caller think the line has been disconnected. [ 22 ]
The company's visual voicemail app is preloaded or recommended by carriers including Viaero Wireless [ 23 ] and RedPocketMobile. [ 24 ]
The company also produces the YouMail Robocall Index, which announced in January 2016 that Americans received over one billion unsolicited or automated calls in December 2015. Atlanta was identified as the area hardest hit by robocalls, with Houston in second. [ 25 ] US robocalls have reached new highs in the years since, [ 26 ] leading to President Trump signing legislation on December 31, 2019 to help reduce the volume of unwanted robocalls. [ 27 ] In March 2020, the index identified an expanding set of robocalls leveraging the COVID-19 pandemic. [ 28 ] Identifying these illegal calls, YouMail notified carriers, enterprises, and the authorities to locate, take down, and punish the callers, helping shut down the COVID-19 scams in just days. [ 29 ]
YouMail virtual numbers provide a second phone number, for example to separate business calls from personal calls, while keeping cell phones private and protected from unwanted calls. [ 30 ]
Third-party developers use YouMail's API to create apps for other platforms, such as MagikMail for Windows Phone . [ 31 ]
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https://en.wikipedia.org/wiki/Youmail
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In mathematics , Young's convolution inequality is a mathematical inequality about the convolution of two functions, [ 1 ] named after William Henry Young .
In real analysis , the following result is called Young's convolution inequality: [ 2 ]
Suppose f {\displaystyle f} is in the Lebesgue space L p ( R d ) {\displaystyle L^{p}(\mathbb {R} ^{d})} and g {\displaystyle g} is in L q ( R d ) {\displaystyle L^{q}(\mathbb {R} ^{d})} and 1 p + 1 q = 1 r + 1 {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}={\frac {1}{r}}+1} with 1 ≤ p , q , r ≤ ∞ . {\displaystyle 1\leq p,q,r\leq \infty .} Then ‖ f ∗ g ‖ r ≤ ‖ f ‖ p ‖ g ‖ q . {\displaystyle \|f*g\|_{r}\leq \|f\|_{p}\|g\|_{q}.}
Here the star denotes convolution , L p {\displaystyle L^{p}} is Lebesgue space , and ‖ f ‖ p = ( ∫ R d | f ( x ) | p d x ) 1 / p {\displaystyle \|f\|_{p}={\Bigl (}\int _{\mathbb {R} ^{d}}|f(x)|^{p}\,dx{\Bigr )}^{1/p}} denotes the usual L p {\displaystyle L^{p}} norm.
Equivalently, if p , q , r ≥ 1 {\displaystyle p,q,r\geq 1} and 1 p + 1 q + 1 r = 2 {\textstyle {\frac {1}{p}}+{\frac {1}{q}}+{\frac {1}{r}}=2} then | ∫ R d ∫ R d f ( x ) g ( x − y ) h ( y ) d x d y | ≤ ( ∫ R d | f | p ) 1 p ( ∫ R d | g | q ) 1 q ( ∫ R d | h | r ) 1 r {\displaystyle \left|\int _{\mathbb {R} ^{d}}\int _{\mathbb {R} ^{d}}f(x)g(x-y)h(y)\,\mathrm {d} x\,\mathrm {d} y\right|\leq \left(\int _{\mathbb {R} ^{d}}\vert f\vert ^{p}\right)^{\frac {1}{p}}\left(\int _{\mathbb {R} ^{d}}\vert g\vert ^{q}\right)^{\frac {1}{q}}\left(\int _{\mathbb {R} ^{d}}\vert h\vert ^{r}\right)^{\frac {1}{r}}}
Young's convolution inequality has a natural generalization in which we replace R d {\displaystyle \mathbb {R} ^{d}} by a unimodular group G . {\displaystyle G.} If we let μ {\displaystyle \mu } be a bi-invariant Haar measure on G {\displaystyle G} and we let f , g : G → R {\displaystyle f,g:G\to \mathbb {R} } or C {\displaystyle \mathbb {C} } be integrable functions, then we define f ∗ g {\displaystyle f*g} by f ∗ g ( x ) = ∫ G f ( y ) g ( y − 1 x ) d μ ( y ) . {\displaystyle f*g(x)=\int _{G}f(y)g(y^{-1}x)\,\mathrm {d} \mu (y).} Then in this case, Young's inequality states that for f ∈ L p ( G , μ ) {\displaystyle f\in L^{p}(G,\mu )} and g ∈ L q ( G , μ ) {\displaystyle g\in L^{q}(G,\mu )} and p , q , r ∈ [ 1 , ∞ ] {\displaystyle p,q,r\in [1,\infty ]} such that 1 p + 1 q = 1 r + 1 {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}={\frac {1}{r}}+1} we have a bound ‖ f ∗ g ‖ r ≤ ‖ f ‖ p ‖ g ‖ q . {\displaystyle \lVert f*g\rVert _{r}\leq \lVert f\rVert _{p}\lVert g\rVert _{q}.} Equivalently, if p , q , r ≥ 1 {\displaystyle p,q,r\geq 1} and 1 p + 1 q + 1 r = 2 {\textstyle {\frac {1}{p}}+{\frac {1}{q}}+{\frac {1}{r}}=2} then | ∫ G ∫ G f ( x ) g ( y − 1 x ) h ( y ) d μ ( x ) d μ ( y ) | ≤ ( ∫ G | f | p ) 1 p ( ∫ G | g | q ) 1 q ( ∫ G | h | r ) 1 r . {\displaystyle \left|\int _{G}\int _{G}f(x)g(y^{-1}x)h(y)\,\mathrm {d} \mu (x)\,\mathrm {d} \mu (y)\right|\leq \left(\int _{G}\vert f\vert ^{p}\right)^{\frac {1}{p}}\left(\int _{G}\vert g\vert ^{q}\right)^{\frac {1}{q}}\left(\int _{G}\vert h\vert ^{r}\right)^{\frac {1}{r}}.} Since R d {\displaystyle \mathbb {R} ^{d}} is in fact a locally compact abelian group (and therefore unimodular) with the Lebesgue measure the desired Haar measure, this is in fact a generalization.
This generalization may be refined. Let G {\displaystyle G} and μ {\displaystyle \mu } be as before and assume 1 < p , q , r < ∞ {\displaystyle 1<p,q,r<\infty } satisfy 1 p + 1 q = 1 r + 1. {\textstyle {\tfrac {1}{p}}+{\tfrac {1}{q}}={\tfrac {1}{r}}+1.} Then there exists a constant C {\displaystyle C} such that for any f ∈ L p ( G , μ ) {\displaystyle f\in L^{p}(G,\mu )} and any measurable function g {\displaystyle g} on G {\displaystyle G} that belongs to the weak L q {\displaystyle L^{q}} space L q , w ( G , μ ) , {\displaystyle L^{q,w}(G,\mu ),} which by definition means that the following supremum ‖ g ‖ q , w q := sup t > 0 t q μ ( | g | > t ) {\displaystyle \|g\|_{q,w}^{q}~:=~\sup _{t>0}\,t^{q}\mu (|g|>t)} is finite, we have f ∗ g ∈ L r ( G , μ ) {\displaystyle f*g\in L^{r}(G,\mu )} and [ 3 ] ‖ f ∗ g ‖ r ≤ C ‖ f ‖ p ‖ g ‖ q , w . {\displaystyle \|f*g\|_{r}~\leq ~C\,\|f\|_{p}\,\|g\|_{q,w}.}
An example application is that Young's inequality can be used to show that the heat semigroup is a contracting semigroup using the L 2 {\displaystyle L^{2}} norm (that is, the Weierstrass transform does not enlarge the L 2 {\displaystyle L^{2}} norm).
Young's inequality has an elementary proof with the non-optimal constant 1. [ 4 ]
We assume that the functions f , g , h : G → R {\displaystyle f,g,h:G\to \mathbb {R} } are nonnegative and integrable, where G {\displaystyle G} is a unimodular group endowed with a bi-invariant Haar measure μ . {\displaystyle \mu .} We use the fact that μ ( S ) = μ ( S − 1 ) {\displaystyle \mu (S)=\mu (S^{-1})} for any measurable S ⊆ G . {\displaystyle S\subseteq G.} Since p ( 2 − 1 q − 1 r ) = q ( 2 − 1 p − 1 r ) = r ( 2 − 1 p − 1 q ) = 1 {\textstyle p(2-{\tfrac {1}{q}}-{\tfrac {1}{r}})=q(2-{\tfrac {1}{p}}-{\tfrac {1}{r}})=r(2-{\tfrac {1}{p}}-{\tfrac {1}{q}})=1} ∫ G ∫ G f ( x ) g ( y − 1 x ) h ( y ) d μ ( x ) d μ ( y ) = ∫ G ∫ G ( f ( x ) p g ( y − 1 x ) q ) 1 − 1 r ( f ( x ) p h ( y ) r ) 1 − 1 q ( g ( y − 1 x ) q h ( y ) r ) 1 − 1 p d μ ( x ) d μ ( y ) {\displaystyle {\begin{aligned}&\int _{G}\int _{G}f(x)g(y^{-1}x)h(y)\,\mathrm {d} \mu (x)\,\mathrm {d} \mu (y)\\={}&\int _{G}\int _{G}\left(f(x)^{p}g(y^{-1}x)^{q}\right)^{1-{\frac {1}{r}}}\left(f(x)^{p}h(y)^{r}\right)^{1-{\frac {1}{q}}}\left(g(y^{-1}x)^{q}h(y)^{r}\right)^{1-{\frac {1}{p}}}\,\mathrm {d} \mu (x)\,\mathrm {d} \mu (y)\end{aligned}}} By the Hölder inequality for three functions we deduce that ∫ G ∫ G f ( x ) g ( y − 1 x ) h ( y ) d μ ( x ) d μ ( y ) ≤ ( ∫ G ∫ G f ( x ) p g ( y − 1 x ) q d μ ( x ) d μ ( y ) ) 1 − 1 r ( ∫ G ∫ G f ( x ) p h ( y ) r d μ ( x ) d μ ( y ) ) 1 − 1 q ( ∫ G ∫ G g ( y − 1 x ) q h ( y ) r d μ ( x ) d μ ( y ) ) 1 − 1 p . {\displaystyle {\begin{aligned}&\int _{G}\int _{G}f(x)g(y^{-1}x)h(y)\,\mathrm {d} \mu (x)\,\mathrm {d} \mu (y)\\&\leq \left(\int _{G}\int _{G}f(x)^{p}g(y^{-1}x)^{q}\,\mathrm {d} \mu (x)\,\mathrm {d} \mu (y)\right)^{1-{\frac {1}{r}}}\left(\int _{G}\int _{G}f(x)^{p}h(y)^{r}\,\mathrm {d} \mu (x)\,\mathrm {d} \mu (y)\right)^{1-{\frac {1}{q}}}\left(\int _{G}\int _{G}g(y^{-1}x)^{q}h(y)^{r}\,\mathrm {d} \mu (x)\,\mathrm {d} \mu (y)\right)^{1-{\frac {1}{p}}}.\end{aligned}}} The conclusion follows then by left-invariance of the Haar measure, the fact that integrals are preserved by inversion of the domain, and by Fubini's theorem .
Young's inequality can also be proved by interpolation; see the article on Riesz–Thorin interpolation for a proof.
In case p , q > 1 , {\displaystyle p,q>1,} Young's inequality can be strengthened to a sharp form, via ‖ f ∗ g ‖ r ≤ c p , q ‖ f ‖ p ‖ g ‖ q . {\displaystyle \|f*g\|_{r}\leq c_{p,q}\|f\|_{p}\|g\|_{q}.} where the constant c p , q < 1. {\displaystyle c_{p,q}<1.} [ 5 ] [ 6 ] [ 7 ] When this optimal constant is achieved, the function f {\displaystyle f} and g {\displaystyle g} are multidimensional Gaussian functions .
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In mathematical analysis , the Young's inequality for integral operators , is a bound on the L p → L q {\displaystyle L^{p}\to L^{q}} operator norm of an integral operator in terms of L r {\displaystyle L^{r}} norms of the kernel itself.
Assume that X {\displaystyle X} and Y {\displaystyle Y} are measurable spaces, K : X × Y → R {\displaystyle K:X\times Y\to \mathbb {R} } is measurable and q , p , r ≥ 1 {\displaystyle q,p,r\geq 1} are such that 1 q = 1 p + 1 r − 1 {\displaystyle {\frac {1}{q}}={\frac {1}{p}}+{\frac {1}{r}}-1} . If
and
then [ 1 ]
If X = Y = R d {\displaystyle X=Y=\mathbb {R} ^{d}} and K ( x , y ) = h ( x − y ) {\displaystyle K(x,y)=h(x-y)} , then the inequality becomes Young's convolution inequality .
Young's inequality for products
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In mathematics , Young's inequality for products is a mathematical inequality about the product of two numbers. [ 1 ] The inequality is named after William Henry Young and should not be confused with Young's convolution inequality .
Young's inequality for products can be used to prove Hölder's inequality . It is also widely used to estimate the norm of nonlinear terms in PDE theory , since it allows one to estimate a product of two terms by a sum of the same terms raised to a power and scaled.
The standard form of the inequality is the following, which can be used to prove Hölder's inequality .
Theorem — If a ≥ 0 {\displaystyle a\geq 0} and b ≥ 0 {\displaystyle b\geq 0} are nonnegative real numbers and if p > 1 {\displaystyle p>1} and q > 1 {\displaystyle q>1} are real numbers such that 1 p + 1 q = 1 , {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}=1,} then a b ≤ a p p + b q q . {\displaystyle ab~\leq ~{\frac {a^{p}}{p}}+{\frac {b^{q}}{q}}.}
Equality holds if and only if a p = b q . {\displaystyle a^{p}=b^{q}.}
Since 1 p + 1 q = 1 , {\displaystyle {\tfrac {1}{p}}+{\tfrac {1}{q}}=1,} p − 1 = 1 q − 1 . {\displaystyle p-1={\tfrac {1}{q-1}}.} A graph y = x p − 1 {\displaystyle y=x^{p-1}} on the x y {\displaystyle xy} -plane is thus also a graph x = y q − 1 . {\displaystyle x=y^{q-1}.} From sketching a visual representation of the integrals of the area between this curve and the axes, and the area in the rectangle bounded by the lines x = 0 , x = a , y = 0 , y = b , {\displaystyle x=0,x=a,y=0,y=b,} and the fact that y {\displaystyle y} is always increasing for increasing x {\displaystyle x} and vice versa, we can see that ∫ 0 a x p − 1 d x {\displaystyle \int _{0}^{a}x^{p-1}\mathrm {d} x} upper bounds the area of the rectangle below the curve (with equality when b ≥ a p − 1 {\displaystyle b\geq a^{p-1}} ) and ∫ 0 b y q − 1 d y {\displaystyle \int _{0}^{b}y^{q-1}\mathrm {d} y} upper bounds the area of the rectangle above the curve (with equality when b ≤ a p − 1 {\displaystyle b\leq a^{p-1}} ). Thus, ∫ 0 a x p − 1 d x + ∫ 0 b y q − 1 d y ≥ a b , {\displaystyle \int _{0}^{a}x^{p-1}\mathrm {d} x+\int _{0}^{b}y^{q-1}\mathrm {d} y\geq ab,} with equality when b = a p − 1 {\displaystyle b=a^{p-1}} (or equivalently, a p = b q {\displaystyle a^{p}=b^{q}} ). Young's inequality follows from evaluating the integrals. (See below for a generalization.)
A second proof is via Jensen's inequality .
The claim is certainly true if a = 0 {\displaystyle a=0} or b = 0 {\displaystyle b=0} so henceforth assume that a > 0 {\displaystyle a>0} and b > 0. {\displaystyle b>0.} Put t = 1 / p {\displaystyle t=1/p} and ( 1 − t ) = 1 / q . {\displaystyle (1-t)=1/q.} Because the logarithm function is concave , ln ( t a p + ( 1 − t ) b q ) ≥ t ln ( a p ) + ( 1 − t ) ln ( b q ) = ln ( a ) + ln ( b ) = ln ( a b ) {\displaystyle \ln \left(ta^{p}+(1-t)b^{q}\right)~\geq ~t\ln \left(a^{p}\right)+(1-t)\ln \left(b^{q}\right)=\ln(a)+\ln(b)=\ln(ab)} with the equality holding if and only if a p = b q . {\displaystyle a^{p}=b^{q}.} Young's inequality follows by exponentiating.
Yet another proof is to first prove it with b = 1 {\displaystyle b=1} an then apply the resulting inequality to a b q {\displaystyle {\tfrac {a}{b^{q}}}} . The proof below illustrates also why Hölder conjugate exponent is the only possible parameter that makes Young's inequality hold for all non-negative values. The details follow:
Let 0 < α < 1 {\displaystyle 0<\alpha <1} and α + β = 1 {\displaystyle \alpha +\beta =1} . The inequality x ≤ α x p + β , f o r a l l x ≥ 0 {\displaystyle x~\leq ~\alpha x^{p}+\beta ,\qquad \,for\quad \ all\quad \ x~\geq ~0} holds if and only if α = 1 p {\displaystyle \alpha ={\tfrac {1}{p}}} (and hence β = 1 q {\displaystyle \beta ={\tfrac {1}{q}}} ). This can be shown by convexity arguments or by simply minimizing the single-variable function.
To prove full Young's inequality, clearly we assume that a > 0 {\displaystyle a>0} and b > 0 {\displaystyle b>0} . Now, we apply the inequality above to x = a b s {\displaystyle x={\tfrac {a}{b^{s}}}} to obtain: a b s ≤ 1 p a p b s p + 1 q . {\displaystyle {\tfrac {a}{b^{s}}}~\leq ~{\tfrac {1}{p}}{\tfrac {a^{p}}{b^{sp}}}+{\tfrac {1}{q}}.} It is easy to see that choosing s = q − 1 {\displaystyle s=q-1} and multiplying both sides by b q {\displaystyle b^{q}} yields Young's inequality.
Young's inequality may equivalently be written as a α b β ≤ α a + β b , 0 ≤ α , β ≤ 1 , α + β = 1. {\displaystyle a^{\alpha }b^{\beta }\leq \alpha a+\beta b,\qquad \,0\leq \alpha ,\beta \leq 1,\quad \ \alpha +\beta =1.}
Where this is just the concavity of the logarithm function.
Equality holds if and only if a = b {\displaystyle a=b} or { α , β } = { 0 , 1 } . {\displaystyle \{\alpha ,\beta \}=\{0,1\}.} This also follows from the weighted AM-GM inequality .
Theorem [ 4 ] — Suppose a > 0 {\displaystyle a>0} and b > 0. {\displaystyle b>0.} If 1 < p < ∞ {\displaystyle 1<p<\infty } and q {\displaystyle q} are such that 1 p + 1 q = 1 {\displaystyle {\tfrac {1}{p}}+{\tfrac {1}{q}}=1} then a b = min 0 < t < ∞ ( t p a p p + t − q b q q ) . {\displaystyle ab~=~\min _{0<t<\infty }\left({\frac {t^{p}a^{p}}{p}}+{\frac {t^{-q}b^{q}}{q}}\right).}
Using t := 1 {\displaystyle t:=1} and replacing a {\displaystyle a} with a 1 / p {\displaystyle a^{1/p}} and b {\displaystyle b} with b 1 / q {\displaystyle b^{1/q}} results in the inequality: a 1 / p b 1 / q ≤ a p + b q , {\displaystyle a^{1/p}\,b^{1/q}~\leq ~{\frac {a}{p}}+{\frac {b}{q}},} which is useful for proving Hölder's inequality .
Define a real-valued function f {\displaystyle f} on the positive real numbers by f ( t ) = t p a p p + t − q b q q {\displaystyle f(t)~=~{\frac {t^{p}a^{p}}{p}}+{\frac {t^{-q}b^{q}}{q}}} for every t > 0 {\displaystyle t>0} and then calculate its minimum.
Theorem — If 0 ≤ p i ≤ 1 {\displaystyle 0\leq p_{i}\leq 1} with ∑ i p i = 1 {\displaystyle \sum _{i}p_{i}=1} then ∏ i a i p i ≤ ∑ i p i a i . {\displaystyle \prod _{i}{a_{i}}^{p_{i}}~\leq ~\sum _{i}p_{i}a_{i}.} Equality holds if and only if all the a i {\displaystyle a_{i}} s with non-zero p i {\displaystyle p_{i}} s are equal.
An elementary case of Young's inequality is the inequality with exponent 2 , {\displaystyle 2,} a b ≤ a 2 2 + b 2 2 , {\displaystyle ab\leq {\frac {a^{2}}{2}}+{\frac {b^{2}}{2}},} which also gives rise to the so-called Young's inequality with ε {\displaystyle \varepsilon } (valid for every ε > 0 {\displaystyle \varepsilon >0} ), sometimes called the Peter–Paul inequality. [ 5 ] This name refers to the fact that tighter control of the second term is achieved at the cost of losing some control of the first term – one must "rob Peter to pay Paul" a b ≤ a 2 2 ε + ε b 2 2 . {\displaystyle ab~\leq ~{\frac {a^{2}}{2\varepsilon }}+{\frac {\varepsilon b^{2}}{2}}.}
Proof : Young's inequality with exponent 2 {\displaystyle 2} is the special case p = q = 2. {\displaystyle p=q=2.} However, it has a more elementary proof.
Start by observing that the square of every real number is zero or positive. Therefore, for every pair of real numbers a {\displaystyle a} and b {\displaystyle b} we can write: 0 ≤ ( a − b ) 2 {\displaystyle 0\leq (a-b)^{2}} Work out the square of the right hand side: 0 ≤ a 2 − 2 a b + b 2 {\displaystyle 0\leq a^{2}-2ab+b^{2}} Add 2 a b {\displaystyle 2ab} to both sides: 2 a b ≤ a 2 + b 2 {\displaystyle 2ab\leq a^{2}+b^{2}} Divide both sides by 2 and we have Young's inequality with exponent 2 : {\displaystyle 2:} a b ≤ a 2 2 + b 2 2 {\displaystyle ab\leq {\frac {a^{2}}{2}}+{\frac {b^{2}}{2}}}
Young's inequality with ε {\displaystyle \varepsilon } follows by substituting a ′ {\displaystyle a'} and b ′ {\displaystyle b'} as below into Young's inequality with exponent 2 : {\displaystyle 2:} a ′ = a / ε , b ′ = ε b . {\displaystyle a'=a/{\sqrt {\varepsilon }},\;b'={\sqrt {\varepsilon }}b.}
T. Ando proved a generalization of Young's inequality for complex matrices ordered
by Loewner ordering . [ 6 ] It states that for any pair A , B {\displaystyle A,B} of complex matrices of order n {\displaystyle n} there exists a unitary matrix U {\displaystyle U} such that U ∗ | A B ∗ | U ⪯ 1 p | A | p + 1 q | B | q , {\displaystyle U^{*}|AB^{*}|U\preceq {\tfrac {1}{p}}|A|^{p}+{\tfrac {1}{q}}|B|^{q},} where ∗ {\displaystyle {}^{*}} denotes the conjugate transpose of the matrix and | A | = A ∗ A . {\displaystyle |A|={\sqrt {A^{*}A}}.}
For the standard version [ 7 ] [ 8 ] of the inequality,
let f {\displaystyle f} denote a real-valued, continuous and strictly increasing function on [ 0 , c ] {\displaystyle [0,c]} with c > 0 {\displaystyle c>0} and f ( 0 ) = 0. {\displaystyle f(0)=0.} Let f − 1 {\displaystyle f^{-1}} denote the inverse function of f . {\displaystyle f.} Then, for all a ∈ [ 0 , c ] {\displaystyle a\in [0,c]} and b ∈ [ 0 , f ( c ) ] , {\displaystyle b\in [0,f(c)],} a b ≤ ∫ 0 a f ( x ) d x + ∫ 0 b f − 1 ( x ) d x {\displaystyle ab~\leq ~\int _{0}^{a}f(x)\,dx+\int _{0}^{b}f^{-1}(x)\,dx} with equality if and only if b = f ( a ) . {\displaystyle b=f(a).}
With f ( x ) = x p − 1 {\displaystyle f(x)=x^{p-1}} and f − 1 ( y ) = y q − 1 , {\displaystyle f^{-1}(y)=y^{q-1},} this reduces to standard version for conjugate Hölder exponents.
For details and generalizations we refer to the paper of Mitroi & Niculescu. [ 9 ]
By denoting the convex conjugate of a real function f {\displaystyle f} by g , {\displaystyle g,} we obtain a b ≤ f ( a ) + g ( b ) . {\displaystyle ab~\leq ~f(a)+g(b).} This follows immediately from the definition of the convex conjugate. For a convex function f {\displaystyle f} this also follows from the Legendre transformation .
More generally, if f {\displaystyle f} is defined on a real vector space X {\displaystyle X} and its convex conjugate is denoted by f ⋆ {\displaystyle f^{\star }} (and is defined on the dual space X ⋆ {\displaystyle X^{\star }} ), then ⟨ u , v ⟩ ≤ f ⋆ ( u ) + f ( v ) . {\displaystyle \langle u,v\rangle \leq f^{\star }(u)+f(v).} where ⟨ ⋅ , ⋅ ⟩ : X ⋆ × X → R {\displaystyle \langle \cdot ,\cdot \rangle :X^{\star }\times X\to \mathbb {R} } is the dual pairing .
The convex conjugate of f ( a ) = a p / p {\displaystyle f(a)=a^{p}/p} is g ( b ) = b q / q {\displaystyle g(b)=b^{q}/q} with q {\displaystyle q} such that 1 p + 1 q = 1 , {\displaystyle {\tfrac {1}{p}}+{\tfrac {1}{q}}=1,} and thus Young's inequality for conjugate Hölder exponents mentioned above is a special case.
The Legendre transform of f ( a ) = e a − 1 {\displaystyle f(a)=e^{a}-1} is g ( b ) = 1 − b + b ln b {\displaystyle g(b)=1-b+b\ln b} , hence a b ≤ e a − b + b ln b {\displaystyle ab\leq e^{a}-b+b\ln b} for all non-negative a {\displaystyle a} and b . {\displaystyle b.} This estimate is useful in large deviations theory under exponential moment conditions, because b ln b {\displaystyle b\ln b} appears in the definition of relative entropy , which is the rate function in Sanov's theorem .
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In mathematics , Young's lattice is a lattice that is formed by all integer partitions . It is named after Alfred Young , who, in a series of papers On quantitative substitutional analysis, developed the representation theory of the symmetric group . In Young's theory, the objects now called Young diagrams and the partial order on them played a key, even decisive, role. Young's lattice prominently figures in algebraic combinatorics , forming the simplest example of a differential poset in the sense of Stanley (1988) . It is also closely connected with the crystal bases for affine Lie algebras .
Young's lattice is a lattice (and hence also a partially ordered set ) Y formed by all integer partitions ordered by inclusion of their Young diagrams (or Ferrers diagrams ).
The traditional application of Young's lattice is to the description of the irreducible representations of symmetric groups S n for all n , together with their branching properties, in characteristic zero. The equivalence classes of irreducible representations may be parametrized by partitions or Young diagrams, the restriction from S n +1 to S n is multiplicity-free, and the representation of S n with partition p is contained in the representation of S n +1 with partition q if and only if q covers p in Young's lattice. Iterating this procedure, one arrives at Young's semicanonical basis in the irreducible representation of S n with partition p , which is indexed by the standard Young tableaux of shape p .
Conventionally, Young's lattice is depicted in a Hasse diagram with all elements of the same rank shown at the same height above the bottom. Suter (2002) has shown that a different way of depicting some subsets of Young's lattice shows some unexpected symmetries.
The partition
of the n th triangular number has a Ferrers diagram that looks like a staircase. The largest elements whose Ferrers diagrams are rectangular that lie under the staircase are these:
Partitions of this form are the only ones that have only one element immediately below them in Young's lattice. Suter showed that the set of all elements less than or equal to these particular partitions has not only the bilateral symmetry that one expects of Young's lattice, but also rotational symmetry: the rotation group of order n + 1 acts on this poset. Since this set has both bilateral symmetry and rotational symmetry, it must have dihedral symmetry: the ( n + 1)st dihedral group acts faithfully on this set. The size of this set is 2 n .
For example, when n = 4, then the maximal element under the "staircase" that have rectangular Ferrers diagrams are
The subset of Young's lattice lying below these partitions has both bilateral symmetry and 5-fold rotational symmetry. Hence the dihedral group D 5 acts faithfully on this subset of Young's lattice.
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Young's modulus (or the Young modulus ) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression . Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material.
Although Young's modulus is named after the 19th-century British scientist Thomas Young , the concept was developed in 1727 by Leonhard Euler . The first experiments that used the concept of Young's modulus in its modern form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years. [ 1 ] The term modulus is derived from the Latin root term modus , which means measure .
Young's modulus, E {\displaystyle E} , quantifies the relationship between tensile or compressive stress σ {\displaystyle \sigma } (force per unit area) and axial strain ε {\displaystyle \varepsilon } (proportional deformation) in the linear elastic region of a material: [ 2 ] E = σ ε {\displaystyle E={\frac {\sigma }{\varepsilon }}}
Young's modulus is commonly measured in the International System of Units (SI) in multiples of the pascal (Pa) and common values are in the range of gigapascals (GPa).
Examples:
A solid material undergoes elastic deformation when a small load is applied to it in compression or extension. Elastic deformation is reversible, meaning that the material returns to its original shape after the load is removed.
At near-zero stress and strain, the stress–strain curve is linear , and the relationship between stress and strain is described by Hooke's law that states stress is proportional to strain. The coefficient of proportionality is Young's modulus. The higher the modulus, the more stress is needed to create the same amount of strain; an idealized rigid body would have an infinite Young's modulus. Conversely, a very soft material (such as a fluid) would deform without force, and would have zero Young's modulus.
Material stiffness is a distinct property from the following:
Young's modulus enables the calculation of the change in the dimension of a bar made of an isotropic elastic material under tensile or compressive loads. For instance, it predicts how much a material sample extends under tension or shortens under compression. The Young's modulus directly applies to cases of uniaxial stress; that is, tensile or compressive stress in one direction and no stress in the other directions. Young's modulus is also used in order to predict the deflection that will occur in a statically determinate beam when a load is applied at a point in between the beam's supports.
Other elastic calculations usually require the use of one additional elastic property, such as the shear modulus G {\displaystyle G} , bulk modulus K {\displaystyle K} , and Poisson's ratio ν {\displaystyle \nu } . Any two of these parameters are sufficient to fully describe elasticity in an isotropic material. For example, calculating physical properties of cancerous skin tissue, has been measured and found to be a Poisson’s ratio of 0.43±0.12 and an average Young’s modulus of 52 KPa. Defining the elastic properties of skin may become the first step in turning elasticity into a clinical tool. [ 3 ] For homogeneous isotropic materials simple relations exist between elastic constants that allow calculating them all as long as two are known:
Young's modulus represents the factor of proportionality in Hooke's law , which relates the stress and the strain. However, Hooke's law is only valid under the assumption of an elastic and linear response. Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however, all solid materials exhibit nearly Hookean behavior for small enough strains or stresses. If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear. Otherwise (if the typical stress one would apply is outside the linear range), the material is said to be non-linear.
Steel , carbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear. However, this is not an absolute classification: if very small stresses or strains are applied to a non-linear material, the response will be linear, but if very high stress or strain is applied to a linear material, the linear theory will not be enough. For example, as the linear theory implies reversibility , it would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure.
In solid mechanics , the slope of the stress–strain curve at any point is called the tangent modulus . It can be experimentally determined from the slope of a stress–strain curve created during tensile tests conducted on a sample of the material.
Young's modulus is not always the same in all orientations of a material. Most metals and ceramics, along with many other materials, are isotropic , and their mechanical properties are the same in all orientations. However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional. These materials then become anisotropic , and Young's modulus will change depending on the direction of the force vector. [ 4 ] Anisotropy can be seen in many composites as well. For example, carbon fiber has a much higher Young's modulus (is much stiffer) when force is loaded parallel to the fibers (along the grain). Other such materials include wood and reinforced concrete . Engineers can use this directional phenomenon to their advantage in creating structures.
Young's modulus is calculated by dividing the tensile stress , σ ( ε ) {\displaystyle \sigma (\varepsilon )} , by the engineering extensional strain , ε {\displaystyle \varepsilon } , in the elastic (initial, linear) portion of the physical stress–strain curve :
E ≡ σ ( ε ) ε = F / A Δ L / L 0 = F L 0 A Δ L {\displaystyle E\equiv {\frac {\sigma (\varepsilon )}{\varepsilon }}={\frac {F/A}{\Delta L/L_{0}}}={\frac {FL_{0}}{A\,\Delta L}}} where
Young's modulus of a material can be used to calculate the force it exerts under specific strain.
where F {\displaystyle F} is the force exerted by the material when contracted or stretched by Δ L {\displaystyle \Delta L} .
Hooke's law for a stretched wire can be derived from this formula:
where it comes in saturation
Note that the elasticity of coiled springs comes from shear modulus , not Young's modulus. When a spring is stretched, its wire's length doesn't change, but its shape does. This is why only the shear modulus of elasticity is involved in the stretching of a spring. [ citation needed ]
The elastic potential energy stored in a linear elastic material is given by the integral of the Hooke's law:
now by explicating the intensive variables:
This means that the elastic potential energy density (that is, per unit volume) is given by:
or, in simple notation, for a linear elastic material: u e ( ε ) = ∫ E ε d ε = 1 2 E ε 2 {\textstyle u_{e}(\varepsilon )=\int {E\,\varepsilon }\,d\varepsilon ={\frac {1}{2}}E{\varepsilon }^{2}} , since the strain is defined ε ≡ Δ L L 0 {\textstyle \varepsilon \equiv {\frac {\Delta L}{L_{0}}}} .
In a nonlinear elastic material the Young's modulus is a function of the strain, so the second equivalence no longer holds, and the elastic energy is not a quadratic function of the strain:
Young's modulus can vary somewhat due to differences in sample composition and test method. The rate of deformation has the greatest impact on the data collected, especially in polymers . The values here are approximate and only meant for relative comparison.
There are two valid solutions. The plus sign leads to ν ≥ 0 {\displaystyle \nu \geq 0} .
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Clark's rule is a medical term referring to a mathematical formula used to calculate the proper dosage of medicine for children aged 2–17 based on the weight of the patient and the appropriate adult dose. [ 1 ] The formula was named after Cecil Belfield Clarke (1894–1970), a Barbadian physician who practiced throughout the UK, the West Indies and Ghana. [ 2 ] [ 3 ]
The procedure is to take the child's weight in pounds , divide by 150 lb, and multiply the fractional result by the adult dose to find the equivalent child dosage. For example, if an adult dose of medication calls for 30 mg and the child weighs 30 lb, divide the weight by 150 (30/150) to obtain 1/5 and multiply 1/5 times 30 mg to get 6 mg.
Though it is more common for physicians to use medications that have suggested manufacturer's doses for children, familiarity of Clark's rule is used as an additional layer of protection against potentially deadly medication errors in clinical practice. [ 4 ] [ 5 ]
Similar to Clark's rule is Fried's rule , by which the formula is modified to be used for infants. [ 6 ] The formula is nearly identical, except with the child's weight replaced by the infant's age in months.
Fried's rule was named after Kalman Fried (1914–1999), an Israeli geneticist and pediatrician who developed his own formula while treating and observing children at the Hebrew University of Jerusalem -affiliated Hadassah Medical Center in the 1960s. Fried though was more renowned as a geneticist rather than a pediatrician . [ citation needed ]
The earlier Young's rule [ 1 ] for calculating the correct dose of medicine for a child is similar: it states that the child dosage is equal to the adult dosage multiplied by the child's age in years, divided by the sum of 12 plus the child's age.
Young's rule was named after Thomas Young (1773–1829), an English polymath, physician and physicist. [ 7 ]
This pharmacology -related article is a stub . You can help Wikipedia by expanding it .
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Young Engineers/ Future Leaders is a Standing Committee of the World Federation of Engineering Organizations . Its membership includes engineering students and engineers are the start of their careers.
The current chair is Zainab Garashi from Kuwait . Vice Chair is Kathryn Johnson from United States and secretary is Christopher Chukwunta from Nigeria .
The YE/FL is run by the YE/FL council. The YE/FL Council is the highest decision making board. Each national engineering association is asked to appoint one official delegate for the YE/FL Council. The Council meets at the regular committee meeting.
While absence of the YE/FL council the chair manages the main tasks, which are to guide the committee through its work, take care of administrative YE/FL responsibilities in between official meetings, to moderate official meetings, and set mile stones to help handle matters on time.
The YE/FL was founded in 2009 during the WFEO Engineering Congress on alternative energy in Kuwait on 3–5 November 2009. The founding members are Zainab Garashi (Chair, Kuwait ), Vice Chair Kathryn Johnson (Vice Chair, United States ) and Felix Firsbach (Secretary, Germany ). YE/FL met yearly during the WFEO conferences 2010 in Buenos Aires, Argentina, 2011 in Geneva, Switzerland and so on.
In 2017, YE/FL was reorganized with active directive from Tasiu Saad Gidari-Wudil , supervisor of the Engineering Regulation, Legislation and Liaison Board, to meet with WFEO‘s directives, engagement of government agencies and facilitation of collaborations. [ 1 ]
In the early years, YE/FL struggled with inter-conference communication, which was mainly via email. Just after the COVID-19 outbreak communication became easier with upcoming video-conference software. Nowadays, YE/FL organizes internal online meetings, international competitions [ 2 ] and was part of COP27 . [ 3 ]
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The working group Young Food Chemists ( Arbeitsgruppe Junge Lebensmittelchemie , AG JLC ) is a group of German university and PhD students as well as young professionals who represent the interests of students and trainees in the field of food chemistry , i.e. analytical chemistry with a focus on food.
The group acts as an independent working group of the German Food Chemical Society [ de ] , an expert group of the Society of German Chemists . [ 2 ] [ 3 ]
In 1996, ten food chemistry students from different cities founded the AG JLC in Freiburg (Breisgau) , Germany. Their goals were the representation of food chemistry students, public relations work and setting up a platform for students from different universities to connect. [ 2 ]
Since its foundation in 1996, over 40 national conferences took place. Through the voluntary work of the members different kinds of guidelines were verbalized, posters designed, workshops at subject -specific as well as interdisciplinary conferences organized and held.
A detailed chronicle was prepared in 2015/2016 and published as a casebound book at the AG JLC's 20th anniversary [ 4 ] in the context of the Deutscher Lebensmittelchemikertag (Congress of German Food Chemists) 2016 in Munich. [ 5 ]
Local acting groups of the AG JLC are present at all German universities which offer courses in food chemistry. They are supported in form of registered student groups at the universities. [ 6 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ]
On a national level the AG JLC is a democratic organization. Elections take place during the main annual meeting. Head of the AG JLC are two spokesperson (usually a woman and a man) who are elected alternatingly for a period of two years. Furthermore, the AG JLC has a representative in the managing board of the German Food Chemical Society ( Lebensmittelchemische Gesellschaft [ de ] ), where he or she takes part in decisions by voting. [ 11 ] The representative is elected every third year, whereas the elections of the treasurer and the secretary take place biennially. [ 2 ] [ 12 ]
Everyone taking part in the national conference is allowed to vote and run for the different positions.
The goals of the AG JLC include: [ 2 ]
To offer non-university education, the local AG JLC groups organize conferences, field trips and workshops. The focus lies on public relations and on broadening the network, too. [ 2 ] [ 3 ] [ 12 ] [ 13 ]
A national conference with members of each local group is held twice a year. Each year, the conference in September is held on the weekend before the Congress of German Food Chemists in the same town. In contrast to this, the spring conference is usually held in March in another town. The discussed topics include current issues, the organization of nationwide projects, networking and the exchange of ideas and experiences.
The steady cooperation of regional and national structures distinguishes the AG JLC from similar organizations. Some results of this successful strategy are:
Regional and national corporation partners are the German Food Chemical Society, the Society of German Chemists with the Young Chemistry Network (JCF), food chemists in governmental positions ( Lebensmittelchemiker/-innen im öffentlichen Dienst (BLC)) [ 14 ] as well as the Food Federation Germany (BLL). The contact is maintained on joint projects, conferences and workshops. [ 2 ] [ 3 ] [ 12 ] [ 15 ]
In 2017 the two AG JLC spokespersons were awarded as STEM -ambassadors during the STEM future conference in Berlin . [ 16 ]
At the Congress of German Food Chemists 2018 in Berlin, the AG JLC, represented by its founding member Dr. Jörg Häseler, was honored with the Adolf-Juckenack-Medal for the efforts for the Food Chemical Society and the profession of Food Chemists. [ 17 ] [ 18 ]
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The Young Woman Engineer of the Year Awards are presented at the Institution of Engineering and Technology , London, England. [ 1 ] Part of the IET Achievement Medals collection, the award was launched in 1978, and was originally known as the Girl Technician of the Year , until renamed in 1988. [ 2 ] [ 3 ] The award was first sponsored by the Caroline Haslett Memorial Trust, which was formed in 1945. [ 4 ] It is now funded and sponsored by the Institution of Engineering and Technology and Women's Engineering Society . [ 2 ] [ 5 ] Awarded to young female engineering apprentices in the UK.
Mary George CBE was the Director and Secretary of the Electrical Association for Women . [ 14 ] The prize is given annually to a young woman apprentice. [ 2 ]
The winners so far have included: [ 8 ]
The Women's Engineering Society Prize is awarded to a young woman engineer who demonstrates exceptional talent within engineering alongside a commitment to improving diversity within engineering. [ 2 ] [ 16 ]
The winners so far have included: [ 16 ]
The Gender Diversity Ambassador Award was introduced in 2019 to recognise an individual who has worked for much of their career to support gender equality in engineering. [ 6 ]
Winners:
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In mathematics , the Young subgroups of the symmetric group S n {\displaystyle S_{n}} are special subgroups that arise in combinatorics and representation theory . When S n {\displaystyle S_{n}} is viewed as the group of permutations of the set { 1 , 2 , … , n } {\displaystyle \{1,2,\ldots ,n\}} , and if λ = ( λ 1 , … , λ ℓ ) {\displaystyle \lambda =(\lambda _{1},\ldots ,\lambda _{\ell })} is an integer partition of n {\displaystyle n} , then the Young subgroup S λ {\displaystyle S_{\lambda }} indexed by λ {\displaystyle \lambda } is defined by S λ = S { 1 , 2 , … , λ 1 } × S { λ 1 + 1 , λ 1 + 2 , … , λ 1 + λ 2 } × ⋯ × S { n − λ ℓ + 1 , n − λ ℓ + 2 , … , n } , {\displaystyle S_{\lambda }=S_{\{1,2,\ldots ,\lambda _{1}\}}\times S_{\{\lambda _{1}+1,\lambda _{1}+2,\ldots ,\lambda _{1}+\lambda _{2}\}}\times \cdots \times S_{\{n-\lambda _{\ell }+1,n-\lambda _{\ell }+2,\ldots ,n\}},} where S { a , b , … } {\displaystyle S_{\{a,b,\ldots \}}} denotes the set of permutations of { a , b , … } {\displaystyle \{a,b,\ldots \}} and × {\displaystyle \times } denotes the direct product of groups . Abstractly, S λ {\displaystyle S_{\lambda }} is isomorphic to the product S λ 1 × S λ 2 × ⋯ × S λ ℓ {\displaystyle S_{\lambda _{1}}\times S_{\lambda _{2}}\times \cdots \times S_{\lambda _{\ell }}} . Young subgroups are named for Alfred Young . [ 1 ]
When S n {\displaystyle S_{n}} is viewed as a reflection group , its Young subgroups are precisely its parabolic subgroups . They may equivalently be defined as the subgroups generated by a subset of the adjacent transpositions ( 1 2 ) , ( 2 3 ) , … , ( n − 1 n ) {\displaystyle (1\ 2),(2\ 3),\ldots ,(n-1\ n)} . [ 2 ]
In some cases, the name Young subgroup is used more generally for the product S B 1 × ⋯ × S B ℓ {\displaystyle S_{B_{1}}\times \cdots \times S_{B_{\ell }}} , where { B 1 , … , B ℓ } {\displaystyle \{B_{1},\ldots ,B_{\ell }\}} is any set partition of { 1 , … , n } {\displaystyle \{1,\ldots ,n\}} (that is, a collection of disjoint , nonempty subsets whose union is { 1 , … , n } {\displaystyle \{1,\ldots ,n\}} ). [ 3 ] This more general family of subgroups consists of all the conjugates of those under the previous definition. [ 4 ] These subgroups may also be characterized as the subgroups of S n {\displaystyle S_{n}} that are generated by a set of transpositions . [ 5 ]
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In mathematics , a Young symmetrizer is an element of the group algebra of the symmetric group S n {\displaystyle S_{n}} whose natural action on tensor products V ⊗ n {\displaystyle V^{\otimes n}} of a complex vector space V {\displaystyle V} has as image an irreducible representation of the group of invertible linear transformations G L ( V ) {\displaystyle GL(V)} . All irreducible representations of G L ( V ) {\displaystyle GL(V)} are thus obtained. It is constructed from the action of S n {\displaystyle S_{n}} on the vector space V ⊗ n {\displaystyle V^{\otimes n}} by permutation of the different factors (or equivalently, from the permutation of the indices of the tensor components). A similar construction works over any field but in characteristic p (in particular over finite fields) the image need not be an irreducible representation. The Young symmetrizers also act on the vector space of functions on Young tableau and the resulting representations are called Specht modules which again construct all complex irreducible representations of the symmetric group while the analogous construction in prime characteristic need not be irreducible. The Young symmetrizer is named after British mathematician Alfred Young .
Given a finite symmetric group S n and specific Young tableau λ corresponding to a numbered partition of n , and consider the action of S n {\displaystyle S_{n}} given by permuting the boxes of λ {\displaystyle \lambda } . Define two permutation subgroups P λ {\displaystyle P_{\lambda }} and Q λ {\displaystyle Q_{\lambda }} of S n as follows: [ clarification needed ]
and
Corresponding to these two subgroups, define two vectors in the group algebra C S n {\displaystyle \mathbb {C} S_{n}} as
and
where e g {\displaystyle e_{g}} is the unit vector corresponding to g , and sgn ( g ) {\displaystyle \operatorname {sgn}(g)} is the sign of the permutation. The product
is the Young symmetrizer corresponding to the Young tableau λ. Each Young symmetrizer corresponds to an irreducible representation of the symmetric group, and every irreducible representation can be obtained from a corresponding Young symmetrizer. (If we replace the complex numbers by more general fields the corresponding representations will not be irreducible in general.)
Let V be any vector space over the complex numbers . Consider then the tensor product vector space V ⊗ n = V ⊗ V ⊗ ⋯ ⊗ V {\displaystyle V^{\otimes n}=V\otimes V\otimes \cdots \otimes V} ( n times). Let S n act on this tensor product space by permuting the indices. One then has a natural group algebra representation C S n → End ( V ⊗ n ) {\displaystyle \mathbb {C} S_{n}\to \operatorname {End} (V^{\otimes n})} on V ⊗ n {\displaystyle V^{\otimes n}} (i.e. V ⊗ n {\displaystyle V^{\otimes n}} is a right C S n {\displaystyle \mathbb {C} S_{n}} module).
Given a partition λ of n , so that n = λ 1 + λ 2 + ⋯ + λ j {\displaystyle n=\lambda _{1}+\lambda _{2}+\cdots +\lambda _{j}} , then the image of a λ {\displaystyle a_{\lambda }} is
For instance, if n = 4 {\displaystyle n=4} , and λ = ( 2 , 2 ) {\displaystyle \lambda =(2,2)} , with the canonical Young tableau { { 1 , 2 } , { 3 , 4 } } {\displaystyle \{\{1,2\},\{3,4\}\}} . Then the corresponding a λ {\displaystyle a_{\lambda }} is given by
For any product vector v 1 , 2 , 3 , 4 := v 1 ⊗ v 2 ⊗ v 3 ⊗ v 4 {\displaystyle v_{1,2,3,4}:=v_{1}\otimes v_{2}\otimes v_{3}\otimes v_{4}} of V ⊗ 4 {\displaystyle V^{\otimes 4}} we then have
Thus the set of all a λ v 1 , 2 , 3 , 4 {\displaystyle a_{\lambda }v_{1,2,3,4}} clearly spans Sym 2 V ⊗ Sym 2 V {\displaystyle \operatorname {Sym} ^{2}V\otimes \operatorname {Sym} ^{2}V} and since the v 1 , 2 , 3 , 4 {\displaystyle v_{1,2,3,4}} span V ⊗ 4 {\displaystyle V^{\otimes 4}} we obtain V ⊗ 4 a λ = Sym 2 V ⊗ Sym 2 V {\displaystyle V^{\otimes 4}a_{\lambda }=\operatorname {Sym} ^{2}V\otimes \operatorname {Sym} ^{2}V} , where we wrote informally V ⊗ 4 a λ ≡ Im ( a λ ) {\displaystyle V^{\otimes 4}a_{\lambda }\equiv \operatorname {Im} (a_{\lambda })} .
Notice also how this construction can be reduced to the construction for n = 2 {\displaystyle n=2} .
Let 1 ∈ End ( V ⊗ 2 ) {\displaystyle \mathbb {1} \in \operatorname {End} (V^{\otimes 2})} be the identity operator and S ∈ End ( V ⊗ 2 ) {\displaystyle S\in \operatorname {End} (V^{\otimes 2})} the swap operator defined by S ( v ⊗ w ) = w ⊗ v {\displaystyle S(v\otimes w)=w\otimes v} , thus 1 = e id {\displaystyle \mathbb {1} =e_{\text{id}}} and S = e ( 1 , 2 ) {\displaystyle S=e_{(1,2)}} . We have that
maps into Sym 2 V {\displaystyle \operatorname {Sym} ^{2}V} , more precisely
is the projector onto Sym 2 V {\displaystyle \operatorname {Sym} ^{2}V} .
Then
which is the projector onto Sym 2 V ⊗ Sym 2 V {\displaystyle \operatorname {Sym} ^{2}V\otimes \operatorname {Sym} ^{2}V} .
The image of b λ {\displaystyle b_{\lambda }} is
where μ is the conjugate partition to λ. Here, Sym i V {\displaystyle \operatorname {Sym} ^{i}V} and ⋀ j V {\displaystyle \bigwedge ^{j}V} are the symmetric and alternating tensor product spaces .
The image C S n c λ {\displaystyle \mathbb {C} S_{n}c_{\lambda }} of c λ = a λ ⋅ b λ {\displaystyle c_{\lambda }=a_{\lambda }\cdot b_{\lambda }} in C S n {\displaystyle \mathbb {C} S_{n}} is an irreducible representation of S n , called a Specht module . We write
for the irreducible representation.
Some scalar multiple of c λ {\displaystyle c_{\lambda }} is idempotent, [ 1 ] that is c λ 2 = α λ c λ {\displaystyle c_{\lambda }^{2}=\alpha _{\lambda }c_{\lambda }} for some rational number α λ ∈ Q . {\displaystyle \alpha _{\lambda }\in \mathbb {Q} .} Specifically, one finds α λ = n ! / dim V λ {\displaystyle \alpha _{\lambda }=n!/\dim V_{\lambda }} . In particular, this implies that representations of the symmetric group can be defined over the rational numbers; that is, over the rational group algebra Q S n {\displaystyle \mathbb {Q} S_{n}} .
Consider, for example, S 3 and the partition (2,1). Then one has
If V is a complex vector space, then the images of c λ {\displaystyle c_{\lambda }} on spaces V ⊗ d {\displaystyle V^{\otimes d}} provides essentially all the finite-dimensional irreducible representations of GL(V).
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In mathematics , a Young tableau ( / t æ ˈ b l oʊ , ˈ t æ b l oʊ / ; plural: tableaux ) is a combinatorial object useful in representation theory and Schubert calculus . It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties.
Young tableaux were introduced by Alfred Young , a mathematician at Cambridge University , in 1900. [ 1 ] [ 2 ] They were then applied to the study of the symmetric group by Georg Frobenius in 1903. Their theory was further developed by many mathematicians, including Percy MacMahon , W. V. D. Hodge , G. de B. Robinson , Gian-Carlo Rota , Alain Lascoux , Marcel-Paul Schützenberger and Richard P. Stanley .
Note: this article uses the English convention for displaying Young diagrams and tableaux .
A Young diagram (also called a Ferrers diagram , particularly when represented using dots) is a finite collection of boxes, or cells, arranged in left-justified rows, with the row lengths in non-increasing order. Listing the number of boxes in each row gives a partition λ of a non-negative integer n , the total number of boxes of the diagram. The Young diagram is said to be of shape λ , and it carries the same information as that partition. Containment of one Young diagram in another defines a partial ordering on the set of all partitions, which is in fact a lattice structure, known as Young's lattice . Listing the number of boxes of a Young diagram in each column gives another partition, the conjugate or transpose partition of λ ; one obtains a Young diagram of that shape by reflecting the original diagram along its main diagonal.
There is almost universal agreement that in labeling boxes of Young diagrams by pairs of integers, the first index selects the row of the diagram, and the second index selects the box within the row. Nevertheless, two distinct conventions exist to display these diagrams, and consequently tableaux: the first places each row below the previous one, the second stacks each row on top of the previous one. Since the former convention is mainly used by Anglophones while the latter is often preferred by Francophones , it is customary to refer to these conventions respectively as the English notation and the French notation ; for instance, in his book on symmetric functions , Macdonald advises readers preferring the French convention to "read this book upside down in a mirror" (Macdonald 1979, p. 2). This nomenclature probably started out as jocular. The English notation corresponds to the one universally used for matrices, while the French notation is closer to the convention of Cartesian coordinates ; however, French notation differs from that convention by placing the vertical coordinate first. The figure on the right shows, using the English notation, the Young diagram corresponding to the partition (5, 4, 1) of the number 10. The conjugate partition, measuring the column lengths, is (3, 2, 2, 2, 1).
In many applications, for example when defining Jack functions , it is convenient to define the arm length a λ ( s ) of a box s as the number of boxes to the right of s in the diagram λ in English notation. Similarly, the leg length l λ ( s ) is the number of boxes below s . The hook length of a box s is the number of boxes to the right of s or below s in English notation, including the box s itself; in other words, the hook length is a λ ( s ) + l λ ( s ) + 1.
A Young tableau is obtained by filling in the boxes of the Young diagram with symbols taken from some alphabet , which is usually required to be a totally ordered set . Originally that alphabet was a set of indexed variables x 1 , x 2 , x 3 ..., but now one usually uses a set of numbers for brevity. In their original application to representations of the symmetric group , Young tableaux have n distinct entries, arbitrarily assigned to boxes of the diagram. A tableau is called standard if the entries in each row and each column are increasing. The number of distinct standard Young tableaux on n entries is given by the involution numbers
In other applications, it is natural to allow the same number to appear more than once (or not at all) in a tableau. A tableau is called semistandard , or column strict , if the entries weakly increase along each row and strictly increase down each column. Recording the number of times each number appears in a tableau gives a sequence known as the weight of the tableau. Thus the standard Young tableaux are precisely the semistandard tableaux of weight (1,1,...,1), which requires every integer up to n to occur exactly once.
In a standard Young tableau, the integer k {\displaystyle k} is a descent if k + 1 {\displaystyle k+1} appears in a row strictly below k {\displaystyle k} . The sum of the descents is called the major index of the tableau. [ 3 ]
There are several variations of this definition: for example, in a row-strict tableau the entries strictly increase along the rows and weakly increase down the columns. Also, tableaux with decreasing entries have been considered, notably, in the theory of plane partitions . There are also generalizations such as domino tableaux or ribbon tableaux, in which several boxes may be grouped together before assigning entries to them.
A skew shape is a pair of partitions ( λ , μ ) such that the Young diagram of λ contains the Young diagram of μ ; it is denoted by λ / μ . If λ = ( λ 1 , λ 2 , ...) and μ = ( μ 1 , μ 2 , ...) , then the containment of diagrams means that μ i ≤ λ i for all i . The skew diagram of a skew shape λ / μ is the set-theoretic difference of the Young diagrams of λ and μ : the set of squares that belong to the diagram of λ but not to that of μ . A skew tableau of shape λ / μ is obtained by filling the squares of the corresponding skew diagram; such a tableau is semistandard if entries increase weakly along each row, and increase strictly down each column, and it is standard if moreover all numbers from 1 to the number of squares of the skew diagram occur exactly once. While the map from partitions to their Young diagrams is injective, this is not the case for the map from skew shapes to skew diagrams; [ 4 ] therefore the shape of a skew diagram cannot always be determined from the set of filled squares only. Although many properties of skew tableaux only depend on the filled squares, some operations defined on them do require explicit knowledge of λ and μ , so it is important that skew tableaux do record this information: two distinct skew tableaux may differ only in their shape, while they occupy the same set of squares, each filled with the same entries. [ 5 ] Young tableaux can be identified with skew tableaux in which μ is the empty partition (0) (the unique partition of 0).
Any skew semistandard tableau T of shape λ / μ with positive integer entries gives rise to a sequence of partitions (or Young diagrams), by starting with μ , and taking for the partition i places further in the sequence the one whose diagram is obtained from that of μ by adding all the boxes that contain a value ≤ i in T ; this partition eventually becomes equal to λ . Any pair of successive shapes in such a sequence is a skew shape whose diagram contains at most one box in each column; such shapes are called horizontal strips . This sequence of partitions completely determines T , and it is in fact possible to define (skew) semistandard tableaux as such sequences, as is done by Macdonald (Macdonald 1979, p. 4). This definition incorporates the partitions λ and μ in the data comprising the skew tableau.
Young tableaux have numerous applications in combinatorics , representation theory , and algebraic geometry . Various ways of counting Young tableaux have been explored and lead to the definition of and identities for Schur functions .
Many combinatorial algorithms on tableaux are known, including Schützenberger's jeu de taquin and the Robinson–Schensted–Knuth correspondence . Lascoux and Schützenberger studied an associative product on the set of all semistandard Young tableaux, giving it the structure called the plactic monoid (French: le monoïde plaxique ).
In representation theory, standard Young tableaux of size k describe bases in irreducible representations of the symmetric group on k letters. The standard monomial basis in a finite-dimensional irreducible representation of the general linear group GL n are parametrized by the set of semistandard Young tableaux of a fixed shape over the alphabet {1, 2, ..., n }. This has important consequences for invariant theory , starting from the work of Hodge on the homogeneous coordinate ring of the Grassmannian and further explored by Gian-Carlo Rota with collaborators, de Concini and Procesi , and Eisenbud . The Littlewood–Richardson rule describing (among other things) the decomposition of tensor products of irreducible representations of GL n into irreducible components is formulated in terms of certain skew semistandard tableaux.
Applications to algebraic geometry center around Schubert calculus on Grassmannians and flag varieties . Certain important cohomology classes can be represented by Schubert polynomials and described in terms of Young tableaux.
Young diagrams are in one-to-one correspondence with irreducible representations of the symmetric group over the complex numbers . They provide a convenient way of specifying the Young symmetrizers from which the irreducible representations are built. Many facts about a representation can be deduced from the corresponding diagram. Below, we describe two examples: determining the dimension of a representation and restricted representations. In both cases, we will see that some properties of a representation can be determined by using just its diagram. Young tableaux are involved in the use of the symmetric group in
quantum chemistry studies of atoms, molecules and solids. [ 6 ] [ 7 ]
Young diagrams also parametrize the irreducible polynomial representations of the general linear group GL n (when they have at most n nonempty rows), or the irreducible representations of the special linear group SL n (when they have at most n − 1 nonempty rows), or the irreducible complex representations of the special unitary group SU n (again when they have at most n − 1 nonempty rows). In these cases semistandard tableaux with entries up to n play a central role, rather than standard tableaux; in particular it is the number of those tableaux that determines the dimension of the representation.
The dimension of the irreducible representation π λ of the symmetric group S n corresponding to a partition λ of n is equal to the number of different standard Young tableaux that can be obtained from the diagram of the representation. This number can be calculated by the hook length formula .
A hook length hook( x ) of a box x in Young diagram Y ( λ ) of shape λ is the number of boxes that are in the same row to the right of it plus those boxes in the same column below it, plus one (for the box itself). By the hook-length formula, the dimension of an irreducible representation is n ! divided by the product of the hook lengths of all boxes in the diagram of the representation:
The figure on the right shows hook-lengths for all boxes in the diagram of the partition 10 = 5 + 4 + 1. Thus
Similarly, the dimension of the irreducible representation W ( λ ) of GL r corresponding to the partition λ of n (with at most r parts) is the number of semistandard Young tableaux of shape λ (containing only the entries from 1 to r ), which is given by the hook-length formula:
where the index i gives the row and j the column of a box. [ 8 ] For instance, for the partition (5,4,1) we get as dimension of the corresponding irreducible representation of GL 7 (traversing the boxes by rows):
A representation of the symmetric group on n elements, S n is also a representation of the symmetric group on n − 1 elements, S n −1 . However, an irreducible representation of S n may not be irreducible for S n −1 . Instead, it may be a direct sum of several representations that are irreducible for S n −1 . These representations are then called the factors of the restricted representation (see also induced representation ).
The question of determining this decomposition of the restricted representation of a given irreducible representation of S n , corresponding to a partition λ of n , is answered as follows. One forms the set of all Young diagrams that can be obtained from the diagram of shape λ by removing just one box (which must be at the end both of its row and of its column); the restricted representation then decomposes as a direct sum of the irreducible representations of S n −1 corresponding to those diagrams, each occurring exactly once in the sum.
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In physics , the Young–Laplace equation ( / l ə ˈ p l ɑː s / ) is an equation that describes the capillary pressure difference sustained across the interface between two static fluids , such as water and air , due to the phenomenon of surface tension or wall tension , although use of the latter is only applicable if assuming that the wall is very thin. The Young–Laplace equation relates the pressure difference to the shape of the surface or wall and it is fundamentally important in the study of static capillary surfaces . It is a statement of normal stress balance for static fluids meeting at an interface, where the interface is treated as a surface (zero thickness): Δ p = − γ ∇ ⋅ n ^ = − 2 γ H f = − γ ( 1 R 1 + 1 R 2 ) {\displaystyle {\begin{aligned}\Delta p&=-\gamma \nabla \cdot {\hat {n}}\\&=-2\gamma H_{f}\\&=-\gamma \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)\end{aligned}}} where Δ p {\displaystyle \Delta p} is the Laplace pressure , the pressure difference across the fluid interface (the exterior pressure minus the interior pressure), γ {\displaystyle \gamma } is the surface tension (or wall tension ), n ^ {\displaystyle {\hat {n}}} is the unit normal pointing out of the surface, H f {\displaystyle H_{f}} is the mean curvature , and R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} are the principal radii of curvature . Note that only normal stress is considered, because a static interface is possible only in the absence of tangential stress. [ 1 ]
The equation is named after Thomas Young , who developed the qualitative theory of surface tension in 1805, and Pierre-Simon Laplace who completed the mathematical description in the following year. It is sometimes also called the Young–Laplace–Gauss equation, as Carl Friedrich Gauss unified the work of Young and Laplace in 1830, deriving both the differential equation and boundary conditions using Johann Bernoulli 's virtual work principles. [ 2 ]
If the pressure difference is zero, as in a soap film without gravity, the interface will assume the shape of a minimal surface .
The equation also explains the energy required to create an emulsion . To form the small, highly curved droplets of an emulsion, extra energy is required to overcome the large pressure that results from their small radius.
The Laplace pressure, which is greater for smaller droplets, causes the diffusion of molecules out of the smallest droplets in an emulsion and drives emulsion coarsening via Ostwald ripening . [ citation needed ]
In a sufficiently narrow (i.e., low Bond number ) tube of circular cross-section (radius a ), the interface between two fluids forms a meniscus that is a portion of the surface of a sphere with radius R . The pressure jump across this surface is related to the radius and the surface tension γ by Δ p = 2 γ R . {\displaystyle \Delta p={\frac {2\gamma }{R}}.}
This may be shown by writing the Young–Laplace equation in spherical form with a contact angle boundary condition and also a prescribed height boundary condition at, say, the bottom of the meniscus. The solution is a portion of a sphere, and the solution will exist only for the pressure difference shown above. This is significant because there isn't another equation or law to specify the pressure difference; existence of solution for one specific value of the pressure difference prescribes it.
The radius of the sphere will be a function only of the contact angle , θ, which in turn depends on the exact properties of the fluids and the container material with which the fluids in question are contacting/interfacing: R = a cos θ {\displaystyle R={\frac {a}{\cos \theta }}}
so that the pressure difference may be written as: Δ p = 2 γ cos θ a . {\displaystyle \Delta p={\frac {2\gamma \cos \theta }{a}}.}
In order to maintain hydrostatic equilibrium , the induced capillary pressure is balanced by a change in height, h , which can be positive or negative, depending on whether the wetting angle is less than or greater than 90°. For a fluid of density ρ: ρ g h = 2 γ cos θ a . {\displaystyle \rho gh={\frac {2\gamma \cos \theta }{a}}.} where g is the gravitational acceleration . This is sometimes known as the Jurin's law or Jurin height [ 3 ] after James Jurin who studied the effect in 1718. [ 4 ]
For a water-filled glass tube in air at sea level :
and so the height of the water column is given by: h ≈ 1.4 × 10 − 5 m 2 a . {\displaystyle h\approx {{1.4\times 10^{-5}}\mathrm {m} ^{2} \over a}.} Thus for a 2 mm wide (1 mm radius) tube, the water would rise 14 mm. However, for a capillary tube with radius 0.1 mm, the water would rise 14 cm (about 6 inches ).
When including also the effects of gravity , for a free surface and for a pressure difference between the fluids equal to Δ p at the level h=0 , there is a balance, when the interface is in equilibrium, between Δ p , the hydrostatic pressure and the effects of surface tension . The Young–Laplace equation becomes: Δ p = ρ g h − γ [ 1 R 1 ( h ) + 1 R 2 ( h ) ] {\displaystyle \Delta p=\rho gh-\gamma \left[{\frac {1}{R_{1}(h)}}+{\frac {1}{R_{2}(h)}}\right]} Note that the mean curvature of the fluid-fluid interface now depends on h .
The equation can be non-dimensionalised in terms of its characteristic length-scale, the capillary length : L c = γ ρ g , {\displaystyle L_{c}={\sqrt {\frac {\gamma }{\rho g}}},} and characteristic pressure p c = γ L c = γ ρ g . {\displaystyle p_{c}={\frac {\gamma }{L_{c}}}={\sqrt {\gamma \rho g}}.}
For clean water at standard temperature and pressure , the capillary length is ~2 mm .
The non-dimensional equation then becomes: h ∗ − Δ p ∗ = [ 1 R 1 ∗ ( h ) + 1 R 2 ∗ ( h ) ] . {\displaystyle h^{*}-\Delta p^{*}=\left[{\frac {1}{{R_{1}}^{*}(h)}}+{\frac {1}{{R_{2}}^{*}(h)}}\right].}
Thus, the surface shape is determined by only one parameter, the over pressure of the fluid, Δ p * and the scale of the surface is given by the capillary length . The solution of the equation requires an initial condition for position, and the gradient of the surface at the start point.
The (nondimensional) shape, r ( z ) of an axisymmetric surface can be found by substituting general expressions for principal curvatures to give the hydrostatic Young–Laplace equations : [ 5 ] r ″ ( 1 + r ′ 2 ) 3 / 2 − 1 r ( z ) 1 + r ′ 2 = z − Δ p ∗ {\displaystyle {\frac {r''}{(1+r'^{2})^{{3}/{2}}}}-{\frac {1}{r(z){\sqrt {1+r'^{2}}}}}=z-\Delta p^{*}} z ″ ( 1 + z ′ 2 ) 3 / 2 + z ′ r ( 1 + z ′ 2 ) 1 / 2 = Δ p ∗ − z ( r ) . {\displaystyle {\frac {z''}{(1+z'^{2})^{3/2}}}+{\frac {z'}{r(1+z'^{2})^{{1}/{2}}}}=\Delta p^{*}-z(r).}
In medicine it is often referred to as the Law of Laplace , used in the context of cardiovascular physiology , [ 6 ] and also respiratory physiology , though the latter use is often erroneous. [ 7 ]
Francis Hauksbee performed some of the earliest observations and experiments in 1709 [ 8 ] and these were repeated in 1718 by James Jurin who observed that the height of fluid in a capillary column was a function only of the cross-sectional area at the surface, not of any other dimensions of the column. [ 4 ] [ 9 ]
Thomas Young laid the foundations of the equation in his 1804 paper An Essay on the Cohesion of Fluids [ 10 ] where he set out in descriptive terms the principles governing contact between fluids (along with many other aspects of fluid behaviour). Pierre Simon Laplace followed this up in Mécanique Céleste [ 11 ] with the formal mathematical description given above, which reproduced in symbolic terms the relationship described earlier by Young.
Laplace accepted the idea propounded by Hauksbee in his book Physico-mechanical Experiments (1709), that the phenomenon was due to a force of attraction that was insensible at sensible distances. [ 12 ] [ 13 ] The part which deals with the action of a solid on a liquid and the mutual action of two liquids was not worked out thoroughly, but ultimately was completed by Carl Friedrich Gauss . [ 14 ] Franz Ernst Neumann (1798-1895) later filled in a few details. [ 15 ] [ 9 ] [ 16 ]
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Yrast ( / ˈ ɪr æ s t / IRR -ast , Swedish: [ˈy̌ːrast] ) is a technical term in nuclear physics that refers to a state of a nucleus with a minimum of energy (when it is least excited) for a given angular momentum . Yr is a Swedish adjective sharing the same root as the English whirl . Yrast is the superlative of yr and can be translated whirlingest , although it literally means "dizziest" or "most bewildered". The yrast levels are vital to understanding reactions, such as off-center heavy ion collisions, that result in high-spin states. [ 1 ]
Yrare is the comparative of yr and is used to refer to the second-least energetic state of a given angular momentum.
An unstable nucleus may decay in several different ways: it can eject a neutron , proton , alpha particle , or other fragment; it can emit a gamma ray ; it can undergo beta decay . Because of the relative strengths of the fundamental interactions associated with those processes (the strong interaction , electromagnetism , and the weak interaction respectively), they usually occur with frequencies in that order. Theoretically, a nucleus has a very small probability of emitting a gamma ray even if it could eject a neutron, and beta decay rarely occurs unless both of the other two pathways are highly unlikely.
In some instances, however, predictions based on this model underestimate the total amount of energy released in the form of gamma rays; that is, nuclei appear to have more than enough energy to eject neutrons, but decay by gamma emission instead. This discrepancy is found by the energy of a nuclear angular momentum, [ 2 ] and documentation and calculation of yrast levels for a given system may be used for analyzing such a situation.
The energy stored in the angular momentum of an atomic nucleus can also be responsible for the emission of larger-than-expected particles, such as alpha particles over single nucleons , because they can carry away angular momentum more effectively. This is not the only reason alpha particles are preferentially emitted, though; another reason is simply that alpha particles (He-4 nuclei) are energetically very stable in and of themselves. [ 3 ]
Sometimes there is a large gap between two yrast states. For example, the nucleus 95 Pd has a 21/2 state that lies below the lowest 19/2, 17/2, and 15/2 states. This state does not have enough energy to undergo strong particle decay , and because of the large spin difference, gamma decay from the 21/2 state to the 13/2 state below is very unlikely. The more likely decay option is beta decay, which forms an isomer with an unusually long half-life of 14 seconds. [ 4 ]
An exceptional example is the J=9 state of tantalum-180 , which is a very low-lying yrast state only 77 keV above the ground state. The ground state has J=1, which is too large a gap for gamma decay to occur. Alpha and beta decay are also suppressed, so strongly that the resulting isomer, tantalum-180m , is effectively stable for all practical purposes, and has never been observed to decay. Tantalum-180m is the only currently known yrast isomer to be observationally stable.
Some superheavy isotopes (such as copernicium -285) have longer-lived isomers with half-lives on the order of minutes. These may be yrasts, but the exact angular momentum and energy is often hard to determine for these nuclides.
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This page provides supplementary chemical data on Ytterbium(III) chloride
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Yttria-stabilized zirconia ( YSZ ) is a ceramic in which the cubic crystal structure of zirconium dioxide is made stable at room temperature by an addition of yttrium oxide . These oxides are commonly called "zirconia" ( Zr O 2 ) and "yttria" ( Y 2 O 3 ), hence the name.
Pure zirconium dioxide undergoes a phase transformation from monoclinic (stable at room temperature) to tetragonal (at about 1173 °C) and then to cubic (at about 2370 °C), according to the scheme
During these transformations, zirconia can experience volume expansion of up to 5-6%. [ 1 ] This change can induce internal stresses, leading to cracking or fracture in ceramic materials. [ 2 ]
Obtaining stable sintered zirconia ceramic products is difficult because of the large volume change, about 5%, accompanying the transition from tetragonal to monoclinic. Stabilization of the cubic polymorph of zirconia over wider range of temperatures is accomplished by substitution of some of the Zr 4+ ions (ionic radius of 0.82 Å, too small for ideal lattice of fluorite characteristic for the cubic zirconia) in the crystal lattice with slightly larger ions, e.g., those of Y 3+ (ionic radius of 0.96 Å). The resulting doped zirconia materials are termed stabilized zirconias . [ 3 ]
Materials related to YSZ include calcia -, magnesia -, ceria - or alumina -stabilized zirconias, or partially stabilized zirconias (PSZ). Hafnia -stabilized zirconia has about 25% lower thermal conductivity , making it more suitable for thermal barrier applications. [ 4 ]
Although 8–9 mol % YSZ is known to not be completely stabilized in the pure cubic YSZ phase up to temperatures above 1000 °C. [ 5 ]
Commonly used abbreviations in conjunction with yttria-stabilized zirconia are:
The thermal expansion coefficients depends on the modification of zirconia as follows:
By the addition of yttria to pure zirconia (e.g., fully stabilized YSZ) Y 3+ ions replace Zr 4+ on the cationic sublattice. Thereby, oxygen vacancies are generated due to charge neutrality: [ 9 ]
meaning that two Y 3+ ions generate one vacancy on the anionic sublattice. This facilitates moderate conductivity of yttrium-stabilized zirconia for O 2− ions (and thus electrical conductivity) at elevated and high temperature. This ability to conduct O 2− ions makes yttria-stabilized zirconia well suited for application as solid electrolyte in solid oxide fuel cells.
For low dopant concentrations, the ionic conductivity of the stabilized zirconias increases with increasing Y 2 O 3 content. It has a maximum around 8–9 mol% almost independent of the temperature (800–1200 °C). [ 3 ] [ 5 ] Unfortunately, 8–9 mol% YSZ (8YSZ, 8YDZ) also turned out to be situated in the 2-phase field (c+t) of the YSZ phase diagram at these temperatures, which causes the material's decomposition into Y-enriched and depleted regions on the nanometre scale and, consequently, the electrical degradation during operation. [ 6 ] The microstructural and chemical changes on the nanometre scale are accompanied by the drastic decrease of the oxygen-ion conductivity of 8YSZ (degradation of 8YSZ) of about 40% at 950 °C within 2500 hours. [ 7 ] Traces of impurities like Ni, dissolved in the 8YSZ, e.g., due to fuel-cell fabrication, can have a severe impact on the decomposition rate (acceleration of inherent decomposition of the 8YSZ by orders of magnitude) such that the degradation of conductivity even becomes problematic at low operation temperatures in the range of 500–700 °C. [ 10 ]
Nowadays, more complex ceramics like co-doped zirconia (e.g., with scandia) are in use as solid electrolytes.
YSZ has a number of applications:
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Yttrium(III) chloride is an inorganic compound of yttrium and chloride . It exists in two forms, the hydrate (YCl 3 (H 2 O) 6 ) and an anhydrous form (YCl 3 ). Both are colourless salts that are highly soluble in water and deliquescent .
Solid YCl 3 adopts a cubic [ citation needed ] structure with close-packed chloride ions and yttrium ions filling one third of the octahedral holes and the resulting YCl 6 octahedra sharing three edges with adjacent octahedra, giving it a layered structure. [ 5 ] [ 1 ] This structure is shared by a range of compounds, notably AlCl 3 .
YCl 3 is often prepared by the " ammonium chloride route," starting from either Y 2 O 3 or hydrated chloride or oxychloride. [ 6 ] [ 7 ] or YCl 3 ·6H 2 O. [ 8 ] These methods produce (NH 4 ) 2 [YCl 5 ]:
The pentachloride decomposes thermally according to the following equation:
The thermolysis reaction proceeds via the intermediacy of (NH 4 )[Y 2 Cl 7 ].
Treating Y 2 O 3 with aqueous HCl produces the hydrated chloride (YCl 3 ·6H 2 O). When heated, this salt yields yttrium oxychloride rather than reverting to the anhydrous form.
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Yttrium ( 90 Y) clivatuzumab tetraxetan (trade name hPAM4-Cide ) is a humanized monoclonal antibody-drug conjugate designed for the treatment of pancreatic cancer . [ 1 ] The antibody part, clivatuzumab (targeted at MUC1 ), is conjugated with tetraxetan , a chelator for yttrium-90 , [ 2 ] a radioisotope which destroys the tumour cells.
The drug was developed by Immunomedics, Inc.
In March 2016 the phase III PANCRIT-1 trial in metastatic pancreatic cancer was terminated early due to lack of improvement of overall survival . [ 3 ]
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Yttrium ( 90 Y) tacatuzumab tetraxetan is an investigational humanized monoclonal antibody intended for the treatment of cancer. [ 1 ] The antibody itself, tacatuzumab, is conjugated with tetraxetan , a chelator for yttrium-90 , [ 2 ] a radioisotope which destroys the tumour cells.
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Yttrium barium copper oxide ( YBCO ) is a family of crystalline chemical compounds that display high-temperature superconductivity ; it includes the first material ever discovered to become superconducting above the boiling point of liquid nitrogen [77 K (−196.2 °C; −321.1 °F)] at about 93 K (−180.2 °C; −292.3 °F). [ 3 ]
Many YBCO compounds have the general formula Y Ba 2 Cu 3 O 7− x (also known as Y123), although materials with other Y:Ba:Cu ratios exist, such as Y Ba 2 Cu 4 O y (Y124) or Y 2 Ba 4 Cu 7 O y (Y247). At present, there is no singularly recognised theory for high-temperature superconductivity.
It is part of the more general group of rare-earth barium copper oxides (ReBCO) in which, instead of yttrium, other rare earths are present.
In April 1986, Georg Bednorz and Karl Müller , working at IBM in Zurich , discovered that certain semiconducting oxides became superconducting at relatively high temperature, in particular, a lanthanum barium copper oxide becomes superconducting at 35 K. This oxide was an oxygen-deficient perovskite -related material that proved promising and stimulated the search for related compounds with higher superconducting transition temperatures. In 1987, Bednorz and Müller were jointly awarded the Nobel Prize in Physics for this work.
Following Bednorz and Müller's discovery, a team led by Paul Ching Wu Chu at the University of Alabama in Huntsville and University of Houston discovered that YBCO has a superconducting transition critical temperature ( T c ) of 93 K. [ 3 ] The first samples were Y 1.2 Ba 0.8 Cu O 4 , but this was an average composition for two phases, a black and a green one. Workers at Bell Laboratories identified the black phase as the superconductor, determined its composition YBa 2 Cu 3 O 7−δ and synthesized it in single phase [ 4 ]
YBCO was the first material found to become superconducting above 77 K, the boiling point of liquid nitrogen , whereas the majority of other superconductors require more expensive cryogens. Nonetheless, YBCO and its many related materials have yet to displace superconductors requiring liquid helium for cooling.
Relatively pure YBCO was first synthesized by heating a mixture of the metal carbonates at temperatures between 1000 and 1300 K. [ 5 ] [ 6 ]
Modern syntheses of YBCO use the corresponding oxides and nitrates. [ 6 ]
The superconducting properties of YBa 2 Cu 3 O 7− x are sensitive to the value of x , its oxygen content. Only those materials with 0 ≤ x ≤ 0.65 are superconducting below T c , and when x ~ 0.07 , the material superconducts at the highest temperature of 95 K , [ 6 ] or in highest magnetic fields: 120 T for B perpendicular and 250 T for B parallel to the CuO 2 planes. [ 7 ]
In addition to being sensitive to the stoichiometry of oxygen, the properties of YBCO are influenced by the crystallization methods used. Care must be taken to sinter YBCO. YBCO is a crystalline material, and the best superconductive properties are obtained when crystal grain boundaries are aligned by careful control of annealing and quenching temperature rates.
Numerous other methods to synthesize YBCO have developed since its discovery by Wu and his co-workers, such as chemical vapor deposition (CVD), [ 5 ] [ 6 ] sol-gel , [ 8 ] and aerosol [ 9 ] methods. These alternative methods, however, still require careful sintering to produce a quality product.
However, new possibilities have been opened since the discovery that trifluoroacetic acid ( TFA ), a source of fluorine, prevents the formation of the undesired barium carbonate (BaCO 3 ). Routes such as CSD (chemical solution deposition) have opened a wide range of possibilities, particularly in the preparation of long YBCO tapes. [ 10 ] This route lowers the temperature necessary to get the correct phase to around 700 °C (973 K; 1,292 °F). This, and the lack of dependence on vacuum, makes this method a very promising way to get scalable YBCO tapes.
YBCO crystallizes in a defect perovskite structure . It can be viewed as a layered structure: the boundary of each layer is defined by planes of square planar CuO 4 units sharing 4 vertices. The planes can sometimes be slightly puckered. [ 5 ] Perpendicular to these CuO 4 planes are CuO 2 ribbons sharing 2 vertices. The yttrium atoms are found between the CuO 4 planes, while the barium atoms are found between the CuO 2 ribbons and the CuO 4 planes. This structural feature is illustrated in the figure to the right.
Although YBa 2 Cu 3 O 7 is a well-defined chemical compound with a specific structure and stoichiometry, materials with fewer than seven oxygen atoms per formula unit are non-stoichiometric compounds . The structure of these materials depends on the oxygen content. This non-stoichiometry is denoted by the x in the chemical formula YBa 2 Cu 3 O 7− x . When x = 1, the O(1) sites in the Cu(1) layer (as labelled in the unit cell ) are vacant and the structure is tetragonal . The tetragonal form of YBCO is insulating and does not superconduct. Increasing the oxygen content slightly causes more of the O(1) sites to become occupied. For x < 0.65, Cu-O chains along the b axis of the crystal are formed. Elongation of the b axis changes the structure to orthorhombic , with lattice parameters of a = 3.82, b = 3.89, and c = 11.68 Å. [ 12 ] Optimum superconducting properties occur when x ~ 0.07, i.e., almost all of the O(1) sites are occupied, with few vacancies.
In experiments where other elements are substituted on the Cu and Ba [ why? ] sites, evidence has shown that conduction occurs in the Cu(2)O planes while the Cu(1)O(1) chains act as charge reservoirs, which provide carriers to the CuO planes. However, this model fails to address superconductivity in the homologue Pr123 ( praseodymium instead of yttrium). [ 13 ] This (conduction in the copper planes) confines conductivity to the a - b planes and a large anisotropy in transport properties is observed. Along the c axis, normal conductivity is 10 times smaller than in the a - b plane. For other cuprates in the same general class, the anisotropy is even greater and inter-plane transport is highly restricted.
Furthermore, the superconducting length scales show similar anisotropy, in both penetration depth (λ ab ≈ 150 nm, λ c ≈ 800 nm) and coherence length, (ξ ab ≈ 2 nm, ξ c ≈ 0.4 nm). Although the coherence length in the a - b plane is 5 times greater than that along the c axis it is quite small compared to classic superconductors such as niobium (where ξ ≈ 40 nm). This modest coherence length means that the superconducting state is more susceptible to local disruptions from interfaces or defects on the order of a single unit cell, such as the boundary between twinned crystal domains. This sensitivity to small defects complicates fabricating devices with YBCO, and the material is also sensitive to degradation from humidity.
Many possible applications of this and related high temperature superconducting materials have been discussed. For example, superconducting materials are finding use as magnets in magnetic resonance imaging , magnetic levitation , and Josephson junctions . (The most used material for power cables and magnets is BSCCO .) [ citation needed ]
YBCO has yet to be used in many applications involving superconductors for two primary reasons:
The most promising method developed to utilize this material involves deposition of YBCO on flexible metal tapes coated with buffering metal oxides. This is known as coated conductor . Texture (crystal plane alignment) can be introduced into the metal tape (the RABiTS process) or a textured ceramic buffer layer can be deposited, with the aid of an ion beam, on an untextured alloy substrate (the IBAD process). Subsequent oxide layers prevent diffusion of the metal from the tape into the superconductor while transferring the template for texturing the superconducting layer. Novel variants on CVD, PVD, and solution deposition techniques are used to produce long lengths of the final YBCO layer at high rates. Companies pursuing these processes include American Superconductor , Superpower (a division of Furukawa Electric ), Sumitomo , Fujikura , Nexans Superconductors, Commonwealth Fusion Systems , and European Advanced Superconductors. A much larger number of research institutes have also produced YBCO tape by these methods. [ citation needed ]
The superconducting tape is used for SPARC , a tokamak fusion reactor design that can achieve breakeven energy production. [ 15 ]
Surface modification of materials has often led to new and improved properties. Corrosion inhibition, polymer adhesion and nucleation, preparation of organic superconductor/insulator/high- T c superconductor trilayer structures, and the fabrication of metal/insulator/superconductor tunnel junctions have been developed using surface-modified YBCO. [ 16 ]
These molecular layered materials are synthesized using cyclic voltammetry . Thus far, YBCO layered with alkylamines, arylamines, and thiols have been produced with varying stability of the molecular layer. It has been proposed that amines act as Lewis bases and bind to Lewis acidic Cu surface sites in YBa 2 Cu 3 O 7 to form stable coordination bonds .
In 1987, shortly after it was discovered, physicist and science author Paul Grant published in the U.K. Journal New Scientist a straightforward guide for synthesizing YBCO superconductors using widely-available equipment. [ 17 ] Thanks in part to this article and similar publications at the time, YBCO has become a popular high-temperature superconductor for use by hobbyists and in education, as the magnetic levitation effect can be easily demonstrated using liquid nitrogen as coolant.
In 2021, SuperOx, a Russian and Japanese company, developed a new manufacturing process for making YBCO wire for fusion reactors. This new wire was shown to conduct between 700 and 2000 Amps per square millimeter. The company was able to produce 186 miles of wire in 9 months, between 2019 and 2021, dramatically improving the production capacity. The company used a plasma-laser deposition process, on a electropolished substrate to make 12-mm width tape and then slit it into 3-mm tape. [ 18 ]
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https://en.wikipedia.org/wiki/Yttrium_barium_copper_oxide
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Yttrium oxalate is an inorganic compound , a salt of yttrium and oxalic acid with the chemical formula Y 2 (C 2 O 4 ) 3 . [ 3 ] The compound does not dissolve in water and forms crystalline hydrates—colorless crystals. [ 4 ]
Precipitation of soluble yttrium salts with oxalic acid : [ 5 ]
Yttrium oxalate is highly insoluble in water and converts to the oxide when heated. [ 6 ] Yttrium oxalate forms crystalline hydrates (colorless crystals) with the formula Y 2 (C 2 O 4 ) 3 • n H 2 O, where n = 4, 9, and 10.
Decomposes when heated:
The solubility product of yttrium oxalate at 25 °C is 5.1 × 10 −30 . [ 1 ]
The trihydrate Y 2 (C 2 O 4 ) 3 •3H 2 O is formed by heating more hydrated varieties at 110 °C. [ 7 ]
Y 2 (C 2 O 4 ) 3 •2H 2 O, which is formed by heating the decahydrate at 210 °C) forms monoclinic crystals with unit cell dimensions a=9.3811 Å, b=11.638 Å, c=5.9726 Å, β=96.079°. [ 8 ]
Several yttrium oxalate double salts are known containing additional cations. Also a mixed-anion compound with carbonate is known.
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https://en.wikipedia.org/wiki/Yttrium_oxalate
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Yttrium perchlorate is the inorganic compound with the chemical formula Y(ClO 4 ) 3 . [ 1 ] [ 2 ] The compound is an yttrium salt of perchloric acid . [ 3 ] [ 4 ]
Dissolving yttrium oxide in perchloric acid solution can produce yttrium perchlorate octahydrate. [ citation needed ]
Potentially explosive. [ 5 ]
The compound is soluble in water and forms a hexahydrate with the formula Y(ClO 4 ) 3 •6 H 2 O . [ 6 ] [ 7 ]
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https://en.wikipedia.org/wiki/Yttrium_perchlorate
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Yttrium and tin form several yttrium stannide intermetallic compounds .
The most tin-rich is YSn 3 , followed by YSn 2 , Y 11 Sn 10 , Y 5 Sn 4 , and Y 5 Sn 3 . None survives above 1,940 °C (3,520 °F), at which point Y 5 Sn 3 melts congruently . [ 1 ] The enthalpy of dissolution is similar to the stannides of other late lanthanoids , [ 2 ] and the intermetallics' overall enthalpies of formation resemble silicides, not germanides or plumbides. [ 3 ]
YSn 3 is an electrical superconductor below 7 K (−447.07 °F). [ 4 ] It was originally thought to be a Type I superconductor , but 7 K may actually be the strong-coupling regime, despite the low temperature. [ 5 ] The density of electronic states has a local maximum at the Fermi level , composed of tin p and d orbitals . [ 4 ] The intermetallic is difficult to form, slowly crystallizing from a mixture of Sn and YSn 2 above 515 °C (959 °F). [ 1 ] This may arise from competing allotropes near room temperature: although its crystal structure is certainly cubic , simulation indicates that both the tricopper auride ( Pm 3 m ) or aluminum-titanium alloy (I4/mmm) structures are stable under standard conditions . [ 6 ]
YSn 2 has unit cell sized 4.39×16.34×4.30 Å . Like DySn 2 , it exhibits the zirconium disilicide crystal structure: [ 1 ] layers of yttrium rhombohedra encapsulating tin atoms alternate with flat planes of tin. Doping with nickel puckers the planes, and Mössbauer spectroscopy suggests that it removes electron density from the tin s orbitals. [ 7 ]
Y 5 Sn 3 has the hexagonal manganese silicide crystal structure, with unit cell 8.88×6.52×0.73 Å. [ 8 ]
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https://en.wikipedia.org/wiki/Yttrium_stannides
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Yuan-Cheng "Bert" Fung (September 15, 1919 – December 15, 2019) was a Chinese-American bioengineer and writer. He is regarded as a founding figure of bioengineering , tissue engineering , and the "Founder of Modern Biomechanics ". [ 1 ]
Fung was born in Jiangsu Province, China in 1919. He earned a bachelor's degree in 1941 and a master's degree in 1943 from the National Central University (later renamed Nanjing University in mainland China and reinstated in Taiwan ), and earned a Ph.D. from the California Institute of Technology in 1948. Fung was Professor Emeritus and Research Engineer at the University of California San Diego . He published prominent texts along with Pin Tong who was then at Hong Kong University of Science & Technology. Fung died at Jacobs Medical Center in San Diego, California, aged 100, on December 15, 2019. [ 2 ] [ 3 ]
Fung was married to Luna Yu Hsien-Shih, a former mathematician and cofounder of the UC San Diego International Center, until her death in 2017. The couple raised two children. [ 4 ]
He is the author of numerous books including Foundations of Solid Mechanics, Continuum Mechanics, and a series of books on Biomechanics. He is also one of the principal founders of the Journal of Biomechanics and was a past chair of the ASME International Applied Mechanics Division . In 1972, Fung established the Biomechanics Symposium under the American Society of Mechanical Engineers. This biannual summer meeting, first held at the Georgia Institute of Technology, became the annual Summer Bioengineering Conference. Fung and colleagues were also the first to recognize the importance of residual stress on arterial mechanical behavior. [ 5 ]
Fung's famous exponential strain constitutive equation for preconditioned soft tissues is
with
quadratic forms of Green-Lagrange strains E i j {\displaystyle E_{ij}} and a i j k l {\displaystyle a_{ijkl}} , b i j k l {\displaystyle b_{ijkl}} and c {\displaystyle c} material constants. [ 6 ] w {\displaystyle w} is a strain energy function per volume unit, which is the mechanical strain energy for a given temperature. Materials that follow this law are known as Fung-elastic . [ 7 ]
Fung was elected to the United States National Academy of Sciences (1993), [ 13 ] the National Academy of Engineering (1979), [ 14 ] the Institute of Medicine (1991), [ 15 ] the Academia Sinica (1968), [ 16 ] and was a Foreign Member of the Chinese Academy of Sciences (1994 election).
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https://en.wikipedia.org/wiki/Yuan-Cheng_Fung
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Yuan Tseh Lee ( Chinese : 李遠哲 ; pinyin : Lǐ Yuǎnzhé ; Wade–Giles : Li³ Yüan³-che² ; Pe̍h-ōe-jī : Lí Oán-tiat ; born 19 November 1936) is a Taiwanese chemist who was awarded the Nobel Prize in Chemistry in 1986 for his contributions to the development of reaction dynamics .
Lee is a professor emeritus at the University of California, Berkeley , and honorary director of the Nagoya University Institute for Advanced Study along with Ryoji Noyori . [ 1 ] [ 2 ] [ 3 ] [ 4 ] He was awarded the Nobel with John C. Polanyi and Dudley R. Herschbach for "contributions to the dynamics of chemical elementary processes". [ 3 ] [ 5 ] He was the first Taiwanese person be awarded the Nobel Prize. His research in physical chemistry concerned the use of advanced chemical kinetics techniques to investigate and manipulate the behavior of chemical reactions using crossed molecular beams . [ 3 ] [ 5 ] From 1994 to 2006, Lee served as the President of the Academia Sinica . [ 4 ] In 2011, he was elected head of the International Council for Science . [ 4 ]
Lee was born to a Hoklo Taiwanese family in Shinchiku City (modern-day Hsinchu city) in northern Taiwan, which was then under Japanese rule , to Lee Tze-fan , an artist, and Ts'ai P'ei ( 蔡配 ; Cài Péi ), an elementary school teacher from Goseikō Town ( 梧棲港街 ) , Taichū Prefecture ( Wuqi , Taichung ). [ 1 ] [ 3 ] [ 4 ] Lee is a Hokkien with ancestry from Nan'an City , China. [ 6 ] Lee played on the baseball and ping-pong teams of Hsinchu Elementary School, and later studied at the Hsinchu Senior High School , where he played tennis , trombone , and the flute .
He was exempted from the entrance examination and directly admitted to National Taiwan University . He earned a B.S. in 1959. [ 1 ] [ 3 ] He earned his M.S. from National Tsing Hua University in 1961 and his Ph.D. from the University of California, Berkeley , in 1965 under the supervision of Bruce H. Mahan . [ 1 ] [ 3 ] He was a member of the Chemistry International Board from 1977 to 1984. [ 4 ]
In February 1967, he started working with Dudley Herschbach at Harvard University on reactions between hydrogen atoms and diatomic alkali molecules and the construction of a universal crossed molecular beams apparatus. After the postdoctoral year with Herschbach he joined the University of Chicago faculty in 1968. In 1974, he returned to Berkeley as professor of chemistry and principal investigator at the Lawrence Berkeley National Laboratory , becoming a U.S. citizen the same year. Lee is a University Professor Emeritus of the University of California system. [ 7 ]
One of the major goals of chemistry is the study of material transformations where chemical kinetics plays an important role. Scientists during the 19th century stated macroscopic chemical processes consist of many elementary chemical reactions that are themselves simply a series of encounters between atomic or molecular species . In order to understand the time dependence of chemical reactions , chemical kineticists have traditionally focused on sorting out all of the elementary chemical reactions involved in a macroscopic chemical process and determining their respective rates.
Swedish chemist Svante Arrhenius studied this phenomenon during the late 1880s, and stated the relations between reactive molecular encounters and rates of reactions (formulated in terms of activation energies ).
Other scientists at the time also stated a chemical reaction is fundamentally a mechanical event , involving the rearrangement of atoms and molecules
during a collision . Although these initial theoretical studies were only qualitative, they heralded a new era in the field of chemical kinetics; allowing the prediction of the dynamical course of a chemical reaction.
In the 1950s, 1960s and 1970s, with the development of many sophisticated experimental techniques, it became possible to study the dynamics of elementary chemical reactions in the laboratory. Such as the analysis of the threshold operating conditions of a chemical laser or the spectra obtained using various linear or non-linear laser spectroscopic techniques.
Professor Lee's research focused on the possibility to control the energies of the reagents, and to understand the dependence of chemical reactivity on molecular orientation, among other studies related to the nature of reaction intermediates, decay dynamics, and identifying complex reaction mechanisms . To do so, Professor Lee used a breakthrough laboratory technique at the time, called the "crossed molecular beams technique" , where the information derived from the measurements of angular and velocity distributions allowed him and his team to understand the dynamics of elementary chemical reactions. [ 8 ]
In 2021, Lee donated his Nobel Prize medal to the National Museum of Taiwan History for exhibition. [ 9 ]
During his tenure, Lee has worked to create new research institutes, advance scientific research within Taiwan, and to recruit and cultivate top scholars for the Academia Sinica .
In 2010, Lee said that global warming would be much more serious than scientists previously thought, and that Taiwanese people needed to cut their per-capita carbon emissions from the current 12 tons per year to just three. This would take more than a few slogans, turning off the lights for one hour, or cutting meat consumption, noting: "We will have to learn to live the simple lives of our ancestors." Without such efforts, he said, "Taiwanese will be unable to survive long into the future". [ 10 ]
Lee was appointed the president of Academia Sinica in 1994 and renounced his U.S. citizenship to take the post. [ 11 ] As president of Academia Sinica he presided over the creation of the Taiwanese history textbook Knowing Taiwan . [ 12 ]
At the request of president Chen Shui-bian , Lee was Taiwan's representative in the 2002 APEC leaders' summit in Mexico . ( Presidents of the Republic of China have been barred from joining the APEC summits because of objections from the People's Republic of China.) Lee represented Chen again in the 2003 and 2004 APEC summits in Thailand and Chile , respectively. [ 13 ]
In July 2024, Lee accepted president Lai Ching-te 's invitation to serve as a consultant on the newly formed National Climate Change Strategy Committee. [ 14 ]
Lee was then elected President of the International Council for Science in 2008 and started his term in 2011. [ 15 ] He has been involved with the Malta Conferences, an initiative designed to bring together Middle Eastern scientists. As part of the initiative, he offered six fellowships to work on the synchrotron in Taiwan. [ 16 ] He is also a member of International Advisory Council in Universiti Tunku Abdul Rahman . [ 17 ]
Lee's father was a painter in Taiwan, and his mother was an elementary school teacher. His elder brother Yuan-Chuan Lee has been a professor at Johns Hopkins University for 40 years and was awarded the honor Special Chair Lectureship in Academia Sinica in Taiwan. His younger brother Yuan-Pern Lee was also awarded this honor. Lee's sister Chi-Mei Lee has served as a professor at National Chung Hsing University . [ 18 ]
In 2003, he was one of 22 Nobel Laureates who signed the Humanist Manifesto . [ 19 ]
During the 2000 Taiwanese presidential election , Lee supported the pan-green coalition which advocates Taiwan independence . In the last week of the election he announced his support for the candidacy of Chen Shui-bian who subsequently defeated James Soong in the election. Chen intended to nominate Lee to become premier .
In January 2004, he and industrial tycoon Wang Yung-ching and theatre director Lin Hwai-min issued a joint statement to both Chen Shui-bian and Lien Chan . He backed Chen again in the 2004 elections , issuing a statement of support for the DPP on 17 March, three days before polls opened.
During the 2012 presidential election , Lee expressed his support for DPP candidate Tsai Ing-wen . In early 2016, he appeared and addressed a rally by New Power Party , a party formed by student activists involved in the Sunflower Movement . [ 20 ]
Yuan Lee has signed the 2015 Mainau Declaration expressing concern about anthropogenic climate change .
Lee was one of the four Nobelists who established the Wu Chien-Shiung Foundation.
In addition to the Nobel Prize, his awards and distinctions include Sloan Fellow (1969); Fellow of American Academy of Arts and Sciences (1975); Fellow Am. Phys. Soc. (1976); Guggenheim Fellow (1977); Member National Academy of Sciences (1979); Member International Academy of Science, Munich, Member Academia Sinica (1980); E.O. Lawrence Award (1981); Miller Professor, Berkeley (1981); Fairchild Distinguished Scholar (1983); Harrison Howe Award (1983); Peter Debye Award (1986); National Medal of Science (1986); Golden Plate Award of the American Academy of Achievement (1987) and Faraday Lectureship Prize (1992). [ 21 ] Yuan Tseh Lee was awarded the Othmer Gold Medal in 2008 in recognition of his outstanding contributions to progress in chemistry and science. [ 22 ] [ 23 ] [ 24 ] His post-doctoral supervisor and fellow Nobel Laureate Dudley Herschbach congratulated Lee. [ 25 ] In 2019 Yuan T. Lee was also awarded the Fray International Sustainability Award by FLOGEN Star Outreach at SIPS 2019. [ 26 ]
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https://en.wikipedia.org/wiki/Yuan_T._Lee
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University of Texas at Austin
Yueh-Lin (Lynn) Loo is a Malaysian-born chemical engineer and the Theodora D. '78 and William H. Walton III '74 Professor in Engineering at Princeton University , where she is also the Director of the Andlinger Center for Energy and the Environment. [ 1 ] She is known for inventing nanotransfer printing . Loo was elected a Fellow of the Materials Research Society in 2020. [ 2 ]
Loo was born in Kuala Lumpur , Malaysia, and later lived in Taipei , Taiwan, where she attended Taipei American School . She moved to the United States to attend the University of Pennsylvania , where she completed bachelor's degrees in chemical engineering and materials science in 1996. [ 3 ] She then pursued graduate studies at Princeton University , where she received a Ph.D. in chemical engineering in 2001 after completing a doctoral dissertation titled "Controlled polymer crystallization through block copolymer self-assembly." [ 4 ] [ 3 ]
She worked as a postdoctoral researcher at Bell Laboratories for a year afterward before joining the University of Texas at Austin 's Chemical Engineering Department. [ 5 ] During her time at Bell Labs, Loo, along with Julia Hsu , accidentally uncovered duplicated figures in two papers by Jan Hendrik Schön, the first of many instances of academic fraud from the researcher . In 2004, she was included by MIT Technology Review on its TR35 list of under-35-year-old innovators for her invention of nanotransfer printing , a technique for printing nanoscale patterns onto plastic surfaces. [ 6 ] This technique allows for the creation of organic electronic devices by printing electrical circuit components onto plastic surfaces. [ 7 ]
In 2007, Loo joined the faculty of Princeton's Chemical and Biological Engineering Department, [ 8 ] where, as of 2015 [update] , she is the Theodora D. '78 and William H. Walton III '74 Professor in Engineering. Her research concerns the periodic structures of block polymers , organic semiconductors , and patterning techniques for plastic electronics. [ 9 ]
Loo launched the Princeton E-ffiliates Partnership (E-ffiliates) in 2012. [ 10 ] [ 11 ]
In 2016 she was appointed director of Andlinger Center for Energy and the Environment. [ 10 ]
Loo's research group studies solution-processable organic semiconductors and conductors. [ 12 ] [ 13 ] She also researches soft lithography. [ 12 ] Using derivatives of Hexabenzocoronene Loo's group developed transparent near-UV solar cells for smart windows, which also contain electrochromic polymers that control the window tint.
Loo co-founded Andluca Technologies in 2017. [ 14 ] [ 15 ]
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https://en.wikipedia.org/wiki/Yueh-Lin_Loo
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The Socialist Federal Republic of Yugoslavia began its own nuclear weapons program in the early 1950s, amid rising tensions with the Soviet Union during the Informbiro period . Yugoslavian leader Josip Broz Tito decided that the development of nuclear technology was in the country's best interest as deterrence from a possible invasion and in order to protect the country's sovereignty.
To protect Yugoslavia's national sovereignty and gain international status, the regime of Josip Broz Tito began a nuclear weapons program in the early 1950s. Yugoslavia would later sign the Non-Proliferation Treaty , which caused the program to shut down. Another nuclear weapons program was started after India tested their nuclear weapons on May 18, 1974. This program would eventually shut down in 1987, but Yugoslavia (and eventually the Republic of Serbia ) kept high grade enriched uranium until 2010, where they then gave their uranium to the Russian Federation . [ 1 ] [ 2 ]
Before the Yugoslavian breakup and the Yugoslav Wars , the Yugoslavian government was able to develop and store several different types of chemical weapons such as mustard gas , sarin agent and blister agents . Mustard gas was prepared and installed at the Prva Iskra factory in the town of Baric . [ 3 ] [ 4 ]
The Yugoslavian government allegedly [ according to whom? ] worked with Libya and Iraq to develop missiles, cruise missiles and anti-naval/land attack missiles capable of carrying weapons of mass destruction and conventional warheads. Serbia is currently the only former Yugoslav member with a missile program. [ 1 ] [ 5 ]
During the Yugoslav Wars , the Yugoslav Army (Federal Republic of Yugoslavia) allegedly [ according to whom? ] used chemical weapons in combat against Bosnian and Croat separatists. Chemical weapons were not confirmed to have been used in the Yugoslav wars by either sides. [ 6 ] [ 7 ]
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https://en.wikipedia.org/wiki/Yugoslavia_and_weapons_of_mass_destruction
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The Yukawa–Tsuno equation , first developed in 1959, [ 1 ] is a linear free-energy relationship in physical organic chemistry . It is a modified version of the Hammett equation that accounts for enhanced resonance effects in electrophilic reactions of para- and meta-substituted organic compounds. This equation does so by introducing a new term to the original Hammett relation that provides a measure of the extent of resonance stabilization for a reactive structure that builds up charge (positive or negative) in its transition state . The Yukawa–Tsuno equation can take the following forms:
where k X and k 0 represent the rate constants for an X-substituted and unsubstituted compound, respectively; ρ represents the Hammett reaction constant ; σ represents the Hammett substituent constant ; σ + and σ − represent the Hammett substituent constants for reactions in which positive or negative charges are built up at the reactive center, respectively; and r represents the Yukawa–Tsuno parameter.
The Hammett substituent constant, σ , is composed of two independent terms: an inductive effect σ I and a resonance polar effect σ R . These components represent the consequences of the presence of a particular substituent on reactivity through sigma and pi bonds, respectively. For a particular substituent, the value of σ is generally assumed to be a constant, irrespective of the nature of the reaction; however, it has been shown that for reactions of para-substituted compounds in which the transition state bears a nearly full charge, σ R does not remain constant, and thus, the sum σ = σ R + σ I {\displaystyle \sigma =\sigma _{R}+\sigma _{I}} is also variable. In other words, for such reactions, application of the standard Hammett Equation does not produce a linear plot. To correlate these deviations from linearity, Yasuhide Yukawa and Yuho Tsuno proposed a modification to the original Hammett equation which accounts exclusively for enhanced resonance effects due to the high electron demand during such reactions.
In their 1959 publication, Yukawa and Tsuno attributed observed deviations from Hammett Plot linearity in electrophilic reactions to additional resonance effects occurring through the pi bonds of substituent groups in their compounds. This implied that the inductive component of the Hammett substituent constant remains constant in such reactions, while the resonance component, σ R , does not. From this assumption, the two scientists defined a new resonance substituent constant, G(R) , that is mathematically represented as follows:
for a reaction in which positive charge is built up at the reactive center in the transition state. In order to quantify the extent of the observed enhanced resonance effects, Yukawa and Tsuno introduced an enhanced resonance parameter, r , that quantifies the "demand for resonance" at the reactive center. [ 2 ] Thus, the resultant Yukawa–Tsuno effective substituent constant is given by:
and the Yukawa–Tsuno equation (modified Hammett equation) takes the form:
Values of σ + − σ {\displaystyle \sigma ^{+}-\sigma } have been determined and catalogued for a number of substituents for quick application of the Yukawa–Tsuno equation. [ 1 ]
The enhanced resonance parameter, r , is a measure of the influence of resonance on a new reaction. When r = 0 {\displaystyle r=0} , the resonance effects for a particular reaction are no different from those for reaction of the unsubstituted reference compound. However, when r > 0 {\displaystyle r>0} , the reaction in question is more sensitive to resonance effects than the standard, and when r < 0 {\displaystyle r<0} , the reaction is less sensitive to such effects. [ 3 ]
The enhanced resonance parameter is determined by first establishing the Hammett Reaction constant from data collected from meta-substituted compounds, and subsequently correlating the remaining data to fit the modified equation described above.
The Yukawa–Tsuno equation allows for treatment of both para- and meta- substituents, and it also better correlates data from reactions with high electron demand than the original Hammett equation. [ 4 ] However, this equation does not take into account the effects of various solvents on organic reactions. Also, Yukawa and Tsuno note that, even within a group of similar reactions, r -values for more electron-withdrawing substituents tend to be higher than predicted—seen as a slight increase in slope on a Yukawa–Tsuno plot—and thus, are not as strongly correlated with the remainder of the data. [ 2 ]
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https://en.wikipedia.org/wiki/Yukawa–Tsuno_equation
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Yulia Sister ( Hebrew : יוליה סיסטר , Russian : Юлия Давидовна Систер ; born September 12, 1936, in Chișinău , Bessarabia , Romania ) is a Soviet Moldavian and Israeli analytical chemist engaged in chemical research with the use of polarography and chromatography , a science historian, and a researcher of Russian Jewry in Israel, France, and other countries. She holds the position of Director General of the Research Centre for Russian Jews abroad and in Israel. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]
Yulia Sister was born in 1936 in Chișinău ( Russian : Kishinev), at the time in the Kingdom of Romania, a city which later became the capital of the Moldavian SSR and since 1991 is the capital of Moldova . Her parents and paternal grandparents were also born in this city. The grandparents were there and survived the pogrom of 1903 . [ 3 ] [ 6 ]
David Iosifovich, Yulia's father, was a doctor educated in Prague at Charles University . He used to tell his daughter about his student years, the Bessarabian association of fellow-countrymen in Prague and his meetings with famous people. Yulia's mother Yevgenia (Bathsheba) Moiseevna copied for her by hand children's verses and Yulia learned to read quite early. Among the first poems was "What Is Good and What Is Bad" by Mayakovsky . [ 6 ] [ 7 ]
Yulia's grandparents stuck to traditions and spoke Yiddish , and grandfather Yosef (Iosif) even wrote Yiddish poetry. But Yulia could hardly remember them. Her grandfather Moshe (Moisei) died before she was born; her parental grandparents lost their lives in the Kishinev Ghetto in the Holocaust and her grandmother Sarah died during the World War II in evacuation. [ 6 ] [ 8 ]
During the 2nd World War Bessarabia was reclaimed and then occupied by the Soviet Union in June 1940. A year later in July 1941 it was reconquered by Germany and Romania, and in August 1944 reoccupied by the Soviet Union. [ 9 ] In her memoirs Yulia recalled the day when the Red Army entered Kishinev. She also remembered the German bombing of the city and the air raids on the roads, by which her family escaped to the East from the Nazis. [ 7 ]
At the beginning of the war David Sister and his family was evacuated to the left bank of the Volga River where he was appointed chief physician at the district hospital and a consultant of the nearby military hospital. The hospital was located in the open steppe between two villages and on the other side of Volga there was Stalingrad . The family lived there a few years. There were no other children in the neighborhood and Yulia had no friends to play with. But she was fascinated by the local nature and made observations of plants and animals. The inhabitants of the hospital could hear the cannonade from the other bank, and during the battle of Stalingrad it became particularly strong. [ 6 ] [ 7 ]
In 1944 Yulia's family moved to Kirovograd where she, after a year's delay, was enrolled in the first grade of primary education. A year later the family came back to the native city of Kishinev. Despite severe post-war shortages and difficulties, the Sister's family succeeded to restore their home, which included a huge library. Among the family friends and guests were writers, actors, musicians and scientists, and Yulia grew up in an atmosphere of thirst for knowledge. [ 6 ]
Between the years of 1945 and 1954 Yulia Sister studied at the School for Girls Number 2 in Kishinev. Chemistry was taught very passionately by a teacher that loved the subject and was able to convey her enthusiasm to the students. On the advice of her teacher Sister participated in the chemistry enrichment program for school children that was carried out by Professor Anton Ablov [ ro ] at the University of Kishinev . [ 8 ]
Yulia Sister entered the Department of Chemistry of the University of Kishinev in the fall 1954. While asked by Professor Iurie Lealicov [ ro ] , who interviewed the applicants to the Department, why she has chosen this Department, she explained that thanks to her school teacher she fell in love with chemistry. At the University Yulia was involved in various campus activities, and served as an editor of the faculty newspaper "Chemist". [ 10 ] Since her second year at the university she became a member of the student scientific society and was engaged in the research of compounds called heteropolyacids . [ 8 ] In 1959 Sister successfully defended her Master's thesis "Precipitation chromatography of heteropolyacids." and graduated with honors from the University of Kishinev. [ 1 ]
Upon completion of the studies Sister was assigned to the laboratory of analytical chemistry headed by Professor Yuri Lyalikov. [ 8 ] The laboratory was a part of the Institute of Chemistry at the Moldavian branch of the Academy of Sciences of the USSR , which became the Academy of Sciences of Moldova in 1961. Working in this laboratory allowed the young chemist Sister to begin her research with new polarographic methods . In order to carry out analysis of organic compounds by the means of alternating-current (ac) polarography Yulia built with her own hands a polarograph and received the first polarograms. Sister was the first in Moldova (with Y. S. Lyalikov), who applied the methods of ac polarography and second harmonic ac polarography for analyzing organic compounds. Then, together with the physicist Vil Senkevich, they assembled an automatic device, and only later began the serial production of polarographs in the USSR. In the early 1960s Yulia published her first research articles. In 1967 she received her Ph.D. from the Institute of Chemistry of the Moldavian Academy of Sciences. [ 1 ] [ 4 ] [ 11 ]
Through 25 years of research at the Institute of Chemistry Sister dealt with a wide range of topics. Her ecology oriented research included analysis of pesticides in environmental samples, food items and biological mediums. She participated in research and analysis of suspensions and was involved in analyzing new organic compounds. Sister made a substantial contribution to the development of such methods as the second harmonic ac polarography, the difference polarography with magnetic recording, the chromatopolarography. For about 20 years Yulia Sister served as a consultant on the use of the polarographic method in biology at the Department of Human and Animal Physiology of the University of Kishinev. [ 1 ] [ 4 ] [ 11 ]
In 1984 Yulia Sister was invited to work with the Institute of Technology and Development where she soon headed the laboratory of physical and chemical methods. The Institute was affiliated to a research and production association in the Ialoveni (formerly Kutuzov). Sister and her laboratory were using a variety of research methods and among them the high-performance liquid chromatography being at that time a new approach in the laboratories of the country. She also contributed as a board member of Moldavian branch of the Mendeleev Chemical Society and led the program "Young Chemist" in the Moldavian Republic. Many of her students, the former young chemists, became later scientists and managers of respectable companies. [ 1 ] [ 8 ]
Yulia Sister and her family repatriated to Israel in 1990. In 1992–1993 she served as a senior researcher of the Department of Inorganic and Analytical Chemistry at the Hebrew University of Jerusalem , and then she was engaged in the topics related to the analysis of biological objects at the Tel Aviv University . During these years, along with her career in chemistry, Yulia Sister became deeply interested in the study of Russian-Jewish culture. [ 1 ] [ 3 ] [ 12 ]
In 1991 Sister began to write for the Shorter Jewish Encyclopedia (SJE) as a non-staff editor. She served as a research fellow covering the field of history of science and wrote about 90 articles for the encyclopedia. Yulia is the author of the articles "Chemistry" (jointly with P. Smorodnitsky), "Veniamin Levich", "Frederick Reines", "Moise Haissinsky", "Yuri Golfand" and many others. [ 1 ] [ 6 ] [ 13 ] [ 14 ]
Yulia Sister's activities in the House of Scientists and Experts of Rehovot started in 1991. Within this forum she organizes lectures, seminars and scientific conferences. She leads the scientific seminars of the House of Scientists that are regularly held at the Weizmann Institute of Science . [ 15 ] In 2008, and then in 2014 she organized conferences devoted to the Bilu movement and to the First Aliyah . [ 16 ] [ 17 ] She also maintains friendly contacts with foreign colleagues, such as the Club of Russian-speaking scientists of Massachusetts. [ 18 ]
In 1997 Mikhail Parkhomovsky initiated creation of the Research Center for Russian Jewry Abroad, which aimed to collect and publish information on Jews, who emigrated from the Russian Empire , Soviet Union or Post-Soviet states and made a contribution to world civilization. Parkhomovsky became the Scientific Director and Chief Editor and Yulia Sister Director General of the Center. [ 19 ] [ 20 ] From 2012 the Center changed its name to Research Centre for Russian Jews abroad and in Israel (Erzi). [ 21 ] The collection, processing and publication of materials related to Russian Jewry are organized by Sister. By 2015 the Center published about 30 volumes of collections, including books devoted to Jews in England, France, U.S., Israel and other countries. In addition to her executive functions, Sister is a frequent editor and author of the Center's collective monographs. She is the editor of the 17th volume ("Let Us Build the Walls of Jerusalem. Book 3"), a coeditor of the 11th volume ("Let Us Build the Walls of Jerusalem. Book 1") and of the monograph "Israel, Russian Roots", and a participant in the editing of the 10th volume. [ 5 ] [ 8 ] [ 15 ]
Sister's activities include the organization of seminars and conferences. The following examples are a small sampling of the events organized by the Director General of the Center. In 1999 she was the coordinator of the conference dedicated to the 50th anniversary of the Weizmann Institute in Rehovot. Together with Prof. Aron Cherniak she published a detailed report on the conference and some of its materials in the 8th volume of the "Russian Jewry Abroad" series. [ 3 ] [ 5 ] In 2003 Sister led a conference in Kiryat Ekron , in which she introduced the contribution of the Russian Aliyah to Israeli science, culture and education. [ 22 ] More than 200 scientists from all over the country participated at the tenth-anniversary of the Center conference in 2007. [ 8 ] [ 23 ] The 2012 conference was devoted to the 130th anniversary of the First Aliyah and the event was covered by the House of Scientists of Rehovot. [ 24 ]
Yulia Sister lives with her family in Kiryat Ekron . Her husband, Boris (Bezalel) Iosifovich Gendler, is a physician with an extensive experience in medical practice and education. After his repatriation from Kishinev Bezalel Gendler worked as a doctor in one of the Israeli hospitals and published several articles, some of them in collaboration with Yulia.
Yulia Sister is the author or co-author of more than 200 scientific publications.
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A yupana (from Quechua : yupay 'count') [ 1 ] is a counting board used to perform arithmetic operations , dating back to the time of the Incas . Very little documentation exists concerning its precise physical form or how it was used.
The term yupana refers to two distinct classes of objects:
Although very different from each other, most scholars who have dealt with table yupanas have extended reasoning and theories to the Poma de Ayala yupana and vice versa, perhaps in an attempt to find a unifying thread or a common method of creation. For example, the Nueva coronica (New Chronicle) discovered in 1916 in the library of Copenhagen contained evidence that a portion of the studies on the Poma de Ayala yupana were based on previous studies and theories regarding table yupanas. [ 2 ]
Several chroniclers of the Indies described, in brief, this Inca abacus and its operation.
The first was Guaman Poma de Ayala around the year 1615 who wrote:
... They count using tables, numbered in increments one hundred thousand to ten thousand, one hundred to ten, and onward until they arrive at one. They keep records of everything that happens in this realm: holidays and Sundays, months and years. The accountants and treasurers of the kingdom are found in every city, town, or indigenous village...
In addition to providing this brief description, Poma de Ayala drew a picture of the yupana: a board of five rows and four columns with each cell holding a series of black and white circles.
Predating Pomo de Ayala's writings, in 1596 The Jesuit father José de Acosta wrote:
... Well, seeing another group which uses kernels of corn is an enchanting thing, as a very embarrassing account, which he will have a very good accountant do by pen and ink, to see how each contribution fits with so many people, taking so much from over there and adding so much from here, with another hundred small pieces, these Indians will take their kernels and put one here, three there, eight I don't know where; they will move a kernel from here, they will barter three from there, and, in fact, they leave with their account done punctually without missing a mark, and much more they know how to put into account and account for what each can pay or give, that we will know how to give to each of them as ascertained by pen and ink. If this is not ingenuity and these men are beasts, let whoever wishes to judge it so judge it, for what I judge to be true is that in what they apply they give us great advantages.
In 1841, Father Juan de Velasco wrote:
... these teachers were using something like a series of trays made of wood, stone, or clay, with different separations, in which they put stones of different shapes, colors and angularities...
Various table yupana have been found across Ecuador and Peru.
The earliest known example of a table yupana was found in 1869 in Chordeleg , Azuay Province , Ecuador . A rectangular table (33x27 cm; 13" x 10¾") of wood consisting of 17 compartments, 14 of which are square , 2 are rectangular , and one of which is octagonal . Two edges of the table contain other square compartments (12x12 cm; 4¾" x 4¾") raised and arranged side by side, upon which two square platforms (7x7 cm; 2¾" x 2¾"), are superimposed. These structures are called "towers". The table's compartments are symmetrical with respect to the diagonal of the rectangular compartments. The four sides of the board are also engraved with images of human heads and a crocodile . [ 2 ] As a result of this discovery, Charles Wiener conducted a systematic study of these objects in 1877. Wiener concluded that the table yupanas served to calculate the taxes that farmers paid to the Incan empire. [ 6 ]
Found at Caraz between 1878 and 1879, this table yupana differs from that of Chordeleg as the material of construction is the stone and the central octagonal compartment is replaced with a rectangular one; towers also have three shelves instead of two. [ 2 ]
A series of table yupanas much different from the first, was described by Erland Nordenskiöld in 1931. These yupana, made of stone, boast a series of rectangular and square compartments. The tower has two rectangular compartments. The compartments are arranged symmetrically with respect to the axis of the smaller side of the table. [ 2 ]
These yupana, made of stone, have 18 triangular compartments. On one side there is a rectangular tower with one level and three triangular compartments. In the central part there are four square compartments. [ 2 ]
Identical to the yupana of Chordeleg, both for the material and the arrangement of the compartments, this table yupana was found in the Chan Chan archaeological complex in Peru in 1967. [ 2 ]
Discovered in the Peruvian province of Pisco , these are two table yupana in clay and bone . The first is rectangular (47x32 cm; 18½" x 12½"), has 22 square (5x5 cm; 2" x 2") and three rectangular (16x18 cm; 6¼" x 7") compartments, and has no towers. The second yupana is rectangular (32x23 cm; 12½" x 9") and has 22 square compartments, two L-shaped compartments and three rectangular compartments in the center. The compartments are arranged symmetrically with respect to the axis of the longer side. [ 2 ]
Discovered in Northern Ecuador by Max Uhle in 1922, this yupana is made of stone and its compartments are drawn onto the surface of the tablet. It has the shape of a pyramid consisting of 10 overlapping rectangles: four on the first level, three on the second, two in the third and one in the fourth. This yupana is the one that is closest to the picture by Poma de Ayala in Nueva Coronica, while having a line fewer and being partially drawn. [ 2 ]
C. Florio presents a study [ 7 ] which does not identify a yupana in these archaeological findings, but an object whose name has been forgotten and remains unknown. Instead, this object is used to connect to the tocapu (an ideogram already used by pre-Incas civilizations) called "llave inca" (i.e. Inca key) to the yanantin-masintin philosophy. The scholar justifies this based on from the lack of objective evidence that recognizes this object as a yupana, a belief that consolidated over years without repetition or demonstration of this hypothesis, and with the crossing of data from the Miccinelli Documents and the tocapu catalogued by Victoria de la Jara.
Supposing to color the different compartments of the table yupana (fig. A), C. Florio identifies a drawing (fig. B) very similar to an existing tocapu (fig. C) catalogued by Victoria de la Jara. In addition, in the tocapu reported in figure D, also catalogued by V. de la Jara, Florio identifies a stylization of tocapu C and the departure point for creating the tocapu "llave Inca" (Inca key). She finds the relation between the table yupana and the Inca key also similar in their connection with the concept of duality: the table yupana structure is clearly dual and Blas Valera in "Exsul Immeritus Blas Valera populo suo" (one of the two Miccinelli Documents) describes the "Inca key" tocapu as representing the concept of the "opposite forces" and the "number 2", both strictly linked to the concept of duality. [ 8 ]
According to C. Florio, the real yupana used by the Incas is that of Guáman Poma, but with more columns and rows. The Poma de Ayala yupana would have represented just the part of the yupana useful for carrying out a specific calculation, which Florio identifies to be multiplication (see below).
In 1931, Henry Wassén studied the Poma de Ayala yupana, proposing for the first time a possible representation of the numbers on the board and the operations of addition and multiplication . He interpreted the white circles as gaps carved into yupana into which the seeds described by chroniclers would be inserted: so the white circles correspond to empty gaps, while the blacks circles correspond to the same gaps filled with a black seed. [ 2 ]
The numbering system at the base of the yupana was positional notation in base 10 (in line with the writings of the chroniclers of the Indies).
The representation of the numbers then followed a vertical progression such that the numbers 1-9 were positioned in the first row from the bottom, the second row contained the tens, the third contained the hundreds, and so on.
Wassen proposed a progression of values of the seeds that depends on their position in the table: 1, 5, 15, 30, respectively, depending on which seeds occupy a gap in the first, second, third and fourth columns (see the table below). Only a maximum of five seeds could be included in a box belonging to the first column, so that the maximum value of that box was 5, multiplied by the power of the corresponding row. These seeds could be replaced with one seed of the next column, useful during arithmetic operations. According to the theory of Wassen, therefore, the operations of sum and product were carried out horizontally.
This theory received a lot of criticism due to the high complexity of the calculations and was therefore considered inadequate and soon abandoned.
The following table shows the number 13457 as it would appear on Wassen's yupana:
Representation of 13457
This first interpretation of the Poma de Ayala yupana was the starting point for the theories developed by subsequent authors, into the modern writing. No researcher moved away from the positional numbering system until 2008.
Emilio Mendizabal was the first to propose in 1976 that the Inca used a representation based on the progression 1, 2, 3, 5 in addition to the decimal representation. [ 9 ] In the same publication, Mendizabal pointed out that the series of numbers 1, 2, 3, and 5, appear in Poma de Ayala's drawing, and are part of the Fibonacci sequence , and stressed the importance of the "magic" that the number 5 contained for civilizations of Northern Peru , similar in significance to the number 8 for the civilizations of Southern Peru . [ 2 ]
In 1979, Carlos Radicati di Primeglio emphasized the difference of table yupana from that of Poma de Ayala, describing the state-of-the-art research and advanced theories so far. He also proposed the algorithms for calculating the four basic arithmetic operations for the Poma de Ayala yupana, according to a new interpretation for which it was possible to have up to nine seeds in each box with a vertical progression of powers of ten. [ 2 ] Radicati associated each gap with a value of 1.
The following table shows the number 13457 as it would appear on Radicati's yupana:
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
••◦◦
◦◦◦◦
◦◦◦◦
◦◦◦◦
Representation of 13457
In 1981, the English textile engineer William Burns Glynn proposed a positional base 10 solution for the yupana of Poma de Ayala. [ 10 ]
Glynn, as Radicati, adopted Wassen's idea of full and empty gaps, as well as a vertical progression of the powers of ten, but proposed an architecture that allowed yupana users to greatly simplify the arithmetic operations themselves.
The horizontal progression of the values of the seeds in its representation is 1, 1, 1 for the first three columns, such that in each row is possible to deposit a maximum of ten seeds (5 + 3 + 2 seeds). Ten seeds in any row corresponds to a single seed in the line above it.
The last column in Glynn's yupana is dedicated to the "memory " , a place that can hold up to ten seeds before they are moved to the upper line. According to the author, this is very useful during arithmetic operations in order to reduce the possibility of error.
Glynn's solution has been adopted in various teaching projects all over the world, and even today some of its variants are used in some schools of South America . [ 11 ] [ 12 ]
The following table shows the number 13457 as it would appear on Glynn's yupana:
In 2001, the Italian engineer Nicolino de Pasquale proposed a positional solution in base 40 of the Poma de Ayala yupana, taking the representation theory of Fibonacci already proposed by Emilio Mendizabal and developing it for the four operations.
De Pasquale's yupana also adopts a vertical progression to represent numbers by powers of 40. The representation of the numbers is based on the fact that the sum of the values of the circles in each row is 39, if each circle takes the value 5 in the first column, 3 in the second column, 2 in the third and 1 in the fourth one; it is thus possible to represent 39 numbers, united to neutral element ( zero or "no seeds" in the table); this forms the basis of 40 symbols necessary for the numbering system. [ 13 ]
The following table shows one of the possible representations of the number 13457 in De Pasquale's yupana:
After its publication, De Pasquale's theory sparked great controversy among researchers who fell into two primary groups: a group supporting the base 10 theory and another supporting the base 40 theory. The Spanish chronicles written of the conquest of the Americas indicated that the Incas used a decimal system and since 2003 the base 10 theory has been proposed as the basis for calculating both with the abacus and the quipu [ 14 ]
De Pasquale has recently proposed the use of yupana as astronomical calendar running in mixed base 36/40 [ 15 ] and provided his own interpretation of the Quechua word huno , translating it as "0.1". [ 16 ] This interpretation diverges from all chroniclers of the Indies, especially Domingo de Santo Tomas [ 1 ] who in 1560 translated huno into chunga guaranga (ten thousand).
In 2008 Cinzia Florio proposed an alternative and revolutionary approach compared to all the theories proposed so far. Florio's newer theory deviated from the positional numbering system and adopted additive, or sign-value notation . [ 17 ] [ 18 ]
Relying exclusively on Poma de Ayala's design, Florio explained the arrangement of white and black circles and interpreted the use of the yupana as a board for computing multiplications , in which the multiplicand is represented in the right column, the multiplier in the two central columns, and the product in the left column, illustrated in the following table:
The theory differs from all the previous in several aspects: first, the white and black circles would not be gaps that could be filled with a seed, but rather different colors of seeds, representing respectively tens and ones (this according to the chronicler Juan de Velasco). [ 5 ]
Secondly, the multiplicand is entered in the first column respecting the sign-value notation: so, the seeds can be entered in any order and the number is given by the sum of the values of these seeds.
The multiplier is represented as the sum of two factors, since the procedure for obtaining the product is based on the distributive property of multiplication over addition .
According to Florio, the multiplication table drawn by Poma de Ayala with provision of the seeds represented the calculation: 32 x 5, where the multiplier 5 is decomposed into 3 + 2. The sequence of numbers 1,2,3,5 would be causal , contingent to the calculation done and unrelated to the Fibonacci series.
Key: ◦ = 10; • = 1; The operation represented is: 32 x 5 = 32 x (2 + 3) = (32 x 2) + (32 x 3) = 64 + 96 = 160
The numbers represented in the columns are, from left to right:
The final number in this computation (which is incorrect) is the basis for all possible criticisms of this interpretation, since 160, not 151, is the sum of 96 and 64. Florio notes, however, that the mistake could have been on the part of Poma de Ayala in the original drawing, in designing a space as being occupied by a black circle instead of a white one. In this case, changing just one black circle into a white one in the final column gives us the number 160, the correct product.
Poma de Ayala's yupana cannot represent every multiplicand either, it is necessary to extend the yupana vertically (adding rows) to represent numbers whose sum of digits exceeds 5. The case is the same for the multipliers: to represent all the numbers is necessary to extend the number of columns. Apart from the supposed erroneous calculation (or erroneous representation by the designer), this is the only theory that identifies in Poma de Ayala's yupana a mathematical and consistent message (multiplication) and not a series of random numbers as in other interpretations.
In October 2010, Peruvian researcher Andrés Chirinos with the support of the Spanish Agency for International Development Cooperation (ACEID) , revised older drawings and descriptions chronicled by Poma de Ayala, and finally deciphered the use of the yupana: a table with eleven holes which Chirinos calls a "Pre-Columbian Calculator", capable of adding, subtracting, dividing, and multiplying, making him hopeful of applying this information to the investigation of how quipus were used and functioned. [ 19 ]
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Yuri Alfredovich Berlin ( Russian : Юрий Альфредович Берлин , born Moscow , USSR , December 12, 1944) is an American physical chemist of Soviet origin. He is a research professor in the department of chemistry at Northwestern University .
Yuri Berlin received his master's degree in Physics from the Moscow Engineering Physics Institute in 1968, studying luminescence of aromatic molecules dissolved in organic liquids. During the period 1968-1974, Berlin worked as a research fellow at the Institute of Chemical Physics , the USSR Academy of Science , and in 1974 completed his PhD studies at the Moscow Institute for Physics and Technology under the supervision of Victor Talrose . His thesis was focused on the development of theory for the ion-pair mechanism of radiolysis of non-polar liquids. [ citation needed ]
After completing his PhD, Berlin held numerous research positions at the N. N. Semenov Institute of Chemical Physics , Russian Academy of Sciences . In 1978, he became a senior research fellow under supervision of Vitalii Goldanski and a lecturer in the faculty of Chemical Physics at the Moscow Institute for Physics and Technology. In 1986, he was promoted to the position of the group leader and the head of the Laboratory of Non-Linear Physical and Chemical Processes. From 1986 until 1998, Berlin was a member of the Academic Council of the N. N. Semenov Institute of Chemical Physics.
In 2005, he became an elected member of the Executive Committee of the Miller Trust for Radiation Chemistry, UK. He also was an organizer, member of program committee and a co-chair of the Russian-French Seminar on Chemical Physics and a co-chair of the European Science Foundation Conference "Charge Transfer in Biosystems". In 1993-1994 Berlin was invited to teach PhD students and to perform scientific research in the Institute for Molecular Science in Okazaki, Japan. After working in Japan, he held the position of guest professor in Chemical Physics and Biophysics at the Institute of Theoretical Physics at Technical University of Munich (TUM), Germany. Following his appointment at TUM, Berlin joined the chemistry department of Northwestern University, where he is a research professor. Berlin was a member of the editorial boards of the scientific journals "Russian Chemical Bulletin", "Chemical Physics Report" and a guest editor of "Chemical Physics". [ 1 ] [ 2 ] [ 3 ]
Berlin has undertaken research on a broad range of areas in both physical and theoretical chemistry , involving stochastic dynamics of complex systems, chemical kinetics and transport of active species in condensed phase and in biological molecules, physical chemistry of liquids and solids, theoretical biophysics and physical aspects of prebiotic evolution, physical methods for the initiation of chemical reactions, in particular cryochemistry , radiation chemistry, photo, and high pressure chemistry . His research covers a vast range of fields, such as the theory of excess electrons in non-polar liquids and liquid noble gases, charge transfer under extreme conditions, chemical processes coupled to structural rearrangements of molecular environment, dispersive kinetics, the effects of correlated fluctuations in chemical and biological properties, [ 4 ] the role of static and dynamic disorder in the mechanism of chemical processes in condensed media. Later works are focused on mechanism and kinetics of charge transfer and transport in DNA, [ 5 ] [ 6 ] culminated in a series of studies of various DNA constructs as building blocks of molecular circuitry. Berlin has published over 170 papers in scientific journals. [ citation needed ]
Berlin is a member of the New York Academy of Science , the American Chemical Society , and the Royal Society of Chemistry . He is a member of the International Society for the Study of the Origin of Life, an honor Member of the European Molecular Liquids Group, a fellow of the Mendeleev Chemical Society and the Russian Physical Society. His work has earned him many awards, including EU Erasmus Mundus Professorship Award (2009) and Scientific Award of Hans Veilberth Foundation, Germany (2007). Most recently, Yuri Berlin was awarded the Maria Sklodowska-Curie Medal (2019) in recognition of his distinguished achievements in radiation research as well as the long-lasting and productive cooperation with Polish scientists.
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https://en.wikipedia.org/wiki/Yuri_Berlin
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Yuri Ivanovich Manin (Russian: Ю́рий Ива́нович Ма́нин ; 16 February 1937 – 7 January 2023) was a Russian mathematician, known for work in algebraic geometry and diophantine geometry , and many expository works ranging from mathematical logic to theoretical physics .
Manin was born on 16 February 1937 in Simferopol , Crimean ASSR, Soviet Union. [ 2 ]
He received a doctorate in 1960 at the Steklov Mathematics Institute as a student of Igor Shafarevich . He became a professor at the Max-Planck-Institut für Mathematik in Bonn , where he was director from 1992 to 2005 and then director emeritus. [ 3 ] [ 2 ] He was also a Trustee Chair Professor at Northwestern University from 2002 to 2011. [ 4 ]
He had over the years more than 40 doctoral students, including Vladimir Berkovich , Mariusz Wodzicki , Alexander Beilinson , Ivan Cherednik , Alexei Skorobogatov , Vladimir Drinfeld , Mikhail Kapranov , Vyacheslav Shokurov , Ralph Kaufmann , Victor Kolyvagin , Alexander A. Voronov , and Hà Huy Khoái . [ 5 ]
Manin died on 7 January 2023. [ 2 ]
Manin's early work included papers on the arithmetic and formal groups of abelian varieties , the Mordell conjecture in the function field case, and algebraic differential equations . The Gauss–Manin connection is a basic ingredient of the study of cohomology in families of algebraic varieties . [ 6 ] [ 7 ]
He developed the Manin obstruction , indicating the role of the Brauer group in accounting for obstructions to the Hasse principle via Grothendieck 's theory of global Azumaya algebras , setting off a generation of further work. [ 8 ] [ 9 ]
Manin pioneered the field of arithmetic topology (along with John Tate , David Mumford , Michael Artin , and Barry Mazur ). [ 10 ] He also formulated the Manin conjecture , which predicts the asymptotic behaviour of the number of rational points of bounded height on algebraic varieties. [ 11 ]
In mathematical physics, Manin wrote on Yang–Mills theory , quantum information , and mirror symmetry . [ 12 ] [ 13 ] He was one of the first to propose the idea of a quantum computer in 1980 with his book Computable and Uncomputable . [ 14 ]
He wrote a book on cubic surfaces and cubic forms , showing how to apply both classical and contemporary methods of algebraic geometry, as well as nonassociative algebra . [ 15 ]
He was awarded the Brouwer Medal in 1987, the first Nemmers Prize in Mathematics in 1994, the Schock Prize of the Royal Swedish Academy of Sciences in 1999, the Cantor Medal of the German Mathematical Society in 2002, the King Faisal International Prize in 2002, and the Bolyai Prize of the Hungarian Academy of Sciences in 2010. [ 2 ]
In 1990, he became a foreign member of the Royal Netherlands Academy of Arts and Sciences . [ 16 ] He was a member of eight other academies of science and was also an honorary member of the London Mathematical Society . [ 2 ]
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https://en.wikipedia.org/wiki/Yuri_Manin
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